Experimental Determination and Thermodynamic Assessmentof Phase Equilibria in the Co­Mo System

K. Oikawa1,2, U. R. Kattner1, J. Sato2, T. Omori2, M. Jiang2, K. Anzai2 and K. Ishida2

1Metallurgy Division, National Institute of Standards and Technology, 100 Bureau Dr., Stop 8554, Gaithersburg, MD 2089, USA2Department of Metallurgy, Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan

Phase equilibria of the solid phases including the magnetic and martensitic transformation temperatures in the Co­Mo system wereinvestigated using two-phase alloys, the diffusion couple technique, differential scanning calorimetry, and vibrating sample magnetometry.Furthermore, ab initio calculations of D019-Co3Mo and several fcc-base ordered structures, including metastable compounds, were carried out toestimate the formation energy. Based on these results, a thermodynamic assessment using the CALPHAD method was performed. A four-sublattice model was used for the fcc-base phase to describe the order­disorder phase transformation. For the ® phase, both a three and a four-sublattice model were applied. The set of thermodynamic values describing the Gibbs energy of the Co­Mo system reproduces the experimentalphase diagram well. The four-sublattice model for the ® phase reproduces the site fractions as well as the phase boundaries better than the three-sublattice model. The calculated metastable fcc-base phase diagram considering chemical and magnetic ordering is also reasonable. This isimportant for estimating the phase stability of the L12 phase in Co-base £/£A superalloys. [doi:10.2320/matertrans.M2012149]

(Received April 18, 2012; Accepted May 7, 2012; Published June 20, 2012)

Keywords: phase diagram, first-principles, thermodynamic, order­disorder transition, superalloys

1. Introduction

Co-base alloys are widely used as high-temperaturematerials for aerospace engines and land-based gas turbinesfor power generation. The mechanical properties of commer-cial Co-base alloys are generally inferior to Ni-base super-alloys strengthened by the £A phase with L12 structurebecause Co-base alloys are strengthened by solid-solutionhardening and carbide precipitation. The Co3(Al,W) ternarycompound with the L12 ordered structure was recentlydiscovered in the Co­Al­W ternary system.1) Since themechanical properties at high temperature of this alloy arecomparable to those of Ni-base superalloys,2­8) the Co-basefcc (face-centered-cubic, A1) alloys strengthened byCo3(Al,W) are considered to be promising candidates for anew class of load-bearing Co-base superalloys.9) Mo is oneof the important alloying elements for the new Co-base £/£Asuperalloys as well as the conventional Co-base alloysbecause Mo partitions to the L12 phase rather than the A1phase1) and can be expected to solid-solution harden thematrix. To understand this behavior in high-alloyed materials,the CALPHAD (CALculation of PHAse Diagrams) methodis useful for calculating multicomponent phase diagrams andthe Co­Mo binary system is a necessary constituent sub-system for these Co-base superalloys.

The experimental Co­Mo phase diagram has beeninvestigated by several researchers10­21) and a comprehensivephase diagram has been compiled in Ref. 22. Details ofthe phase boundary information of the paramagnetic hcp(hexagonal-closed pack, A3) phase have not been exper-imentally clarified yet. For the CALPHAD type assessment,the pioneering work on this system was carried out byKaufman and Nesor23) who used simple regular solution andline compound models. Davydov and Kattner assessed thissystem using the regular solution model with magnetic termand compound energy models.24) However, these assess-ments did not include the metastable order­disorder phase

transition of the fcc-base compounds, which are important forthe Co-base £/£A superalloys. In the present study, the phasediagram of the Co­Mo binary system has been experimen-tally investigated using electron probe micro analysis(EPMA), differential scanning calorimetry (DSC) andvibrating sample magnetometry (VSM) measurements toestablish the phase boundaries in the Co-rich region. Inaddition, the formation energy of L12(Co3Mo, CoMo3),L10(CoMo), D019(Co3Mo) and disordered CoMo3 with A1symmetry have been calculated by means of the densityfunctional theory using the Vienna ab initio simulationpackage (VASP).25,26) The disorder structure of A1-CoMo3is approximated by the special quasi structure (SQS) of16 atoms with 75mol% Mo.27) Based on these results athermodynamic assessment using the CALPHAD methodhas been performed.

2. Experimental Procedure

2.1 Specimen preparationAlloys with different compositions of Co­(0, 3, 5, 10, 16,

18, 19, 20, 25, 35, 52) mol% Mo (mol% is used to abbreviate“percent of mole fraction”) labeled as Co, 3Mo, 5Mo, 10Mo,16Mo, 18Mo, 19Mo, 20Mo, 25Mo, 35Mo and 52Morespectively, were prepared by arc melting using high purityCo (99.9%) and Mo (99.9%) under an argon atmosphere.They were melted more than five times to obtain homoge-neous buttons.

2.2 Heat treatmentSmall pieces of specimens were cut from the alloy buttons.

These specimens were wrapped in molybdenum foil to avoidreaction with the quartz capsules. The specimens were sealedin quartz capsules that have been evacuated and backfilledwith argon gas and then solution treated at 1623K for 24 h,followed by quenching in ice water. The chemical compo-sitions of the 3Mo and 18Mo alloys after solution treatment

Materials Transactions, Vol. 53, No. 8 (2012) pp. 1425 to 1435©2012 The Japan Institute of Metals

were chemically analyzed with atomic absorption spectrom-etry. The compositions were 3.06mol% Mo and 17.8mol%Mo, respectively, which is in good agreement with thenominal value. The standard deviation for both compositionanalysis was «0.02mol%. These two samples were used asstandards to calibrate the compositions obtained by EPMA.After solution treatment the wrapped 10Mo, 16Mo, 18Mo,19Mo, 20Mo, 25Mo 35Mo 52Mo and 70Mo alloys wereresealed in quartz capsules and equilibrated at 1173 to 1623Kfor 2 to 1440 h. After the heat treatment, the specimens werequenched in ice water and mechanically polished to observethe microstructure. Equilibrium compositions of the two-phase alloys were determined by EPMA.

Diffusion couples (DC) were also prepared to confirmthe measurements in narrow two-phase regions. Solutiontreated Co and 10Mo or 25Mo specimens were joinedtogether using a clamp consisting of Mo bolts and nuts ofstainless steel and annealed in evacuated quartz capsules at1273K for 2 h. Further details method for DC preparation canbe found elsewhere.28) The DC specimens were then sealedin a quartz capsule and annealed at 1173 to 1573K. Afterquenching, cross sections of these DC specimens werepolished and composition­penetration curves were measuredby EPMA.

2.3 DSC and VSM measurementsCompositional dependence of the Curie temperature (TC)

and saturation magnetization (Is) of the alloys were inves-tigated by VSM. Magnetization­temperature (M­T) curvesunder a magnetic field of 0.3MA/m were measured at aheating rate of 1K/min. TC was defined as the minimum inthe plot of the temperature derivative of the magnetization(dM/dT). The Is was determined from the magnetizationcurve (M­H) measured at 83 and 293K with an appliedmagnetic field strength of 1.6MA/m. Invariant reactionswere investigated by DSC under an argon atmosphere usingheating rates of 10K/min.

3. Ab Initio Calculations

The crystal structure and total energy calculations ofthe A1-Co, A3-Co, D019-Co3Mo, L12-Co3Mo, L10-CoMo,L12-CoMo3, A1-CoMo3, A1-Mo and A2-Mo phases wereperformed using VASP to obtain the formation energy. Thedisordered structure of A1(CoMo3) is approximated by thespecial quasirandam structure (SQS) of 16 atoms with75mol% Mo.27) The supercell structure of A1-CoMo3 wastaken from previous work.29) The energy calculations werecarried out using the projector augmented-wave (PAW)approach in the generalized gradient approximation(GGA).30,31) For Mo atoms the pseudopotential treating thesemi-core p state as valence states was used. The calculationswere performed for 0K without pressure. Brillouin-zonesampling was performed using the ¥ centered Monkhorst­Pack scheme with a 15 © 15 © 15 mesh grid.32) The plane-wave energy cutoff was 500 eV. The unit cell volume andshape as well as all internal atomic positions of the structures,were fully relaxed except for the A1-CoMo3 structure. Onlythe volume of A1-CoMo3 was relaxed because the fullyrelaxed structure of A1-CoMo3 is quite different from the

original symmetry. The chosen energy cutoff, k-points andconvergence parameters were checked to ensure a con-vergence in energy of the order of 1meV/atom.

The T = 0K formation enthalpy per mole of Co1¹xMoxcompounds can be calculated from the following equation:

�HðCo1�xMoxÞ¼ EðCo1�xMoxÞ � ð1� xÞEðCoÞ � xEðMoÞ ð1Þ

where E(Co), E(Mo) and E(Co1¹xMox) are the ab initio totalenergies per mole of A3-Co, A2-Mo and the intermetalliccompounds, respectively. Here, x is the molar fraction of Moin the compounds.

4. Thermodynamic Models

In the present study, the Gibbs energies of pure Co andMo in the stable and metastable states are taken from theSGTE pure element database.33) The liquid, A1 (fcc), A2(bcc) and A3 (hcp) phases were described by the sub-regularsolution model. The molar Gibbs energy of phase º is givenby:

Gºm ¼

XMo

i¼Co

xi�Gº

i þ RTXMo

i¼Co

xi ln xi

þ xCoxMo

Xnm¼0

mLºCo,MoðxCo � xMoÞm ð2Þ

where xi, �Gºi , R and T are the mole fraction of an element i,

the Gibbs energy of i with the structure º, the gas constant,and temperature, respectively. The second and third terms onthe right-hand side are the ideal entropy term and the excessGibbs energy term, respectively. mLº

Co,Mo are the Redlich­Kister coefficients and can be temperature-dependent in theform mLº

Co,Mo ¼ Aþ BT .The fcc-base ordered L12-Co3Mo, L10-CoMo and L12-

CoMo3 phases were described by four-sublattice model.34,35)

The molar Gibbs energy equation for a four-sublattice phaseusing the compound energy formalism is given by:

G4slm ¼

XMo

i¼Co

XMo

j¼Co

XMo

k¼Co

XMo

l¼Co

yð1Þi yð2Þj yð3Þk yð4Þl�Gi:j:k:l

þ RT1

4

X4m¼1

XMo

i¼Co

yðmÞi ln yðmÞ

i

þ X

m

Xn>m

Xo>n

Xp>o

XMo

i¼Co

XMo

j¼Co

� yðmÞCo y

ðmÞMoy

ðnÞCoy

ðnÞMoy

ðoÞi yðpÞj

0LCo,Mo:Co,Mo:i:j

!ð3Þ

where, yðmÞi , �Gi:j:k:l, and 0L are the site fraction of the

element i on the sublattice m, compound energies, andinteraction parameters, respectively. A colon in the suffixof compound energies and interaction parameters separateselements on different sublattices, and a comma separateselements on the same sublattice. Equation (3) can alsodescribe the disordered state when all site fractions yðmÞ

i areequal to the mole fractions, xi:

yð1Þi ¼ yð2Þi ¼ yð3Þi ¼ yð4Þi ¼ xi ð4Þ

K. Oikawa et al.1426

From the fact that the sublattices are identical and that theGibbs energy expression also represents the disordered state,the following relations must be fulfilled:35)

�GCo:Co:Co:Mo ¼ �GCo:Co:Mo:Co ¼ �GCo:Mo:Co:Co

¼ �GMo:Co:Co:Co ¼ 3ð¯ð1ÞCo:Mo þ ¡Co3MoÞ ¼ G4slCo3Mo

�GCo:Co:Mo:Mo ¼ �GCo:Mo:Co:Mo ¼ �GCo:Mo:Mo:Co

¼ �GMo:Co:Co:Mo ¼ �GMo:Co:Mo:Co ¼ �GMo:Mo:Co:Co

¼ 4¯ð1ÞCo:Mo ¼ G4slCo2Mo2

�GCo:Mo:Mo:Mo ¼ �GMo:Co:Mo:Mo ¼ �GMo:Mo:Co:Mo

¼ �GMo:Mo:Mo:Co ¼ 3ð¯ð1ÞCo:Mo þ ¡CoMo3Þ ¼ G4slCoMo3

ð5Þwhere ¡Co3Mo and ¡CoMo3 are adjustable parameters, and¯ð1ÞCo:Mo is the first neighbor pair interaction energy. The factors3 and 4 in front of the interaction energies originate from thenumber of pair bonds per atom in each ordered structures.The reciprocal terms are given by the first neighbor pairinteraction energy and can have a concentration dependencyas follows:34,35)

0LCo,Mo:Co,Mo:Co:Co ¼ ¯ð1ÞCo:Mo þ ¡Co3Mo

0LCo,Mo:Co,Mo:Co:Mo ¼ ¯ð1ÞCo:Mo

0LCo,Mo:Co,Mo:Mo:Mo ¼ ¯ð1ÞCo:Mo þ ¡Co3Mo ð6Þ

The molar Gibbs energy for the ordered structures can bedescribed by two parts as:

Gordm ¼ Gdis

m ðxiÞ þ�Gordm ðyiÞ ð7Þ

where Gdism ðxiÞ is the molar Gibbs energy of the disordered

state and �Gordm ðyiÞ is the molar ordering energy. When the

phase is disordered, the ordering energy is zero. This isautomatically given in the model by the expressing the orderenergy as follows:

�Gordm ¼ G4sl

m ðyiÞ �G4slm ðyi ¼ xiÞ

Gdism ðxiÞ ¼ G4sl

m ðyi ¼ xiÞ ¼ GA1m ðxiÞ ð8Þ

From these equations the relation of the parameters betweenthe regular solution model and the four-sublattice model canbe simply derived as follows:34)

0LA1i;j ¼ G4sl

Co3Mo þ 1:5G4slCo2Mo2

þG4slCoMo3

þ 0:3750L4slCo,Mo:Co,Mo:Co:Co

þ 0:750L4slCo,Mo:Co,Mo:Co:Mo

þ 0:3750L4slCo,Mo:Co,Mo:Mo:Mo

1LA1Co,Mo ¼ 2G4sl

Co3Mo � 2G4slCoMo3

þ 0:750L4slCo,Mo:Co,Mo:Co:Co

� 0:750L4slCo,Mo:Co,Mo:Mo:Mo

2LA1Co,Mo ¼ G4sl

Co3Mo � 1:5G4slCo2Mo2

þG4slCoMo3

� 1:50L4slCo,Mo:Co,Mo:Co:Mo

3LA1Co,Mo ¼ �0:750L4sl

Co,Mo:Co,Mo:Co:Co

þ 0:750L4slCo,Mo:Co,Mo:Mo:Mo

4LA1Co,Mo ¼ �0:3750L4sl

Co,Mo:Co,Mo:Co:Co

þ 0:750L4slCo,Mo:Co,Mo:Co:Mo

� 0:3750L4slCo,Mo:Co,Mo:Mo:Mo ð9Þ

The ® phase with the D85 structure includes fivecrystallographic sites. In an idealized description as stoicho-metric Co7Mo6 compound, Mo atoms occupy the sites 6c1,6c2 and 6c3, while Co atoms occupy sites 3a and 18h.36) Theconventional model for this phase is the three-sublatticemodel37) represented as (Co,Mo)7Mo2(Co,Mo)4 (model I). Inthis model the sites 3a and 18h and the sites 6c2 and 6c3 arecombined to decrease the number of the fitting parameters.The molar Gibbs energy for formula unit is expressed by:

G®m ¼

XMo

i¼Co

XMo

j¼Co

yð1Þi yð3Þj�G®

i:Mo:j þ 7RTXMo

i¼Co

yð1Þi ln yð1Þi

þ 4RTXMo

i¼Co

yð3Þi ln yð3Þi þXMo

i¼Co

yð1ÞCoyð1ÞMoy

ð3Þi

0L®Co,Mo:Mo:i

þXMo

i¼Co

yð1Þi yð3ÞCoyð3ÞMo

0L®i:Mo:Co,Mo ð10Þ

where �G®i:Mo:j, y

ðmÞi , 0L are compound energy and the site

fractions of Co and Mo on the m site and interaction energy,respectively. Recently, based on the detailed crystallog-raphic information,36) a four-sublattice model was recom-mend for the ® phase, which is represented as (Co,Mo)1-Mo4(Co,Mo)2(Co,Mo)6 (model II).36) In this model, the sites6c1 and 6c2 are occupied by Mo atoms only, while the otherssites are occupied by Co and Mo. The molar Gibbs energyper formula unit is expressed by:

G®m ¼

XMo

i¼Co

XMo

j¼Co

XMo

k¼Co

yð1Þi yð3Þj yð4Þk�G®

i:Mo:j:k

þ RTXMo

i¼Co

yð1Þi ln yð1Þi þ 2RTXMo

i¼Co

yð3Þi ln yð3Þi

þ 6RTXMo

i¼Co

yð4Þi ln yð4Þi ð11Þ

where �G®i:Mo:j:k and yðmÞ

i are the compound energies and thesite fractions of Co and Mo on the m site. No excess term wasused.

The Co3Mo compound with the D019 structure is describedby a simple line compound model because of its narrowhomogeneity range.

A term for the magnetic contribution to the Gibbs energy isintroduced for the A1, A2 and A3 and fcc-based orderedphase. The magnetic term, magGm is expressed by Hillert andJarl38) as follows:

magGm ¼ RT fð¸Þ lnð¢ þ 1Þ ð12Þwhere R is gas constant, T is temperature and f(¸) is theintegral function fitted to the contribution to the heat capacitydue to the magnetic transition. ¸ is T/TC and ¢ is the averageBohr magneton number per atom. The ordering dependenceof the TC is described in the same way as for the Gibbsenergy, i.e.

T totalC ¼ T disorder

C þ�T orderC

�T orderC ¼ T order

C ðyÞ � T disorderC ðy ¼ xÞ ð13Þ

An analogous formalism is used for the description of ¢.�T order

C and �¢oder are assumed to be zero due to the lack ofinformation.

Experimental Determination and Thermodynamic Assessment of Phase Equilibria in the Co­Mo System 1427

5. Results and Discussion

5.1 MicrostructureTypical micrographs are shown in Figs. 1 and 2 and the

chemical compositions determined by EPMA are summariz-ed in Table 1. Figure 1(a) shows the optical micrograph ofthe 3Mo alloy annealed at 1623K for 24 h, in which amartensitic structure with a high density of twins is observed,as shown in Fig. 1(b). This martensitic structure is evidencethat this phase was the A1 phase at the annealing temperatureand transformed to the A3 phase during the cooling.

A two-phase structure has been observed in the 18Moalloy annealed at 1523K for 10 h (Fig. 1(c)). The matrixphase with the twinned structure was the A1 phase at theannealing temperature that transformed to the A3 phase. Theprecipitated phase is not observed in the twinned structure,although the chemical composition difference with the matrixphase is about 2% as shown in Table 1. This phase isconsidered to be the A3 phase according to the literature.19,24)

Although this phase is not stable at lower temperatures itdoes not show evidence of having undergone a phasetransformation in the micrograph. Figures 1(d) and 1(e) showthe optical micrographs of the 25Mo alloy annealed at1573K for 42 h and 1523K for 30 h, respectively. Althoughthe chemical compositions of the matrix phases in bothsamples are very similar as listed in Table 1, the matrixstructures in Figs. 1(d) and 1(e) could be identified as theA1 and A3 from the presence or absence of the twinnedstructure, respectively. The precipitated phase in bothsamples is considered as the ® phase from the chemicalcomposition.22) These results suggest that a peritectoidreaction (A1 + ® § A3) occurs between 1523 and 1573K.

Figures 2(a) and 2(b) show the compositional images inthe back-scattered electron image (BSE) mode of the 52Moand 70Mo annealed at 1623K, respectively. The 52Mo alloyshows the two-phase structure, as shown in Fig. 2(a). Fromthe chemical composition,22) the bright and dark colorregions are considered as · and ® phases, respectively. Inthe 70Mo alloy, there are three phases, which are indentifiedas the A2, · and ® from the chemical composition analysis.

This suggests that the 70Mo alloy did not reach equilibriumwith the present heat treatment condition: longer heattreatment is necessary for the 70Mo alloy to obtain theequilibrium state due to the low diffusivity. The chemicalcomposition of all two or three phase alloys is listed inTable 1.

5.2 Diffusion couplesThe compositional images in the BSE mode of the Co/

25Mo DC specimen annealed at 1373K for 120 h is shown inFig. 3(a). The A3 + ® two-phase structure is observed in the25Mo side. Near the diffusion zone, the boundary is formedas shown in Fig. 3(a). The concentration-penetration curvenear the boundary measured by EPMA along the dashed linein Fig. 3(a) is shown in Fig. 3(b). An obvious compositionstep is observed, corresponding to the boundary with thecontrast step in the compositional images in the BSE mode.The equilibrium compositions listed in Table 1 weredetermined by extrapolating the composition-penetrationprofile to the interfacial boundary, which agrees well withcompositions of the two-phase alloys. Similar results wereobtained in the Co/25Mo DC specimens annealed at 1573and 1273K. The compositional images in the BSE mode ofthe Co/10Mo DC specimen annealed at 1173K for 120 h isshown in Fig. 4(a). The 10Mo alloy consists of a two-phasestructure of A1 and D019. The concentration-penetrationcurve near the boundary, delineated by the broken line inFig. 4(a), was measured by EPMA along the dashed line asshown in Fig. 4(b), where an obvious composition stepcorresponding to the boundary is observed. According to themagnetic measurement results, the regions to the left and theright side are considered to be the ferromagnetic and

150 μm

15 μm

(b)

(a)

σ

μ

A2

Fig. 2 Compositional images in BSE mode of (a) 52Mo alloy annealed at1623K for 15 h and (b) 70Mo annealed at 1623K for 336 h.

15 μm50 μm

10 μm

50 μm

(a) (b) (c)

(d) (e)

20 μm

A3

μ

μ

Fig. 1 Optical micrographs of (a) and (b) 3Mo alloy annealed at 1623K for24 h, (c) 18Mo alloy annealed at 1523K for 10 h, (d) 25Mo alloy annealedat 1573K for 42 h and (e) 25Mo alloy annealed at 1523K for 30 h.

K. Oikawa et al.1428

paramagnetic, respectively, at the annealing temperature. Thisphase boundary may correspond to the phase separation ofthe ferromagnetic A1 and paramagnetic A1 phases predictedby the thermodynamic calculations.24) A similar phaseseparation has been experimentally observed in several Co­X systems such as the Co­Cr,39,40) Co­V,41) Co­W42,43) andCo­Ge.44)

5.3 DSC and VSM measurementsFigure 5 shows the DSC curves on heating of 16Mo,

19Mo and 25Mo alloys. Several endothermic peaks areobserved. Each of the peaks is identified, as noted in Fig. 5,and summarized in Table 2. The microstructural observationswere taken into account for the interpretation of the DSCpeaks.

The magnetization­temperature (M­T) curves on heatingobtained from 3Mo, 10Mo, 12Mo and 16Mo alloys quenchedfrom 1623K are shown in Fig. 6(a). Their microstructuresconsist of martensitic A3 and residual A1 as shown inFig. 1(a). The magnetization increases with increasingtemperature, with a peak at around 870K for the 3Mo alloy.This temperature corresponds to the inverse martensitictransformation temperature of the matrix phase. The TC of the3Mo alloys could not be obtained due to the upper limit of

the equipment. The magnetization of 12Mo alloy decreaseswith increasing temperature in two steps. Since the TC of theA3 phase has a tendency to be higher than that of A1 phase inCo­Cr40) and Co­W43) alloys, the lower and higher temper-ature steps are interpreated as TC for A1 and A3, respectively.Only the lower step could be observed in the 10Mo alloybecause of the temperature limit of the equipment. Thecompositional dependence of the saturation magnetization(Is) at 83 and 298K is shown in Fig. 6(b). The Is at 83Kdisappears at around 25mol% Mo according to theextrapolation of the measured results. The magnetic behavioris similar to that of the Co­W system.43) The results of themagnetic measurements are summarized in Table 3.

Table 1 Equilibrium phase compositions in the Co­Mo system.

AlloysTemp.(K)

Time(h)

Mo content (mol%)

A1ferro A1para A3para Liquid Co3Mo ® · A2

10Mo 1173 1440 7.2 23.1

16Mo 1373 24 14.6 17.0

1273 48 15.3 22.6

18Mo 1523 10 17.7 19.8

19Mo 1373 24 18.3 40.7

1273 48 15.5 22.3

20Mo 1373 24 18.0 40.7

1273 96 15.6 22.5

25Mo 1623 2 18.3 26.1

1613 12 20.2 41.3

1573 42 19.5 41.4

1523 30 20.2 41.3

1473 36 20.1 41.8

1423 5 19.5 41.0

1373 120 19.3 41.6

1323 240 23.3 41.2

35Mo 1623 2 24.8 48.1

52Mo 1623 15 48.8 63.0

1573 15 48.6 61.3

1473 48 49.2 62.2

1373 96 48.8 62.6

1173 336 48.2 62.6

70Mo 1623 336 49.6* 65.0* 96.7*

1573 264 49.4* 63.5* 97.6*

1373 144 49.6* 63.3* 92.0*

Co/10MoDC 1173 1440 3.6 6.0

Co/25MoDC 1573 12 19.8 21.0

1373 120 13.7 16.7

1273 120 11.5 15.7

*Three phases were observed in the alloys. The average standard deviation for the composition is less than «0.2.

Table 2 Phase transformation temperatures determined by DSC on heating.

Phase transformation temperature (K)Reaction

16Mo 19Mo 25Mo Ref. 2)

1655 A1 / A1 + Liquid

1614 1612 1608 A1 + ®¼ Liquid

1325 1320 1298 D019 ¼ A3 + ®

1268 1270 1291 A1 + D019 ¼ A3

The average standard deviation for the temperature is less than «5K.

Experimental Determination and Thermodynamic Assessment of Phase Equilibria in the Co­Mo System 1429

The experimental phase diagram evaluated from thepresent investigation is shown in Fig. 7 together with thephase diagram compiled in Ref. 22). Compared to thepreviously accepted phase diagram the temperature of theA1 + ® § A3 peritectoid reaction is 100K higher and theA3 § A1 + D019 eutectoid reaction is 20K lower. Thehomogeneous region of D019 phase deviates to the Co-richside from the stoichiometric composition. The magneticallyinduced phase separation of A1ferro + A1para is confirmednear the TC. The homogeneity ranges of the ® and · phasesare similar to previous results. The · § ® + A2 eutectoidreaction could not be determined by the present study; itcould be lower than 1173K.

5.4 ab initio calculationsThe formation enthalpies of D019-Co3Mo L12-Co3Mo,

L10-CoMo, L12-CoMo3 and A1-CoMo3 from the ab initio

5

9

13

17

21

25

0 5 10 15 20 25 30

Mo

cont

ent (

mol

%) (b)

A3para

A1para

A3para/A1para

Measurement point (μm)

(a)

10μm

25Mo pure Co

A1A3+μ

Fig. 3 (a) Compositional image in BSE mode of the Co/25Mo diffusioncouple annealed at 1373K and (b) composition penetration curve near thephase boundary.

Temperature, T/K1000 1100 1200 1300 1400 1500 1600 1700

Exo

ther

mic

(ar

b. u

nit)

A1+D019 A3

A1+D019 A3μ A3+D019

μ A3+D019

A1 L

A1+μ L

A1+μ L

16Mo

19Mo

25Mo

inverse martensitic

inverse martensitic

Fig. 5 DSC curves of the 16Mo, 19Mo and 25Mo alloys on heating.

10 200

Mo

cont

ent (

mol

%)

0

2

4

6

8

10

10Mopure Co(a)

(b)

A1ferro

A1para

A1ferro/A1para

A1 A1+D019

Measurement point (μm)

Fig. 4 (a) Compositional image in BSE mode of the Co/10Mo diffusioncouple annealed at 1173K and (b) composition penetration curve near thephase boundary.

0

0.2

0.4

0.6

0.8

250 450 650 850 1050

3Mo

10Mo

12Mo

Temperature, T/K

Mag

netiz

atio

n (a

rb. u

nit)

magnetictransition

magnetictransition

inversemartensitic

0

0.4

0.8

1.2

1.6

Mag

netiz

atio

n, I S

/ 10

0 5 10 15 2520Mo content (mol%)

Saturation magnetization83 K 298 K

(b)

(a)

2A

·m2 ·

kg-1

Fig. 6 VSM measurement results. (a) Thermomagnetization curves onheating and (b) composition dependence of the saturation magnetizationat 83 and 298K.

K. Oikawa et al.1430

calculations are shown in Table 4 and Fig. 8, together withthe evaluated value45) from the experimental data of the D019-Co3Mo phase.16,20) This value is in good agreement with ourcalculations. Table 4 also gives the comparison between theab initio and experimentally measured lattice parameters ofthe D019-Co3Mo phase.46) It can be seen that the ab initio

results agree to within 1% of the experimental data. The c/aratio of the tetragonal L10-CoMo deviates slightly from apseudocubic ratio.

The formation energies of the L10-CoMo, L12-CoMo3 andA1-CoMo3 are positive while that of L12-Co3Mo is slightlynegative as shown in Fig. 8. The formation energy of theordered L12-CoMo3 is higher than that of disordered A1-CoMo3. It is noteworthy that the ab initio energy of A1-Mo,which is known as a mechanically unstable phase,47,48) isconsiderably higher than the SGTE value. The ab initioenergies of the L12-CoMo3 and A1-CoMo3 are also relativelyhigher than the SGTE value for A1-Mo. The requirement formechanical stability in a cubic crystal is (C11 ¹ C12) > 0,(C11 + 2C12) > 0, C11 > 0 and C44 > 0, where Cij are theelastic constants.49) Strain energies for tetragonal and trigonaldistortions are related to C11 ¹ C12 and C44, respectively. Thelattice instabilities along the tetragonal (Bain) distortion pathbetween bcc and fcc with the constant volume are evaluatedfor A1-Mo, L12-CoMo3, A1-CoMo3, L10-CoMo and L12-Co3Mo using results from VASP calculations (Fig. 9(a)). Atc/a ratios of 1 and

ffiffiffi2

pthe structure is equivalent to the bcc

Table 4 Ab initio formation enthalpies and lattice constants in the Co­Mo system. Reference states are spin-polarized A3 and A2 for Coand Mo, respectively.

PhaseFormationenergy(J/mol)

Experimental45)

(J/mol)

Magneticmoment

(Bohr/unit)

Calculatedlattice constant

(nm)

Experimentallattice constant46)

(nm)

D019-Co3Mo ¹5695 ¹5300 0.92a = 0.511c = 0.408

a = 0.512c = 0.411

L12-Co3Mo ¹549 ® 0.72 a = 0.359 ®

L10-CoMo 2956 ® 0.00a = 0.375c = 0.370

®

L12-CoMo3 19227 ® 0.00 a = 0.388 ®

A1-CoMo3 13209 ® 0.00 a = 0.325 ®

Liq.

Ref. 22)(a)

Co 20 40 60 80 MoMo content (mol%)

673

1073

1473

1873

2273

Tem

pera

ture

, T/K

A2

σ

μ

A1para

A3para

D019A3ferro

A1ferro

Tc of A1

Diffusion coupleDSC

Two-phase alloy

Co 10 20 30Mo content (mol%)

1073

1473

1273

1873

1673

Tem

pera

ture

, T/K

(b) Liq.

A1para

A3para

D019

A1ferro

Tc

Fig. 7 Experimental phase diagrams of the Co­Mo system. (a) Wholesystem and (b) Co-rich region.

Table 3 Saturation magnetization, Is, Curie temperature, Tc, and martensitic transition temperatures Ms, Mf, As, Af of the Co­Mo alloys.

AlloysIs at 83K Is at 300K Tc (K) Tc (K)

Ms (K) Mf (K) As (K) Af (K)A·m2·kg¹1 A·m2·kg¹1 A1 A3

3Mo 143.7 143.5 672 628 1023 1103

10Mo 91.5 86.4 893 1078 1223

12Mo 81.5 73.8 709 787 1093 1228

16Mo 54.4 35.3 404

The average standard deviation for the saturation magnetization is less than «3A·m2·kg¹1.

Co 20 40 60 80 Mo-10

0

10

20

30

40

Mo content (mol%)

ab-initio fcc-based structures

Exp. data ab-initio D019

fcc from SGTE 33)

L10

L12

L12

D019μ

σ

A1(SQS)

For

mat

ion

enth

alpy

, ΔH

/kJ·

mol

-1

Fig. 8 Formation enthalpies of the compounds in the Co­Mo system.Reference states are spin polarized A3 and A2 for Co and Mo,respectively.

Experimental Determination and Thermodynamic Assessment of Phase Equilibria in the Co­Mo System 1431

and fcc symmetry, respectively. It can be seen that A1-Mohas a local maximum at c/a =

ffiffiffi2

p, while for L12-Co3Mo,

L10-CoMo a minimum occurs near c/a =ffiffiffi2

p. The L12-

CoMo3 shows a fairly flat curve with a shallow minimum atc/a =

ffiffiffi2

p. These results suggest that for Mo-rich composi-

tions the bcc structure is stable and the fcc structure isunstable, and L12-Co3Mo, L10-CoMo have stable, nearly,ideal fcc structures. Figure 9(b) shows the total energy-straincurves for tetragonal distortion of L12-Co3Mo and L12-CoMo3 and the trigonal distortion of L12-CoMo3. The curveof tetragonal distortion of the L12-CoMo3 is fairly flatcompared to the other curves. The fairly small value of30GPa of C11 ¹ C12 for L12-CoMo calculated from thiscurve. These small differences further emphasize the need forthe calculation of the vibrational entropy and an accurateab initio treatment such as the FLAPW-LDA method50) toobtain accurate predictions for the stabilities of differentstructures. Therefore, the calculated formation energy valuesfor L12-CoMo3 and A1-CoMo3 were not used in theCALPHAD assessment.

5.5 Thermodynamic calculationsSince earlier experimental information of phase equilibria

and thermochemical data were compiled in a previousreport,24) the review of these data is omitted in this paper.The thermodynamic assessment was performed using thepresent experimental data and liquidus data from Ref. 15).The formation enthalpies of D019-Co3Mo, L12-Co3Mo andL10-CoMo obtained from ab initio calculations are also usedto the present assessment. Using eq. (5) and thermodynamic

values of the formation enthalpies listed in Table 4, thefirst-neighbor interaction energy ¯

ð1ÞCo:Mo and the adjustable

parameter ¡Co3Mo were derived as ¹2223.9 J/mol and¹1134.8 J/mol, respectively. G4sl

CoMo3is assumed to be zero.

For model I of the ® phase, four end-members have to betaken into account. For the formation energy of Mo:Mo:Mo,which is a highly non-stable compound, a value of 5000J/mol per atom is usually accepted. Other conventionalsimplifications24) for the optimization was accepted formodel I. For model II, eight end-members have to beconsidered. The formation enthalpies of four compounds*:Mo:*:Mo, corresponding to compositions far from thestable region are fixed at 30 kJ/mol by taking into accountthe ab initio ® phase lattice stability51) of 29 kJ/mol andconverting the reference state from A1 to A2 using the valuefrom the present results. A 4th order polynominal was usedfor evaluating the parameters the magnetic contribution forthe A1 and A3 phases to avoid abnormal TC behavior onthe Mo-rich side. Other parameters were evaluated from thephase diagram information using the Parrot module inThermo-Calc.52,53) The parameter set obtained by the presentassessment is summarized in Table 5.

0

10

20

30

40

50

0.8 1.0 1.2 1.4 1.6 1.8

bcc fcc

c/a ratio

Bai

n st

rain

ene

rgy,

EB

/kJm

ol L12-Co3MoL12-CoMo3L10-CoMo

A1-Mo

0.0 1.0 2.0 3.0-1.0-2.0-3.0Strain (%)

0.0

50

100

150

200

250

Str

ain

ener

gy, E

s /MJ·

m

L12-CoMo3, trigonal

L12-Co3Mo, tetragonalL12-CoMo3, tetragonal

(a)

(b)

A1-CoMo3

-3-1

Fig. 9 (a) Bain strain energy of L12-Co3Mo, L10-CoMo, L12-CoMo3, A1-CoMo3 and A1-Mo along a tetragonal distortion. (b) Strain energy nearthe ideal fcc-base structure.

500

1000

1500

2000

2500

3000Present, EPMAPresent, DSC

10)

21)

18)15)

19)

13)

Liq.

Co 20 40 60 80 MoMo content (mol%)

Tem

pera

ture

, T/K

A2

σ

μA1para

D019

A1ferro

800

1000

1200

1400

1600

1800

Co 10 20 30 40 50Mo content (mol%)

Tem

pera

ture

, T/K μA3para

D019

Liq.

A1para

A1ferro

(a)

(b)

Tc A1

Fig. 10 Calculated phase diagrams of the Co­W system compared withexperimental data: (a) whole system and (b) Co-rich corner.

K. Oikawa et al.1432

Figures 10(a) and 10(b) show the calculated Co­Mo phasediagrams using model II for the ® phase in comparison withvarious experimental data. It can be seen that most of thepresent experimental phase equilibria data are reproduced.The solubility of Mo in the Co-rich A1 phase shows anabrupt decrease with decreasing temperature following thephase separation into the ferromagnetic and paramagnetic A1phase as a result of the magnetic contribution to the Gibbs

energy.24,39­44) This kind of phase separation is observed insystems exhibiting a very strong compositional dependenceof TC. Table 6 gives the comparisons of all invariant reactionsfrom the present calculation, a previous calculation24) andhandbook evaluation.22) The A3para stable temperature regionwas determined in great detail in the present work and it wasfound that the temperatures of invariant reactions with the A3phase differ significantly from those reported earlier.

Table 5 Optimized thermodynamic parameters for the Co­Mo system.

Phase Model Evaluated parameters (J/mol)

Liquid (Co,Mo)

0Lliq:Co,Mo ¼ �34999þ 9:232T

1Lliq:Co,Mo ¼ �22999þ 10:782T

2Lliq:Co,Mo ¼ �11606þ 0:829T

A1(fcc),L12-Co3Mo,L10-CoMoL12-CoMo3

(Co,Mo)(Co,Mo).25(Co,Mo),25(Co,Mo).25

(Co,Mo).25

¯ð1ÞCo:Mo ¼ �2223:9þ 0:6237T

¡Co3Mo ¼ �1334:8þ 1:1104T

TA1C ¼ 1396xCo þ ð�3250� 4796ðxCo � xMoÞ

� 813ðxCo � xMoÞ2 þ 5699ðxCo � xMoÞ3ÞxCoxMo

¢A1 ¼ 1:35xCo þ ð�2:927� 4:769ðxCo � xMoÞ� 4:549ðxCo � xMoÞ2 þ 1:014ðxCo � xMoÞ3ÞxCoxMo

A2(bcc) (Co,Mo)0LA2

Co,Mo ¼ þ41370� 5:811T0TA2

CCo,Mo¼ �3700; 0¢A2Co,Mo ¼ �3:445

A3(hcp) (Co,Mo)

0LA3Co,Mo ¼ �31023þ 20:406T

1LA3Co,Mo ¼ �28717þ 0:690T

2LA3Co,Mo ¼ þ28845� 4:530T

TA3C ¼ 1396xCo þ ð�3730� 3899ðxCo � xMoÞ

þ 1323ðxCo � xMoÞ2 þ 5289ðxCo � xMoÞ3ÞxCoxMo

¢A3 ¼ 1:35xCo þ ð�2:927� 4:769ðxCo � xMoÞ� 4:549ðxCo � xMoÞ2 þ 1:014ðxCo � xMoÞ3ÞxCoxMo

® (Co,Mo)7Mo2(Co,Mo)4, model I

�G®Co:Mo:Co ¼ GMUAAþ 7GCOFCCþ 2GHSERMOþ 4GCOBCC

�G®Mo:Mo:Co ¼ GMUBAþ 7GMOFCCþ 2GHSERMOþ 4GCOBCC

�G®Co:Mo:Mo ¼ GMUABþ 7GCOFCCþ 6GHSERMO

�G®Mo:Mo:Mo ¼ GMUBBþ 7GMOFCCþ 6GHSERMO

0L®Co,Mo:Mo:Co ¼ 0L®

Co,Mo:Mo:Mo ¼ þ16984þ 19:999T0L®

Co:Mo:Co,MO ¼ 0L®Mo:Mo:Co,Mo ¼ þ119362þ 1:279T

GMUAA ¼ �106572þ 29:803T

GMUAB ¼ �118425þ 14:107T

GMUAB ¼ GMUAAþ GMUBBþ GMUAB

GMUBB ¼ 65000

® (Co,Mo)Mo4(Co,Mo)2(Co,Mo)6, model II

�G®Mo:Mo:Mo:Mo ¼ 13GMOMUþ 13GHSERMO

�G®Co:Mo:Mo:Mo ¼ 13GMOMUþGHSERCOþ 12GHSERMO

�G®Mo:Mo:Co:Mo ¼ 13GMOMUþ 2GSERCOþ 11GHSERMO

�G®Co:Mo:Co:Mo ¼ 13GMOMUþ 3GSERCOþ 10GHSERMO

�G®Mo:Mo:Mo:Co ¼ �73323� 7:5305T þ 6GSERCOþ 7GHSERMO

�G®Co:Mo:Mo:Co ¼ �121413þ 13:649T þ 7GSERCOþ 6GHSERMO

�G®Mo:Mo:Co:Co ¼ þ8GSERCOþ 5GHSERMO

�G®Co:Mo:Co:Co ¼ �93471þ 22:453T þ 7GSERCOþ 6GHSERMO

GMOMU ¼ 30000

· (Co)8Mo4(Co,Mo)18

�G·Co:Mo:Co ¼ 923210þ 356:573T þ 26GHSERCOþ 4GHSERMO

�G·Co:Mo:Mo ¼ 1656� 39:930T þ 8GHSERCOþ 22GHSERMO

0L·Co:Mo:Co,Mo ¼ �217513þ 64:202T

D019 Co3Mo �GD019Co:Mo ¼ �48375þ 18:434T þ 3GHSERCOþGHSERMO

Others Ref. 33)GHSERCO ¼

þ310:241þ 133:36601T � 25:0861T lnðT Þ � 0:002654739T 2

�1:7348 � 10�7T 3 þ 72527=T ð298:15 � T < 1768Þ�17197:666þ 253:28374T � 40:5T lnðT Þ þ 9:3488 � 1030T�9 ð1768 � T < 6000Þ

GHSERMO ¼�7746:302þ 131:9197T � 23:56414T lnðT Þ � 0:003443396T 2

þ5:66283 � 10�7T 3 þ 65812=T � 1:30927 � 10�10T 4 ð298:15 � T < 2896Þ�30556:41þ 283:559746T � 42:63829T lnðT Þ � 4:849315 � 1033T�9 ð2896 � T < 5000Þ

GCOFCC ¼ þ427:59� 0:615248T þ GHSERCO

GMOFCC ¼ þ15200þ 0:63T þ GHSERMO

GCOBCC ¼ þ2938� 0:7138T þ GHSERCO

Experimental Determination and Thermodynamic Assessment of Phase Equilibria in the Co­Mo System 1433

The metastable fcc-based phase diagram, including theorder­disorder transitions, is shown in Fig. 11. There are noexperimental data except for the A1 phase in the Co-richregion; however, for extrapolations to higher-order systems forCo-base £/£A superalloys knowledge of the stability of theseordered phase is important. The predicted maximum of theA1/L12 order­disorder transition temperature is about 580Kwhich is significantly lower than the 1349K order­disordertransition temperature of the ternary L12-Co3(Al,W).54) There-fore, addition Mo appears to decrease the order­disordertransiton temperature of the Co3(Al,W).1) A miscibility gapin the paramagnetic A1 phase is also predicted in the Mo-rich region. This is in agreement with the positive formationenergy of the L12-CoMo3 phase from the ab initio calculationwhen the SGTE lattice stabilities of the pure elements33) areused as reference states (Fig. 8). However, this formationenergy was not used in the thermodynamic assessment.

Figure 12 shows the calculated formation enthalpies at298K as a function of composition. The calculated values arein poor agreement with the values recommended in Ref. 45).According to Ref. 24), these values should be considered lessreliable because they were derived from emf data17,20) thatdisagree with the accepted phase boundary data.

The calculated and experimental site fractions36) for the ®

phase using model II are plotted in Fig. 13. On deviationfrom the ideal stoichiometry to the Co-rich side, Mo on site6c3 is replaced by Co, while on deviation to the Mo-rich side,

Co is first replaced by Mo on site 3a and then on site 18h.This site occupancy behavior is similar to the experimentalresults. The comparison of the calculated phase diagrams nearthe ® phase stable region using the models I and II for the ®phase and the result from the previous calculation24) is shownin Fig. 14. The phase boundaries obtained by using model Ifor the ® phase are in poor agreement with the experimentaldata compared that of model II. The results from the previouscalculation also using model I are also in poor agreementwith the experimental data. In model I, sites 3a and 18hand sites 6c2 and 6c3 are assumed to have the same siteoccupation. This assumption is in disagreement with theexperimentally observed site occupancy behavior and has asignificant effect on the mixing entropy. Therefore, model IIis preferred to describe the ® phase of the Co­Mo system.

6. Conclusions

The phase equilibria of the Co­Mo system were inves-tigated experimentally and thermodynamically with ab initio

-6

-5

-4

-3

-2

-1

0

For

mat

ion

enth

alpy

, ΔH

/kJ·

mol

-1

45) 298 Kab-initio

Co 20 40 60 80 MoMo content (mol%)

D019

σ

μ

Fig. 12 Calculated and estimated formation enthalpy at 298K.

200

400

600

800

1000

1200

1400

1600

Co 20 40 60 80 MoMo content (mol%)

Tem

pera

ture

, T/K

A1ferro

A1para

L12

L10

A1para+A1para1 2

Tc A1

Present, EPMAPresent, TC

A1

Fig. 11 Calculated phase diagram for fcc-base phases with all other phasessuspended from the calculation.

Table 6 Invariant reaction temperatures in the Co­Mo system.

Invariant reaction Present (K) Ref. 22) (K) Ref. 24) (K)

Liquid +A2 = · 1893 1893 1893

Liquid + · = ® 1783 1783 1783

Liquid = A1para + ® 1614 1608 1608

A1para + ® = A3para 1573 1473 1473

A3para + ® = D019 1322 1298 1319

A3para = A1para + D019 1267 1291 1291

A1para = A1ferro + D019 1170 ® 1143

· = ® + A2 830 1273 1273

A1ferro + D019 = A3ferro 691 973 805

0

0.2

0.4

0.6

0.8

1.0

Mo

site

frac

tion

30 40 50 60 70

3a6c16c26c318h

Mo content (mol%)

18h

3a

6c3 homogeneous range of μ phase

Ref. 36)

idealstoichiometry

Fig. 13 Experimental and calculated site fractions for the ® phase at1273K.

K. Oikawa et al.1434

and CALPHAD calculations. The stable temperature regionof the A3 phase has been determined in great detail. Theperitectoid A1 + ® § A3 reaction is 100K higher comparedto the phase diagram compiled in Ref. 22).

The thermodynamic assessment of the present experimen-tal data was performed with help of the results from theab initio calculations. The calculated results reproduce thecharacteristic features of the experimental phase diagramwell. The calculated metastable fcc-base phase diagram usinga four-sublattice model is also reasonable. It was found thatthe four-sublattice model is better suited than the conven-tional three-sublattice thermodynamic model for the ® phase.The new set of parameters can be used for estimating thestability of the L12-£A phase in Co-base £/£A superalloys.

Acknowledgement

The authors wish to thank the excellent young researchersoverseas visit program of JSPS for its support.

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800

900

1000

1100

1200

1300

1400

1500

1600

1700

1800

0.3 0.4 0.5 0.6 0.7

Present, EPMAPresent, DSC

10)

18)15)

μ

σLiq.

model IImodel I

Mo content (mol%)

Tem

pera

ture

, T/K

D019+μ

A3para+μ

Ref. 24)

Fig. 14 Calculated phase diagrams in the vicinity of the ® phase. Brokenlines and solid lines are phase boundaries from using the models I and II,respectively. The results from the previous assessment result24) are shownas dashed line.

Experimental Determination and Thermodynamic Assessment of Phase Equilibria in the Co­Mo System 1435