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Correlation of thermodynamic properties of AIIBVI and AIIIBVI phases

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Correlation of thermodynamic properties of AIIBV and AIIIBVI phases
 ISSN 0020-1685, Inorganic Materials, 2007, Vol. 43, No. 2, pp. 115–124. © Pleiades Publishing, Inc., 2007.
Original Russian Text © V.P. Vasil’ev, 2007, published in Neorganicheskie Materialy, 2007, Vol. 43, No. 2, pp. 155–164.
115
INTRODUCTION
The thermodynamic properties of III–V compound
semiconductors with the ZnS structure were analyzed
by Vasil’ev and Gachon [1]. The enthalpy of formation
∆
f
H
0
(298 K)
, Gibbs energy of formation ∆
f
G
0
(298 K),
and standard entropy S
0
(298 K) of the III–V phases
were found to correlate with the melting points of inter-
mediate phases, with correlation coefficients from
0.999 to 0.940, respectively. In addition, some other
correlations were revealed.
Correlations between the Thermodynamic Properties of II–VI and III–VI Phases
V. P. Vasil’ev
Moscow State University, Vorob’evy gory 1, Moscow, 119899 Russia
e-mail: wassiliev@veernet.ru
Received May 5, 2006
Abstract
—Simple correlation models are considered that can be used to predict unknown and refine question-
able thermodynamic properties of II–VI and III–VI semiconductors. An empirical rule is proposed: for a par-
ticular combination of Periodic Groups, the enthalpy and Gibbs energy of formation of isostructural A
n
B
m
com-
pounds are linear functions of the melting point.
DOI: 10.1134/S0020168507020045
Table 1. Enthalpies of formation and melting points of II–VI phases
Phase
T
m
, K Ref.
–
∆
f
(298 K),
kJ/g-at
Ref.Method
–
∆
f
(298 K), kJ/g-at
ZnS (hexagonal, wurtzite)
2048 ±
5
[2]
102.7 ±
1
[2] Compilation 102.4
1993 [4]
102.5 ±
1
[4] Optimization
1991 [3]
102.3 ±
2
[5] EMF measurements
ZnSe (cubic, sphalerite) 1793 ±
15 [2] 82.2 ±
2 [2] Compilation 83.3
1799 [3] 88.8 ±
5 [5] EMF measurements
ZnTe (cubic, sphalerite) 1563 ±
8 [6] 64.9 ±
5 [7] Solution calorimetry 66.1
1563 ±
8 [8] 61.5 ±
4 [9] Direct synthesis calorimetry
1573 ±
10 [2] 59.6 ±
2 [2] Compilation
CdS (hexagonal, wurtzite)
1748 ±
15
[2]
78.5 ±
2
[2] Compilation 79.9
CdSe (cubic, sphalerite)
1563 ±
10
[2]
71.5 ±
2
[2] Compilation 66.1
CdTe (cubic, sphalerite)
1365 ±
5
[2]
50.6 ±
0.5
[10] EMF measurements 51.2
1365 ±
5 [8]
51.5 ±
1
[11] Optimization
1371 [13]
50.5
[13] Optimization
1368 [3]
50.4 ±
0.5
[12] Solution calorimetry
HgS (hexagonal, wurtzite)
1098 ±
5
[2]
29.5 ±
2
[2] Compilation 31.2
1098 [3]
HgSe (cubic, sphalerite)
1072 ±
5
[2]
29.7 ±
1
[2] Compilation 29.3
1072 [3]
HgTe (cubic, sphalerite)
943 ±
5
[2]
18.1 ±
1
[11] Optimization 19.6
943 [3]
21.8 ±
1
[12] Solution calorimetry
Note: The most reliable data are set in bold.
H
meas
0
H
calc
0
116
INORGANIC MATERIALS
Vol. 43
No. 2
2007
VASIL’EV
This paper deals with simple correlation models that
can be used to predict unknown and refine questionable
thermodynamic properties of II–VI and III–VI semi-
conductors.
II–VI COMPOUND SEMICONDUCTORS
Consider the correlation between the enthalpy of
formation of the zinc, cadmium, and mercury chalco-
genides (ZnS structure) and their melting points T
m
,
which have been investigated in sufficient detail
(Table 1). Some of the heats of formation and melting
points were taken from the handbook by Glushko [2]
and supplemented with later data. In the case of ZnTe,
also included are the enthalpies of formation reported
previously. The values set in bold are believed to be the
most reliable.
As seen in Fig. 1, the ∆
f
H
0
(298 K) of the Group IIA
chalcogenides is a linear function of T
m
, with a correla-
tion coefficient r
= 0.996:
∆
f
H
0
(298 K) = 51.06 – 0.07494
T
m
.(1)
The calculated enthalpies of formation of the II–VI
phases (confidence interval of ±
1.5
kJ/g-at) coincide
with the experimentally determined values to within the
error of determination, except for CdSe.
The enthalpy of formation of CdSe following from
Eq. (1), –66.1 ±
1.5 kJ/g-at, appears preferable to the
experimentally determined value: –71.5 ±
2.0 kJ/g-at
[2]. Indeed, from the correlation between the enthalpy
of formation and band gap E
g
of the II–VI phases
(Fig. 2) [14], we obtain
∆
f
H
0
(298 K) = –21.11 – 22.253
E
g
,
r
= 0.98.(2)
It follows from this relation that the calculated enthalpy
of formation of CdSe cannot be lower than –66.1 kJ/g-at.
III–VI COMPOUND SEMICONDUCTORS
III–VI compounds have predominantly covalent
bonding, with a degree of ionic or metallic bonding,
depending on the system. The most typical stoichiome-
tries in this family are M
2
X
3
and MX (X = chalcogen),
which are encountered in most of the Ga–S, Ga–Se,
Ga–Te, In–S, In–Se, In–Te, Tl–S, Tl–Se, and Tl–Te sys-
tems. The Tl–S and Tl–Se systems contain no 2 : 3
phases. In contrast, all of the aluminum chalcogenides
have the 2 : 3 stoichiometry.
In Table 2, the formulas of the congruently melting
and peritectically forming phases are set in bold and
roman, respectively. An increase in the degree of metal-
lic bonding results in a larger number of intermediate
phases (gallium, indium, and thallium tellurides). The
only exception is the Tl–S system, in which extra
phases appear owing to the formation of polymeric sul-
fide chains.
Whereas aluminum chalcogenides are stable com-
pounds, in which aluminum is always trivalent, gallium
and indium in their chalcogenides may be in different
oxidation states, from 3+ to 1+. The oxidation state of
thallium in its sulfides, selenides, and tellurides is typi-
cally 1+.
The maximum melting point of the intermediate
phases in the III–VI systems decreases in going from
sulfur to tellurium in the 2 : 3 aluminum, gallium, and
–120
–80
–40
0
0
1
2
3
4
HgTe
CdSe
ZnS
∆
f
H
0
(298 K), kJ/g-at
E
g
, eV
Fig. 2. Correlation between the enthalpy of formation and
band gap of Group IIA chalcogenides.
800
1200
1600
2000
2400
0
–40
–80
–120
HgTe
HgSe
HgS
CdTe
ZnTe
CdSe
CdS
ZnSe
ZnS
T
m
, K
∆
f
H
0
(298 K), kJ/g-at
Fig. 1. Correlation between the enthalpy of formation of
Group IIA chalcogenides and their melting points.
INORGANIC MATERIALS
Vol. 43
No. 2
2007
CORRELATIONS BETWEEN THE THERMODYNAMIC PROPERTIES
117
indium chalcogenides and increases in the 1 : 1 phases.
Among the thallium sulfides and selenides, the 2 : 1
phases have the highest melting point. In the Tl–Te sys-
tem, the melting point has a maximum at the 5 : 3 sto-
ichiometry. The closer are the constituent components
in atomic number, the smaller is the difference between
the maximum and minimum melting points of the inter-
mediate phases in the system, and vice versa (e.g., in
the In–Te and Tl–S systems).
The enthalpy of formation of the III–VI compounds
has been studied in greater detail—for the most part, by
calorimetry and emf measurements—than their other
thermodynamic properties. As a rule, the enthalpies of
formation of indium and gallium sulfides determined
by combustion calorimetry are notably more negative
than those evaluated by other methods (Table 3). It
seems likely that the high pressures generated in calori-
metric bombs at temperatures above 1000 K may lead
to the formation of metastable ordered high-pressure
phases, resulting in larger exotherms.
Using emf measurements, Abbasov [28] determined
the basic thermodynamic functions of formation of
indium–sulfur alloys. His calculations of integral quan-
tities were not quite accurate. He studied sulfur-rich
compositions in the temperature range 513–633 K,
where the higher sulfide is in equilibrium not with pure
sulfur but with the melt, whose composition depends on
temperature. Abbasov [28] did not take this into
account, which led to errors in the temperature coeffi-
cient ∆
E
/
∆T and, hence, in the enthalpies and entropies
of formation of intermediate phases. This can be seen
from comparison between the values of S
0
(In
2
S
3
,
298 K): 21 [28] and 33.7 ± 0.8 J/(K g-at) [44]. The lat-
ter value was extracted from low-temperature heat
capacity measurements. The data from [28] were not
used in this study.
Thomson et al. [29] investigated the In–Se system
by the heterogeneous equilibrium method. Their
∆
f
H
0
(298 K) data suffer a significant uncertainty, up to
±7 kJ/g-at. Vapor pressure measurements were used to
study Al
2
Te
3
[36] and In
2
S
3
[31]. Optimization was per-
formed for four systems: Tl–Te [15], Tl–Se [19], Ga–Te
[21], and Al–S [38]. Oh and Lee [21] used only the cal-
orimetric data reported by Castanet and Bergman [18],
while those reported by Hahn and Burow [22] and the
emf data obtained by Abbasov et al. [30] were left out
of consideration.
Figure 3 shows the enthalpy of formation as a func-
tion of melting point for Group III chalcogenides. It can
be seen that these compounds can be divided into three
distinct groups corresponding to different types of
structures.
The compounds of the first group have layered
structures. This group comprises the thallium and
indium chalcogenides and Al
2
Te
3
.
The second group comprises the compounds with
the α-Ga
2
S
3
, γ-Ga
2
S
3
, and GaS structures. The gallium
tellurides are intermediate in position between the first
and second groups.
The third group comprises a number of 2 : 3 com-
pounds with the α-Al
2
O
3
structure (aluminum, indium,
and thallium oxides), aluminum sulfide, and aluminum
selenide. Al
2
Se
3
has the β-Ga
2
S
3
structure, which is iso-
morphic with the α-Al
2
O
3
structure [45]. It is reason-
able to expect that, at high pressures, the compounds
with the α- and γ-Ga
2
S
3
structures may undergo a tran-
sition to the α-Al
2
O
3
type. The α-Ga
2
S
3
and α-Al
2
O
3
structures have many features in common (Fig. 4,
Table 4).
0
500
1500
2000
2500
0
–100
–200
Al
2
Se
3
Al
2
S
3
T
m
, K
∆
f
H
0
(298 K), kJ/g-at
In
2
Se
3
Tl
2
O
3
In
2
O
3
Ga
2
O
3
Al
2
O
3
I
II
III
1000
–300
1
2
3
4
5
Fig. 3. Enthalpy of formation as a function of melting point
for Group III chalcogenides: (1) thallium chalcogenides,
(2) indium chalcogenides, (3) gallium chalcogenides,
(4) aluminum chalcogenides, (5) M
2
O
3
(M = Tl, In, Ga, Al)
oxides; (I–III) different structures (see text).
Table 2. Intermediate phases in III–VI systems
Degree of ionic bonding Al–Te Al–Se Al–S
Al
2
Te
3
Al
2
Se
3
Al
2
S
3
Ga–Te Ga–Se Ga–S
GaTe, Ga
3
Te
4
, Ga
2
Te
3
GaSe, Ga
2
Se
3
GaS, Ga
2
S
3
In–Te In–Se In–S
InTe, In
3
Te
4
, In
2
Te
3
, In
2
Te
5
In
4
Se
3
, InSe, In
2
Se
3
InS, In
2
S
3
Tl–Te Tl–Se Tl–S
Tl
2
Te, Tl
5
Te
3
, TlTe, Tl
2
Te
3
Tl
2
Se, TlSe Tl
2
S, Tl
4
S
3
, TlS, TlS
2
, Tl
2
S
5
Degree of metallic bonding
118
INORGANIC MATERIALS Vol. 43 No. 2 2007
VASIL’EV
Table 3. Standard enthalpies of formation of Group IIIA chalcogenides
SystemCompoundStructure typeSp. gr.
Crystal
system
T
m
, K
–∆
f
H
0
(298 K), kJ/g-at
Method, reference
–∆
f
H
0
(298 K),
kJ/g-at (calcu-
lation by (3))
–∆
f
H
0
(298 K), kJ/g-at (calcu-
lation by (8))
Tl–TeTl
2
Te
3
ParentCcMonoclinic512 [15]18.0 ± 0.2EMF measurements [16]18.419.6
508 [3]17.0Optimization [15]
TlTe ParentI4/mcmTetragonal583 [15]21.9 ± 0.2EMF measurements [16]22.922.4
573 [3]20.9Optimization [15]
Tl
5
Te
3
In
5
Bi
3
I4/mcmTetragonal716 [15]27.1 ± 0.2EMF measurements [16]31.427.5
728 [3]26.3 ± 0.2Direct synthesis calorimetry [17]
24.9Optimization [15]
Tl
2
Te UnknownC2/cMonoclinic690 [15]26.8 ± 0.3EMF measurements [16]29.726.5
698 [3]25.4Optimization [15]
Tl–SeTlSe ParentI4/mcmTetragonal623 [3]30.5 ± 0.3EMF measurements [16]25.527.8
627 [19]30.2Optimization [19]
Tl
2
Se UnknownP4/nTetragonal663 [3]30.8 ± 0.3EMF measurements [16]28.329.6
670 [19]31.9Optimization [19]
Tl–STl
2
S
5
ParentP2
1
2
1
21
Orthorhombic373 [16]14.2 ± 0.8EMF measurements [16](9.6)(19.6)
TlS
2
UnknownP4
2
/nmTetragonal418 [16]15.9 ± 1.0EMF measurements [16](12.5)(22.0)
TlS ParentI4/mcmTetragonal506 [16]26.4 ± 0.3EMF measurements [16](18.1)26.6
Tl
4
S
3
ParentP2
1
/aMonoclinic547 [16]28.2 ± 0.9EMF measurements [16](20.7)28.8
Tl
2
SParentR3Hexagonal727 [16]30.4 ± 0.8EMF measurements [16]32.1(38.2)
In–Te
In
2
Te
5
Parent
Rm
Hexagonal740 [3]33.27Optimization [20]32.931.3
In
3
Te
5
Unknown
Rm
Cubic898 [3]40.1Optimization [20]42.937.9
In
2
Te
3
Parent
F3m
Cubic940 [3]39.8 ± 3Combustion calorimetry [22]45.639.7
938 [20]41.8 ± 2Direct synthesis calorimetry [23]
949 [2]38.3 ± 0.6Tin-solution calorimetry [24]
39.2Optimization [20]
37.6 ± 0.5Direct synthesis calorimetry [25]
In
3
Te
4
ParentPnnmOrthorhombic923 [20]37.41Optimization [20]44.539.0
InTe TlSeI4/mcmTetragonal969 [3]39.7 ± 1EMF measurements [28]47.540.9
991 [2]48.1 ± 2Combustion calorimetry [22]
35.8 ± 0.5Tin-solution calorimetry [24]
35.6 ± 1Direct synthesis calorimetry [26]
33.7Optimization [20]
In
4
Te
3
In
4
Se
3
PnnmOrthorhombic735 [2]33.6 ± 0.3Direct synthesis calorimetry [27]32.631.1
3
3
4
INORGANIC MATERIALS Vol. 43 No. 2 2007
CORRELATIONS BETWEEN THE THERMODYNAMIC PROPERTIES
119
Table 3. (Contd.)
SystemCompoundStructure typeSp. gr.
Crystal
system
T
m
, K
–∆
f
H
0
(298 K), kJ/g-at
Method, reference
–∆
f
H
0
(298 K),
kJ/g-at (calcu-
lation by (3))
–∆
f
H
0
(298 K), kJ/g-at (calcu-
lation by (8))
In–SeIn
2
Se
3
ParentP6
1
Hexagonal1163 [2](53.6 ± 4)EMF measurements [28]59.856.5
1158 [3]63.6 ± 3Direct synthesis calorimetry [23]
68.6 ± 3Combustion calorimetry [22]
InSe ParentC12/m1Monoclinic933 [2](58.2 ± 4)EMF measurements [28]45.245.3
873 [3](59.0 ± 4)Combustion calorimetry [22]
In–SIn
2
S
3
ParentI4
1
/amdTetragonal1363 [3]71.7 ± 7Heterogeneous equilibrium [29]72.577.1
1363 [2]69.9 ± 5Vapor pressure measurements [31]
(84.9 ± 3)Combustion calorimetry [22]
(50.2 ± 3)EMF measurements [28]
InS ParentPnnmOrthorhombic956 [3](54.4 ± 4)EMF measurements [28]46.654.1
953 [2](61.9 ± 6)Combustion calorimetry [29]
(70.3 ± 6)Combustion calorimetry [22]
–∆
f
H
0
(298 K),
kJ/g-at (calcu-
lation by (4))
Ga–TeGa
2
Te
3
γ-Ga
2
S
3
F3m
Cubic1071 [3]68.6 ± 4EMF measurements [30]62.165.2
1065 [2]54.4 ± 3Combustion calorimetry [22]
1078 [21](39.8 ± 3)Direct synthesis calorimetry [18]
(39.2)Optimization [21]
GaTe GaSP6
3
/mmHexagonal1098 [3]62.6 ± 4EMF measurements [30]65.766.9
1098 [21]59.8 ± 6Combustion calorimetry [22]
1108 [2](39.4 ± 3)Direct synthesis calorimetry [18]
(39.2)Optimization [21]
Ga–SeGa
2
Se
3
γ-Ga
2
S
3
F3m
Cubic1278 [3]87.9 ± 3Combustion calorimetry [22]89.985.9
1293 [2]88.4 ± 3EMF measurements [32]
(92.0 ± 4)Combustion calorimetry [33]
(73.6 ± 3)Direct synthesis calorimetry [23]
GaSe GaSP6
3
/mmHexagonal1211 [3]82.4 ± 3EMF measurements [32]80.981.4
1233 [2]73.2 ± 6Combustion calorimetry [22]
4
4
120
INORGANIC MATERIALS Vol. 43 No. 2 2007
VASIL’EV
Table 3. (Contd.)
SystemCompound
Structure type
Sp. gr.
Crystal
system
T
m
, K
–∆
f
H
0
(298 K), kJ/g-at
Method, reference
–∆
f
H
0
(298 K),
kJ/g-at (calcu-
lation by (3))
–∆
f
H
0
(298 K), kJ/g-at (calcu-
lation by (8))
Ga–SGa
2
S
3
α-Ga
2
S
3
P6
1
Hexagonal1373 [3]102.5 ± 3EMF measurements [32]102.7103.3
1288 [2](114.6 ± 3)Combustion calorimetry [22]
GaS ParentP6
3
/mmHexagonal1288 [3]97.0 ± 3Combustion calorimetry [22]91.396.9
1288 [2]97.9 ± 3EMF measurements [32]
Al–TeAl
2
Te
3
β-Al
2
Te
3
P12
1
C1Monoclinic1173 [2]63.76 ± 1Direct synthesis calorimetry [34]60.4 (1)60.6
1168 [3](65.3 ± 4)Direct synthesis calorimetry [35]
1167 [21](65.91)Optimization [21]
(52 ± 1)Vapor pressure measurements [36]
–∆
f
H
0
(298 K),
kJ/g-at (calcu-
lation by (5))
Al–SeAl
2
Se
3
β-Ga
2
S
3
C
1
C
1
Monoclinic1233 [3]113.4 ± 2Direct synthesis calorimetry [35]110.6
108.5 ± 3Combustion calorimetry [37]
113.4Compilation [2]
Al–S
Al
2
S
3
Al
2
O
3
Rc
Hexagonal1373 [3]144.7 ± 4Direct synthesis calorimetry [35]139.2
1373 [2]144.6Optimization [38]
144.7 ± 10Compilation [2]
(130.2 ± 1)Solution calorimetry [39]
Tl–OTl
2
O
3
Al
2
O
3
Rc
Hexagonal1107 [2]78.1 ± 1Compilation [2]84.9
In–OIn
2
O
3
Al
2
O
3
Rc
Hexagonal1660 [2]185.2 ± 2Compilation [2]197.8
185.4 ± 2EMF measurements [40]
(179.0 ± 2)EMF measurements [41]
Ga–OGa
2
O
3
Al
2
O
3
Rc
Hexagonal1998 [2]258.6 ± 2EMF measurements [42]266.8
(217.8 ± 5)Compilation [2]
Al–O
Al
2
O
3
Al
2
O
3
Rc
Hexagonal2326 [2]335.1 ± 1Compilation [2]333.7
2327 [43]335.1Compilation [43]
Note:The values given in parentheses were not included in calculations.
3
3
3
3
3
INORGANIC MATERIALS Vol. 43 No. 2 2007
CORRELATIONS BETWEEN THE THERMODYNAMIC PROPERTIES
121
The enthalpies of the high-pressure transitions of
Ga
2
Se
3
and Ga
2
S
3
to the α-Al
2
O
3
structure can be evalu-
ated using the correlation equations (4) and (5) (Table 5),
derived from the data in Table 3.
The chalcogenides of the second and, especially, first
groups have a variety of crystal structures (Table 3).
Moreover, for some of these compounds, the experi-
mentally determined heats of formation scatter signifi-
cantly, e.g., from –50.2 to –71.7 kJ/g-at for In
2
S
3
and
from –73.6 to –92.0 kJ/g-at for Ga
2
Se
3
. As a conse-
quence, it is impossible to obtain good correlations
between ∆
f
H
0
(298 K) and T
m
in the first and second
groups of III–VI compounds (Table 5). Nevertheless,
the correlation equations derived here are useful in
selecting the most reliable heats of formation of
Group III chalcogenides (set in bold in Table 3).
The selected heats of formation of the Group III
chalcogenides were used to correlate the reduced
enthalpy of formation, ∆
f
H(298 K)/T
m
, with the half-
sum of bond distances in the crystal lattices of their con-
stituent components, 1/2Σ(d
A–A
+ d
B–B
) (Table 6). The
∆
f
H
0
(298 K)/T
m
= f(1/2Σ(d
A–A
+ d
B–B
)) (7)
data for the Group III chalcogenides (Fig. 5) are well
represented by the linear best fit equation
∆
f
H
0
(298 K) = (–184.80 + 484.9d)T
m
,r = 0.96.(8)
Equation (8) applies well to the 1 : 1 chalcogenides. At
large uncertainties in experimental data, the role of sto-
ichiometric coefficients is insignificant, and this corre-
lation is applicable in the composition range
40−60 at % X, and in some cases even in the range
33−67 at %. For accurately determined enthalpies of
formation (set in bold in Table 3), the maximum devia-
tion of the calculated value from the experimentally
determined one is within 10%. The only exceptions are
Tl
2
S
5
, TlS
2
, and Tl
2
S: the data for these phases fall
beyond the applicability limits of the correlation equa-
tion (8). It seems likely that the structural differences
and the marked difference in melting point between the
thallium sulfides compared to the other chalcogenides
are among the major reasons for the discrepancy
between the experimentally determined and calculated
heats of formation of these phases.
(a) (b)
Fig. 4. Crystal structures of (a) α-Al
2
O
3
and (b) α-Ga
2
S
3
[46].
Table 4. Crystal structures of α-Ga
2
S
3
and α-Al
2
O
3
[46]
Structure type Sp. gr.Crystal system a, nm Ò, nm c/a V, nm
3
α-Ga
2
S
3
P6
1
Hexagonal 0.6385 1.804 2.825 0.637
α-Al
2
O
3
R3c Hexagonal 0.482 1.317 2.73 0.265
Table 5. Correlation equations ∆
f
H
0
(298 K) = a + bT
m
for different structure types
Compound Equation no.∆
f
H
0
(298 K), kJ/g-at r Structure type
A
III
B
VI
(3) 14.06 – 0.06348T
m
0.86 Parent, layered
A
III
B
VI
(4) 81.83 – 0.1344T
m
0.88 Ga
2
S
3
, GaS
A
III
B
VI
(5) 141.02 – 0.2041T
m
0.998 Al
2
O
3
A
III
B
V
(6)
14.91 – 0.03619
0.998 ZnS
A
II
B
VI
(1) 51.06 – 0.07494T
m
0.996 ZnS
Note:Equation (5) was derived using data from Table 3.
* Data from [1].
T
m
*
122
INORGANIC MATERIALS Vol. 43 No. 2 2007
VASIL’EV
Structural differences between III–VI compounds
have no significant effect on the correlation coefficient
in Eq. (8), which is governed by the sizes of the constit-
uent atoms.
The plot of the standard entropy versus melting
point for III–VI compounds (Fig. 6) also suggests that
these compounds can be divided into at least three
groups: those with the α-Al
2
O
3
and GaS structures and
with layered structures based on indium and thallium
chalcogenides. The thallium chalcogenides Tl
2
Te and
Tl
2
Se are probably similar in structure to indium
monoselenide and indium monosulfide. The more chal-
cogen-rich thallium compounds constitute independent
structural groups, as can be illustrated by the example
of the thallium sulfides. Consequently, correlations
between S
0
(298 K) and T
m
can be used to estimate
unknown standard entropies or to reveal structural sim-
ilarity between intermediate phases.
For example, using the correlation equation
S
0
(A
2
O
3
, 298 K) = 51.42 – 0.01760T
m
,r = 0.994,(9)
we obtain S
0
(Al
2
S
3
, 298 K) = 27.3 J/(K g-at),
S
0
(Al
2
Se
3
, 298 K) = 29.7 J/(K g-at), and S
0
(Tl
2
O
3
,
298 K) = 31.9 J/(K g-at).
CONCLUSIONS
The thermodynamic properties of II–VI and III–VI
compound semiconductors were analyzed, and the
∆
f
H
0
(298 K) and S
0
(298 K) of intermediate phases were
shown to correlate with their melting points.
The present results indicate that the correlations for
III–V, II–VI, and III–VI compounds can be applied to
other groups of alloys.
An empirical rule is proposed: for a particular com-
bination of Periodic Groups, the enthalpy and Gibbs
energy of formation of isostructural A
n
B
m
compounds
are linear functions of the melting point.
The enthalpies of formation and standard entropies
of unexplored III–VI phases were estimated.
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INORGANIC MATERIALS Vol. 43 No. 2 2007
CORRELATIONS BETWEEN THE THERMODYNAMIC PROPERTIES
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