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Thermodynamic propweties of AIIIBV compounds

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Thermodynamic propweties of AIIIBV compounds
 ISSN 0020-1685, Inorganic Materials, 2006, Vol. 42, No. 11, pp. 1176–1187. © Pleiades Publishing, Inc., 2006.
Original Russian Text © V.P. Vasil’ev, J.-C. Gachon, 2006, published in Neorganicheskie Materialy, 2006, Vol. 42, No. 11, pp. 1293–1303.
1176
INTRODUCTION
In recent years, a great deal of attention has been
paid to the optimization of thermodynamic properties
and phase diagrams. In selecting reliable thermody-
namic constants, however, one is confronted with the
problem of evaluating and systematizing contradictory
data. One approach to this problem is to use correla-
tions stemming from the Periodic Law [1].
Since experimental determination of thermody-
namic constants requires considerable effort and time,
various comparative techniques for evaluating thermo-
dynamic parameters appear attractive for gaining miss-
ing information.
The systematization of thermodynamic data for III–
V compounds is useful for adequate optimization of
related multicomponent systems since, for example, the
use of inaccurate data for the binary systems Ga–As,
Ga–P, and Ga–Sb [2] may lead to improper description
of the ternary systems Ga–In–P, Ga–As–P, and Ga–P–
Sb [3, 4].
In this paper, we present critical evaluation and sys-
tematization of available data on the thermodynamic
properties of III–V compounds.
CRYSTAL STRUCTURE
OF III–V COMPOUNDS
Under normal conditions, most of the III–V com-
pounds have a cubic structure of the sphalerite type,
except for aluminum, gallium, and indium nitrides,
which have a hexagonal structure of the wurtzite type.
The structure of boron nitride under normal conditions
(
α
-BN) is similar to the hexagonal structure of graph-
ite. At high pressures (
≤
10 GPa), boron nitride has the
sphalerite structure (
β
-BN). The other Group III
nitrides have the rock-salt structure (sp. gr. Fm m
) at
high pressures [5]. Hypothetically, aluminum, gallium,
3
and indium nitrides may also have the sphalerite struc-
ture [6]. The unit cell of InBi can be thought of as cubic
with tetragonal distortion. The lattice parameters of
InBi differ little from one another: a = 0.4972 nm, c
=
0.483 nm [7].
Thus, the structures of the III–V compounds have
many features in common, and these compounds can be
regarded as a series of phases across which chemical
bonding gradually changes from covalent to metallic.
The bond energy in the III–V compounds is deter-
mined, for the most part, by the (tetrahedral) nearest
neighbor environment of the atoms. The coordination
number in the sphalerite and wurtzite structures is 4/4.
In such structures, each atom has dissimilar nearest
neighbors, while its second neighbors are atoms of the
same kind. The contribution of more distant neighbors
to the lattice energy is insignificant.
In the structure of InBi, the coordination number is
close to 8/8. Nevertheless, this phase is worthy of being
considered together with the III–V compounds.
ENTHALPIES OF FORMATION OF THE III–V COMPOUNDS
The enthalpies of formation of the III–V compounds
have been studied better than the other thermodynamic
properties (Table 1). Table 1 also lists the melting
points of the III–V compounds.
In Table 1, the data reported before 1973 are cited
from the review by Gorbov [8], who considered all of
the III–V compounds except nitrides and boron-based
alloys.
Among the many III–V phases studied to date, the
most contradictory thermodynamic data were reported
for nitrides and phosphides. Those data must, therefore,
be critically evaluated. Boron pnictides are essentially
unexplored, except for boron nitrides, and available
Thermodynamic Properties of III–V Compounds
V. P. Vasil’ev
a
and J.-C. Gachon
b
a
Moscow State University, Vorob’evy gory 1, Moscow, 119899 Russia
b
Université Henri Poincaré, UMR 7555, Nancy, France
e-mail: wassiliev@veernet.ru
Received February 14, 2006
Abstract
—Available thermodynamic data for III–V compounds have been systematized and critically evalu-
ated. The results demonstrate that the enthalpies of formation ∆
f
H
0
(298 K)
, Gibbs energies ∆
f
G
0
(298 K)
, and
standard entropies S
0
(298 K)
of some of these compounds correlate with their melting points (correlation coef-
ficients from 0.999 to 0.94). A number of other correlations have also been revealed.
DOI: 10.1134/S0020168506110021
INORGANIC MATERIALS
Vol. 42
No. 11
2006
THERMODYNAMIC PROPERTIES OF III–V COMPOUNDS
1177
Table 1. Enthalpies of formation and melting points of III–V compounds
III–V
T
m
, K Source
–
∆
f
H
0
(298 K),
kJ/g-at
Source Method
BN
3800
±
50
(
p
= 6 GPa)
This work
(recommended)
126.0
±
3
This work
(recommended)
Correlation
3770
(
p
= 6 GPa)
[9]
127.0
±
2
[10] Bomb calorimetry
126.1
±
2
[11] Direct synthesis calorimetry
125.1
±
2
[13] Vapor pressure
BP 1700 ±
100 This work (estimate) 46.6 ±
2 [12] Bomb calorimetry
1800 ±
200 This work (estimate) 50.4 ±
4 [14] Compilation
AlN
4800
±
100
(
p
≈
8 GPa)
This work
(recommended)
159.0
±
2
This work
(recommended)
Correlation
~3500
(
p
≈
10 MPa)
[15]
159.2
±
4
[14] Compilation
160.0
±
1
[18] Direct synthesis calorimetry
3300 [16] 159.2
±
1
[19] Compilation
3073 [17]
159.2
±
4
[13] Vapor pressure
159.2
[20] Calculation
155.6
±
3
[24] Solution calorimetry
AlP
2790
±
20
This work
(recommended)
86.0
±
2
This work
(recommended)
Correlation
2793
±
20
[17]
82.6
±
2
[8] Solution calorimetry
2824 [21]
90.2
±
5
[22] Solution calorimetry
2827 [2]
83.3
±
2
[14] Compilation
82.2
±
2
[23] Compilation
83.2
±
2
[8] Compilation
82.2
[21] Optimization
74.2 [2] Optimization
AlAs
2058
±
10
This work
(recommended)
58.5
±
1
This work
(recommended)
Correlation
2039
[21]
58.2
±
2
[14] Compilation
2058
[2] 58.2 ± 2 [8] Solution calorimetry
2043 ± 10 [17] 58.5 [21] Optimization
1873 [8] 58.6 [2] Optimization
1740 [14] 60.4 ± 1 [25] Precipitation calorimetry
AlSb 1330 ± 2 This work
(recommended)
32.9 ± 2 This work
(recommended)
Correlation
1332 ± 2 [26] 32.9 [26] Optimization
1331 ± 3 [17] 31.8 ± 2 [8] EMF measurements
1331 [27] 36.75 [27] Optimization
1331 [28] 39.16 [28] Optimization
1328 [29] 40.63 [29] Optimization
1336 [30] 41.0 [30] Vapor pressure + optimization
1332 [2] 24.48 [2] Optimization
1333 ± 3 [14] 24.6 ± 1 [14] Compilation
25.0 [21] Optimization
25.0 ± 1 [25] Precipitation calorimetry
1178
INORGANIC MATERIALS Vol. 42 No. 11 2006
VASIL’EV, GACHON
Table 1. (Contd.)
III–V T
m
, K Source
–∆
f
H
0
(298 K),
kJ/g-at
Source Method
GaN 2570 ± 50 This work
(recommended)
78.5 ± 2 This work
(recommended)
Correlation
2573 ( = 6 GPa) [33] 78.4 ± 1 [35] Vapor pressure
78.4 ± 8 [36] Solution calorimetry
2700 ( = 9.3 GPa) [31] 78.8 ± 1 [34] Equilibrium pressure
78.9 [33] Equilibrium pressure
~2800 ( ≈ 4.5 GPa) [15] 75.0 [32] Optimization
70.3 [31] Optimization
2792 [37] 58.6 [37] Optimization
1963 ± 5 [17] 54.8 ± 4 [14] Compilation
GaP 1790 ± 10 This work
(recommended)
50.0 ± 1 This work
(recommended)
Correlation
1740 ± 5 [17] 51.0 ± 2 [8] Mass spectrometry
1790 ± 20 [14] 51.3 ± 3 [14] Compilation
1730 ± 5 [38] 50.2 ± 5 [38] Optimization
1749 [2] 52.3 ± 1 [25] Solution calorimetry
51.0 ± 1 [8] Compilation
50.0 ± 1 [39] Vapor pressure
57.3 [2] Optimization
GaAs 1511 ± 2 This work
(recommended)
39.5 ± 1 This work
(recommended)
Correlation
1511 ± 2 [17] 40.8 ± 1 [25] Precipitation calorimetry
1511 ± 2 [8] 39.8 ± 2 [8] EMF measurements
1511 ± 2 [14] 40.6 ± 4 [8] EMF measurements
1510 ± 2 [2] 41.9 ± 1 [40] Optimization
1512 ± 2 [21] 37.7 ± 1 [26] Optimization
1510 ± 2 [26] 37 ± 2 [8] Mass spectrometry
1511 [41] 37.7 ± 5 [8] Mass spectrometry
1514 [42] 37.7 ± 5 [8] Mass spectrometry
37.0 ± 3 [14] Compilation
43.8 ± 1 [43] Tin-solution calorimetry
44.4 [41] Optimization
44.4 [2] Optimization
GaSb 981 ± 2 This work
(recommended)
21.0 ± 1 This work
(recommended)
Correlation
981 ± 2 [21] 20.8 ± 1 [8] Tin-solution calorimetry
983 [2] 20.79 ± 1 [44] Optimization
985 ± 3 [14] 20.68 ± 1 [45] Compilation
976 ± 2 [8] 19.7 ± 2 [8] EMF measurements
987 ± 2 [44] 20.5 ± 2 [8] EMF measurements
20.9 ± 1 [8] Compilation
20.8 [21] Optimization
23 ± 4 [8] Bomb calorimetry
22.8 ± 1 [43] Tin-solution calorimetry
22.1 ± 1 [14] Compilation
22.4 [2] Optimization
INORGANIC MATERIALS Vol. 42 No. 11 2006
THERMODYNAMIC PROPERTIES OF III–V COMPOUNDS
1179
Table 1. (Contd.)
III–V T
m
, K Source
–∆
f
H
0
(298 K),
kJ/g-at
Source Method
InN 2050 ± 100
(p = 6.3 GPa)
This work
(recommended)
56.0 ± 3 This work
(recommended)
Correlation
2146 [52] 55.2 ± 2 [16] Vapor pressure
1714 (p = 6.3 GPa) [47] 56.5 ± 5 [48] Vapor pressure
48.3 [47] Optimization
1473 ± 10 [17] 63.8 ± 4 [49] Vapor pressure
1473 ± 10 [14] 65.7 ± 5 [50] Vapor pressure
1373 [16] 62.5 [51] Compilation
InP 1344 ± 5 This work
(recommended)
35.0 ± 2 This work
(recommended)
Correlation
1344 ± 5 [17] 34.7 ± 2 This work EMF measurements
1341 [26] 35.0 ± 2 [46] EMF measurements
(revaluated)
1327 [2] 37.2 [2] Optimization
1335 ± 5 [38] 38.8 ± 2 [53] Mass spectrometry
1328 [21] 30.3 ± 1 [54] Tin-solution calorimetry
1340 [42] 30.9 ± 2 [38] Optimization
28.2
± 1 [25] Precipitation calorimetry
43.9 ± 4 [8] Bomb calorimetry
42.9 ± 4 [14] Compilation
43.8 ± 3 [43] Tin-solution calorimetry
InAs 1215 ± 2 This work
(recommended)
29.0 ± 1 This work
(recommended)
Correlation
1215 ± 2 [17] 30.0 ± 1 [8] Tin-solution calorimetry
1215 ± 2 [8] 30.8 ± 2 [8] EMF measurements
1215 ± 2 [14] 28.9 ± 1 [8] Bomb calorimetry
1215 [21] 29.4 ± 1 [54] Mass spectrometry
1211 [2] 28.9 ± 2 [14] Compilation
1210 ± 2 [26] 30.96 ± 1 [45] Compilation
1221 [42] 31.0 ± 2 [8] Tin-solution calorimetry
1211 [41] 31.0 ± 2 [55] EMF measurements
29.2 [41] Optimization
29.2 [2] Optimization
28.3 ± 1 [8] Mass spectrometry
InSb 800 ± 1 This work
(recommended)
15.4 ± 0.3 This work
(recommended)
Correlation
800 ± 1 [17] 15.4 ± 0.3 This work EMF measurements +
optimization
800 ± 2 [2] 15.31 ± 0.3 [8] Tin-solution calorimetry
798 ± 2 [8] 15.35 ± 1 [8] EMF measurements
798 ± 2 [14] 15.48 [44] Optimization
798 ± 2 [21] 15.48 [45] Optimization
15.25 ± 1 [8] Compilation
15.27 ± 0.5 [14] Compilation
15.0 [21] Optimization
16.2 [2] Optimization
InBi 383 ± 1 This work
(recommended)
0.7 ± 0.2 This work
(recommended)
Correlation
383 ± 1 [17] 0.71 ± 0.1 [56] Direct synthesis calori-
metry
1180
INORGANIC MATERIALS Vol. 42 No. 11 2006
VASIL’EV, GACHON
data are unreliable, because such systems are difficult
to study.
The melting points of the Group IIIA nitrides scatter
widely. These compounds begin to decompose, loosing
nitrogen, well below their melting points, and the liqui-
dus curve in their T–x phase diagrams deviates from the
maximum melting point toward the nonvolatile compo-
nent (Fig. 1).
To maintain equilibrium in the system, the melting
points of the nitrides should be determined at high
nitrogen pressures, 6 to 10 GPa. The equilibrium melt-
ing point of AlN has not yet been determined. It seems
likely that it considerably exceeds the calculated value,
3500 K, reported by Van Vechten [15]. Note that, at such
pressures and room temperature, nitrogen is in a solid
state. In particular, the transition of nitrogen from a crys-
talline to fluid state occurs at 308 K and 2.8 GPa [57].
The T
m
(AlN) = 4800 ± 100 K found with the use of
correlation equations and the enthalpy of formation of
aluminum nitride,
∆
f
H
0
(298 K) = 14.78 – 0.03627T,r = 0.9994,(1)
(2)
(r is the correlation coefficient), logically completes the
temperature dependence of ∆
f
H
0
(298 K) both for the
entire III–V series and for the aluminum pnictides. The
equilibrium melting point of AlN must correspond to an
equilibrium nitrogen pressure in the range 6–10 GPa.
(In Table 1, the enthalpies of formation and melting
points set in bold are believed to be the most reliable
according to the correlative determination method.)
The enthalpies of formation of the III–V compounds
can be related to Table 2 their melting points by a linear
expression [Eq. (1)] (Fig. 2). The polynomial equa-
tion (2) gives a better fit to the low-temperature data.
Table 2 lists the enthalpies of formation calculated
by both equations. The deviations of the calculated
enthalpies of formation from the values recommended
∆
f
H
0
298 K( ) 12.94 0.03431T–=
– 3.816 10
7–
T
2
×,r 0.9990=
500
0.20
0.4
0.6
0.8
1.0
1000
1500
2000
2500
GaN + L
1 MPa
2700 K
L + GaN
L
0.1 MPa
100 MPa
10 MPa
1000 MPa
5000 MPa
302.9
T, K
Ga x
N
N
p
N
2
≈ 9300 MPa
Fig. 1. Calculated phase diagram of the Ga–N system [31].
Table 2. Recommended and calculated [Eqs. (1) and (2)] enthalpies of formation of III–V compounds
Compound T
m
, K
–∆
f
H
0
(298 K), kJ/g-at
recommended (1) (2)
BN 3800 ± 50 126.0 ± 3 123.0 123.0
AlN 4800 ± 100 159.0 ± 2 159.3 160.5
AlP 2790 ± 20 86.0 ± 2 86.4 85.8
AlAs 2058 ± 10 58.5 ± 1 59.9 59.3
AlSb 1330 ± 2 32.9 ± 2 33.5 33.4
GaN 2570 ± 50 78.5 ± 2 78.4 77.8
GaP 1790 ± 10 50.0 ± 2 50.1 49.7
GaAs 1511 ± 2 39.5 ± 1 40.0 39.8
GaSb 981 ± 2 21.0 ± 1 20.8 21.1
InN 2050 ± 100 56.0 ± 3 59.6 59.0
InP 1344 ± 5 35.0 ± 2 34.0 33.9
InAs 1215 ± 2 29.0 ± 0.5 29.3 29.3
InSb 800 ± 1 15.4 ± 0.3 (14.2) 14.8
InBi 383 ± 1 0.7 ± 0.2 (–0.9) 0.26
INORGANIC MATERIALS Vol. 42 No. 11 2006
THERMODYNAMIC PROPERTIES OF III–V COMPOUNDS
1181
here are within the estimated uncertainties in the
enthalpies and melting points of the III–V compounds.
Similarly, using the data in Table 3, the correlation
between the Gibbs energies of formation of the III–V
compounds and their melting points can be represented
by the equation
∆
f
G
0
(298 K) = 13.06 – 0.03299T,r = 0.998.(3)
For the III–V compounds, one can use yet another
correlation, analogous to that found earlier for III–VI
compounds. Vasil’ev et al. [60] considered the relation-
ship between the reduced enthalpy ∆
f
H
0
(298 K)/T
m
and
the sum of bond distances in the crystal lattices of the
constituent components of III–VI compounds.
Instead of the sum of bond distances in the constitu-
ent components, one can use the sum of their atomic
numbers. The atomic number of an element carries
information not only about the number of electrons in
its atoms; in addition, it can be regarded, in some sense,
as their size.
The relation between the reduced enthalpy of for-
mation of the III–V compounds and the sum of the
atomic numbers, ΣA
i
, can be represented by the linear
equation
(4)
(see Fig. 3). In deriving Eq. (4), the data for InBi were
left out of consideration. One possible reason for the
deviation from linearity in the case of this phase is that
the coordination number in its structure is 8/8, whereas
in the other III–V compounds the coordination number
is 4/4.
∆
f
H
0
298 K( ) –36.06 0.1635ΣA
i
+( )T
m
,=
r 0.97=
–20
200
–25
–30
–35
40
60
80
100
InSb
GaSb
GaAs
GaP
GaN
AlP
BN
AlN
InAs
InP
InN
ΣA
i
∆
f
H
0
(298 K)/T
m
, kJ/(K g-at)
AlSb
AlAs
–15
Fig. 3. Correlation between the reduced enthalpy of forma-
tion, ∆
f
H
0
(298 K)/T
m
, and the sum of the atomic numbers,
ΣA
i
, of the constituent elements of the III–V compounds.
–40
10000
–80
–120
–160
2000
3000
4000
5000
InBi
InSb
GaSb
AsSb
GaAs
GaP
AlAs
GaN
AlP
BN
AlN
InAs
InP
InN
T
m
, K
∆
f
H
0
(298 K), kJ/g-at
Fig. 2. Correlation between experimentally determined
enthalpies of formation of III–V compounds and their melt-
ing points (see Table 2).
20
20000
40
60
4000
6000
T
m
, K
1
2
3
S
0
(298 K), J/(K g-at)
Fig. 4. Correlation between the standard entropy S
0
(298 K)
of III–V compounds and their melting points (see Table 4):
(1) InB
V
; (2) GaB
V
, (3) AlB
V
.
1182
INORGANIC MATERIALS Vol. 42 No. 11 2006
VASIL’EV, GACHON
The correlation between the standard entropies
of III–V compounds and their melting points is illus-
trated in Fig. 4:
(5)
The unknown entropy S
0
(298 K) of indium bismuth-
ide was evaluated by the additivity rule, by analogy
S
0
298 K( ) J/(K
g-at)
( )
= 167.36 18.65
T
m
,
r
ln 0.94.=–
with the intermetallic phase AuSn, for which the
reported S
0
(298 K)
= 48.95 ±
1 J/(K g-at) [23] is very
close to the additivity rule value: 49.40 J/(K g-at).
Consider yet another correlation, between the
entropy of formation and the III–V bond distance in the
unit cell of III–V compounds (Fig. 5):
(6)
∆S
0
298 K( ) J/(K
g-at)
( )
= 84.66– 271.5
d
,
r
0.99=+
Table 3. Gibbs energies of formation ∆
f
G
0
(298 K) of III–V compounds
Compound
T
, K –
∆
G
0
(298 K), kJ/g-at Source
–
∆
G
0
(298 K),
kJ/g-at (calculation)
BN 3800 113.4 [58] 112.3
AlN 4800 143.5 [14] 145.3
AlP 2790 79.96 [14] 79.0
(90.1) [2] AlAs 2058 57.41 [2] 54.9
AlSb 1330 31.36 [27] 30.8
28.3 [8]
(34.53) [29]
(23.41) [2]
GaN 2570 73.9 [31] 71.8
(61.1) [37]
GaP 1790 46.68 [14] 46.0
(65.0) [2]
GaAs 1511 35.16 [14] 36.8
(42.4) [2]
GaSb 981 19.27 [28] 19.3
20.47 [14]
20.43 [2]
InN 2050 53.0 [47] 54.6
InP 1344 30.7 ±
2 This work 31.3
31.2 ±
2 [46]
(36.87) [14]
32.0 [2]
InAs 1215 26.23 [14] 27.0
26.80 [2]
InSb 800 13.10 ±
0.3 This work 13.4
12.83 [14]
InBi 383 13.56 [2]
0.7 Estimate (–0.4)
Note:The values given in parentheses were not included in calculations.
INORGANIC MATERIALS
Vol. 42
No. 11
2006
THERMODYNAMIC PROPERTIES OF III–V COMPOUNDS
1183
Table 4. Standard entropies S
0
(298 K) of III–V compounds
Compound
T
, K
S
0
(298 K), J/(K g-at) Method Source
S
0
(298 K),
J/(K g-at) (calculation)
BN 3800
(7.7 ±
1)
Compilation
[23]
13.6
AlN 4800 10.1 ±
0.5 Calorimetry [62] 9.3
AlP 2793 23.65 ±
2 Compilation [14] 19.4
AlAs 2058 28.11 Optimization [2] 25.1
30.12 ±
0.5 Compilation [14]
AlSb 1330 33.33 Optimization [2] 33.2
32.13 ±
0.5 Compilation [14]
31.69 Optimization [29]
32.13 ± 0.5 Calorimetry [61]
GaN 2570 18.45 ± 0.2 Calorimetry [62] 20.9
18.25 ± 0.2 Calorimetry [63]
18.25 Optimization [32]
GaP 1790 25.73 ± 0.5 Compilation [14] 27.7
29.87 ± 0.5 Calorimetry [61]
25.31 Optimization [39]
25.73 Optimization [2]
(23.0) Optimization [38]
GaAs 1511 32.09 ± 0.5 Calorimetry [61] 30.8
32.09 ± 0.5 Compilation [14]
31.44 Optimization [41]
GaSb 981 38.03 ± 0.5 Calorimetry [61] 38.9
38.03 ± 0.5 Compilation [14]
36.45 Optimization [2]
InN 2050 25.0 Compilation [51] 25.2
InP 1344 31.4 ± 0.8 Optimization [14] 33.0
29.87 ± 0.5 Calorimetry [61]
29.74 Optimization [39]
31.96 Optimization [2]
(35.6) EMF measurements This work
InAs 1215 37.86 ± 0.5 Calorimetry [61] 34.9
38.53 Optimization [2]
37.87 ± 0.5 Compilation [14]
InSb 800 43.09 ± 0.5 Calorimetry [61] 42.7
43.55 ± 0.5 Compilation [14]
42.63 Optimization [2]
43.62 EMF measurements This work
InBi 383 57.19 ± 1 Estimate This work 56.4
Note:The values given in parentheses were not included in calculations.
1184
INORGANIC MATERIALS Vol. 42 No. 11 2006
VASIL’EV, GACHON
–10
0.200.16
–30
0.24
0.28
0.32
d, nm
∆S
0
(298 K), J/(K g-at)
0
–20
1
2
3
Fig. 5. Correlation between the calculated entropy of for-
mation ∆
f
S
0
(298 K) (Table 4) from solid components and
the III–V bond distance in the unit cell of III–V compounds
(data from Tables 4 and 5): (1) InB
V
; (2) GaB
V
, (3) AlB
V
.
2
–400
4
6
∆
f
H
0
(298 K), kJ/g-at
1
2
3
E
g
, eV
–80
–120
–160
Fig. 6. Correlation between the experimentally determined
enthalpy of formation ∆
f
H
0
(298 K) (Table 2) and the band
gap E
g
[67] of III–V compounds: (1) InB
V
; (2) GaB
V
,
(3) AlB
V
.
for InB
V
and
(7)
for AlB
V
and GaB
V
.
In calculating ∆
f
S
0
(298 K), we used the entropy of
solid nitrogen reported by Sychev et al. [65] and the
entropies of the other elements from Dinsdale [66]. The
entropy of solid nitrogen S
0
(298 K) as a function of
pressure was found by extrapolating the reference data
from [65] using the equation
S
0
(298 K) (J/(K g-at)) = 87.92 – 5.0896lnp. (8)
Therefore, S
0
(N
2
, solid, 298 K) = 47.07 ± 1 J/(K g-at)
∆S
0
298 K( ) J/(K
g-at)
( )
= 84.54– 306.3
d
,
r
0.94=+
at
p
= 2.80 ±
0.01 GPa. ∆
f
S
0
(III–V, 298 K) was found
from the relation
(9)
The ∆
f
S
0
(III–V, 298 K) calculation results are presented
in Table 4.
Figure 6 illustrates the correlation between the
enthalpy of formation and band gap [67] of III–V com-
pounds. This correlation was used to refine the experi-
mentally determined values of E
g
for a number of III–V
compounds saturated with the Group V element:
E
g
(eV) = –0.11 – 0.03774
∆
f
H
0
(298 K),
r
= 0.94.(10)
CONCLUSIONS
The available thermodynamic data for III–V com-
pounds have been systematized and critically evalu-
ated. Our results are the first to demonstrate that the
enthalpies of formation ∆
f
H
0
(298 K), Gibbs energies
∆
f
G
0
(298 K), and standard entropies S
0
(298 K) of some
of these compounds correlate with their melting points.
In addition, their reduced enthalpies ∆
f
H
0
(298 K)/
T
m
correlate with the sum of the atomic radii of their com-
ponents, and the entropies of formation ∆
f
S
0
(298 K) of
these compounds correlate with the III–V bond dis-
tances in their unit cells.
∆
f
S
0
AB, 298 K
( )
= S
0
AB, 298 K
( )
–
S
0
A, 298
K
( )
S
0
B 298 K
,( )
.–
Table 5. Bond distances d
III–V
in III–V compounds [64]
Compound
d
III–V
, nm Compound
d
III–V
, nm
AlN 0.1900 GaSb 0.2641 AlP 0.2366 InN 0.2135 AlAs 0.2451 InP 0.2533 AlSb 0.2657 InAs 0.2624 GaN 0.1929 InSb 0.2802 GaP 0.2360 InBi 0.3106 GaAs 0.2447 INORGANIC MATERIALS
Vol. 42
No. 11
2006
THERMODYNAMIC PROPERTIES OF III–V COMPOUNDS
1185
The proposed relations can be used to evaluate and
select the most reliable values among the large body of
experimental data and calculation results. The calcu-
lated ∆
f
H
0
(298 K) and ∆
f
G
0
(298 K) values agree with
recommended ones to within experimental uncertain-
ties.
The melting point of AlN found from Eq. (1),
T
m
(AlN) = 4800 ±
100 K, logically completes the cor-
relation both for the entire III–V series and for the alu-
minum pnictides. According to the congruent melting
condition, the melting point of AlN must correspond to
an equilibrium nitrogen pressure in the range 6–
10 GPa.
The relations considered in this work illustrate well
that the chemical bonding in the III–V compounds
ranges from metallic (InBi) to ionic–covalent (BN) and
that the enthalpy of formation and melting point of
these compounds increase with increasing bond cova-
lence, while their standard entropy decreases, which
corresponds to stronger chemical bonding.
The proposed relations can be used to assess
unknown thermodynamic and some physical properties
and critically evaluate the existing experimental and
optimized data for other groups of compounds, e.g., II–
VI and III–VI.
All of these relations stem from the Periodic Law.
ACKNOWLEDGMENTS
We are grateful to L.A. Aslanov (Moscow State Uni-
versity) for providing us the opportunity of using the
Pauling File 2002 Database.
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