# Thermodynamic propweties of AIIIBV compounds

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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. 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