Mobilities and diffusivities in fcc Co–X (X=Ag, Au, Cu, Pd and Pt) alloys

CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 33 (2009) 695–703

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Mobilities and diffusivities in fcc Co–X (X = Ag, Au, Cu, Pd and Pt) alloys Yajun Liu a,∗ , Dong Liang b , Yong Du c , Lijun Zhang c , Di Yu d a

Western Transportation Institute, Montana State University, Bozeman, MT, 59715, USA

b

DNV Columbus, Dublin, OH, 43017, USA State Key Laboratory of Powder Metallurgy, Central South University, Changsha, Hunan, 410083, PR China

c d

American Water Chemicals Inc., Tampa, FL, 33619, USA

article

info

Article history: Received 13 July 2009 Received in revised form 2 September 2009 Accepted 3 September 2009 Available online 17 September 2009 Keywords: Diffusion Mobility Fcc Co alloys CALPHAD Dictra

abstract The mobilities and diffusivities in fcc Co–X (X = Ag, Au, Cu, Pd and Pt) alloys have been critically assessed by the CALPHAD method, based on the reported experimental data and published thermodynamic parameters. The atomic mobilities are expressed as functions of temperature and compositions in the CALPHAD format. Comprehensive comparisons between the calculated and measured diffusivities, such as self-diffusivities, impurity diffusivities, intrinsic diffusivities, and interdiffusivities, are made, where the proposed mobility parameters for Ag, Au, Co, Cu, Pd and Pt enable most of the experimental values to be reproduced. The effect of magnetic ordering on diffusion in fcc Co–Pd and Co–Pt alloys is discussed. This work contributes to the establishment of a Co mobility database, which can aid the computational study of microstructure evolution in Co-based alloys at high temperatures. Published by Elsevier Ltd

1. Introduction In recent years, there has been an increasing demand for novel high-temperature alloys that feature a combination of hightemperate strength, high-melting points, high toughness, excellent thermal fatigue resistance, and good oxidation resistance [1]. New Co-based alloys satisfy such requirements, and have been successfully utilized as structural materials in gas turbines [2,3]. Although Co-based alloys have not been widely used in high-temperature applications, they show a larger high-temperature strength than Ni-based alloys [4]. Designing Co-based alloys entails an in-depth understanding of their thermodynamic and kinetic behaviors. Inspired by the thermodynamic achievements in CALPHAD, Andersson and Ågren [5] proposed an efficient way to study mobilities in substitutional solution phases, where the activation enthalpies and the logarithm of the frequency factors for tracer diffusion coefficients are expanded in terms of the Redlick–Kister polynomials. The mobility end-members and interaction parameters are obtained through inverse parameterization on experimental data, in conjunction with the CALPHAD-based thermodynamic descriptions [6–8]. Such an elegant method provides a convenient means of studying kinetic properties for complex systems, where phase transformations of stable and metastable phases in multicomponent alloys are

∗

Corresponding author. Tel.: +1 404 513 1544. E-mail addresses: [email protected], [email protected] (Y. Liu).

0364-5916/$ – see front matter. Published by Elsevier Ltd doi:10.1016/j.calphad.2009.09.001

present [9]. Among many binary fcc alloys containing Co, only the atomic mobilities for Co–Fe and Co–Ni binaries have been evaluated [10]. Accordingly, this work aims to assess the mobilities and diffusivities in fcc Co–X (X = Ag, Au, Cu, Pd and Pt) alloys and to provide further insights into diffusion behaviors by computational studies. 2. Model description For an n-component system where the nth element is chosen as the dependent element, the temporal and spatial evolution of element i in a substitutional solution phase is governed by the mass-conservation law as:

∂ Ci + ∇ · Ji = 0 ∂t

(1)

where Ci is the volume concentration of element i; Ji is the interdiffusion flux of element i given by: Ji = −

X

Dnij ∇ Cj

(2)

j

where Dnij is the interdiffusion coefficient expressed as [5,11]: Dnij

  X ∂µk ∂µk = (δik − xi )xk Mk − ∂ xj ∂ xn k

(3)

where δik is the Kronecker delta; xk and µk are the mole fraction and the chemical potential of element k, respectively; Mk is the atomic mobility of element k.

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Neglecting the ferromagnetic contribution in fcc alloys, the mobility for element k can be divided into a frequency factor, Mk0 , and an activation enthalpy, Qk∗ , by [11–13]: Mk =



1 RT

exp

−Qk + RT ln(

Mk0

∗

)



1

=

RT

RT

 exp

Φk



RT

(4)

where R is the gas constant; T is the temperature; Φk is a composition-dependent property that can be expressed by the Redlick–Kister polynomials as below [11–13]:

Φk =

X

xi Φki

XX

+

i

xi xj

" X

j >i

i

r

i ,j Φk

# (xi − xj )

r

(5)

r

i ,j

where Φki and r Φk are the mobility parameters for the endmembers and the interactions, respectively. The tracer diffusion coefficient of element i, denoted by D∗i , can be related to its atomic mobility by [11–13]: Di = RTMi . ∗

(6)

The intrinsic diffusion coefficient of element i in response to the concentration gradient of element j, denoted by I Dnij , can be related to its mobility through: I

Dnij = xi Mi



∂µi ∂µi − ∂ xj ∂ xn



.

(7)

For a substitutional solution, the chemical potential of element i is evaluated through:

µi = Gm +

∂ Gm X ∂ Gm xk − ∂ xi ∂ xk k

(8)

where Gm is the molar Gibbs free energy expressed by: Gm =

X

xi 0 Gi + RT

X

xi ln xi + ex Gm + mag Gm

(9)

i

i

where 0 Gi is the molar Gibbs free energy of pure element i; ex Gm is the excess Gibbs free energy; mag Gm stands for the magnetic effect defined by: mag

Gm = RT ln(1 + β)f (τ )

(10)

where τ is given as τ = T /TC with TC being the Curie temperature for ferromagnetic ordering of Co; β is the mean atomic moment. The term f (τ ) is expressed by the following polynomials [14]: f (τ ) = 1 −

 × f (τ ) = −

1 A

1

"

A

τ3 6



79τ −1 140p

+

τ −5 10

τ9 135

+

+ +

τ −15 315

474 497

τ 15

(p−1 − 1) #

for τ < 1

600

+

τ −25 1500

(11)

3.2. The Co–Au system With Co vapor-deposited on Au polycrystals, Fogelson et al. [17] measured the impurity diffusion coefficients of Co in fcc Au from 973 to 1323 K by diffraction analysis. Herzig et al. [18] investigated the impurity diffusion coefficients of 57 Co in fcc Au single crystals from 1030 to 1335 K by microtome sectioning. Duhl et al. [19] applied electroplated 60 Co to measure the impurity diffusion coefficients of Co in fcc polycrystalline Au from 975 to 1221 K by means of the residual activity method. There has been no reported experimental data on the impurity diffusion coefficients of Au in fcc Co in the literature. Although an appreciable solubility exists in both Co-rich and Au-rich fcc solid solutions, related interdiffusion coefficients, intrinsic diffusion coefficients and concentration curves in diffusion couples have not been well established. 3.3. The Co–Cu system The impurity diffusion coefficients of Co in fcc Cu have been extensively studied. Employing 60 Co and lathe sectioning, Mackliet [20] investigated the impurity diffusion coefficients of Co in fcc Cu single crystals from 975 to 1351 K. With 60 Co, Döhl et al. [21] measured the impurity diffusion coefficients of Co in fcc Cu single crystals from 640 to 848 K by sputter sectioning and secondary ion mass spectrometry (SIMS) analysis. Using 60 Co, Sakamoto [22] carried out experiments on diffusion of Co into fcc Cu single crystals from 973 to 1223 K, where the samples were sectioned on a precession lathe and analyzed by counting technique. Kuzmenko et al. [23] investigated the impurity diffusion of 60 Co in fcc Cu from 973 to 1223 K, where the activated layer in each sample was mechanically removed and the thickness was determined by weighting on a microbalance. The dependence of the integral activity on depth was then constructed for diffusion analysis. Badrinarayanan and Mathur [24] studied the impurity diffusion coefficients of 60 Co in polycrystalline Cu by lathe sectioning from 1163 to 1306 K. Arita et al. [25] reported the diffusion of Cu in Co and Co–Cu alloys with solid–liquid diffusion couples at 1158 and 1273 K, where the liquid phase consisted of Cu and Ag. The electron probe microanalysis (EPMA) yielded penetration profiles of Cu in Co and Co–Cu alloys. Most of the reported diffusivities were for Cu-Co alloys with less than 3 at.% Cu. As such, those values can be treated as impurity diffusion coefficients, as practiced in the compilation of Mehrer [26]. Bruni and Christian [27] carried out the interdiffusion study with diffusion couples made of pure Co and pure Cu, which were annealed at temperatures from 1073 to 1346 K, and then characterized by EPMA. A modified form of Hall’s method was used to extract interdiffusivities at each temperature. 3.4. The Co–Pd system



for τ ≥ 1

(12)

where A = (518/1125) + (11692/15975)(p−1 − 1); p = 0.28 for fcc phases. 3. Experimental information 3.1. The Co–Ag system Bernardini and Cabané [15] studied the impurity diffusion of Co in fcc Ag single crystals from 973 to 1214 K, where the diffusion coefficients were determined by 60 Co with the electrolytical sectioning method. Using 58 Co and 60 Co isotopes on Ag single crystals and lapping with SiC papers, Lundy and Padgett [16] determined the impurity diffusion coefficients of Co in fcc Ag at 1200 K. There has been no report in literature on the impurity diffusion coefficients of Ag in fcc Co.

Using 103 Pd and 112 Pd isotopes, Peterson [28] measured the Pd self-diffusion coefficients from 1323 to 1773 K in Pd single crystals by mechanical sectioning. Fillon and Calais [29] investigated the 103 Pd self-diffusion coefficients from 1373 to 1523 K in polycrystalline Pd by the grinder sectioning method. Iijima and Hirano [30] measured the interdiffusion coefficients and intrinsic diffusion coefficients in fcc Co–Pd alloys. The Co/Pd diffusion couples were annealed at temperatures from 1153 to 1466 K, after which Balluffi’s method was employed to determine the interdiffusion coefficients. The displacements of Kirkendall markers were also studied, which were found to move towards the Co-rich side. Formation of voids on the Co-rich side was also detected. The intrinsic diffusion coefficients of Co and Pd on the Kirkendall plane at 1422 K were obtained by Darken’s analysis. Borovskiy et al. [31] investigated interdiffusion in fcc Co–Pd alloys by means of Co/Pd diffusion couples at 1423, 1373 and 1318 K. The concentration profiles were obtained by EPMA along the diffusion

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Table 1 Mobility parameters for Ag, Au, Co, Cu, Pd and Pt in fcc Co–X (X = Ag, Au, Cu, Pd and Pt) alloys (all in SI units). Phase

Model

Mobility

Parameters

Ag

ΦAg = −175892 − 93.50 T [42] Co Co ΦAg = ΦCo

Au

Au ΦAu = −176600 − 95.70 T [43] Co Co ΦAu = ΦCo

Ag

Cu ΦCu = −205872 − 82.53 T [42]

Cu

Co ΦCu = −275013 − 76.57 T 0

fcc

(Co, X)1 (Va)1

Co,Cu ΦCu = −89735.64

Co ΦCo = −296542.9 − 74.48 T [44] Cu ΦCo = −215759.29 − 80.35 T 0

Co

Co,Cu ΦCo = −117927.63 Ag

ΦCo = −198811.70 − 74.63 T Au ΦCo = −180655.55 − 91.45 T Pd ΦCo = −258375.24 − 91.37 T 0

Co,Pd ΦCo = 269685.06 − 70.46 T

1

Co,Pd ΦCo = 101371.92

Fig. 1. Calculated Co–Ag binary phase diagram according to the thermodynamic description of Zhu et al. [37].

Pt ΦCo = −262032.12 − 91.78 T

Pd

Pt

0

Co,Pt ΦCo = 71480.84 − 27.30 T

1

Co,Pt ΦCo = 97350.42

Pd ΦPd = −279931.89 − 79.51 T Co ΦPd = −256834.22 − 92.36 T 0

Co,Pd ΦPd = 12011.65 − 35.60 T

1

Co,Pd ΦPd = 127298.30

Pt ΦPt = −261426.93 − 99.17 T [45] Co ΦPt = −283931.89 − 79.51 T 0

Co,Pt ΦPt = −48888.16 − 32.95 T

1

Co,Pt ΦPt = 16184.32

Note: (a) Mobility parameters for self-diffusion of Ag, Au, Co, Cu and Pt are taken from Refs. [42–45]. (b) Due to the lack of more experimental data, the underlined relations are assumed in this work.

direction, and the interdiffusion coefficients were evaluated by the Boltzmann–Matano method. 3.5. The Co–Pt system Million and Kučera [32] applied 193m Pt to measure the impurity diffusion coefficients of Pt in fcc Co polycrystals from 1354 to 1481 K by means of the residual activity method. Employing 57 Co and the surface decrease method, Kučera and Zemčik [33] reported the impurity diffusion coefficients of Co in fcc Pt polycrystals from 1023 to 1323 K. Iijima et al. [34] studied the interdiffusion in fcc Co–Pt alloys from 1271 to 1673 K within the whole composition range. The Co/Pt diffusion couples were annealed in a quartz tube with argon gas, after which the samples were crossed sectioned, polished and characterized by EPMA along the diffusion direction. The interdiffusion coefficients were calculated by Matano’s method. For

Fig. 2. Calculated and experimentally measured temperature dependence of impurity diffusion coefficients of Co in fcc Ag.

all the temperatures investigated, it was found that the interdiffusion coefficients increase up to about 40 at.% Pt, beyond which they decrease gradually. The movement of Kirkendall markers towards the Co-rich side and the formation of voids in that region were also observed. The intrinsic diffusion coefficients for Co and Pt on the Kirkendall plane, characterized by 21 at.% Pt, were reported. Borovskiy et al. [35] investigated the interdiffusion in the binary Co–Pt system by Co/Pt diffusion couples. Diffusion annealing was undertaken at 1573, 1523, 1473, and 1398 K, respectively, after which the diffusion couples were characterized by the Boltzmann–Matano analysis with the aid of EPMA. 4. Results and discussion Dictra is a software package that works within the CALPHAD frame, which simultaneously couples the thermodynamic and mobility parameters to explore complex kinetic behaviors [36]. The

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Fig. 3. Calculated Co–Au binary phase diagram according to the thermodynamic description of Okamoto et al. [38].

Fig. 5. Calculated Co–Cu binary phase diagram according to the thermodynamic description of Turchanin and Agraval [39].

Fig. 4. Calculated and experimentally measured temperature dependence of impurity diffusion coefficients of Co in fcc Au.

Fig. 6. Calculated and experimentally measured temperature dependence of impurity diffusion coefficients of Co in fcc Cu.

Parrot module in Dictra serves as a convenient means of performing inverse studies to derive atomic mobilities from kinetic quantities, such as self-diffusion coefficients, impurity diffusion coefficients, tracer diffusion coefficients, intrinsic diffusion coefficients and interdiffusion coefficients. In this work, the thermodynamic parameters for the Co–Ag, Co–Au, Co–Cu, Co–Pd and Co–Pt binary systems are taken from the assessments of Zhu et al. [37], Okamoto et al. [38], Turchanin and Agraval [39], Ghosh et al. [40], and Oikawa et al. [41], respectively. The mobility parameters for the self-diffusion coefficients in fcc Ag, Au, Co and Pt are taken from the earlier works on the Ti–Ni–Ag [42], Au–Ni [43], Co–Si [44] and Cu–Pt [45] binary systems, respectively. The mobility endmembers and the interaction parameters obtained in this work are tabulated in Table 1, where the published mobility end-members adopted in this work are also given for convenience.

4.1. The Co–Ag system The calculated Co–Ag binary phase diagram according to the thermodynamic assessment of Zhu et al. [37] is given in Fig. 1, which shows an immiscible behavior between fcc Ag and fcc Co. The calculated and measured impurity diffusion coefficients of Co in fcc Ag are presented in Fig. 2, where the logarithm values are plotted against reciprocal temperature. The results follow the traditional Arrhenius behavior, which is manifested by a straight line in the current plot. There are no experimental data reported on the impurity diffusion of Ag in fcc Co. Following the CALPHAD practice in constructing a general mobility database, the mobility end-member of Ag in fcc Co is set to be the same as that of Co in fcc Co [11].

Y. Liu et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 33 (2009) 695–703

Fig. 7. Calculated and experimentally measured temperature dependence of impurity diffusion coefficients of Cu in fcc Co.

Fig. 8. Calculated and experimentally measured interdiffusion coefficients in dilute Co–Cu alloys at various temperatures.

4.2. The Co–Au system The calculated Co–Au binary phase diagram according to the thermodynamic description of Okamoto et al. [38] is presented in Fig. 3, which shows an appreciable solubility for the fcc phase at high temperatures, compared with the Co–Ag binary phase diagram. The calculated and measured impurity diffusion coefficients of Co in fcc Au are given in Fig. 4, where the experimental data from Fogelson et al. [17], Herzig et al. [18], and Duhl et al. [19] are selfconsistent. The good agreement between the calculated and experimentally measured values is evident, which qualifies the mobility end-member of Co in fcc Au obtained in this work. The experimental information on the impurity diffusion coefficients of Au in fcc Co has not been reported, and the mobility end-member of Au in fcc Co is set to the same as that of Co in fcc Co. In addition, such is the case for the interdiffusion coefficients in this binary system.

699

Fig. 9. Calculated Co–Pd binary phase diagram according to the thermodynamic description of Ghosh et al. [40].

Fig. 10. Calculated thermodynamic factors at various temperatures for fcc Co–Pd alloys.

Accordingly, the interaction parameters for both elements are not considered in this work. 4.3. The Co–Cu system The calculated Co–Cu binary phase diagram according to the thermodynamic description of Turchanin and Agraval [39] is illustrated in Fig. 5, which shows a larger solubility in Co-rich fcc solution at high temperatures, compared with the Co–Au phase diagram. The calculated and experimentally measured impurity diffusion coefficients of Co in fcc Cu are given in Fig. 6, where the experimental values from various authors are pretty consistent. The calculated impurity diffusion coefficients of Cu in fcc Co are presented in Fig. 7, along with the experimental values from Arita et al. [25]. The interdiffusion coefficients measured by Bruni and Christian [27] are plotted in Fig. 8 for 1345, 1314, 1288, 1225, 1172, 1128 and 1072 K, together with the calculated values at

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Fig. 11. Calculated and experimentally measured temperature dependence of selfdiffusion coefficients of Pd in fcc Pd.

Fig. 12. Calculated and experimentally measured intrinsic diffusion coefficients and interdiffusion coefficients in fcc Co–Pd alloys.

such temperatures. There exists an acceptable agreement between the calculated and experimentally measured values in Fig. 8. As is evident, the interdiffusion coefficients generally decrease with the Co content within the investigated composition range, which is consistent with the increase of the solidus temperature in Fig. 5 around the Cu-rich side.

Fig. 13. Calculated and experimentally measured interdiffusion coefficients in fcc Co–Pd alloys at various temperatures.

Fig. 14. Calculated and experimentally measured Co concentration profile in a Co/Pd diffusion couple.

miscibility gap near such a region, it may have a negligible effect on the mobility assessment as the mutual and intrinsic diffusion coefficients utilized in this work are all measured above 1200 K. The fcc phase features a continuous solid solution across the whole composition range, in which the thermodynamic factor can be defined by [46]:

4.4. The Co–Pd system F = The calculated Co–Pd binary phase diagram according to the thermodynamic description of Ghosh et al. [40] is given in Fig. 9, where the liquidus curve shows a significant concave nature, and there exists a congruent transformation around 40 at.% Pd. In the assessment by Ghosh et al. [40], the hcp phase was not taken into consideration. As such, such a phase is not utilized for Fig. 9. The calculated Co–Pd binary phase diagram is thus a metastable one at low temperatures near the Co side. Although there exists a

xCo ∂µCo RT ∂ xCo

.

(13)

The calculated thermodynamic factors for various temperatures are plotted in Fig. 10, and the discontinuous jumps are evident for 1200, 1000 and 800 K, which characterize the critical limits for paramagnetic and ferromagnetic states in fcc solid solutions. The calculated and experimentally measured self-diffusion coefficients of Pd in fcc Pd are given in Fig. 11, where the experimental results from Peterson [28], and Fillon and Calais [29] are also

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701

Fig. 15. Calculated Co–Pt binary phase diagram according to the thermodynamic description of Oikawa et al. [41].

Fig. 17. Calculated and experimentally measured/extrapolated temperature dependence of impurity diffusion coefficients of Pt in fcc Co.

Fig. 16. Calculated thermodynamic factors at various temperatures for fcc Co–Pt alloys.

Fig. 18. Calculated and experimentally measured/extrapolated temperature dependence of impurity diffusion coefficients of Co in fcc Pt.

superimposed. The calculated intrinsic diffusion coefficients of Co and Pd for 1422 K are given in Fig. 12, together with the experimental values from Iijima and Hirano [30]. As is evident, the Co intrinsic diffusion coefficients are generally greater than the Pd intrinsic diffusion coefficients except the Co-rich side at 1422 K. In bcc metals and alloys, it was found that the temperature dependence of self-diffusion coefficients, impurity diffusion coefficients, tracer diffusion coefficients in ferromagnetic materials deviates from the Arrhenius relationship near the Curie temperature [47]. In the current CALPHAD treatment, the magnetic ordering effect on atomic mobilities in fcc phases is not considered due to the negligible influence [47]. However, the interdiffuson coefficients depend on both the atomic mobilities and the thermodynamic factors, which enables the interdiffusion coefficients to be affected by the magnetic ordering through the thermodynamic part. As such, the interdiffusion coefficients below the Curie temperature are lower than those extrapolated from the paramagnetic

region. The calculated and experimentally measured interdiffusion coefficients at various temperatures are provided in Fig. 13, where the discontinuous jumps on the curves for 1278 and 1223 K correspond to the location of the Tc line in Fig. 9. As is evident, the calculated curves and the experimental data are self-consistent around the pure Co part for 1466, 1422 and 1388 K. However, relatively large discrepancies exist around this portion for 1323, 1278 and 1223 K, which are still present even if the magnetic contribution has been removed. As such, more experiments will be needed to refine the diffusion coefficients around this region. The calculated Co composition profile in a Co/Pd diffusion couple and the corresponding experimental data from Borovskiy et al. [31] are shown in Fig. 14, where the initial alloy configuration, annealing time and temperature are also superimposed. The measured and calculated curves are generally in accordance with each other. As can be expected, the concentration curve features an almost symmetric characteristic around the Matano plane, which is typical for the

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Y. Liu et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 33 (2009) 695–703

Fig. 19. Calculated and experimentally measured intrinsic diffusion coefficients and interdiffusion coefficients in fcc Co–Pt alloys.

Fig. 21. Calculated and experimentally measured interdiffusion coefficients in fcc Co–Pt alloys at various temperatures.

Fig. 20. Calculated and experimentally measured intrinsic diffusion coefficients and interdiffusion coefficients in fcc Co-21 at.% Pt alloy.

interdiffusion coefficients that show an almost symmetric composition dependence with respect to xPd = 0.6. 4.5. The Co–Pt system The calculated Co–Pt binary phase diagram according to the thermodynamic assessment of Oikawa et al. [41] is presented in Fig. 15, where the fcc phase features a continuous solid solution. The ordered phases at low temperatures and the hcp phase were not considered by Oikawa et al. [41] in their assessment. Accordingly, such phases are not present in Fig. 15. The thermodynamic factors calculated with Eq. (13) for 1600 and 1200 K are given in Fig. 16, and are greater than unity except around the two concentration limits, indicating a stable structure at such temperatures. The calculated impurity diffusion coefficients of Pt in fcc Co are presented in Fig. 17, along with the experimental data from

Fig. 22. Calculated and experimentally measured interdiffusion coefficients in fcc Co–Pt alloys at various temperatures.

Million and Kučera [32] and the extrapolated values from the interdiffusion coefficients of Iijima et al. [34] at xPt → 0. As is evident, the extrapolated impurity diffusion coefficients and the experimentally measured ones are generally consistent. A similar scenario exists in Fig. 18, where the experimental impurity diffusion coefficients of Co in fcc Pt from Kučera and Zemčik [33] and the extrapolated values from the interdiffusion coefficients of Iijima et al. [34] at xPt → 1 are given. The calculated and experimentally measured intrinsic diffusion coefficients of Co and Pt and the interdiffusion coefficients are given in Figs. 19 and 20, where Co atoms generally diffuse faster than Pt atoms. The interdiffusion coefficients measured by Iijima et al. [34] and Borovskiy et al. [35] are presented in Figs. 21 and 22, respectively,

Y. Liu et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 33 (2009) 695–703

along with the calculated results. The presently obtained mobility parameters are in favor of the interdiffusion coefficients measured by Iijima et al. [34] in Fig. 21. The calculated results in Fig. 22 show a large deviation from the experimental data at 1573 and 1523 K, as those experimental values suffer from a good extrapolation ability to derive impurity diffusion coefficients at both temperatures.

[12] [13] [14] [15] [16] [17]

5. Conclusions

[19] [20] [21] [22] [23]

Based on the various kinds of diffusion coefficients and thermodynamic descriptions reported in the literature, the atomic mobilities in fcc Co–X (X = Ag, Au, Cu, Pd and Pt) alloys are critically assessed with the CALPHAD method. The atomic mobilities derived in this work enable a great majority of the experimental data to be reproduced, including self-diffusion coefficients, impurity diffusion coefficients, intrinsic diffusion coefficients and interdiffusion coefficients. The effect of magnetic ordering on the interdiffusion coefficients for fcc alloys is discussed. In addition, a Co/Pd diffusion couple is computationally studied, and the calculated Co distribution curve is generally consistent with the reported values. Appendix. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.calphad.2009.09.001. References

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