ISSN 0020-1685, Inorganic Materials, 2006, Vol. 42, No. 11, pp. 1171–1175. © 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. 1287–1292.
Thermodynamic Properties of InP V. P. Vasil’eva and J.-C. Gachonb a
Moscow State University, Vorob’evy gory 1, Moscow, 119899 Russia b Université Henri Poincaré, UMR 7555, Nancy, France e-mail:
[email protected] Received February 14, 2006
Abstract—The emf of an electrochemical cell of the type (–) W, In(l) | ZnCl2 + KCl + NaCl + InCl | (InP(s) + P(black)), W(+) has been measured in the temperature range 500–600 K. The change in the chemical potential of this cell (∆µIn = –52.50 + 19.01 × 10–3T kJ/mol) corresponds to the reaction In(l) + P(black) InP(s). The standard enthalpy of formation of InP from solid indium and white phosphorus is determined to be ∆f H0(298 K) = −69.3 ± 3 kJ/mol. We have performed thermodynamic analysis of the literature data for the In–P system, with consideration for different phosphorus allotropes. DOI: 10.1134/S002016850611001X
INTRODUCTION Indium phosphide is a III–V compound semiconductor widely used in optoelectronics. Experimental data for group IIIA phosphides are difficult to interpret because of the phosphorus polymorphism [1–6] (Table 1). Nine phosphorus allotropes have been identified to date: two white (α, stable from 0 to 195.4 K, and β, stable from 195.4 to 317.3 K), five red (P(I) to P(V); P(II) and P(III) have not yet been identified with certainty), and two black (orthorhombic and amorphous) allotropes [7]. Recently, Ruck et al. [8] have described the structure of P(IV) red phosphorus (Hittorf’s phosphorus). According to their results, it has a triclinic unit cell, in contrast to the monoclinic cell reported by Thurn and Krebs [9]. The lack of reliable data for different forms of phosphorus leads to misinterpretation of the enthalpy of formation of phosphides in studies where different allotropes of phosphorus are examined (in experiment or calculation). For example, Sharifov and Gadzhiev [10] showed by decomposing indium phosphide in a calorimetric bomb that the final products of that process were indium and two forms of phosphorus: white and red. The white phosphorus (33–45%) was separated from the red form by dissolving it in carbon disulfide, CS2 . The heat of transformation of red to white phosphorus was not indicated in their report. A number of publications before 1988, including the handbook by Glushko [4] (Table 1), give inaccurate enthalpies of the transformation α-P ( white ) P ( black ), ∆ tr H = – 38.9 ± 4 kJ/mol.
(1)
A more reasonable value for this transformation is ∆trH = –21.2 ± 2 kJ/mol [6]. Indeed, using the heats of transformation indicated in Table 1 (lines 1 and 3), we obtain for reaction (1) ∆trH kJ/mol, which coincides with the value reported by O’Hare and Levis [6] to within experimental uncertainties. Table 1. Enthalpies of transformation of phosphorus allotropes Transformation P(I)(red) P(black, orthorhombic) P(I)(red)
P(V)(red)
–∆trH0(298 K), kJ/mol
Ref.
16.4
[1]
1.1
[1]
7.32 ± 1.2
[2]
α-P(white)
P(I)(red)
α-P(white)
P(IV)(red)
13.07 ± 1.2
[2]
α-P(white)
P(I)(red)
16.32 ± 1.7
[3]
P(IV)(red)
P(V)(red)
5.0 ± 4
[3]
α-P(white)
P(V)(red)
17.4 ± 0.1
[4]
α-P(white)
P(V)(red)
16.3 ± 6
[3]
α-P(white)
P(V)(red)
17.5 ± 0.1
[5]
α-P(white) P(black, orthorhombic)
38.9 ± 4
[4]
α-P(white) P(black, orthorhombic)
21.2 ± 2
[6]
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VASIL’EV, GACHON
Table 2. Enthalpy of formation of indium phosphide according to different reports –∆fH0(298 K), kJ/mol
Method
Ref.
–∆fH0(298 K), kJ/mol
56.4 ± 2
Precipitation calorimetry
[11]
85.8 ± 5
Compilation
[17]
60.6 ± 2
Tin-solution calorimetry
[12]
87.6 ± 5
Tin-solution calorimetry
[20]
61.8 ± 2
Optimization
[13]
87.8 ± 5
Bomb calorimetry
[10]
74.48
Optimization
[15]
90.0 ± 6
Bomb calorimetry
[18]
76.8
Optimization
[16]
92.5
Mass spectrometry
[23]
77.6 ± 2
Mass spectrometry
[14]
93.7 ± 4
EMF measurements
[19]
78.2 ± 3
Vapor pressure
[22]
97.8
Optimization
[21]
As a result of such discrepancies, the heat of formation of indium phosphide from solid indium and white phosphorus was variously reported to be 56.4 to 97.8 kJ/mol (Table 2). The purpose of this work was to reinvestigate the thermodynamic properties of phases in the In–P system using liquid-electrolyte emf measurements. EXPERIMENTAL We measured the emf of an electrochemical cell of the type ( – )W, In ( l )
ZnCl 2 + KCl + NaCl
+ InCl (InP ( s ) + P ( black ) ) , W(+),
(I)
in the temperature range 500–600 K.1 The lattice parameter of InP was determined to be a = 0.5870 ± 0.0001 nm, which agrees within experimental uncertainties with that reported by Antyukhov [24]: a = 0.58688 ± 0.00001 nm. In our experiments, we used a low-melting-point (479 K) eutectic based on zinc chloride. A mixture of dry KCl, NaCl, and ZnCl2 in the weight ratio 18 : 12 : 70 was dehydrated before melting as described previously [25]. The isothermal vacuum cell made from high-temperature glass was also described in [25]. Indium chloride was formed in situ in the cell. Black phosphorus is best suited for the preparation of a heterogeneous mixture of InP and P for emf measurements. This form of phosphorus is thermodynamically stable up to 823 K [16] and has the lowest vapor pressure among all of the phosphorus allotropes at elevated temperatures (Table 3). The temperature range 1 Indium
phosphide was synthesized at the State Research Institute for the Rare-Metals Industry. Black phosphorus was prepared at the Shubnikov Institute of Crystallography, Russian Academy of Sciences (Moscow).
Method
Ref.
we selected, 480–600 K, is appropriate for studying the system in question. We performed two experiments with heterogeneous mixtures of InP and P(black) at overall phosphorus contents of 55.0 and 61.0 at %. The emf of the cells and temperature of a calibrated thermocouple were measured every hour. The cell was held at constant temperature until the results of the last three or four emf measurements coincided to within 0.3 mV. Each experiment took two weeks. Reproducible results were obtained more than four days after the beginning of the experiment. The slow equilibration rate is associated with the high melting point of InP (1344 K) and the use of unannealed InP + P heterogeneous mixtures. No indication of phosphorus sublimation was detected after the measurements. RESULTS AND DISCUSSION The experimental E(T) data for cell (I) are presented in Table 4. Using linear least squares fitting, we obtained E (V) = 0.5441 – 0.197 × 10–3T, 2S0 = ±5.0 × 10–3 V. (2) The present results can be compared to the experimental data reported by Abbasov et al. [19], who also Table 3. Vapor pressure over different allotropes of phosphorus in the temperature range 500–650 K [26] p, GPa Allotrope 500 K α-P(white)
510
550 K 961
600 K
650 K
*
P(V)(red)
0.84
8.77
61.86
323.31
P(black)
0.031
0.648
8.13
68.66
* Tm = 553 K. INORGANIC MATERIALS
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THERMODYNAMIC PROPERTIES OF InP
performed emf measurements, but at higher temperatures, 640–740 K. They used an electrochemical cell of the type ( – )W, In ( l ) KCl + LiCl + InCl (InP ( s ) + P ( black ) ) , W(+).
1173
ëp, J/(K mol) 25
(II)
20
E (V) = 0.560 – 0.201 × 10–3T, 2S0 = ±5.0 × 10–3 V.(3)
15
The best fit to their results is provided by Temperature-dependent emf data can be used to determine thermodynamic quantities using the relations ∆µIn = –zFE = RT ln aIn ,
(4)
∆µ In = ∆H ( In ) – T ∆S ( In ),
(5)
∆H ( In ) = ∆µ In – T ( ∂∆µ In /∂T ) p .
5
(6)
Here z = 1, F = 96485.34 C/mol, R = 8.31447 J/(K mol), ∆µIn is the change in the chemical potential of indium, ∆H (In) is the partial enthalpy of indium, and ∆S (In) is the partial entropy of indium. Using Eqs. (2)–(6), one can find the change in the chemical potential of cell (I), ∆µ In = – 52.50 + 19.01 × 10 T , –3
2S 0 = ± 0.5 kJ/mol,
(7)
and cell (II) [19], ∆µ In = 54.03 + 19.39 × 10 T ,
0
100
200
300 T, K
Fig. 1. Heat capacity as a function of temperature for different allotropes of phosphorus: (1) P(IV), (2) P(V), (3) P(white), (4) P(black) [7], (5) P(black) [27].
As seen in Fig. 1 and Table 5, the heat capacities of black and red phosphorus differ very little at low temperatures. It is reasonable to expect that, at temperaTable 5. Entropy and heat capacity of indium, phosphorus, and indium phosphide at 298 K according to different reports
–3
2S 0 = ± 0.5 kJ/mol.
1 2 3 4 5
10
(8)
Abbasov et al. [19] performed emf measurements at temperatures of up to 740 K, where the vapor pressure over black phosphorus approaches atmospheric pressure. They, however, left this important point out of consideration. Table 4. Experimental E(T) data for cell (I)
Allotrope
S0(298 K), J/(K mol)
Cp(298 K), J/(K mol)
Ref.
α-P(white)
40.42 ± 0.2
23.48 ± 0.04
[7]
α-P(white)
41.09 ± 0.5
23.85 ± 0.04
[4]
α-P(white)
41.09 ± 0.1
23.82 ± 0.01
[29]
P(IV)(red)
22.85 ± 0.1
20.96 ± 0.05
[7]
P(V)(red)
22.52 ± 0.1
20.88 ± 0.05
[7]
P(red)
22.57 ± 0.05
23.05 ± 0.05
[29]
T, K
at % P
E, V
T, K
at % P
E, V
P(black)
22.27 ± 0.05
21.24 ± 0.05
[7]
498
55
0.447
533
55
0.442
P(black)
22.50 ± 0.05
21.27 ± 0.05
[27]
503
55
0.446
544
61
0.435
P(black)
22.68 ± 0.1
21.59 ± 0.05
[4]
508
55
0.444
549
55
0.436
P(red)
22.86 ± 0.2
21.20 ± 0.2
[29]
In(s)
55
0.444
561
61
0.439
57.82 ± 2
26.74 ± 0.5
[17]
515
In(s)
57.65 ± 0.1
26.90 ± 0.01
[29]
517
55
0.44
585
61
0.428
InP(s)
63.92
46.185
[15]
517
61
0.439
600
61
0.429
InP(s)
62.76 ± 1
45.52 ± 1
[17]
525
55
0.443
InP(s)
59.75 ± 0.5
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45.5 ± 1.5
[31]
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VASIL’EV, GACHON
et al. [15] fit better with available experimental data [31, 32] (Fig. 2). The error in ∆Cp(InP) calculations from the data presented in [15, 28] is insignificant.
ëp, J/(K mol) 56
The thermodynamic functions of formation of indium phosphide from black or white phosphorus and solid indium were calculated by Eqs. (2) and (3) using data from [6, 7, 15, 29, 31]. Our results agree well with the data reported by Abbasov et al. [19] (Table 6).
52
48 1 2 3 4 5
44
40 200
400
600
800
1000 T, K
Fig. 2. Heat capacity as a function of temperature for indium phosphide according to different reports: experimental data from [30] (1), [31] (2), and [32] (3); calculations from [15] (4); and estimates from [28] (5).
tures from 298 to 800 K, the heat capacity of black phosphorus (not studied here) is identical to that of red phosphorus (P(IV) and P(V)), like at low temperatures. The heat capacity of indium phosphide has not been measured just above 300 K. Itagaki and Yamaguchi [30] measured the heat capacity of InP from 800 to 1340 K. They obtained (J/(K mol)) C p = 50.2 + 5.08 × 10 T – 5.02 × 10 T , –3
5
2
800–900 K; C p = 53.0 + 1.82 × 10 T – 6.76 × 10 T , –3
5
2
910–1340 K. The calculated heat capacity of indium phosphide for temperatures above 298 K was reported in [15, 28]. Near room temperature, the data obtained by Ansara
The standard entropy ∆S0(298 K) of InP was evaluated from the experimentally determined entropy of formation of InP by the reaction In(l) + P(black) = InP(s) and the entropy of solid indium, white phosphorus, and black phosphorus [7, 29] (Table 5). The entropy of indium phosphide calculated from our data, ∆S0(298 K) = 71.3 ± 3 J/(K mol), differs from the values reported in [15, 17, 31] (Table 5), probably because our emf data, obtained with cell (I), may be slightly distorted by the exchange reaction between zinc chloride, used as the electrolyte, and liquid indium, serving as the reference electrode. This effect may be particularly pronounced in determining the slope (∂∆µΙn/∂T)p [Eq. (6)]. One approach to this problem is to use an InSb + Sb heterogeneous mixture, instead of pure indium, as the reference electrode [25]. According to the present results, the enthalpy of formation of indium phosphide from solid indium and white phosphorus is ∆f H0(298 K) = –69.3 ± 3 kJ/mol (Table 6). This value strongly depends on the choice of the enthalpy of the transformation P(white) P(black) and the uncertainty in it. In evaluating the enthalpy of formation of indium phosphide from solid indium and white phosphorus, we took the enthalpy of this transformation to be –21.2 ± 2 kJ/mol [6]. Using the reference value for this transformation, –38.9 ± 4 kJ/mol [17], and the present data for the reaction In(s) + P(white) InP(s), we obtain for the enthalpy of formation of indium phosphide ∆f H0(298 K) = −87.0 ± 4 kJ/mol, which is very close to the ∆f H0(298 K) = –85.8 ± 4 kJ/mol given in [17]. We, however, prefer the value reported by O’Hare and Levis [6]. This choice will be substantiated in a subsequent communication, dealing with the thermodynamic properties of III–V compounds.
Table 6. Thermodynamic functions of formation of indium phosphide from solid indium and phosphorus at 298 K –∆fG0(298 K) –∆fH0(298 K)
Reaction
kJ/mol In(s) + P(black) In(s) + P(white)
InP(s) InP(s)
–∆fS0(298 K)
S0(298 K) Source
J/(K mol)
45.54 ± 1
48.1 ± 2
8.6 ± 3
71.3 ± 3
This work
46.5 ± 1
48.8 ± 2
7.7 ± 3
72.2 ± 3
[19]
61.3 ± 2
69.3 ± 3
26.8 ± 3
71.3 ± 3
This work
62.3 ± 2
70.0 ± 3
25.8 ± 3
72.2 ± 3
[19]
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CONCLUSIONS We redetermined the standard thermodynamic functions of formation of indium phosphide and performed thermodynamic analysis of the literature data for the In–P system, with consideration for different phosphorus allotropes.
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