Accepted Manuscript

Experimental investigation and thermodynamic prediction of the Ag–Ge–Sbphase diagram

Milena Premović, Dragan Manasijević, Duško Minić, Dragana Živković

PII: S0925-8388(14)01041-XDOI: http://dx.doi.org/10.1016/j.jallcom.2014.04.208Reference: JALCOM 31173

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Received Date: 11 March 2014Revised Date: 24 April 2014Accepted Date: 28 April 2014

Please cite this article as: M. Premović, D. Manasijević, D. Minić, D. Živković, Experimental investigation andthermodynamic prediction of the Ag–Ge–Sb phase diagram, (2014), doi: http://dx.doi.org/10.1016/j.jallcom.2014.04.208

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Experimental investigation and thermodynamic prediction of the Ag–Ge–Sb phase diagram

Milena Premović a,*, Dragan Manasijević b, Duško Minić a, Dragana Živković b

a University in Priština, Faculty of Technical Science, Kos. Mitrovica, Serbia

b University of Belgrade, Technical Faculty, Bor, Serbia ABSTRACT

Phase diagram of the Ag–Ge–Sb ternary system has been investigated experimentally and

extrapolated using optimized thermodynamic parameters for the constitutive binary systems.

Experimental results obtained using differential thermal analysis (DTA), scanning electron

microscopy (SEM) with energy dispersive spectrometry (EDS), and X-ray powder diffraction

(XRD) methods were compared with predicted phase equilibria.

Identification of coexisting phases in the chosen as-cast samples and samples annealed at 400 °C

was performed using SEM-EDS and XRD methods. Liquidus temperatures for selected samples

with overall compositions along three vertical sections Ag–Ge0.5Sb0.5, Ge–Ag0.5Sb0.5 and Sb–

Ge0.5Ag0.5 were measured by DTA. Ternary eutectic reaction was experimentally determined by

means of applied experimental techniques.

Keywords: Ag–Ge–Sb system, Phase diagram, DTA, XRD, SEM-EDS. * Corresponding author. Tel.: +381 653005603 E-mail addresses: milena.premovic@gmail.com (M. Premović)

1. Introduction It is well known that silver and silver alloys represent excellent heat and electricity conductors.

For example, alloys of Ag–Sb system are widely used in electronic industry [1-3]. Also,

germanium based alloys are extensively studied because of their semiconducting properties and

applications in the electronic industry [4-7]. In addition to these applications, special attention is

given to materials which contain Ge, due to the large application in the modern technology for

making optical discs, DVD, Blue-Ray discs, flash memories [8,9]. Also, Sb-rich alloys of Ge,

Ag, In, Ga are important for development of phase change memory materials [10].

The aim of this study is complementary experimental and computational investigation of phase

transitions and microstructure of the alloys in ternary Ag–Ge–Sb system which has not yet been

studied from this point of view in literature. Hereby, selected alloys of the Ag–Ge–Sb ternary

system were prepared and studied using a combination of different experimental techniques

(DTA, SEM-EDS, XRD). Experimentally obtained results were compared with predicted phase

equilibria.

2. Experimental procedure All samples with total masses of about 3 g were prepared from Ge, Sb and Ag shots of 99.99%

purity in an induction furnace under high purity argon atmosphere. After melting, the samples

were put into quartz glass ampoules, sealed under vacuum, annealed at 400 °C for two weeks and

quenched into ice water. Additionally, four as-cast samples were prepared for microstructure

investigation.

The compositions of coexisting phases were determined using JEOL JSM-6460 scanning

electron microscope with energy dispersive spectrometry, EDS (Oxford Instruments).

Powder XRD data for phase identification of samples were recorded on a D2 PHASER (Bruker)

powder diffractometer equipped with a dynamic scintillation detector and ceramic X-ray Cu

tube (KFL-Cu-2K) in a 2θ range from 5° to 75° with a step size of 0.02°. The patterns were

analyzed using the Topas 4.2 software, ICDD databases PDF2 (2013).

Phase transition temperatures were determined by DTA method. The DTA measurements were

performed on a SDT Q600 (TA instruments). Alumina crucibles were used and measurements

were performed under flowing argon atmosphere. Samples weighing between 20 and 30 mg were

investigated at heating rate of 5 °C/min. The sample masses and heating rates were determined

by analysis of one sample at different testing conditions. The reference material was empty

alumina crucible. The overall uncertainty of the determined phase transformation temperatures

was estimated to be ±1 °C.

3. Literature data To the best of our knowledge, there are no published data regarding the phase equilibria and

thermodynamics of the ternary Ag–Ge–Sb system. Boundary binary systems have been

investigated extensively.

3.1. The Ag–Ge binary system The Ag–Ge binary system is a simple eutectic system, which consists of three condensed phases:

liquid phase, (Аg) and (Ge) solid solutions. Temperature and composition of eutectic reaction

and the position of the liquidus line have been investigated by Briggs et al. [11], Maucher [12]

and Predel and Bamlstahl [13] using thermal analysis.

Owen and Rowlands [14] determined solubility of Ge in the (Ag) phase below the eutectic

temperature using X-ray powder method. Also, Pollock [15] reported the composition of the

(Ag) phase at the temperature about 300 K from thermoelectric measurements.

The enthalpies of mixing of liquid Ag–Ge alloys were measured by Catanet et al. [16,17] at 1280

K and Batalin et al. [18] at 1430 K. Activities of Ag in the liquid Ag–Ge alloys were determined

by Batalin et al. [18], Eremenko et al. [19], Martin-Garin et al. [20] and Oktay [21].

This system was first thermodynamically optimized by Chevalier [22]. In order to achieve the

thermodynamic compatibility of the database in the multi-component systems, the

thermodynamic parameters of different phases in the Ag-Ge binary system were evaluated by

Wang at al. [23].

3.2. The Ge–Sb binary system The Ge–Sb binary system is an eutectic system. Phase equilibria of this system have been

investigated by several authors [24-29].

A very small solubility of antimony in germanium was determined by Zhurikin et al. [26],

Trumbore [30], Trumbore et al. [31], Akopyan and Abdullayev [32], and Glazov and Abdullyev

[33].

The enthalpies of mixing in liquid Ge–Sb alloys were determined by Predel and Stein [34] and

Alfer et al. [35]. Activities Ge and Sb in the liquid state at 1073, 1173, 1273 K were investigated

by Кostov et al. [6].

The binary Ge–Sb system was initially thermodynamically optimized by Chevalier [36] based on

experimentally determined phase diagram by Olesinski et al. [37,38]. Later, it was re-optimized

by Liu at al. [39] using new experimental results by Nasir et al. [40].

3.3. The Ag–Sb binary system

The Ag–Sb system exhibits five phases: liquid phase, (Аg) and (Sb) solid solutions, ζ (Ag9Sb)

and ε (Ag3Sb) intermetallic phases.

The liquidus is constructed by Hansen et al. [41] based on previous experimental results

published in literature [42-45]. Okamoto [46] reported two intermediate phases: ζ (Ag9Sb) and ε

(Ag3Sb) that form by peritectic reactions at 702.5 and 562 °C, and the eutectic reaction at 485

°C. Feschotte et al. [47] determined the compositional range of stability of the ε (Ag3Sb) phase

using X-ray powder diffraction measurements.

Thermodynamic assessment of this system was performed by Lee et al. [48] and Oh et al. [49].

The latest thermodynamic assessment, including their own experimental results, was done by

Zoro et al. [50].

3.4. Thermodynamic extrapolation of the Ag–Ge–Sb phase diagram In this work phase diagram of the Ag–Ge–Sb ternary system has been thermodynamically

predicted using Gibbs energy values for pure elements (4.4SGTE) [51] and optimized

thermodynamic parameters for the binary Ag–Ge system from Wang et al. [23], for the binary

Ge–Sb from Liu et al. [39], and for the binary system Ag–Sb from Zoro et al. [50]. Calculations

were performed using PANDAT software [52].

Optimized thermodynamic parameters for the boundary binary systems are listed in Table 1.

Table 1. The optimized binary parameters used in this study.

The phases from constitutive binary subsystems considered for thermodynamic calculation with

their crystallographic data are listed in Table 2.

Table 2. Considered phases and their crystal structures. Fig. 1 represents calculated phase diagrams of the constitutive binary systems using

thermodynamic parameters given in Table 1.

a) b)

c) Fig. 1. Calculated phase diagram of: a) Ag-Ge [23], b) Ge-Sb [39] and

c) Ag-Sb [50] binary system.

4. Results and discussion 4.1. Liquidus projection of the Ag–Ge–Sb ternary system Preliminary investigation of the phase diagram and phase transitions in the ternary Ag–Ge–Sb

ternary system was done using thermodynamic prediction of phase equilibria based on

thermodynamic parameters obtained by [23, 39, 50]. Calculated liquidus projection of the

ternary Ag–Ge–Sb system is given in Fig. 2. Fig. 2 shows predicted liquidus monovariant lines

(in black) and the primary crystallization fields together with calculated liquidus isotherms (in

red) with 50 °C temperature increments in the ternary Ag–Ge–Sb system.

According to the results of thermodynamic extrapolation there are totally five fields of primary

crystallization: (Ge), (Sb), (Ag), ε (Ag3Sb) and ζ (Ag9Sb). As it can be seen from Fig 2, prevailing

composition region of primary crystallization belongs to the (Ge) solid solution. Beside

dominant composition region of (Ge) crystallization, there are significantly smaller primary

crystallization fields of (Sb), (Ag), ε and ζ phases, situated in the vicinity of the Ag–Sb boundary

binary system.

Fig. 2. Predicted liquidus projection of the ternary Ag–Ge–Sb system with marked overall

compositions of the investigated as-cast samples (blue squares).

Three ternary invariant reactions involving liquid phase have been predicted in the ternary Ag–

Ge–Sb system. Two of them are quasi-ternary peritectic reactions or transition reactions (U-

type) and the third reaction is ternary eutectic reaction (E-type). Predicted invariant reactions as

well as the corresponding reaction temperatures and the compositions of ternary invariant points

are listed in Table 3.

Table 3. Predicted invariant reactions involving the liquid phase

in the Ag–Ge–Sb ternary system.

In order to experimentally study primary crystallization phases and to make comparison with

predicted results shown in Fig. 2, microstructures of four as-cast samples were investigated using

SEM-EDS.

Average overall chemical compositions of the investigated samples in the as-cast state and

determined average compositions of co-existing phases obtained by EDS analysis are given in

Table 4.

Table 4. Experimentally determined overall and phase compositions of the as-cast samples

of the Ag–Ge–Sb ternary system by EDS analysis.

Experimentally determined overall compositions of the samples A, B, C and D are marked in

Fig. 2 for comparison with calculation. According to the results of thermodynamic binary-based

prediction given in Fig. 2, (Ge) phase is predicted primary crystallization phase for the samples

B and C. Calculated primary crystallization phases for the samples A and D are (Sb) and (Ag),

respectively.

Characteristic SEM micrographs for the samples A, C and D with labeled names of identified

phases are presented in Fig. 3 as an illustration. Based on the results of SEM-EDS analysis, as-

cast samples A and B have three-phase microstructure: (Ge) (Sb) and ε (Ag3Sb).

Fig 3a represent microstructure of sample A. Large bright primary solidified crystals of

predominant (Sb) phase are visible in the microstructure of the sample A, which is in agreement

with predicted liquidus projection. (Ge) and ε phases are uniformly precipitated at the (Sb) grain

boundaries.

Sample C consist of two co-existing phases (Ge) and ε (Ag3Sb) and microstructure of the sample

D includes (Ge) and ζ (Ag9Sb) phases.

Microstructure of the sample C is shown in Fig. 3b.The dendritic morphology of the dark (Ge)

phase indicates that this is the primary solidification phase. This result is in agreement with

predicted liquidus projection (Fig. 2).

Predicted primary solidification phase (Ag) was not experimentally identified in the

microstructure of the sample D (Fig 3c). As it can be seen from Table 4, only two detected

phases for the sample D are (Ge) and ζ. This could be explained by the occurrence of predicted

invariant reaction L+(Ag)→(Ge)+ ζ, which takes place during cooling and solidification of the

sample D.

(a)

(b)

(c) Fig. 3. SEM micrograph of the as-cast sample: (a) (Ag9.15Sb81.77Ge9.08),

(b) (Ag59.85Sb19.17Ge20.98) and (c) (Ag81.07Sb10.01 Ge8.92). 4.2. Results of thermal analysis

Phase transition temperatures of 12 selected samples with nominal overall compositions along

three chosen isopleths Ge–Ag50Sb50, Sb–Ge50Ag50 and Ag–Ge50Sb50 were experimentally

determined using DTA method. The solidus temperatures (first peak obtained during heating)

were taken from the extrapolated onset on heating. All others phase transition temperatures

(peaks 2 and 3) were taken from the peak maximum temperature [53] on heating. To check

reproducibility of thermal effects and to estimate experimental uncertainty of obtained phase

transition temperatures totally three heating runs were conducted for every investigated sample.

In general, the first heating cycle was ignored and the mean value of temperatures on the second

and third curves was taken as the phase transition or the liquidus temperatures. The total

experimental error of measured temperatures was in the order of ±1 °C.

The comparative presentation of the extrapolated and experimentally determined average

temperatures of phase transitions obtained by DTA measurements are given in Table 5.

Table 5. Experimentally determined (DTA) and predicted phase transition temperatures for selected samples of the ternary Ag–Ge–Sb system.

Comparison between calculated isopleths and experimentally determined phase transition

temperatures is presented in Fig. 4.

a) b)

c) Fig. 4. Predicted vertical sections of the Ag–Ge–Sb ternary system compared with DTA

results from the present study: a) Ge–AgSb, b) Sb–AgGe and c) Ag–GeSb.

According to the results of thermodynamic prediction shown in Table 5 and Fig. 4, solidus

temperatures for all investigated samples, except for the sample Ag80Ge10Sb10, correspond to the

predicted ternary eutectic reaction L↔(Ge)+(Sb)+ε at calculated temperature 460.2 °C.

Experimentally determined solidus temperatures of investigated samples are nearly identical, as

it is expected by the predicted ternary eutectic, but the average value of experimentally measured

ternary eutectic temperature is 477.2 °C which is considerably higher than predicted value of

460.2 °C.

Also, as can also be seen from Table 5 and Fig. 4, experimentally determined liquidus

temperatures are significantly higher from corresponding predicted liquidus temperatures.

DTA heating curve for the sample Ge40Ag30Sb30 is given in Fig. 5 as an example. The

extrapolated onset of the first peak at 477.6 °C is related to the occurrence of ternary eutectic

reaction (Ge)+(Sb)+ε→Liquid, while the second peak maximum temperature 766.4 °C

represents liquidus temperature.

Fig. 5. DTA heating curve for the sample Ge40Ag30Sb30.

4.3. Microstructure investigation of annealed samples Microstructures of five chosen samples annealed at 400 °C were investigated using SEM-EDS

and XRD methods. Their overall compositions and compositions of coexisting phases

determined by SEM-EDS method as well as related calculated phase compositions are given in

Table 6.

Table 6. Predicted and experimentally determined phase compositions in the ternary Ag–Ge–Sb system at 400 °C.

The calculated isothermal section of the ternary Ag–Ge–Sb system at 400 °C and experimentally

determined overall compositions and phase compositions for five samples investigated using

SEM-EDS are presented in Fig. 6. Experimentally obtained phase compositions and overall

compositions of individual samples are marked using identical symbols with the same color.

Samples 1, 2 and 3 belong to the three-phase field (Ge)+(Sb)+ε. Sample 4 is within two-phase

field (Ge)+ε as well as sample 5 ((Ge)+ζ). Based on the results presented in Table 6 and Fig. 6 it

can be concluded that predicted phase structure of investigated samples is in very good

agreement with experimentally obtained results.

Fig. 6. Calculated isothermal section of the ternary Ag–Ge–Sb system at 400 °C with overall and phase compositions for samples obtained by SEM-EDS analysis.

Fig. 7 is SEM micrograph of the sample 1 (Ag37.33Ge29.03Sb33.64) annealed at 400 °C for two

weeks. Three different phases are visible. Dark phase represent primary solidified (Ge) crystals

Grey and bright areas in the base represent uniformly distributed ε and (Sb) phases.

Fig. 7. SEM micrograph of the sample 1 (Ag37.33Ge29.03Sb33.64).

SEM micrograph of the sample 4 (Ag53.77Ge28.83Sb17.40) is presented in Fig. 8. Microstructure of

this sample includes two phases: dark primary solidified crystals of (Ge) phase in the

predominant base of ε phase (bright areas).

Fig. 8. SEM micrograph of the sample 4 (Ag53.77Ge28.83Sb17.40).

Samples 1,2 and 3 with overall composition given in Table 6 were additionally investigated by

XRD analysis. All samples are from the largest three-phase region ((Ge)+(Sb)+ε) of isothermal

section at 400 °C (Fig. 6).

The results of XRD analysis are in mutual agreement with the results of SEM-EDS analysis and

thermodynamic prediction. Additionally, lattice parameters of identified phases were determined

from XRD data and presented in Table 7.

Table 7. Results of XRD analysis for the Ag–Ge–Sb samples annealed at 400 °C.

XRD pattern for the sample 1 with identified phases is shown in Fig. 9 as an illustration.

Fig. 9. XRD pattern for the alloy 1 (Ag37.33Ge29.03Sb33.64 (at. %)).

Obtained values of lattice parameters for (Ge) and (Sb) phases are in good agreement with

literature data [54,55]. By means of X-ray diffraction Westgren et al. [56] studied the Ag-Sb

system in detail. They identified an orthorhombic structure and determined the change in lattice

parameters within the composition of the ε (Ag3Sb) phase for alloys annealed at 400 °C (a=2.986

- 2.996 Å, b=5.180 -5.246Å, c=4.774 - 4.854 Å). Our results, presented in the Table 7, are in

good agreement with the results published by Westgren et al. [56] and latest results by C. Lee at

al. [57] and C.-Y. Lin et al. [58].

5. Conclusion

Phase equilibria of the Ag–Ge–Sb ternary system have been experimentally investigated for the

first time. Also, phase diagram of the Ag–Ge–Sb ternary system has been extrapolated using

optimized thermodynamic parameters for the constitutive binary systems from literature and

compared with experimental data. Liquidus projection and invariant equilibria were calculated.

In the experimental part of the work selected samples were investigated using DTA, SEM-EDS

and XRD methods. The occurrence of ternary eutectic reaction L↔(Ge)+(Sb)+ε has been

experimentally determined at measured temperature of 477.2 °C which is significantly higher

than predicted value 460.2 °C. Predicted isothermal section at 400 °C is in general agreement

with the results of microstructural investigations of annealed samples obtained by SEM-EDS and

XRD analysis although limited solubility of Ge in the ζ (Ag9Sb) phase was detected. Lattice

parameters of identified phases were determined using XRD analysis and compared with

literature data. Liquidus temperatures measured on heating using DTA technique are fairly

higher than corresponding predicted liquidus temperatures. Results presented in this study

provide a basis for a future experimental work and thermodynamic optimization/assessment of

the Ag–Ge–Sb system.

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Cap. Figures

Fig. 1. Calculated phase diagram of: a) Ag-Ge [23], b) Ge-Sb [39] and c) Ag-Sb [50] binary system.

Fig. 2. Predicted liquidus projection of the ternary Ag-Ge-Sb system with marked overall compositions of the investigated as-cast samples (blue squares).

Fig. 3. SEM micrograph of the as-cast sample: (a) (Ag9.15Sb81.77Ge9.08), (b) (Ag59.85Sb19.17Ge20.98) and (c) (Ag81.07Sb10.01 Ge8.92).

Fig. 4. Predicted vertical sections of the Ag-Ge-Sb ternary system compared with DTA results from the present study: a) Ge-AgSb, b) Sb-AgGe and c) Ag-GeSb.

Fig. 5. DTA heating curve for the sample Ge40Ag30Sb30.

Fig. 6. Calculated isothermal section of the ternary Ag-Ge-Sb system at 400 °C with overall and phase compositions for samples obtained by SEM-EDS analysis.

Fig. 7. SEM micrograph of the sample 1 (Ag37.33Ge29.03Sb33.64).

Fig. 8. SEM micrograph of the sample 4 (Ag53.77Ge28.83Sb17.40).

Fig. 9. XRD pattern for the alloy 1 (Ag37.33Ge29.03Sb33.64 (at. %)).

a) b)

c)

Fig. 1. Calculated phase diagram of: a) Ag-Ge [23], b) Ge-Sb [39] and c) Ag-Sb [50] binary system.

Fig. 2. Predicted liquidus projection of the ternary Ag-Ge-Sb system with marked overall

compositions of the investigated as-cast samples (blue squares).

(a)

(b)

(c)

Fig. 3. SEM micrograph of the as-cast sample: (a) (Ag9.15Sb81.77Ge9.08), (b) (Ag59.85Sb19.17Ge20.98) and (c) (Ag81.07Sb10.01 Ge8.92).

b) b)

c)

Fig. 4. Predicted vertical sections of the Ag-Ge-Sb ternary system compared with DTA results from the present study: a) Ge-AgSb, b) Sb-AgGe and c) Ag-GeSb.

Fig. 5. DTA heating curve for the sample Ge40Ag30Sb30.

Fig. 6. Calculated isothermal section of the ternary Ag-Ge-Sb system at 400 °C with overall

and phase compositions for samples obtained by SEM-EDS analysis.

Fig. 7. SEM micrograph of the sample 1 (Ag37.33Ge29.03Sb33.64).

Fig. 8. SEM micrograph of the sample 4 (Ag53.77Ge28.83Sb17.40).

Fig. 9. XRD pattern for the alloy 1 (Ag37.33Ge29.03Sb33.64 (at. %)).

Cap. Tables

Table 1. The optimized binary parameters used in this study. Table 2. Considered phases and their crystal structures. Table 3. Predicted invariant reactions involving the liquid phase in the Ag-Ge-Sb ternary system. Table 4. Experimentally determined overall and phase compositions of the as-cast samples of the Ag-Ge-Sb ternary system by EDS analysis. Table 5. Experimentally determined (DTA) and predicted phase transition temperatures for selected samples of the ternary Ag-Ge-Sb system. Table 6. Predicted and experimentally determined phase compositions in the ternary Ag-Ge-Sb system at 400 °C. Table 7. Results of XRD analysis for the Ag-Ge-Sb samples annealed at 400 °C.

Table 1. The optimized binary parameters used in this study. Phase and thermodynamic

model Thermodynamic parameters (J/mol) Ref.

Liquid (Ag, Ge, Sb)

T9876.74779.964LLiquidSb,Ag

0−−= [50]

T1738.7357.21481LLiquidSb,Ag

1+−= [50]

0766.9992LLiquidSb,Ag

2−= [50]

T822.687.7636LLiquidGe,Ag

0−= [23]

T761.514.14500LLiquidGe,Ag

1+−= [23]

56.7029LLiquidGe,Ag

2−= [23]

T5212.07.3289LLiquidSb,Ge

0−+= [39]

Fcc_A1 (Ag, Ge, Sb)1(Va)1

T4033.66027.30164L 1A_FccVa:Sb,Ag

0+−= [50]

T6783.675741.8714L 1A_FccVa:Sb,Ag

1−= [50]

T917.947.5696L 1A_FccVa:Ge,Ag

0+= [23]

27.20237L 1A_FccVa:Ge,Ag

1−= [23]

Hcp_A3 (Ag, Sb)1(Va)0.5

T2101.4495.24173L 3A_HcpVa:Sb,Ag

0+−= [50]

T1982.499664.2341L 3A_HcpVa:Sb,Ag

1−−= [50]

AgSb_ortho (Ag, Sb)3(Ag,Sb)1

5000GL SerAg

ortho_AgSbAg:Ag

0+= [50]

5000GL SerSb

ortho_AgSbSb:Sb

0+= [50]

T8229.38398.411G25.0G75.0L SerSb

SerAg

ortho_AgSbSb:Ag

0−−+= [50]

T8229.38398.10411G25.0G75.0L SerAg

SerSb

ortho_AgSbAg:Sb

0+++= [50]

5398.5788L ortho_AgSbSb,Ag:Ag

0−= [50]

79.10491L ortho_AgSbSb:Sb,Ag

0= [50]

0L ortho_AgSbAg:Sb,Ag

0= [50]

0L otrho_AgSbSb,Ag:Sb

0=

[50] Diamond_A4

(Ge, Sb) T8000.191.79210L 4A_Diamond

Sb,Ge0

−+= [39]

Rhombo_A7 (Ge, Sb)

T5572.60.10695L 7A_bohomRSb,Ge

0−+= [39]

Table 2. Considered phases and their crystal structures.

Thermodynamic database name Common name Space group

symbol Strukturbericht

designation Pearson’s

symbol LIQUID Liquid

FCC_A1 (Ag) Rm

−

3 m A1 cF4

HCP_A3 ζ (Ag9Sb) P63/mmc A3 hP2 AGSB_ORTHO ε (Ag3Sb) Pmm2 oP4

RHOMBO_A7 (Sb) R

−

3 m A7 hR2

DIAMOND_A4 (Ge) Fd

−

3 m A4 cF8

Table 3. Predicted invariant reactions involving the liquid phase in the Ag-Ge-Sb ternary system.

T (°C) Reaction x(Ag) x(Sb) Type 514.9 L+(Ag)→(Ge)+ ζ 0.705 0.203 U1 504.1 L+ζ→(Ge)+ ε 0.694 0.222 U2 460.2 L→(Ge)+(Sb)+ ε 0.560 0.380 E1

Table 4. Experimentally determined overall and phase compositions of the as-cast samples of the Ag-Ge-Sb ternary system by EDS analysis

Sample Overall composition

(at. %) Determined

phases Composition of phase (at. %)

Ag Sb Ge

A Ag9.15Sb81.77Ge9.08 (Ge) (Sb)

ε (Ag3Sb)

- -

73.59±0.85

2.97±0.25 98.00±0.80 26.41±0.56

97.03±0.80 2.00±0.20

-

B Ag18.55Sb61.47Ge19.98

(Ge) (Sb)

ε (Ag3Sb)

- -

73.50±1.10

1.05±0.32 97.79±0.90 26.50±0.45

98.95±0.20 2.21±0.40

-

C Ag59.85Sb19.17Ge20.98 (Ge)

ε (Ag3Sb) -

73.68±0.95 0.72±0.20 26.32±0.20

99.28±0.50 -

D Ag81.07Sb10.01 Ge8.92 (Ge) ζ

- 87.31±1.20

1.04±0.20 10.67±0.40

98.96±0.85 2.02±0.30

Table 5. Experimentally determined (DTA) and predicted phase transition temperatures for selected samples of the ternary Ag-Ge-Sb system.

Alloy nominal composition

(at. %)

Phase transition temperatures (°C) Solidus

temperature Other peak temperature Liquidus temperature

Experimental Calculated Experimental Calculated Experimental Calculated Ge-Ag50Sb50 vertical section Ge20Ag40Sb40 477.1 460.2 - 502 652.5 636

Ge40Ag30Sb30 477.6 460.2 - 502 766.4 754

Ge60Ag20Sb20 478.2 460.2 - 502 821.3 817

Ge80Ag10Sb10 477.5 460.2 - 502 873.5 870

Sb-Ag50Ge50 vertical section

Sb20 Ag40Ge40 476.8 460.2 - 483 784.3 775

Sb40Ag30Ge30 477.2 460.2 509.5 518 715.5 700

Sb60Ag20Ge20 477.4 460.2 533.5 538 654.3 614

Sb80Ag10Ge10 476.7 460.2 562.3 546 588.4 572

Ag-Ge50Sb50 vertical section

Ag20Ge40Sb40 476.5 460.2 524.6 530 756.5 737

Ag40Ge30Sb30 477.3 460.2 - 475 748.6 720

Ag60Ge20Sb20 477.3 474.3 534.2 503 686.5 664

Ag80Ge10Sb10 - 514.9 615.4 567 675.3 667

Table 6. Predicted and experimentally determined phase compositions in the ternary Ag-Ge-Sb system at 400 °C.

Sample Overall

composition (at. %)

Determined phases Compositions of phases (at. %)

Theoretical SEM-EDS Ag Ge Sb

Exp. Cal. Exp. Cal. Exp. Cal.

1 29.03 Ge 37.33 Ag 33.64 Sb

(Ge) (Sb)

ε (Ag3Sb)

(Ge) (Sb)

ε (Ag3Sb)

0.22±0.30 0.73±0.70

72.21±0.90

- -

74.20

99.21±0.20 1.75±1.00 1.08±0.10

100 1.18

-

0.57±0.10 97.52±0.30 26.71±0.20

- 98.82 25.80

2 70.94 Ge 12.82 Ag 16.24 Sb

(Ge) (Sb)

ε (Ag3Sb)

(Ge) (Sb)

ε (Ag3Sb)

0.39±0.10 0.89±0.40

72.86±0.80

- -

74.20

98.70±1.00 0.98±0.10 0.89±0.40

100 1.18

-

0.91±0.90 98.13±0.70 26.25±0.50

- 98.82 25.80

3 14.33 Ge 9.44 Ag 76.23 Sb

(Ge) (Sb)

ε (Ag3Sb)

(Ge) (Sb)

ε (Ag3Sb)

1.07±0.20 0.57±0.60

72.68±0.20

- 0.04 74.20

98.34±0.90 1.83±0.40 0.85±0.10

100 1.18

-

0.59±0.10 97.60±0.70 26.47±0.50

- 98.82 25.80

4 28.83 Ge 53.77Ag 17.40Sb

(Ge) ε (Ag3Sb)

(Ge) ε (Ag3Sb)

0.25±0.30 74.45±0.70

- 75.55

99.03±0.60 0.80±0.10

100 -

0.72±0.10 24.75±0.20

- 24.45

5 14.65 Ge 75.00Ag 10.35Sb

(Ge) ζ

(Ge) ζ

0.80±0.20 85.67±0.40

- 87.87

98.69±1.00 2.11±0.70

100 -

0.51±0.50 12.22±0.10

- 12.13

Table 7. Results of XRD analysis for the Ag-Ge-Sb samples annealed at 400 °C.

Sample Overall

composition (at. %)

Phase Lattice parameters (Å)

Prediction Experiment a b c

1 29.03 Ge 37.33 Ag 33.64 Sb

(Ge) (Sb)

ε (Ag3Sb)

(Ge) (Sb)

ε (Ag3Sb)

5.6568(5) 4.2318(8) 2.9897(1)

- -

5.2354(9)

- 11.3740(2) 4.848(8)

2 70.94 Ge 12.82 Ag 16.24 Sb

(Ge) (Sb)

ε (Ag3Sb)

(Ge) (Sb)

ε (Ag3Sb)

5.6568(3) 4.2643(6) 2.9932(2)

- -

5.2353(1)

- 11.3739(2) 4.8524(1)

3 14.33 Ge 9.44 Ag 76.23 Sb

(Ge) (Sb)

ε (Ag3Sb)

(Ge) (Sb)

ε (Ag3Sb)

5.6567(8) 4.3728(1) 2.9908(1)

- -

5.237(4)

- 11.374(2) 4.8506(7)

\

Highlights

► Phase equilibria of the Ag-Ge-Sb ternary system have been experimentally investigated for the first

time.

► Isothermal section at 400 °C was investigated using SEM-EDS and XRD techniques on annealed

samples.

► Phase transition temperatures in the wide composition region were measured using DTA and the

existence of ternary eutectic reaction was detected.

► Experimental results were compared with thermodynamically extrapolated phase diagram.