Thermodynamic description of the Al–Ge–Ni system over the whole composition and temperature ranges

CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 58 (2017) 138–150

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Thermodynamic description of the Al–Ge–Ni system over the whole composition and temperature ranges Chenyang Zhou, Jiaxin Cui, Cuiping Guo, Changrong Li, Zhenmin Du

MARK

⁎

Department of Materials Science and Engineering, University of Science and Technology Beijing, Beijing 100083, PR China

A R T I C L E I N F O

A BS T RAC T

Keywords: Al–Ge–Ni system CALPHAD method Thermodynamic modeling

The phase equilibria and thermodynamic properties of the Al–Ge–Ni system are useful for understanding the diffusion process during the transient liquid phase (TLP) bonding. In this work, the thermodynamic description of the Al–Ge–Ni system over the whole composition and temperature ranges was performed by means of the CALPHAD (CALculation of PHAse Diagrams) method. The enthalpies of mixing of the liquid phase, three isothermal sections at 973, 823, and 673 K and nine vertical sections at 10, 20, 35, 55, 60, 70, 75, and 80 at% Ni and at a constant Al:Ni ratio of 1:3 were taken into account in the present optimization work. A set of selfconsistent thermodynamic parameters of the Al–Ge–Ni system was first obtained. The liquidus projection and reaction scheme were constructed according to the thermodynamic parameters obtained in this work. The phase equilibria and thermodynamic properties calculated by the present thermodynamic description show satisfactory agreement with the available experimental information.

1. Introduction During the last few decades, Ni-based superalloys have attracted considerable attention owing to their striking properties at elevated temperatures, such as high tensile and compressive yield strength, and superior creep and corrosion resistance [1,2] and thus these alloys are extensively found in the aerospace, nuclear power, gas turbine and chemical processing industries [3]. However, conventional fusion welding process is not possible for the formation of most precipitation hardening Ni-based superalloys with a large number of Al and Ti due to their high susceptibility to heat affected zone (HAZ) cracking. TLP bonding process, first developed by Duvall et al. [4], is one of the most suitable and cost-effective bonding process of the superalloys [5] and has been widely used for jointing Ni-based superalloys [6–11]. In general, the filler materials for the TLP bonding process ideally possess low melting point and similar chemical composition in comparison to the parent materials. Germanium, forming eutectics with Al and Ni, is an ideal candidate as melting point depressant (MPD) elements. For a better understanding of diffusion processing and development of new filler materials, the detailed information about the related phase equilibria and thermodynamic properties is essential, which require reasonable thermodynamic description of the Al–Ge–Ni system. In the present work, the thermodynamic modeling of the Al–Ge–Ni system over the whole composition and temperature ranges with the

⁎

Corresponding author. E-mail address: [email protected] (Z. Du).

http://dx.doi.org/10.1016/j.calphad.2017.06.006 Received 28 March 2017; Received in revised form 23 June 2017; Accepted 24 June 2017 0364-5916/ © 2017 Elsevier Ltd. All rights reserved.

CALPHAD method is presented on the basis of the available experimental information. A set of self-consistent and reliable thermodynamic parameters of the Al–Ge–Ni system is first obtained. 2. Literature review 2.1. Al–Ge system Ansara et al. [12], McAlister and Murray [13] and Srikanth and Chattopadhyay [14] thermodynamically assessed the Al–Ge system and their calculated results were in good agreement with the available experimental data. However, the optimized thermodynamic parameters for the pure elements in their work were not completely taken from the SGTE (Scientific Group Thermodata Europe) database, which could not be easily extrapolated to the multicomponent system. In order to overcome above shortcoming and further assess the Al–Ge– Mg system, Islam et al. [15] re-optimized the Al–Ge system. So the thermodynamic description of the Al–Ge system of Islam et al. [15] is accepted and the calculated Al–Ge phase diagram is shown in Fig. 1. 2.2. Al–Ni system The thermodynamic assessment of the Al–Ni system was firstly carried out by Kaufman and Nesor [16] and revised by Ansara et al. [17], but the phase Al3Ni5 was not included in their work. Then, Du

C. Zhou et al.

CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 58 (2017) 138–150

Fig. 3. Calculated Ge–Ni phase diagram using the thermodynamic parameters from [24].

Fig. 1. Calculated Al–Ge phase diagram using the thermodynamic parameters from [15].

2.3. Ge–Ni system The thermodynamic description of the Ge–Ni system was performed by Liu et al. [23]. Fundamental consistency was shown between the experimental data and their calculated results, except for the enthalpies of formation of the compounds. Furthermore, the thermodynamic models of the compounds Ge2Ni3, Ge12Ni19, βGe3Ni5 and αGeNi3 in their work were only selected according to the homogeneity ranges. For these reasons, Jin et al. [24] determined and calculated the enthalpies of formation of the partial compounds by direct reaction calorimetry and first-principles calculations, respectively. And then they improved thermodynamic models to match with the corresponding crystal structure, and re-assessed the Ge–Ni system on the basis of the available experimental information. The thermodynamic parameters optimized by Jin et al. [24] are adopted in the present work and the calculated Ge–Ni phase diagram is presented in Fig. 3. 2.4. Al–Ge–Ni system Ochiai et al. [25] determined the solid solubility between AlNi3 and αGeNi3 by means of metallographic and X-ray diffraction (XRD) methods, and confirmed that a complete solid solution was formed at 1273 K. Yanson et al. [26] used same method as [25] to measure the isothermal section at 770 K in the Al–Ge–Ni system. A ternary phase AlGeNi4 was first found, but its crystal structure was still unknown. These early experimental information were reviewed by Villars et al. [27]. Recently, the Ni-poor part of the Al–Ge–Ni system was investigated using optical microscopic, different thermal analysis (DTA), XRD, scanning electron microscope (SEM) and electron probe microanalysis (EPMA) techniques by Reichmann et al. [28], who detected three ternary phases τ1, τ2 (Detailed information of its crystal structure was reported separately [29].) and τ3. Two isothermal sections at 973 and 673 K and three vertical sections at the Al0.90Ni0.10–Ge0.90Ni0.10, Al0.80Ni0.20–Ge0.80Ni0.20, Al0.65Ni0.35–Ge0.65Ni0.35 joints were constructed, and eleven reactions and the corresponding liquidus projection were derived. Later on, Jandl et al. [30] determined the Ni-rich part of the Al–Ge–Ni system by optical microscopic, DTA, XRD and SEM with energy dispersive X-ray spectroscopy (EDX) measurements, in which two ternary phases τ4 and τ5 were confirmed, two isothermal sections at 973 and 823 K were obtained, six vertical sections at 55, 60, 70, 75 and 80 at% Ni and at a constant Al:Ni ratio of 1:3 were determined, and four invariant reactions, the partial liquidus projec-

Fig. 2. Calculated Al–Ni phase diagram using the thermodynamic parameters from [21] after refinement.

and Clavaguera [18] considered the phase Al3Ni5, used the associate model to describe liquid phase and re-assessed the Al–Ni system, but they did not considered the order-disorder transformation between the phases fcc-A1 and fcc-L12. Later, Ansara et al. [19] used a single model to represent the transformation from the disordered phase fcc-A1 to ordered one fcc-L12 for the first time, but Huang and Chang [20] thought a single model with too many parameters was not beneficial to the establishment of the Ni-based database. However, Dupin et al. [21] disagreed with the opinion of Huang and Chang [20] because additional thermodynamic parameters were still used for the ordered phase in their work [20], and thus they revised some thermodynamic parameters on the basis of the assessment of Ansara et al. [19] to correspond with the new experimental data and also used a single function to model the disorder phase bcc-A2 and its ordered one bccB2. Recently, Wang and Cacciamani [22] introduced the Al4Ni3 phase, but it was not found in the Al–Ge–Ni system. So the thermodynamic modeling of the Al–Ni system of Dupin et al. [21] after refinement is accepted and the calculated Al–Ni phase diagram is presented in Fig. 2. Detail information of the refinement is discussed in Section 4. 139

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Table 1 Crystal structures and thermodynamic models of all phases relevant for this study. Phase

Pearson symbol

Space group

Prototype

Thermodynamic model

Ref.

Liquid Al

– cF4

– Cu

(Al,Ge,Ni)1 (Al,Ge,Ni)1Va1

– [42]

Ge Ni

cF8 cF4

C Cu

(Al,Ge,Ni)1 (Al,Ge,Ni)1Va1

[43] [44]

Al3Ni Al3Ni2 AlNi

oP16 hP5 cP2

NiAl3 Ni2Al3 CsCl

Al0.75Ni0.25 (Al,Ge)3(Al,Ni)2(Ni,Va)1 (Al,Ge,Ni,Va)0.5(Al,Ge,Ni,Va)0.5Va3

[45] [45] [46]

Al3Ni5 AlNi3

oC16 cP4

– Fm3m Fd 3m Fm3m Pnma P 3m1 Pm3m Cmmm

Pb5Ga3 Cu3Au

Al0.375Ni0.625 (Al,Ge,Ni)0.75(Al,Ge,Ni)0.75Va1

[47] [48]

GeNi αGe3Ni5 βGe3Ni5 GeNi2 Ge2Ni5 αGeNi3

oP8 mS32 hP6 oP12 hP84 cP4

MnP Ni5Ge3 NiAs Ni2Si Pd5Sb2 Cu3Au

(Al,Ge)0.5Ni0.5 Ge0.375Ni0.625 (Al,Ge)1Ni1(Ni,Va)1 Ge0.335Ni0.665 Ge0.28Ni0.72 (Al,Ge,Ni)0.75(Al,Ge,Ni)0.75Va1

[49] [49] [49] [49] [49] [49]

βGeNi3 τ1 τ2 τ3 τ4 τ5

– oC24 cI88 cF12 hP66 oP12

– CoGe2 Al15Ge4Ni3 CaF2 Ga3Ge6Ni13 Co2Si

Ge0.256Ni0.744 Al0.167Ge0.5Ni0.333 Al0.682Ge0.182Ni0.136 Al0.25Ge0.4Ni0.35 (Al,Ge)0.409Ni0.591 (Al,Ge)0.333Ni0.667

– [28] [29] [28] [30] [30]

Pm3m Pnma C121 P 63/mmc Pnma P 63/mmc Pm3m – Cmca I 43m Fm3m P3121 Pnma

3.2. Substitutional solution phases

tion and reaction scheme were derived. It should be noted that the isothermal section at 770 K determined by Yanson et al. [26] was unreasonable according to the new experimental information [28,30]. Yanson et al. [26] only reported a ternary phase τ5 near AlGeNi4. However, Reichmann et al. [28] confirmed that ternary phases τ1 and τ3 were stable at 973 and 673 K by using a combination of XRD, SEM and EPMA and concluded that these phases τ1 and τ3 were stable at 770 K on the basis of DTA data. With the same method of Reichmann et al. [28], Jandl et al. [30] also proved the existence of the ternary phase τ4 at 770 K. All above experimental information were reviewed by Raghavan [31,32]. In addition, Sudavtsova et al. [33] used high temperature calorimetry to determine the enthalpies of mixing of liquid phase with three constant ratios of xGe/xNi = 0.7/0.3, 0.5/0.5, and 0.3/0.7 at 1800 K in the Al–Ge–Ni system.

For the substitutional solution phases ϕ (ϕ = liquid, fcc-A1 and bccA2), the molar Gibbs energy is expressed as the following form:

Gmϕ(T ) =

i

ϕ ϕ Gmϕ = xAlxGe∑ jLAl,Ge (xAl − xGe ) j + xAlxNi∑ jLAl,Ni (xAl − xNi ) j j

j ϕ ϕ +xGe1LAl,Ge,Ni + xNi2LAl,Ge,Ni )

jth binary interaction paraare the ternary interaction parameters to be evaluated in the present work. The magnetic contribution to the molar Gibbs energy mgGmϕ (ϕ = fccA1 and bcc-A2) is described by the equation same as that used for the unary phases. But the parameters β and Tc are the functions related to the compositions, which can be described by the following expressions:

−1

+ fT

ϕ ϕ ϕ ϕ βmϕ = xAlβAl + xGeβGe + xNiβNi + xAlxGe∑ jβAl,Ge (xAl − xGe ) j

3

j ϕ ϕ +xAlxNi∑ jβAl,Ni (xAl − xNi ) j +xGexNi∑ jβGe,Ni (xGe − xNi ) j

(1)

j

where HiSER represents the molar enthalpy of the elements i at 298.15 K and 101,325 Pa in its standard element reference (SER) state, fcc for Al and Ni, and Ge for diamond; Gmag(T ) is the magnetic contribution to the molar Gibbs energy and is only applied for the phases fcc-A1 and bcc-A2. The magnetic contribution can be described as the following expression proposed by Inden [35] and then modified by Hillert and Jarl [36]:

G

(T ) = RT ln(β + 1)f (τ )

(4)

ϕ ϕ ϕ , jLAl,Ni and jLGe where jLAl,Ge , Ni are the 0 ϕ 1 ϕ ϕ meters; LAl,Ge,Ni , LAl,Ge,Ni , and 2LAl,Ge,Ni

Giϕ(T ) = 0Giϕ(T ) − HiSER(298.15K)

mag

j

ϕ j 0 ϕ +xGexNi∑ jLGe , Ni (x Ge − xNi ) + xAlx GexNi(xAl LAl,Ge,Ni

The molar Gibbs energy of the pure elements i (i = Al, Ge and Ni) is taken from SGTE database for the pure elements compiled by Dinsdale [34].

+gT −9 + hT 7 + G mag(T )

(3)

E

3.1. Unary phases

=a + bT + cT ln T + dT + eT

i

where xi denote the molar fractions of the pure elements i(i = Al, Ge, Ni); EGmϕ is the molar excess Gibbs energy, given by the Redlich–Kister polynomial [37] as follows:

3. Thermodynamic models

2

∑ xiGiϕ(T ) + RT ∑ xi ln xi + EGmϕ + mgGmϕ

j

ϕ +xAlxGexNi jβAl,Ge,Ni

(5)

ϕ Tcm = xAlTcϕAl + xGeTcϕGe + xNiTcϕNi + xAlxGe∑ jT cϕAl,Ge(xAl − xGe ) j j

+xAlxNi∑ jT cϕAl,Ni(xAl − xNi ) j +xGexNi∑ jT cϕGe,Ni(xGe − xNi ) j j

j

+xAlxGexNi jT cϕAl,Ge,Ni ϕ βAl ,

(2)

ϕ βGe ,

ϕ βNi ,

TcϕAl ,

(6)

TcϕGe ,

TcϕNi

where are the average atomic moments and ϕ ϕ ϕ , jβAl,Ni , jβGe,Ni , the critical temperatures of the unary phases; jβAl,Ge

where β is the average atomic moment, which in most cases is set equal to the molar Bohr magnetons; τ is defined as T/Tc, and Tc is the critical temperature for the magnetic ordering, which in most cases is set equal to the curie temperature.

j ϕ T cAl,Ge , jT cϕAl,Ni , jT cϕGe,Ni are the jth binary magnetic interaction paraϕ and jT cϕAl,Ge,Ni are the jth ternary magnetic interaction meters; jβAl,Ge,Ni

parameters. 140

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Table 2 Optimized thermodynamic parameters of the Al–Ge–Ni system.a Phase

Thermodynamic parameters

References

Liquid

0 liq. LAl,Ge = − 14869.0 − 1.1000T 1 liq. LAl,Ge = + 3325.0 − 3.6700T 0 liq. LAl,Ni = − 207109.3 + 41.3150T 1 liq. LAl,Ni = − 10185.8 + 5.8714T 2 liq. LAl,Ni = + 81204.8 − 31.9571T 3 liq. LAl,Ni = + 4365.4 − 2.5163T 4 liq. LAl,Ni = − 22101.6 + 13.1634T 0 liq. L Ge,Ni = − 167121.3 + 155.0000T 1 liq. L Ge,Ni = + 84737.5 − 25.0140T 2 liq. L Ge,Ni = + 37441.6 − 16.0010T 3 liq. L Ge,Ni = − 63650.3 + 21.8930T 0 liq. LAl,Ge,Ni = + 180387.8 1 liq. LAl,Ge,Ni = + 65019.5 2 liq. LAl,Ge,Ni = + 6201.1 − 103.2122T 0 fcc LAl,Ge = + 20563.5 − 28.7600T 0 fcc LAl,Ni = − 162407.8 + 16.2130T 1 fcc LAl,Ni = + 73417.8 − 34.9140T 2 fcc LAl,Ni = + 33471.0 − 9.8370T 3 fcc LAl,Ni = − 30758.0 + 10.253T 0 fcc TcAl,Ni = − 1112.0 1 fcc TcAl,Ni = + 1745.0 0 fcc L Ge,Ni = − 122000.0 + 36.8800T 1 fcc L Ge,Ni = + 134000.0 − 46.8000T 0 fcc TcGe,Ni = − 3750.0 0 fcc LAl,Ge,Ni = + 104988.8 1 fcc LAl,Ge,Ni = + 160012.2 2 fcc LAl,Ge,Ni = − 47010.1

[15]

fcc(disordered part of L12)

L12

[15] [21] [21] [21] [21] [21] [24]

− 15.0000T × ln(T )

[24] [24] [24] This work This work This work [15] [21] [21] [21] [21] [21] [21] [24] [24] [24] This work This work This work

The functions of the two-sublattice model are given by the Ref. [21]. The values of the parameters are expressed as the following expression: U1A1Ni = − 14808.7 + 2.9307T 1 LAl,Ni = + 7203.6 − 3.7427T

[24] [24]

U1GeNi = − 15609.1 + 1.0167T 1 L Ge,Ni = + 7900.0 − 3.2400T

This work This work

U1AlGe = + 10574.5 − 8.0025T 1 LAl,Ge = + 2294.8 − 3.2223T

bcc(disordered part of B2)

0 bcc LAl,Va

B2

[40]

0

bcc G Va = + 0.2RT αAlVa = + 10000.0 − T − 0.2RT λAlVa = + 150000.0 αGeVa = αNiVa = + 162397.3 − 27.4058T − 0.2RT λ GeVa = λNiVa = − 64024.4 + 26.4942T αAlNi = − 152397.3 + 26.4058T λAlNi = − 52440.9 + 11.3012T

0

bcc L Ge,Va

0

bcc LNi,Va

[21] [21]

[41] [21] [41] [21] [21] [21] [21]

= + αAlVa + λAlVa

This work

= + αGeVa + λ GeVa

[21]

= + αNiVa + λNiVa 0 bcc LAl,Ni = + αAlNi + λAlNi 0 bcc LAl,Ge,Ni = + 555539.7 + 99.9866T 1 bcc LAl,Ge,Ni = + 1177113.0 + 68.8894T 2 bcc LAl,Ge,Ni = − 654161.5 + 95.1211T 0 B2 0 B2 GAl:Va = G Va:Al = 0.5(αAlVa − λAlVa )

[21] This work This work This work [21] (continued on next page)

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Table 2 (continued) Phase

Thermodynamic parameters

References

0

0

This work

0

[21]

B2 B2 GGe:Va = G Va:Ge = 0.5(αGeVa − λ GeVa )

0

Diamond Al3Ni5

B2 B2 G Ni:Va = G Va:Ni = 0.5(αNiVa − λNiVa ) 0 B2 0 B2 GAl:Ni = G Ni:Al = 0.5(αAlNi − λAlNi ) 0 B2 0 B2 LAl,Ni:Ge = L Ge:Al,Ni = + 362000.2 − 80.0011T 0 diamond GAl:Ge = + 16980.0 − 22.4900T Al3Ni5 GAl:Ni = + 0. 375GHSERAl + 0.625GHSERNi

[21] This work [15] [21]

−55507.8 + 7.2648T Al3Ni2

Al Ni

[21]

Al Ni

[21]

3 2 = + 5GBCC + 30000.0 − 3.0000T GAl:Al:Va Al

Al Ni

[21]

Al3Ni2 GAl:Ni:Va

[21]

3 2 = + 5GBCC + GBCC − 39466.0 GAl:Al:Ni Al Ni +7.8953T 3 2 = + 3GBCC + 3GBCC − 427191.9 GAl:Ni:Ni Al Ni +79.2173T

= + 3GBCCAl + 2GBCCNi − 357726.0 +68.3220T

Al Ni

This work

3 2 = + 3GBCC GGe:Ni:Ni Ge + 3GBCCNi + 30000

Al Ni

This work

Al3Ni2 GGe:Al:Va = + 3GBCCGe + 2GBCCNi + 25000 Al3Ni2 GGe:Ni:Va = + 3GBCCGe + 32GBCCNi + 25000 0 Al Ni 0 Al Ni 3 2 3 2 LAl:Al,Ni:Ni = LAl:Al,Ni:Va = − 193484.2 + 131.7900T 0 Al Ni 0 Al Ni 3 2 3 2 LAl:Al:Ni,Va = LAl:Ni:Ni,Va = − 22001.7 + 7.0332T 0 Al Ni 3 2 LAl,Ge:Ni:Va = − 380635.8 + 146.7976T 2 Al Ni 3 2 LAl,Ge:Ni:Va = − 414868.9 + 144.1977T 0 Al Ni 3 2 L Ge:Al,Ni:Va = + 119030.2

This work

3 2 = + 3GBCC GGe:Al:Ni Ge + 2GBCCAl + GBCCNi +30000

Al3Ni βGeNi3

This work [21] [21] This work This work This work

Al Ni

[21]

βGeNi

[24]

Ge Ni

3 = + 0. 75GHSER + 0.25GHSER GAl:Ni Al Ni −48483.7 + 12.2991T

GGe:Ni 3 = + 0. 256GHSER Ge + 0.744GHSERNi −34315.0 + 4.3010T

Ge2Ni5

2 5 = + 0. 28GHSER GGe:Ni Ge + 0.72GHSERNi −34918.0 + 3.6900T

[24]

GeNi2

GeNi2 GGe:Ni = + 0. 335GHSER Ge + 0.665GHSERNi −38227.2 + 4.8490T

[24]

αGe3Ni5 βGe3Ni5

αGe Ni5

GGe:Ni3

[24]

= + 0.375GHSER Ge + 0.625GHSERNi −37350.6 + 3.3280T

βGe Ni

[24]

3 5 = + GHSER GGe:Ni:Va Ge + GHSERNi − 54286.3 −5.6240T

βGe Ni

[24]

0

[24]

3 5 = + GHSER GGe:Ni:Ni Ge + 2GHSERNi − 110540.0 +11.7170T

βGe Ni

3 5 L Ge:Ni:Ni,Va = − 2655.9 − 2.9320T

1 βGe Ni 3 5 L Ge:Ni:Ni,Va

[24]

= − 17558.1

βGe Ni

This work

3 5 = + GHSER + GHSER − 106332.8 GAl:Ni:Va Al Ni +17.8858T + 10000

βGe Ni

This work

0 βGe Ni 3 5 LAl,Ge:Ni:Ni = − 102030.8 + 33.4031T 1 βGe Ni 3 5 LAl,Ge:Ni:Ni = − 17213.1 − 23.4192T 0 βGe Ni 3 5 LAl,Ge:Ni:Va = − 5655.7 − 28.1030T 2 βGe Ni 5 3 LAl,Ge:Ni:Va = − 59666.7 + 23.3333T

This work

GeNi GGe:Ni

[24]

3 5 = + GHSER + 2GHSER − 148015.8 GAl:Ni:Ni Al Ni +19.3722T + 15000

GeNi

This work This work This work

= + 0.5GHSER Ge + 0.5GHSERNi − 30992.5 +0.9670T − 0.1000T ln T + 6.0150 × 10−5T 2 −9.4710 × 10−8T 3 + 2.3930 × 10−22T 7 −14960.4910T −1

This work

GeNi GAl:Ni = + 0.5GHSERAl + 0.5GHSERNi − 53166.4 +8.9429T + 5000

0 GeNi LAl,Ge:Ni

This work

= − 36566.0 + 19.2011T

(continued on next page)

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Table 2 (continued) Phase

τ1

Thermodynamic parameters

References

2 GeNi LAl,Ge:Ni = − 32821.7 + 18.4216T τ1 GAl:Ge:Ni = + 0.167GHSERAl + 0.5GHSER Ge

This work This work

+0.333GHSERNi − 35873.8 + 3.4698T τ2

τ2 GAl:Ge:Ni = + 0.682GHSERAl + 0.182GHSER Ge +0.136GHSERNi − 28166.1 + 8.8667T

τ3

3 GAl:Ge:Ni = + 0.25GHSERAl + 0.4GHSER Ge +0.35GHSERNi − 42827.4 + 4.4711T

This work

τ4

τ4 GAl:Ni = + 0.409GHSERAl + 0.501GHSERNi −54870.9 + 7.1272T + 5000

This work

τ4 GGe:Ni = + 0.409GHSER Ge + 0.501GHSERNi −35318.8 + 3.1470T + 5000

This work

0 τ4 LAl,Ge:Ni = − 46292.8 − 6.8933T 1 τ4 LAl,Ge:Ni = + 33486.7 − 6.6667T τ5 GAl:Ni = + 0.333GHSERAl + 0.667GHSERNi

This work

This work

τ

τ5

This work This work

−38106.8 + 4.8069T + 5000 τ

a

5 GGe:Ni = + 0.333GHSER Ge + 0.667GHSERNi −38227.2 + 4.8490T + 5000

This work

0 τ5 LAl,Ge:Ni = − 66794.8 + 16.1538T 1 τ5 LAl,Ge:Ni = − 14643.0 − 20.1908T

This work This work

In SI units (Joule, mole of the formula units and Kelvin).

Fig. 4. Calculated isothermal section of the Al–Ge–Ni system at 973 K compared with the experimental data [28,30].

Fig. 5. Calculated isothermal section of the Al–Ge–Ni system at 823 K compared with the experimental data [30].

3.3. Intermetallic compounds

sublattices; au are the corresponding stoichiometric coefficients; EGmϕ is the molar excess Gibbs energy and can be expressed as following:

Two ternary compounds τ4(AlxGe9-xNi13-y) and τ5(AlGeNi4) with the homogeneity ranges more than 5 at% presented the typical XRD patterns of Ga3Ge6Ni13 and Co2Si. Al and Ge atoms occupied the site Ga and Ge for the compound τ4 and occupied Si for the compound τ5 at random, respectively. Thus τ4 and τ5 were described as (Al,Ge)xNiy according to their crystal structures in the current work. In short, for seven intermetallic compounds ϕ (ϕ = Al3Ni2, GeNi, βGe3Ni5, fcc-L12, bcc-B2, τ4 and τ5) with homogeneity ranges, the molar Gibbs energy with two sublattice is taken as an example by the following expression:

Gmϕ(T ) =

∑ yi′∑ yi′′Giϕ: j(T ) + RT ∑ ∑ auyiu ln yiu + EGmϕ i

where

yiu

j

u

i

E

Gm =

⎡

⎤

∑ yi′∑ yk′′⎢⎢∑ yv′∑ jLi,v: k (yi′ − yv′) j + ∑ yv′′∑ jLi : k,v(yi′′ − yv′′) j ⎥⎥ i

k

⎣ v>i

j

v>k

j

⎦ (8)

where jLi, v : k and jLi : k , v are the jth interaction parameter between the corresponding elements on the first and second sublattice, respectively. For nine intermetallic compounds ϕ (ϕ = Al3Ni, Al3Ni5, αGe3Ni5, GeNi2, Ge2Ni5, βGeNi3, τ1, τ2, and τ3) with their negligible homogeneity ranges, the molar Gibbs energy in the form of AlxGeyNiz is taken as an example and can be expressed as: fcc diamond fcc Gmτ1 = xGAl + yGGe + zGNi + a + bT

(7)

are the site fractions of the components i of the respective

(9)

where a and b are the parameters to be assessed in the present work. 143

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CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 58 (2017) 138–150

Fig. 6. Calculated isothermal section of the Al–Ge–Ni system at 673 K compared with the experimental data [28].

Fig. 9. Calculated vertical section of the Al–Ge–Ni system at the Al0.65Ni0.35– Ge0.65Ni0.35 joint compared with the experimental data [28].

Fig. 7. Calculated vertical section of the Al–Ge–Ni system at the Al0.90Ni0.10– Ge0.90Ni0.10 joint compared with the experimental data [28]. Fig. 10. Calculated vertical section of the Al–Ge–Ni system at the Al0.45Ni0.55– Ge0.45Ni0.55 joint compared with the experimental data [30].

3.4. Order-disorder transformation Ansara et al. [19] and Dupin et al. [21] have derived a single Gibbs energy function to describe the disordered phase fcc-A1 and its ordered one fcc-L12 as well as disorder phase bcc-A2 and its ordered one bccB2, respectively. The single Gibbs energy function is composed of the following three terms:

Gmdis,ord = Gmdis(xi ) + ΔGmord(yi′, yi′) =Gmdis(xi ) + Gmord(yi′, yi′) − Gmord(xi )

(10)

where Gmdis(xi ) represents the molar Gibbs energy of the disordered state and can be described by Eq. (3); Gmord(yi′, yi") is the contribution of the ordered state and can be expressed by Eq. (7); Gmord(xi ) represents the ′ = yAl ", contribution from disorder state to the ordered one. When yAl ′ = yNi ′ = yGe " , the phase is in the disorder state. In this case, " , and yNi yGe ΔGmord(yi′, yi") = 0 .

Fig. 8. Calculated vertical section of the Al–Ge–Ni system at the Al0.80Ni0.20– Ge0.80Ni0.20 joint compared with the experimental data [28].

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Fig. 11. Calculated vertical section of the Al–Ge–Ni system at the Al0.40Ni0.60– Ge0.40Ni0.60 joint compared with the experimental data [30].

Fig. 14. Calculated vertical section of the Al–Ge–Ni system at the Al0.15Ni0.85– Ge0.15Ni0.85 joint compared with the experimental data [30].

Fig. 12. Calculated vertical section of the Al–Ge–Ni system at the Al0.30Ni0.70– Ge0.30Ni0.70 joint compared with the experimental data [30].

Fig. 15. Calculated vertical section of the Al–Ge–Ni system at the Al0.25Ni0.75–Ge joint compared with the experimental data [30].

4. Assessment procedure The present optimization work was performed with the aid of the optimization module PARROT of the thermodynamic software Thermo-Calc [38,39], which can handle various kinds of the experimental data. In the assessment procedure, the weight was chosen by the personal judgment and was changed according to the error and the adjustable coefficients until most of experimental phase equilibria and thermochemical data were reproduced well. For the phase bcc-A2 in the Al–Ni system, Dupin et al. [21] bcc−A2 considered that the molar Gibbs energy of thermal vacancies GVa bcc−A2 was equal to zero, while Franke [40] concluded that GVa should be given a critical value to ensure the existence of the single equilibrium states. The limiting value 0.2RT, which is closer to (ln2–1/2)RT, was recommended by Franke [40]. However, Peng et al. [41] found that the calculated Al–Ni phase diagram was different from the assessment of bcc−A2 Dupin et al. [21] when only this change of GVa was accepted. Therefore, they suggested that a term –0.2RT should be included in the bcc−A2 bcc−A2 and GNi:Va . In the present work, the thermodycoefficients GAl:Va namic parameters from the original dataset of Dupin et al. [21] after

Fig. 13. Calculated vertical section of the Al–Ge–Ni system at the Al0.25Ni0.75– Ge0.25Ni0.75 joint compared with the experimental data [30].

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Table 3 Calculated invariants and special points in the Al–Ge–Ni system. Reaction

refinement according to Refs. [40,41] are adopted, which are listed in Table 2. In short, the thermodynamic parameters of the liquid phase were first obtained in terms of the determined enthalpies of mixing of the liquid phase [33]. Then, the thermodynamic parameters of other phases were optimized based on the following experimental data [28,30], including three isothermal sections at 973, 823 and 673 K and nine vertical sections at the Al0.90Ni0.10–Ge0.90Ni0.10, Al0.80Ni0.20– Ge0.80Ni0.20, Al0.65Ni0.35–Ge0.65Ni0.35, Al0.45Ni0.55–Ge0.45Ni0.55, Al0.40Ni0.60–Ge0.40Ni0.60, Al0.30Ni0.70–Ge0.30Ni0.70, Al0.25Ni0.75– Ge0.25Ni0.75, Al0.15Ni0.85–Ge0.15Ni0.85 and Al0.25Ni0.75–Ge joints. 5. Results and discussion The thermodynamic assessment of the Al–Ge–Ni system is performed in the present work. Most of the experimental data can be well reproduced by the present model within the limits of experimental uncertainties. Crystal structure and thermodynamic model of all phases relevant for this study are given in Table 1 together with corresponding citations [28–30,42–49]. And the optimized thermodynamic parameters together with corresponding citations [15,21,24,40,41] are shown in Table 2. Figs. 4–6 present the calculated isothermal sections at 973, 823 and 673 K in comparison with the experimental data [28,30], but a few acceptable discrepancies are still existed. In Figs. 4–6, the solubility ranges of the phase GeNi are in disagreement with the experimental data due to that the phase relations such as the two-phase region B2 + GeNi need to be ensured. Next, the alloy compositions of phases for the three-phase region B2 + τ4 +βGe3Ni5 have a few deviations in order to fit the related vertical section in Figs. 10–12. Besides, the calculated tie-lines between fcc-A1 and fcc-L12 in Fig. 4 are not consistent with the experimental data [30]. It is worth mentioning that a lot of efforts have been made during the optimization but any other attempts to reproduce these tie-lines would cause a worse overall agreement with the other experimental data. Figs. 7–15 show the calculated vertical sections at the Al0.90Ni0.10– Ge0.90Ni0.10, Al0.80Ni0.20–Ge0.80Ni0.20, Al0.65Ni0.35–Ge0.65Ni0.35, Al0.45Ni0.55–Ge0.45Ni0.55, Al0.40Ni0.60–Ge0.40Ni0.60, Al0.30Ni0.70– Ge0.30Ni0.70, Al0.25Ni0.75–Ge0.25Ni0.75, Al0.15Ni0.85–Ge0.15Ni0.85 and Al0.25Ni0.75–Ge joints, respectively. The satisfied results are basically obtained, but some disagreements are still existed. As shown in Fig. 10, Jandl et al. [30] suppose that three top hollow circles should correspond

T (K)

Compositions of liquid

Refs.

x (Al)

x (Ge)

x (Ni)

0.161 0.730 0.013 0.136 0.148 0.091 0.026 – – – – 0.138 0.140 0.002

0.195 0.010 0.282 0.742 0.682 0.592 0.639 – – – – 0.164 0.160 0.290

0.644 0.260 0.705 0.122 0.170 0.317 0.335 – – – – 0.698 0.700 0.708

Calc. Calc. Calc. Calc. [28] Calc. Calc. Calc. Calc. Calc. Calc. Calc. [30] Calc.

B2 + βGe3Ni5 Al3Ni2 + B2 βGe3Ni5 + L12 B2 + diamond

Max1 Max2 Min1 Max3

liq. + τ1 + τ3 liq. + diamond + GeNi B2 + βGe3Ni5 + τ4 βGe3Ni5 + L12 + τ5 αGe3Ni5 + βGe3Ni5 + τ4 βGe3Ni5 + GeNi2 + τ4 liq. + B2 → βGe3Ni5 + L12a

Max4 Max5 Max6 Max7 Max8 Max9 U1

liq. + βGeNi3 → Ge2Ni5 + L12 liq. + Ge2Ni5 → βGe3Ni5 + L12 liq. + B2 → Al3Ni2 + diamond

U2

1515 1444 1376 1136 1133 1071 1045 1173 969 662 579 1488 1488 1378

U3

1378

0.003

0.290

0.707

Calc.

U4

1125

0.176

0.762

0.062

Calc.

1125 1094 1095 1071 1071 1066 1106 1065 1082 1063 1063 1042 1036 851

0.280 0.116 0.080 0.090 0.063 0.088 0.020 0.089 0.085 0.087 0.040 0.055 0.000 0.570

0.630 0.598 0.665 0.597 0.667 0.547 0.550 0.552 0.610 0.550 0.600 0.607 0.670 0.429

0.090 0.286 0.255 0.312 0.270 0.365 0.430 0.359 0.305 0.363 0.360 0.338 0.330 0.001

[28] Calc. [28] Calc. [28] Calc. [30] Calc. [28] Calc. [28] Calc. [28] Calc.

0.590 0.708 0.705 0.738 0.715 0.728 0.713 – – – – – –

0.400 0.292 0.285 0.262 0.275 0.272 0.286 – – – – – –

0.010 0.000 0.010 0.000 0.010 0.000 0.001 – – – – – –

[28] Calc. [28] Calc. [28] Calc. [28] Calc. [30] Calc. [30] Calc. Calc.

–

–

–

Calc.

liq. liq. liq. liq.

Fig. 16. Calculated enthalpies of mixing of liquid phase at 1800 K compared with the experimental data [33].

Type

+ + + +

liq. + B2 + diamond → τ3

P1

liq. + τ3 → diamond + τ1

U5

liq. + βGe3Ni5 → B2 + GeNi

U6

liq. + τ3 → B2 + τ1b

U7

liq. + B2 → GeNi + τ1

U8

liq. → diamond + GeNi + τ1

E1

liq. + Al3Ni2 → Al3Ni + diamond

U9

liq. + Al3Ni + diamond → τ2

P2

liq. + Al3Ni → fcc + τ2

U10

liq. → diamond + fcc + τ2

E2

B2 + βGe3Ni5 → GeNi + τ4c

U11

βGe3Ni5 + L12 → B2 + τ5d

U12

B2 + βGe3Ni5 → τ4 + τ5 βGe3Ni5 → αGe3Ni5 + GeNi + τ4 βGe3Ni5 → αGe3Ni5 + GeNi2 + τ4

U13 E4

831 717 717 710 710 698 698 1039 1033 953 953 750 657

E5

543

It was recommended as liq. + B2 + L12 → βGe3Ni5 in Ref. [30]. It was recommended as liq. + τ3 + B2 → τ1 in Ref. [28]. c It was recommended as B2 + βGe3Ni5 + GeNi → τ4 in Ref. [30]. d It was recommended as B2 + βGe3Ni5 + L12 → τ5 in Ref. [30]. a

b

to the invariant reaction liq. + βGe3Ni5 → B2 + GeNi at 1106 K. Since this reaction is located near βGe3Ni5, only the ternary interaction parameters for the phase βGe3Ni5 are useful. Besides, it should be mentioned that the invariant thermal effect or other one are very hard to be judged from the DTA measurements. To satisfy the experimental data especially for the vertical section at 60 at% Ni, the three hollow circles would be regarded as other thermal effect in the current work. Fig. 16 presents the calculated enthalpies of mixing of liquid phase at 1800 K, which are in satisfactory agreement with the experimental measurements [33]. Table 3 shows the temperatures and the liquid compositions for the invariant reactions in the Al–Ge–Ni system, and the corresponding projection of the liquidus surface and the complete reaction scheme are presented in Figs. 17 and 18. As shown in the Table 3, the deviation of 146

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Fig. 17. a). Calculated projection of the liquidus surface in the Al–Ge–Ni system. b). Enlarged section of (a). c). Enlarged section of (a). d). Enlarged section of (a).

temperature is 17 K in the invariant reaction liq. + τ3 → B2 + τ1. As shown in Fig. 9a, the two-phase region between the phase bcc-B2 and τ1 is impossible to offset to the left of the hollow circles to meet the reaction type and the temperature [28]. So in this work, the reaction liq. + τ3 → diamond + τ1 not liq. + τ3 → B2 + τ1 is given a greater weight. Besides, the error of temperature is 20 K in the invariant reaction liq. + Al3Ni2 → Al3Ni + Diamond. It should be noted the temperature mainly depends on the thermodynamic parameters of the phase Al3Ni2. A lot of efforts are made during the optimization, but the entropy of the interaction parameters of the phase Al3Ni2 almost needs +50 J/(K mol of atoms) when the temperature is consistent between the calculated and the experimental data, which will lead to instability of the phase bcc-B2 at low temperature. Therefore, the above deviations are accepted in the present work.

6. Conclusion On the basis of the available experimental information, the thermodynamic assessment of the Al–Ge–Ni system over the entire composition and temperature ranges has been performed for the first time. The calculated isothermal sections, vertical sections and enthalpies of mixing of the liquid phase show a high consistency with the experimental data. In the present work, the liquidus projection and reaction scheme of the whole Al–Ge–Ni system are presented, which are good for understanding the diffusion process during the transient liquid phase (TLP) bonding. Furthermore, a set of selfconsistent and reliable thermodynamic parameters is obtained, which can be used for a variety of thermodynamic calculations of practical interest.

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Fig. 18. a). Calculated invariant reaction scheme in the Al–Ge–Ni system. b). Calculated invariant reaction scheme in the Al–Ge–Ni system.

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Fig. 18. (continued)

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