DEVELOPMENT OF NI-MN-BASED FERROMAGNETIC

SHAPE MEMORY ALLOYS

Zhigang Wu

School of Mechanical and Chemical Engineering

The University of Western Australia

This thesis is presented for the degree of Doctor of Philosophy of Engineering of The University of Western Australia

(2011)

i

 

Abstract ________________________________________________________________________________ 

Since the discovery of Ni2MnGa ferromagnetic shape memory alloys some 15 years ago,

intensive research has been conducted to search and develop new and more powerful

magnetically activated shape memory alloys. The effort has been severely hampered by the

low magnetic driving force, intrinsically limited by the magnitude of magnetic

crystallographic anisotropy, for mechanical actuation. The discovery of metamagnetic

phase transformation in Ni-Mn-Z (Z=In,Sn,Sb) system in 2004, with their large

magnetization difference across the transformation, made a breakthrough and brought new

promise for creating magnetically activated shape memory alloys. This study is concerned

with the development of Ni-Mn-Z (Z=In,Sn) ternary ferromagnetic martensitic alloys.

Whereas having high promise owing to their large magnetization difference between their

nonmagnetic martensite and ferromagnetic austenite, these alloys face the challenges of

high mechanical resistance to deformation and brittleness. In response to these challenges,

this study is focused on two main objectives: (1) to further enhance the magnetization

difference of the metamagnetic reverse transformation of the alloys, and (2) to improve the

toughness and ductility of the alloys, through alloying.

(1) Enhance the Magnetization Difference

New alloy design is accomplished in order to increase the magnetization difference

between the austenitic and martensitic phases in Ni-Mn-Z (Z=In,Sn) alloys. The first step

of the composition design is to maximise the use of Mn content to provide the potentially

largest magnetization. Then, the proportion between Ni and In/Sn contents is adjusted to

alter the chemical order for obtaining ferromagnetic structure. Lastly, Co addition is

employed to modify the e/a ratio and to enhance the magnetic ordering of these alloys. In

the new compositions of Mn50Ni40-xIn10Cox and Mn50Ni42-xSn8Cox alloys, a martensitic

transformation from an Hg2CuTi-type austenite to body centred tetragonal martensite was

observed. In both systems, the magnetization of the austenite increased significantly,

ii

 

whereas that of the martensite changed much less prominently with increasing the Co

substitution for Ni, leading to the significantly enhanced magnetization difference across

the transformation. The increased magnetization of the austenite is attributed to (i)

formation of ferromagnetically coupled Mn-Mn atoms due to the new atomic configuration

in off-stoichiometric composition, (ii) higher magnetic moment contribution of Co relative

than Ni, and (iii) widening of temperature window for ferromagnetic austenite. The low

magnetization of the martensite, relative to that of the austenite, is due to the significantly

shortened distance between Mn-Mn, which leads to the disappearance of the local

ferromagnetic structure in a tetragonal martensitic structure.

(2) Improve the Alloy Ductility

Fe is utilised to substitute for Mn in Ni-Mn-Z(Z=In, Sn) alloys to form a phase in the

matrix to increase the ductility of the alloys. Whereas much attention has been given to the

ductility improvement, metallurgical origins of the influences of fourth element addition on

the martensitic and magnetic properties are much less understood. In Ni50Mn38-xIn12Fex and

Ni50Mn40-xSn10Fex alloys, a martensitic transformation from a B2 austenite to an

orthorhombic martensite was realised. Substitution of Fe for Mn at above 3 at% introduced

an fcc phase in the microstructure, the amount of which increased with increasing Fe

addition in both systems. The Curie temperature of the parent phase increased slightly,

whereas the Curie temperature of the martensite increased rapidly with increasing Fe

addition. Changes in the temperatures of the martensitic and magnetic transformations are

confirmed to directly relate to the e/a ratio of the matrix caused by the formation of phase.

Fe addition effectively weakens the antiferromagnetic ordering of the austenite in the

matrix phase, leading to the increase of magnetization difference across the martensitic

transformation. The relative shape memory effect decreased from 94 % to 37 % after 4 at%

Fe addition. These findings clarify the metallurgical origins of the side effects of Fe

addition on martensitic and magnetic properties and provide reference on alloy design for

Ni-Mn-based alloy systems.

iii

 

Publications arising from this thesis ________________________________________________________________________________ 

This thesis is written as a series of research publications, and my contribution to each

publication is indicated as following:

1. Wu Z (70%), Liu Z, Yang H, Liu Y, Wu G, “Metamagnetic phase transformation in

Mn50Ni37In10Co3 polycrystalline alloy”, Applied Physics Letters, 2011, 98, pp.

061904(1-3). (1st paper in Chapter 2)

2. Wu Z (80%), Liu Z, Yang H, Liu Y, Wu G, “Effect of Co addition on martensitic

phase transformation and magnetic properties of Mn50Ni40-xIn10Cox polycrystalline

alloys”, Intermetallics, 2011, 19, pp.1839-1848. (2nd paper in Chapter 2)

3. Wu Z (80%), Liu Z, Yang H, Liu Y, Wu G, “Martensitic phase transformation and

magnetic properties of Mn50Ni42-xSn8Cox polycrystalline alloys”, Journal of Physics

D: Applied Physics, 2011, 44, 385403(1-8). (3rd paper in Chapter 2)

4. Wu Z (80%), Liu Z, Yang H, Liu Y, “Effect of Fe addition on the martensitic

transformation behaviour, magnetic properties and mechanical performance of

Ni50Mn38-xIn12Fex polycrystalline alloys”, submitted to Journal of Alloys and

Compounds. (1st paper in Chapter 3)

5. Wu Z (60%), Liu Z, Yang H, Liu Y, Wu G, Woodward RC, “Metallurgical origin of

the effect of Fe doping on the martensitic and magnetic transformation behaviours of

Ni50Mn40-xSn10Fex magnetic shape memory alloys”, Intermetallics, 2011, 19, pp 445-

452. (2nd paper in Chapter 3)

Candidate signature: ……………………………... Coordinating supervisor signature: ……………………………....

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Acknowledgements ________________________________________________________________________________ 

I acknowledge my outstanding supervisor Winthrop Professor Yinong Liu. I received

world-class academic trainings of being a scientist, and enjoyed our many discussions

about scientific issues we had through my PhD study. He has been caring, wise, friendly

and supportive, and my debt to his is enormous. I acknowledge Associate Professor Hong

Yang, who has been a mentor to my research. I appreciate her genuine helps to my wife and

myself to set up our life in Australia when we first arrived in Perth and all the assistances

afterwards through the years.

Colleagues in our research group have had a huge influence on my career, which is

reflected in this thesis. In particular, I acknowledge Dr Zhuhong Liu, Qinglin Meng, Mu

Zhang, Jingyang Li, Xiaoxue Xu, Yimeng Yang, Bashir Samsam, Mazlina Mat Darus, and

Mingliang Wang. Their wisdom, support and friendship over the years have been most

important to me.

I acknowledge Dr Alexandra Suvorova, Dr Martin Saunders and Dr Janet Muhling, who

gave me all possible assistances in using the facilities in CMCA. Their knowledge and

experience on materials characterisation are valuable contribution to my research work. I

acknowledge Dr Robert Woodward in School of Physics, who assisted me to measure

magnetic properties of my samples, which weigh ~50% of the total experimental work, and

helped me a lot with understanding of magnetism in many discussions we had.

I have always valued the contribution of my wife, Meifang Lai, who gave enormous

support to my research. She has been a great listener and a true friend in my life. It is her

company and encouragement that made my PhD research possible. I dedicate this work to

her. I have been also receiving tremendous support from my parents in China, who gave me

best education at that time. They have made huge sacrifices to allow me to pursue my

dreams, and for their unconditional support and love, I will always be so grateful.

v

 

Table of contents ________________________________________________________________________________ 

 

Abstract i

Publications arising from this thesis iii

Acknowledgements iv

Table of Contents v

Chapter 1: Introduction 1

Chapter 2: Increasing magnetic driving force of Ni-Mn-based alloys 37

Chapter 3: Increasing ductility of Ni-Mn-based alloys 97

Chapter 4: Closing Remarks 142

CHAPTER 1 1

 

CHAPTER 1. Introduction

________________________________________________________________________________ 

 

1.1 Magnetomechanicaleffectofmaterials

Transducing materials are becoming increasingly important in modern technologies,

which combine large strain, high specific force output and fast dynamic response during an

actuation event. The functionality of these materials is based on the physical mechanisms

responsible for the thermal, electrical, optical, chemical or magnetic energy transformations

into mechanical work, which produce actuation. For example, conventional shape memory

alloys (NiTi) are widely used as thermal actuators. By heating up a typical NiTi alloy to

above the martensitic transformation temperature, a strain of ~6% can be produced, or

recovered, accompanying a force output of up to ~850 MPa. During such an actuating

event, thermal energy is converted to mechanical work. Magnetic-field-induced mechanical

actuation is another type of energy conversion, which has the advantages of high response

frequency, good cycling stability, and environmentally friendliness compared to

conventional shape memory alloys. The most well known magnetoactuators are the

traditional magnetostrictive materials.

Magnetostriction is a common phenomenon for all solid magnetic materials, but

only in a few the effect is large enough for engineering exploitation. It refers to the

phenomenon in which a material changes its physical dimensions in response of changes in

magnetisation state. The best known magnetostrictive materials are cubic Laves-phase

intermetallics, often in the form of (RE)(TM)2 (TM=Fe, Co, Ni and Mn) [1-3]. The largest

ever measured Laves-phase intermetallic is in TbMn2 (0.6 % at 40 K) and the most

successful in application is TbxDy1-xFe2, the infamous Terfenol-D [4].

CHAPTER 1 2

 

The magnitude of magnetostrain in magnetostrictive materials (<0.6%) is

considered rather small, which severely hinders their engineering applications in many

aspects. Therefore, development of new types of magnetoactuation materials with large

magnetostrains has become an intensive research interest to widen the application realm of

magnetoactuation.

1.2 Largemagnetostrainbymartensitevariant

reorientation

In 1996, Ni2MnGa alloy was found to generate a strain of ~0.2% under the

influence of an applied magnetic field of 8 kOe [5]. This material combines the properties

of ferromagnetism with those of a thermoelastic martensitic transformation, thus denoted as

a ferromagnetic shape memory alloy (FSMA). With this discovery, tremendous effort has

been made on searching for larger magnetostrains by adjusting the compositions to off-

stoichiometric derivatives in Ni-Mn-Ga alloys. These alloys in their martensite state allow

for a stress- or magnetic-field-induced rearrangement of twin variants, resulting in giant

magnetostrains, 5-10% having been reported in the literature [6-9]. The enhanced

magnetostrains, caused by twin boundary motion in Ni-Mn-Ga single crystals, led to

intensively active research in the interdisciplinary field of ferromagnetic martensite in the

following decade. The aforementioned record-breaking values of magnetostrain and the

extreme magnetocaloric effect rekindled the interest in Ni-Mn-Ga and related

multifunctional materials nowadays. FSMAs have been developed into a new class of

functional materials that are capable of magnetic-field-induced actuation, mechanical

sensing and magnetic refrigeration.

1.2.1 Mechanism of magnetostrain in Ni‐Mn‐Ga via martensite 

reorientation 

The magnetostrain in Ni-Mn-Ga alloys is associated with the orientation change of

the martensite variants via twin boundaries movement. The change of variant orientation

CHAPTER 1 3

 

induced by the magnetic field is a process to allow the growth of the martensite variants

with the easy magnetisation axis aligned with the applied magnetic field at the expense of

others. This requires the martensite of Ni-Mn-Ga to have both structural anisotropy and

magnetisation anisotropy.

Structural anisotropy of the martensite

The stoichiometric Ni2MnGa undergoes a martensitic phase transformation at

202 K. The austenite shows a superlattice cubic structure, i.e. Heusler structure or L21

structure at higher temperature, a=0.582 nm, while the martensite exhibits a tetragonal

structure, a=b=0.590 nm, c=0.544 nm [10]. The cubic structure of the austenite contracts

along the c direction by 4.45 % and elongates along the a and b directions by 1.63 % to

complete the structural transformation. The crystal structures of martensite are strongly

sensitive to the chemical composition. With the increase of Mn substitution of Ga, the

martensite structure exhibits 5 M, 7 M and can be also non-modulated martensite, leading

to the transformation from tetragonal to orthorhombic [11]. The tetragonal or orthorhombic

structure of the martensite provides the structural anisotropy for the potential shape change.

Magnetic anisotropy of the martensite

Both the austenitic and martensitic phases are ferromagnetic, although the

magnetisation of martensite is slightly bigger than that of austenite in modified composition

[12]. Within the martensite structure, the easy magnetic axis lies along the tetragonal c-axis,

i.e. the short axis. Figure 1 shows the magnetisation measurement of Ni48Mn30Ga22 single

crystal along the easy magnetisation direction ([001] axis) and the hard magnetisation

direction ([100] axis). The magnetic crystallographic anisotropy energy (Ku), which is the

enclosed area between the magnetisation curves along a and c axes, provides the magnetic

driving force for field-induced deformation in the tetragonal martensite.

CHAPTER 1 4

 

Figure 1 Magnetisation curves along easy ([001]) and hard ([100]) axes of Ni48Mn30Ga22

constrained in single variant martensite. [13]

High mobility of twin boundary of martensite

To complete the magnetostrain in the martensite, sufficient magnitude of Ku and

good twin boundary mobility are essential. It is important to note that the Ku is orientation

dependent and limited with a saturated field. A typical Ku for Ni-Mn-Ga alloys is between

300-500 kJ/m3 [14-16]. Given the shape change is typically 6%, this yields a magnetically

generated stress of 5-8 MPa. Therefore, to achieve a magnetic-field-induced shape change,

the detwining stress level needs to be lower than the magnetostress.

Figure 2 shows stress-strain curve of a single-variant sample of the

Ni48.8Mn29.7Ga21.5 alloy along the [100] direction by a compression test at 300 K. The

critical stress for martensite reorientation is very small, at around 1-2 MPa. Such conditions

can be satisfied by the alloys which transform from cubic austenite to 5 M and 7 M

martensite mentioned above [7, 17] . The magnetostrain is restricted to the tetragonality or

orthorhombility of martensite, denoted as 1-c/a. So far, giant magnetostrain of 6% for 5 M

and 9.5% for 7 M were successfully obtained in single crystals [6, 7]. Very recently, Straka

et al have successfully lowered the critical stress of initiating the twin boundary motion

CHAPTER 1 5

 

down to 0.1 MPa [18] by modifying the twins microstructure, which greatly improves the

ease of magnetostrain in Ni-Mn-Ga alloys.

Figure 2 Stress-strain curve for compression of a single-variant sample of the Ni48.8Mn29.7Ga21.5 alloy along the [100] direction at 300 K [7].

As aforementioned, the crystallographic anisotropy, magnetisation anisotropy, the

extremely good mobility of the twin boundaries of the martensite determines the success of

yielding large magnetostrains in Ni-Mn-Ga alloys.

1.2.2 Development of other FSMAs 

However, there are some serious concerns with Ni-Mn-Ga alloys for their industrial

applications. One is the brittleness of the material, which is due to its intrinsic nature of an

intermetallic compound. Furthermore, the high cost of pure element Ga impedes its

practical production on a large scale. Last but not least, the mechanical work output of Ni-

Mn-Ga, provided by the intrinsically weak magnetic anisotropy energy, is extremely small

as a driving force for mechanical actuations. Even though the critical stress of twinning can

be modified to as low as 0.1 MPa [19], the force generated is still restricted by the limited

magnitude of Ku, at a few MPa [20]. To overcome these problems and to increase the

fundamental knowledge of this alloy system, other ferromagnetic shape memory alloys

with Heusler structure have been investigated since last years.

CHAPTER 1 6

 

Ni-Mn-Al has been developed as another candidate of FSMAs. The austenite shows

a B2 or L21 structure, while the martensite shows non-modulated tetragonal phase with low

Al and Mn content and 5M and 7M tetragonal martensite with high Al and Mn content

alloys [21]. The magnetostrain of Ni-Mn-Al is rather small: at about 0.17% in single

crystals and 0.01% in polycrystals. A high magnetic field (7 T) is required to yield the

magnetostrain [22]. The ductility of Ni-Mn-Al alloys is improved by the precipitation of γ

phase particles with the addition of other elements, such as Fe, Co or Cr [23].

Thermoelastic martensitic transformations in the ferromagnetic state were obtained

in a large compositional range of Ni-Fe-Ga alloys. Austenite phases have L21 structures

while martensite phases have 5M and 7M orthorhombic structures [24]. The critical stress

for variants reorientation is very low, at 2-3 MPa [25]. The Ku in single crystals of 7M

martensite is 130-180 kJ/m3 [26]. Nevertheless, the magnetostrain is much smaller in Ni-

Fe-Ga than those in Ni-Mn-Ga alloys. The largest strain reported for Ni54.2Fe19.3Ga26.5

single crystals in single variant state is only 0.02 % at 100 K [26]. The magnetostrain can

be enhanced to 0.7 % by doping Co in Ni-Fe-Ga alloys [27]. The stress-assisted

magnetostrain of 8.5 % was also achieved in Ni-Fe-Ga-Co alloys [28]. The ductility of Ni-

Fe-Ga is improved by the presence of the precipitates of γ phase, and the amount and

distribution of γ phase can be modified by suitable heat treatments [29-31]. Though the

ductility is increased, the transformation strain is reduced due to the presence of γ phase of

the material [32].

Co-Ni-Al is being investigated in the last years as another ferromagnetic shape

memory alloy system. The parent phase has the B2 structure and martensitic phase has the

L10 structure [33-35]. The Ku of Co-Ni-Al is about 320 kJ/m3 at 5 K and 200 kJ/m3 at 300

K for Co41Ni32Al27 alloys in single variants state [36]. However, the values of

magnetostrain reported so far are very low: 0.06% in single crystals [37] or 0.013% in

polycrystals [38]. The reason for the small strain induced by the relative large magnetic

field may be due to the elevated critical stress for variant reorientation of L10 structure.

Similar to Ni-Mn-Al and Ni-Fe-Ga, the ductility of Co-Ni-Al alloys is improved by the γ

phase.

CHAPTER 1 7

 

Co-Ni-Ga is another promising ferromagnetic shape memory alloy system induced

by Wuttig et al in 2001 [39]. It shows the similar properties as in Co-Ni-Al, like the crystal

structures of the two phases (B2 for austenite and L10 for martensite respectively) and the

martensitic transformation happens around the room temperature [39]. The values of

magnetostrain are still small: 0.011% in melt-spun ribbons and 0.003% in polycrystals [40].

Giant magnetostrain triggered by martensite reorientation have been investigated in

ordered Fe-Pt and disordered Fe-Pd alloys. The parent phase of Fe-based alloys is fcc phase

(γ phase) which can be retained at the room temperature by quenching and the martensite

structures of these two alloys are both fct [41]. In Fe-Pt alloys, the martensite

transformation temperature is always much below the room temperature (85 K for Fe3Pt)

[42]. In Fe-Pd alloys, the transformation temperature is around the room temperature and

decreases sharply with the increment of Pd concentration [43]. In Fe-Pt single crystals, the

amount of magnetostrain is up to 2.3 % measured at 4.2 K [41]. However, very low

martensitic phase transformation temperature restricts its application. For Fe-Pd alloys, the

values of magnetostrain of 3.1 % have been measured in single crystals and 0.01 % to 0.05

% in polycrystals depending on the size and shape of the grains [44, 45].

Clearly, the magnetostrains obtained in the aforementioned FSMAs are significantly

lower than those found in Ni-Mn-Ga alloys. To date, Ni-Mn-Ga shows the best

performance of magnetostrain with the mechanism of martensite reorientation under the

influence of a magnetic field.

1.3 Magnetoactuationviamartensitictransformation

Because of the success of Ni-Mn-Ga magnetic shape memory alloys, Ni-Mn-

Z(Z=In,Sn,Sb) were introduced for In, Sn and Sb are the neighbor elements within the same

or neighbor groups as Ga. This satisfies the requirement of Z position should be taken by sp

element in Heusler structure denoting as X2YZ and then taken as the potentially ideal

substitution for Ga. In 2004, Sutou et al discovered Ni50Mn50-xZx (Z=In,Sn,Sb; x=10-16.5)

alloys system [46], and this new system has attracted much interest due to its distinctive

CHAPTER 1 8

 

magnetic properties. The stoichiometric composition of Ni2MnZ(Z=In,Sn,Sb), exhibit TC

lower than Ni-Mn-Ga, but can be elevated by increasing the Mn content. In fact, Ni50Mn50-

xZx (Z=In,Sn,Sb; x=10-16.5) alloys show thermoelastic martensitic transformation below

the TC temperature. In this case, the magnetic actuation is possible to be carried out by

magnetic-field-induced martensitic phase transformation. This group of alloys is normally

regarded as Ni-Mn-based FSMAs.

1.3.1 Concurrent structural and magnetic transformation

The charm of Ni-Mn-based FSMAs lies on their concurrent martensitic and

magnetic transformation. Figure 3 shows the thermomagnetisation behaviour of

Ni50Mn34In16, Ni50Mn37Sn13 and Ni50Mn37Sb13 alloys [46]. The TC temperature is defined as

the temperature at which the slope of the magnetisation versus temperature is the largest.

The martensitic transformation can be identified by the abrupt dropping upon cooling and

rising upon heating of the magnetisation curves with the variation of temperature, with an

obvious temperature hysteresis. Similar with other conventional FSMAs, the parent phase

is ferromagnetic at higher temperature, with a L21 structure. However, the martensite phase

performs a much weaker ferromagnetism at lower temperature, with a 4M Orthorhombic

structure [46]. The largest saturation magnetisation difference between the austenite and

martensite (ΔM) among Ni50Mn50-xZx (Z=In,Sn,Sb) alloys is ~60 emu/g, found in

Ni50Mn34In16 alloy [47, 48]. The large ΔM is beneficial for magnetic-field-induced

martensitic transformation. By slightly adjusting the composition, alloy Ni46Mn41In13 has

been found to present an enhanced ΔM of ~100 emu/g, which holds the highest ΔM record

in Ni50Mn50-xZx (Z=In,Sn,Sb) alloys. The crystal structure is still L21 structure even the all

these three element have deviated from their own proper concentration, evidenced by XRD

and TEM results [49]. However, the low phase transformation temperatures at around 200

K still impede the further mechanical study and real applications.

CHAPTER 1 9

 

Figure 3 Thermomagnetisation curves of (a) Ni50Mn34In16, (b) Ni50Mn37Sn13 and (c) Ni50Mn37Sb13 alloys.

1.3.2 Magnetic driving force for magnetostrain in Ni-Mn-Z (Z=In,Sn,Sb) alloys

Different from the magnetic driving force in Ni-Mn-Ga alloys, which is the

magnetic crystallographic anisotropy constant (Ku), the Zeeman energy (ZE) is responsible

for triggering the actuation of Ni-Mn-based FSMAs. The comparison between the magnetic

driving forces for Ni-Mn-Ga and Ni-Mn-based alloys are illustrated in Figure 4. The

magnitude of Ku is the enclosed area between the magnetisation responses from two

differently oriented variants shown in Figure 4 (a). Once the Ku is larger than the energy

required for the twin boundary motion, the variants with the easy magnetisation direction

CHAPTER 1 10

 

parallel to the magnetic field will grow at the expense of others, resulting in the

macroscopic shape change. It is obvious that the magnitude of the maximum Ku is limited.

Therefore, the low force output has been proven to be a main limitation for the application

of these materials for mechanical actuation.

(a) (b)

Figure 4 Illustration of the maximum magnetocrystalline energy (Ku) in Ni-Mn-Ga alloys responsible for magnetic-field-induced martensite variant reorientation and Zeeman energy (ZE) in Ni-Mn-based alloys responsible for magnetic-field-induced phase transformation.

An intrinsic solution to this problem is to increase the magnetic driving power for

the martensitic transformation. This mechanism is analogous to stress- or temperature-

induced martensitic transformations in conventional shape memory alloys. Different from

the Ku, the ZE plays an important role in magnetic-field-induced phase transformations,

which stems from the difference in the saturation magnetisations of the phases as shown in

Figure 4 (b). Unlike the Ku, the ZE does not strongly depend on crystal orientation, which

provides an opportunity to utilise polycrystals for actuator applications. With increasing the

applied field, the ZE grows continuously with an open end until the phase transformation

occurs. However, for a realistic point of view, one should always expect to achieve a

magnetostrain at a reasonable magnitude of field. In this case, the ZE should be increased

by enhancing the ΔM, such as when a ferromagnetic phase transforms to a paramagnetic or

antiferromagnetic phase, or vice versa.

1.3.3 Effect of Co addition on increasing ΔM

CHAPTER 1 11

 

The magnetostrain cannot be achieved in Ni-Mn-Z(Z=In,Sb,Sb) ternary alloys until

the Co substitution for Ni was taken as an effective modification for improving the

distinctive magnetic properties between the austenite and martensite. As a matter of fact,

the ΔM can be significantly increased by substitution Co for Ni in Ni-Mn-

Z(Z=In,Sn,Sb,Al,Ga) alloys [50-55]. The most successful compositions with respect to the

production of magnetostrain are Ni-Co-Mn-In alloys, which have been found to

demonstrate a magnetostress level of 140 MPa/T with 1.2% axial strain under compression

[56]. The magnetostrain and magnetostress levels are both significantly higher than those

from the existing magnetostrictive materials and Ni-Mn-Ga alloys.

Figure 5 shows the thermomagnetisation measurements of the Ni45Co5Mn36.6In13.4

alloy in several magnetic fields. In this alloy, Co was added into Ni-Mn-In alloy to increase

the Curie temperature. The magnetisation of the austenite is increased and that of the

martensite is decreased after Co addition, resulting in an enlarged ΔM of about 100 emu/g

across the martensitic transformation. The martensitic transformation temperatures

decreased with increasing magnetic field. The increase of magnetic field from 0.5 to 70

kOe resulted in a decrease in the transformation temperature of about 30 K.

Figure 5 Thermomagnetisation curves of the Ni45Co5Mn36.6In13.4 alloy measured in several magnetic fields by the sample extraction method.

CHAPTER 1 12

 

Figure 6 shows that magnetisation curves of the Ni45Co5Mn36.6In13.4 alloy between

200 K and 320 K. The alloy presents non-magnetic and ferromagnetic behaviours at 200

and 320 K, respectively. The field induced reverse martensitic transformation from a non-

magnetic phase to a ferromagnetic phase is achieved at 270 and 290 K with a large

hysteresis. The enlarged ΔM between the phases greatly increases the magnetic driving

force for inducing a magnetic-field-induced reverse phase transformation.

Figure 7 shows large magnetostrain of 2.9% in Ni45Co5Mn36.7In13.3 alloy [51]. The

alloy is of martensite state at the testing temperature of 298 K. A compressive pre-strain of

about 3% was applied to the alloy, with the magnetic field applied in parallel to the

compressive axis of the specimen and the length change parallel to the compressive axis

was measured. The shape recovery is due to magnetic-field-induced reverse transformation,

which is called the “metamagnetic shape memory effect” by the authors.

Figure 6 Magnetisation versus magnetic field curves for the Ni45Co5Mn36.6In13.4 alloy between 200 K and 320 K.

CHAPTER 1 13

 

Figure 7 Recovery strain at 298K induced by a magnetic field for Ni45Co5Mn36.7In13.3.

This magnetostrain is a true “magnetic shape memory effect”, as it involves the

reverse martensitic transformation. The martensitic transformation temperatures are around

room temperature and TC is 387 K. The parent phase shows L21 Heusler ordered structure

where a=0.5978 nm and martensite phases have the modulated structure of monoclinic

where a=0.4349 nm, b=0.2811 nm, c=2.989 nm and β=93.24°, respectively, confirmed by

XRD.

Wang et al have investigated the magnetic-field-induced martensitic transformation

behaviour in Ni45Co5Mn36.6In13.4 polycrystalline alloy, with or without an imposed stress, at

various temperatures using a high-energy synchrotron X-ray diffraction. The reversible

magnetic-field-induced martensitic transformation was observed with the application of 5 T

under stress, suggesting the potential of the application in the real world [57]. The further

investigation on the mechanical properties of Ni45Co5Mn36.6In13.4 single crystal was

systematically done by Karaca et al in 2008. The effects of temperature and bias stress on

the pseudoelastic response and the shape memory effect were explored. A transformation

strain of 5.4% was obtained by thermal cycling under 125 MPa. Temperature hysteresis

changes from 50 to 75 K depending on the applied stress level. Pseudoelastic response was

CHAPTER 1 14

 

obtained with a large stress hysteresis of 110 MPa and a Clausius-Clapeyron slope of 2.1

MPa/K [58].

Ni43Co7Mn39Sn11 is another successful alloy which yields large magnetostrain by

magnetic-field-induced martensitic transformation discovered by Kainuma et al later in

2006 [50]. The idea of substitution of Co for Ni is similar to that in Ni-Co-Mn-In alloys.

The martensite and reverse transformations were detected in the temperature range from

300 to 350 K and TC is about 430 K. The crystal structures of parent phase and martensite

phase are as same as in Ni45Co5Mn36.7In13.3 alloy with slightly different lattice parameters.

The recovery strain of 1 % which is 77 % of the pre-stain of 1.3 % was confirmed in a

magnetic field strength of 8 T in polycrystalline samples. Moreover, a length change of 0.3

% after releasing the magnetic field was detected, known as the two-way shape memory

alloy effect [50]. Similarly, the substituent of Co atoms in Ni-Co-Mn-Sb alloys help align

the Mn moments in a ferromagnetic ordering, giving rise to a significantly enhanced

magnetisation in the austenite and a large ΔM across the transformation [52].

Since the effect of Co doping on increasing the magnetisation difference across the

phases in Ni-Mn-Z(Z=In,Sn,Sb) alloys has been well realised, similar effect is then also

expected in early found Ni-Mn-Ga and Ni-Mn-Al alloys. It is found that Co substitution for

Ni in Ni50Mn30Ga20 alloy significantly lowered the martensitic transformation temperature,

and elevated the Curie transition temperature. The magnetisation for the ferromagnetic

austenite has been largely increased, while that of the martensite has been lowered to some

extent. This results in the increase of the ΔM across the phases, leading to successful

magnetic-field-induced phase transformation in Ni33Co13Mn32Ga18 alloys [54] and in

Ni40Mn33Co10Al17 alloy [53].

Co substitution for Ni effectively increases the ΔM across the martensitic

transformation, thus enhancing the magnetic driving force for magnetoactuation. The

positive effects of Co can be summarised to a few aspects [52]: (i) it decreases the

martensitic transformation temperatures and increases the Curie transition temperature of

the austenite, thus guaranteeing the concurrent martensitic and magnetic transformation in a

large temperature window, (ii) Co atoms at Ni site contribute larger magnetic moment

CHAPTER 1 15

 

(~1.0 µB) compared to that of Ni (~0.3 µB) in the austenite, (iii) it strengthens the

ferromagnetic ordering in the austenite by turning the magnetic moments of Mn atoms into

a ferromagnetic ordering instead of the previous antiferromagnetic one [55].

1.4 Energyevaluationofmagnetostrainassociatedwith

martensitictransformationinNi‐Mn‐basedFSMAs

To evaluate the current FSMAs with regard to their potential for magnetic actuation,

it is essential to consider the energy conversion from magnetic energy to mechanical work

associated with the magnetic-field-induced martensitic transformation. For a complete

magnetomechanical actuation, the magnetic energy must overcome the mechanical

resistance of the matrix to deformation, and the remainder of the magnetic energy

transforms to mechanical work output. To clarify the ability of magnetic actuation of

FSMAs, each energy term involved in a magnetic-field-induced shape change via

martensitic transformation is analysed. These energy terms can be grouped into three

components: (i) the magnetic driving force, (ii) the frictional resistance and (iii) the work

output. It is also a useful tool to draw a common criterion for the present FSMAs for

practical applications.

1.4.1 Thermodynamicsformagnetomartensiticphasetransformations

Owing to its lattice distortion, a martensitic transformation is a mechanical event as

well as a thermodynamic event. The Gibbs free energy change of such an event may

include not only the more familiar internal energy, volume-pressure energy and

temperature-entropy energy, but also all other reversible energies involved, such as the

force-displacement elastic potential energy (FL), magnetic energy (BM), optical energy,

etc. The relations among the multiple energy terms can be expressed as:

G U P V T S F L B M (1)

CHAPTER 1 16

 

For a normal thermoelastic martensitic transformation, we may consider only the

thermal and the mechanical energies. It gives

G U P V T S F L (2)

Based on F A , L L , 1

AL V

, Equation (2) can be written as

G H T S

(3)

When a martensitic phase transformation occurs, the system is in equilibrium state,

thus 0G and hence

d S

dT

(4)

This is the famous Clausius-Clapeyron Equation. Similarly, for an isothermally

magnetic-field-induced martensitic transformation, we may only consider thermal and

magnetic energies. So the equation (1) is now

G U P V T S B M (5)

Once the magnetic energy term BΔM makes a large contribution to the Gibbs free

energy change, the transformation occurs, and then 0G . It gives

dB S

dT M

(6)

The transformation temperature change (dT) induced by the magnetic field change

(dB) is determined by M

S

. To utilise magnetic field to induce martensitic transformation,

a combination of a large ΔM and small ΔS is required for the martensitic transformation.

CHAPTER 1 17

 

1.4.2 Energyconversionofmagnetostrainviamartensitictransformation

Magnetic energy input 

The magnetic energy input is ZE shown in Figure 4 (b), which is the area between

the magnetisation curves of the austenite and martensite. It can be expressed as

ZE B M , corresponding to the last energy term in equation 5. Obviously, with

increasing the magnitude of the applied field B or magnetisation difference ΔM, the ZE

increases.

Resistances for magnetomartensitic actuation 

For actuation via magnetic-field-induced martensitic transformation, the ZE must

overcome two energy barriers: (1) Gibbs free energy deficit for the phase transformation at

the testing temperature and (2) mechanical resistance of the matrix to shape change.

(1) Gibbs free energy deficit for magnetomartensitic 

transformation 

Figure 8 shows thermal- and magnetic-induced martensitic phase transformations,

in which the elastic energy of the phase transformation is neglected. To is the equilibrium

transformation temperature. Because of the irreversible energy of the structural

transformation, the transformation hysteresis always exists between the forward and reverse

phase transformation. Therefore, the transformation temperatures can be regarded as TM

(the forward transformation temperature) at below To and TA (the reverse transformation

temperature) at above To. To induce a reverse transformation at any given temperature T

below TA, the thermodynamic energy deficit may be estimated to be

( )th AE T T S (7)

CHAPTER 1 18

 

Figure 8 Schematic diagrams of thermal- and magnetic-field-induced martensitic transformations without elastic energy.

It is seen that the irreversible energy consumption of the transformation can be

given by ( )ir A oE T T S . This energy consumption is due to the friction stemming from

the phase interface movement for the crystallographic transition. However, this irreversible

energy barrier can be avoided by deliberately choosing the testing temperature close to TA,

and then applying the magnetic field. Accordingly, a small ΔS and testing temperature close

to TA are expected for easy magnetic actuations.

In a real situation of structural transition, the elastic energy always accompanies, i.e.

the “elasticity” of the transformation. This leads to the temperature-, stress- and magnetic

field-span between the starting and finishing of the transformation. Therefore, the

transformation temperatures are commonly measured as forward and reverse

transformation starting and finishing temperatures (Ms, Mf, As and Af) shown in Figure 9.

Within the transformation span, there is a frictional energy, as part of Eir. For a complete

transformation being induced at any given temperature T, the total thermal deficit can be

rewritten as

CHAPTER 1 19

 

fA

th

T

E SdT (8)

Given the testing temperature is chosen at As, the frictional energy to be overcome

is shown as the blue shadow area in Figure 9, which corresponds to the minimum energy

requirement for the completion of a magnetic-field-induced transformation:

min

f

s

A

A

E SdT (9)

Figure 9 Schematic diagrams of thermo- and magnetic-field-induced martensitic transformation with transformation elastic energy.

(2) Mechanical resistance for magnetomartensitic transformation 

from pre‐straining 

For obtaining a magnetostrain via martensitic transformation, a pre-strain to the

alloy at the martensite state is required before applying the magnetic field. The process of

CHAPTER 1 20

 

generating a pre-strain is to convert the self-accommodated martensite variants to become

reoriented variants, and thus the recovery from the deformed martensite back to the

austenite requires extra energy due to the pure mechanical resistance from the

crystallographic transition. This energy is denoted as Emech. The magnitude of Emech roughly

equals the mechanical work for obtaining the oriented martensite from a self-

accommodated state near As temperature, which is illustrated in Figure 10. The critical

stress for inducing the martensite variant rearrangement is denoted σo, and the maximum

strain is εmax, thus

Emech σo εmax (10)

Figure 10 Schematic illustration of stress-strain curve for martensite reorientation at As temperature.

In fact, Emech equals to the extra thermal energy requirement for the transformation

from the oriented martensite back to austenite by heating, which is known as the

“martensite stabilisation” behaviour in NiTi alloys [67-69]. Figure 11 shows the illustration

for these extra thermal or magnetic energies for thermal- or magnetic-induced martensitic

reverse transformation. In the S-T relation, it is seen that the transformation temperatures

(As and Af) shift to higher temperature range for inducing the reverse transformation from

the orientated martensite to austenite relative to those from the self-accommodated

martensite to austenite. Similarly, in M-H relation, the magnetic field increase to higher

magnitude to meet the requirement from the transformation between a pre-strained

CHAPTER 1 21

 

martensite to austenite magnetically. The extra energy corresponding to Emech is caused by

the “martensite stabilisation” given as the red shadow area in Figure 11. In this case, the

mechanical resistance due to the martensite stabilisation can be also converted to the form

of thermodynamic energy deficit (shadow area in Figure 11), which is

'

( ' )f

f

A

mech f f

A

E SdT A A S (11)

Figure 11 Extra thermal and magnetic energy requirement for inducing reverse martensitic transformation caused by pre-strained martensite.

1.4.3 CriteriaofevaluationforFSMAs

Criteria I: completion of magnetic‐field‐induced martensitic 

transformation 

The resistance for a magnetic-field-induced reverse transformation comes only from the thermodynamic deficit for the reverse transformation. Therefore, the magnetic energy input for driving a martensitic transformation at temperature T is given by:

CHAPTER 1 22

 

mag thE E

As magE B M , and fA

th

T

E SdT , so the condition is

fA

T

B M SdT (12)

Apparently, the minimum magnetic energy requirement for completion of magnetic-field-

induced martensitic transformation is f

s

A

A

B M SdT .

Criteria II: completion of magnetostrain via martensitic 

transformation 

In addition to the thermal deficit, to transform the deformed martensite back to austenite magnetically requires extra energy input to overcome the mechanical resistance brought by “martensitic stabilisation”. The magnetic driving force now needs to meet

mag th mechE E E

As magE B M ,fA

th

T

E SdT and' f

f

A

mech

A

E SdT , where 'fA is the martensitic reverse

transformation temperature for an oriented martensite transforming to austenite. ' 'f f f

f

A A A

T A T

B M SdT SdT SdT (13)

The minimum magnetic energy requirement for shape recovery via magnetic-field-induced

martensitic transformation is ' f

s

A

A

B M SdT .

Criteria III: completion of two‐way magnetostrain via 

martensitic transformation 

To obtain a two-way shape memory effect by a magnetic field, the magnetising

temperature T must be at lower than Mf temperature to have the austenite transforming back

to the martensite after releasing the magnetic field, as seen in Figure 11. The minimum

magnetic energy input can be obtained when T=Mf, that equals

CHAPTER 1 23

 

' f

f

A

M

B M SdT (14)

Based on the analysis above, the energy barriers for a magnetic-field-induced

martensitic transformation or any event related can be ascribed to a thermodynamic energy

deficit. The magnetic driving force must be larger than this thermodynamic energy deficit

to accomplish the energy conversion from magnetic energy to mechanical work output, i.e.

magnetic actuation.

1.5 Challengesformagnetostrainviamartensitic

transformationinNi‐Mn‐basedFSMAs

Although the magnetostrain has been successfully achieved in Ni45Co5Mn36.7In13.3

single crystal and Ni43Co7Mn39Sn11 polycrystalline alloys, no work output was produced.

For instance, the success for inducing magnetostrain of 2.9% in Ni45Co5Mn36.7In13.3 single

crystal is still significantly smaller than the theoretical transformation strain (5-6% based

on the compression direction shown in ref [51]). This indicates that the magnetic field

(~3T) is not able to accomplish the complete martensitic transformation with full strain

recovery. Based on the analysis on energy conversion in Section 1.4, the best alloy

(Ni45Co5Mn36.7In13.3 single crystal) discovered so far cannot fully satisfy energetic criteria

II. This is because the magnetic driving force (or energy input) is completely consumed

during the reverse transformation process, largely by the mechanical resistance, thus

resulting in nil energy to output. Besides, the brittleness of Ni-Mn-based FSMAs still

impedes their engineering applications. The main challenges for developing FSMAs as

engineering magnetoactuators include three aspects as followings.

1.5.1 To increase the magnetic driving force 

Failures to have magnetostrain in Ni-Mn-based FSMAs can be always ascribed to

the limited magnetic driving force for such an actuating event. In fact, since Ni-Mn-

Z(Z=In,Sn,Sb) alloys have distinct magnetic states between the austenite and martensite,

CHAPTER 1 24

 

the ZE can be infinitely increased by applying larger magnetic field B. However, the

magnetostrain needs to be induced using a reasonable magnitude of magnetic field for a

practical consideration. Therefore, the challenge of increasing the magnetic driving force

becomes to increase the ΔM between the austenite and martensite for FSMAs, which is

illustrated in Figure 12. With this consideration, solutions should be sought to increase the

magnetisation of the austenite or to decrease that of the martensite, or both.

sAM

sMM

Figure 12. Illustration of enhancement of Zeeman energy (ZE) in Ni-Mn-based alloys responsible for magnetic-field-induced phase transformation.

1.5.2 To decrease the mechanical resistance 

On the other side of the being a successful FSMA candidate, small resistance during

a magnetic-field-induced shape change is also essential, apart from the required large

magnetic driving force. Based on the discussion in Section 1.4, it is known that the

resistances include thermodynamic barrier (Eth) and mechanical resistance (Emech). The

thermodynamic barrier can be realistically decreased by selecting the testing temperature

close to As, and the minimum energy requirement is min

f

s

A

A

E SdT . However, the pure

mechanical resistance originating from transformation between the prestrained martensite

and the austenite is inevitable. It is known that this part of energy corresponds to the extra

CHAPTER 1 25

 

thermodynamic energy deficit as the “martensite stabilisation” or roughly equals to

mechanical energy required for turning the self-accommodated martensite to reoriented

martensite. This portion of energy must be overcome by the magnetic energy input to meet

criteria II. It is known that the success of having large magnetostrain in Ni-Mn-Ga alloys is

simply due to the high mobility between the twin boundaries of the martensite variants.

Unlike Ni-Mn-Ga alloys, the twining movement of the martensite variant has been proven

very poor in Ni-Co-Mn-In alloys, with a compressive stress of ~100 MPa to initiate

detwining [51, 56, 58]. Therefore, the ZE is mainly depleted by the mechanical resistance

due to the poor mobility of martensite twin boundaries in Ni-Mn-Co-In alloys. Owing to

this consideration, to lower the mechanical resistance is as equally important as to increase

the magnetic driving force during, as it saves the magnetic driving force in another sense,

thus possibly to yield work output.

1.5.3 Brittleness of FSMAs 

From an engineering application point of view, reasonable mechanical properties

are needed to draw attention of FSMAs, such as the ductility, the cyclic stability, the

ambient stability and frequency etc. Among all of these requirements, good ductility is

most crucial for the real engineering applications. It is known that Ni-Mn-Z (Z=Ga, Al, In,

Sn and Sb) alloys are intermetallic compounds, which are intrinsically brittle. For a

polycrystalline, the ductility is even worse, due to the volume change before and after the

martensitic transformation. Consequently, this may easily induce cracking during the

actuation process in polycrystalline alloys. Therefore, one of the most the realistic

challenges is to increase the ductility of Ni-Mn-based FSMAs.

1.6 SolutionstothechallengesofFSMAs

In this thesis, solutions for increasing the magnetic driving force and ductility of Ni-

Mn-based FSMAs are explored. On one hand, new composition design in Mn-Ni-In(Sn)-Co

alloys has been carried out with the aim to increase the magnetic driving force for

actuation. On the other hand, introduction of the phase by substitution of Fe for Mn in Ni-

CHAPTER 1 26

 

Mn-In(Sn) alloys effectively improves the ductility of FSMAs, however, the research

focuses on the metallurgical origin of the changes in transformation behaviour and

magnetic properties brought by the formation of the second phase in these alloys.

1.6.1 Increasing the magnetic driving force ‐ new compositions 

design of Ni‐Mn‐based FSMAs 

Step I-maximise the use of Mn

The magnetic moments of the constituents in Ni-Mn-based FSMAs can be

estimated from those in the stoichiometric compositions. The magnetic moments are 3.5-

3.7 µB/Mn, 0.1-0.3 µB/Ni and ~0 µB/Z, and the net magnetic moments are 4.0-4.2 µB/f.u. in

Ni2MnZ(Z=Ga,In,Sn,Sb) alloys [70]. It is seen that the net magnetic moment mainly comes

from the contribution of Mn atoms in the unit cell. For this reason, it is reasonable to

consider that the magnetisation of the austenite may be maximised by increasing the Mn

content up to 50 at% with the assumption of ferromagnetic alignment between Mn atoms.

The first step of alloy design is to employ as much Mn content as possible in the

new composition. Therefore, Mn50Ni25Z25(Z=In,Sn) was chosen as the base alloy

compositions.

Step II-stacking order adjustment

The type of magnetic interaction between the Mn atoms is very sensitive to the

distance between them. Early studies found that the type of magnetic interaction between

Mn atoms changes from antiferromagnetic to ferromagnetic when the Mn-Mn distance is

increased to above a critical value of approximately 0.30 nm and exhibits a maximum

around 0.37 nm [71-73]. In case of Mn2NiIn and Mn2NiSn alloys, which have an Hg2CuTi

superlattice structure, Mn atoms occupy A and B sites, which form the nearest neighbour.

The distance between Mn(A) and Mn(B) is 3 / 4a , which is ~0.26 nm, in case of a=0.6

nm. The short distance between Mn(A)-Mn(B) leads to the antiferromagnetic interaction.

One solution is to substitute Z element by Ni in the nominal composition. In this case, the

composition becomes Mn50Ni25+xZ25-x. It is seen that some portion of Mn atoms at A site

CHAPTER 1 27

 

have been replaced by Ni atoms, and these new Mn atoms share D site with In atoms. This

hypothesis is based on the rule of preferential site occupation in Mn2YZ (Y: 3d elements;

Z: III-V A group elements) alloys reported by Liu et al [63]. They observed that Y elements

on the right hand side of Mn in the Periodic Table of Elements prefer to occupy (A,C) sites,

whereas Y elements to the left of Mn have strong preference for B site occupancy. In

Mn2YZ (Y = V, Cr, Mn, Fe, Co and Ni; Z =Al, Ga, In, Si, Ge, Sn and Sb) Heusler alloys,

this rule of atomic occupancy has been shown to be well obeyed [61, 63, 66]. According to

this principle, Ni substitution for In will have the priority to take A site in preference to Mn.

The distance between the new Mn atoms at D site and Mn atoms at B site is ~0.3 nm,

which may favor the ferromagnetic exchange interaction between the Mn atoms. Therefore,

the magnitude of antiferromagnetic alignment between Mn(A) and Mn(B) is reduced, and

the new Mn atoms at D site form ferromagnetic interaction with the Mn atoms at B site.

The second step of alloy design is to substitute Ni for Z element to separate Mn(A)-

Mn(B) to become Mn(B)-Mn(D), thus the new composition becomes Mn50Ni25+xZ25-

x(Z=In,Sn).

Step III-Co doping

One main problem with continuous substitution of Ni for Z is that the martensitic

transformation temperature increases rapidly and exceeds the Curie transition temperature

of the austenite at the Ni content of 40 at%, leading to the transformation being from

paramagnetic austenite to paramagnetic martensite. The solution is to utilise Co to

substitute for Ni in the nominal composition, which increases the Curie transition

temperature of the austenite and decreases of the martensitic transformation temperatures in

the meantime time, thus giving rise to more temperature room for a concurrent martensitic

and magnetic transformation.

The third step of alloy design is to substitute Co for Ni element to separate the

Curie transition and martensitic transformation temperature, hence the final composition

becomes Mn50Ni25+x-yZ25-xCoy(Z=In,Sn).

CHAPTER 1 28

 

1.6.2 Ductility improvement and metallurgical origins of changes 

in martensitic and magnetic properties caused by Fe addition 

of Ni‐Mn‐based alloys 

The only solution to increase the ductility is to introduce a ductile second phase (

phase) into the matrix of Ni-Mn-based alloys. The phase was first found in Co-Ni-Al [23,

38, 74], Co-Ni-Ga [75] and Ni-Fe-Ga [76] alloy. Fe and Co as dopants were also found

effectively to form phase in Ni-Mn-based alloys [77-82]. Whereas the purpose is to

improve ductility, addition of a fourth element to the ternary Ni-Mn-Z alloys inevitably

alters the matrix composition, hence changing the structure, thermal and magnetic

properties. Whereas much attention has been given to the influences of fourth element

addition on ductility improvement and transformation properties of these alloys in the

literature, given the level of complexity associated with the quaternary systems, much less

is understood of the metallurgical origins of these influences. In this thesis, this

fundamental issue was examined by investigating the effects of Fe substitution for Mn in

Ni-Mn-In and Ni-Mn-Sn alloys. Fe bears much resemblance to Mn in these alloy systems,

which provides an opportunity to examine the metallurgical influence of Fe addition to the

properties of the alloys, in addition to being a selected element for ductility improvement

for some common ferromagnetic shape memory alloys.

1.7 Thesisorganisation

This thesis is arranged as a series of 5 papers, including 4 published and 1 submitted

papers. Below is an overview of the structure of the thesis.

1.7.1 Chapter 1 (Introduction)

Chapter 1 has provided a concise literature review on ferromagnetic shape memory

alloys, including the development of FSMAs, survey of magnetostrain in various

compositions of FSMAs, and current knowledge in the mechanisms of magnetostrain. It

CHAPTER 1 29

 

also includes a detailed analysis on the energy conversion of magnetic actuation associated

with the martensitic transformation. Three energetic criteria are established for evaluating

the feasibility of magnetostrain of FSMAs. Followed by the energy analysis, the problems

are identified of FSMAs, leading to the objectives of this thesis. The objectives of the thesis

can be summarised as following:

1. To increase the magnetic driving force by optimising the composition of Ni-Mn-

based alloys.

2. To investigate the metallurgical origins of Fe addition on martensitic and

magnetic properties of Ni-Mn-based alloys.

1.7.2 Chapter 2 (Paper 1, Paper2 and Paper3) 

The martensitic transformation and magnetic behaviour of the newly designed

compositions of Mn-rich Ni-Mn-based alloys are illustrated in Paper 1, Paper 2 and Paper 3

in details with the concern of increasing ΔM across the transformation.

Paper 1: Metamagnetic phase transformation in Mn50Ni37In10Co3 polycrystalline

alloy, Zhigang Wu, Zhuhong Liu, Hong Yang, Yinong Liu, Guangheng Wu, Applied

Physics Letters, 2011, 98, pp. 061904(1-3).

This work reports on a new composition design of Mn50Ni37In10Co3, in which a

large magnetisation difference of 89 emu/g was obtained. The complete magnetic-field-

induced martensitic transformation was achieved. It is well demonstrated that the magnetic

driving force in Mn-rich Ni-Mn-based alloys was successfully increased.

Paper 2: Effect of Co addition on martensitic phase transformation and magnetic

properties of Mn50Ni40-xIn10Cox polycrystalline alloys, Zhigang Wu, Zhuhong Liu, Hong

Yang, Yinong Liu, Guangheng Wu, Intermetallics, 2011, 19, pp.1839-1848.

This work reports a complete alloy series design of Mn50Ni40-xIn10Cox alloys. The

effects of Co addition on the martensitic and magnetic properties were investigated. The

origin of the increase of ΔM across the transformation was well interpreted and the

CHAPTER 1 30

 

magnetic moment interactions between the constituents were demonstrated in the proposed

model.

Paper 3: Martensitic phase transformation and magnetic properties of Mn50Ni42-

xSn8Cox polycrystalline alloys, Zhigang Wu, Zhuhong Liu, Hong Yang, Yinong Liu,

Guangheng Wu, Journal of Physics D: Applied Physics, 2011, 44, 385403(1-8).

A complete alloy series design of Mn50Ni42-xSn8Cox alloy was carried out aiming to

increase the ΔM for magnetic actuation in this work. Co substitution for Ni was found

effective on increasing the magnetisation of the austenite, while that of the martensite

remained unchanged at a very low level, leading to the continuously gained ΔM across the

martensite transformation.

1.7.3 Chapter 3 (Paper4 and Paper5)  

Changes on the martensitic transformation behaviour, magnetic properties,

mechanical properties and shape memory effect caused by the formation of phase with the

original purpose of increasing the ductility are clarified in Ni-Mn-based FSMAs. The

studies are carried out in Ni-Mn-In and Ni-Mn-Sn alloys with Fe addition illustrated in

Paper 4 and Paper 5 respectively.

Paper 4: Effect of Fe addition on the martensitic transformation behaviour,

magnetic properties and mechanical performance of Ni50Mn38-xIn12Fex polycrystalline

alloys, Zhigang Wu, Zhuhong Liu, Hong Yang, Yinong Liu, submitted to Journal of Alloys

and Compounds, September 2011.

This work investigates on the martensitic transformation, magnetic properties and

mechanical behaviour of Ni50Mn38-xIn12Fex alloys. Fe substitution for Mn at above 3 at%

was found to create a phase, which greatly alters the composition of the matrix phase. The

martensitic transformation and magnetic transition temperatures were affected by the

change of composition of the matrix phase. Mechanical behaviour and shape memory effect

were also investigated.

CHAPTER 1 31

 

Paper 5: Metallurgical origin of the effect of Fe doping on the martensitic and

magnetic transformation behaviours of Ni50Mn40-xSn10Fex magnetic shape memory

alloys, Zhigang Wu, Zhuhong Liu, Hong Yang, Yinong Liu, Guangheng Wu, Robert

Woodward, Intermetallics, 2011, 19, pp 445-452.

The metallurgical origin of the effect of Fe doping on the martensitic transformation

and magnetic properties was investigated in Ni50Mn40-xSn10Fex alloys in this work. The

findings clarify the origin of the effect of Fe addition and provide useful reference on alloy

design in Ni-Mn-Sn alloy system.

1.7.4 Chapter 4 (Closing remarks)  

The final chapter presents a short summary of the main findings and the

significance of the work in this thesis. The immediate future works as continuation of the

current work are proposed.

CHAPTER 1 32

 

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CHAPTER 2 37

 

CHAPTER 2. Increasing magnetic

driving force of Ni-Mn-based alloys

________________________________________________________________________________ 

Paper1

Metamagnetic phase transformation in Mn50Ni37In10Co3 polycrystalline alloy

Zhigang Wu 1, Zhuhong Liu 2, Hong Yang 1, Yinong Liu 1, Guangheng Wu 3

1 School of Mechanical and Chemical Engineering, The University of Western Australia,

Crawley, WA 6009, Australia

2 Department of Physics, University of Science and Technology Beijing, Beijing 100083,

China

3 Beijing National Laboratory for Condense Matter Physics, Institute of Physics, Chinese

Academy of Science, Beijing 100080, China

This paper reports on an alloy design of Mn50Ni37In10Co3 based on the principle of

Mn-Mn ferromagnetic coupling via Co doping. The alloy is shown to exhibit a

metamagnetic martensitic transformation and a high saturation magnetization of 118 emu/g

in its austenitic state. The transformation generates a large magnetization difference of

89 emu/g, more than 200% of what reported in the literature for similar alloys. A complete

magnetic field induced martensitic transformation was achieved at 170 K. Such high

magnetization difference provides a strong driving force for magnetic-field-induced

transformation, making this material a promising candidate for magnetic actuation

applications.

CHAPTER 2 38

 

Since the discovery of the magnetic-field-assisted shape memory effect in Mn2NiGa

single crystal in 2005,1 much effort has been made to develop better Mn-rich ferromagnetic

shape memory alloys (FSMAs). In Mn2NiX (Ga,In,Sn,Sb) system, the alloys hold the

promise for higher saturation magnetisation owning to its higher Mn content. Mn-rich Mn-

Ni-In alloys have been found to exhibit concurrent magnetic and martensitic

transformations, i.e., metamagnetic transformations.2,3 The magnetic driving force for such

metamagnetic phase transformations is provided by the Zeeman energy EZeeman=µ0MH,

where M is the saturation magnetization difference between the austenite and martensite

and H corresponds to the strength of the applied field. This energy is dependent on the M,

which is typically ~40 emu/g for Mn50Ni40In10.2,3 Largely due to the low ΔM, a complete

reversible metamagnetic transformation is yet to be achieved in Mn-rich FSMAs. At the

meantime, Co doping has been reported to have prominent effect on increasing M in

Mn48CoxNi32-xGa20 alloys4, due to its effect on promoting ferromagnetic alignment of the

moments of the nearest neighboring Mn atoms. This paper reports on a Mn50Ni37In10Co3

alloy, which has a significantly increased ΔM for its metamagnetic transformation.

A polycrystalline Mn50Ni37In10Co3 button ingot was prepared using an arc melting

furnace in argon atmosphere from high purity (99.99 %) elemental metals. The ingot (~4 g)

was heat treated at 1073 K for 24 hours in vacuum followed by quenching in water to

ensure composition homogeneity. Phase identification and crystal structures were

determined by means of X-ray powder diffraction (XRD) using Cu-Kα radiation, phase

transformation behavior was measured by means of differential scanning calorimetry

(DSC) with a cooling/heating rate of 10 K/min, and magnetic properties were studied using

a superconducting quantum interference device magnetometer (SQUID).

Figure 1 shows an XRD spectrum of powder sample of Mn50Ni37In10Co3 alloy at

room temperature. The alloy shows a single phase structure with bcc fundamental lattice

reflections of (220), (400), (422) and (440) and superlattice reflections of (111), (200),

(311) and (222). The superlattice structure can be determined by comparing the relative

intensities of (111) and (200).5 It is evident that I111/I200>1, implying that the superlattice is

of the Hg2CuTi-type, consistent with other Mn2NiX (Ga,Sn,Sb) alloys.5-7

CHAPTER 2 39

 

20 30 40 50 60 70 80 90 100

X-r

ay in

ten

sity

2 (o)

22

0

111

20

0

42

2

40

0

440

222

311

140 160 180 200 220 240

Hea

t flo

w

Temperature (K)

FIG. 1. X-ray diffraction spectrum of powder sample of Mn50Ni37In10Co3 alloy; inset: DSC

curve of the martensitic transformation behavior of the alloy.

In this structure, Mn atoms occupy A (0,0,0) site and B (1/4,1/4,1/4) site, leaving C

(1/2,1/2,1/2) site to Ni atoms and D (3/4,3/4,3/4) site to the third element atoms. Such

structure can be expressed in a stacking order of MnMnNiX ( 43F m space group) along the

diagonal [111] direction of the cubic unit cell. The lattice constant is determined to be

a=0.6013 nm. The inset in the figure shows DSC measurement of the transformation. The

peak transformation temperatures are determined to be 169 K and 195 K and the latent heat

of the transformation is 2.9 J/g.

Figure 2 shows the zero-field cooled (ZFC) and field cooled (FC) M(T) curves with

a cooling/heating rate of 10 K/min of the alloy in magnetic fields of different strengths. At

a low field of 50 Oe, the martensitic and austenitic transformation starting and finishing

temperatures are determined to be 186 KsM , 153 KfM , 179 KsA and 212 KfA ,

respectively.

CHAPTER 2 40

 

0

50

100

0 50 100 150 200 250 300 350

Mag

net

izat

ion

(em

u/g)

Temperature (K)

5x10-3T5x10-2T

2T5T

7T

FC

ZFH

M=

89

em

u/g

FIG. 2. Zero-filed cooled (ZFC) and field cooled (FC) M(T) curves of Mn50Ni37In10Co3

alloy under various fields measured by SQUID.

The transformation hysteresis is determined to be 26 Kf sA M , which is

consistent with the DSC result. It is also seen that at low field strengths the magnetization

behavior exhibited complete reversible phase transformation, shown as the closed ZFC and

FC pathways. At high field strengths (≥2T) the FC pathway did not overlap with ZFC

pathway at 10 K after a cycle of MAM transformation. It is obviously due to the

kinetic arrest of the martensitic transformation under the influence of high magnetic field,

which has been observed and discussed in the literature for several Ni-Mn-In alloys in the

past few years. 8-10 The same phenomenon has also been observed in a similar

Mn49.5Ni40.4In10.1 ribbon alloy, as reported by Sanchez Llamazares recently.11 The increased

magnetization at the finishing point on the FC curves indicates that the amount of the

arrested austenite increased with higher magnetic field applied. It is worth noting that upon

heating (ZFC curves) ΔM between the austenite and the martensite increased progressively

with increasing the magnetic field. The maximum M AM achieved is 89 emu/g in a field

of 7 T.

CHAPTER 2 41

 

Recently, Charkrabarti and Barman conducted theoretical calculation on the

ferrimagnetism of Mn50Ni25In25 alloy, and showed that the net magnetic moment is 0.47 µB

per formula unit (f.u.) for the austenite,12 corresponding to 9.27 emu/g. The crystal structure

of the austenite is considered as Hg2CuTi-type superlattice bcc structure, which is the same

structure as the present Mn50Ni37Co3In10 alloy. This calculation is based on the condition

that Mn-Mn atoms within the lattice form antiferromagnetic coupling. The austenite of our

alloy showed a much higher magnetization of ~118 emu/g at 7 T. The drastically increased

magnetization is a strong indication that the Mn-Mn interaction in the lattice of the

Mn50Ni37In10Co3 alloy has changed to ferromagnetic coupling. This is attributed to two

reasons: (i) change of magnetic exchange status due to the composition change of the

lattice, and (ii) doping effect of Co.

The exchange interaction between Mn atoms is known to depend strongly on Mn-

Mn distance in the lattice. Early studies found that the type of magnetic interaction between

Mn atoms changes from antiferromagnetic to ferromagnetic when the Mn-Mn distance is

increased to above a critical value of approximately 0.30 nm.13 For Mn-Mn-Ni-X stacking

order, the distance between A site and B site is 3 / 4AB a =0.2604 nm and the distance

between B site and D site is / 2 0.3007BD a nm for the current alloy with a=0.6013

nm. This implies that Mn(A)-Mn(B) form antiferromagnetic interaction and Mn(B) and

Mn(D) form ferromagnetic interaction. In Mn50Ni25In25 alloy, the calculated spin magnetic

moments for the austenite are -3.08, 3.42, 0.13 and 0 µB/f.u. for Mn (A site), Mn (B site),

Ni (C site), and In (D site), respectively.12 However, in Mn50Ni40In10 alloy, the saturation

magnetization of the austenite is ~75 emu/g, as reported by Sanchez Llamazares etc.2,3 This

suggests the change of antiferromagnetic coupling between Mn-Mn atoms in the

stoichiometric alloy to ferromagnetic coupling in the non-stoichiometric alloy. One

scenario is that in MnMnNiX-type lattice, excess Ni above 25 at% has priority to take A

site, displacing Mn from A site to D site. In this case the magnitude of antiferromagnetic

alignment between Mn(A) and Mn(B) is reduced, and the new Mn at D site

ferromagnetically aligns with the Mn at B site. In Mn50Ni40In10 alloy, the “extra” Ni (15

at%) may displace 15 at% Mn from A site to D site, thus forming domains of NiMnNiMn

stacking structure. In this case, the matrix of the alloy may be considered to contain two

CHAPTER 2 42

 

mixed domains: Mn-Mn-Ni-In domains (40 % in volume) and Ni-Mn-Ni-Mn domains (60

% in volume). In the MnMnNiIn domain, the Mn(A)-Mn(B) interaction is

antiferromagnetic, as in the case of stoichiometric Mn50Ni25In25. In the NiMnNiMn domain,

the Mn(B)-Mn(D) interaction is ferromagnetic. Liu et al reported that the magnetic moment

of Mn(A) and Mn(C) in MnNiMnGa is 2.99 µB.5 Using this value, and assuming the

magnetic moment of Ni is unchanged at 0.13 µB, the net moment of NiMnNiMn can be

estimated to be 6.24 µB. Combining with the net moment of 0.47 µB for the MnMnNiIn

domain, the total magnetic moment of the alloy can be calculated to be

6.240.6+0.470.4=3.94 µB, corresponding to 76 emu/g, as summarized in Table I. This is

in excellent agreement with the experimental evidences reported in the literature.2,3

TABLE I. Magnetization calculation of Ni50Mn25In25, Mn50Ni40In10, and Mn50Ni37In10Co3 alloys at room temperature.

alloy stacking couple

Mn(A)

(µB)

Mn(B)

(µB)

Mn(D)

(µB)

Ni

(µB)

In

(µB)

f.u.

(µB)

total

(emu/g)

Mn50Ni25In25 Mn-Mn-Ni-In anti -3.08 3.42 - 0.13 0 0.47 9.27

Mn50Ni40In10 Mn-Mn-Ni-In (40%) anti -3.08 3.42 - 0.13 0 0.47 76

Ni-Mn-Ni-Mn (60%) ferro - 2.99 2.99 0.13 - 6.24

Mn50Ni37In10Co3

Mn-Mn-(Ni,Co)-In (40%)

ferro 3.08 3.42 - 0.13 0 6.63 123

Ni-Mn-Ni-Mn (60%) ferro - 2.99 2.99 0.13 - 6.24

However, the magnetization of the present alloy is still significantly higher than

thus predicted. This is believed to be related to the effect of Co doping in the crystal

structure of the austenite. There have been evidences that Co doping enhances

ferromagnetic ordering of the austentie.14,15 In Mn48Ni32-xCoxGa20 alloys Co doping

converts the coupling between the nearest neighboring Mn-Mn atoms from

antiferromagnetic into ferromagnetic.4 Assuming the same effect in our alloy, neglecting

the net moment of the 3 at% Co, and converting the moment for Mn(A) from -3.08 µB to

3.08 µB, the lattice magnetization of the Mn-Mn-(Ni,Co)-In (40%) domain may be

estimated to be 6.63 µB. In this case, the total magnetic moment for the alloy is expected to

be 6.630.4+6.240.6=6.39 µB, which corresponds to 123 emu/g. This is a good agreement

CHAPTER 2 43

 

with the value determined experimentally (118 emu/g). It has been suggested that the

presence of Co in the matrix alters the states of Mn 3d electrons, which leads to the

enhanced ferromagnetic exchange in the austenite.16 This argument is also expected to

apply to the Mn50Ni37In10Co3 alloy.

Figure 3 shows isothermal magnetization loops of the alloy at different

temperatures. The sample showed typical soft magnetic behavior in martensitic state at 5 K

with a saturation magnetization of 29 emu/g under 7 T, which is consistent with previous

findings.2,3 At 200 K, the austenite magnetized in a similar way to saturation at 113 emu/g.

At 170 K, which is 42 K below fA , the sample quickly magnetized at below 0.5 T,

corresponding to the magnetization of the martensite, and then magnetized again at above 2

T, corresponding to the reverse MA transformation. The magnetization reached

saturation level (~118 emu/g) of the austenite at 6 T, indicating the completion of the

metamagnetic transformation. Similar behavior is also observed at 165 K (47 K below fA ),

but the transformation occurred at moderately increased field strength. Consequently, the

transformation was not complete at the maximum field applied (7 T) and the maximum

magnetization reached (~108 emu/g) was slightly below the saturation magnetization of the

austenite.

CHAPTER 2 44

 

0

20

40

60

80

100

120

0 1 2 3 4 5 6 7

Mag

net

izat

ion

(em

u/g

)

Magnetic field (T)

5 K

165 K

170 K

200 K

FIG. 3. Isothermal magnetization loops of Mn50Ni37In10Co3 alloy at different temperatures.

In Summary, the Mn50Ni37In10Co3 alloy shows a martensitic transformation at

186 KsM .

The crystal structure of the austenite is Hg2CuTi-type superlattice bcc

structure with lattice constant of a=0.6013 nm. The saturation magnetization of the

austenite is 118 emu/g and that of the martensite is 29 emu/g at 7 T, resulting in a large ΔM

of 89 emu/g across the martensitic transformation. The largely improved magnetization for

the austenite is attributed to (i) change of magnetic exchange status due to the composition

change of the lattice, and (ii) doping effect of Co. The calculations for the magnetization of

the austenite show excellent agreement with the experimental measurements. Co doping of

3 at% has increased the magnetization of the austenite by 42 emu/g. A complete

metamagnetic transformation is induced isothermally at 170 K in a magnetic field up to 7

T, indicating this alloy a promising candidate for magnetic actuation applications.

The authors wish to acknowledge the financial supports by the Department of

Innovation Industry, Science and Research of the Australian Government in ISL Grant

CHAPTER 2 45

 

CH070136, by the National Natural Science Foundation of China in Grant No. 10774178

and by the Fundamental Research Funds for the central universities.

Reference 1 G. D. Liu, J. L. Chen, Z. H. Liu, X. F. Dai, and G. H. Wu, Appl. Phys. Lett. 87, 262504

(2005). 2 J. L. Sanchez Llamazares, T. Sanchez, J. D. Santos, M. J. Perez, M. L. Sanchez, B.

Hernando, L. Escoda, J. J. Sunol, and R. Varga, Appl. Phys. Lett. 92, 012513 (2008). 3 J. L. Sanchez Llamazares, B. Hernando, V. M. Prida, C. Garcia, J. Gonzalez, R. Varga,

and C. A. Ross, J. Appl. Phys. 105, 07A945 (2009). 4 L. Ma, H. W. Zhang, S. Y. Yu, Z. Y. Zhu, J. L. Chen, G. H. Wu, H. Y. Liu, J. P. Qu, and

Y. X. Li, Appl. Phys. Lett. 92, 032509 (2008). 5 G. D. Liu, X. F. Dai, S. Y. Yu, Z. Y. Zhu, J. L. Chen, G. H. Wu, H. Zhu, and J. Q. Xiao,

Phys. Rev. B: Condens. Matter 74, 054435 (2006). 6 R. B. Helmholdt and K. H. J. Buschow, Journal of the Less-Common Metals 128, 167

(1987). 7 H. Luo, G. Liu, Z. Feng, Y. Li, L. Ma, G. Wu, X. Zhu, C. Jiang, and H. Xu, J. Magn.

Magn. Mater. 321, 4063 (2009). 8 W. Ito, K. Ito, R. Y. Umetsu, R. Kainuma, K. Koyama, K. Watanabe, A. Fujita, K.

Oikawa, K. Ishida, and T. Kanomata, Appl. Phys. Lett. 92, 021908 (2008). 9 R. Y. Umetsu, W. Ito, K. Ito, K. Koyama, A. Fujita, K. Oikawa, T. Kanomata, R.

Kainuma, and K. Ishida, Scripta Mater. 60, 25 (2009). 10 V. K. Sharma, M. K. Chattopadhyay, and S. B. Roy, Phys. Rev. B 76, 140401 (2007). 11 J. L. Sanchez Llamazares, B. Hernando, J. J. Sunol, C. Garcia, and C. A. Ross, J. Appl.

Phys. 107, 09A956 (2010). 12 A. Chakrabarti and S. R. Barman, Appl. Phys. Lett. 94, 161908 (2009). 13 T. Yamada, N. Kunitomi, Y. Nakai, D. E. Cox, and G. Shirane, J. Phys. Soc. Jpn. 28, 615

(1970). 14 S. Y. Yu, Z. X. Cao, L. Ma, G. D. Liu, J. L. Chen, G. H. Wu, B. Zhang, and X. X. Zhang,

Appl. Phys. Lett. 91, 102507 (2007).

CHAPTER 2 46

 

15 S. Y. Yu, L. Ma, G. D. Liu, Z. H. Liu, J. L. Chen, Z. X. Cao, G. H. Wu, B. Zhang, and X.

X. Zhang, Appl. Phys. Lett. 90, 242501 (2007). 16 B. Gao, F. X. Hu, J. Shen, J. Wang, J. R. Sun, and B. G. Shen, J. Magn. Magn. Mater.

321, 2571 (2009).

 

CHAPTER 2 47

 

Paper2

Effect of Co addition on martensitic phase transformation and magnetic

properties of Mn50Ni40-xIn10Cox polycrystalline alloys

Zhigang Wu a, Zhuhong Liu b, Hong Yang a, Yinong Liu a,*, Guangheng Wu c

a School of Mechanical and Chemical Engineering, The University of Western Australia,

Crawley, WA 6009, Australia

b Department of Physics, University of Science and Technology Beijing, Beijing 100083,

China

c Beijing National Laboratory for Condense Matter Physics, Institute of Physics, Chinese

Academy of Science, Beijing 100080, China

Keywords:A:magneticintermetallics;B:alloydesign;B:shape‐memoryeffects;B:

martensitictransformations;B:magneticproperties.

Abstract

This study investigated the use of Co to enhance the magnetic driving force for

inducing the martensitic transformation of Mn50Ni40-xIn10Cox alloys. These alloys present a

martensitic transformation from a Hg2CuTi-type austenite to a body centered tetragonal

martensite, with a large lattice distortion of 15.7% elongation along the c direction and

8.2% contraction along a and b directions. The martensitic transformation temperatures,

transformation enthalpy and entropy changes decreased with increasing the Co content in

these alloys. The maximum magnetization of the austenite increased significantly, whereas

that of the martensite changed much less prominently with increasing the Co substitution

CHAPTER 2 48

 

for Ni, leading to increase of the magnetic driving force for the transformation. The

magnetization increase of the austenite is found to be due to (i) formation of

ferromagnetically coupled Mn-Mn due to new atomic configuration in off-stoichiometric

composition, (ii) magnetic moment contribution of Co and (iii) widening of the temperature

window for magnetization of the austenite. These findings clarify the effect of Co addition

on martensitic transformation and magnetic properties in Mn-rich ferromagnetic shape

memory alloys, and provide useful understanding for alloy design for magnetoactuation

applications.

1.Introduction

Ternary Ni-Mn-Z(Z=In,Sn,Sb) alloys have attracted much attention in the past few

years as a new type of ferromagnetic shape memory alloys (FSMAs) since their discovery

in 2004 [1]. Unlike Ni2MnGa alloy [2], which relies on magnetic crystallographic

anisotropy of the martensite, these Ni-Mn-Z(Z=In,Sn,Sb) alloys exhibit a martensitic

transformation between a ferromagnetic austenite and a paramagnetic martensite. The

different magnetic states between the two phases provide a much greater magnetic driving

force, thus the possibility for a magnetic-field-induced martensitic transformation. Such

transformations are referred to as metamagnetic transformations in recognition of their

concurrent metallurgical and magnetic changes. The magnetic driving force for a

metamagnetic transformation is provided by the Zeeman Energy EZeeman=µ0MH, where

µ0 is the permeability of a vacuum, M is the saturation magnetization difference between

the austenite and martensite and H corresponds to the strength of the applied field. The M

between the ferromagnetic austenite and the paramagnetic martensite, as in the case of Ni-

Mn-Z(Z=In,Sn,Sb), is much greater than the M between the easy and hard magnetization

directions of the same crystal structure, as in the case of Ni-Mn-Ga alloys, thus giving

possibility for much more powerful magnetic-field-induced martensitic phase

transformation and mechanical actuation.

In Ni2MnZ(Z=In,Sn,Sb) alloys, the net magnetic moment mainly comes from the

contribution of Mn [3]. By substituting Mn for X, ΔM has been found to increase in

Ni2Mn1+xIn1-x alloys but to decrease in Ni2Mn1+xSn1-x alloys [4, 5]. At the meantime,

CHAPTER 2 49

 

increasing Mn content also causes rapid increase of the martensitic transformation

temperatures, to above the Curie temperature of the austenite [6, 7]. This results in the

transformation being between a paramagnetic austenite to a paramagnetic martensite, thus

losing the advantage of large magnetic driving force for transformation and jeopardizing

the possibility for magnetic actuation. This limits the range of Mn content feasible in

Ni2MnX(In,Sn,Sb) alloys.

A new approach is to develop Mn2NiZ(Z=Ga,In,Sn,Sb) alloys. These alloys have

the obvious advantage by having more Mn in the matrix, which has the highest

magnetization contribution among the three constituents [3]. A magnetic-field-assisted

shape change of ~4 % has been achieved in single crystalline Mn2NiGa [8]. However, the

magnetic driving force in this alloy is small due to the limited magnetization difference (~9

emu/g) between the austenite and martensite [8, 9]. A progress has been made recently with

off-stoichiometric Mn50Ni40In10 [10, 11] and Mn48CoxNi32-xGa20 [12] alloys, which showed

a relative large ΔM of about 40 emu/g and 30 emu/g respectively, making these alloys valid

candidates for ferromagnetic shape memory actuation. To further improve ΔM, we have

recently reported our study on a Mn50Ni37In10Co3 polycrystalline alloy. This alloy exhibited

a large ΔM of ~89 emu/g and a complete reversible metamagnetic transformation [13].

These limited early findings indicate a possible solution to challenge of enhancing magnetic

driving force for inducing metamagnetic transformation, a prerequisite for magnetically

actuated shape memory alloys.

The saturation magnetization of the alloys depends greatly on the magnetic moment

distribution from Mn atoms. However, the study on the magnetic moment distribution of

Mn in the off-stoichiometric alloys is much lacking. Very recently, Lazpita et al. proposed

a model of magnetic interaction between Mn atoms in the off-stoichiometric Ni-Mn-Ga

alloys [14]. In their model, the excess of Mn atoms at Ga sites couple antiferromagnetically

with the Mn at Mn sites when Ni atoms are at their proper sties, while the Mn at Ga sites

couple ferromagnetically with the Mn at Mn sites when Mn excess occupies Ni sites.

However, the systematic analysis on atomic configuration in Mn-rich off-stoichiometric

Mn-Ni-Z(Z=In,Sn,Sb) alloys is still missing. Moreover, the magnetic interactions between

the constituents may rise up to another level of complexity after Co doping in these ternary

CHAPTER 2 50

 

alloys, since Co doping in Ni-Mn-Z(Ga,Al,In,Sn,Sb) has been found to be effective in

inducing its metamagnetic transformation [15-19]. These findings all indicate that Co

doping in Ni-Mn-Z alloys greatly enhances the ferromagnetic interaction of the austenite,

resulting in the significantly increased the magnetic driving for metamagnetic

transformation. A popular argument is that when Co enters the Ni-Mn-Z Heusler lattice, it

has the effect of turning the antiferromagnetically coupled Mn-Mn atoms into

ferromagnetically couples ones [12, 19]. However, detailed explanation of this effect is yet

to be established. In this study, we further expand our investigation on a series of Mn50Ni40-

xIn10Cox alloys, with an emphasis on analyzing the magnetic moment interactions between

Mn-Mn and Mn-Co atoms in our proposed model.

2.ExperimentalProcedures

Polycrystalline Mn50Ni40-xIn10Cox (x=0, 1, 2 and 3) alloy ingots were prepared by

means of arc melting in argon atmosphere using high purity (99.99 at.%) elemental metals.

The samples are referred to as Co0, Co1, Co2, and Co3, respectively. The button shaped

ingots were heat treated at 1173 K for 24 hours in vacuum followed by quenching into

water for homogenization. Transformation behaviour of the alloys was studied by means of

differential scanning calorimetry (DSC) using a TA Q10 DSC instrument with a

cooling/heating rate of 10 K/min. Phase identification and crystal structures were

determined by means of X-ray powder diffraction using Cu-Kα radiation. The compositions

were determined by means of quantitative X-ray energy dispersive spectrometry (EDS)

equipped on a Zeiss 1555 field-emission scanning electron microscope (FESEM). The

magnetic properties were studied using a superconducting quantum interference device

magnetometer (SQUID).

CHAPTER 2 51

 

3.ExperimentalResults

3.1 Crystal structure 

Fig. 1 shows XRD spectra of powder samples of Mn50Ni40-xIn10Cox alloys measured

at room temperature.

20 30 40 50 60 70 80 90 100

Co0

2 (o)

X-r

ay I

nten

sity

(044

) M

(022

) M

(220

) M

(004

) M

(400

) M

(224

) M

(422

) M

(044

) M

Co1

(022

) M

(220

) M

(004

) M

(400

) M

(224

) M

(422

) M

(044

) M

(422

) A

(400

) A

(220

) A Co2

(022

) M

(220

) M

(004

) M

(400

) M

(224

) M

(422

) M

(440

) A

(222

) A

(422

) A

(400

) A(220

) A

24 28 32

(111)

(200)

Co3

Fig. 1. X-ray diffraction spectra of Mn50Ni40-xIn10Cox alloys.

The diffraction peaks of Co0 and Co1 alloys are indexed to body-centered

tetragonal non-modulated martensite structure, which is also observed in Mn2NiGa alloys

[8]. The Co2 alloy has a mixed structure of body-centered cubic austenite and tetragonal

martensite. This indicates that the addition of 2 at.% of Co lowers the martensitic

CHAPTER 2 52

 

transformation temperatures to below the room temperature. The Co3 alloy shows a pure

austenite structure with bcc fundamental lattice reflections of (220), (400), (422) and (440)

and superlattice reflections of (111), (200), (311) and (222). The superlattice structure can

be determined by comparing the relative intensities of (111) and (200). It is evident that

I111/I200>1, as shown in the inset of Fig. 1, implying that the superlattice is of the Hg2CuTi-

type, consistent with other Mn2NiZ(Z=Ga,Sn,Sb) alloys [20-22].

Fig. 2 shows the effect of Co addition on the lattice parameters and unit cell

volumes for the austenite and martensite at room temperature. It is seen that the

transformation from the cubic austenite to tetragonal martensite is realized by an expansion

in the c direction and equal contractions in the a and b directions (a=b), which is consistent

with Mn2NiGa alloy [8].

  

0 1 2 30.52

0.56

0.60

0.64

0.68

0.72

0.76AusteniteMartensite

aA

cM

aM

VM

VA

Co Addition (at%)

Lat

tice

Con

stan

ts (

nm)

V

0.204

0.208

0.212

0.216

0.220

0.224

Unit C

ell Volum

e (nm3)

 

Fig. 2. Effect of Co addition on lattice parameters and unit cell volume of Mn50Ni40-

xIn10Cox alloys.

The lattice distortion can be estimated to be (cM-aA)/aA=15.7 % along the c direction

and (aM-aA)/aA= -8.2 % for the a and b directions for alloy Co2. Both the expansion in c

direction and contractions in a and b directions are larger than those in Ni2MnGa alloy,

which are 8.4 % and -6.6 % respectively [2]. This large lattice deformation implies higher

frictional resistance to the propagation of transformation interfaces, leading to large

CHAPTER 2 53

 

transformation hysteresis. The unit cell volumes of both the austenite and martensite are

found to slightly increase with increasing substitution of Co for Ni, obviously related to the

slightly larger size of Co atom relative to Ni. It is also evident that the transformation from

the austenite to martensite is accompanied by a volume contraction, of -2.4%. The large

volume change may induce cracking in the material during transformation cycles.

3.2 Alloy composition 

All these alloys show single phase microstructure, as confirmed by SEM

observation. The compositions of these alloys were determined by quantitative EDS

analysis, as summarized in Table 1. The Mn contents for all four alloys are approximately

49 at.%, indicating a volatilization loss of ~1 at.% of Mn during the arc-melting process.

The continuous reduction of Ni is compensated well by the addition of Co, as the designed

nominal compositions. The content of In remained nearly unchanged for all four alloys, at

between 9.9 at.% and 10.5 at.%. The valence electron concentrations of the alloys (e/a

ratio) are calculated using the compositions obtained from the EDS analysis based on the

sum of s, p and d electrons for Mn (7), Ni (10), Co (9) and In (3). It is seen that the e/a ratio

of the alloys decreased from 7.837 to 7.756 with increasing Co substitution for Ni from 0 to

3 at.%, obviously due to the smaller number of valence electrons of Co (9) relative to that

of Ni (10).

Table 1. Composition and e/a ratio of Mn50Ni40-xIn10Cox alloys.

Mn

at.%

Co

at.%

Ni

at.%

In

at.%

e/a

ratio

x=0 49.0 - 41.1 9.9 7.837

x=1 48.8 0.9 40.0 10.3 7.806

x=2 49.3 1.9 38.5 10.3 7.781

x=3 49.3 3.0 37.2 10.5 7.756

CHAPTER 2 54

 

3.2 Martensitic transformation 

Fig. 3 shows DSC curves of the Mn50Ni40-xIn10Cox alloys. It is seen that the

martensitic transformation behaviour evolves progressively, to lower temperatures, with

increasing the Co content of the alloys.

100 150 200 250 300 350 400 450 500

Hea

t Flo

w

Co0

Co1

Co2

Temperature (K)

Co30.

1 w

/g

Fig. 3. DSC curves of the martensitic transformation of Mn50Ni40-xIn10Cox alloys.

The transformation thermal parameters, including starting, finishing and peak

temperatures (Ms, Mf, Mp, As, Af and Ap) for the forward and reverse transformation,

transformation hysteresis (ΔT=Ap-Mp), enthalpy change (ΔH) and entropy change (ΔS), of

the alloys are summarised in Table 2. H is obtained directly from the DSC measurement,

and S is calculated as 0

HS

T

, where 0

1( )

2 p pT M A .

Table 2. The martensitic and austenitic transformation starting, finishing and peak

temperatures (Ms, Mf, Mp ,As, Af, Ap), transformation hysteresis (ΔT= Ap- Mp),

enthalpy change (ΔH) and entropy change (ΔS) of Mn50Ni40-xIn10Cox alloys.

Ms

(K)

Mf

(K)

Mp

(K)

As

(K)

Af

(K)

Ap

(K)

ΔT

(K)

ΔH

(J/g)

ΔS

(J/Kkg)

CHAPTER 2 55

 

x=0 381 350 373 373 403 396 23 9.7 25.0

x=1 318 302 316 334 348 341 25 6.7 23.4

x=2 262 239 249 257 282 269 20 4.6 17.8

x=3 175 161 169 185 199 195 26 2.9 15.9

Fig. 4 shows the effect of Co substitution for Ni on phase transformation

temperatures (Mp and Ap) and transformation hysteresis (ΔT) of the alloys.

0 1 2 3

150

200

250

300

350

400

450

Ap

Mp

Co Addition (at%)

Tra

nsfo

rmat

ion

Tem

pear

ture

(K

)

T

0

5

10

15

20

25

30

35

40

45

50

Transform

ation Hysteresis (K

)

Fig. 4. Effect of Co addition on phase transformation peak temperatures (Mp and Ap) and

transformation hysteresis (ΔT).

It is seen that the transformation temperatures decreased progressively with

increasing the Co content. This is in good agreement with the effect of Co doping in Ni-

Mn-Ga [23] and Ni-Mn-Sb [24] alloys. This is obviously related to the e/a ratio decrease

with the increase of Co substitution for Ni. The ΔT remained practically unchanged,

between 20 and 26 K for the alloys of different Co content. It is known that the

transformation hysteresis generally corresponds to the frictional resistance to the

martensitic transformation, stemming largely from the lattice mismatch, distortion and

volume change of the transformation. Generally, a larger lattice distortion means the

martensitic transformation requires higher energy to overcome the friction during the

motion of the phase boundaries, thus leading to larger transformation hysteresis. It is seen

CHAPTER 2 56

 

in Fig. 2 that the lattice distortions and the volume change are practically the same for all

the four alloys, thus resulting in nearly constant transformation hysteresis for the

transformation.

Fig. 5 shows the effects of Co addition on the transformation enthalpy (ΔH) and

entropy (ΔS) changes of the alloys, as functions of transformation temperature To in (a) and

e/a ratio in (b). It is to be noted that for the martensitic transformation both ΔH and ΔS are

negative values and the plot customarily neglects this. It is seen that both the enthalpy and

entropy changes increased continuously with increasing To and with e/a ratio, caused by Co

addition. The influence of e/a ratio on the entropy change of martensitic transformation has

been reported for Ni50+xMn25-xGa25 [25], Ni50Mn50-xInx [7], and Ni50Mn50-xSnx [6] alloys. In

these alloy systems, ΔS increases with increasing transformation temperatures and e/a ratio,

which is in good agreement with the findings of this study. Similar phenomenon has also

been observed in Ni50Mn40-xSn10Fex and Ni50Mn37(In,Sb)13 alloys in our previous studies

[26, 27].

150 200 250 300 350 4000

2

4

6

8

10

increase Co addition

S

To (K)

Ent

halp

y C

hang

e (J

/g)

a

H

16

18

20

22

24

26

Entropy C

hange (J/K-kg)

CHAPTER 2 57

 

7.74 7.76 7.78 7.80 7.82 7.840

2

4

6

8

10

increase Co addition

bS

e/a Ratio

Ent

halp

y C

hang

e (J

/g)

H

16

18

20

22

24

26

Entropy C

hange (J/K-kg)

Fig. 5. Effect of Co addition on enthalpy and entropy changes, (a) as function of

transformation temperature To=(Mp+Ap)/2, and (b) as function of e/a ratio.

3.3 Thermomagnetization behaviour 

Fig. 6 shows the thermomagnetization behaviour of the four alloys. The sample was

first cooled down to 10 K in a zero magnetic field prior to the measurement. A magnetic

field was applied at 10 K and then the measurement was taken upon heating to 395 K at a

rate of 10 K/min and cooling back again to 10 K in the same field. Fig. 6(a) shows the M(T)

curves of the alloys between 10 and 395 K in a field of 50 Oe. It is seen that the Co0 alloy

showed a mild decrease of magnetization at between 320 and 340 K upon heating, owing to

the Curie transition of the alloy. Based on the DSC measurement (Fig. 3), the Ms

temperature of this alloy is 381 K. However, the M(T) data shows that the hysteresis

between the heating and cooling curves prevailed at between 320 and 340 K, and continued

to present down to 100 K, as shown in the inset of Fig.6 (a). This implies that the

martensitic transformation is not complete and the austenite coexists in this alloy at very

low temperature. Therefore, the Curie temperature corresponds to that of the remaining

austenite at below Ms temperature, denoted ACT =322 K of Co0.

CHAPTER 2 58

 

0 50 100 150 200 250 300 350 400

0

1

2

3

4

5

6

7

8

100 200 300 4000.0

0.4

0.8

TC

ACo0

TC

A

Co3

Co1

Co2

Mag

netiz

atio

n (e

mu/

g)

Temperature (K)

Co0

TC

A

a

H=50 Oe

0 50 100 150 200 250 300 350 400

0

20

40

60

80

100

120

Co0

Co1

Co2

Co3

Mag

netiz

atio

n (e

mu/

g)

Temperature (K)

H=70 kOeb

Fig. 6. Thermomagnetization behaviour of Mn50Ni40-xIn10Cox alloys under a field of (a)

H=50 Oe and (b) H=70 kOe.

In the Co1 alloy, the martensite is antiferromagnetic-like at low temperatures, as

evidenced by the nil magnetization. It is also worth noting the cooling curve retraced the

heating curve at the entire low temperature regime below the martensitic transformation.

Normally a splitting phenomenon between the zero field cooled and field cooled M(T)

curves is observed at low temperatures in Ni-Mn based alloys [6, 7], which indicates the

coexistence of ferromagnetic and antiferromagnetic ordering at the martensitic state.

However, the M(T) data of Co1 suggests that the ferromagnetic structure is vanished and

CHAPTER 2 59

 

the antiferromagnetic exchange is dominant at the martensitic phase. The antiferromagnetic

martensite started transforming to ferromagnetic austenite at 320 K upon heating, followed

immediately by the Curie transition of the austenite at ACT =345 K. Upon cooling, the

magnetization of the austenite increased rapidly through its Curie transition, followed by a

short magnetization plateau before demagnetization rapidly at 325 K upon further cooling

via the transformation from the ferromagnetic austenite to antiferromagnetic martensite.

The martensitic transformation in Co2 alloy can be clearly observed, shown as the

magnetization change upon both heating and cooling, as evidenced by the obvious

transformation hysteresis. The Curie transition for the austenite occurred at 378 K. Similar

to Co1 alloy, the nil magnetization and superposition of M(T) curves at below the

martensitic transformation suggest that the martensite is mainly antiferromagnetic ordered.

Co3 showed clear martensitic transformation as the abrupt magnetization change

upon heating and cooling in the temperature range between 170 and 195 K. The ACT of Co3

is determined to be 393 K. Unlike Co1 and Co2, the separation between the heating and

cooling curves appeared at below 50 K in Co3, suggesting the coexistence of ferromagnetic

ordering and antiferromagnetic ordering at its martensitic state. It is seen that the

martensitic transformation shifted to lower temperatures whereas the Curie transition

shifted to higher temperatures with increasing Co content in these alloys. The increased ACT

is attributed to the fact that the exchange interaction between Co-Mn is stronger than that

between Ni-Mn [12].

Fig. 6(b) shows the M(T) curves of the four alloys between 10 and 395 K in a field

of 70 kOe. The magnetization of the Co0 alloy did not change much during the heating and

cooling cycle, at between 12 and 17 emu/g. The minor increase of the magnetization from

12.5 to 15.5 emu/g at around 380 K upon heating corresponds to the partial occurrence of

the martensitic transformation. With increasing the Co content, it is clear that the

martensitic transformation shifted to lower temperatures. More notably, for alloys through

Co1 to Co3, the magnetization of the austenite increased steadily with increasing Co

content at given temperatures. For example, the magnetization increased from 52 to 70

CHAPTER 2 60

 

emu/g with the increase of Co content from 1 to 3 at.% at 350 K, giving rise to an average

increase of 9 emu/g per 1 at.% Co.

It is also seen that the magnetization behaviour of Co1 and Co2 were completely

reversible after a complete transformation cycle under 70 kOe. In contrast, the

magnetization loop of alloy Co3 did not close at 10 K. It is due to the kinetic arrest of the

austenite phase under the influence of high magnetic field. This effect has also been

observed in several Ni-Mn-In alloys [28-30]. The magnetization at the finishing point on

the cooling curve comprises of the contributions of the newly formed martensite and the

retained austenite. The enhanced magnetization of Co3 at the end of the cooling implies

that more austenite has been retained by the high magnetic field. This is reasonable given

the significantly lowered martensitic transformation temperature, i.e., reduced

thermodynamic driving force for the transformation, of this alloy.

3.4 Magnetization 

The maximum magnetizations of the austenite and martensite ( AM and MM ) are

taken at fA and sA from the heating M(T) curves under 70 kOe. The magnetization

difference between the austenite and martensite is obtained from A MM M M .

The AM , MM , M , and A

CT are summarized in Table 3.

Table 3. Effect of Co addition on maximum magnetizations of the austenite and

martensite obtained at Af and As ( AM and MM ), magnetization difference of

the transformation ( M ), and Curie temperatures of the austenite ( ACT ).

AM MM M A

CT

Co0 15.5 12.5 3 322

Co1 55 3 52 345

Co2 78 5 73 378

Co3 118 29 89 393

CHAPTER 2 61

 

Fig. 7 shows AM , MM and M as functions of Co content. It is seen that AM

increased greatly with the increase of Co content, from 15.5 emu/g in Co0 to 118 emu/g in

Co3, meanwhile MM first decreased from 12.5 emu/g in Co0 to 3 emu/g in Co1, and then

it increased to 29 emu/g in Co3 alloy. ΔM shows a steady increasing trend with increasing

Co content in the alloys, giving rise to a maximum value of 89 emu/g in Co3 alloy. The

greatly increased M is beneficial for obtaining large magnetic driving force for

metamagnetic transformation, i.e. Zeeman Energy, in these alloys.

0 1 2 3

0

20

40

60

80

100

120

M

MA

Mag

netiz

atio

n (e

mu/

g)

Co Addition (at%)

MM

Fig. 7. The maximum magnetization of the austenite and martensite (MA and MM) and

magnetization difference between the phases (ΔM) as a function of Co addition.

The giant magnetization difference across the martensitic transformation is

obviously due to the distinct magnetic states between the austenite and martensite. To

further examine the magnetic configurations in the austenitic and martensitic phases, M(H)

curves were carried out at 5 and 350 K for the Co0, Co1, Co2 and Co3 alloys, respectively.

Fig. 8 shows the magnetization of the alloys at (a) 5 K and (b) 350 K. It is known that all

the alloys are at martensitic state at 5 K based on the thermomagnetization measurements

(Fig. 6).

CHAPTER 2 62

 

0 10 20 30 40 500

5

10

15

20

25

30

Mag

neti

zati

on (

emu/

g)

Magnetic field (kOe)

Co0

Co1

Co2

Co3a T=5 K

0 10 20 30 40 50

0

10

20

30

40

50

60

70

80Co3

Co2

Mag

netiz

atio

n (e

mu/

g)

Magnetic field (kOe)

Co1

b T=350 K

Fig. 8. Magnetization curves at (a) 5 K and (b) 350 K of Mn50Ni40-xIn10Cox alloys.

Fig. 8(a) shows that Co0 has a relatively quick magnetizing behaviour at the

beginning of M(H) curve, indicating the existence of ferromagnetic ordering at its

martensitic state. However, based on the form of M(H) curve and the low magnetisation of

15 emu/g at 50 kOe, the antiferromagnetic exchange is expected to coexist with

ferromagnetic structure at 5 K. Co3 alloy shows a similar M(H) behaviour, but with

stronger magnetic correlations than that in Co0, evidenced by the higher magnetisation of

26 emu/g at 50 kOe. The M(H) curves of Co1 and Co2 are nearly linear, particularly for

Co1, strongly suggesting the existence of long-range antiferromagnetic ordering at the

martensitic state of these alloys.

CHAPTER 2 63

 

Fig. 8(b) shows the magnetization behaviour of the austenitic phase at 350 K of

Co1, Co2 and Co3 alloys. The absence of M(H) data of Co0 is due to its martensitic state at

350K, which is irrelative for comparison with other alloys at the austenitic state. The

austenite of Co1 showed a gradual magnetization growth and maximized at 42 emu/g upon

magnetizing. It is known that the ACT (345 K) of Co1 is very close to the magnetizing

temperature (350 K), therefore, the shape of the M(H) data indicates the existence of

magnetic short-range correlations in the paramagnetic austenitic state. Co2 and Co3

presented very typical ferromagnetic behaviour due to the rapid increase of magnetization

at the initial portion of M(H) curves and the high magnetization magnitude of 59 and 70

emu/g, respectively.

4.Discussion

4.1 Entropy change 

It is seen in Fig. 5 that the value of the entropy change of the transformation

decreased significantly with Co doping, by 36 % reduction with addition of 3 at.% Co.

Entropy change (ΔS) of a martensitic phase transformation is a measure of the difference of

degree of order between the austenite and martensite. In addition to being a function of

temperature itself, ΔS is generally considered to have three contributions, including crystal

structural ordering (ΔSlatt), magnetic structure ordering (ΔSmag) and electronic structure

ordering (ΔSel). In Ni2+xMn1-xGa and X2MnSn (X=Co, Ni, Pd, Cu) alloys, it has been shown

that the electronic contribution ΔSel to ΔS is small [25, 31]. The crystal structural

contribution ΔSlatt to ΔS depends on the crystal structures of the transformation. For the

present four alloys, the structural change is the same and the magnitudes of lattice

distortions of the transformation are similar according to the XRD measurements. Thus, the

crystal structural contribution to the entropy change is also expected to be unchanged for

these alloys. In this regard, the increase of total entropy change ΔS with Co content is

attributed to the magnetic ordering contribution, neglecting the temperature effect.

CHAPTER 2 64

 

Fig. 9 shows a schematic of the contributions of ΔSlatt, ΔSmag to ΔS as functions of

Co content in the alloys.

Fig. 9. Illustration of the effect of Co addition on entropy change of the alloys.

It is known that A Mlatt lattS S , thus the 0M A

latt latt lattS S S for the forward AM

transformation. In the Figure ΔSlatt remains a constant negative value irrespective of Co

content. On the other hand, it is known that A Mmag magS S , thus 0M A

mag mag magS S S . This

is because of the higher magnetic ordering in the austenite relative to the martensite. The

introduction of Co enhances the ferromagnetic ordering of the austenite [13, 16, 19], thus

decreasing the magnetic entropy of the austenite. Meanwhile, the magnetic interaction

between the atomic constituents in the martensite is not significantly affected, relative to

the austenite, as evident in Fig. 7. This results in positive increase of magnetic entropy

change of the transformation with increasing Co content. Consequently, the total entropy

change for the AM transformation becomes less negative with increasing Co content, as

observed in Fig. 5.

4.2 Magnetic moment interactions 

4.2.1. Structure of stoichiometric Mn2NiIn

Co content

ΔS

ΔSlatt

ΔSmag

ΔS=ΔSlatt

+ΔSmag

0

+

- ΔS

CHAPTER 2 65

 

The crystal structure of the austenite is Hg2CuTi-type super lattice cubic structure.

This structure is commonly observed in Mn-rich Heusler alloys, such as Mn2NiGa [20] and

Mn2CoZ(Z=Al,Ga,Ge,In,Sn,Sb) [32]. In this structure, Mn atoms occupy A (0,0,0) site and

B (1/4,1/4,1/4) site, leaving C (1/2,1/2,1/2) site to Ni atoms and D (3/4,3/4,3/4) site to the

third element atoms. This structure is illustrated in Fig. 10, showing the unit cell models for

both the austenite in (a) and martensite in (b) of a stoichiometric Mn2NiIn alloy. Such

structure can be expressed in a stacking order of Mn-Mn-Ni-X ( 43F m space group) along

the diagonal direction of the unit cell.

Fig. 10. Atomic configuration in the unit cell of Mn2NiIn alloy: (a) unit cell of the

austenite with Mn-Mn-Ni-In stacking order (Hg2CuTi structure) and (b) unit cell of the

martensite with Mn-Mn-Ni-In tetragonal structure.

Based on the calculation by Chakrabarti et al [9], the spin magnetic moments of

Mn(A), Mn(B) and Ni in Mn2NiIn alloy are -3.08, 3.42 and 0.13 µB , respectively. The

magnetic moment of In is very small and is neglected in the present discussion. The spin

magnetic moments of Mn atoms are symbolically depicted using arrows on the atoms

shown in Fig. 10. The length of the arrows roughly represents the magnitude of the

magnetic moment of the atom. The exchange interaction between Mn atoms is known to

CHAPTER 2 66

 

depend strongly on Mn-Mn distance in the lattice. Early studies have shown that the

magnetic interaction between Mn atoms changes from antiferromagnetic to ferromagnetic

when the Mn-Mn distance is increased to above a critical value of approximately 0.30 nm

[33]. For the austenite with Mn-Mn-Ni-In stacking order in the unit cell (Fig. 10(a)), the

distance between the nearest neighboring Mn at A site and B site is 3 / 4AB a =0.2604

nm and the distance between the second nearest neighboring Mn at two adjacent A sites is

2 / 2AA a =0.4251 nm using the lattice constant of a=0.6013 nm for the Co3 alloy. This

implies that the moments of Mn(A)-Mn(B) form antiparrallel coupling and Mn(A)-Mn(A)

form parallel coupling. It is seen that the spin directions of Mn magnetic moments at A site

are antiparrallel with those of Ni at C site, and they are also opposed to those of Mn at B

site. This forms a ferrimagnetic structure in this atomic configuration, with antiparrallel

aligned magnetic moments between (A,C) and (B,D) sub-lattices.

Assuming that the stoichiometric Mn2NiIn alloy also undergoes the same structural

transformation to a tetragonal martensite as for the present alloys, the distance between A

site and B site changes very little by the transformation, at 3 / 4AB a =0.2612 nm in the

martensite, and the distance between two adjacent A sites is shortened to

2 / 2AA a =0.3899 nm as shown in Fig. 10(b). Therefore, Mn(A)-Mn(B) still forms

antiferromagnetic interaction and Mn(A)-Mn(A) forms ferromagnetic interaction in the

martensite. This implies that the magnetic exchange interactions in the martensite are

similar with those in the austenite, which is ferrimagnetic.

4.2.2. Atomic configuration in off-stoichiometric Mn2Ni1+xIn1-x

In Ni-rich off-stoichiometric Mn2Ni1+xIn1-x alloys, the magnetization has been found

to increase greatly relative to its mother alloy Mn2NiIn, as evidenced by the magnetization

of ~75 emu/g (at 230 K) in Mn50Ni40In10 [10] comparing to 9.27 emu/g in Mn2NiIn [9]. The

drastic increase of the magnetization cannot be solely attributed to the magnetic moment

contribution from the “extra” Ni which substitutes for In, as the magnetic moment of Ni is

small, typically ~0.13 µB. This suggests that the increase may originate from the biggest

magnetic moment contributor Mn atoms. This implies that the atomic configuration must

have changed after the Ni substitution for In.

CHAPTER 2 67

 

Fig. 11 shows the atomic configuration in the unit cell of the austenite in (a) and the

martensite in (b) of the Co0, with the nominal composition of Mn50Ni40In10.

Fig. 11. Atomic configurations in the unit cell of Co0 alloy (Mn50Ni40In10): (a) unit cell of

the austenite and (b) unit cell of the martensite. The number of displaced atoms does not

represent the actual proportion of substitution, which is only for qualitative interpretation.

It is seen that some portion of Mn atoms at A site have been replaced by Ni atoms,

and these new Mn atoms share D site with In atoms. This hypothesis is based on the rule of

preferential site occupation in Mn2YZ (Y: 3d elements; Z: III-V A group elements) alloys

reported by Liu et al. [32]. They observed that Y elements on the right hand side of Mn in

the Periodic Table of Elements prefer to occupy (A,C) sites, whereas Y elements to the left

of Mn have strong preference for B site occupancy. In Mn2YZ (Y = V, Cr, Mn, Fe, Co and

Ni; Z =Al, Ga, In, Si, Ge, Sn and Sb) Heusler alloys, this rule of atomic occupancy has

been shown to be well obeyed [22, 32, 34-36]. According to this principle, Ni substitution

for In will have the priority to take A site in preference to Mn. The distance between the

new Mn atoms at D site and Mn atoms at B site is 0.3007 nm, which favors ferromagnetic

exchange interaction between the Mn atoms. Therefore, the magnitude of antiferromagnetic

CHAPTER 2 68

 

alignment between Mn(A) and Mn(B) is reduced, and the new Mn atoms at D site form

ferromagnetic interaction with the Mn atoms at B site.

In Fig. 11(a), the spin magnetic moments of the new Mn(D) align parallel with

those of Mn(B). At the meantime, the new (A,C) sub-lattice after the replacement of Ni for

Mn at A site also forms ferromagnetic interaction with Mn(B) and Mn(D), thus creating a

local ferromagnetic structure of Mn(B)-Ni-Mn(D) in the alloy. This explains the increase of

the magnetization of the austenite in off-stoichiometric Mn2Ni1+xIn1-x alloy after Ni

substitution for In compared to the stoichiometric Mn2NiIn alloy.

In the martensite unit cell (Fig. 11(b)), the distance change between the nearest

Mn(A)-Mn(B) atoms is very small, from 0.2604 to 0.2612 nm, which suggests that the

coupling between Mn(A)-Mn(B) does not change after the transformation, still showing

antiferromagnetic interaction between them. However, along the a and b directions in the

tetragonal unit cell, the distance between A and C sites (same for B and D sites) is

shortened to AC=BD=0.2758 nm, which strongly favours antiferromagnetic coupling

between Mn(B)-Mn(D) [37, 38]. This explains the presence of antiferromagnetic

interaction at the martensitic phase obtained from the M(H) data shown in Fig. 8 (a). In this

regard, it is reasonable to attribute the disappearance of the local ferromagnetic structure of

Mn(B)-Ni-Mn(D) in the martensite to the significant decrease of the Mn(B)-Mn(D)

distance.

4.2.3. Magnetic moment contribution from Co

Fig. 12 shows the atomic configuration in the unit cells for the austenite (a) and the

martensite (b) after Co doping in off-stoichiometric Mn50Ni40In10 alloys. Followed by the

rule of selectivity of atomic configuration in Heusler alloys as aforementioned, Co

substitution for Ni should just replace Ni at either A site or C site, and no new atomic

configuration is formed. By assuming that Co atoms replace the Ni atoms at A site, a

stronger local ferromagnetic structure of Mn(B)-Co-Mn(D) will be formed, shown in Fig.

12(a). Each Co atom at the site of Ni contributes a larger magnetic moment (~1.2 µB)

relative to Ni (0.13 µB), based on the calculation of magnetic moments in Mn2NiCoxGa1-x

CHAPTER 2 69

 

alloys [37]. This results in the further increment of the magnetization of the austenite due to

the magnetic moment contribution from Co.

Fig. 12. Atomic configurations in the unit cell of Co doped Mn50CoxNi40-xIn10 (x≥1): (a)

unit cell of the austenite and (b) unit cell of the martensite. The number of displaced

atoms does not represent the actual proportion of substitution, which is only for

qualitative interpretation.

 

4.2.4. Maximum magnetization of ferromagnetic austenite

It is evident in Fig. 6(b) that the magnetization of the ferromagnetic austenite

increased progressively with decreasing temperature. The temperature window for

ferromagnetic austenite is limited by two temperatures, the Curie temperature of the

austenite ( ACT ) as the upper boundary and the (reverse) martensitic transformation

temperature ( fA ) as the lower boundary. The maximum magnetization of the austenite

( AM ) is achieved at fA (upon heating), as seen on the M(T) curves (Fig. 6(b)) of these

alloys. It is also seen in Fig. 3 that the transformation temperatures decreased significantly

with increasing Co content. This means that the AM values were actually taken at different

CHAPTER 2 70

 

temperatures for these alloys and the increase of AM with increasing Co content, shown in

Fig. 7 is really due to the widening of the temperature window of the ferromagnetic

austenite, instead of purely due to the effect of alloying. The effect of alloying may be

estimated by measuring the magnetization of the alloys at a given temperature. As

aforementioned, the magnetization at 350 K increased from 52 emu/g for Co1 to 70 emu/g

for Co3. On the other hand, the maximum magnetization at fA increased from 55 emu/g

for Co1 to 118 emu/g for Co3, corresponding to the magnetization increase of 31.5 emu/g

per at.% of Co addition. It is evident that widening of the temperature window is the more

prominent factor relative to Co alloying contributing to the large ΔM in these alloys.

4.3 Transformation diagram 

Fig. 13 shows the effect of e/a ratio, as a result of Co doping, on the martensitic

transformation temperatures Mp and Ap obtained from the DSC measurement and on the

Curie transition temperature ACT obtained from the magnetization measurements of the

Mn50Ni40-xIn10Cox alloys. It is seen that Mp and Ap decreased linearly with decreasing e/a

ratio and ACT increased. This observation is consistent with the general observation of

positive dependence of martensitic transformation temperatures on e/a ratio reported in the

literature for Ni-Mn-Z(Z=Ga,In,Sn,Sb) alloy systems [6, 7, 39]. The linear coefficient is

estimated to be 25 K per 0.01 change of e/a ratio, which is comparable to the value

determined for Ni50Mn40-xSn10Fex alloys [26].

CHAPTER 2 71

 

7.68 7.72 7.76 7.80 7.840

100

200

300

400

500

A

M (antiferro)Mp

A (ferro)

Co0

Co1

Co2

Tra

nsfo

rmat

ion

Tem

pera

ture

(K

)

e/a Ratio

Co3

A (para)

Ap

TA

C

Fig. 13. Effect of e/a ratio on Mp, Ap and ACT temperatures of Mn50Ni40-xIn10Cox alloys.

The temperature-e/a ratio space shown in Fig. 13 can be tentatively divided into

three regions representing different crystallographic and magnetic states for the alloys,

including austenite (paramagnetic), austenite (ferromagnetic) and martensite

(antiferromagnetic). Among the three states, two transformation schemes may occur. In the

region to the right of point A, the alloy undergoes a single step transformation between

paramagnetic austenite and antiferromagnetic martensite. This transformation is of low

interest for magnetic actuation. To the left of point A, the alloy undergoes the

transformation sequence from paramagnetic austenite to ferromagnetic austenite and then to

antiferromagnetic martensite upon cooling, expressed as

( ) ( ) ( )A para A ferro M antiferro . In this expression, the single arrow represents

magnetic transition and the double arrow represents the martensitic transformation (in this

case it is also a concurrent magnetic transition). The phase area of the ferromagnetic

austenite opens up with the decrease of e/a ratio, thus providing a wider temperature

window for ( ) ( )A ferro M antiferro transformation.

CHAPTER 2 72

 

5.Conclusions

The effects of Co substitution for Ni on the martensitic transformation and magnetic

behaviour of Mn50Ni40-xIn10Cox alloys were investigated. The experimental evidences and

the discussions lead to the following conclusions:

(1) Co substitution for Ni up to 3 at.% greatly decreases the martensitic

transformation temperature from 381 K to 175 K in these alloys. The martensite

has a non-modulated tetragonal structure, and the crystal structure of the austenite

is determined to be Hg2CuTi-type superlattice cubic structure.

(2) The decrease of the phase transformation temperatures is attributed to the

decrease of the e/a ratio for the alloys with increasing Co substitution for Ni. The

enthalpy and entropy changes of the transformation are both found to increase

with increasing the e/a ratio of the alloys.

(3) The maximum magnetization of the austenite (under 70 kOe) is significantly

increased from 15.5 emu/g in the Co0 alloy to 118 emu/g in the Co3 alloy,

whereas that of the martensite shows much less significant change from 12.5

emu/g in the Co0 alloy to 29 emu/g in the Co3 alloy. Consequently,

magnetization difference between the austenite and the martensite increases

significantly with increasing Co substitution for Ni. The largest ΔM for the

martensitic transformation obtained is 89 emu/g in alloy Co3.

(4) The increased magnetization of the austenite is attributed to three reasons: (i)

formation of ferromagnetic structure of Mn(B)-Ni-Mn(D) in off-stoichiometric

Mn2Ni1+xIn1-x, due to the readjustment of atomic configuration in the unit cell

caused by Ni substitution for In, (ii) higher magnetic moment contribution of Co

relative to Ni, and (iii) widening of the temperature window for ferromagnetic

austenite.

(5) The low magnetization of the martensite, relative to that of the austenite, is due to

the significantly shortened distance between Mn(B)-Mn(D), which leads to the

disappearance of the local ferromagnetic structure in a tetragonal martensitic

structure.

CHAPTER 2 73

 

Acknowledgements

The authors wish to acknowledge the financial supports by the Department of

Innovation Industry, Science and Research of the Australian Government in ISL Grant

CH070136, and by National Natural Science Foundation of China in Grant No. 51001010.

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CHAPTER 2 76

 

Paper 3

Martensitic and magnetic transformation behaviours in Mn50Ni42-xSn8Cox

polycrystalline alloys

Zhigang Wu 1, Zhuhong Liu 2, Hong Yang 1, Yinong Liu 1, Guangheng Wu 3

1 School of Mechanical and Chemical Engineering, The University of Western Australia,

Crawley, WA 6009, Australia

2 Department of Physics, University of Science and Technology Beijing, Beijing 100083,

China

3 Beijing National Laboratory for Condense Matter Physics, Institute of Physics, Chinese

Academy of Science, Beijing 100080, China

Abstract

This study investigated the effect of Co substitution for Ni in Mn50Ni42Sn8 alloy

with the aim to increase the magnetic driving force for inducing its martensitic

transformation. The martensitic transformation temperatures, enthalpy and entropy changes

are found to decrease progressively with increasing the Co content, while the

transformation hysteresis increased. Co substitution for Ni also significantly increased the

magnetization of the austenite, but with negligible effect on that of the martensite. A large

magnetization difference 109 emu/g was achieved across the transformation in a

Mn50Ni34Sn8Co8 alloy. The large magnetization difference between the two phases provides

enhanced thermodynamic driving force for the transformation. Consequently, the

martensitic transformation was induced by the application of a magnetic field in

Mn50Ni36Sn8Co6 and Mn50Ni34Sn8Co8 alloys. The effect of Co substitution for Ni on the

magnetic interaction among the constituents for the austenite and martensite was clarified

in this study, which provides a guide for alloy design for magnetoactuation applications.

CHAPTER 2 77

 

Keywords: A: magnetic intermetallics; B: alloy design; B: shape-memory effects; B:

martensitic transformations; B: magnetic properties.

1.Introduction

Magnetomartensitic transformations in certain alloys have attracted extensive

research interest in the past 15 years, since the discovery of giant magnetic-field-induced

strains (MFIS) of 5-10 % in near stoichiometric Ni-Mn-Ga alloys in 1996 [1-3]. The large

MFIS is associated with the rearrangement of martensite variants, driven by the

magnetocrystalline anisotropy of these variants. The magnetic driving force for this type of

actuation, which is derived from the magnetic anisotropy of the martensite variant, is

generally small, of the order of 300-400 kJ/m3 [4]. Given that the shape change is typically

6%, this yields a magnetically generated stress of 5-6 MPa. Such stress is barely enough to

overcome the mechanical resistance for martensite variant detwining [2, 4]. The low force

output has been proven to be a main limitation for the application of these materials for

mechanical actuation. An intrinsic solution to this problem is to increase the magnetic

driving power for the martensitic transformation. To increase power density, a new group

of off-stoichiometric Heusler Ni-Mn-Z(Z=In,Sn,Sb) alloys have been developed. These

alloys present concurrent martensitic and magnetic transformation, in which one phase (the

martensite) has much lower magnetization compared to the other (the austenite) [5]. In

Ni50Mn34In16 alloy, the magnetization difference between the two transforming phases is

around 70 emu/g, which gives rise to large magnetic power of 700 kJ/m3 at 1 Tesla field.

This large magnetization difference provides the necessary thermodynamic diving force,

thus the opportunity for obtaining a magnetic-field-induced reverse martensitic

transformation.

In the recent few years, much effort has been put into increasing the magnetic

driving force for martensitic transformation in Ni-Mn-Z(Z=In,Sn,Sb) alloys. This driving

force is the Zeeman Energy EZeeman=µ0MH, where µ0 is the permeability of a vacuum,

M is the saturation magnetization difference between the austenite and martensite and H

corresponds to the strength of the applied field. Co substitution for Ni has been found

CHAPTER 2 78

 

effective for increasing M between the phases in Ni-Mn-Z(Z=In,Sn,Sb) alloys, leading to

the successful field induced phase transformation in these alloys [6-10]. In these alloys, it is

known that the net magnetic moment mainly comes from the contribution of Mn [11], and

the magnetic moment distribution of Mn is very sensitive to interatomic distance. The

magnetic interaction between the Mn atoms can change from ferromagnetic to

antiferromagnetic alignment when the distance becomes below a critical value, which is

~0.3 nm [12]. With the objective of increasing M for the magnetic-field-induced

transformation, understanding of the magnetic moment contribution of Mn in off-

stoichiometric is essential.

In our previous study on Mn50Ni40-xIn10Cox alloys, we proposed an atomic

configuration model in which the mechanism of magnetic exchange interaction between

Mn-Mn and Mn-Co was explained. For better understanding of the properties of structural

and magnetic transitions in other Mn-rich Mn-Ni-based alloys, it is necessary to extend the

studies to a new series of Mn50Ni42-xSn8Cox alloys, with a focus on the effect of Co

substitution for Ni on the martensitic transformation and magnetic properties.

2.ExperimentalProcedures

Polycrystalline Mn50Ni42-xSn8Cox (x=0, 2, 4, 6 and 8) alloy ingots were prepared by

means of arc melting in argon atmosphere using high purity (99.99 %) elemental metals.

The samples are referred to as Co0, Co2, Co4, Co6 and Co8, respectively. The button

shaped ingots were heat treated at 1173 K for 24 hours in vacuum followed by quenching

into water for homogenization. Transformation behaviour of the alloys was studied by

means of differential scanning calorimetry (DSC) using a TA Q10 DSC instrument with a

cooling/heating rate of 10 K/min. Phase identification and crystal structures were

determined by means of X-ray powder diffraction using Cu-Kα radiation. Microstructures

of the samples were studied with optical microscopy and the compositions were determined

by means of X-ray energy dispersive spectrometry (EDS). The magnetic properties were

studied using a superconducting quantum interference device magnetometer (SQUID).

CHAPTER 2 79

 

3.Resultsanddiscussion

3.1 Crystal structure 

Figure 1 shows XRD spectra of Mn50Ni42-xSn8Cox alloys at room temperature. It is

seen that from Co0 through to Co6, the alloys show nearly identical diffraction patterns of

the martensite with a non-modulated body centered tetragonal structure. The lattice

parameters of the martensite are determined to be a=b=0.545 nm, and c=0.697 nm. Alloy

Co8 shows a single phase structure with bcc fundamental lattice reflections of (220), (400)

and (422) and superlattice reflections of (111), (200) and (311). The superlattice structure

can be determined by comparing the relative intensities of (111) and (200) [13]. It is

evident that I111/I200>1, implying that the superlattice is of the Hg2CuTi-type, shown in the

inset of Figure 1(e). This observation is consistent with those observed in Mn2NiZ (Z=In,

Sn and Sb) alloys [14, 15] and Mn50Ni37In10Co3 alloy [16]. In this structure, one Mn

sublattice occupies A (0, 0, 0) site (referred to as Mn(A)), the other Mn sublattice is at B

site (0.25, 0.25, 0.25) (referred to as Mn(B)), Ni atoms occupy C site (0.5, 0.5, 0.5) and Z

atoms occupy D site (0.75, 0.75, 0.75). Such structure can be expressed in a stacking order

of MnMnNiX ( 43F m space group) along the diagonal [111] direction of the cubic unit

cell. The lattice parameter of the austenite in Co8 is determined to be a=0.602 nm.

CHAPTER 2 80

 

20 30 40 50 60 70 80 90

Co0(a)

2 (o)

(022

) M

(004

) M

(400

) M

(224

) M

(422

) M

X-r

ay I

nten

sity

Co2

(b)

Co4(c)

Co6

(d)

Co8(e) (2

20) A

(311

) A

(400

) A

(422

) A

Figure 1. X-ray powder diffraction spectra of the Mn50Ni42-xSn8Cox alloys. Inset of (e)

shows the comparison between the relative intensities of (111) and (200) reflections.

3.2 Microstructure and alloy composition 

Figure 2 shows optical micrographs of the microstructures of Co6 and Co8 alloys

after homogenization treatment. Both alloys have a single phase throughout the matrix.

Alloy Co6 presents evident martensite plates, indicating the martensite state at room

temperature. Co8 shows a few martensite plates in the austenite matrix, which may be due

to the occurrence of partially stress-induced martensitic transformation. Cracks are visible

along the columned grain boundaries for both alloys, indicating the brittleness of these

materials.

24 26 28 30 32

(200

)

(111

)

CHAPTER 2 81

 

Figure 2. Optical micrographs for (a) alloy Co6 and (b) alloy Co8.

The composition of these alloys was determined by quantitative EDS analysis. The

results are summarized in Table 1. For all the alloys, the Mn contents are approximately 49

at.%, indicating that the volatilization loss of Mn is ~1 at.% during the arc-melting process.

The continuous reduction of Ni is compensated well by the addition of Co. The Sn content

remained nearly unchanged, at between 8.6 at.% and 8.9 at.%. The valence electron

concentration per atom (e/a ratio) was calculated using the compositions obtained from the

EDS analysis with the sum of s, p and d electrons for Mn (7), Ni (10), Co (9) and Sn (4). It

is seen that the e/a ratio decreased from 8.011 to 7.925 with increasing Co substitution for

Ni from 0 to 8 at.%, obviously due to the smaller number of valence electrons of Co (9)

relative to that of Ni (10).

Table 1. Composition and e/a ratio of the Mn50Ni42-xSn8Cox alloys.

Mn (at%) Co (at%) Ni (at%) Sn (at%) e/a

x=0 49.1 - 42.3 8.6 8.011

x=2 48.8 2.1 40.3 8.8 7.987

x=4 48.6 4.1 38.4 8.9 7.967

x=6 48.6 6.1 36.6 8.7 7.959

x=8 49.1 8.0 34.2 8.7 7.925

CHAPTER 2 82

 

3.3 Martensitic transformation 

Figure 3 shows DSC curves of the Mn50Ni42-xSn8Cox alloys. It is seen that the

martensitic transformation behaviour evolves progressively with increasing the Co addition.

200 240 280 320 360 400 440 480

1 J/

gCo8

Co6

Co4

Co2

Hea

t Flo

w

Temperature (K)

Co0

Figure 3. DSC curves of the Mn50Ni42-xSn8Cox alloys.

Both the transformation temperatures and the enthalpy change decreased. The

transformation temperatures (TM: the forward transformation peak temperature, TA: the

reverse transformation peak temperature and 1

( )2o M AT T T ), transformation hysteresis

(ΔT=TA-TM), enthalpy change (H) and entropy change (S) of the alloys are summarized

in Table 2. The H values were determined directly from the DSC measurements, and S is

estimated based on o

HS

T

.

Table 2. Thermal and thermodynamic parameters of the martensitic transformation of the

Mn50Ni42-xSn8Cox alloys.

TM (K) TA (K) To (K) ΔT (K) ΔH (J/g) ΔS (J/Kkg)

CHAPTER 2 83

 

x=0 377 391 384 14 16.23 42.27

x=2 369 383 376 14 15.84 42.13

x=4 362 375 369 13 14.30 38.75

x=6 330 348 339 18 11.21 33.07

x=8 278 304 291 26 4.69 16.12

Figure 4 shows the effect of e/a ratio on phase transformation temperatures (TM, TA

and To) and hysteresis (ΔT) of the alloys. It is seen that TM and TA increased with increasing

e/a ratio (decreasing Co content). This is consistent with the general trend of positive

dependence of martensitic transformation temperatures on e/a ratio observed in Ni-Mn-

Z(Z=Ga, In, Sn and Sb) alloys [17]. It appears that there are two linear dependences of the

transformation temperatures on e/a ratio. At below e/a=7.967, corresponding to 4 at.% of

Co, the linear coefficient is 18 K per 0.01 e/a unit for To. At above e/a=7.967, the

coefficient is 3.5 K per 0.01 e/a unit. Similarly, ΔT also shows two distinct dependences on

e/a ratio. It increases with more Co content at below 7.967 and remains independent of e/a

ratio at above.

CHAPTER 2 84

 

7.92 7.94 7.96 7.98 8.00 8.02260

280

300

320

340

360

380

400

To

TM

TA

e/a Ratio

Tra

nsfo

rmat

ion

Tem

pera

ture

(K

)

T

increasing Co centent10

12

14

16

18

20

22

24

26

28T

ransformation H

ysteresis (K)

Figure 4. Effect of Co addition on phase transformation temperatures and hysteresis

expressed as functions of e/a ratio.

Figure 5 shows the effects of Co addition on the transformation enthalpy and

entropy changes of the alloys, shown as functions of transformation temperature To in (a)

and of e/a ratio in (b). It is seen that both the enthalpy and entropy changes increased

continuously with increasing To and with e/a ratio, caused by Co addition. The influence of

e/a ratio on the entropy change of martensitic transformation has been reported for

Ni50+xMn25-xGa [18, 19], Ni50Mn50-xInx [20], and Ni50Mn50-xSnx [21] alloys. In these alloy

systems, ΔS increases with increasing transformation temperatures and e/a ratio, which is in

good agreement with the findings in the present study. The change of ΔS is mainly

attributed to the change of the magnetic component of the total ΔS caused by increasing the

Co addition. With increasing the Co content, the magnetic entropy change increases in the

alloys. This argument is supported by the evidence that the magnetization of the austenite

increases while that of the martensite remains unchanged with increasing the Co content in

the alloys, as shown in Figure 7(b). For the forward transformation, ΔSA-M, the (positive)

increase of magnetic entropy change reduces the (negative) lattice entropy change, thus

resulting in the decrease of the total (negative) ΔS for these alloys.

CHAPTER 2 85

 

280 300 320 340 360 380 4000

2

4

6

8

10

12

14

16

18

To (K)

Ent

alpy

Cha

nge

(J/g

) H

S

increasing Co content

a

12

16

20

24

28

32

36

40

44

48

Entropy C

hange (J/K-kg)

7.92 7.94 7.96 7.98 8.00 8.020

2

4

6

8

10

12

14

16

18

e/a Ratio

Ent

alpy

Cha

nge

(J/g

)

H

S

b

increasing Co content12

16

20

24

28

32

36

40

44

48

Entropy C

hange (J/K-kg)

Figure 5. Effect of Co addition on enthalpy and entropy changes of the Mn50Ni42-xSn8Cox

alloys, (a) as function of transformation To=(TM+TA)/2, and (b) as function of e/a ratio.

3.4 Thermomagnetization 

Figure 6 shows the magnetization of the alloys during a heating-cooling cycle

between 200 and 395 K in a field of 50 Oe (Figure 6(a)) and 70 kOe in (Figure 6(b)). The

sample was first cooled down to 200 K in a zero magnetic field prior to the measurement. A

magnetic field was applied at 200 K and then the sample was heated at a rate of 10 K/min

up to 395 K and cooled back again to 200 K in the same field.

CHAPTER 2 86

 

200 250 300 350 400

0.00

0.05

0.10

0.15

0.20

0.25

350 360 370 380 3900.00000.00010.00020.00030.00040.00050.0006

Co8

Co6

Mag

netiz

atio

n (e

mu/

g)

Temperature (K)

Co4

H=50 Oe

a

Magnetization (em

u/g)

Temperature (K)

Co2

Co0

200 250 300 350 4000

20

40

60

80

100

120

Co8

Co6

Co4

Co2

Mag

neti

zatio

n (e

mu/

g)

Temperature (K)

Co0

H=70 kOeb

M=

109

emu/

g

Figure 6. Thermomagnetization curves in a magnetic field of (a) H=50 Oe and (b) H=70

kOe for Mn50Ni42-xSn8Cox.

At a low field of 50 Oe, as shown in Figure 6(a), alloys Co4, Co6 and Co8 undergo

a structural transformation between a ferromagnetic austenite and a ferrimagnetic

martensite with obvious transformation hysteresis between the heating and cooling curves.

For Co4, the magnetization drop of the austenite upon heating to ~380 K is due to the Curie

transition of the austenite, denoted as 380ACT K . The Curie transition was not observed in

Co6 and Co8 within the testing temperature range, suggesting higher Curie transition

CHAPTER 2 87

 

temperatures at above 400 K for these two alloys. In the inset of Figure 6(a), alloys Co2

and Co4 present similar martensitic transformation, but with much smaller magnitude of

magnetizations of the austenite compared to those of Co4, Co6 and Co8. The Curie

temperatures of the austenite of Co0 and Co2 alloys seem close to 400 K, which are higher

than that of Co4. Normally, with more Co substitution for Ni, the Curie temperature is

expected to increase, due to the stronger exchange interaction between Co-Mn than that

between Ni-Mn [22]. The anomaly of ACT in these alloys is not clear at this stage.

It is evident that the martensitic transformation temperature decreased with

increasing Co content in these alloys, consistent with the observation from DSC

measurement (Figure 3). The Curie temperatures of these alloys are obviously higher than

those in Ni2Mn1+xSn1-x [21, 23, 24] alloys, which are around 320 K. It has been reported

that CT is 588 K in Mn2NiGa alloy [25], suggesting the generally higher CT in Mn-rich

Mn2NiZ alloys relative to Ni-rich Ni2MnZ alloys. It is also worth noting that the

transformation hysteresis is around 40 K for Co8, which is much larger than the value

determined from DSC measurement (26 K). The large hysteresis usually means higher

frictional resistance to the propagation of the transformation interfaces. This may lead to

large difficulty for two-way magnetic-field-induced martensitic transformation in Co8

alloy.

Figure 6(b) shows the thermomagnetization behavior of the five alloys between 200

and 395 K at a field of 70 kOe. The martensitic transformation temperatures were lowered

under the influence of the higher magnetic field. For alloy Co8, the transformation

temperatures are * 255 KMT and * 285 KAT at 70 kOe, which are approximately 30 K

lower than those at 50 Oe.

Figure 7 shows magnetization of the austenite at the martensitic transformation

starting temperature Ms (s

AMM ), magnetization of the martensite at the martensitic

transformation finishing temperature Mf (f

MMM ), magnetization difference across the

transformation (s f

A MM MM M M ), at 70 kOe as functions of Co content in the alloys. It is

CHAPTER 2 88

 

seen that s

AMM increased rapidly from 13 emu/g in Co0 to 117 emu/g in Co8, while

f

MMM remained almost constant (~5 emu/g), thus resulting in an increasing M across the

martensitic transformation with increasing the Co content. The maximum M is 109 emu/g

in alloy Co8.

0 2 4 6 80

20

40

60

80

100

120

Mag

netiz

atio

n (e

mu/

g)

Co Content (at %)

Figure 7. The magnetization of the austenite at Ms (s

AMM ), the magnetization of the

martensite at Mf (f

MMM ), and the magnetization difference across the martensitic

transformation (s f

A MM MM M M ) at a field of 70 kOe as functions of Co content in

Mn50Ni42-xSn8Cox.

3.5 Magnetic coupling  

Figure 8 shows the atomic configuration in the unit cell of Mn50Ni42-xSn8Cox alloys.

Illustration (a) represents the unit cell of the austenite with Mn-Mn-Ni-Sn stacking order

(Hg2CuTi-type structure) and illustration (b) represents the unit cell of the martensite with

Mn-Mn-Ni-Sn tetragonal structure.

s

AMM

M

f

AMM

CHAPTER 2 89

 

Figure 8. Atomic configuration in the unit cell of Mn50Ni42-xSn8Cox alloys: (a) unit cell of

the austenite with Mn-Mn-Ni-Sn stacking order (Hg2CuTi structure) and (b) unit cell of

the martensite with Mn-Mn-Ni-Sn tetragonal structure.

For Mn2YZ (Y: 3d elements; Z: III-V A group elements) compounds, it has been

observed that Y elements with more valence electrons prefer to occupy A and C sites,

whereas Y elements with fewer valence electrons have preference for B site occupancy

[26]. For the Mn50Ni42-xSn8Cox alloys, Co substitutes Ni at C site, and the excess Ni atoms

prefer to occupy A sites, displacing Mn(A) to Mn(D) site, as illustrated in Figure 8(a).

Based on this rule, the atomic occupation for Mn50Ni42-xSn8Cox alloys can be written as

[Mn(A)Ni(A)]25Mn(B)25[Co(C)Ni(C)]25[Sn(D)Mn(D)]25.

In the austenite (Figure 8(a)), the Mn(A) and Mn (B) are the nearest neighbors with

a distance of 0.26 nm ( 3 / 4a ) in between. The nearest distance between Mn(B) and

Mn(D) atoms is 0.301 nm (a/2). It has been found that the magnetic interaction between Mn

atoms changes from ferromagnetic to antiferromagnetic alignment when the Mn-Mn

CHAPTER 2 90

 

distance reduces to below a critical value of approximately 0.30 nm [12]. Therefore,

Mn(A)-Mn(B) is expected to form antiferromagnetic alignment, whereas Mn(B)-Mn(D)

forms ferromagnetic alignment in the austenite. After the replacement of Mn(A) by Ni(A),

there will be a significant increase of the net magnetic moment for the austenite, which is

due to the reduction of the antiferromagnetic Mn(A)-Mn(B) coupling and the formation of

the ferromagnetic Mn(B)-Mn(D) coupling. Co substitution for Ni at C site also provides

magnetic moment contribution to some extent due to its larger magnetic moment (~1 µB)

relative to that of Ni (~0.3 µB).

The significant increase of s

AMM can also be attributed to the enlarged temperature

window for the ferromagnetic austenite to develop, caused by Co addition. The s

AMM is

measured at sM (upon cooling), as seen on the M-T curves (Figure 6(b)) of these alloys. It

is also seen in Figure 3 that the transformation temperatures decreased significantly with

increasing Co content. This means that the s

AMM values were actually taken at different

temperatures for these alloys. Therefore, the increase of s

AMM with increasing Co content is

largely due to the widening of the temperature window of the ferromagnetic austenite, in

addition to the effect of Co alloying as aforementioned.

Upon the martensitic transformation, the crystallographic transformation changes

the crystal lattice in the unit cell, consequently altering the exchange coupling of the

magnetic atoms. Upon transforming form the cubic austenite (Figure 8(a)) to the tetragonal

martensite (Figure 8(b)), a and b axes shrink by 9.5% and c axis elongates by 15.7%.

Through the transformation, the nearest distance between Mn(B)-Mn(D) decreases from

0.301 nm (a/2, parent phase) to 0.273 nm (a/2, martensite phase) which is below the critical

distance for ferromagnetic coupling. This leads to the moments of Mn(B) and Mn(D) to

change from in parallel alignment in the austenite to antiparrallel alignment in the

martensite. The distance between Mn(A)-Mn(B) changed from 0.261 nm ( 3 / 4a ) in the

austenite to 0.260 nm in the martensite, which causes no change to the magnetic alignment

between Mn(B) and Mn(D). Exchange interaction between Mn(A) and Mn(B) is still

CHAPTER 2 91

 

antiparrallel alignment. Therefore, the magnetic coupling of the martensite is expected to be

ferrimagnetic.

3.6 Magnetic‐field‐induced martensitic transformation  

The magnetic driving force for a magnetic-field-induced martensitic phase

transformation arises from the Zeeman Energy EZeeman=µ0MH. The M for the present

Mn50Ni42-xSn8Cox alloys has been significantly increased by substituting Co for Ni. To

verify this increased M in regards to benefiting the field induced martensitic

transformation, alloys Co6 and Co8 were magnetized isothermally at different

temperatures, as shown in Figure 9.

0 10 20 30 40 50 60 700

10

20

30

40

50

60

70

80

340 K

335 K

390 K

Mag

netiz

atio

n (e

mu/

g)

Magnetic Field (kOe)

5 K

a

CHAPTER 2 92

 

0 10 20 30 40 50 60 70

0102030405060708090

100110b

290 K

280 K

390 K

5 K

Mag

netiz

atio

n (e

mu/

g)

Magnetic Field (kOe)

Figure 9. Isothermal magnetization behaviours of (a) alloy Co6 and (b) alloy Co8 at

different temperatures.

Figure 9(a) shows the magnetization behaviour of alloy Co6. At 5 K, the martensite

shows low magnetization of 11 emu/g (at 70 kOe). At 390 K, the austenite shows a typical

soft ferromagnetic behaviour, with a saturation magnetization of 68 emu/g. At 335 K, the

martensite shows a very low saturation magnetization (~2 emu/g) at below 20 kOe. Upon

increasing the magnetic field to above 50 kOe, the magnetization increased rapidly,

signifying the phase transformation from the martensite to the austenite. The maximum

magnetization reached is 30 emu/g at 70 kOe. This magnetization is much lower than the

saturation magnetization of the austenite (~70 emu/g). This is obviously due to the fact that

the transformation is incomplete at 335 K. At 340 K (8 K below TA), the martensite starts to

transform to the austenite at 30 kOe and saturates at 72 emu/g at 7 T, indicating the

completion of the reverse transformation. Upon removal of the external magnetic field, the

magnetization decreases slowly at above 30 kOe, and then quickly drops to 20 emu/g,

indicating the occurrence of the forward martensitic transformation.

Figure 9(b) shows the magnetization behaviour of alloy Co8. The magnetization

behaviours of the martensite at 5 K and the austenite at 390 K are similar to those of Co6.

At 280 K, the martensite starts to transform to austenite at the field of 30 kOe upon

magnetizing. The magnetization maximized at 75 emu/g at 70 kOe, indicating the

CHAPTER 2 93

 

incomplete magnetic-field-induced transformation. At 290 K (14 K below TA), the

martensite starts to transform to the austenite at 10 kOe and saturates at ~100 emu/g at 70

kOe, indicating the completion of the reverse transformation. Upon removal of the external

magnetic field, the austenite remained saturated and did not transform back to the

martensite. This is due to the large transformation hysteresis in Co8. The testing

temperature of 290 K is well above the forward transformation temperature (TM=278 K),

thus resulting in the retained austenite after demagnetization. It is worth nothing that the

complete field-induced transformation can be achieved at lower temperature below TA in

Co8 (14 K below TA) than that in Co6 (8 K below TA), which is due to the larger ΔM across

the transformation of Co8 relative to that of Co6. This indicates that the magnetic driving

force is increased with increasing the Co content in Mn50Ni42-xSn8Cox alloys in a certain

field, thus easier for obtaining a field-induced transformation.

4.Conclusions

In this study, the effects of Co substitution for Ni on the martensitic transformation

and magnetic behaviour of Mn50Ni42-xSn8Cox alloys were investigated. The experimental

evidences and the discussions lead to the following conclusions:

(1) The Mn50Ni42-xSn8Cox alloys exhibit a martensitic transformation from an

Hg2CuTi-type austenite to a non-modulated tetragonal martensite. The martensitic

transformation temperatures were found to decrease significantly with increasing

Co substitution for Ni, due to the decreasing e/a ratio in the alloys. The enthalpy

and entropy changes of the transformation are both found to decrease with

increasing Co addition.

(2) The magnetization of the austenite is significantly increased from 13 emu/g in the

Co0 alloy to 117 emu/g in the Co8 alloy, whereas that of the martensite remains

unchanged at ~5 emu/g. Consequently, magnetization difference between the

austenite and the martensite increases significantly with increasing Co

substitution for Ni. The largest ΔM for the martensitic transformation obtained is

109 emu/g in alloy Co8.

CHAPTER 2 94

 

(3) The increased magnetization of the austenite is attributed to two reasons: (i)

higher magnetic moment contribution of Co relative to Ni, and (ii) widening of

the temperature window for ferromagnetic austenite to magnetize.

(4) The low magnetization of the martensite is due to the significantly shortened

distance between Mn(B)-Mn(D), which leads to the antiparallel alignment of the

magnetic moments of neighbouring Mn atoms in the tetragonal martensitic

structure.

(5) The magnetic-field-induced martensitic transformation from ferrimagnetic

martensite to ferromagnetic austenite was successfully induced in alloys Co6 and

Co8 under a field within the range of 30~70 kOe.

Acknowledgements

The authors wish to acknowledge the financial supports by the Department of

Innovation Industry, Science and Research of the Australian Government in ISL Grant

CH070136, and by National Natural Science Foundation of China in Grant No. 51001010.

CHAPTER 2 95

 

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CHAPTER 3 97

CHAPTER 3. Increasing ductility of Ni-

Mn-based alloys

________________________________________________________________________________ 

Paper 4

Effect of Fe addition on the martensitic transformation behaviour,

magnetic properties and mechanical performance of Ni50Mn38-xIn12Fex

polycrystalline alloys

Zhigang Wu1, Zhuhong Liu2, Hong Yang1 and Yinong Liu1

1 School of Mechanical and Chemical Engineering, The University of Western Australia,

Crawley, WA 6009, Australia

2 Department of Physics, University of Science and Technology Beijing, Beijing 100083,

China

Abstract

CHAPTER 3 98

 

This study investigated the effect of Fe substitution for Mn on the transformation,

magnetic and mechanical behaviours of Ni50Mn38-xIn12Fex (x=0, 3, 4, 5, 6) alloys. These

alloys show a martensitic transformation from a B2 austenite to an orthorhombic martensite

at above the room temperature. Substitution of Fe for Mn at above 3 at.% introduced a fcc γ

phase in the microstructure, the amount of which increased with increasing the Fe addition.

The formation of γ phase influenced the composition of the matrix phase, particularly the

Mn and In contents, leading to a series of changes in alloy properties. The e/a ratio of the

matrix phase decreased rapidly with increasing Fe addition, resulting in the decrease of

martensitic transformation temperature and enthalpy change. Fe addition also effectively

weakens the antiferromagnetic ordering of the austenite in the matrix phase, leading to the

increase of magnetisation difference across the martensitic transformation. The

compressive strength and ductility appear to optimise at 4~5 at.% Fe addition, reaching 770

MPa and 14.3 %, respectively. The relative shape memory effect decreased from 94 % to

37 % after 4 at.% Fe addition.

Keywords: Shape memory alloy; martensitic transformation; magnetic properties;

intermetallics

1. Introduction

Ferromagnetic shape memory alloys Ni-Mn-Z (Z=In, Sn, Sb) have been widely

investigated in the past few years as potential candidates for magnetic actuation. The large

difference in magnetic state between the austenite and martensite produces high magnetic

driving force for magnetic-field-induced martensitic transformation [1]. Substitution of Ni

by Co is found to increase the magnetic ordering of the austenite and to decrease that of the

martensite, further increasing the magnetisation difference of the martensitic

transformation in Ni-Mn-Z (Z=Ga, Al, In, Sn, Sn, Sb) alloys [2-8]. As a result, >1% strain

has been realised in Ni45Co5Mn36.7In13.3 and Ni43Co7Mn39Sn11 alloys [2, 3], demonstrating

the promise of the alloys for actuation applications in smart systems.

Unfortunately, the intrinsic brittleness of these intermetallic compounds severely

hinders their engineering application. To date, it has not been possible to process

polycrystalline Ni-Mn-Z (Z=In, Sn, Sb) ferromagnetic shape memory alloys using

CHAPTER 3 99

 

conventional methods. It is known that the introduction of a ductile second phase is helpful

in improving the ductility of the alloys, as initially discovered in Ni-Fe-Ga [9], Co-Ni-Ga

[10] and Co-Ni-Al [11] alloys. Later, adding Fe and Co was found to form a ductile phase

in Ni-Mn-Z (Z=Ga, In, Sn) [12-17], accordingly increasing the ductility of these alloys.

Apart from the improved ductility, addition of a fourth element to the ternary Ni-

Mn-Z (Z=Ga, In, Sn, Sb) alloys alters the matrix composition, which causes a number of

changes in the structure, thermal and magnetic properties. The effect of Fe substitution for

Mn in Ni-Mn-Sn alloys has been found to decrease the martensitic transformation

temperatures and increase the Curie transition temperatures of both the austenite and the

martensite [18, 19]. In our previous study on Ni50Mn40-xSn10Fex alloys, Fe substitution for

Mn changed the composition of the matrix phase in addition to forming the phase [20]. It

is revealed that changes in Mn and Sn contents in the matrix phase are the actual reasons

for the property changes. This study investigated the effects of the formation of the phase

caused by Fe substitution for Mn in Ni50Mn38-xIn12Fex. The addition of Fe is expected to

alter the composition of the matrix phase, thus affecting the magnetic state and valence

electron number of the alloys. Besides concerning on changes of the physical properties

influenced by the phase, mechanical performance and shape memory effect were also

investigated in Ni50Mn38-xIn12Fex alloys.

2. Experimental procedures

Bulk ingots of polycrystalline Ni50Mn38-xIn12Fex (x=0, 3, 4, 5, 6) alloys were

prepared by means of arc melting in argon atmosphere using high purity Ni (99.99 at.%),

Mn (99.99 at.%), In (99.99 at.%) and Fe (99.95 at.%). The samples are referred to as Fe0,

Fe3, Fe4, Fe5 and Fe6, based on the atomic percentage of Fe addition in the alloys. The

button shaped ingots were heat treated at 1173 K in vacuum for homogenisation followed

by furnace cooling to room temperature. Transformation behaviour of the alloys was

studied by means of differential scanning calorimetry (DSC) using a TA Q10 DSC

instrument with a cooling/heating rate of 10 K/min. Phase identification and crystal

structures were determined by means of X-ray powder diffraction using a Siemens D5000

instrument with Cu-Kα radiation and transmission electron microscopy (TEM) using a Jeol

CHAPTER 3 100

 

2100 instrument. Microstructures of the samples were studied with TEM and scanning

electron microscopy (SEM) using a Zeiss 1555 instrument. The compositions were

determined by means of X-ray energy dispersive spectrometry (EDS) equipped on SEM.

Magnetic properties were studied using a superconducting quantum interference device

magnetometer (SQUID).

3. Results and discussion

3.1 Microstructure and alloy composition

Figure 1 shows back-scattered electron (BSE) micrographs of the microstructures of

the Ni50Mn38-xIn12Fex (x=0, 3, 4, 5, 6) alloys after homogenisation treatment.

(a) (b)

  (c)

grain boundaries

  (c)

grain boundaries

CHAPTER 3 101

 

(e)

Figure 1. Back-scattered electron images of the Ni50Mn38-xIn12Fex alloys: (a) Fe0, (b) Fe3, (c) Fe4, (d) Fe5, and (e) Fe6 alloys.

The BSE microstructures of the alloys were examined without etching. The Fe0 and

Fe3 samples (micrograph (a) and (b)) showed uniform single phase structure, without sign

of a second phase. The black spots are solidification shrinkage pores formed during ingot

casting. The Fe4, Fe5 and Fe6 samples showed a continuous matrix in light contrast and

dispersed γ phase particles in dark contrast. The volume fraction of the γ phase increased

with increasing Fe addition. It is also seen that the γ phase particles tend to form along the

grain boundaries in Fe4 and Fe5 alloys, as shown in micrograph (c) and (d). The alloy Fe6

showed distinctive texture of the γ phase compared to Fe4 and Fe5, with straight and

elongated γ phase grains.

Table 1 shows compositions of the phases in the samples as determined by

quantitative EDS analysis. It is seen that the matrix phase of the Fe-doped alloys contained

about 49 at.% Ni. The content of Mn decreased continuously from 37.8 to 32.5 % with

increasing Fe addition from 2.9 to 3.8 % in the matrix. The content of In was also found to

increase from 12.8 to 14.8 %. The γ phase is effectively a Ni-Mn-Fe alloy containing a

small amount of In (~1.1 at.%). The volume fraction of the γ phase is determined by image

analysis from the SEM micrographs using Image J.

Table 1. Composition, e/a ratio and γ proportion of Ni50Mn38-xIn12Fex (x=0, 3, 4, 5, 6)

alloys.

CHAPTER 3 102

 

Matrix (at.%) The γ phase (at.%)

Ni Mn In Fe e/a

ratio

Ni Mn In Fe γ (%)

X=0 49.4 37.8 12.8 - 7.970 - - - - -

X=3 48.6 35.3 13.2 2.9 7.962 - - - - -

X=4 49.1 34.0 13.7 3.2 7.958 54.5 31.1 1.1 13.3 6.8

X=5 49.1 33.0 14.4 3.5 7.936 54.0 30.9 1.1 14.0 11.5

X=6 48.9 32.5 14.8 3.8 7.913 52.5 30.2 1.1 16.2 14.0

The increase of In content in the matrix phase is apparently related to the increase of

the fraction of γ phase, which contains very little In. The valence electron concentrations

per atom (e/a ratio) of the matrix phase was calculated using the compositions obtained

from EDS analysis from the sum of s, p and d electrons for Mn (7), Ni (10), Fe (8) and In

(3). It is obvious that the e/a ratio decreases with increasing In and decreasing Mn contents

of the alloys.Figure 2 shows the effect of Fe addition on the matrix phase composition

(graph (a)) and the e/a ratio (graph (b)) of the alloys. With increasing Fe addition, both Fe

and In contents in the matrix phase increased, and the Mn content decreased. The e/a ratio

of the alloy decreased continuously with increasing Fe addition in the alloys, shown in

graph (b). The decrease of the e/a ratio is obviously related to the composition change in

the matrix phase caused by the formation of the phase. More specifically, the decrease of

Mn (7 valence electrons) and increase of In (3 valence electrons) contents are the main

reasons for the decrease of the e/a ratio, though Fe (8 valence electrons) content slightly

increased as well in the matrix phase. It is worth noting that there are two different negative

dependencies of the e/a ratio on Fe addition, which are 0.003 per at.% for Fe≤4 and 0.023

for 4≤Fe≤6. This indicates that the e/a ratio of the matrix phase decreased more rapidly

when Fe addition is above 4 at.% in the alloys.

CHAPTER 3 103

 

0 1 2 3 4 5 6

12

16

20

24

28

32

36

40

Fe

In

Fe Addition (at.%)

In, M

n C

on

ten

t (a

t.%

)

Mn(a)

0

1

2

3

4

5

Fe

Conten

t (at.%)

0 1 2 3 4 5 6

7.91

7.92

7.93

7.94

7.95

7.96

7.97

e/a

Ra

tio o

f Mat

rix

Ph

ase

Fe Addition (at. %)

(b)

transformationdisappears

Figure 2. Effects of Fe addition on (a) element concentrations and (b) e/a ratio of the matrix

phase of the Ni50Mn38-xIn12Fex alloys.

3.2 Martensitic transformation behaviour

Figure 3 presents DSC curves of the Ni50Mn38-xIn12Fex alloys. It is seen that the

martensitic transformation behaviour evolved progressively with increasing Fe addition in

these alloys.

CHAPTER 3 104

 

100 150 200 250 300 350 400 450 500 550

TA

Fe6

Fe5

Fe4

Fe3

He

at F

low

Temperature (K)

Fe0

0.2

w/g

TM

Figure 3. DSC measurements of martensitic transformation behaviour of the Ni50Mn38-

xIn12Fex alloys.

The martensitic transformation is clearly observed for Fe0, Fe3 and Fe4 alloys, and

the transformation temperatures decreased with increasing Fe addition in these alloys.

However, no transformation was detected in Fe5 and Fe6.

Figure 4 shows the effect of e/a ratio on transformation temperature To and

transformation enthalpy change ΔH. To is defined as To=1/2(TM+TA), where TM and TA are

the peak temperatures of the forward and the reverse transformations, and ΔH is obtained

from the forward transformation. It is seen that the transformation temperatures of Fe0, Fe3

and Fe4 increased practically linearly with increasing the e/a ratio of the alloys. This

observation is consistent with the findings of the effect of e/a ratio on transformation

temperatures in Ni-Mn-Z (Al, Ga, In, Sn and Sb) alloys [21-23]. It is also evident that the

ΔH increased with increasing e/a ratio of the matrix.

CHAPTER 3 105

 

7.945 7.950 7.955 7.960 7.965 7.970

280

320

360

400

440

Fe4

Fe3

e/a Ratio

To

(K)

Fe0

To

H

0

2

4

6

8

10

12

14

16

H

(J/g)

Figure 4. Effects of Fe addition on transformation temperature To=(TM+TA)/2 and

transformation enthalpy change ΔH. The arrow pointing to the e/a ratio axis indicates the

threshold e/a ratio value below which the martensitic transformation is expected to vanish.

Extending ΔH curve to zero tentatively defines the threshold value of e/a ratio

below which the martensitic transformation is expected to vanish. The threshold value, as

indicated by the arrow in Figure 4, is estimated to be e/a = 7.948. The e/a ratio value

corresponds to an Fe addition of 4.5 at.% estimated from Figure 2 (b). For Fe addition of

more than 4.5 at.% in the system, no martensitic transformation is expected. This explains

the disappearance of martensitic transformation in Fe5 and Fe6.

3.3 Crystal structure

Figure 5 shows the crystal structures of the Ni50Mn38-xIn12Fex alloys examined by

X-ray diffraction at room temperature. The non-modulated orthorhombic martensite

structure can be observed in Fe0, Fe3 and Fe4 alloys. The observation of martensitic phase

is consistent with the results obtained from DSC (Figure 3), which indicate the martensitic

state at room temperature of these alloys. Apart from the martensite structure, diffraction

peaks of the fcc phase can also be identified in the spectrum of Fe4 alloy, which is

consistent with its microstructure (Figure 1 (c)). Alloy Fe5 exhibits a more complicated

case, showing a mixed structure of the orthorhombic martensite, the bcc austenite and the

CHAPTER 3 106

 

fcc γ phase. Alloy Fe6 presents a two-phase structure, with the bcc austenite and the fcc γ

phase.

20 30 40 50 60 70 80 90 100

Fe6

Fe5

Fe4

Fe3

X-r

ay

Inte

nsi

ty

2 (o)

A M

Fe0

Figure 5. X-ray spectra of the crystal structure of the Ni50Mn38-xIn12Fex alloys at room

temperature. The phases are identified with labeled symbols: (○) represents phase, A

(▼) represents the austenite phase and M (■) represents the martensite phase.

The lattice parameters of the γ phase in Fe4, Fe5 and Fe6 are very close, with an

average value of a=0.366 nm at room temperature. The lattice parameter of the bcc

austenite is determined to be a=0.2991 nm for Fe5 and Fe6 alloys. The lattice parameter of

the orthorhombic martensite is determined to be a=0.6535 nm, b=0.5928 nm, c=0.5701 nm

for Fe0, Fe3 and Fe4 alloys. Figure 6 shows TEM observation of the microstructure and

crystal structure of Fe4 and Fe5 alloys at room temperature. Micrograph (a) shows a bright

field image of Fe4. Two phases are present in the microstructure, which are the matrix

phase in dark contrast and the phase in light contrast. Selected area diffraction pattern

(SADP) from area A of the matrix phase is shown in Figure 6(b), which can be indexed to

B2 structure along its [001] zone axis. Presence of (010) reflection is the evidence of the

superlattice B2 structure. Figure 6(c) shows the SADP of area B of the phase. The pattern

is indexed to fcc system along [011] zone axis. Fe5 also exhibits two phases in the

microstructure, including the matrix and the phases. The SADPs obtained from area C

CHAPTER 3 107

 

and D are presented in Figure 6(e) and Figure 6(f), respectively. Similarly, the matrix phase

shows a B2 structure austenite and the phase is confirmed to be fcc structure.

  (a) (b)

[001]

000010

110

110_

0.5 μm

A

B

Matrix phase

phase

(c)

[011]

200

200

111

111_ _ _

_

 (d)

(f)

[011]

000

200

200

111

111_ _ _

_

0.5 μm

C

D

Matrix phase

phase

000010110

110_

[001]

(e)

Figure 6. Room temperature TEM micrographs and selected area diffraction patterns

(SADPs) of the matrix and phase of Fe4 and Fe5 alloys. (a) bright field image of Fe4, (b)

and (c) SADPs obtained from areas A and B of Fe4, (d) bright field image of Fe5, (e) and

(f) SADPs obtained from areas C and D of Fe5.

3.4 Magnetic properties

CHAPTER 3 108

 

In Ni50Mn25+xIn25-x alloys, it is known that magnetic moments of the excessive Mn

atoms occupying the In sites align in parallel formation with respect to those of the Mn

atoms at the Mn sites, thus introducing extra ferromagnetic coupling between the two,

leading to increase in the saturation magnetisation with increasing Mn substitution for In

[24]. In Ni50Mn38-xIn12Fex alloys, the concentration of Mn can be up to 38 at.%. That means

13 at.% of Mn occupy the In sites. In this case, it is expected that ferromagnetic interactions

of the off-stoichiometric Ni50Mn38-xIn12Fex are increased compared to the stoichiometric

Ni50Mn25In25 alloy. Figure 7 shows the M(T) curves of the Ni50Mn38-xIn12Fex alloys in a

small magnetic field of 50 Oe. The sample was first cooled down from 390 to 10 K inside

the instrument without applying a magnetic field. A 50 Oe field was applied at 10 K and

then the magnetisation of the sample was measured upon heating to 390 K. Subsequently,

without removing the external field, the measurement was made upon cooling to 10 K.

0 50 100 150 200 250 300 350 400

0.00

0.02

0.04

0.06

0.08

0.10 TC

M

Mag

net

isat

ion

(em

u/g)

Temperature (K)

(a) Fe0

TC

A

0 50 100 150 200 250 300 350 400

0.0

0.5

1.0

1.5

2.0

2.5

TC

M

Mag

net

isat

ion

(em

u/g

)

Temperature (K)

(b) Fe3

TC

A

0 50 100 150 200 250 300 350 400

0

1

2

3

4

5

6

TC

M

Ma

gn

etis

atio

n (

em

u/g

)

Temperature (K)

(c) Fe4

TC

A

0 50 100 150 200 250 300 350 4000

1

2

3

4

5

Mag

netis

atio

n (

emu/

g)

Temperature (K)

(d) Fe5

TC

A

CHAPTER 3 109

 

0 50 100 150 200 250 300 350 4000

1

2

3

4

5

6

7

Ma

gnet

isa

tion

(em

u/g

)

Temperature (K)

(e) Fe6

TC

A

Figure 7. Thermomagnetisation behaviour of Ni50Mn38-xIn12Fex alloys in a field of 50 Oe.

As seen in Figure 7(a), Fe0 presents a very small magnetisation at 10 K when the 50

Oe field was applied, at 0.05 emu/g. The magnetisation of the heating curve showed a

broad hump at ~70 K. The abrupt decrease of magnetisation upon heating at ~300 K is

attributed to the Curie transition of the austenite, of the small amount of residual austenite

in the matrix [22]. This temperature is denoted ACT . The heating curve did not follow the

cooling curve at below ACT , apparently due to the application of the magnetic field on this

second cooling. The rapid increase of magnetisation at below 70 K upon cooling is

attributed to the Curie transition of the martensite, denoted MCT =70 K.

The magnetisation behaviour of Fe3 is similar to that of Fe0. The TA temperature is

~355 K (Figure 3), and similar to Fe0, the Curie transition at ~315 K corresponds to that of

the remnant austenite in this alloy. The Curie transition of the martensite is determined to

be MCT =100 K. Fe4 showed a similar thermomagnetic behaviour to Fe3. The M

CT and ACT

are determined to be about 155 K and 320 K for Fe4 alloy, respectively. Fe5 and Fe6

showed different magnetisation behaviour to the previous three samples. The magnetisation

was fairly constant at below or above ACT . These two samples showed no martensitic

transformation within the testing temperature range, thus the absence of the Curie transition

of the martensite on the curves.

It is seen that the ACT temperature increased slightly from 300 to 320 K with the

increase of Fe addition from 0 to 6 at.%. However, the MCT temperature was more

CHAPTER 3 110

 

significantly affected by Fe addition, from 70 to 155 K with increasing Fe addition up to 4

at.%.

For alloy Fe4, the martensitic transformation temperature TM (319 K) is very close

to the Curie transition temperature ACT (320 K). This implies that the martensitic

transformation overlaps with the Curie transition of the austenite, i.e., the phase

transformation is “hidden” on the M(T) curve. To reveal the martensitic transformation via

the M(T) measurement, a higher magnetic field is applied, which lowers TM without

affecting ACT , thus delaying the AM transformation to after the completion of the Curie

transition of the austenite [8].

Figure 8 shows the thermomagnetisation behaviour of alloy Fe4 in a high field of 70

kOe. It is seen that the magnetisation changed abruptly at ~300 K with a hysteresis of 10 K

between the heating and cooling curves. This is obviously due to the martensitic

transformation of this alloy. The forward transformation temperature is estimated to be

*MT =300 K, which is 10 K below that obtained from the DSC measurement, obviously due

to the effect of the applied magnetic field. It is seen that the ferromagnetic interactions in

the austenite are much stronger than that in martensitic phase, which leads to 40 emu/g

magnetisation difference across the transformation.

0 50 100 150 200 250 300 350 400

20

30

40

50

60

70

80

Mag

netis

atio

n (e

mu

/g)

Temperature (K)

Fe4

H=7 T

T*

M

CHAPTER 3 111

 

Figure 8. Thermomagnetisation behaviour of Fe4 alloy in a field of 70 kOe.

To reveal the magnetic structure of the austenite and martensite, M(H)

measurements were carried out of the Ni50Mn38-xIn12Fex alloys at 5 K. The measurements

are shown in Figure 9. At 5 K, the matrix phase is in martensitic state for Fe0, Fe3 and Fe4,

whereas it is in austenitic state for Fe5 and Fe6. It is seen that Fe5 and Fe6 showed typical

soft ferromagnetic behaviour, with saturation magnetisation of 105 and 108 emu/g,

respectively. The M(H) data of Fe4 also showed the characteristics of ferromagnetic

ordering in its martensitic state, but with a much reduced magnetisation of 47 emu/g. The

initial slope of M(H) curve of Fe3 indicates the short range ferromagnetic correlations

together with antiferromagnetic exchange in the martensitic phase. The coexistence of the

ferromagnetic and antiferromagnetic structures can also be seen as the splitting between the

heating and cooling M(T) curves (Figure 7b). In Ni50Mn38-xIn12Fex alloys, extra Mn atoms

occupy In sites, forming a ferromagnetic coupling between the Mn(Mn site) and Mn(In

site) atoms in the austenitic phase [24]. Through the martensitic transformation, the

distance between the Mn(Mn site)-Mn(In site) decreases and favours antiferromagnetic

interaction in the martensitic phase. However, the Mn atoms at the Mn site still form

ferromagnetic interaction in the martensitic phase. Therefore, the inhomogeneous magnetic

structure is common to observe in the martensitic state of the Mn-rich Ni-Mn-

Z(Z=In,Sn,Sb) alloys [21, 22, 25]. The magnetisation of Fe0 showed nearly linear

dependence on the applied magnetic field up to 40 kOe. The linearity of M(H) data suggests

that it is antiferromagnetic in the martensitic state of this alloy. The saturation

magnetisations are determined to be 13.6 and 27.7 emu/g for Fe0 and Fe3, respectively.

CHAPTER 3 112

 

0 10 20 30 40 50 60 70 80

0

20

40

60

80

100

120

M

Fe6

Fe5

Fe4

Fe3

Ma

gnet

isat

ion

(em

u/g

)

Magnetic Field (kOe)

Fe0

T=5 KA

Figure 9. Magnetisation measurements of the Ni50Mn38-xIn12Fex alloys at 5 K. A represents

austenitic state and M represents martensitic state.

It is seen that the saturation magnetisation increased with increasing the Fe addition

in these alloys. Based on the composition determination, it is known that the Mn

concentration decreased in the matrix phase with more Fe addition. With high

concentration of Mn, antiferromagnetic exchange is expected to dominate, as the

composition is close to the antiferromagnet Ni50Mn50. This explains the linearity of M(H)

data in the martensitic state of Fe0 which has the highest Mn concentration (37.8 at.% Mn)

among the Ni50Mn38-xIn12Fex alloys. With the decrease of Mn content (increase of Fe

addition), the antiferromagnetic ordering weakens, and gradually the long-range

ferromagnetic ordering forms in the matrix phase.

3.5 Mechanical properties

Figure 10 shows compressive deformation behaviour of the alloys, with (a) showing

the stress-strain curves and (b) showing the effect of Fe content on the maximum stress and

strain.

CHAPTER 3 113

 

0 2 4 6 8 10 12 14 160

100

200

300

400

500

600

700

800

Fe6

Fe5Fe4

Fe3

Str

ess

(M

Pa

)

Strain (%)

Fe0

0 1 2 3 4 5 6450

500

550

600

650

700

750

800

Fe Content (at.%)

Ma

xim

um

Co

mp

ress

ive

Str

ess

(M

Pa

)

10

11

12

13

14

15 Ma

ximu

m C

om

pre

ssive S

train

(%)

Figure 10. Compressive deformation behaviour of Ni50Mn38-xIn12Fex alloys; (a) stress-strain

curves; (b) maximum compressive stress and strain as functions of Fe content.

Fe0 and Fe3 showed obvious stress plateau corresponding to the reorientation of

martensite variants. However, stress-strain curves for Fe4, Fe5 and Fe6 suggest that the

deformation was mainly due to the dislocation mechanisms rather than the martensite

detwining process, since the stress plateau corresponding to the reorientation of martensite

variants did not appear in the stress-strain curves. It is also seen that the compressive

strength first increased and then decreased with increasing Fe content, reaching a maximum

of 770 MPa at 5 at.% Fe. The compressive strain showed similar tendency with increasing

Fe addition. The maximum strain reached was 14.3 % at 3 at.% Fe.

CHAPTER 3 114

 

These observations are in contrast to those made in Ni50Mn34In16-yFey and

Ni50Mn34In16-yCoy alloys, which show continuous increase of strength and strain with

increasing the amount of Fe or Co (or the amount of the phase) in the alloys [17, 26]. The

decrease of the compressive strength and strain at high levels of Fe addition in this case is

attributed to the particular morphology of the phase. It is seen in Figure 1 that the phase

in Fe6 exists as thin and elongated grains in parallel arrays in the matrix phase. This

morphology is detrimental for the strength and ductility of this material. More importantly,

the grain boundaries of matrix phase of Fe6 are not covered nicely by phase grains like

those in Fe4 and Fe5 alloys [27], evidenced by the microstructural observations of these

alloys shown in Figure 1. Therefore, Fe6 showed more intergranular cracking under

compression tests (Figure 11(e)), thus presenting relative low strength and ductility

compared to Fe4 and Fe5. It should be noted that the ductility of Fe0 and Fe3 is associated

with the martensite variant reorientation, and there is not much “real plastic deformation”

before failure. Good ductility is actually given by Fe4 and Fe5, which contain 6.8 % and

11.5 % of the phase, respectively.

Figure 11 shows the fracture morphologies of the Ni50Mn38-xIn12Fex alloys after

compressive testing. It is seen from micrographs (a) and (b) that Fe0 and Fe3 fractured via

typical intergranular cracking. With the increase of Fe addition, the fracture becomes a

mixture of intergranular cracking and transgranular cracking. Some pull-out holes are also

evident due to the pulling out of the phase particles, implying improvement of the

ductility of Fe4 and Fe5 alloys, shown in micrographs (c) and (d). The cracks in Fe6 mainly

formed along the elongated grains in the microstructure, as seen in micrograph (e), leading

to the decrease in strength and ductility.

CHAPTER 3 115

 

(a)

100 µm

(b)

100 µm

(c)

20 µm

(d)

20 µm

(e)

20 µm

Figure 11. SEM micrographs of the fractured surfaces of Ni50Mn38-xIn12Fex alloys after

compressive testing. (a) Fe0, (b) Fe3, (c) Fe4, (d) Fe5 and (e) Fe6.

Figure 12 shows the compressive stress-strain curves at room temperature and the

strain recovery after heating to above the TA temperature of Fe3 and Fe4 alloys. Fe3 was

deformed to 7.3 % strain. It exhibited a spontaneous recovery of 2.5 % upon unloading,

CHAPTER 3 116

 

leaving a residual strain of 4.8 %. The arrowed curves below the x-axis represent the strain

recoveries upon heating to 500 K for 5 min. The recovered strain is 4.5 % and the recovery

ratio is 94 % for Fe3. Fe4 had a compressive strain of 6.7 %, and generated a residual strain

of 2.4 % after unloading. After heating to 500 K for 5 min, the strain recovery was 0.9 %,

giving the total recovery ratio of 37 % for Fe4. It is also worth noting that the critical stress

to initiate the detwining of the martensite variants is about 130 MPa in Fe3 which is much

lower than that of 330 MPa in Fe4. The disappearance of stress plateau in Fe4 is due to the

strain hardening effect caused by the phase. Accordingly, it can be envisaged that the

shape memory effect of the two-phase Fe4 alloy is poor due to the presence of the phase,

which does not participate in the reversible martensitic transformation.

0 1 2 3 4 5 6 7 80

50

100

150

200

Str

ess

(M

Pa

)

Strain (%)

(a) Fe3

SME

0 1 2 3 4 5 6 70

100

200

300

400

500

Str

ess

(MP

a)

Strain (%)

(b) Fe4

SME

Figure 12. Shape memory effect of Fe3 and Fe4 alloys.

4. Conclusions

This study investigated the effects of Fe addition for Mn on the properties of

Ni50Mn38In12. The main findings may be summarised as following:

(1) Fe substitution for Mn in Ni50Mn38-xIn12Fex alloys at above 3 at.% causes formation

of an fcc phase. The phase is a Ni-Mn-Fe solid solution phase with small amount

of In dissolved. Formation of phase results in the decrease of Mn and increase of

In contents of the matrix phase. Consequently, the e/a ratio of the matrix phase

decreases with increasing Fe addition.

CHAPTER 3 117

 

(2) The critical temperature (To), the enthalpy change (ΔH) of the martensitic

transformation decreased with increasing Fe addition, due to the decrease of e/a

ratio of the matrix phase caused by the formation of the phase. A threshold value

of e/a ratio is identified at ΔH=0 to be 7.948, below which no martensitic

transformation is expected in Ni50Mn38-xIn12Fex alloys. This value corresponds to Fe

substitution of 4.5 at.% for Mn.

(3) The Curie temperature of the martensite ( MCT ) increased rapidly from 70 to 155 K

with Fe addition to 4 at.%, whereas that of the austenite ( ACT ) increased slightly

from 300 to 320 K with Fe addition to 6 at.%, The austenite shows much stronger

ferromagnetic characteristic relative to that of the martensite. The ferromagnetic

ordering of the martensite was enhanced with increasing Fe addition, due to the

reduced content of antiferromagnetically coupled Mn in the martensitic phase.

(4) Compressive stress and strain did not simply increase with increasing amount of the

phase. Good compressive strength and ductility are exhibited by Fe4 and Fe5

alloys.

(5) The shape memory effect decreased significantly with the introduction of phase.

The alloy without phase in the microstructure (Fe3) showed a shape memory

effect of 94 %, while the alloy containing 6.8 % phase (Fe4) presented a shape

memory effect of 37 %.

Acknowledgement

The authors wish to acknowledge the financial supports by the Department of

Innovation Industry, Science and Research of the Australian Government in ISL Grant

CH070136, and by National Natural Science Foundation of China in Grant No. 51001010.

CHAPTER 3 118

 

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Ishida K, Neumann KU, Ziebeck KRA. Journal of Magnetism and Magnetic Materials

2009;321:773.

[25] Khan M, Dubenko I, Stadler S, Ali N. Journal of Physics-Condensed Matter

2008;20:235204.

[26] Feng Y, Sui JH, Gao ZY, Dong GF, Cai W. Journal of Alloys and Compounds

2009;476:935.

[27] Ishida K, Kainuma R, Ueno N, Nishizawa T. Metallurgical and Materials

Transaction A 1991;22:441.

 

CHAPTER 3 120

 

Paper 5

Metallurgical origin of the effect of Fe doping on the martensitic and

magnetic transformation behaviours of Ni50Mn40-xSn10Fex magnetic shape

memory alloys

Zhigang Wu1, Zhuhong Liu1,2 , Hong Yang1, Yinong Liu1, Guangheng Wu3 and Robert

Woodward4

1. School of Mechanical Engineering, The University of Western Australia, Crawley, WA

6009, Australia

2. Department of Physics, University of Science and Technology Beijing, Beijing 100083,

China

3. Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese

Academy of Sciences, Beijing 100080, China

4. School of Physics, The University of Western Australia, Crawley, WA 6009, Australia

Abstract

This study investigated the metallurgical origin of the effects of Fe substitution for

Sn on the martensitic and the magnetic transformation behaviours of Ni50Mn40-xSn10Fex

(x=0, 3, 4, 5, 6) alloys. Substitution of Fe for Mn at above 3 at% introduced an fcc γ phase

in the microstructure. Formation of the γ phase influenced the composition of the bcc/B2

matrix, leading to decrease in martensitic transformation temperatures and transformation

entropy change. The Curie temperature of the parent phase increased slightly, whereas the

Curie temperature of the martensite increased rapidly with increasing Fe addition. Changes

in the temperatures of the martensitic and magnetic transformations are confirmed to

directly relate to the e/a ratio of the matrix caused by formation of γ phase. The minimum

e/a ratio value for the occurrence of the martensitic transformation is estimated to be 8.045

for the alloy system studied. A narrow e/a ratio range of 8.113~8.137 is estimated for the

occurrence of metamagnetic transformation ( ) ( )M para A ferro . This metamagnetic

CHAPTER 3 121

 

reverse transformation was induced by a magnetic field at 225 K within a range of 3~7 T in

the Ni50Mn35Sn10Fe5 alloy. The magnetic work required to induce the transformation is

estimated to be ~176 J/kg, comparable to the thermodynamic energy deficit for the

transformation at the testing temperature estimated from thermal measurement. These

findings clarify the origin of the effects of Fe doping in Ni50Mn40-xSn10 alloys and provides

reference on alloys design for this system.

Keywords: A. magnetic intermetallics; B. alloy design; B. shape-memory effects; B.

martensitic transformations; B. magnetic properties

1.Introduction

Ni-Mn-X (In, Sn and Sb) alloys have attracted much attention since the discovery of

magnetic field induced reverse martensitic transformation by Sutou et al. in 2004 [1]. In

these alloy systems, the martensitic transformation coincides with the magnetic

transformation from a L21 structure ferromagnetic austenite to an orthorhombic

paramagnetic martensite. The difference in magnetisation between the two phases provides

a driving force for the structural transformation under the influence of magnetic field. In

2006, Kainuma et al. achieved shape recovery accompanying the martensitic transformation

in Ni-Co-Mn-In single crystalline and Ni-Co-Mn-Sn polycrystalline alloys [2, 3],

demonstrating the promise of the alloys for actuation applications in smart systems. In

addition to magnetoactuation, these alloy systems also exhibit several other interesting

properties. The electrical resistance of the parent phase exhibits a typical metallic

behaviour, whereas it is semimetal-like for martensite in such alloy systems [4]. Since

magnetic transition coincides with a first order martensitic phase transformation, the giant

magnetoresistance effect [4-6] and giant magnetocaloric effect [7-9] have also been

discovered. Beside the investigation on Ni-Co-Mn-In (Sn) alloys, many other alloys with

similar compositions have also been extensively studied recently in a number of aspects,

including the thermal and stressed induced martensitic transformation behaviours [10, 11],

phase separation and magnetic properties [12, 13] , martensitic transformation

characteristics [14], time effect [15] and aging effect [16].

CHAPTER 3 122

 

One main hindrance to engineering application of these materials is the intrinsic

brittleness associated with the intermetallic compound nature of the alloys. Similar problem

is also found in Ni-Mn-Ga alloys. To improve ductility, a second ductile γ phase has been

introduced by introducing Co or Fe into Ni-Mn-Ga alloys [17-20]. Recently, Feng et al.

reported that substitution of Fe for In in Ni-Mn-In alloys introduces the γ phase and

enhances the ductility of the alloys [21].

Whereas the purpose is to improve ductility, addition of a fourth element to the

ternary Ni-Mn-X (In, Sn and Sb) alloys inevitably alters the matrix composition, hence the

structure and thermal and magnetic properties. Passamani and Fukushima have recently

investigated the effect of Fe substitution for Mn in Ni-Mn-Sn alloys on their magnetic

properties. They found that the martensitic transformation temperatures decrease rapidly

whereas the Curie transition temperatures of both austenite and martensite increase with the

increasing Fe substitution [22, 23]. It was also found that the addition of Fe leads to the

enhancement of FM exchange interaction in the austenitic and martensitic phases, and the

magnetic exchange bias effect was detected in the samples with Fe substitution below 10

at.% [22]. Whereas much attention has been given to the influences of fourth element

addition on the magnetic and transformation properties of these alloys, given the level of

complexity associated with the quaternary systems, much less is understood of the

metallurgical origins of these influences. This study is concerned with this fundamental

issue by investigating the effects of Fe substitution for Mn in Ni50Mn40-xSn10Fex. Fe bears

much resemblance to Mn in this alloy system, including magnetic state and valence

electron number, thus providing an opportunity to examine the metallurgical influence of

the addition to the properties of the alloys, in addition to being a selected element for

ductility improvement for some common ferromagnetic shape memory alloys.

2.ExperimentalProcedures

Polycrystalline Ni50Mn40-xSn10Fex (x=0, 3, 4, 5, 6) alloy ingots were prepared by

means of arc melting in argon atmosphere using high purity (99.99 %) elemental metals.

The samples are referred to as Fe0, Fe3, Fe4, Fe5 and Fe6, respectively. The button shaped

ingots were heat treated at 1173 K in vacuum for homogenisation followed by furnace

CHAPTER 3 123

 

cooling to room temperature. Transformation behaviour of the alloys was studied by means

of differential scanning calorimetry (DSC) using a TA Q10 DSC instrument with a

cooling/heating rate of 10 K/min. Phase identification and crystal structures were

determined by means of X-ray powder diffraction using Cu-Kα radiation. Microstructures

of the samples were studied with optical microscopy and scanning electron microscopy

(SEM) and the compositions were determined by means of X-ray energy dispersive

spectrometry (EDS). The magnetic properties were studied using a superconducting

quantum interference device magnetometer (SQUID).

3.Resultsanddiscussion

3.1 Microstructure and crystal structure 

Figure 1 shows back-scattered SEM micrographs of the microstructures of the

Ni50Mn40-xSn10Fex (x=3, 4, 5, 6) alloys after homogenization treatment. The Fe3 sample

(micrograph (a)) showed a uniform single phase structure, without any sign of a second

phase. A few black spots presented in alloy Fe3 are solidification shrinkage pores formed

during ingot casting. These pores are also presented in the other alloy samples. The

microstructure of the F0 sample is essentially identical to that of F3, except the actual

chemical composition of the matrix. The Fe4, Fe5 and Fe6 samples showed a continuous

matrix in light contrast and dispersed γ phase particles in dark contrast. The volume

proportion of γ phase obviously increased with more Fe content from alloy Fe4 to Fe6. The

Fe6 alloy showed much smaller γ phase particles and a different texture compared to the

other two alloys.

CHAPTER 3 124

 

100 µm

100 µm 100 µm

100 µm

(a) (b)

(c) (d)

Figure 1. Back-scattered electron images of Ni50Mn40-xSn10Fex alloys: (a) x=3; (b) x=4; (c)

x=5 and (d) x=6.

Figure 2 shows XRD spectra of the Ni50Mn40-xSn10Fex alloys. Alloys Fe0 and Fe3

showed an orthorhombic martensite crystal structure. Alloy Fe4 exhibited a more

complicated case, showing a mixed structure of the orthorhombic martensite, the bcc

austenite and the γ phase. Alloy Fe5 presented a two-phase structure, with the fcc γ phase

and the bcc austenite. Alloy Fe6 also showed a two-phase structure, but with the fcc γ phase

and a B2 austenite. The lattice parameters of the martensite are similar for Fe0, Fe3 and Fe4

alloys, and the values are listed in Table 1. The lattice parameters of the γ phase in Fe4, Fe5

and Fe6 are very close, with an average value of a=0.365 nm at room temperature. The

lattice parameter of the bcc austenite was determined to be a=0.2982 nm for Fe4 and

0.2988 nm for Fe5. The lattice parameter of the B2 phase in Fe6 was determined to be

a=0.2996 nm. The phases present in the samples are summarised in Table 1. It is evident

that the intensity of the characteristic peaks of the γ phase increased with increasing Fe

content, which is consistent with the microstructure observations presented above.

CHAPTER 3 125

 

30 40 50 60 70 80 90 100

AM

X-r

ay

Inte

nsi

ty

2 (deg.)

Fe0

Fe3

Fe4

Fe5

Fe6

Figure 2. X-ray diffraction spectra of the Ni50Mn40-xSn10Fex alloys at room temperature.

Table 1. Effect of Fe addition on phase formation at room temperature (lattice parameters

in nm)

Sample Fe0 Fe3 Fe4 Fe5 Fe6

Fe addition

(at.%)

3 4 5 6

Austenite (bcc)

a=0.2982

a=0.2988

(B2)

a=0.2996

phase (fcc)

a=0.365

Martensite

(orthorhombic)

a=0.6526

b=0.5946

c=0.5704

a=0.6530

b=0.5916

c=0.5695

a=0.6522

b=0.5912

c=0.5685

CHAPTER 3 126

 

3.2 Alloy composition  

Table 2 shows compositions of the phases in the samples as determined by

quantitative EDS analysis. It is seen that the matrix phase of the Fe-doped alloys contained

~2.9 at% Fe, regardless of the total amount of Fe added (the lowest amount added is 3 at%),

implying the solubility limit of Fe in the bcc/B2 matrix phase in the Ni-Mn-Sn system. This

is consistent with a previous study [21]. Adding Fe to above 3 at% did not cause further

increase of the Fe content in the matrix, but an obvious reduction of Mn, which is

compensated by the relative increase of Sn. The increase of Sn in the matrix is apparently

related to the increase of the fraction of the γ phase, which contained very low levels of Sn,

as seen in Table 1. The Ni content remained unchanged with the addition of Fe, at ~49 at%.

The γ phase is effectively a Ni-Mn-Fe alloy containing a small amount of Sn (~1.4 at%).

Table 2. Composition, e/a ratio and γ proportion of Ni50Mn40-xSn10Fex (x=0, 3, 4, 5, 6)

alloys.

Matrix γ phase

Ni

(at%)

Mn

(at%)

Sn

(at%)

Fe

(at%)

e/a

ratio

Ni

(at%)

Mn

(at%)

Sn

(at%)

Fe

(at%)

γ

(vol%)

X=0 49.49 39.90 10.61 - 8.166 - - - - -

X=3 49.47 36.99 10.73 2.81 8.190 - - - - -

X=4 49.07 35.84 12.14 2.95 8.137 52.84 34.01 1.36 11.79 11.9

X=5 48.78 34.62 13.69 2.91 8.082 53.05 33.36 1.38 12.21 22.0

X=6 48.70 34.22 14.19 2.89 8.064 51.66 32.36 1.39 14.59 25.5

The volume fractions of the phases in each alloy were obtained by image analysis

using ImageJ, and the volume fraction of the γ phase determined is listed in Table 1. It

shows that the amount of the γ phase increased with increasing Fe addition, with 25.5 % of

the γ phase present in alloy Fe6.

CHAPTER 3 127

 

The valence electron concentrations per atom (e/a ratio) of the matrix phase was

calculated using the compositions obtained from EDS analysis from the sum of s, p and d

electrons for Mn (7), Ni (10), Fe (8) and Sn (4). It is obvious that the e/a ratio decreases

with increasing Sn and decreasing Mn contents for the Fe-doped alloys. Figure 3 shows the

effect of Fe addition on the matrix phase composition (graph (a)) and the e/a ratio (graph

(b)) of the alloys. It is to be noted that the Fe0 alloy has a lower value of e/a ratio compared

to Fe3, despite that it contained the least Sn. This is obviously related to the absence of Fe,

which has a higher electron concentration than Mn, making its total e/a ratio to appear in

between those of Fe3 and Fe4. It is clear that the e/a ratio of the alloy decreased

continuously with increasing Sn/Mn atomic ratio in the alloys, as expected.

0 1 2 3 4 5 60

2

4

6

8

10

12

14

Sn,

Fe

Con

cent

ratio

n (a

t %

)

(a)

Sn

Fe

Mn

30

32

34

36

38

40

42

44

Mn C

oncentration (at %)

0 1 2 3 4 5 6

8.06

8.08

8.10

8.12

8.14

8.16

8.18

8.20

8.22

Sn/Mne/a

Fe addition (at %)

e/a

(b)

0.26

0.28

0.30

0.32

0.34

0.36

0.38

0.40

0.42

Sn/M

n Ratio

CHAPTER 3 128

 

Figure 3. Effects of Fe addition on elemental concentrations and e/a ratio of the matrix

phase of the Ni50Mn40-xSn10Fex alloys.

3.3 Martensitic transformation 

Figure 4 presents DSC curves of the Ni50Mn40-xSn10Fex alloys. It is seen that the

martensitic transformation behaviour evolved progressively with increasing Fe addition for

these alloys. The transformation behaviour of alloy Fe0, however, appeared in between

those of Fe3 and Fe4, consistent with the relative position of the alloy in terms of e/a ratio.

100 200 300 400 500

TA

TM

Fe6

Fe5

Fe4

Fe3

Hea

t Flo

w

Temperature (K)

Fe0

Figure 4. DSC measurements of martensitic transformation behaviour of the Ni50Mn40-

xSn10Fex alloys.

Figure 5 shows the effect of e/a ratio on the martensitic transformation

temperatures, characterised by the peak temperatures for the forward transformation TM, the

reverse transformation TA and the median temperature To, of the alloys. Also shown in the

figure is the hysteresis of the transformation, MAT TT . It is seen that the

transformation temperatures increased practically linearly with increasing the e/a ratio of

the alloys, with a coefficient of 17 K per 0.01 change of e/a ratio. This observation is

consistent with the findings of the effect of e/a ratio on transformation temperatures in other

CHAPTER 3 129

 

Ni-Mn-X (Al, Ga, In, Sn and Sb) alloys [24-26]. It is also evident that the transformation

hysteresis increased significantly with decreasing e/a ratio. This is consistent with

expectation for a decreased transformation entropy change S with transformations at

lower temperatures according to thermodynamic principles [27, 28].

8.06 8.08 8.10 8.12 8.14 8.16 8.18 8.20 8.22

150

200

250

300

350

400

T

To

TM

TA

e/a

Tra

nsfo

rmat

ion

Tem

pera

ture

(K

)

10

12

14

16

18

20

22

24

26

28

Transform

ation Hysteresis (K

)

Figure 5. Effect of Fe addition on martensitic transformation temperatures and hysteresis of

Ni50Mn40-xSn10Fex alloys, expressed as functions of the e/a ratio. TM: martensite

transformation peak temperature, TA: austenite transformation peak temperature, To=(TM+

TA)/2.

Figure 6 shows the effects of Fe addition on the transformation enthalpy and

entropy changes of the alloys, shown as functions of transformation temperature To in (a)

and e/a ratio in (b). The enthalpy change is determined from the DSC curves directly, and

the values have been normalised to the volume fractions of the b.c.c/B2 austenite. The

entropy changes are estimated based on 0

HS

T

. It is seen that both H and S

decreased continuously with decreasing To and with e/a ratio, caused by Fe addition.

CHAPTER 3 130

 

150 200 250 300 350 4000

5

10

15

20

To (K)

Ent

halp

y C

hang

e (J

/g)

(a)

12

16

20

24

28

32

36

40

44

S

H

Entropy C

hange (J/K K

g)

8.04 8.06 8.08 8.10 8.12 8.14 8.16 8.18 8.200

5

10

15

20

S

H

e/a

Ent

hal

py

Cha

nge

(J/g

)

(b)

12

16

20

24

28

32

36

40

44

Entropy C

hange (J/K K

g)

Figure 6. Effects of Fe addition on enthalpy and entropy changes of the Ni50Mn40-xSn10Fex

alloys, (a) as function of transformation temperature To=(TM+ TA)/2, and (b) as function of

e/a ratio. The arrows indicate the threshold values of To and e/a ratio below which the

martensitic transformation is expected to vanish.

CHAPTER 3 131

 

For a given transformation in a given alloy, 0

HS

T

is expected to be a constant.

In this case, Fe addition has changed the composition (and the e/a ratio) and effectively

created different alloys among the samples, giving rise to the variation of S with Fe

addition. In particular, the continuous decrease of S with increased Fe addition appears to

correlate to the continuous increase of Sn/Mn ratio in the matrix, as shown in Figure 3.

Another possible contribution to the variation of S among the samples is the

change of the magnetic state of the transformation [24, 29]. The martensitic transformation

in Fe0, Fe3 and Fe4 occurred in the paramagnetic state, i.e., it is )()( paraMparaA

transformation, whereas the transformation in Fe5 and Fe6 occurred in ferromagnetic state,

i.e., it is ( ) ( )A ferro M ferro transformation, as shown below in Figure 8. Ito et al. have

shown that S decreases with the change of the transformation from

)()( antiferroMparaA to )()( antiferroMferroA in NiMnIn and NiCoMnIn alloys

[30], which bears resemblance to the current finding. In addition, they also stated that

smaller S can be obtained from specimens with larger ( )AC sT M . Referring to the results

presented in Figure 8 below, it may be stated that S decreases with increasing ( )AC MT T

and with decreasing ( )MM CT T . However, it is our view that both the changes in S and in

transformation temperatures ( MT , AT , MCT , A

CT ) are consequences of the change in chemical

composition of the matrix phase, and are not causes and results of one to another.

It is seen that H diminishes with increased Fe addition. Extending H curve to

zero tentatively defines threshold values of To and e/a ratio below which the martensitic

transformation is expected to vanish. The threshold values, as indicated by the arrows in (a)

and (b), are estimated to be To = 142 K and e/a = 8.045. The e/a ratio value corresponds to

an Fe addition of 7.2 at% estimated from Figure 3. For Fe addition of more than 7.2 at% in

the system, no martensitic transformation is expected. Obviously, these threshold values are

dependent on the concentrations of the other elements in the matrix of the alloy. Feng et al.

detected a martensitic phase transformation at ~320 K in a Ni50Mn27Sn13Fe10 alloy, which

has an e/a ratio of 7.969. This is inconsistent with the findings of the present work [31].

CHAPTER 3 132

 

This is possibly related to the difference in the Mn content in these two alloys, but the

actual explanation is yet to be established.

3.4 Magnetic properties  

In Ni50Mn25+xSn25-x alloys, it is well recognised that magnetic moments of the

excessive Mn atoms occupying the Sn sites align in anti-parallel formation with respect to

the Mn at the Mn sites, thus introducing antiferromagnetic coupling between the two,

leading to reduction in the saturation magnetisation with increasing Mn substitution for Sn

[24, 32, 33]. In Ni50Mn40-xSn10Fex alloys, the concentration of Mn can be up to 40 at%,

which means 15 at% of Mn occupy Sn sites. In this case, it is reasonable to believe that

antiferromagnetic interactions are widespread in the alloys. Consequently, the magnetic

structure of the austenite may be regarded as coexistence of ferromagnetic and

antiferromagnetic structures. The magnetic structure is less clear in martensite , which may

contain ferromagnetic, ferrimagnetic and spin glass state at below TC, as reported by

Umetsu et al based on the Mössbauer study [34]. Given the lack of certainty with regard to

the magnetic states of phases in these alloys, the austenite and the martensite phases are

referred to as ferromagnetic in this discussion, since both phases show spontaneous

magnetisation at below their Curie transition temperatures.

Figure 7 shows the thermomagnetisation behaviour of the alloys under a small

magnetic field of 50 Oe. The sample was first cooled down to 100 K under a zero field

inside the instrument prior to the measurement. A 50 Oe field was applied at 100 K and

then the sample was heated at a rate of 10 K/min up to 390 K and cooled back again to 100

K in the same field.

 

CHAPTER 3 133

 

100 150 200 250 300 350

0

2

100 150 200 250 300 350

0

2

4

100 150 200 250 300 350

0

2

100 150 200 250 300 350

0

2

4

6

8

(a) Fe3

(b) Fe4

(c) Fe5

Temperature (K)

Mag

netis

atio

n (e

mu/

g)

(d) Fe6

Figure 7. Thermomagnetisation behaviour of the Ni50Mn40-xSn10Fex alloys in a field of 50

Oe.

As seen in Figure 7(a), alloy Fe3 presented a very small magnetisation at the

starting point at 100 K when the 50 Oe field was applied. The magnetisation gradually

increased with the increasing temperature up to 170 K, then followed by a decrease with

further heating within 175~220 K, due to the Curie transition of the ferromagnetic

martensite. The transition temperature, MCT , is 188 K for alloy Fe3. The sA temperature of

this sample is 370 K (Figure 4). There is no obvious change in magnetisation upon heating

to above this temperature, implying that both M and A are in paramagnetic state.

M

CT

A

CT

fM

A

CT

A

CT

sM

sA

M

CT

sM

sA

sA

CHAPTER 3 134

 

The cooling curve showed an identical magnetic behaviour with the heating curve at

temperatures above 170 K, going through the Curie transition of the martensite. With

further cooling the magnetisation continued to increase, resulting in a splitting of the

magnetisation state between the cooling and the heating curves of the martensite. This

splitting is attributed to the existence of exchange bias effect in martensite at low

temperatures [24, 25, 35, 36]. As discussed earlier, the distance between Mn at Mn site and

Mn at Sn site is small enough to introduce AFM exchange between each other. The AFM

interaction is strengthened in the martensitic transformation, leading to a reduction of

magnetisation below TM [32]. The AFM interaction can pin the FM domains in various

configurations depending on whether the sample is cooled though TC in an external field or

not, thus separating the heating and cooling curves presented in the studied alloys.

Figure 7(b) shows that the magnetic behaviour of alloy Fe4 was similar to alloy Fe3

at below 270 K upon heating, but higher MCT = 234 K temperatures. The martensite reached

a magnetisation plateau at between 150 and 220 K, followed by the Curie transition at MCT .

The paramagnetic martensite started transforming to ferromagnetic austenite at ~300 K,

followed immediately by the Curie transition of the austenite at ACT (310 K). Upon cooling,

magnetisation of the austenite increased rapidly through its Curie transition, followed

immediately by a decrease associated with the forward transformation from the

ferromagnetic austenite to the paramagnetic martensite. It is seen that the magnetisation

reached is higher than that achieved on cooling (at 300 K). This is apparently due to the

hysteresis of sM relative to fA which gives more room for the austenite to develop. With

further cooling, the Curie transition of the martensite occurred, and the magnetisation of the

martensite continued to increase with decreasing the temperature to 100 K, as in the case of

alloy Fe3.

In Figure 7(c), alloy Fe5 presented the Curie transition of the austenite at 315 K and

sM at 220 K. Curie transition of the martensite was not observed within the temperature

range. The relative magnetisation of the martensite on the cooling curve may indicate that

the martensite was in ferromagnetic state, i.e., MCT is above sM . In figure 7(d), alloy Fe6

CHAPTER 3 135

 

showed a similar magnetisation behaviour to alloy Fe5, with ACT =320 K and sM =182 K.

The phase transformation hysteresis of Fe5 and Fe6 is determined to be 24 and 27 K,

respectively, which are consistent with the DSC measurements.

Figure 8 shows a phase diagram with the MT and AT obtained from the DSC

measurements and with the MCT and A

CT obtained from the SQUID measurements against

e/a ratio for the Ni50Mn40-xSn10Fex alloys. It is seen that MT and AT showed a positive linear

dependence on the e/a ratio, whereas MCT and A

CT decreased with the increase of the e/a

ratio, with different coefficients of dependencies. These critical temperatures divide the

space into four areas representing four different crystallographic and magnetic states of the

alloys. The transformation behaviour of the alloys among these four states can be divided

into three regions on e/a ratio. In region I, the alloy undergoes

( ) ( ) ( )A para A ferro M ferro transformation upon cooling, in region II the alloy

undergoes a transformation sequence of ( ) ( ) ( ) ( )A para A ferro M para M ferro , and

in region III the alloy undergoes ( ) ( ) ( )A para M para M ferro . In these expressions,

the single arrows represent magnetic transformations and the double arrows represent the

crystallographic transformations. Among these transformations, the ( ) ( )A ferro M para

transformation in region II is a simultaneous magnetic and crystallographic transformation,

offering the possibility for magnetically induced crystallographic transformation. Such

transformations offer high magnetisation difference between the austenite and martensite,

thus the opportunity for magnetic field induced phase transformation and shape memory

effect. For this particular alloy system, the magnetic field induced transformation is the

reverse transformation from the paramagnetic martensite to the ferromagnetic austenite.

The e/a ratio values at the boundaries of region II are estimated to be 8.113 and 8.137.

CHAPTER 3 136

 

8.06 8.08 8.10 8.12 8.14 8.16 8.18 8.20 8.22

150

200

250

300

350

400

Mferro

Mpara

Aferro

IIIIII

Tra

nsfo

rmat

ion

Tem

pera

ture

(K

)

e/a

Apara

 

Figure 8. Effects of valence electron concentration on AT , MT , MCT and A

CT temperatures of

the Ni50Mn40-xSn10Fex alloys.

It is seen in Figure 7 that alloys Fe5 and Fe6 exhibited martensitic transformation in

ferromagnetic state with different magnetisations between the parent and the product

phases, giving rise to the possibility to induce the transformation by a magnetic field. To

verify this, alloy Fe5 was magnetized isothermally at three different temperatures of 210 K,

225 K and 240 K. The magnetisation curves are shown in Figure 9. The curves have been

normalised to the volume fractions of the matrix phase in the samples. At 210 K, which is

16 K below the sA temperature, the ferromagnetic martensite showed soft magnetisation

behaviour to saturation at 51 emu/g (at 7 T). At 240 K, which is just above the fA

temperature, the austenite magnetised in a similar way to saturation at 79 emu/g. At 225 K,

which is 1 K below the sA temperature, the sample magnetised to ~44 emu/g at below 3 T,

corresponding to the magnetisation of the martensite. Upon increasing the external field to

above 3 T, the transformation from the martensite to austenite was induced. The

magnetisation reached the saturation magnetisation level of the austenite at 7 T, signalling

the completion of the reverse transformation. The magnetisation curve at 210 K also

MCT

ACT

ATMT

CHAPTER 3 137

 

demonstrates that field strength of 7 T is not enough to induce the ( ) ( )M ferro A ferro

transformation.

0 1 2 3 4 5 6 70

10

20

30

40

50

60

70

80

90

Ma

gn

etis

atio

n (

em

u/g

)

Magnetic field (T)

210 K 240 K 225 K

Figure 9. Magnetisation curves of Ni50Mn35Sn10Fe5 at 210 K, 225 K and 240 K, showing

the magnetic field induced metamagnetic ( ) ( )M ferro A ferro transformation at 225 K.

In inducing the metamagnetic ( ) ( )M ferro A ferro transformation shown in

Figure 9, the external magnetic field performed a magnetic work, which is estimated to be

79

0

0

magE HdM ≈ 176 J/kg. At this temperature (T*=225 K), the thermodynamic deficit for

inducing the transformation may be estimated as*

fA

th

T

E SdT . Using data determined

from the thermal measurement of the transformation (shown in Figure 4), this energy may

be estimated to be *

fA

th

T

E SdT ≈181 J/kg. The calculated values showed a good

satisfactory comparison between the two, i.e., mag thE E , demonstrating the feasibility of

the magnetically induced martensitic transformation.

CHAPTER 3 138

 

4.Conclusions

The effects of Fe substitution for Mn on the martensitic transformation and

magnetic behaviours of Ni50Mn40-xSn10Fex alloys were investigated. The experimental

evidences and the discussions lead to the following conclusions:

(1) Fe substitution for Mn in Ni-Mn-Sn alloys at above 3 at% Fe causes formation of an

fcc γ phase. The γ phase is a Ni-Mn-Fe solid solution phase with small amount of

Sn dissolved. Formation of the γ phase leads increase of Sn content without

affecting the Ni and Fe contents of the bcc/B2 matrix phase. Consequently, the

valence electron concentration of the bcc/B2 matrix phase decreases with Fe

addition. The solubility of Fe in the bcc/B2 matrix phase is slightly below 3 at%.

The effects of Fe addition on the transformation and magnetic behaviours are via

the changes of Sn and Mn contents in the matrix bcc/B2 phase.

(2) As a result of Fe addition, or more specifically the decrease of e/a ratio and the

change of the matrix composition, the critical temperature ( oT ), the enthalpy change

( H ) and the entropy change ( S ) of the transformation decreased whilst the

transformation temperature hysteresis ( T ) increased. oT Exhibited a practically

linear dependence on e/a ratio, with a coefficient of 17 K per 0.01 increase of e/a

ratio. The increase of T is attributed to the decrease of S . A threshold value of

e/a is identified at 0H , to be 8.045, below which no martensitic transformation

is expected in the Ni50Mn40-xSn10Fex alloy system. This value corresponds to Fe

addition of 7.2 at% for substitution of Mn.

(3) The Ni50Mn40-xSn10Fex alloys experience several transformation sequences of

different combinations between the structural martensitic transformation and the

magnetic Curie transition, including (on cooling)

( ) ( ) ( )A para A ferro M ferro at e/a ratio range of 8.045~8.113,

( ) ( ) ( ) ( )A para A ferro M para M ferro at 8.113~8.137, and

( ) ( ) ( )A para M para M ferro at above 8.137. At below e/a=8.045 no

CHAPTER 3 139

 

martensitic transformation is expected. The ( ) ( )A ferro M para and

( ) ( )A ferro M ferro transformations are metamagnetic transformations.

(4) The ( ) ( )M ferro A ferro transformation was induced in alloy Fe5 under a field

within the range of 3~7 T. The magnetic work done by the external field to the

system in inducing the transformation is estimated to be ~176 J/kg. This energy is

comparable to the thermodynamic energy deficit for the transformation at the

testing temperature, estimated to be ~181 J/g based on the DSC measurements.

(5) The saturation of magnetisation of the ferromagnetic bcc austenite is 79 emu/g and

that of the ferromagnetic orthorhombic martensite is 51 emu/g at the ambient

temperature in alloy Fe5.

Acknowledgment

The authors wish to acknowledge the financial supports by the Department of

Innovation Industry, Science and Research of the Australian Government in ISL Grant

CH070136 and by the National Natural Science Foundation of China in Grant No.

10774178.

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CHAPTER 4. Closing Remarks

________________________________________________________________________________ 

4.1Journeyofferromagneticshapememoryalloys

It has been a 15-year journey of exploring and searching for new

magnetomartensitic materials for mechanical actuation since the discovery of magnetic-

field-induced strain of 0.2% in a Ni2MnGa alloy in 1996. Extensive research has been

carried out afterwards in the interdisciplinary field of ferromagnetic shape memory alloys,

as evidenced by over 14,000 publications [Google Scholar] produced to date on this topic.

Within a very short period research has advanced the discovery to achieving a giant

magnetic field induced strain of 10% in this Heusler alloy. This is an unprecedented

historical achievement. Encouraged by such success, extensive effort has been made to

search for other alloys, both within the Heusler family and outside, for example Ni-Mn-Al,

Ni-Fe-Ga, Co-Ni-Al, Co-Ni-Ga, Fe-Pt and Fe-Pd alloys. However, the magnetostrains

obtained in these alloys are all significantly smaller than those found in Ni-Mn-Ga alloys.

With the very limited success in finding other alloys, the attention has remained

strong on Ni2MnGa. Limited by its intrinsic low magnetic driving force from the magnetic

crystallographic anisotropy, the effort has been on reducing the already extremely low

mechanical resistance to deformation, from 1 MPa to 0.1 MPa. This is practically pushing

the theoretical limit to the minimum resistance to deformation in a metallic matrix. This

effort has enabled the nearly complete energy conversion from magnetic driving force to

the mechanical work. However, the magnetostress level is still 100 times lower compared

to that of its thermoelastic counterpart, NiTi.

The discovery of 2.9% of magnetostrain in Ni-Co-Mn-In alloy in 2006 made a

breakthrough. These alloys exhibit metamagnetic martensitic transformations with large

CHAPTER 4 143

 

magnetisation difference across the transformation as the driving force for mechanical

activation. To develop these alloys into useful and practical magnetoactuation materials, the

strategy has been on two aspects: to fully realise the potential of magnetisation difference

across the martensitic phase transformation and to lower the metallurgical resistance of the

matrix to deformation.

To lower the metallurgical resistance to shape change, it is preferable to have

intermetallic compound matrices with highly mobile twin boundaries and large grains, as

opposed to ductile solid solution matrices prone to plasticity. This inevitably renders the

alloys high brittleness. These problems severely impede the development of ferromagnetic

shape memory alloys from being successful magnetoactuation materials. These are the

challenges we are facing today. In this thesis, some the solutions to these two problems are

explored, and some key findings are of significance to the research community of

ferromagnetic shape memory alloys.

4.2Significanceofthisthesis

This study contributed to the development of ferromagnetic shape memory alloys in

three aspects: (i) energy balance analysis to determine the criteria of magnetoactuation and

limitations of FMSAs, (ii) alloy design to enhance ΔM of the martensitic transformation in

Ni-Mn-based alloys, and (iii) alloy design to reduce brittleness of Ni-Mn-based alloys. The

main achievements of this study are summarised below.

(1) Evaluation criteria were proposed with respect to energy conversion within

magnetic-field-induced martensitic transformation of FSMAs. Based on the analysis, three

criteria need to be met with regard to different requirements: Criteria I (completion of

magnetic-field-induced martensitic transformation):f

s

A

A

B M SdT ; Criteria II (completion

of shape change via magnetic-field-induced martensitic transformation): ' f

s

A

A

B M SdT ;

Criteria III (completion of two-way shape memory via magnetic-field-induced martensitic

CHAPTER 4 144

 

transformation): ' f

f

A

M

B M SdT . Using these criteria, current FSMAs can be evaluated

regarding their ability or potential as magnetic actuation materials. The challenges for

developing FSMAs are also clarified, which are to further increase the magnetic driving

force or/and to decrease the mechanical resistance of the metallic matrix to shape change.

(2) Exploration on composition design to increase the magnetic driving force was

made, targeting at the maximisation of ΔM between the austenite and martensite of Ni-Mn-

based alloys. The work was conducted on two alloy systems, including Mn-Ni-In-Co and

Mn-Ni-Sn-Co. The findings demonstrate the importance of Mn magnetic moment

contribution and clarify the magnetic interactions between Mn atoms in different

crystallographic structures of the austenitic and martensitic phases. The effect of Co

substitution for Ni on increasing ΔM is clearly interpreted, which is mainly due to the

enlargement of temperature window for ferromagnetic austenite. Large ΔM of 89 emu/g

and 109 emu/g were obtained in Mn50Ni40-xIn10Cox and Mn50Ni42-xSn8Cox alloy systems,

respectively. The increased ΔM greatly assisted the processing of magnetic-field-induced

martensitic transformation.

(3) It has been a common strategy to improve the ductility of the polycrystalline

alloys by introducing a phase into the matrix of Ni-Mn-alloys. This research investigated

the side effects of the phase on the martensitic transformation, magnetic properties and

shape memory effect of Ni-Mn-based alloys. The formation of the phase by Fe addition

alters the composition of the matrix, thus changing the e/a ratio of the transformation phase.

Consequently, the martensitic transformation behaviour and magnetic ordering of the alloys

are both altered significantly. This finding clarifies a common negligence in the effort to

improve ductility by the introduction of the phase. Furthermore, ductility depends not

only on the amount but also the morphology of the phase in the microstructure. Therefore,

the side effects of phase are prominent based on this research and need to be drawn

attention apart from of being an approach of increasing the ductility of Ni-Mn-based alloys.

CHAPTER 4 145

 

4.3ConcernswithNi‐Mn‐basedalloysandpossiblefuture

researchfocus

One of the biggest challenges of Ni-Mn-based alloys lies in the massive

metallurgical resistance of the matrix to deformation relative to the limited magnetic

driving force for actuation. With using Mn which has the largest magnetic moment to

replace Ni as the main constituent of the Heusler alloys and by optimising the alloy

composition and crystal structure, we have managed to achieve ΔM of the transformation as

high as ~110 emu/g. This is approaching the theoretical limit of ~138 emu/g in

Mn2NiZ(Z=In,Sn) alloys, given all Mn atoms form ferromagnetic coupling in the austenitic

structure and antiferromagnetic coupling in the martensitic structure. At an applied

magnetic field of 1T, this yields 1.1 MJ/m3 energy output, or ~18 MPa force output at 6%

strain. This corresponds to ~10% of the energy output of NiTi and is insufficient in many

practical applications.

The lack of success is intrinsically due to the dilemma between the limited magnetic

driving force associated with Zeeman energy (at moderate magnetic field strengths) and the

relative large mechanical resistance of the metallic matrix to shape change. For all alloy

systems that exhibit such magnetic energy output, it has been found that the magnetic

energy is merely enough to induce the metamagnetic martensitic transformation, and is well

below the mechanical resistance of the matrix to deformation, typically 100 MPa. In this

regard, the main obstacle to developing practical Ni-Mn-based ferromagnetic shape

memory alloys for mechanical actuation is to reduce the mechanical resistance to shape

change, more precisely the critical resolved shear stress for twining of the alloys. This will

most probably be achieved through metallurgical means.

To date, Ni-Mn-Ga system is the only one exhibiting the extraordinary performance

of low twinning stress, at below 1 MPa, which leads to the success of large magnetostrain.

Such phenomenon has not been seen in any other Ni-Mn-based intermetallics. Perfection in

single crystal and modification of modulation of the martensite structure may need to be

pursued. However, this may still not guarantee the same ease of twin boundary movement

CHAPTER 4 146

 

of martensite variants as in Ni-Mn-Ga. Another option is to search for alloys with a similar

mechanical behaviour as Ni-Mn-Ga, and then try to modify magnetic properties and

martensitic transformation behaviour afterwards.

Overall, the perspective of ferromagnetic shape memory alloys with high work

output still faces high challenges. To date, Ni-Mn-based alloys have not become truly

successful materials carrying the dream of magnetoactuation. However, enormous

knowledge has been established for the understanding of the magnetomartensitic behaviour

in ferromagnetic shape memory alloys in this study. Effort should be kept making to search

for better alloys with a similar mechanical performance of Ni-Mn-Ga alloys and

metamagnetic behaviour of Ni-Mn-based alloys. Continuation of this research will carry on

for achieving this goal in the future.