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Phase equilibria calculation of Zn-Cd-Te system
CALPHAD Vol.16.No.2, PrintedintheUSA.
pp.161-172. 1992
0364-5916/92$5.00+.00 (c)l992 Pergamon
Press Ltd.
PHASEEQUILIBRIA CALCULATION OF ZN-CD-TESYSTE?l BY A.
Indian (*Present
K.
Deoartmcnt Institute address:
Sinoh* and Romesh C. Sharma of tletalluraical Enofncerino of Technology Kanour. UP-208016 1 tlangal Das
Road,
Punt
bll
001
India India)
ABSTRACT A quasi subregular associated solution model is used to describe The thermodynamic orooertics of the liauid phase in Zn-Cd-Te system. ternary compound. (ZnyCdl_y)Te. is described as a subregular solution of stoichiometric compounds, ZnTe and CdTc. different Dhascs arc obtained by simultaneous to the phase available thermodynamic and diagrams are, then, calculated by usino the and compared with the experimental data.
The model parameters for ootimiration with respect Phase data. cauilibria optimized model parameters
I.INTRODUCTION Semi-conducting compounds ZnTe and CdTe form a comolctc series of solid solutions with cubic zincblcndc structure with varying band QaDS. Phase cauilibria in Zn-Cd-Tc system is important because of interest in the growth of alloy crystals from liauid solutions. There have been numerous thermodynamic cauilibria and investigations into phase Proocrtics in binary Zn-Tc and Cd-Te systems. Sharma and Chana cl.21 have recently phase assessed and calculated Zn-Te and Cd-Tc binary ZnTc-CdTc pseudo-binary diagrams by using associated solution models. phase liauidus diagram and limited points on the ternary Zn-Cd-Tc Zabdyr cd] have surface have been determined by Stcininaer et. al. (33. determined solid the thermodynamic the ZnTc-CdTc properties of solutions. Szapiro 151 and Lauaicr [6] have calculated the Zn-Cd-Te ternary solid-liquid eauilibria by using regular associated solution model. Sharma shown that regular associated and Chang cl.21 have solution does not adeauately describe the binary Zn-Tc and Cd-Tc phase diagrams and therefore. its USC for Zn-Cd-Te ternary system cannot be satisfactory. In the present work Zn-Cd-Te ternary DhOSC diaoram has been calculated by extending the models used br Sharma and Chano cl.21 to the ternary system where associated solution model is used. however. it is not restricted to be only regular solution.
161
162
A.K.SlNGH andRCSHARMA
II. tiauid
THERllODYNAhIC
TIODELS
Phase:
The associated solution model used br Sharma and Chang 11.23 to describe thermodynamic properties of the liquid Phase in binary Zn-Te and Cd-Te systems is extended to ternary liauid Phase in Zn-Cd-Te system. Accordingly the ternerv liquid solution of Zn. Cd and Te is considered as a Pseudo-PentwarY solution of lZn'+ 'Cd'. lTe'. 'ZnTe' governed by the followins internal CQuilibrium and 'CdTe' sPecies reactions: 'Zn'(ll
+ 'le'(l1
* *ZnTe'(l)
(1)
'Cd'(l)
+ 'Te'fl)
* *CdTe'(l)
(21
and
with
the
eauilibrium
respectivelv,
constants.
KI
and
K2
of
reactions
(1)
and
(21,
as: (f‘Y‘1
Kl =
(flYlf
(31
(f3Y3)
(f5Y5f
K2 = where y3.
f
Y&
(f2Y2)
1' and
f2.
f3.
~5 are
'Cdle' species. The equilibrium function
(II
(f3Y3) fI, and the
f5 are
mole
activity
fractions,
respectively. constants Kl
of tcmoerature
the
in the and K2
of
and
coefficients
'Zn*.
'Cd'.
'Te',
yl,
'ZnTe'
y2,
and
pseudo-Pentsnary liquid solution. are. in general, expressed as a
as (1.23:
Ai In Ki = 7 + Bi
(51
the mole fractions ~i's of are constants. The and 5i i pseudo-oentsnary solution are related to the actual mole fractions. XZ,,,
uherc
A
and xTe in the Zn-Cd-Te 'Cd esuations (73: '1 = 'Zn + 'ZnY5 '2 = 'Cd + *CdY4
ternary
liauid
by the follouino
- (1'xznl
Y&
(61
- (l"XCdl
Y5
(7)
mass
balance
and '3 = 'Te The excess
- (l-xTe)
molar
Gibbs
Y& - (l-XT,) energy,
Y5
(81
dGxs. of the pseudo-PentanarY
solution
is
PHASE EQlJlLl6RlA CALCULATION OF Zn-Cd-Te SYSTEM
now
exDressed
XS
AG -=c
as
G
5 c
RT
i=l
with
solution
171:
p+
uJi
j=i+l
+ uiJ-
uji
.(YJ_
Yi)
- IVijYiYj]YiYj
(9)
2
2
Parameters
u
and
ij
vij.
in general.
exPressed
as
C1.2.71:
A . .
=A+0
uij
(10)
ij
T
C
=ij+D
vij uhere
A
ij' any
of
fP*
(11)
iJ
T
and
6
ij' ciJ' sDecies P
The
D
are constants. ij the Pseudo-PentanarY
in
activity
Solution
is
coefficient. then
given
as
(73:
-xs CG i
5
-=lnf
=
RT
uiP+
=
P
uDi
+
cu
r
i=l
ip-uDiI~yD-~l
- 8VipYiYp]Yi
2
IZP
6
5
-1
uiJ+
j=i+l
Nou.
vill'v-IiPseudo-Pentanary D
+
(u
(12)
- 12VijYiYj]YiYj
ij-uji)(YJ-YiI
2
uith
a
uji
1
c
i=l
the
solution
activity. is
given (p=l
= fPYD
OD*
of
any
soecies.
D.
in
the
as: to
51
(13)
lZn'. and since the activities of species Cd(l) solution uith Zn(l). pseudo-Dentsnary states, are the same as those of re+PectivelY. in the ternary Zn-Cd-Te liquid solution:
'Cd' and and Te(l) comoonents
aZn
=
YZn
xZn
= al
= fl
aCd
= Ycd
xCd
= a2
= f2Y2
(15)
aTe
=
xTe
= a3
= f3Y3
(161
*Te* in the as reference Zn, Cd and Te
(16)
y1
and YTe
1 the activity coefficients of Zn. Cd and Te. and YTe are Zn' 'Cd respect ivelv. for the Zn-Cd-Te liquid solution and are different from The chemical potential or Partial molar Gibbs energy of fl, 12 and f3. uhere
any
comDonent,
i.
in
Zn-Cd-Te
liquid
is then
given
as:
A.K.SlNGH andR.C.SHARMA
164
c = “G: Now,
+ RT
if
marsmeters,
the
w
In si
(i = Zn. Cd or Te1
equilibrium
and
vi3
are
constants known.
Ki
eas.
end
(3)
to
K2
(171 and
f17)
the
can
interaction
be
solved for if the thermodynamic Properties of the ternary Zn-Cd-Te liauid solution. The values of simultaneous these parsmeters sre determined by OPtimitation with respect to the oh8se esuilibris and thermodynamic dsts. (zny=dl_Y )Te Compound: The
ternary
compound.
(ZnyCdl_y~fe, sub-regular The Gibbs
is considered as 8 Quasi ZnTe Cdle. compounds and 8CCOrdinQlY
6’
given =
Y OGinTe
and
8 stands
in the
solution energy
of of
Zn-Cd-Te
SYStem,
stoichiometeric (ZnyCdl_y)Te is
8s: +
(1-v) OtCedTe + RT[Y
+ RT Y IX-Y) where
formed
for
In
(l-v)]
1 o21y + =12li-y)l
tZnyCdl_y )Te phase
a21 are expressed
In Y + (1-y)
(18)
and
solid
solution
Parameters
a12
as:
a1 =12 = F + "2
(19)
and
a3 a2l = 7 where
(20)
+ "4
a 1, a2, a3 end
of ZnTe
and CdTe
ar, are
The partial
constants.
in 8 are then
molar
Gibbs
energies
as:
given
Ge ZnTcr
ZnTe OG8
+ RT In Y + RT
Fe Cdfe=
0G8CdTe
+ RT In Y + RT y21a21 C2Y-11
(1-v12
12 021+Q._[1-2y)]
(211
and
III. PHASE
+ 2 a,,(l-rI3
(221
EQUILIBRIA
between liauid end 8 is In the ternary Zn-Cd-Te system. eauilibrium Zn and Cd melt at relatively low temperatures and% of main interest. therefore, eauilibria involving solid Zn and Cd phases is not considered There is also a liquid miscibility oao in the tn-ZnTc region of here. Zn-Te phase diagram (1) which would extend into the ternary SYStem.
165
PHASE EQUlLlBRlACALCULATlONOFZn-Cd-T@ SYSTEM
Esuilibrium
bctuccn
liquid
and
(ZnyCdl _ y 1Te
at
any
temperature
is
given
by:
EL Zn
-L + GTc
-_ ge ZnTe
(231
i+ Cd
-L + GCd
= $
(2L1
and CdTe
where
all terms arc CIS defined earlier. NOW for the (L+S) equilibrium at a given temperature there are three compositional unknowns. tuo for the liquid phase and one for 8 Phase. BY fixing one of these, l QS_ (23) and (2fi) may be solved to define one tic line in the (L+Sl region and a calculation of number of such tie lines over the whole two phase region would define it completely. In given
the
liquid
miscibility
gap,
tuo
phase
(Ll+L2)
equilibrium
is
by: iL1
= ;:2
i
Of
the
four
(i = Zn. comDositiona1
Cd.
unknowns
Tel for
(25a.b.c) (L1+L2)
equilibrium,
two
for
one is fixed and cos. each phase, (25s) to (25~1 are solved for other three to Qive one tie line. A calculation of number of tie lines throughout the (L1+ L2) equilibrium region would comlctclv define the miscibility
gaD
at IV
(I)
Pure
ComDonent
a aiven
temDerataure,
EVALUATION and
OF
TIOOEL PARAMETERS
ComDounds:
The enthalpies of melting of pure Zn, Cd Hultgrcn et. al [83 were used by Sharma and Chano the Gibbs energies of melting of these components. Table 1 is used in this study. The Gibbs energies and CdTe compounds arc also taken from the work cl.21 and are given in Table 1. (ii)
Lisuid
and
and Te assessed by (1, 21 to arrive at There data aiven in of formation of ZnTc of
Sharma
and
Chana
8 phases:
Sharma and Chang El.21 have used associated solution mode1 to adequately describe the thermodynamic properties and phase equilibrium in Zn-Te and Cd-7c systems. In the present study their model has been extended to ternary Zn-Cd-Te system. In es. (9) number of uiJ snd vi3 parameters Zn-Te and and Chana between Zn parameters the enthalw These are
for the liquid phase, that arc obtainable from the binary Cd-Te systems are. therefore, taken from the work of Sharma (1.21 and are listed in Table 2. The interaction parameters and Cd in the liouid phase are arrived at by oDtimising these with rcsacct to the asscssed data of Hultorcn ct. al [9] for and entcropv of mixing of binary Zn-Cd liquid solutions. also listed in Table 2. The remaining parameters for the
166
A.K. SINGH and R.C. SHAAMA
liquid Phase as well as 8 phase arc ootimization with respect to the l xcwrimentel (mainly Dseudo-binary ZnTe-CdTe diagram) and TABLE
1:
Lattice
OGL Cd
-
OGS Cd
=
OGL fn
-
OS GZn
=
OGL Te
-
OGS Te
OG8 Cdle
-
00 G2nTe
TABLE
2:
Kl
=
-
CornPound 6190.0
- 10.617
T
7322.0
- 10.572
1
- 26.20
1
= 17689.0
OGL Cd
- OGke
OGL
-
Zn
Stabilities
OGL
7e
+ 62.1536
=
+ 53.62
-
167.600.0
10638.0/T
for
- 2.0177
"13 u16
= 888.19/T =O
In K,
= 3037.5/T = O
u23
= 0
u26
= '
u36 u35 "65 =12
u21 u31
u15
"25
+ 0.11506
u61 "51 u32 u62
= 6635.0/T
- 3.8565
us2
= 0.0
"63
= 608.2/T
"53
= 1136.33/T
=
1662.59/T
a2l
=
1
1065.7217
+ 0.1090
-5.0132
=o = ' -0 = 6635.0/T = 376.5/T = 608.2/T
=
-
a phases. 'CdTe' ) - 1.10 v12 v13
= 12673.0/T
=
and 5:
* 9567.7/T
=o
u56
simultaneous diagram data in Table 2.
1
the liquid 6: 'ZnTc'.
L
u12
bY Dhsse given
(J/mole).
= - 125.659.0
Solution model parameters 'Zn'. 2: 'Cd', 3: ‘Te’.
( 1: In
and
obtsined ternary are also
-1235.13/T 226.19/T
- 3.8565
v16
=O = O = 978.0/T
VI5
= 0
v23
= 0
v23
= '
v25
= 0
v36
= '
v35
= O
VL5
= 0
167
PHASE EQUlLlSf?iA CAlClJLATlON OF Zn-Cd-Te SYSTEM
‘6001-----0 Sttmingrr
rt. al.
lSS0 -
y
1500 .
f % & lLS0 E c’ 1400 -
1350
t 13ooi
I O.2
I 0.4
CdTe Fig.
1:
Calculated
0 Cd
I
I
0.6
0.8
%nrr CdTe-Znlc
cvxudo-binary
i!nTt ohase
diagram.
0 Zn
A.K. SINGH
and R.C. SHARMA
1 s 1460
0.1
0.2
0.3
0.5
0.4
0.6
0.7
K
0.9
0.6
Fig.
3:
Calculated
1.0 tn
Cd isotherm
of
Zn-Cd-Te
A
phase
diagram
T t 1420
K
at
l&50
K.
at
1620
K.
Te
1.0
0.9
Ffa.
I:
Cslcu1sted
isotherm
of
Zn-Cd-Tc
phase
dioorsm
169
PHASE EQUlLlBRlA CALCULATION OF Zn-cd-Te SYSTEM
Cd
Fig.
5:
Fig.
6:
Calculsted
Calculated
Zn
X2"
isotherm
isotherm
of
of
Zn-Cd-fc
Zn-Cd-Te
DhaSC
Dhase
diagram
diagrem
at
at
1380
1300
K.
K.
A.K+ SINGH and R.C. SHARMA
174
a
fn
*Zn
Fiat
7:
Fio.
Csiculatcd
8:
Calculated
isothc~m
isotherm
of
tn-Cd-Trr
of
Zn-Cd-lc
ahasc
diagrsm
P~~SC’
dfeoram
et
320~ K.
at
1lOO
K.
171
PHASE EQUILIBRIA CALCULATION OF Zn-Cd-Te SYSTEM
Cd
Fig.
9:
Li cwidus
Zn
X2” crojection
V.
of
RESULTS
Zn-Cd-Te
AND
phase
diagram
(calculated).
DISCUSSION
Zn-Te the CdTe and compounds systems. Znle In Cd-Te and The compound melt congruently st 1371K and 1573K, resocctivclv c1.21. In lisuidus in both the systems extends very close to pure components. sddit ion, a liquid miscibility QOP exists in Zn-ZnTe portion of the Zn-Te phae diagram, uith a critical Point at -1613K. uhich interacts with the ZnTe liauidus leading to a monotectic at -1488K Cl]. CdTe and ZnTe compounds have In the ternary Zn-Cd-Te system. FiO. 1 shous calculated CdTe-ZnTe complete miscibility in solid state. data of pseudo-binary diagram slonauith the experimental phase Steininoer et al. (31. The aareement. in oeneral. is very good. Figs. 2 to 8 qive the calculated isotherms of Zn-Cd-Te ternary diagram at 1500K. 1450K. 1GZOK. 1380K. 1300K. 12OOK and 1100K. respectively. In addition to the compound liauidus. belou the critical Point of the miscibility OC)P in the Zn-Te system at 1613K. liauid miscibility cap starting from the Zn-Te side extends into the ternary system (for example see 15OOK isotherm in Fig. 2). Belou the monotectic (*1&88K) in binary Zn-Te system. the miscibility gap in the ternary Zn-Cd-Te system interacts uith the compound liquidus to give three Phase (Ll+L2+8) louilibrium as
A.K.SlNGHand R.C.SHARMA
172
seen in 16SOK and lL20K isotherms in Figs. 3 end 6. respectively. At still lower temperatures. less than 4390K. the miscibility gap becomes metsstable with respect to the comoound lisuidus and does not appear in the stable DhaSe diagram as seen in Zn-Cd-Te isotherms at lower temoeratures in Figs. 5 to 8. No exoerimental data on l&L) tie lines or miscibility Qao in the Zn-Cd-Te system exists in literature and, therefore, comoarison with experimental data is not Dossible. Finally. Fig. 9 gives calculated liauidus at various temperatures in the Zn-Cd-Te system. Also shown in Fig. 9 is the lxoerimental data on liauidus temperatures for number of Zn-Cd-Te alloys from Steinineer et-al. [S]. The agreement in the Te-rich side (xTe)0.5) is very good. however. a Door
agreement
is obtain
for four
alloys
with
xTe<0.5.
During 0Rtimisation parameters for additional ternary only CdTe-ZnTe oseudo-binary phase diagram data was used. Other liauidus data could not be used for the lack of tie line information. Due to the limited data, some of the parameters had to be set to zero a Driori. To obtain a better set of parameters. some tie line information on (G+L) eauilibrium at some temperatures would be essential. Still the agreement with liauid data Some the in Te-sich side is auitc good. more experimental information is needed to arrive at better calculated diagram. CONCLUSIONS Zn-Cd-fe phase diagram has been calculated by using associated solution model for the liauid phase and sub-regular solution model for 1Te phase. The calculated diagrams agree well with most of the (ZnyCdl_y the limited experimental data that is available in literature. More experimental the agreement is not very good in some parts. reauired to arrive at a better descriotion of the system.
However, data is
ACKNOWLEDGEMENT The authors gratefully acknowledge the financial suooort Department of Electronics, Government of India, New Delhi.
from
the
REFERENCES 1. 2. 3.
6.
5. 6. 7. 8.
9.
R. C. Sharma and Y.A. Chang, J. Cryst. Growth, a. 193 (1988). 1536 R. C. Sharma and Y.A. Ghana. J. Electrochem. sot.. 136, (19891 J. Steininger. A.J. Strauss and R. F. Brebrick. J. Electrochem. sot. LLL. 1305 (19701. L.A. Zabdyr. J. Electrochem. Sot.. 131. 2157 (1986). S. Szaoiro, J. Electr. Rater., 3. 223 (19761. A. Laugier. Rev. de Phys. aopl., 8. 259 (1973). R. Schmid and Y. A. Chang, CALPHAD, 2. 363 (19851. R. Hultgren. P.D. Desai, D.T. Hawkins. n. Gleiser. K. K. Keller and .Selectd values of the Thermodynamic Properties of 0. 0. Uagman. the Elements'. ASH. 1973. R. Hultoren. P.D. Desai. D.T. Hawkins, H. Gleiser, K.K. Kelly and Selected Values of Thermodynamic Properties of Binary 0. Waoman, Alloys. ASH. Retals Park. OH. 1973.
pp.161-172. 1992
0364-5916/92$5.00+.00 (c)l992 Pergamon
Press Ltd.
PHASEEQUILIBRIA CALCULATION OF ZN-CD-TESYSTE?l BY A.
Indian (*Present
K.
Deoartmcnt Institute address:
Sinoh* and Romesh C. Sharma of tletalluraical Enofncerino of Technology Kanour. UP-208016 1 tlangal Das
Road,
Punt
bll
001
India India)
ABSTRACT A quasi subregular associated solution model is used to describe The thermodynamic orooertics of the liauid phase in Zn-Cd-Te system. ternary compound. (ZnyCdl_y)Te. is described as a subregular solution of stoichiometric compounds, ZnTe and CdTc. different Dhascs arc obtained by simultaneous to the phase available thermodynamic and diagrams are, then, calculated by usino the and compared with the experimental data.
The model parameters for ootimiration with respect Phase data. cauilibria optimized model parameters
I.INTRODUCTION Semi-conducting compounds ZnTe and CdTe form a comolctc series of solid solutions with cubic zincblcndc structure with varying band QaDS. Phase cauilibria in Zn-Cd-Tc system is important because of interest in the growth of alloy crystals from liauid solutions. There have been numerous thermodynamic cauilibria and investigations into phase Proocrtics in binary Zn-Tc and Cd-Te systems. Sharma and Chana cl.21 have recently phase assessed and calculated Zn-Te and Cd-Tc binary ZnTc-CdTc pseudo-binary diagrams by using associated solution models. phase liauidus diagram and limited points on the ternary Zn-Cd-Tc Zabdyr cd] have surface have been determined by Stcininaer et. al. (33. determined solid the thermodynamic the ZnTc-CdTc properties of solutions. Szapiro 151 and Lauaicr [6] have calculated the Zn-Cd-Te ternary solid-liquid eauilibria by using regular associated solution model. Sharma shown that regular associated and Chang cl.21 have solution does not adeauately describe the binary Zn-Tc and Cd-Tc phase diagrams and therefore. its USC for Zn-Cd-Te ternary system cannot be satisfactory. In the present work Zn-Cd-Te ternary DhOSC diaoram has been calculated by extending the models used br Sharma and Chano cl.21 to the ternary system where associated solution model is used. however. it is not restricted to be only regular solution.
161
162
A.K.SlNGH andRCSHARMA
II. tiauid
THERllODYNAhIC
TIODELS
Phase:
The associated solution model used br Sharma and Chang 11.23 to describe thermodynamic properties of the liquid Phase in binary Zn-Te and Cd-Te systems is extended to ternary liauid Phase in Zn-Cd-Te system. Accordingly the ternerv liquid solution of Zn. Cd and Te is considered as a Pseudo-PentwarY solution of lZn'+ 'Cd'. lTe'. 'ZnTe' governed by the followins internal CQuilibrium and 'CdTe' sPecies reactions: 'Zn'(ll
+ 'le'(l1
* *ZnTe'(l)
(1)
'Cd'(l)
+ 'Te'fl)
* *CdTe'(l)
(21
and
with
the
eauilibrium
respectivelv,
constants.
KI
and
K2
of
reactions
(1)
and
(21,
as: (f‘Y‘1
Kl =
(flYlf
(31
(f3Y3)
(f5Y5f
K2 = where y3.
f
Y&
(f2Y2)
1' and
f2.
f3.
~5 are
'Cdle' species. The equilibrium function
(II
(f3Y3) fI, and the
f5 are
mole
activity
fractions,
respectively. constants Kl
of tcmoerature
the
in the and K2
of
and
coefficients
'Zn*.
'Cd'.
'Te',
yl,
'ZnTe'
y2,
and
pseudo-Pentsnary liquid solution. are. in general, expressed as a
as (1.23:
Ai In Ki = 7 + Bi
(51
the mole fractions ~i's of are constants. The and 5i i pseudo-oentsnary solution are related to the actual mole fractions. XZ,,,
uherc
A
and xTe in the Zn-Cd-Te 'Cd esuations (73: '1 = 'Zn + 'ZnY5 '2 = 'Cd + *CdY4
ternary
liauid
by the follouino
- (1'xznl
Y&
(61
- (l"XCdl
Y5
(7)
mass
balance
and '3 = 'Te The excess
- (l-xTe)
molar
Gibbs
Y& - (l-XT,) energy,
Y5
(81
dGxs. of the pseudo-PentanarY
solution
is
PHASE EQlJlLl6RlA CALCULATION OF Zn-Cd-Te SYSTEM
now
exDressed
XS
AG -=c
as
G
5 c
RT
i=l
with
solution
171:
p+
uJi
j=i+l
+ uiJ-
uji
.(YJ_
Yi)
- IVijYiYj]YiYj
(9)
2
2
Parameters
u
and
ij
vij.
in general.
exPressed
as
C1.2.71:
A . .
=A+0
uij
(10)
ij
T
C
=ij+D
vij uhere
A
ij' any
of
fP*
(11)
iJ
T
and
6
ij' ciJ' sDecies P
The
D
are constants. ij the Pseudo-PentanarY
in
activity
Solution
is
coefficient. then
given
as
(73:
-xs CG i
5
-=lnf
=
RT
uiP+
=
P
uDi
+
cu
r
i=l
ip-uDiI~yD-~l
- 8VipYiYp]Yi
2
IZP
6
5
-1
uiJ+
j=i+l
Nou.
vill'v-IiPseudo-Pentanary D
+
(u
(12)
- 12VijYiYj]YiYj
ij-uji)(YJ-YiI
2
uith
a
uji
1
c
i=l
the
solution
activity. is
given (p=l
= fPYD
OD*
of
any
soecies.
D.
in
the
as: to
51
(13)
lZn'. and since the activities of species Cd(l) solution uith Zn(l). pseudo-Dentsnary states, are the same as those of re+PectivelY. in the ternary Zn-Cd-Te liquid solution:
'Cd' and and Te(l) comoonents
aZn
=
YZn
xZn
= al
= fl
aCd
= Ycd
xCd
= a2
= f2Y2
(15)
aTe
=
xTe
= a3
= f3Y3
(161
*Te* in the as reference Zn, Cd and Te
(16)
y1
and YTe
1 the activity coefficients of Zn. Cd and Te. and YTe are Zn' 'Cd respect ivelv. for the Zn-Cd-Te liquid solution and are different from The chemical potential or Partial molar Gibbs energy of fl, 12 and f3. uhere
any
comDonent,
i.
in
Zn-Cd-Te
liquid
is then
given
as:
A.K.SlNGH andR.C.SHARMA
164
c = “G: Now,
+ RT
if
marsmeters,
the
w
In si
(i = Zn. Cd or Te1
equilibrium
and
vi3
are
constants known.
Ki
eas.
end
(3)
to
K2
(171 and
f17)
the
can
interaction
be
solved for if the thermodynamic Properties of the ternary Zn-Cd-Te liauid solution. The values of simultaneous these parsmeters sre determined by OPtimitation with respect to the oh8se esuilibris and thermodynamic dsts. (zny=dl_Y )Te Compound: The
ternary
compound.
(ZnyCdl_y~fe, sub-regular The Gibbs
is considered as 8 Quasi ZnTe Cdle. compounds and 8CCOrdinQlY
6’
given =
Y OGinTe
and
8 stands
in the
solution energy
of of
Zn-Cd-Te
SYStem,
stoichiometeric (ZnyCdl_y)Te is
8s: +
(1-v) OtCedTe + RT[Y
+ RT Y IX-Y) where
formed
for
In
(l-v)]
1 o21y + =12li-y)l
tZnyCdl_y )Te phase
a21 are expressed
In Y + (1-y)
(18)
and
solid
solution
Parameters
a12
as:
a1 =12 = F + "2
(19)
and
a3 a2l = 7 where
(20)
+ "4
a 1, a2, a3 end
of ZnTe
and CdTe
ar, are
The partial
constants.
in 8 are then
molar
Gibbs
energies
as:
given
Ge ZnTcr
ZnTe OG8
+ RT In Y + RT
Fe Cdfe=
0G8CdTe
+ RT In Y + RT y21a21 C2Y-11
(1-v12
12 021+Q._[1-2y)]
(211
and
III. PHASE
+ 2 a,,(l-rI3
(221
EQUILIBRIA
between liauid end 8 is In the ternary Zn-Cd-Te system. eauilibrium Zn and Cd melt at relatively low temperatures and% of main interest. therefore, eauilibria involving solid Zn and Cd phases is not considered There is also a liquid miscibility oao in the tn-ZnTc region of here. Zn-Te phase diagram (1) which would extend into the ternary SYStem.
165
PHASE EQUlLlBRlACALCULATlONOFZn-Cd-T@ SYSTEM
Esuilibrium
bctuccn
liquid
and
(ZnyCdl _ y 1Te
at
any
temperature
is
given
by:
EL Zn
-L + GTc
-_ ge ZnTe
(231
i+ Cd
-L + GCd
= $
(2L1
and CdTe
where
all terms arc CIS defined earlier. NOW for the (L+S) equilibrium at a given temperature there are three compositional unknowns. tuo for the liquid phase and one for 8 Phase. BY fixing one of these, l QS_ (23) and (2fi) may be solved to define one tic line in the (L+Sl region and a calculation of number of such tie lines over the whole two phase region would define it completely. In given
the
liquid
miscibility
gap,
tuo
phase
(Ll+L2)
equilibrium
is
by: iL1
= ;:2
i
Of
the
four
(i = Zn. comDositiona1
Cd.
unknowns
Tel for
(25a.b.c) (L1+L2)
equilibrium,
two
for
one is fixed and cos. each phase, (25s) to (25~1 are solved for other three to Qive one tie line. A calculation of number of tie lines throughout the (L1+ L2) equilibrium region would comlctclv define the miscibility
gaD
at IV
(I)
Pure
ComDonent
a aiven
temDerataure,
EVALUATION and
OF
TIOOEL PARAMETERS
ComDounds:
The enthalpies of melting of pure Zn, Cd Hultgrcn et. al [83 were used by Sharma and Chano the Gibbs energies of melting of these components. Table 1 is used in this study. The Gibbs energies and CdTe compounds arc also taken from the work cl.21 and are given in Table 1. (ii)
Lisuid
and
and Te assessed by (1, 21 to arrive at There data aiven in of formation of ZnTc of
Sharma
and
Chana
8 phases:
Sharma and Chang El.21 have used associated solution mode1 to adequately describe the thermodynamic properties and phase equilibrium in Zn-Te and Cd-7c systems. In the present study their model has been extended to ternary Zn-Cd-Te system. In es. (9) number of uiJ snd vi3 parameters Zn-Te and and Chana between Zn parameters the enthalw These are
for the liquid phase, that arc obtainable from the binary Cd-Te systems are. therefore, taken from the work of Sharma (1.21 and are listed in Table 2. The interaction parameters and Cd in the liouid phase are arrived at by oDtimising these with rcsacct to the asscssed data of Hultorcn ct. al [9] for and entcropv of mixing of binary Zn-Cd liquid solutions. also listed in Table 2. The remaining parameters for the
166
A.K. SINGH and R.C. SHAAMA
liquid Phase as well as 8 phase arc ootimization with respect to the l xcwrimentel (mainly Dseudo-binary ZnTe-CdTe diagram) and TABLE
1:
Lattice
OGL Cd
-
OGS Cd
=
OGL fn
-
OS GZn
=
OGL Te
-
OGS Te
OG8 Cdle
-
00 G2nTe
TABLE
2:
Kl
=
-
CornPound 6190.0
- 10.617
T
7322.0
- 10.572
1
- 26.20
1
= 17689.0
OGL Cd
- OGke
OGL
-
Zn
Stabilities
OGL
7e
+ 62.1536
=
+ 53.62
-
167.600.0
10638.0/T
for
- 2.0177
"13 u16
= 888.19/T =O
In K,
= 3037.5/T = O
u23
= 0
u26
= '
u36 u35 "65 =12
u21 u31
u15
"25
+ 0.11506
u61 "51 u32 u62
= 6635.0/T
- 3.8565
us2
= 0.0
"63
= 608.2/T
"53
= 1136.33/T
=
1662.59/T
a2l
=
1
1065.7217
+ 0.1090
-5.0132
=o = ' -0 = 6635.0/T = 376.5/T = 608.2/T
=
-
a phases. 'CdTe' ) - 1.10 v12 v13
= 12673.0/T
=
and 5:
* 9567.7/T
=o
u56
simultaneous diagram data in Table 2.
1
the liquid 6: 'ZnTc'.
L
u12
bY Dhsse given
(J/mole).
= - 125.659.0
Solution model parameters 'Zn'. 2: 'Cd', 3: ‘Te’.
( 1: In
and
obtsined ternary are also
-1235.13/T 226.19/T
- 3.8565
v16
=O = O = 978.0/T
VI5
= 0
v23
= 0
v23
= '
v25
= 0
v36
= '
v35
= O
VL5
= 0
167
PHASE EQUlLlSf?iA CAlClJLATlON OF Zn-Cd-Te SYSTEM
‘6001-----0 Sttmingrr
rt. al.
lSS0 -
y
1500 .
f % & lLS0 E c’ 1400 -
1350
t 13ooi
I O.2
I 0.4
CdTe Fig.
1:
Calculated
0 Cd
I
I
0.6
0.8
%nrr CdTe-Znlc
cvxudo-binary
i!nTt ohase
diagram.
0 Zn
A.K. SINGH
and R.C. SHARMA
1 s 1460
0.1
0.2
0.3
0.5
0.4
0.6
0.7
K
0.9
0.6
Fig.
3:
Calculated
1.0 tn
Cd isotherm
of
Zn-Cd-Te
A
phase
diagram
T t 1420
K
at
l&50
K.
at
1620
K.
Te
1.0
0.9
Ffa.
I:
Cslcu1sted
isotherm
of
Zn-Cd-Tc
phase
dioorsm
169
PHASE EQUlLlBRlA CALCULATION OF Zn-cd-Te SYSTEM
Cd
Fig.
5:
Fig.
6:
Calculsted
Calculated
Zn
X2"
isotherm
isotherm
of
of
Zn-Cd-fc
Zn-Cd-Te
DhaSC
Dhase
diagram
diagrem
at
at
1380
1300
K.
K.
A.K+ SINGH and R.C. SHARMA
174
a
fn
*Zn
Fiat
7:
Fio.
Csiculatcd
8:
Calculated
isothc~m
isotherm
of
tn-Cd-Trr
of
Zn-Cd-lc
ahasc
diagrsm
P~~SC’
dfeoram
et
320~ K.
at
1lOO
K.
171
PHASE EQUILIBRIA CALCULATION OF Zn-Cd-Te SYSTEM
Cd
Fig.
9:
Li cwidus
Zn
X2” crojection
V.
of
RESULTS
Zn-Cd-Te
AND
phase
diagram
(calculated).
DISCUSSION
Zn-Te the CdTe and compounds systems. Znle In Cd-Te and The compound melt congruently st 1371K and 1573K, resocctivclv c1.21. In lisuidus in both the systems extends very close to pure components. sddit ion, a liquid miscibility QOP exists in Zn-ZnTe portion of the Zn-Te phae diagram, uith a critical Point at -1613K. uhich interacts with the ZnTe liauidus leading to a monotectic at -1488K Cl]. CdTe and ZnTe compounds have In the ternary Zn-Cd-Te system. FiO. 1 shous calculated CdTe-ZnTe complete miscibility in solid state. data of pseudo-binary diagram slonauith the experimental phase Steininoer et al. (31. The aareement. in oeneral. is very good. Figs. 2 to 8 qive the calculated isotherms of Zn-Cd-Te ternary diagram at 1500K. 1450K. 1GZOK. 1380K. 1300K. 12OOK and 1100K. respectively. In addition to the compound liauidus. belou the critical Point of the miscibility OC)P in the Zn-Te system at 1613K. liauid miscibility cap starting from the Zn-Te side extends into the ternary system (for example see 15OOK isotherm in Fig. 2). Belou the monotectic (*1&88K) in binary Zn-Te system. the miscibility gap in the ternary Zn-Cd-Te system interacts uith the compound liquidus to give three Phase (Ll+L2+8) louilibrium as
A.K.SlNGHand R.C.SHARMA
172
seen in 16SOK and lL20K isotherms in Figs. 3 end 6. respectively. At still lower temperatures. less than 4390K. the miscibility gap becomes metsstable with respect to the comoound lisuidus and does not appear in the stable DhaSe diagram as seen in Zn-Cd-Te isotherms at lower temoeratures in Figs. 5 to 8. No exoerimental data on l&L) tie lines or miscibility Qao in the Zn-Cd-Te system exists in literature and, therefore, comoarison with experimental data is not Dossible. Finally. Fig. 9 gives calculated liauidus at various temperatures in the Zn-Cd-Te system. Also shown in Fig. 9 is the lxoerimental data on liauidus temperatures for number of Zn-Cd-Te alloys from Steinineer et-al. [S]. The agreement in the Te-rich side (xTe)0.5) is very good. however. a Door
agreement
is obtain
for four
alloys
with
xTe<0.5.
During 0Rtimisation parameters for additional ternary only CdTe-ZnTe oseudo-binary phase diagram data was used. Other liauidus data could not be used for the lack of tie line information. Due to the limited data, some of the parameters had to be set to zero a Driori. To obtain a better set of parameters. some tie line information on (G+L) eauilibrium at some temperatures would be essential. Still the agreement with liauid data Some the in Te-sich side is auitc good. more experimental information is needed to arrive at better calculated diagram. CONCLUSIONS Zn-Cd-fe phase diagram has been calculated by using associated solution model for the liauid phase and sub-regular solution model for 1Te phase. The calculated diagrams agree well with most of the (ZnyCdl_y the limited experimental data that is available in literature. More experimental the agreement is not very good in some parts. reauired to arrive at a better descriotion of the system.
However, data is
ACKNOWLEDGEMENT The authors gratefully acknowledge the financial suooort Department of Electronics, Government of India, New Delhi.
from
the
REFERENCES 1. 2. 3.
6.
5. 6. 7. 8.
9.
R. C. Sharma and Y.A. Chang, J. Cryst. Growth, a. 193 (1988). 1536 R. C. Sharma and Y.A. Ghana. J. Electrochem. sot.. 136, (19891 J. Steininger. A.J. Strauss and R. F. Brebrick. J. Electrochem. sot. LLL. 1305 (19701. L.A. Zabdyr. J. Electrochem. Sot.. 131. 2157 (1986). S. Szaoiro, J. Electr. Rater., 3. 223 (19761. A. Laugier. Rev. de Phys. aopl., 8. 259 (1973). R. Schmid and Y. A. Chang, CALPHAD, 2. 363 (19851. R. Hultgren. P.D. Desai, D.T. Hawkins. n. Gleiser. K. K. Keller and .Selectd values of the Thermodynamic Properties of 0. 0. Uagman. the Elements'. ASH. 1973. R. Hultoren. P.D. Desai. D.T. Hawkins, H. Gleiser, K.K. Kelly and Selected Values of Thermodynamic Properties of Binary 0. Waoman, Alloys. ASH. Retals Park. OH. 1973.