A

toRtp©

K

1

aeat�ip

ataatSmt

0d

Journal of Alloys and Compounds 438 (2007) 171–177

A thermodynamic assessment of the Sb–Zn system

Jing-Bo Li a, Marie-Christine Record b,∗, Jean-Claude Tedenac c

a Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences,P.O. Box 603, Beijing 100080, PR China

b TECSEN, UMR CNRS 6122, Universite Paul Cezanne, Aix-Marseille III, FST St. Jerome case 251, Av. De l’EscadrilleNormandie-Niemen, 13397 Marseille Cedex 20, France

c Laboratoire de Physico-chimie de la Matiere Condensee, UMR CNRS 5617, cc03, Universite Montpellier II,Place E. Bataillon, 34095 Montpellier Cedex 5, France

Received 1 August 2006; received in revised form 11 August 2006; accepted 14 August 2006Available online 12 September 2006

bstract

The thermodynamic assessment is made for the Sb–Zn system using the CALPHAD approach (calculation of phase diagram). The liquid phase,he intermediate compounds of SbZn, Sb3Zn4 (three modifications of �, � and �′) and Sb2Zn3 (two modifications of � and �) and the terminal phasesf rhombohedral-Sb and hcp-Zn are taken into consideration in this optimization. Liquid phase is described by a substitutional solution model with

edlich–Kister polynomials. The intermediate compounds are treated as stoichiometric. Two terminal phases are taken as unary phases according

o literature. A set of self-consistent thermodynamic parameters is obtained and the calculated phase diagram and thermodynamic properties areresented and compared with experimental data obtained from literature.

2006 Elsevier B.V. All rights reserved.

ies; T

tc

wmmp

2

2

Xa

eywords: Thermoelectric materials; Phase diagrams; Thermodynamic propert

. Introduction

�-Sb3Zn4 is a compound of great interest for its potentialpplications in thermoelectricity [1]. Indeed, this materialxhibits an exceptionally low network thermal conductivityrising from a complex structure [2]. So far, no higher value ofhe figure of merit has been reported in the literature than for-Sb3Zn4 for which, ZT = 1.3 at 673 K [1]. However, the util-sation of �-Sb3Zn4 is limited in temperature (at 700 K) by theresence of structural transformations at higher temperatures.

The Sb–Zn phase diagrams published in the literaturere conflicting. The most recent one [3] shows two phaseransformations for �-Sb3Zn4 occurring at 767 K (� → �) andt about 800 K (� → �′), respectively. The same authors havelso performed X-ray diffraction (XRD) measurements versusemperature on several alloys with compositions close to that of

b3Zn4 [4]. The results confirm the existence of the two above-entioned high-temperature phases, � and �′. New phase rela-

ions were constructed for this system [3]. Therefore, the aim of

∗ Corresponding author.E-mail address: m-c.record@univ-cezanne.fr (M.-C. Record).

l

bfetfi

925-8388/$ – see front matter © 2006 Elsevier B.V. All rights reserved.oi:10.1016/j.jallcom.2006.08.035

hermodynamic modeling

his work is to validate this phase diagram by using CALPHADalculations.

In a first step, all phase diagram and thermochemical dataere collected and critically evaluated. Subsequently, the opti-ization of the thermodynamic functions was performed byeans of the PARROT module [5] of the Thermo-Calc software

ackage [6].

. Literature

.1. Experimental phase diagram

The phase diagram of this system has been studied since theIXth century, and the first results were obtained from thermal

nalysis on cooling. Therefore, only an approximation for theiquidus was obtained [7–11].

The first measurement of the liquidus on heating was doney Curry [12]. Later, Takei [13] constructed a phase diagram

or this system according to their thermal analysis on heating,lectric and dilatometric measurements. The phase relations inhe central part of the phase diagram were made clear for therst time. Three compounds of SbZn, Sb3Zn4 and Sb2Zn3 were

1 and C

op[bAlspt

pnitst�lfdtr[

tcras

lpaPs[[

[me

tg[

rTr

bepphdcS

2

c[

2

be

TL

R

[[

[[[

[[[[[[[

[[

72 J.-B. Li et al. / Journal of Alloys

bserved in this system with the existence of high-temperatureolymorphic transformations for the Sb3Zn4 and Sb2Zn3 phases13]. Oelsen and Middel [14] investigated the phase diagramy thermal analysis, electric and dilatometric measurements.ccording to their results, Sb2Zn3 does not seem to exist at

ow temperature. Nevertheless, they proposed a phase diagramimilar to that of Takei [13]. Tydlitat [15] also accepted Takei’shase diagram, according to XRD analyses, but suggested thathe Sb2Zn3 phase did not exist at low temperature.

Vuillard and Piton [16] reported a new high-temperaturehase Sb5Zn6 based on thermal analysis only, but it wasot checked by XRD. The thermal analysis results [16] aren agreement with Takei’s diagram [13] but do not confirmhe stability of Sb2Zn3 at low temperature. The decompo-ition temperature of the new phase Sb5Zn6 coincides withhe transformation temperature of Sb3Zn4 (corresponding to→ �′) at high temperature as proposed by Takei [13]. Vuil-

ard and Piton [16] disregarded the high-temperature trans-ormation of Sb3Zn4 in order to fit Sb5Zn6 into their phaseiagram, and ignored the experimental thermal events relatedo the polymorphic transformation of Sb3Zn4 on the Zn-ich side of Sb3Zn4 that were also observed by Tydlitat15].

Mayer et al. [17] investigated both the crystal structure,he homogeneity range and the stability of the intermediateompounds by XRD analysis on annealed samples. They did noteport the existence of the Sb5Zn6 phase at high temperature,nd the Sb2Zn3 phase was found unstable at low temperatureupporting Tydlitat’s results [15].

Koneska and Mavrodiev [18] interpreted their results as Vuil-ard and Piton [16] did, accepting the existence of the Sb5Zn6hase. It is worth to mention that in their work, a prolongednnealing of samples were done in contrast to Vuillard and

iton’s work [16] in which annealing was not performed. Theolubility limits of Sb3Zn4 reported by Koneska and Mavrodiev18] do not agree with those of Vuillard and Piton [16] and Takei13].

ZtTm

able 1iterature details of measurements on the phase diagram

eferences Method Reported phases

7] Thermal analysis on cooling (TAc)8] TAc

9] TAc SbZn, Sb2Zn3

10] TAc SbZn, Sb2Zn3

11] TAc

12] Thermal analysis on heating (TAh)13] TAh, electric and dilatometric measurements SbZn, Sb3Zn4, Sb2Zn14] TAh, electric and dilatometric measurements SbZn, Sb3Zn4, Sb2Zn15] X-ray diffraction SbZn, Sb3Zn4, Sb2Zn16] TAh SbZn, Sb5Zn6, Sb3Zn17] X-ray diffraction on annealed samples SbZn, Sb3Zn4, Sb2Zn18] Dilatometric and calorimetric measurements

on annealed samplesSbZn, Sb5Zn6, Sb3Zn

22] TAh, X-ray diffraction SbZn, Sb3Zn4, Sb2Zn3] TAh, X-ray diffraction SbZn, Sb3Zn4, Sb2Zn

ompounds 438 (2007) 171–177

Psarev and Dobryden [19], Psarev et al. [20] and Dobryden21] studied the solidification of several alloys. Several ther-al events were observed and interpreted as possible metastable

quilibria between SbZn and Sb2Zn3 or Sb3Zn4.A Ph.D. thesis done by Adjajd-Bouharkat [22] investigated

he whole system. The results [22,23] support Takei’s phase dia-ram [13]. The phase Sb5Zn6 proposed by Vuillard and Piton16] was not reported [22,23].

In a thermodynamic assessment on this system Liu et al. [24]eported new measurements on the liquidus at the Zn-rich side.heir results lead to a liquidus shape simpler than the previous

eported ones.Recently, the Sb–Zn phase diagram has been re-investigated

y Izard et al. [3]. New experimental information was reported,specially in the central part of the diagram: no evidence sup-orted the existence of Sb5Zn6, and a new high-temperaturehase �′-Sb3Zn4 with a congruent melting was proposed. Theomogeneity range of the compound Sb3Zn4 was quantitativelyetermined. XRD measurements performed at high temperatureonfirm the existence of two high-temperature modifications ofb3Zn4 [4], namely �-Sb3Zn4 and �′-Sb3Zn4.

The literature information is summarized in Tables 1 and 2.

.2. Thermodynamic properties

The thermodynamic properties of liquid alloys and Sb–Znompounds were studied by various experimental methods25–42]. They are reviewed in the following subsections.

.2.1. Liquid phaseElectromotive force (EMF) measurements were performed

y DeWitt and Seltz [25], Kleppa and Thalmayer [26], Kozukat al. [27], Gerasimenko et al. [28], Rubin et al. [29], Ptak and

abdyr [30], Gerling and Predel [31] and Seltz and De Witt [32]

o determine the thermodynamic properties of the liquid phase.he enthalpies of mixing of liquid alloys were measured byeans of calorimetry by Kawakami [33], Scheil and Lukas [34]

Comments

Liquidus dataLiquidus data

A transformation was observed between 593 and 633 K

Liquidus data

3 Several forms exist for Sb3Zn4 and Sb2Zn3

3 Several forms exist for Sb3Zn4 and Sb2Zn3

3 Sb2Zn3 exists for T > 678 K

4, Sb2Zn3 Sb5Zn6 exists for 766 < T < 800 K. Sb2Zn3 exists for T > 682 K

3 Sb2Zn3 exists for T > 682 K

4, Sb2Zn3 Sb2Zn3 exists for T > 682 K. A shifted solubility range wasreported for Sb3Zn4

3 Sb2Zn3 exists for T > 680 K

3 Sb2Zn3 exists for T > 682 K, two polymorphs have beenevidenced. Three forms exist for Sb3Zn4. A shifted solubilityrange was reported for Sb3Zn4

J.-B. Li et al. / Journal of Alloys and Compounds 438 (2007) 171–177 173

Table 2Experimental invariant reactions reported in Ref. [3] and calculated values

Reaction Temperature (K) Estimated composition at.% Zn Reaction type References

L1 ↔ Sb 903 0 0 Melting [3]

L ↔ Sb + �SbZn 779.05 37.1 0 50 Eutectic [44]780.15 31.3 2 50 [24]782 31 0 50 [3]774 31.5 0 50 This work

L + �Sb3Zn4 ↔ �SbZn 814.95 47.4 57.2 50 Peritectic [44]819.15 47.7 57.5 50 [24]

L + �’Sb3Zn4 ↔ �SbZn 820 47 55.8 50 Peritectic [3]817 46.6 55.8 50 This work

L ↔ �Sb3Zn4 835.75 57.1 57.1 Congruent [44]

L ↔ �′Sb3Zn4 841 55.8 55.8 Congruent [3]836.2 55.8 55.8 This work

L + �Sb2Zn3 ↔ �Sb3Zn4 834.15 55.9 60 57.5 Peritectic [24]

L ↔ �′Sb3Zn4 + �Sb2Zn3 835.65 57.7 57.1 60 Eutectic [44]839 55.9 55.8 59.50 [3]836 57.2 55.8 59.5 This work

L ↔ �Sb2Zn3 837.1 60 60 Congruent [44]836.15 60 60 [24]841 59.5 59.5 [3]836.8 59.5 59.5 This work

�SbZn + �Sb3Zn4 ↔ �Sb5Zn6 801.15 50 57.5 55 Peritectoid [24]

�′Sb3Zn4 ↔ �SbZn + �Sb3Zn4 798 55.8 50 55.9 Eutectoid [3]801.5 55.8 50 55.9 This work

�’Sb3Zn4 + �Sb2Zn3 ↔ �Sb3Zn4 805 55.8 59.5 55.9 Peritectoid [3]802 55.8 59.5 55.9 This work

�Sb5Zn6 ↔ �SbZn + �Sb3Zn4 764.55 55 50 57.5 Eutectoid [24]�Sb3Zn4 ↔ �Sb3Zn4 765.25 57.1 57.1 Congruent [44]

�Sb3Zn4 ↔ �SbZn + �Sb3Zn4 767 55.9 50 56.5 Eutectoid [3]767.3 55.9 50 57.14 This work

�Sb3Zn4 ↔ �Sb3Zn4 + �Sb2Zn3 764.85 57.5 57.5 60 Eutectoid [24]�Sb3Zn4 + �Sb2Zn3 ↔ �Sb3Zn4 767 55.9 59.5 56.5 Peritectoid [3]

767.6 55.9 59.5 57.14 This work

�Sb2Zn3 ↔ �Sb2Zn3 717.65 60 60 Congruent [44]

�Sb2Zn3 ↔ �Sb3Zn4 + �Sb2Zn3 713.15 60 57.5 62 Eutectoid [24]714 59.5 57 60 [3]715 59.5 57.14 60 This work

�Sb2Zn3 + L ↔ �Sb2Zn3 728.15 60 92.8 62 Peritectic [24]731 59.5 89.7 60 [3]733.2 59.5 96.1 60 This work

�Sb2Zn3 ↔ �Sb3Zn4 + Zn 678.25 60 57.1 100 Eutectoid [44]681.15 62 57.5 100 [24]677 60 57 100 [3]678 60 57.14 100 This work

L ↔ �Sb2Zn3 + Zn 684.65 98.3 60 100 Eutectic [44]682.15 97.8 62 100 [24]686 97.8 60 100 [3]687 98.75 60 100 This work

L ↔ Zn 692 100 100 Congruent [3]

174 J.-B. Li et al. / Journal of Alloys and C

Table 3Available literature details on thermodynamic properties of the liquid phase inthe Sb–Zn system

Phase Method Concentrationrange, XZn

Temperaturerange (K)

References

Liquid emf 0.15–0.92 753–893 [25]0.78–0.948 850 [26]0.10–0.90 815–938 [27]0.10–0.90 973 [28]0.10–0.90 823–923 [29]0.15–0.90 773–953 [30]0.05–0.90 860–1078 [31]

0.1–0.9 823 [32]

Liquid Calorimetry 0.197–0.918 973 [33]0.19–0.97 843 [34]

0.072–0973 913 [35]

L

altTt

2

sdaolbddLZa

aaStS

ooS

l

2

[oh[wtmtpcmscmtuw[

TC

P

S

�

�

�

�

0.1–0.9 923 [36]

iquid Vapor-pressure 0.23–0.76 1058 [37]

nd Wittig and Gehring [35,36]. The activities of elements in theiquid phase were obtained by measuring the vapor pressure ofhe corresponding elements over the liquid alloys in Ref. [37].he details of measurements on thermodynamic properties for

he liquid phase in literature can be found in Table 3.

.2.2. Solid compoundsThe enthalpy of formation of the SbZn compound was mea-

ured using direct calorimetry by Oelsen and Middel [14] andissociation-pressure measurements by Hirayama [38]. DeWittnd Seltz [25] deduced the standard thermodynamic propertiesf the three compounds SbZn, Sb3Zn4 and Sb2Zn3 from both theiquidus and the activities of elements in liquid phase measuredy EMF. The EMF method was also employed to determineirectly the thermodynamic properties of compounds by Zab-

yr [39], Goryacheva and Geiderikh [40] and Goncharuk andukashenko [41]. However, the measurements performed byabdyr [39] were done on slowly cooled melting alloys. Gory-cheva and Geiderikh [40] performed experiments on quenched

wOt

able 4omparison of thermodynamic properties of formation for compounds assessed in th

hase This work Literature

Gibbs energy Enthalpy Gibbs energy Enthal

bZn −9.508 −11.455 −9.7 −10.9−8210 −11.455 −7.946 −9.51

−11.459 −14.85−11.459 −12.84

−8.233 −25.086 −8.115 −20.01−11.459 −15.05

−7.674 −15.149 −7.465 −11.89

′-Sb3Zn4 −7.947 −16.028 −8.032 −20.55

-Sb3Zn4 −7.982 −17.878 −7.903 −12.37−7.200 −10.707 −7.126 −4.35

-Sb3Zn4 −8.494 −9.378 −8.8 −10.7−8.115 −9.378 −6.99 −5.28

-Sb2Zn3 −7.131 −9.839 −6.916 −5.78

ompounds 438 (2007) 171–177

lloys. And Goncharuk and Lukashenko [41] worked on wellnnealed and pressed samples. The enthalpies of formation ofbZn and Sb2Zn3 were obtained by calorimetric determina-

ion of their enthalpies of reaction with hydrochloric acid byhchukarev et al. [42].

Hulgren et al. [43] evaluated the thermodynamic propertiesbtained from literature and reported a set of mixing enthalpiesf the liquid phase and the standard enthalpy of formation ofbZn.

The thermodynamic properties of compounds reported in theiterature are listed in Table 4.

.3. Thermodynamic description

Two assessments have been made on this system by Zabdyr44,45] and Liu et al. [24]. The first thermodynamic modelingf this system was made by Zabdyr [44]. Then, he extendedis work to the calculation of the ternary Cd–Zn–Sb system45]. In these calculations [44,45], Takei’s phase diagram[13]as accepted though without considering the high-temperature

ransformation of the Sb3Zn4 phase, and all the compounds wereodeled as stoichiometric. For the liquid phase two models were

ested: a substitutional solution model using Redlich–Kisterolynomials and an associated model, trying to describe theomplex short-range order in the liquid phase. Since many ther-odynamic and physical measurements on the liquid phase

uggest the existence of Sb3Zn4 entities [46–50], Sb3Zn4 washosen as the modeled associate in liquid [44,45]. With bothodels [44], a large number of modeling coefficients were used

o fit the thermodynamic properties and the curvy-shape of liq-idus in the Zn-rich part. In the ternary system the solution modelith 11 coefficients of Redlich–Kister polynomials were used

45].

Liu et al. [24] employed the substitutional solution model

ith Redlich–Kister formulas to describe the liquid phase.nly six coefficients were used for the liquid phase based on

heir own measured liquidus in the Zn-rich part. In this model

is work with the experimental data in literature (kJ/mol atom)

Reference state References

py

Rhombohedral-Sb and hcp-Zn at 420 K emf [40]7 Rhombohedral-Sb and hcp-Zn at 700 K Evaluated [43]3 Rhombohedral-Sb and hcp-Zn at 298.15 K Vapor [38]5 Rhombohedral-Sb and hcp-Zn at 298.15 K emf [25]1 Liquid-Sb and -Zn at 804 K emf [25]2 Rhombohedral-Sb and hcp-Zn at 298.15 K Calorimetry [14]

Rhombohedral-Sb and liquid-Zn at 750 K emf [39]

1 Liquid-Sb and -Zn at 826 K emf [25]

9 Liquid-Sb and -Zn at 806 K emf [25]Rhombohedral-Sb and liquid-Zn at 800 K emf [39]

Rhombohedral-Sb and hcp-Zn at 420 K emf [40]Rhombohedral-Sb and hcp-Zn at 600 K emf [39]

Rhombohedral-Sb and liquid-Zn at 800 K emf [39]

and C

tpa

ot

3

gTao(

�

w0

rttatecb

s(

G

we[TR

To

tm[

4

widdee�tt[

[tidtouf

roaocaoi

TO

P

L

S�

�

�

�

�

J.-B. Li et al. / Journal of Alloys

he temperature dependence of mixing enthalpy of the liquidhase was not considered. Sb5Zn6 was accepted without furthernalysis in Liu’s work [24].

Considering the new results on the phase relations [3] andn the thermodynamic properties [40,41] in this system, a newhermodynamic description is necessary.

. Models

All compounds in the Sb–Zn system present a narrow homo-eneity range which is less than 2 at.% at low temperatures [3].hey are then treated as stoichiometric compounds in this work,s they were in previous calculations [24,44]. The Gibbs energiesf formation of the stoichiometric compounds can be written asin unit of J/mole of formula),

GSbmZnn = 0GSbmZnn − m0GA7Sb − n0G

hcpZn

= a + bT + cT lnT + dT 2 + eT−1 + fT 3 (1)

here 0GSbmZnn is the Gibbs energies of the compound SbmZnn.GA7

Sb and 0GhcpZn are the standard Gibbs energies of the

hombohedral-A7 of Sb and hcp-A3 of Zn unary phases, respec-ively. The thermodynamic parameters of pure elements areaken from Dinsdale’s unary database [51]. a, b, c, d, e and fre coefficients to be optimised. c, d, e and f are determined byhe heat capacities of compounds. a and b are mainly defined bynthalpies and entropies. Because none of the heat capacities ofompounds are available, only two coefficients, a and b are toe optimised.

The Gibbs energy of the liquid phase is described by aubstitutional solution model with Redlich–Kister polynomialsJ/mol atom),

Liq = xSbGLiqSb + xZnG

LiqZn + RT (xSb lnxSb + xZn lnxZn)

+ xSbxZn

n∑

k=0

LLiqk (xSb − xZn)k (2)

here GLiqi is the standard Gibbs energy of formation of pure

lement i in the liquid phase and taken from Dinsdale’s database51]. xi is the molar fraction of element i in the liquid phase.he third term is the excess Gibbs energy, expressed using theedlich–Kister formula. LLiq

k=0,1... are the interaction parameters.

5

m

able 5ptimized parameters for the Sb–Zn system

hase Chemical formula Temperature ran

iquid 298.15 < T < 200

bZn SbZn 298.15 < T < 816′-Sb3Zn4 Sb3.094Zn3.906 801.5 < T < 836.-Sb3Zn4 Sb3.087Zn3.913 767.3 < T < 802-Sb3Zn4 Sb3Zn4 298.15 < T < 767-Sb2Zn3 Sb2.025Zn2.975 715 < T < 836.8-Sb2Zn3 Sb2Zn3 678 < T < 733.2

ompounds 438 (2007) 171–177 175

hey are temperature dependent (a + bT + · · ·) and they are to bebtained by optimization.

Both the rhombehedral-A7 (Sb) and hexagonal-A3 (Zn)erminal phases are treated without solubility. Their ther-

odynamic functions are taken from Dinsdale’s database51].

. Optimization

The PARROT module [5] of the Thermo-Calc software [6]as used for the optimization. The least squares theory is applied

n the software to perform the optimization of thermodynamicescriptions using experimental phase equilibria and thermo-ynamic data. All the experimental data were first criticallyvaluated and selected. According to the investigations of Izardt al. [3,4] and Takei [13], the high-temperature modification′ of Sb3Zn4 was accepted as existing above about 820 K, andhe Sb5Zn6 is unstable in this system. The Sb2Zn3 phase wasreated to be unstable below about 678 K according to Refs.3,15–18,22].

For the liquidus, the results from thermal analysis on cooling7–11] were not taken into account in this work. Consideringhe high vapor-pressure of elements, the uncertainties on exper-mental data may be large. In fact, the liquidus reported areispersive, especially in the Zn-rich part. The extrapolation ofhe liquidus reported by Curry [12] decreases the melting pointf Sb2Zn3 for more than 30 K, so Curry’s work [12] was notsed in the optimization. All the other liquidus data were takenor the optimization.

The calorimetric results of Kawakami [33] for liquid wereejected for their inconsistency with other data. The enthalpiesf formation of compounds reported by Shchukarev et al. [42]re 3 times larger than others, so they were discarded from theptimization. Zabdyr [39] performed the EMF measurements onooled melting alloys. The obtained thermodynamic data [39]re much smaller than others. They can result from the instabilityf the compounds. Therefore, Zabdyr’s data [39] were not usedn the optimization.

. Results and discussion

Eighteen coefficients of the Gibbs energy functions were opti-ized, among which six are pertaining to the liquid phase. The

ge (K) Parameter (J/mole of formula)

0 0LLSb,Zn −11951 − 1.1174T

1LSb,Zn −3325.6 + 1.0004T2LL

Sb,Zn 29432 − 23.6303T

.7 0GSb,Zn −22909 + 9.2716T3 0Gδ′

-Sb3 −21785 − 41.2819T0Gδ-Sb3Zn4 −45931 − 11.1711T

.6 0Gε-Sb3Zn4 −65647 + 14.7403T0Gξ-Sb2Zn3 −27137 − 14.8975T0Gη-Sb2Zn3 −30667 − 9.4925T

176 J.-B. Li et al. / Journal of Alloys and Compounds 438 (2007) 171–177

Fi

tlro

ptfitq

wTdp(cpe

Ft

cCpm

(SbZaAdepSb3Zn4 entities was tested in this work and the results definitelyconfirm that this model cannot reasonably describe the liquid.

ig. 1. Calculated phase diagram of the Sb–Zn system compared with the exper-mental data.

hermodynamic parameters, resulting from this optimization, areisted in Table 5. Total 650 experimental data were used and theatio between the number of experimental data and the numberf the optimized variables is 36 in the optimization.

The calculated phase diagram is shown in Fig. 1 and com-ared with the experimental data. An enlarged central part ofhis phase diagram is given in Fig. 2. The calculated liquidusts well with recent reports [3,24]. For the invariant reactions,

he agreement between the calculated and experimental data isuite good as listed in Table 2.

Enthalpies of mixing of the liquid phase calculated at 913 Kere plotted with the appropriate experimental data in Fig. 3.he calculated values are well consistent with the experimentalata from Ref. [34]. Fig. 4 compares the calculated chemicalotentials of Zn in the liquid phase at various temperaturesT = 823, 873, 973 and 1073 K) with the experimental data. The

alculated activities of Zn in the liquid phase at various tem-eratures (T = 830–870–950–1058 K) are shown in Fig. 5 withxperimental data. The calculated thermodynamic properties of

Fig. 2. Enlarged central part of the calculated phase diagram.

o

Ft

ig. 3. Enthalpies of mixing of liquid alloys calculated at 913 K compared withhe experimental data.

ompounds are listed in Table 3 with the experimental values.onsidering the uncertainty on experimental thermodynamicroperties, the agreement between the calculated and experi-ental data is good.As it was suggested in Ref. [3], two kinds of associates

Sb3Zn4 and Sb2Zn3) could exist in the Sb–Zn melt. Indeed,b3Zn4 entities have been clearly evidenced in the liquid phasey Ref. [30,47–50] and a maximum excess volume for 60 at.%n, reported by Ref. [52] from density measurements at 923 K,ssumes the existence of Sb2Zn3 clusters at higher temperatures.s a consequence, an associate model should be a good candi-ate to describe the liquid phase if it takes into account Sb3Zn4ntities near the liquidus and Sb2Zn3 clusters at higher tem-eratures. Like Zaddyr did in [44,45], an associate model with

Nevertheless, much more experimental work should be donen this system to improve the modelling of the liquid phase. The

ig. 4. Calculated chemical potentials of Zn in the liquid phase compared withhe experimental data (T = 823, 873, 973 and 1073 K).

J.-B. Li et al. / Journal of Alloys and C

Ft

lZb

6

sdspocd

A

t

R

[[[[[

[[[

[[[

[[

[

[

[[[

[

[[[[[[[[[[[[

[[

[

[[[[[

ig. 5. Calculated activities of Zn in the liquid phase compared with experimen-al data (T = 830, 870, 950 and 1058 K).

iquidus should be determined more precisely, specially in then-rich part, and further thermodynamic measurements shoulde performed on the liquid phase and on the compounds.

. Conclusion

The optimization of Gibbs energies of all phases in the Sb–Znystem has been performed based on the available experimentalata. All the compounds were treated as stoichiometric. Theubstitutional solution model was used to describe the liquidhase. Two terminal phases were treated as unary phases. A setf self-consistent thermodynamic parameters was obtained. Thealculated results are in good agreement with the experimentalata.

cknowledgment

The work is supported by National Natural Science Founda-ion of China, under contract No. 50542006.

eferences

[1] T. Caillat, J.P. Fleurial, A. Borshchevsy, J. Phys. Chem. Solids 58 (1997)1119–1125.

[2] S.G. Kim, I.I. Mazin, D.J. Singh, Phys. Rev. B 57 (11) (1998) 6199–6203.[3] V. Izard, M.C. Record, J.C. Tedenac, S.G. Fries, Calphad 25 (2001)

567–581.

[4] V. Izard, M.C. Record, J. Haines, J.C. Tedenac, Mat. Res. Soc. Symp. Proc.

691 (2002) G8.35.313.[5] B. Jansson, Ph.D. thesis, Royal Institute of Technology, Stockholm, Swe-

den, 1984.[6] B. Sundman, B. Jansson, J.O. Andersson, Calphad 9 (1985) 153–190.

[[[[

ompounds 438 (2007) 171–177 177

[7] R. Gosselin, Bull. Soc. Encourag. Ind. Natl. 5 (1896) 1301–1310.[8] C.T. Heycock, F.H. Neville, J. Chem. Soc. 4 (1897) 383–422.[9] K. Monkemeyer, Z. Anorg. Chem. 43 (1905) 182–196.10] S.F. Zemczuzny, Z. Anorg. Chem. 49 (1906) 384–399.11] P.T. Arnemann, Z. Ges. Hutt. 13 (1910) 201–211.12] B.E. Curry, J. Phys. Chem. 13 (1909) 589–597.13] T. Takei, Sci. Rep. Tohoku Univ. 16 (1927) 1031–1056.14] W. Oelsen, W. Middel, K.W. Mitt, Inst. Eisenforsch. Dusseldorf 19 (1937)

1–26.15] T. Tydlitat, Czesh. J. Phys. 9 (1959) 638–640.16] G. Vuillard, J.P. Piton, C.R. Acad. Sci. Paris 263 (1966) 1018–1021.17] H.W. Mayer, I. Mikhail, K. Schubert, J. Less-Common Met. 59 (1978)

43–52.18] S. Koneska, G. Mavrodiev, Fizica 12 (1) (1980) 137–142.19] V.I. Psarev, K.A. Dobryden, Inorg. Mater. 2 (1970) 203–207.20] V.I. Psarev, V.G. Kirii, V.A. Andronnikov, Inorg. Mater. 17 (3) (1981)

260–264.21] K.A. Dobryden, Inorg. Mater. 19 (4) (1983) 494–501.22] F. Adjadj-Boucharkat, Ph.D. thesis, Universite Claude Bernard—Lyon I:

Le diagramme d’equilibres entre phases du systeme ternaire Bi–Sb–Zn,1995.

23] F. Adjadj, E.-D. Belbacha, M. Bouharkat, J. Alloys Compd. 430 (2007)85–91.

24] X.J. Liu, C.P. Wang, I. Ohnuma, R. Kainuma, K. Ishida, J. Phase Equilibr.21 (2000) 432–442.

25] B. DeWitt, H. Seltz, J. Am. Chem. Soc. 61 (1939) 3170–3173.26] O.J. Kleppa, C.E. Thalmayer, J. Phys. Chem. 63 (1959) 1953–1958.27] Z. Kozuka, J. Moriyama, I. Kushima, J. Electrochem. Soc. Japan 29 (2)

(1961) E104.28] N.L. Gerasimenko, V.A. Zaitsev, N.L. Lozhkin, A.G. Morachevski, V.U.Z.

Izv, Tsvetn. Metall. 3 (1966) 44–45.29] I.B. Rubin, K.L. Komarek, E. Miller, Z. Met. Kd. 65 (1974) 191–199.30] W. Ptak, L. Zabdyr, Arch. Hutn. 20 (1975) 379–387.31] U. Gerling, B. Predel, Z. Met. Kd. 77 (1986) 17–25.32] H. Seltz, B.J. De Witt, Trans. Electrochem. Soc. 77 (1940) 233–259.33] M. Kawakami, Z. Anorg. Chem. 167 (1927) 345–363.34] E. Scheil, H.L. Lukas, Z. Met. Kd. 52 (1961) 417–422.35] F.E. Wittig, E. Gehring, Ber. Bunsenges 70 (1966) 717–723.36] F.E. Wittig, N. Saes, W. Waldherr, Rev. Chim. Miner. 9 (1972) 71–113.37] K. Jellinek, H.H. Wannow, Z. Elektrochem. 41 (1935) 346–362.38] C. Hirayama, J. Electrochem. Soc. 110 (1963) 88–91.39] L.A. Zabdyr, Can. Met. Quart. 19 (4) (1981) 359–362.40] V.I. Goryacheva, V.A. Geiderikh, Russ. J. Phys. Chem. 71 (4) (1997)

526–529.41] L.V. Goncharuk, G.M. Lukashenko, Zh. Prikl. Khim. 1 (1989) 10–13.42] S.A. Shchukarev, M.P. Morozova, Yu.P. Sapozhnikov, Zhur. Obshchet.

Khim. 26 (1956) 304–307.43] R. Hulgren, P. Desai, D. Hawkins, M. Gleiser, K. Kelley, Selected Values

of the Thermodynamic Properties of Binary Alloys, ASM, Cleveland, OH,1973, pp. 920–924.

44] L.A. Zabdyr, Calphad 17 (3) (1993) 269–280.45] L.A. Zabdyr, Calphad 21 (1997) 349–358.46] A. Sinha, E. Miller, Metall. Trans. 1 (1970) 1365.47] A. Bath, J.G. Gasser, R. Kleim, Phys. Lett. 91A (7) (1982) 355–357.48] M.R. Mian, A. Mikula, K.L. Komarek, W. Neumann, Z. Met. Kd. 77 (3)

(1986) 133–139.

49] Y. Tsuchiya, S. Kanai, J. Non-Cryst. Solids 156–158 (1993) 434–436.50] L.C. Prasad, Mikula, J. Alloys Compd. 299 (2000) 175–182.51] A.T. Dinsdale, Calphad 15 (1991) 317–425.52] L. Dim, A. Bath, J.G. Gasser, J.L. Bretonnet, R. Kleim, Phys. Lett. 84A7

(1981) 375–377.