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An assessment of phase diagram and thermodynamic properties of the gallium-1ndium-antimony system
Pergamon 0364-5916(94)00007-7
CufphadVol. 18, No. 2, pp. 185175, 1994 Copyright 0 1994 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0384-5916/94 $7.00 + 0.00
AN ASSESSMENT OF PHASE DUGRAM AND THERMODYNAMIC PROPERTIES OF THE GALLIUWINDIUM-A SYSTEM
YangJianrong’ and Andy Watson Depprtmnt of Rttgineuing Mat&ala, PortobeRo St, Univemity of Shcklield, U.K. S13JD l
Shanghai Institute of Technical Physica, Chinese Academy of Science, Shanghai 200083, China
The cxp-tal thumodynsmic and phase diagram data of the Ga-In-Sb tx ~~2 been critically asaes&. A thermodynamic description that is conmakn experimental data has been pnxhrced with the aid of ternary optinking program TERGSS. Calculation of thermodynamic properties and phase diagrams were carried out using MTDATA.
It is well known that III-V aaniconductor compounds have an extremely important application in high speed and high frequency devices. In the III-V semiconductor family Ga-In-Al-S&k, thee am tat ternary snbsyatems. By aelecting different compositions within these subsysteans, electrical and optical prop&or of the materials can be changed in order to satisfy different applications. In this worh, the Ga-In-Sb try&an has been asses& as a first stage in the study of the Ga-In-Al-%-As system. Since Liao et al[l] calculated the Ga-In-Sb syatan in 1982, new thermodynamic expcrkntal dudiea have heat undat$cen by Aaelage and Andason(S], Chang et al[3], and Rugg and Bryanq4]. The three binary sub~~withthtternaryGa-In-Sbhavealsobecnassessedby~&AnserdS],and~et al[6]. More recently, a thamodynamic analysis and calculation of the phase equilii of the tanary ayatan haa been tmdatahut by Sharma and Muhajbe(7l although they had not used the moat recent deacriptiona of the antimonide binary ayatuna. It is also important to m-evaluate the ternary with the enthalpiea of formation of the (Ga,In)Sb solid sohttion[4] which were not available to Sharma and Mulcerjee, as it is from such wttr that the stability of the phase can be aases&. The experimental phase diagmm and thermodynamic data available in the litaature for the Ga-In-Sb system have been critically aaaea& and by using unary data for the elementa aa rccommQLded by SGTE[8], thermodynamic descriptiona of the ternary liquid and (Ga,In)Sb phaaea which are con&tent with the expekattal data, have been produced This was achieved with the aid of the ternary optimization program TERGSS lcindly donated by Dr. H. L. Lul@9,10] of the MPI Stuttgart.
IL1 Pbraa dlaglxm data
Measurement of the Ga-In-Sb liquidus has been made by Blom and Pla&ett(l I], AnwlZ] and M&i et al[ 131 using a weight loss method, and by Gorshhov and Goryunova[l4], Utimtaev et al[ IS], Woolley and Lc@l6], and Joullit et al[ 17] using heating and cooling curve analyaia. Direct visual obaavatiort of melting tanpaoavts was wal by Ahrohvah and Gashcazon[l8]. For thermal methoda and direct obaavatioa, supacoolingiscollsidetedtobethtmain~~ofuncatainty.Inweightlossmdhodr,thaeisnoarpacooline probletn However, there ie a possibility of uncertainty with thin method and with thate typea of systems, owing to equilibrium not being established. This method relies on the dissolution of a GaSb crystal into a mlt until the liquid becom#l @urated. An interface layer of the ternary compound in equilibrium with this liquid is then formed on the surface of the crystal. The liquidus composition is then detumined by the weight loss of the Original
version received on 11 June 1993, Revised version on 8 October 1993 165
166
J. YANG AND A. WATSON
qstal. However, the diffusion rates of the components are very low, and so there may be difficulties in anaining equiliium. Also,no account is tahen of diffusion of indium from the melt to the crystal which would have an affect on weight loss calculations. An m technique was used by Gratton and Wcolleyll9], Blom and P-1 11, and Woolley and Smith(ZO] to measure the solid&liquidus equilibria. X-ray studies of the annealed and quenched specimene mveakd the compositions of the phases in equilibrium. Blom and Plaskett used a microprobe technique in pmfaence to x-rays. Gratton and Woolley extrapolated their solidus -ts to the liquidus curves as given by Blom and Pkakett, Joullit et al[l7], and Antypas[l2], in order to calculate the associated equilibria. As these derived liquidus data were heavily depcr&nt on those of other workers they were not considered in this optimisauon. LPE methods ware used by An~lZ], Joullib et al[171,[21], Rode et al[22] and Miki et al[13] for the &ammation of the solidus compositions. AnnAing techniques allow experimental conditions close to squilibriumthusallowingabe#aaccuracyinthemeaslPemntoftcanpaaturc than LPE methcds, however, the uncatamty in composition is of the same order. By comparmgaUtheexperimentalphasediagramdata,itcouldbe raenthtthaewPI~~88ebCI13Qltbdwccnthedatawithintheuncataintitsassignedinthisaapcssment. The pseudobinaty GaSb-InSb phase diagram data of Woolley and Smith[20], and Woolley and Lees[ 161 have large differences from those of Gorshkov and Goryunova(l4], and Ufimtsev et al[lS]. Both Woolley and Smith and Gorshkov and Goryunova used the same annealing technique, but Woolley and Smith followed the heat tmatment of their alloys by quenching, whereas Gorshkov and Goryunova did not. It is therefore more likely that the compositions detamined by Woolley and Smith would reflect the equilibria at the annealing temperature than those determmed by Gorshkov and Goryunova The optimization result also shows that the data of Woolley and Smith fit other experimental data better than those of Gorshkov and Goryunova, or Ufimtaev et al. For these reasons Wcolky and Smith’s data were taken in this work and those of Gorshkov and Goryunova and Ufbntsev et alwereomittedinthetinaloptimisation. ThesesamedatawcrealsodiaregatdedintheworkofLiaottal[l]and Blom and Plasheqll]. ILII llranttodynnmk
data
Enthalpiea of mixing of liquid alloys have been measu& by Ansara et al[23] and Vecher et al[24] using direct reaction calorimetry and quantitative differential thetmal analysis respectively. The agreement between the twosetsofdatairpoor.Insomecases,thedifferencesarelargerthan50%ofthemeasuredvalues.Thc expaimatal results of Vecher et al were presented in the form of an isothermal ternary section showing contours mpresenting mixing enthalpies without indicating specific expcairmmtal mcasuremglts. This resulted in a fairly large uncertainty being ascribed to the data (+/- 20% in the eduhalpies of mixing) owing to the difficulties in reading the data accurately. The mixing enthalpies of pseudobinaty liquid were measwed only by Gerdes and Predel[ZS]. Enthalpies of mixing of the (Ga,In)Sb pseudobinary solid solution have been measmed by Rugs and Bryanq4], and Mechkovskii et al[26] the latter calculating the enthalpies of mixing of the solution t?om the difference between the atthalpies of mixing of the binary Ga-Sb, In-Sb and ternary Ga-In-Sb liquids. The former calculated anhalpies of mixing from measumd enthalpies of solution of the binary GaSb and JnSb compounds, and pseudobinary alloys in tin and indium. The uncertainty in both sets of vts of the enthalpies of mixing of the ternary solid solution are high, their small numerical values being compamble in magnitude to the expaimGntal scatter. Gn comparing these two sets of results, it was found that they had opposing signs. Partial Gibbs energies of gallium in the liquid phase have been measumd by Aselage and Anderson(2], and Chang et al[3] using an electrochemical method. An experimental accuracy of 5% was given for the data by the authors. However, under comparison, it was evident that the temperanve dependence of the emf was of opposing rienfotthetwosctsofresults.Thisirnpliesthattheuncataintyfactoremustbclarggthanquotbdoroneactof dataare -us. Table 1 gives a summary of the experimental data available in the litaature together with the exper+mtal techniques employed and their assigned uncutainties used in this assessmnt. The sekcted data and mkcrtamties were used in the subsequent ternary optimization.
ASSESSMENT
OF THE Ga-In-Sb
167
SYSTEM
Many thcrmadynamic models have been previously proposed to describe the thamudynamic propatiea of the tanary Ga-In-Sb liquid, for example the regular solution model, the sub-regular solution model, the awchtcd solution model and 0th~~ modified models[3],[13]. There has been no cxpuimcntal evidcwe of assohtion bchaviour in the Ga-In-Sb liquid as has bezn found in II-VI systcm@7]. If the unc&aintica of the expehental data arc taken into consition, it can be found that the sub-regular model is adequate to dwribe both the Ga-In-Sb liquid and the (Ga,In)Sb pseudobinary compound. The thcamodynamc descriptions of the three binary systems were extrapolated into the ternary using Muggianu’s[28] expression. The excess Gibbs energy of the liquid phase owing to ternary intcaactions of the three components was expressed by Ge(l) = x(Ga)x(In)x(Sb)(a’+b’T)
( J g-atom-‘)
(1)
The solid solution between the GaSb and InSb was treatal as a pseudobinary solution rather than a true ternary, and thus the cxct88 Gibbs cnagy was dcscrikd by an expression equivalent to the Rcdlich-Kistcr formalism [29] used for the binary liquid phases
Ge(s) = x(GaSb)x(InSb) (a’ +bl’)
(J mol-’Wxb., )W
(2)
168
J. YANG AND A. WATSON
~HSJX-A+BT+ChT+~+l!fP+Flr+
B
A
2OO.oocToo2.92K
-21312331
30292aQ9OO.OK
-7055.643
w 200.oocT402.92K
GT’+IW
D
C
P
585.263691 .I08328783 0.22715564 -1.1857526E-r 439954
G
A
0.0
0.0
-0.040173E-6
.118332
0.0
I .645E+23
-15821.03 567.189696 .I08228783 0.22715564 .1.18575263-(
439954
-7.0173-17
0.0
-0.040173E-6
.I 18332
0.0
0.0
-22906
0.0
.211708
0.0
3O2.92.fR29OO.OK -1389.19
132.7302
.26.0692906 0.1506E3
114.049043 .26.0692906 0.1506E3
200.M429.75K
-6978.89
92338115
-21.8386
.5.72566B3 -2.120322E-6
429.7HB.OK
-7033.52
124.476588
-27.4562
5.46@7E4
ligpia 200.m429.75K
-3696.798
84.701255
-21.8386
.5.72566E3 -2.12032lE-6
429.7~Q9OO.OK
-3749.8 I
116.857840
-27.4562
5.4607E-4
298.WTa3.78K
-9242.858
156.154689 .30.5130752 1.748768B3 -3.003415e-6
pO3.78qB.OK
-I 1738.830 169.485872
w 298.WZ3.78K
10579.470
@03.78~~.OK
8175.36
-8.367E-8
-8367E8
-22906
.5.590583-2C
.211708
0.0
100625
0.0
0.0
0.0
0.0 .53116E+22 0.0 0.0
ltwdhdd-A7
T&k%
0.0
0.0
134.231525 ,30.5130752 1.7487683-3 -3.0034153-6 147.455986
lhmodymmk G”-
-31.38
0.0
0.0
-31.38
IO0625 0.0
puucrar.f~Wl,Grsb(~~~~Lippld==
x(1-x)[(A,+A,T+A,TlaT)+
( B,+B,T)(Mx)
(J gjtom”)
+ C,(lA)~
,1.74847&2(1 0.0
0.0 .61685E+27 0.0 0.0
ASSESSMENT OF THE Ga-in&b
llm
x .
SYSTEM
m-m
1 Figure1 Awesed Ga-Sb Phase -4
D I-
Figure 2 Asses& In-Sb Pti Diagm46]
Figure 3 Amessed Ga-In Phase D&mu@]
199
J. YANG AND A. WATSON
170
Table 34. ‘llwmodynamic A
B
Data for GsSb ud fnSb Binary Cempomb. G-HSER J mot’ D
C
E
F
G
H
G8sb 2OO.OWR302.92K 302.92.fh903.78K 903.78cr<29oo.OK
-74031.389 -59774.701
720.3431
-133.356106 0.23214859 -1.21578~04
267.809609 -51.1966138 0.00514355 -3.043588BO6
-62270.673 281.140792 -52.0635386 -0.00260522 -4.0173BOS
540579
0
0
-17707
0
1.645Fi+23
-118332
0
1.6170145E+27
IBsb 2OO.W<429.75K
-47920.348
429.7HW3.78K
-47974.978 281.217555 -553821132 0.00829484 -3.087085B06
903.78-fR29OO.OK -50470.95
249.079082 -49.7645132 0.00202311 -5.123737BO6 294.548738 -56.249038 0.00054607
-8.367B-08
77719
0
-111083
0
3.53116OOE+22
0
-211708
0
1,6168853B+27
The ternary optimising program, TERGSS, was used to produce Gibbs energy coefficients for the ternaty liquid and pseudobinary phases, that were consistent with the selected experimental data. Initially, all the experimental thermodynamic and phase diagram data were given the same weight in the optimisation procedure based upon the assessed experimental uncertainties. Early results showed that some of the data were in obvious disagreement with the majority of the data. For this reason, the data of Vecher et al[24], Gorahkov and Goryunova[l4], and the pseudobinary phase diagram data of Ufimtaev et al[ 151 were omitted from the data set. The enthalpies of mixing of the solid solution data of Mechkovskii et al[26] were also omitted as the optimisation suggested that values of an opposite sign to that of those data would be in closer agreement. Therefore, Rugs and Bryant’s[4] data were accepted as their data had the appropriate sign. The weight of the pa&l Gibbs energy data of Aselage and Anderson[2] was reduced to 50% of that given totherestofthedata. Thiswasbecausethese&tacolnprised400/0ofthttotal&taset,andthusthertmayhave been a tendency of the optimisation to be biased in favour of these data purely because of their number. A weight of 50% was also used for Ansara et al’s data[23] as there was a certain degree of disagreement between these and the rest of the data. In the final result, there is about 20% discrepancy between these data and the optinkd curves. Incidently, even though Vecher et al’s data[24] were omitted, it is worth noting that these data lie on the opposite side of the optimised curve from that of Ansara et al’s data. Table 4. Optimii Excess Gibbs Energy Ceefficieata for the Ga4n-Sb System a
b
liquid
-5072.76
-10.8842
(GoJn)Sb
9093.00
-2.8698
The resulting coefficients from the final optimisation are given in table 4. The phase diagrams with the tielines and experimental data (shown as fig.45) have been plotted using MTDATA[30] and the parameters in table 4. It can be seen that most of the phase diagram data are in agreement with the calculated liquid isotherms except for some near the In-Sb boundary, such as those of Antypas[lZ] at 773.15K and Joullie et al [17] at 653.15K. These data did not fit well because they conflicted with the description of In-fib binary. It is in&resting to note that certain amount of disagreement was found between the extrapolated liquidus data of Gratton and Woolley[l9] and the calculated curves. Sharma and Mukerjee[7] on the other hand, found a better fit of these data to their calculated curve. It is felt that this may be, because including such a large amount of data in their optimisation which were extrapolations to other experimental data, a bias had been imposed on theirSnalresult. The GaSb-InSb pseudobii phase diagram together with the experimental data of Woolley[20], and Blom and Plaskett[l l] is shown in fig.6. This result has no obvious differences from that obtained using an 888oci8tbd solution model for the liquid[l]. Most of the solidus experimental data was found to fit with the calculated curve. However, an intemsting feature of the calculation is the appearance of the miscibility gap in the (Ga,In)Sb solid solution. The critical &upemmm was calculated to be 466.3K The presence of the miscibility gaphasnotbeenumfkmed experimentally owing to sluggish diffusion rates at the relatively low temperature.
ASSESSMENT
OF THE Ga-In-Sb
SYSTEM
171
h
Figures4&5 Calculated Liquidus Phase Boundaries with Experimental Data
h
7
(b
bd
0.6
0.6
0.4
0.2
sb
172
J. YANG AND A. WATSON
Howeva, it could have profond implicatiom for devicea mde from such mamials an there is a possibility of tbcirdcgr&tionwithtim. Asimilartcmpemm for Tc was proposed by Chang d al[3] (433K) resulting lkom tkir ulculations. The level of agreunmt ia aaxptable comkking the qaimaltal diflialltiea atm** in maaning the enthalpits of mixing of the solid solution -41, which had a sign&ant effect on detammm tbcmiaciitygapintbiswork. Tht~cnthalpieaofmixineofthcpacudobiDlryphucwatf~to~ well. witb to imeasc thewcightofthwcdatadutingtbc . . the calculatai curva~. Howeva, it was nectary m in odm to pmduce well &find Gibbs amgy coefficienta. for the a&lpiof mixing of the liquid Thereisalargcdkmpmcybctwcencalculatiunandqminmt agraxnmtwiththephase pIwe (ace Fig.7). Thin ia a caneaquenccoftbcdatanotbcinginparticularlygood diagmmdat8.Thi8illalm&owIlinLi8octal’swork. Uwxpcedly, the mixing cntbalpy data of pseudobinary liquid could be fitted very well. These dsta me ahowninfi~8~withthecalculatadheatcurveproducodfromtheoptimisotion. Thefsctthatthiswar not fcktal in Sbamu and Mukajae’s(7l work was probably mainly due to a typographical m-or in tbc original publicatiot~. However, their calculated curve still gives largez valum for the heat of mixing than wme found hm.
173
ASSESSMENT OF THE Ga-ln-Sb SYSTEM
-m
I 5
.
-1ooc4 8
.
l
.
-
L
_
-em0
P
-awe
B a _ii 6
-mwo
-=3ol- Es’
’
050
’
en
loo0 la5
la0
1075 1100 11.
Figure9dsowstbecrlculrtedportinlGibbr~~of~~intbe~dphuecomprredwiththe dqxndamofgalliumputhl cxpuimcntaldataOfAaelageMdAndason[2].Itcanbcseenthatdte~ Gibbaawgyfitswcllwiththecalculatedvalw.s. 1twasfoundtlwmostofthachtamuldbcfittalwcllif2036
Athr#~aquilibriumnsion~~fo~intbeSb-richsiderttanpartPrsr similar~thatintbeA8-Ga-Inphaac~31]. Thisis&owninfigurc1O. respccttodeviccmanuf~willbcdiscussedinafimnepublicatim
fnnu768Kto86OK Theimpliatioaaoftlhwith
174
J. YANG AND A. WATSON
F&we. 10 calculrtedSectionofthe Ga-Jn-Sb System at 800°C Showing llllee Flme Region.
The authors would like to thank Dr. Leo Lukas of the Max Planck Institute, Stuttgart for the provision of TERGSS and the help and advice throughout this and other work, and also to the NPL Teddiqton for the use of MTDATA[30] and all the help in its implementation. Dr Yang Jianrong would also like to thauk his Institute, the Shaughai Institute of Technical Physics, Chinese Academy of Science, and the British Council for support for his visit to the UK with respect to this work. Gratitude is also extended to the EC and SERC for support at the begbming of this research programme.
[l] Pok-Kai Liao, Ching-Hua Su, Tse Tung, and RF. Brebrick, CALPMD, 6(Z), 141(1982) [2] T. L. Aselage and T.J. Anderson, High Temp. Ski., 20,207 (1985) [3] KM. Chang, C.A. Coughanowr, T.J. Anderson, Chem. Eng. Cornmutt., 38,275 (1985) [4] B.C. Rugg and A.W. Bryant, To Be Published (1993) [5] T.J. Anderson and I. Ansara, Journ.ul ofPhuse Equilibria 12(l), 64 (1991) [6] IAnsara, CChatillon, H.L.Lukas, T.Nishizawa, H.Ohtani, IcIshida, M.Hillert, B.Sundman, B.B.Argent, A.Watson, T.G.Chart, and T.J.Andemon, To be published in CALPIUD, H(2), (1994) [7] RC. Shatma and I. Mukerjee, J. Phase Equifibria, 13(l), 5 (1992) (81 A.T. Dinsdale, CALPHAD, H(4), 317 (1989) [9] H.L. Lukas, E.T. Henig, B. Zimmennann,
CXPlUD,
1,225 (1977)
ASSESSMENT
[lo] H.L. Lukaa, J. Weissand
OF THE Ga-ln-Sb
E.T. H&g, CupHAD,
175
SYSTEM
6,229(1982)
[11] G.B. Blom aml T.S. Plaakctt, J. Ele&uchem. Sot., 118, (2). 1831 (1971) [12] G. Antypas,J. Cry& Gmwth, 16,181(1972) [13] Hidejiro M&i,
JapaneseJ. &I.
Kmuaki Scgawa, Mutsuyuki Otsubo, Kiyoti
[14]LYe. Gor&kovandN.A. [IS] V.B. Ufimtw, [lqJ.C.
Shhhata
and Kciji Fujtbryuhi,
Phys., 17(12), 2079 (1978) GotyunovqU.
Ntwtg. KXim.,3,668(1958)
A.S. Timo&in, andG.V. Kostin, NeorgMer., 7,2029(1971)
WoolleymdD.G.LeeaJ.Lcrs-CommonMetclls,
1,192(1959)
[ 17] A. Joullit, R Dedica, J. Chcvria and G. Bougnot, Revue de Physique Apphqut!e, 9,455 (1974) [18] J.K. Abrokwah and hf. Gcxahawm,J.
Elecrtm. M&r.., 10(2), 379 (19el)
[19] M.F. Gratton and J.C. Woollcy,J. Eltxmhem. [20] J.C. Woollcy and B.A. Smith, Pm.
Sot., 125(4), 657 (1978)
Phys. SIC., 72 214 (1958)
[21] A. JoulliC, R Aulombard and G. Bougnot J. Ctyst. Growth, 24/25,276 (1974) [22] J.R Rode, E.R Gwtncr, A.M. Andnws, D.T. Chcung and W.E. Tcnnant, J. Elecmn. Muter., 7(2), 337 (1978) [23] I. Ansam, M. Gambino and J-P, Bros,J. Ctysr. Gnoti, [24] A&.)Vccher,
32,101(1979
E.I. Vonmova, L.A. Me&kov&ii and A.S. Skoropanov. Zh. Fiz. Khim., 4g(4), 584
[25] F. Ga&a and B. Predcl, J. Less-comnwn Met&
64,285 (1979) and private communication.
[26] L.A. Mechkovskii, A.A. !&&&ii, V.F. Shmrs and A.A. Vccheq zlr. Fiz. RMm., 45, (8) 2016 (1971) [27] Tat Tung, Ching-Hua Sy Pok-Kai Liao and RF. B&rick, J. Yuc. .%I. Technof., 21, 117 (1982) [28] Y.-M. Muggianu, M. Gambino and J.-P. Bras, J. C&.
Phys. 72, 83 (1975)
[29] 0. Redlichand A.T. Kistcr, Ind. Eng. Chem., 2,345 (1948) [30] RH. Davies, A.T. Dinsdale, T.G. Chart, T.I. Bany & M.H. Rand, High Temp. .%A, 26 251(1990) [31] J-Y. Shea, C. Chatillon, I. Ansara, B. C. Rugg, T.G. Chart, A. Watson, B.B. Argcnt. To bepublkhtd.
CufphadVol. 18, No. 2, pp. 185175, 1994 Copyright 0 1994 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0384-5916/94 $7.00 + 0.00
AN ASSESSMENT OF PHASE DUGRAM AND THERMODYNAMIC PROPERTIES OF THE GALLIUWINDIUM-A SYSTEM
YangJianrong’ and Andy Watson Depprtmnt of Rttgineuing Mat&ala, PortobeRo St, Univemity of Shcklield, U.K. S13JD l
Shanghai Institute of Technical Physica, Chinese Academy of Science, Shanghai 200083, China
The cxp-tal thumodynsmic and phase diagram data of the Ga-In-Sb tx ~~2 been critically asaes&. A thermodynamic description that is conmakn experimental data has been pnxhrced with the aid of ternary optinking program TERGSS. Calculation of thermodynamic properties and phase diagrams were carried out using MTDATA.
It is well known that III-V aaniconductor compounds have an extremely important application in high speed and high frequency devices. In the III-V semiconductor family Ga-In-Al-S&k, thee am tat ternary snbsyatems. By aelecting different compositions within these subsysteans, electrical and optical prop&or of the materials can be changed in order to satisfy different applications. In this worh, the Ga-In-Sb try&an has been asses& as a first stage in the study of the Ga-In-Al-%-As system. Since Liao et al[l] calculated the Ga-In-Sb syatan in 1982, new thermodynamic expcrkntal dudiea have heat undat$cen by Aaelage and Andason(S], Chang et al[3], and Rugg and Bryanq4]. The three binary sub~~withthtternaryGa-In-Sbhavealsobecnassessedby~&AnserdS],and~et al[6]. More recently, a thamodynamic analysis and calculation of the phase equilii of the tanary ayatan haa been tmdatahut by Sharma and Muhajbe(7l although they had not used the moat recent deacriptiona of the antimonide binary ayatuna. It is also important to m-evaluate the ternary with the enthalpiea of formation of the (Ga,In)Sb solid sohttion[4] which were not available to Sharma and Mulcerjee, as it is from such wttr that the stability of the phase can be aases&. The experimental phase diagmm and thermodynamic data available in the litaature for the Ga-In-Sb system have been critically aaaea& and by using unary data for the elementa aa rccommQLded by SGTE[8], thermodynamic descriptiona of the ternary liquid and (Ga,In)Sb phaaea which are con&tent with the expekattal data, have been produced This was achieved with the aid of the ternary optimization program TERGSS lcindly donated by Dr. H. L. Lul@9,10] of the MPI Stuttgart.
IL1 Pbraa dlaglxm data
Measurement of the Ga-In-Sb liquidus has been made by Blom and Pla&ett(l I], AnwlZ] and M&i et al[ 131 using a weight loss method, and by Gorshhov and Goryunova[l4], Utimtaev et al[ IS], Woolley and Lc@l6], and Joullit et al[ 17] using heating and cooling curve analyaia. Direct visual obaavatiort of melting tanpaoavts was wal by Ahrohvah and Gashcazon[l8]. For thermal methoda and direct obaavatioa, supacoolingiscollsidetedtobethtmain~~ofuncatainty.Inweightlossmdhodr,thaeisnoarpacooline probletn However, there ie a possibility of uncertainty with thin method and with thate typea of systems, owing to equilibrium not being established. This method relies on the dissolution of a GaSb crystal into a mlt until the liquid becom#l @urated. An interface layer of the ternary compound in equilibrium with this liquid is then formed on the surface of the crystal. The liquidus composition is then detumined by the weight loss of the Original
version received on 11 June 1993, Revised version on 8 October 1993 165
166
J. YANG AND A. WATSON
qstal. However, the diffusion rates of the components are very low, and so there may be difficulties in anaining equiliium. Also,no account is tahen of diffusion of indium from the melt to the crystal which would have an affect on weight loss calculations. An m technique was used by Gratton and Wcolleyll9], Blom and P-1 11, and Woolley and Smith(ZO] to measure the solid&liquidus equilibria. X-ray studies of the annealed and quenched specimene mveakd the compositions of the phases in equilibrium. Blom and Plaskett used a microprobe technique in pmfaence to x-rays. Gratton and Woolley extrapolated their solidus -ts to the liquidus curves as given by Blom and Pkakett, Joullit et al[l7], and Antypas[l2], in order to calculate the associated equilibria. As these derived liquidus data were heavily depcr&nt on those of other workers they were not considered in this optimisauon. LPE methods ware used by An~lZ], Joullib et al[171,[21], Rode et al[22] and Miki et al[13] for the &ammation of the solidus compositions. AnnAing techniques allow experimental conditions close to squilibriumthusallowingabe#aaccuracyinthemeaslPemntoftcanpaaturc than LPE methcds, however, the uncatamty in composition is of the same order. By comparmgaUtheexperimentalphasediagramdata,itcouldbe raenthtthaewPI~~88ebCI13Qltbdwccnthedatawithintheuncataintitsassignedinthisaapcssment. The pseudobinaty GaSb-InSb phase diagram data of Woolley and Smith[20], and Woolley and Lees[ 161 have large differences from those of Gorshkov and Goryunova(l4], and Ufimtsev et al[lS]. Both Woolley and Smith and Gorshkov and Goryunova used the same annealing technique, but Woolley and Smith followed the heat tmatment of their alloys by quenching, whereas Gorshkov and Goryunova did not. It is therefore more likely that the compositions detamined by Woolley and Smith would reflect the equilibria at the annealing temperature than those determmed by Gorshkov and Goryunova The optimization result also shows that the data of Woolley and Smith fit other experimental data better than those of Gorshkov and Goryunova, or Ufimtaev et al. For these reasons Wcolky and Smith’s data were taken in this work and those of Gorshkov and Goryunova and Ufbntsev et alwereomittedinthetinaloptimisation. ThesesamedatawcrealsodiaregatdedintheworkofLiaottal[l]and Blom and Plasheqll]. ILII llranttodynnmk
data
Enthalpiea of mixing of liquid alloys have been measu& by Ansara et al[23] and Vecher et al[24] using direct reaction calorimetry and quantitative differential thetmal analysis respectively. The agreement between the twosetsofdatairpoor.Insomecases,thedifferencesarelargerthan50%ofthemeasuredvalues.Thc expaimatal results of Vecher et al were presented in the form of an isothermal ternary section showing contours mpresenting mixing enthalpies without indicating specific expcairmmtal mcasuremglts. This resulted in a fairly large uncertainty being ascribed to the data (+/- 20% in the eduhalpies of mixing) owing to the difficulties in reading the data accurately. The mixing enthalpies of pseudobinaty liquid were measwed only by Gerdes and Predel[ZS]. Enthalpies of mixing of the (Ga,In)Sb pseudobinary solid solution have been measmed by Rugs and Bryanq4], and Mechkovskii et al[26] the latter calculating the enthalpies of mixing of the solution t?om the difference between the atthalpies of mixing of the binary Ga-Sb, In-Sb and ternary Ga-In-Sb liquids. The former calculated anhalpies of mixing from measumd enthalpies of solution of the binary GaSb and JnSb compounds, and pseudobinary alloys in tin and indium. The uncertainty in both sets of vts of the enthalpies of mixing of the ternary solid solution are high, their small numerical values being compamble in magnitude to the expaimGntal scatter. Gn comparing these two sets of results, it was found that they had opposing signs. Partial Gibbs energies of gallium in the liquid phase have been measumd by Aselage and Anderson(2], and Chang et al[3] using an electrochemical method. An experimental accuracy of 5% was given for the data by the authors. However, under comparison, it was evident that the temperanve dependence of the emf was of opposing rienfotthetwosctsofresults.Thisirnpliesthattheuncataintyfactoremustbclarggthanquotbdoroneactof dataare -us. Table 1 gives a summary of the experimental data available in the litaature together with the exper+mtal techniques employed and their assigned uncutainties used in this assessmnt. The sekcted data and mkcrtamties were used in the subsequent ternary optimization.
ASSESSMENT
OF THE Ga-In-Sb
167
SYSTEM
Many thcrmadynamic models have been previously proposed to describe the thamudynamic propatiea of the tanary Ga-In-Sb liquid, for example the regular solution model, the sub-regular solution model, the awchtcd solution model and 0th~~ modified models[3],[13]. There has been no cxpuimcntal evidcwe of assohtion bchaviour in the Ga-In-Sb liquid as has bezn found in II-VI systcm@7]. If the unc&aintica of the expehental data arc taken into consition, it can be found that the sub-regular model is adequate to dwribe both the Ga-In-Sb liquid and the (Ga,In)Sb pseudobinary compound. The thcamodynamc descriptions of the three binary systems were extrapolated into the ternary using Muggianu’s[28] expression. The excess Gibbs energy of the liquid phase owing to ternary intcaactions of the three components was expressed by Ge(l) = x(Ga)x(In)x(Sb)(a’+b’T)
( J g-atom-‘)
(1)
The solid solution between the GaSb and InSb was treatal as a pseudobinary solution rather than a true ternary, and thus the cxct88 Gibbs cnagy was dcscrikd by an expression equivalent to the Rcdlich-Kistcr formalism [29] used for the binary liquid phases
Ge(s) = x(GaSb)x(InSb) (a’ +bl’)
(J mol-’Wxb., )W
(2)
168
J. YANG AND A. WATSON
~HSJX-A+BT+ChT+~+l!fP+Flr+
B
A
2OO.oocToo2.92K
-21312331
30292aQ9OO.OK
-7055.643
w 200.oocT402.92K
GT’+IW
D
C
P
585.263691 .I08328783 0.22715564 -1.1857526E-r 439954
G
A
0.0
0.0
-0.040173E-6
.118332
0.0
I .645E+23
-15821.03 567.189696 .I08228783 0.22715564 .1.18575263-(
439954
-7.0173-17
0.0
-0.040173E-6
.I 18332
0.0
0.0
-22906
0.0
.211708
0.0
3O2.92.fR29OO.OK -1389.19
132.7302
.26.0692906 0.1506E3
114.049043 .26.0692906 0.1506E3
200.M429.75K
-6978.89
92338115
-21.8386
.5.72566B3 -2.120322E-6
429.7HB.OK
-7033.52
124.476588
-27.4562
5.46@7E4
ligpia 200.m429.75K
-3696.798
84.701255
-21.8386
.5.72566E3 -2.12032lE-6
429.7~Q9OO.OK
-3749.8 I
116.857840
-27.4562
5.4607E-4
298.WTa3.78K
-9242.858
156.154689 .30.5130752 1.748768B3 -3.003415e-6
pO3.78qB.OK
-I 1738.830 169.485872
w 298.WZ3.78K
10579.470
@03.78~~.OK
8175.36
-8.367E-8
-8367E8
-22906
.5.590583-2C
.211708
0.0
100625
0.0
0.0
0.0
0.0 .53116E+22 0.0 0.0
ltwdhdd-A7
T&k%
0.0
0.0
134.231525 ,30.5130752 1.7487683-3 -3.0034153-6 147.455986
lhmodymmk G”-
-31.38
0.0
0.0
-31.38
IO0625 0.0
puucrar.f~Wl,Grsb(~~~~Lippld==
x(1-x)[(A,+A,T+A,TlaT)+
( B,+B,T)(Mx)
(J gjtom”)
+ C,(lA)~
,1.74847&2(1 0.0
0.0 .61685E+27 0.0 0.0
ASSESSMENT OF THE Ga-in&b
llm
x .
SYSTEM
m-m
1 Figure1 Awesed Ga-Sb Phase -4
D I-
Figure 2 Asses& In-Sb Pti Diagm46]
Figure 3 Amessed Ga-In Phase D&mu@]
199
J. YANG AND A. WATSON
170
Table 34. ‘llwmodynamic A
B
Data for GsSb ud fnSb Binary Cempomb. G-HSER J mot’ D
C
E
F
G
H
G8sb 2OO.OWR302.92K 302.92.fh903.78K 903.78cr<29oo.OK
-74031.389 -59774.701
720.3431
-133.356106 0.23214859 -1.21578~04
267.809609 -51.1966138 0.00514355 -3.043588BO6
-62270.673 281.140792 -52.0635386 -0.00260522 -4.0173BOS
540579
0
0
-17707
0
1.645Fi+23
-118332
0
1.6170145E+27
IBsb 2OO.W<429.75K
-47920.348
429.7HW3.78K
-47974.978 281.217555 -553821132 0.00829484 -3.087085B06
903.78-fR29OO.OK -50470.95
249.079082 -49.7645132 0.00202311 -5.123737BO6 294.548738 -56.249038 0.00054607
-8.367B-08
77719
0
-111083
0
3.53116OOE+22
0
-211708
0
1,6168853B+27
The ternary optimising program, TERGSS, was used to produce Gibbs energy coefficients for the ternaty liquid and pseudobinary phases, that were consistent with the selected experimental data. Initially, all the experimental thermodynamic and phase diagram data were given the same weight in the optimisation procedure based upon the assessed experimental uncertainties. Early results showed that some of the data were in obvious disagreement with the majority of the data. For this reason, the data of Vecher et al[24], Gorahkov and Goryunova[l4], and the pseudobinary phase diagram data of Ufimtaev et al[ 151 were omitted from the data set. The enthalpies of mixing of the solid solution data of Mechkovskii et al[26] were also omitted as the optimisation suggested that values of an opposite sign to that of those data would be in closer agreement. Therefore, Rugs and Bryant’s[4] data were accepted as their data had the appropriate sign. The weight of the pa&l Gibbs energy data of Aselage and Anderson[2] was reduced to 50% of that given totherestofthedata. Thiswasbecausethese&tacolnprised400/0ofthttotal&taset,andthusthertmayhave been a tendency of the optimisation to be biased in favour of these data purely because of their number. A weight of 50% was also used for Ansara et al’s data[23] as there was a certain degree of disagreement between these and the rest of the data. In the final result, there is about 20% discrepancy between these data and the optinkd curves. Incidently, even though Vecher et al’s data[24] were omitted, it is worth noting that these data lie on the opposite side of the optimised curve from that of Ansara et al’s data. Table 4. Optimii Excess Gibbs Energy Ceefficieata for the Ga4n-Sb System a
b
liquid
-5072.76
-10.8842
(GoJn)Sb
9093.00
-2.8698
The resulting coefficients from the final optimisation are given in table 4. The phase diagrams with the tielines and experimental data (shown as fig.45) have been plotted using MTDATA[30] and the parameters in table 4. It can be seen that most of the phase diagram data are in agreement with the calculated liquid isotherms except for some near the In-Sb boundary, such as those of Antypas[lZ] at 773.15K and Joullie et al [17] at 653.15K. These data did not fit well because they conflicted with the description of In-fib binary. It is in&resting to note that certain amount of disagreement was found between the extrapolated liquidus data of Gratton and Woolley[l9] and the calculated curves. Sharma and Mukerjee[7] on the other hand, found a better fit of these data to their calculated curve. It is felt that this may be, because including such a large amount of data in their optimisation which were extrapolations to other experimental data, a bias had been imposed on theirSnalresult. The GaSb-InSb pseudobii phase diagram together with the experimental data of Woolley[20], and Blom and Plaskett[l l] is shown in fig.6. This result has no obvious differences from that obtained using an 888oci8tbd solution model for the liquid[l]. Most of the solidus experimental data was found to fit with the calculated curve. However, an intemsting feature of the calculation is the appearance of the miscibility gap in the (Ga,In)Sb solid solution. The critical &upemmm was calculated to be 466.3K The presence of the miscibility gaphasnotbeenumfkmed experimentally owing to sluggish diffusion rates at the relatively low temperature.
ASSESSMENT
OF THE Ga-In-Sb
SYSTEM
171
h
Figures4&5 Calculated Liquidus Phase Boundaries with Experimental Data
h
7
(b
bd
0.6
0.6
0.4
0.2
sb
172
J. YANG AND A. WATSON
Howeva, it could have profond implicatiom for devicea mde from such mamials an there is a possibility of tbcirdcgr&tionwithtim. Asimilartcmpemm for Tc was proposed by Chang d al[3] (433K) resulting lkom tkir ulculations. The level of agreunmt ia aaxptable comkking the qaimaltal diflialltiea atm** in maaning the enthalpits of mixing of the solid solution -41, which had a sign&ant effect on detammm tbcmiaciitygapintbiswork. Tht~cnthalpieaofmixineofthcpacudobiDlryphucwatf~to~ well. witb to imeasc thewcightofthwcdatadutingtbc . . the calculatai curva~. Howeva, it was nectary m in odm to pmduce well &find Gibbs amgy coefficienta. for the a&lpiof mixing of the liquid Thereisalargcdkmpmcybctwcencalculatiunandqminmt agraxnmtwiththephase pIwe (ace Fig.7). Thin ia a caneaquenccoftbcdatanotbcinginparticularlygood diagmmdat8.Thi8illalm&owIlinLi8octal’swork. Uwxpcedly, the mixing cntbalpy data of pseudobinary liquid could be fitted very well. These dsta me ahowninfi~8~withthecalculatadheatcurveproducodfromtheoptimisotion. Thefsctthatthiswar not fcktal in Sbamu and Mukajae’s(7l work was probably mainly due to a typographical m-or in tbc original publicatiot~. However, their calculated curve still gives largez valum for the heat of mixing than wme found hm.
173
ASSESSMENT OF THE Ga-ln-Sb SYSTEM
-m
I 5
.
-1ooc4 8
.
l
.
-
L
_
-em0
P
-awe
B a _ii 6
-mwo
-=3ol- Es’
’
050
’
en
loo0 la5
la0
1075 1100 11.
Figure9dsowstbecrlculrtedportinlGibbr~~of~~intbe~dphuecomprredwiththe dqxndamofgalliumputhl cxpuimcntaldataOfAaelageMdAndason[2].Itcanbcseenthatdte~ Gibbaawgyfitswcllwiththecalculatedvalw.s. 1twasfoundtlwmostofthachtamuldbcfittalwcllif2036
Athr#~aquilibriumnsion~~fo~intbeSb-richsiderttanpartPrsr similar~thatintbeA8-Ga-Inphaac~31]. Thisis&owninfigurc1O. respccttodeviccmanuf~willbcdiscussedinafimnepublicatim
fnnu768Kto86OK Theimpliatioaaoftlhwith
174
J. YANG AND A. WATSON
F&we. 10 calculrtedSectionofthe Ga-Jn-Sb System at 800°C Showing llllee Flme Region.
The authors would like to thank Dr. Leo Lukas of the Max Planck Institute, Stuttgart for the provision of TERGSS and the help and advice throughout this and other work, and also to the NPL Teddiqton for the use of MTDATA[30] and all the help in its implementation. Dr Yang Jianrong would also like to thauk his Institute, the Shaughai Institute of Technical Physics, Chinese Academy of Science, and the British Council for support for his visit to the UK with respect to this work. Gratitude is also extended to the EC and SERC for support at the begbming of this research programme.
[l] Pok-Kai Liao, Ching-Hua Su, Tse Tung, and RF. Brebrick, CALPMD, 6(Z), 141(1982) [2] T. L. Aselage and T.J. Anderson, High Temp. Ski., 20,207 (1985) [3] KM. Chang, C.A. Coughanowr, T.J. Anderson, Chem. Eng. Cornmutt., 38,275 (1985) [4] B.C. Rugg and A.W. Bryant, To Be Published (1993) [5] T.J. Anderson and I. Ansara, Journ.ul ofPhuse Equilibria 12(l), 64 (1991) [6] IAnsara, CChatillon, H.L.Lukas, T.Nishizawa, H.Ohtani, IcIshida, M.Hillert, B.Sundman, B.B.Argent, A.Watson, T.G.Chart, and T.J.Andemon, To be published in CALPIUD, H(2), (1994) [7] RC. Shatma and I. Mukerjee, J. Phase Equifibria, 13(l), 5 (1992) (81 A.T. Dinsdale, CALPHAD, H(4), 317 (1989) [9] H.L. Lukas, E.T. Henig, B. Zimmennann,
CXPlUD,
1,225 (1977)
ASSESSMENT
[lo] H.L. Lukaa, J. Weissand
OF THE Ga-ln-Sb
E.T. H&g, CupHAD,
175
SYSTEM
6,229(1982)
[11] G.B. Blom aml T.S. Plaakctt, J. Ele&uchem. Sot., 118, (2). 1831 (1971) [12] G. Antypas,J. Cry& Gmwth, 16,181(1972) [13] Hidejiro M&i,
JapaneseJ. &I.
Kmuaki Scgawa, Mutsuyuki Otsubo, Kiyoti
[14]LYe. Gor&kovandN.A. [IS] V.B. Ufimtw, [lqJ.C.
Shhhata
and Kciji Fujtbryuhi,
Phys., 17(12), 2079 (1978) GotyunovqU.
Ntwtg. KXim.,3,668(1958)
A.S. Timo&in, andG.V. Kostin, NeorgMer., 7,2029(1971)
WoolleymdD.G.LeeaJ.Lcrs-CommonMetclls,
1,192(1959)
[ 17] A. Joullit, R Dedica, J. Chcvria and G. Bougnot, Revue de Physique Apphqut!e, 9,455 (1974) [18] J.K. Abrokwah and hf. Gcxahawm,J.
Elecrtm. M&r.., 10(2), 379 (19el)
[19] M.F. Gratton and J.C. Woollcy,J. Eltxmhem. [20] J.C. Woollcy and B.A. Smith, Pm.
Sot., 125(4), 657 (1978)
Phys. SIC., 72 214 (1958)
[21] A. JoulliC, R Aulombard and G. Bougnot J. Ctyst. Growth, 24/25,276 (1974) [22] J.R Rode, E.R Gwtncr, A.M. Andnws, D.T. Chcung and W.E. Tcnnant, J. Elecmn. Muter., 7(2), 337 (1978) [23] I. Ansam, M. Gambino and J-P, Bros,J. Ctysr. Gnoti, [24] A&.)Vccher,
32,101(1979
E.I. Vonmova, L.A. Me&kov&ii and A.S. Skoropanov. Zh. Fiz. Khim., 4g(4), 584
[25] F. Ga&a and B. Predcl, J. Less-comnwn Met&
64,285 (1979) and private communication.
[26] L.A. Mechkovskii, A.A. !&&&ii, V.F. Shmrs and A.A. Vccheq zlr. Fiz. RMm., 45, (8) 2016 (1971) [27] Tat Tung, Ching-Hua Sy Pok-Kai Liao and RF. B&rick, J. Yuc. .%I. Technof., 21, 117 (1982) [28] Y.-M. Muggianu, M. Gambino and J.-P. Bras, J. C&.
Phys. 72, 83 (1975)
[29] 0. Redlichand A.T. Kistcr, Ind. Eng. Chem., 2,345 (1948) [30] RH. Davies, A.T. Dinsdale, T.G. Chart, T.I. Bany & M.H. Rand, High Temp. .%A, 26 251(1990) [31] J-Y. Shea, C. Chatillon, I. Ansara, B. C. Rugg, T.G. Chart, A. Watson, B.B. Argcnt. To bepublkhtd.