A

ttli©

K

1

sttsg

tatsirMmpdantm

0d

Materials Science and Engineering A 445–446 (2007) 392–397

Thermodynamics of nanocrystilline formation in surfacelayer of Hadfield steel by shot peening

Weilin Yan a,∗, Liang Fang a, Kun Sun a, Yunhua Xu b

a State Key Laboratory for Mechanical Behavior of Materials, Xian Jiaotong University, Xian 710049, PR Chinab Institute of Wear Resistance Material, Xian University of Architecture & Technology, Xian 710055, PR China

Received 11 June 2006; received in revised form 15 September 2006; accepted 19 September 2006

bstract

Conventional shot peening tests of Hadfield steel have shown that a nanostructured grains layer can be easily produced. Theoretically, nanos-

ructure formation thermodynamics becomes an important issue to coarse grains transformating into nanocrystalline. In the present paper,hermodynamics of strain induced nanosized microstructure in Hadfield steel after shot peening was discussed based on Pringogine’s nonequi-ibrium thermodynamics and Miedema semi-experimental theory. It was concluded that the difference of Gibbs free energy should be at leastncreased to 0.1380 kJ/mol in the alloy system by strain hardening, compared to the previous Gibbs energy before the treatment.

2006 Elsevier B.V. All rights reserved.

isntoi

ismlcrr

lib

eywords: Hadfield steel; Nanocrystalline; Amorphous; Thermodynamics

. Introduction

In the past 20 years nanosized grain materials were exten-ively investigated. It has been shown that some properties ofhe nanosized materials are appreciably improved compared tohe similar coarse-grained polycrystalline materials. Recently,evere plastic deformation methods for producing nanosizedrains have been recommended by some researchers [1].

Surface nanocrystallization has been observed and inves-igated by shot peening [2–4]. Many investigators have paidttention to the nanocrystallization mechanism by X-ray diffrac-ion (XRD), scanning electron microscope (SEM) and transmis-ion electron microscope (TEM). Traditionally, thermodynamicnvestigation for an alloy system plays an important role inesearch and application of materials. It has been noticed that

iani et al. [5] evaluated the mechanochemical power transfor-ation in the mechanosynthesis of nanophase Fe–C and Fe–Cu

owders from Miedema model. Taking into account the size

ependence of the Gibbs free energy of nanocrystals, Wang etl. [6–8] developed a quantitative thermodynamic model at theanometer scale based on the Laplace–Young formula and thehermodynamic equilibrium phase diagram to describe the ther-

odynamic phenomenon of the metastable phase nucleation

∗ Corresponding author. Tel.: +86 29 82665479; fax: +86 29 82665479.E-mail address: yanwl@eyou.com (W. Yan).

atg

2

1

921-5093/$ – see front matter © 2006 Elsevier B.V. All rights reserved.oi:10.1016/j.msea.2006.09.061

n the strongly unstable regions of the metastable structuraltates. They have elucidated the nucleation of diamond and c-BNanocrystals upon the pulsed-laser ablation in liquid, in whichhe diamond nucleation takes place in the stable phase regionf diamond in the carbon phase diagram. Those works are quitenteresting and valuable.

Surface shot peening is an effective approach to create local-zed plastic deformation, resulting in grain refinement progres-ively down to the nanometer region in the surface layer ofetallic materials [2–4]. Strain induced surface nanocrystal-

ization is a mechanical method to produce nanostructures ofonventional materials which is a nonequilibrium process. It isequired to discuss the issue from the view point of nonequilib-ium thermodynamics.

In the present paper, the thermodynamics of nonequi-ibrium grain refinement of Hadfield steel by shot peen-ng was discussed. A thermodynamic model was proposedased on Pringogine’s nonequilibrium thermodynamics [9]nd Miedema semi-experimental theory [10–12] to describehe enthalpy change and Gibbs free energy change of coarserain–nanocrystalline transformation.

. Experimental procedures

Chemical compositions of test alloy in weight percentage are:.20 C, 12.86 Mn, 0.87 Si, 0.05 S and 0.09 P. The samples were

Engi

sqiStSldw

dwXlta

3

3

letT

•••

w

e

δ

wfl

3

�

waa

3

pafp

mobctetWumfe

�

watvCh

�

wdb

a

�

wrabe

f

S

X

Cw

�

�

W. Yan et al. / Materials Science and

olid solution treated at 1050 ◦C for 2 h, and then were wateruenched. After this heat treatment the investigated alloy exhib-ted a single austenite phase, with grain sizes about 100–200 �m.amples of 40 mm × 75 mm were prepared for shot peening

reatment. The samples were shot peened by a machine type170R with a shooting area 100% sample surface. Cast steel bil-

iards was used with 0.2 mm nominal diameter and the impactedirection to the sample surface was limited to 85◦. Air pressureas 0.18 MPa and the shooting duration was 60 min.Structure of the sample surface was examined by X-ray

iffraction (XRD) in a X’ Pert MPD RRO X-ray diffractometerith Cu K� radiation. The average grain size was obtained fromRD line broadening [13]. Microstructure features in surface

ayer were also characterized by a JEM-3010 high-resolutionransmission electron microscope (HREM, operating at a volt-ge of 300 kV).

. Thermodynamical analysis

.1. Nonequilibrium thermodynamics

Progogine [9] extended the dissipative structure to nonequi-ibrium state successfully. Using classical thermodynamicsquations and local equilibrium hypothesis, Progogine proposedhat “excess entropy production” is a general evolution criterion.he general evolution criterion can be described as

δXP = 0, in marginal state.δXP > 0, in asymptotically stable reference state.δXP < 0, in unstable reference state.

here δXP is the excess entropy production.On the other hand, the excess entropy production δXP can be

xpressed as

XP =∫

dv (δXδJ) (1)

here X is the thermodynamical force J the thermodynamicalow, and V is the volume.

.2. Kirchhoff equation

From Kirchhoff equation, it has a form of

HT2 = �HT1 +∫ T2

T1

�Cp dT (2)

here T1, T2 and �Cp are, individually, the temperature before,fter reaction and the thermal capacity difference of resultantnd reactant in invariable pressure.

.3. Miedema model

In another way, Miedema et al. [10–12] developed a sim-

le model to predict the formation enthalpies of binary metalliclloys. This model becomes an extension to Pauling’s schemeor the calculation of the formation enthalpy of alloys and com-ounds in standard state. In Pauling’s scheme, the heat of for-

weoA

neering A 445–446 (2007) 392–397 393

ation of simple molecules is proportional to the summationf the squared electronegativity differences, over all chemicalonds. Pauling’s scheme only included, however, a negativeontribution to the formation enthalpy. In order to overcomehis problem, Miedema added a positive contribution, due to thelectronic redistribution, which is proportional to the square ofhe cubic root of the electronic charge density difference at the

inger–Seitz boundary. An experimental work function can besed, instead of Pauling’s electronegativity. Several other adjust-ents are made to accurately describe the heat of formation

or every binary metallic compound of a transition metal. Thenthalpy of formation of a solid solution can be written as

Hs = �Hchem + �Helast + �Hstr (3)

here �Hchem, �Helast, and �Hstr, are the chemical, elasticnd structural contributions due to two different atoms mixing,he atom size mismatch taking into account the difference inalence and crystal structure of solute and solvent, respectively.ompared with the first two items, the structural contributionsave little effect, which can be ignored [14]. It becomes

Hs = �Helast = �Hes + �HeV (4)

here �Hes and �HeV are the distorted energy results fromifferent atoms dissolution in lattice and distorted energy ofoundary, respectively.

On the other hand, the chemical contribution can be expresseds

Hchem = 2f SAB(XAV

2/3A + XBV

2/3B )

n−1/3A + n

−1/3B

× [−p(�φ)2 + Q(�n1/3)2] (5)

here XA, VA, f SAB, p, Q, �φ, n, are the atomic concentration,

oom temperature molar volume„ structural parameter whichccounts for the degree to which atoms of type A are surroundedy atoms of type B, empirical coefficients in Miedema model,lectronegativity and electron density, respectively.

Structural parameter can be written as

SAB = XS

AXSB (7)

urface concentrations can be written as

SA = XAV

2/3A

XAV2/3A + XBV

2/3B

(6)

onsidering amorphous producing, formation enthalpy can beritten as

Ha = �Hachem + XA�Ha

A + XB�HaB (8)

HaA = 3.5Tm,A (9)

here �Ha, �Hachem, �Ha

A, �HaB, and Tm,A are the formation

nthalpy of amorphous, chemical contributions due to mixingf the two different atoms, the enthalpy of formation of elementand B and the melting temperature. Structural parameter can

3 Engi

b

f

T

�

3a

ecs

aftf

X

J

wmsa

a

n

wst

δ

Td

�

w

pnsd

Teb

�

�

�

�

�

�

bacfneptas

se

�H snm = �HeV = 3rbVS

d(23)

where rb, Vs and d are the large-angle boundary energy, the molarvolume of alloys and the grain size, respectively.

94 W. Yan et al. / Materials Science and

e written as

aAB = Xs

AXsB[1 + 5(Xs

AXsB)2] (10)

he chemical contributions, therefore, can be written as (5)

Hachem = 2f a

AB(XAV2/3A + XBV

2/3B )

n−1/3A + n

−1/3B

× [−p(�φ)2 + Q(�n1/3)2] (11)

.4. Nanocrystallization thermodynamics in subsurfacefter shot peening

Considering a shot peening process of alloy, the excessntropy production δXP arising from plastic strain, of course,an be written as integral of nucleation forces X and flows J, ashown in Eq. (1).

Chemical gradient −�(μi/T), temperature gradient �(1/T),nd outside force MiFi/T can be considered as generalizedorces. Heat flow jq, matter flow ji and reaction rate can behought of as the flows. The related parameters can be obtainedrom following equations:

= �Hm�T

T 22

(12)

= ρnv (13)

here �Hm, �T, T2, ρ, n and ν are the enthalpy of grain refine-ent, surface temperature increase because of shot peening, real

urface temperature after shot peening, density, nucleation ratend marginal nucleation volume, respectively.

Nucleation rate without considering diffusion can be writtens [15]

= A exp

(−�G∗

kT

)

= A exp

( −16πσ3

3(�Hm�T )2k(T1 − �T )

)(14)

here �G*, k, A and σ is the activation energy, Boltzman’s con-tant, nucleation rate coefficient and boundary tension, respec-ively.

Let δXP = 0, it has

XδJ = 0 (15)

he temperature changing because of shot peening can beirectly estimated from (15)

T = 2

3T1 (16)

here T1 is ambient temperature. 300 K is assumed here.In nonequilibrium states, the nanocrystallization and amor-

hization process of coarse grains or a coarse grain–anocrystalline–amorphous transformation can be treated as aolid state phase transformation following the classical thermo-ynamic theory of crystallization from the supercooled liquid.

neering A 445–446 (2007) 392–397

he thermodynamic parameters of the enthalpy change, �H, thentropy change, �S, and the Gibbs free energy change �G, cane estimated in the following equations:

H sn = �H snm +

∫ T2

T1

(Cnp − Cs

p) dT

= �H snm +

∫ T2

T1

�Csnp dT (17)

H sa = �H sam +

∫ T

T1

(Cap − Cs

p) dT

= �H sam +

∫ T2

T1

�Csap (18)

Ssn = �H snm

T2−

∫ T2

T1

�Csnp

TdT (19)

Ssa = �H sam

T2−

∫ T2

T1

�Csap

TdT (20)

Gsn = �H sn − T2�Ssn (21)

Gsa = �H sa − T2�Ssa (22)

Let �Csnp = �H sn

m /T , �Csap = �H sa

m /T is a constant,ecause (∂H/∂T)p = Cp, where �Hsn,�Hsa, �Ssn, �Ssa, �Gsn

nd �Gsa are the thermodynamic parameters of the enthalpyhange, the entropy change, and the Gibbs free energy changerom coarse grain to nanocrystalline or amorphous underonequilibrium state, respectively.�H sn

m and �H sam are the

nthalpy change from coarse grain to nanocrystalline or amor-hous under equilibrium state, respectively. Cs

p, Cnp and Ca

p arehe molar heat capacities for the coarse grain, nanocrystallinend amorphous, respectively. T1 and T2 are the temperature ofample surface before and after shot peening.

During grain refinement, because different atoms have dis-olve dissolution in lattice before shot peening. Formationnthalpy can be written as

Fig. 1. XRD patterns of Hadfield steel before and after shot peening.

W. Yan et al. / Materials Science and Engineering A 445–446 (2007) 392–397 395

Table 1Parameters of the Miedema–Niessen model [10,16,17]

Material n1/3 (cm−1) φ (V) Tm (K) P (kJ V−2 cm−1) Q (kJ cm) rb (J m−2) VS (cm3 mol−1) V2/3 (cm2)

Fe 1.77 4.93 1808.5 7.10 3.70M

icam

Fmp

4

14.1n 1.61 4.45 1517

Parameters of the Miedema model [10,16,17] were shownn Table 1. In thermodynamic calculation, Hadfield steel

an be simply modeled as Fe87Mn13 alloy to ignore otherlloy elements, such as, carbon, silicon, et al. VS = 7.1 cm3

ol−1.

ig. 2. (a) Bright-field and (b) dark-field TEM images showing planaricrostructures of top surface layer in shot preening treated Hadfield steel sam-

le.

abtswci

6tStaioF

6ga

gt

Fl

132.54 0.55 7.35 3.78

. Results

Fig. 1 shows X-ray diffraction patterns of the samples beforend after shot peening treated. The Bragg-diffractional peakroadening in the shot peening treated samples may be attributedo grain refinement and/or an increase in the atomic-level latticetrain. It can be found that all the samples consist of austeniteithout any martensite. Quantitative XRD measurements indi-

ate that the grain size in surface layer of 60 min treated samples decreased to about 11.1–17.4 nm.

Fig. 2 shows typical TEM images of surface layer after0 min shoot peening. Nanostructured grains with random crys-allographic orientations are easily recognized, as indicated byAED pattern. The grain size is about 3–10 nm, which is smaller

han the XRD result (11.1–17.4 nm). That might be partiallyttributed to the fact that the XRD result averages the structurenformation of the top surface layer of about 5 �m thick. A closebservation of the nanostructure in surface was also shown inig. 3.

Fig. 4 shows a TEM observation at about 20 �m deep from0 min shot peening treated surface. One can see nanoscalerains of which the shape is roughly equiaxed. The grain size is

bout 30–80 nm.

The calculated Gibbs free energy difference of coarserain–nanocrystalline and coarse grain–amorphous transforma-ion is, respectively, 0.1380 and 7.3093 kJ/mol from above

ig. 3. A plane-view HRTEM image of the nanostructure in the top surfaceayer.

396 W. Yan et al. / Materials Science and Engineering A 445–446 (2007) 392–397

Fa

pcntmdiimiosta

F(

beo

5

cAmifsrFnatgobRttpw

6

bsishown that coarse grain changes into nanocrystalline whenGibbs free energy change in system reach 0.1380 kJ/mol

ig. 4. (a) A bright-field and (b) a dark-field cross-sectional TEM images atbout 20 �m deep from the top treated surface.

roposed thermodynamics calculation. The thermodynamicalalculation results suggested that Gibbs free energies to formanocrystalline and amorphous are positive, which means theransformation cannot occur spontaneously. Events occurring

ust be with the aid of external work, such as, severe plasticeformation to increase the internal energy of the system. Dur-ng shot penning, the system can increase the internal energy byncreasing microstructure defect density. Therefore, grain refine-

ent and nanocrystalline transformation finally can occur if thenternal energy is increased to some critical value. Relationshipsf enthalpy change and Gibbs free energy change with grain

ize was shown in Fig. 5. Definitely, when crystal size is smallerhan about 1.89 nm, nanocrystalline will be transformed into themorphous because the free energy difference of amorphous will

abt

ig. 5. Relationship of enthalpy change (�H) and Gibbs free energy changes�G) with grain size.

e smaller than that of nanocrystallines. The value of Gibbs freenergy difference 7.3093 kJ/mol should be transformation pointf nanocrystalline–amorphous.

. Discussions

The present shot peening experiments showed that strainan induce surface layer nanocrystallization of Hadfield steel.s discussed from thermodynamics a strong plastic defor-ation will increase the Gibbs free energy of system. With

ncreasing strain and strain rate, enthalpy change and Gibbsree energy change is increased rapidly. When crystal sizes aremaller than about 1.89 nm, nanocrystalline becomes unstableelative to the amorphous because of their higher free energy.ree energy simulation by Wang et al. [18] suggested thatanocrystalline–amorphous transformation would occur belowgrain size of about 1.4 nm. Jang and Koch [19] reported

hat amorphous is produced adjacent to nanocrystalline whenrain dimensions reach 2 nano-millimeters in certain regionsf intermetallic compound Ni3Al. A nanostructure Si preparedy glow discharge decomposition from silane was noticed byaman spectroscopy to change into amorphous Si if the crys-

al size was reduced below a critical value of a few nanome-ers [20,21]. Above reports convinced that the present pro-osed thermodynamic model fits the experimental data veryell.

. Conclusions

A nanostructured layer can be formed in Hadfield steely shot peening. The transformation from a coarse graintate to a nanocrystalline or amorphous can be effectivelynvestigated by nonequilibrium thermodynamic theory. It is

nd when grain size below a crystal size about 1.89 nm, itecomes possible to be changed to amorphous from nanocrys-alline.

Engi

A

fPT

R

[[[

[

[

[

[

[

W. Yan et al. / Materials Science and

cknowledgement

The present authors are appreciated to the financial supportrom the National High Technology Research and Developmentrogram of China (863 Program), the Ministry of Science andechnology of China (Grant 2002AA302509).

eferences

[1] R.Z. Valiev, R.K. Islamgaliev, I.V. Alexandrov, Prog. Mater. Sci. 45 (2000)103–189.

[2] N.R. Tao, Z.B. Wang, W.P. Tong, M.L. Sui, J. Lu, K. Lu, Acta Mater. 50(2002) 4603–4646.

[3] X. Wu, N. Tao, Y. Hong, B. Xu, J. Lu, K. Lu, Acta Mater. 50 (2002)2075–2084.

[4] H.W. Zhang, Z.K. Hei, G. Liu, J. Lu, K. Lu, Acta Mater. 51 (2002)1871–1881.

[5] F. Miani, H.J. Fecht, Int. J. Refract. Met. H 17 (1999) 133–139.[6] C.X. Wang, Y.H. Yang, G.W. Yang, Appl. Phys. Lett. 84 (2004) 3034–3036.[7] C.X. Wang, G.W. Yang, Mater. Sci. Eng. R 49 (2005) 157–202.

[[[[

neering A 445–446 (2007) 392–397 397

[8] Q.X. Liu, C.X. Wang, G.W. Yang, Phys. Rev. B 71 (2005) 155422.[9] G. Nicolis, I. Pringogine, Self-organization in Nonequilibrium System,

John Wiley & Sons, New York, 1977, p. 49.10] A.R. Miedema, P.F. de Chatel, F.R. de Boer, Physica B 100 (1980) 1–28.11] A.K. Niessen, A.R. Miedema, Phys. Chem. 87 (1983) 717–725.12] A.K. Niessen, F.R. de Boer, R. Brown, P.F. de Chatel, C.W. Matters, A.R.

Miedema, Calphad 7 (1983) 51–70.13] H.P. Klug, L.E. Alexander, X-ray Diffraction Procedures for Polycrystalline

and Amorphous Materials, Wiley, New York, 1974, p. 661.14] J.M. Lopez, J.A. Alonso, L.J. Gallego, Phys. Rev. B 36 (1987) 3716–

3722.15] W. Kurz, D.J. Fisher, Fundamentals of solidification. Adermannsdorf, Trans

Tech Publications Ltd., Switzerland, 1984, p. 211.16] J.D. Verhoven, Fundamentals of Physical Metallurgy, John Wiley & Sons,

New York, 1975, p. 176.17] F.R. de Boer, R. Boom, W.C. Mattens, A.R. Miedema, A.K. Niessen, Cohe-

sion in Metals, Amsterdam, North-holland, 1988, p. 71–74.

18] J. Wang, D. Wolf, S.R. Phillpot, H. Gleiter, Phil. Mag. A 73 (1996) 517–555.19] J.S.C. Jang, C.C. Koch, J. Mater. Res. 4 (1990) 498–510.20] Z. Iqbal, A.P. Webb, S. Veprek, Appl. Phys. Lett. 36 (1980) 163–165.21] S. Veprek, Z. Iqbal, H.R. Oswald, A.P. Webb, J. Phys. C 14 (1981)

295–308.