Thermodynamic Properties of Solid Binary Antimonides - American

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Thermodynamic Properties of Solid Binary Antimonides Mark E. Schlesinger* Department of Materials Science and Engineering, Missouri University of Science and Technology, 1400 North Bishop Avenue, Rolla, Missouri 65409-0340, United States widely disseminated. Recommended thermodynamic properties for compounds will be generated where quality data are available, along with recommendations for further study. A brief review of the thermodynamic properties of elemental antimony is also included.

2. EXPERIMENTAL TECHNIQUES AND MODELING Thermodynamic measurements of antimony and its compounds can be divided into three classifications: measurement of heat capacity or enthalpy relative to a reference state, measurement of enthalpies of formation of antimonide compounds, and measurements leading to calculation of Gibbs energies of formation of these compounds. These three classifications will be discussed, focusing on experimental methods and models that have been used to estimate related thermodynamic properties.

CONTENTS 1. Introduction 2. Experimental Techniques and Modeling 2.1. Heat Capacity 2.2. Enthalpy of Formation 2.3. Gibbs Energy of Formation 3. Thermodynamic Properties of Elemental Antimony 4. Alkali Metals 5. Alkaline-Earth Metals 6. Group 3: Rare-Earth Elements and Actinides 7. Group 4 8. Group 5 9. Groups 6 and 7 10. Groups 8−10 11. Group 11 12. Group 12 13. Group 13 14. Group 14 15. Groups 15 and 16 16. Conclusions and Recommendation Author Information Corresponding Author Notes Biography References

A A A B B B D E H I I K L P Q R U U V V V V W W

2.1. Heat Capacity

The measurement of heat capacities can be classified into two types: low-temperature (below-ambient) and high-temperature. Low-temperature measurements which lead to the calculation of compound entropies at ambient temperature (S°298) will be considered here. These have been almost entirely conducted by adiabatic calorimetry.1−11 The most common experimental method for high-temperature heat-capacity measurements has been drop calorimetry.6,12−23 Copper-block calorimeters have been the most popular, but diphenyl ether has also been used, as has water on at least one occasion. More recent investigations have relied on continuous methods, including ac calorimetry,7,298 hightemperature adiabatic calorimetry,1,2,4,24−26 and differential scanning calorimetry.27,28 The most common modeling approach for estimating compound activities is the Neumann−Kopp law, which proposes that the heat capacity of an alloy (or intermetallic compound) is the sum of the heat capacities of its constituent elements, in the same physical state, e.g.

1. INTRODUCTION For many years, interest in the intermetallic compounds formed with antimony resulted primarily from the presence of the element as an impurity in the ores of other metals, especially copper and silver. This changed when the semiconductivity of III−V antimonide compounds was discovered, leading to several electronic applications. Since then, the electronic and optical properties of other antimonides have resulted in a variety of potential applications for this class of compounds. Over the years, a substantial body of research has appeared on the thermodynamic properties of binary antimonides, but the lack of significance of these compounds has limited interest in compiling and evaluating these results. In this review I will assess the available data, including results that have not been © XXXX American Chemical Society

Cp(FeSb2 , c) = Cp(Fe, c) + 2Cp(Sb, c)

(1)

The Neumann−Kopp law presumes that the entropy of formation of the compound is small, which is less likely to be accurate in nonintermetallic phases. Figure 1 tests the accuracy of the Neumann−Kopp law using published heat capacities of three compounds: AlSb, CrSb2, and Mn2Sb. The x-axis plots heat capacities (J/(mol K)) calculated for these three compounds using the Neumann−Kopp law and the y-axis experimentally obtained values at the same temperature as the calculated value. The difference between the two is substantial Received: January 29, 2013

A

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atures and stability of many antimonides make possible the use of several crucible materials, including metals, graphite, and glass. Nonequilibrium effusion techniques have also been tried on occasion.86−88 Alkali-metal antimonides decompose at lower temperatures than other compounds in this class and generate metal vapor as well as antimony; as a result, Langmuir and dewpoint methods have been used for these compounds.69,87,89−91 The accuracy of this technique depends on the accuracy of the measured Gibbs energies of formation of the vapor species Sb, Sb2, and Sb4. For Sb4, this is not a concern, as Hultgren et al., have pointed out;92 for the other two species, the degree of uncertainty is greater. EMF measurements are the most common method employed to find Gibbs energies of formation of solid antimonides. Both solid and molten-salt electrolytes have been used, depending on the melting point of the particular antimonide and of the constituent elements. The reacting element is the usual choice of electrode, although elemental Sb is used on occasion.93−95 The challenges of using EMF techniques include ensuring that intermediate compounds are not part of the electrode reaction, making sure that equilibrium EMFs are measured and that the compound being studied does not react with the electrolyte.96 Polarographic methods are sometimes used.97−101 ΔG° for antimonide compounds can also be calculated by modeling based on the phase diagram and measured (or predicted) activities in the liquid phase.102−107 This concept has been enlarged into numerous CALPHAD-type (CALPHAD = calculation of phase diagrams) optimizations for Sb-containing binary and ternary systems, generally using the Redlich−Kister polynomial expansion to model liquid and solid solutions.

Figure 1. Accuracy of the Neumann−Kopp law in predicting heat capacities of AlSb, CrSb2, and Mn2Sb. Data derived from refs 3, 19, and 255.

in some cases. As a result, the Neumann−Kopp law is not a suitable substitute for experimentally obtained values of antimonide heat capacities. 2.2. Enthalpy of Formation

Early efforts to measure ΔH° for antimonide compounds included the use of acid-solution calorimetry and combustion calorimetry.29−38 Acid-solution calorimetry is impacted by the reaction of antimony with aqueous solutions to generate stibine (SbH3) gas; the accuracy of combustion calorimetry is limited by the accuracy to which the enthalpies of formation of the resulting oxides are known, as well as uncertainty over just what the combustion product is. As a result, neither of these approaches has been used for over 40 years. A more common approach to measurement of ΔH° of antimonides is metal-solution calorimetry. Tin is usually the solvent,39−51 but bismuth and iron−sulfur melts have also been used.52−54 Comparing the enthalpy of solution of the compound with that of the elements added separately determines the enthalpy of formation of the compound. This need for accurate and reproducible measurements of both enthalpies of solution increases the uncertainty of results obtained using this approach. Direct-reaction calorimetry is also a popular method of measuring ΔH° for antimonides. The formation of some antimonides is sufficiently exothermic that these experiments can be conducted by heating a mixture of the elemental powders in a sealed calorimeter and measuring the enthalpy generated by the reaction.55−62 In a few cases, the calorimetric effect of adding antimony or the second element to an antimonide melt has been used to calculate enthalpies of formation.63−65 This may be useful in studying less exothermic antimonide compounds. Miedema and co-workers developed a semiempirical cellular model for calculating the enthalpy of formation of binary metallic alloys in both the solid and liquid states. The model is based on the Wigner−Seitz concept of atomic cells and has been used to predict ΔH° for intermetallic phases as well as solid solutions. Predictions have been made for several antimonide compounds using this approach.66,67,201

3. THERMODYNAMIC PROPERTIES OF ELEMENTAL ANTIMONY The thermodynamic properties of elemental antimony tabulated in most compilations can be traced to the critical assessment of existing data produced by Hultgren et al. in 1973.92 Although the experimental work on the element since that time is limited, new results have appeared which recommend a revision of this assessment. The newer data include two studies of the heat capacity of solid antimony: the low-temperature investigation (46−352 K) by Vecher et al.108 and the high-temperature (486−858 K) drop-calorimetry study of Konings and van der Laan.18 The new high-temperature results are more accurate than older data109 and provide a better fit with the low-temperature results. On the basis of these results, Konings and van der Laan recommended a slightly lower value of S°298.15 for elemental antimony (45.42 J/(mol K)) than that recommended by Hultgren et al. (45.52 J/(mol K)).92 The recommended heat capacity of solid antimony above ambient is represented by Cp (J/(mol K)) = 19.5569 + (12.28274 × 10−3)T + (1.83207 × 105)T −2

(2)

The heat capacity of liquid antimony recommended by Hultgren et al., 31.378 J/(mol K), is based on studies conducted in 1918 and 1926 and presumes that the value is constant with temperature.92 Mardykin and Filippov used a radial-wave technique to determine a value of approximately 33.5 J/(mol K) in 1968;110 however, heat-capacity values for other elements obtained using this approach differ substantially from literature values. Two groups have also used pseudopo-

2.3. Gibbs Energy of Formation

Almost all direct measurements of ΔG° for antimonide compounds have been made using one of two experimental techniques: vapor-pressure or electromotive force (EMF) measurements. The primary tool for measuring elemental vapor pressures is Knudsen effusion,68−85 usually in combination with mass spectrometry. The low experimental temperB

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tential theory to predict the heat capacity of liquid antimony: Joarder et al. (18.69 J/(mol K)) and Zahid et al. (28.80 J/(mol K)).111,112 Updated measurement using purer raw materials and more accurate instrumentation would be desirable. The enthalpy of fusion of antimony has also been controversial, with experimental values ranging from 10.493 to 20.757 kJ/mol. More recent results obtained using differential scanning calorimetry have favored higher values, with smaller levels of uncertainty. Hultgren et al. recommended an enthalpy of fusion of 19.873 ± 0.626 kJ/mol; the 1999 assessment by Stølen and Grønvold recommended 19.792 ± 0.598 kJ/mol.113 Table 1 lists recalculated thermodynamic properties of solid antimony. These use the entropy and heat-capacity values for

Table 2. Thermodynamic Properties of Sb2 and Sb4 Vapor (kJ/mol) Sb2

Table 1. Recommended Thermodynamic Properties of Condensed-Phase Antimony temp (K)

C°p (J/(mol K))

298.15 300 400 500 600 700 800 900 903.9 903.9 1000 1100 1200 1300 1400 1500

25.28 25.28 25.62 26.43 27.44 28.53 29.67 30.84 30.88 31.38 31.38 31.38 31.38 31.38 31.38 31.38

S° −(G° − H°298)/T (J/mol) (J/(mol K)) 45.42 45.58 52.88 58.67 63.58 67.89 71.77 75.34 75.47 97.37 100.54 103.53 106.26 108.77 111.09 113.26

45.42 45.42 46.41 48.30 50.45 52.64 54.79 56.88 56.96 56.96 61.00 64.73 68.08 71.11 73.89 76.44

H°T − H°298 (J/mol) 0 47 2585 5185 7877 10675 13585 16610 16730 36522 39538 42676 45814 48952 52090 55228

Sb4

temp (K)

ΔH°

ΔG°

ΔH°

ΔG°

298.15 400 500 600 700 800 900 904 904 1000 1100 1200 1300 1400 1500

232.3 230.0 228.0 226.4 224.5 222.0 218.9 218.8

182.4 165.8 140.5 134.6 119.5 104.6 90.0 89.8 89.8 79.9 70.2 60.7 51.5 42.4 33.6

206.1 204.6 202.2 199.4 196.5 193.6 190.6 190.5

150.7 139.7 123.7 108.3 93.4 78.8 64.6 64.1 64.1 59.4 54.9 50.8 47.1 43.8 40.7

by applying mass-balance calculations to the total antimony pressure measured in higher temperature (923−1908 K) transport and boiling-point investigations, presuming that calculated equilibrium partial pressures of Sb4 were correct. Any vapor not present as Sb4 was presumed to be Sb2 or Sb, and the partial pressures of these species were calculated accordingly. This approach is subject to uncertainty, especially at lower temperatures. As a result, the recommended partial pressures of Sb2 differ from experimental values by 20−50%. Since the review by Hultgren et al.,92 three high-temperature investigations of the vaporization of elemental antimony have been reported. Prasad et al. measured transpiration rates over pure antimony and two antimony-containing alloys, along with the results of boiling-point measurements, to obtain equilibrium partial pressures of Sb4 and Sb2 (1072−1265 K).114 Their equilibrium partial pressures of Sb2 are less than those in Hultgren’s tabulation, while their values of pSb4 are greater. Sullivan et al. (798−898 K) and Drowart et al. (876−1390 K) studied vaporization equilibria using Knudsen effusion/mass spectrometry.116,117 The results of Drowart et al. feature a wider temperature range than other investigations and are in good agreement with the earlier results of DeMaria et al.97 As a result, these two sets of data have been combined to redetermine the thermodynamic properties of Sb2. For the reaction

solid antimony recommended by Konings and van der Lann,18 the enthalpy of fusion recommended by Stølen and Grønvold,113 and the heat capacity for liquid antimony chosen by Hultgren et al.92 The levels of uncertainty are surprising for a relatively low melting point element, and more reliable experimental results would be desired. The vaporization of antimony results in four vapor species: Sb, Sb2, Sb3, and Sb4. Sb4 is predominant at lower temperatures, but the experimental literature disagrees over the temperature at which the formation of Sb2 becomes significant.114 The vapor pressures of Sb and Sb3 are insignificant at lower temperatures and have not been extensively studied. The assessment by Hultgren et al. determined recommended thermodynamic properties for Sb4 by primarily considering the results of low-temperature (618−861 K) effusion studies,92 which generated a vapor consisting almost entirely of the tetramer. The recommended ΔH°298 value (206.512 kJ/mol) was within the margin of error of five separate investigations. Since then, transpiration and boiling-point measurements by Prasad et al. (1072−1265 K) have further confirmed this recommendation, as have the Knudsen-effusion measurements of Rosenblatt and Lee (683−829 K).114,115 Table 2 provides recalculated thermodynamic properties for Sb4, based on the values provided by Hultgren et al. and the values for condensed-phase antimony from Table 1. The thermodynamic values for Sb2 recommended by Hultgren et al. are more problematical.92 These were obtained

Sb4 ⇄ 2Sb2

(3)

ΔG°(2) (kJ/mol) = 286.878 + 0.0399T ln T − (14.28 × 10−6)T 2 − 0.439T

(4)

Applying the revised values for condensed-phase Sb and Sb4 vapor leads to recalculated values of standard properties for Sb2, which appear in Table 2. The experimental database for Sb(g) is so small that calculated thermodynamic properties for this species would be unreliable. As a result, no tabulation of properties for this species is presented here. There is a need for additional studies, particularly of the heat of fusion and heat capacity of molten antimony and of the partial pressure of Sb(g) vapor. C

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Table 4. Experimental Values of ΔG° for Sodium Antimonides

4. ALKALI METALS The five alkali-metal−antimony systems have two things in common: a congruently melting A3Sb compound and significant levels of uncertainty over compound stabilities and phase-transition temperatures. The Li−Sb and Na−Sb systems are the simplest of the five; Cs−Sb and Rb−Sb are the most complex. The Li−Sb system features two stable compounds (stable defined as the equilibrium state for the given stoichiometry at a particular temperature and 1 atm of pressure), Li3Sb and Li2Sb.118 Li3Sb is of commercial interest as an electrode material for lithium ion batteries; it transforms to a hightemperature phase above 923 K and melts at 1423 K. A limited number of thermodynamic investigations of these compounds have been performed. Kubaschewski and Seith reported ΔH° for nonexistent Li3Sb2,119 and Shchukarev et al. used acidsolution calorimetry to determine ΔH°298 for Li3Sb (−325.5 kJ/mol).37 Neither of these results is considered reliable. Morachevskii and co-workers performed a series of polarographic studies using both lithium and antimony as the cathode,97,99,101 and Weppner and Huggins performed an EMF investigation (628−773 K) against a molten Li−Al alloy electrode. The standard Gibbs energies of formation of Li3Sb and Li2Sb resulting from these experiments are shown in Table 3; the consistency between studies is impressive. On the basis

temp (K)

Li2Sb Li2Sb Li2Sb Li2Sb Li2Sb Li2Sb Li2Sb Li3Sb Li3Sb Li3Sb Li3Sb Li3Sb Li3Sb Li3Sb

723 650 423 423 723 650 423 723 650 423 423 723 650 423

type of investigation polarography polarography polarography polarography EMF293 EMF293 EMF293 polarography polarography polarography polarography EMF293 EMF293 EMF293

(Sb electrode)99 (Sb electrode)101 (Li electrode)292 (Sb electrode)292

(Sb electrode)99 (Sb electrode)101 (Li electrode)292 (Sb electrode)292

temp (K)

type of investigation

ΔG° (kJ/mol)

NaSb NaSb NaSb Na3Sb Na3Sb Na3Sb Na3Sb

523 523 523 523 523 523 523

polarography (Sb electrode)122 EMF121 Knudsen effusion73,80 Knudsen effusion80 polarography (Sb electrode)122 EMF121 Knudsen effusion73,80

−74.8 −67.1 −66.7 −185.4 −186.1 −195.4 −186.7

investigations; the results are similar, but not consistent. The entropies of formation of the two compounds determined by the vapor-pressure measurements (−92 J/(mol K) for Na3Sb, −7 J/(mol K) for NaSb) differ substantially from those resulting from EMF measurements (−60 and −17 J/(mol K)). As a result, recommending a best value is difficult. Lowtemperature heat-capacity measurements that determined S°298 for Na3Sb and NaSb would help resolve the dispute. The K−Sb system features four stable compounds: K3Sb, K5Sb4, KSb, and KSb2.123 As with Na3Sb, K3Sb is used in photocathodes. The only direct ΔH° measurement is that of Morozova et al. for K3Sb (−298.7 kJ/mol at 298 K),30 using acid-solution calorimetry. Gibbs-energy measurements have been performed by the same groups that studied the Na−Sb system, including vapor-pressure measurements by Voronin and co-workers (459−679 K),73,82 polarographic studies by Morachevskii and co-workers (Sb cathode, 513 and 600 K),98,100 and EMF measurements by Borodkina (K electrode, 490 K; quoted by Morachevskii and Bochagina).124 Table 5

Table 3. Experimental Values of ΔG° for Lithium Antimonides compd

compd

ΔG° (kJ/mol) −174.5 −176.6 −185.8 −185.4 −174.2 −176.6 −183.8 −257.7 −261.4 −272.9 −272.3 −257.7 −261.3 −272.5

Table 5. Experimental Values of ΔG° for Potassium Antimonides ΔG°513 (kJ/mol) compd

Voronin et al. (vapor pressure)73,82

Borodkina (EMF)124

Morachevskii et al. (polarography)98,100

K3Sb K5Sb4 KSb KSb2

−163.2 −369.9 −82.2 −86.7

−196.8 −432.9 −95.0

−202.0 −423.9 −90.6 −104.7

compares ΔG°513 for potassium antimonides from the three investigations. The results of Borodkina and of Morachevskii et al. are comparable. However, Borodkina claimed that KSb2 was not a stable compound in the system. As a result, using the currently available results to generate recommended thermodynamic values for potassium antimonides cannot be done at this time. A new EMF study would be of value, along with heatcapacity measurements for the four compounds. Figure 2 shows the currently assessed Rb−Sb phase diagram.125 Some of the compounds reported for this system in 1961 are unconfirmed, and the vaporization study (392−690 K) of Voronin et al. casts doubt on the existence of Rb2Sb and Rb5Sb2.73,81 Voronin’s results are the only available thermodynamic data for rubidium antimonides, but results achieved in the same investigation for compounds in the K−Sb and Na−Sb systems suggest that they are reliable. Table 6 lists the thermodynamic properties of rubidium antimonides determined by Voronin et al. The uncertainty of these values grows with the Rb/Sb ratio, due to the need for accurate ΔH° and ΔG° values for the “previous” compound. As before,

of the results of Weppner and Huggins, ΔH°298 and ΔG°298 for Li2Sb are −192.5 and −185.9 kJ/mol; for Li3Sb, these values are −286.2 and −275.8 kJ/mol. Future research to be performed includes measurement of the heat capacities of the two compounds and measurement of the exact temperature and enthalpy of transition for the high-temperature phase of Li3Sb.118 Na3Sb and NaSb are the two stable compounds in the Na− Sb system.120 Na3Sb is a semiconductor, used in photocathode structures. No heat-capacity measurements have been made in the system, but two determinations of ΔH°298 have been reportedKubaschewski and Seith for Na3Sb (−197.5 kJ/mol) and NaSb (−66 kJ/mol),119 using direct-reaction calorimetry, and Morozova et al. for Na3Sb (−212.5 kJ/mol),29 by acidsolution calorimetry. ΔG° determinations are more common and include vapor-pressure measurement (528−700 K),73,80 EMF studies (405−625 K),121 and polarization measurements (523 K).122 Table 4 compares ΔG° at 523 K from the different D

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Figure 2. Rubidium−antimony phase diagram. Reprinted with permission from ref 294. Copyright 1992 ASM International (www.asminternational. org).

Table 6. Thermodynamic Properties of Rubidium Antimonides (kJ/mol)73,81 Rb3Sb7

RbSb2

RbSb

Rb5Sb4

Rb3Sb

temp (K)

ΔH°

ΔG°

ΔH°

ΔG°

ΔH°

ΔG°

ΔH°

ΔG°

ΔH°

ΔG°

298.15 312.63 312.63 400 500 600 700 800 900

−314 −314 −322 −322 −322 −322 −322

−290 −289 −289 −280 −270 −259 −248

−103 −103 −105 −105 −105 −105

−95 −94 −94 −91 −88 −85

−101 −101 −104 −104 −104 −104 −104 −104

−93 −92 −92 −89 −85 −81 −77 −74

−452 −452 −463 −463 −463 −463 −463

−412 −410 −410 −395 −378 −362 −345

−176 −176 −182 −182 −182 −182 −182 −182 −182

−158 −157 −157 −150 −142 −135 −127 −119 −111

5. ALKALINE-EARTH METALS Until recently, practical interest in antimonide compounds from this group was limited to the interaction between magnesium and antimony in high-strength cast irons and the use of calcium for antimony removal in the refining of steel and lead bullion.102,130 However, a surprising amount of thermodynamic data exist for these systems. A few stable beryllium antimonides have been reported, including BeSb2, Be3Sb2, and Be13Sb; little is known about them.297 There is only one stable magnesium antimonide, Mg3Sb2. Mg3Sb2 has a small solid-solubility range and a transformation occurring over the range 1167−1203 K. The heat capacity of Mg3Sb2 was measured in 1910 by Schimpff (290−463 K)13 and is of limited value in determining thermodynamic properties for the compound. Two direct ΔH° measurements have been made. The first, by Kubaschewski and Villa using direct-reaction calorimetry, determined ΔH°923 = −284.5 kJ/mol (ΔH°298 = −318.8 kJ/mol).131,132

confirmation of these results by another experimental method would be desirable, as would low-temperature heat-capacity measurements. The Cs−Sb system is the most complex of the group, as shown in Figure 3.126 Cs3Sb is also a well-known photocathode material. Due to the increasing vapor pressure of alkali-metal elements with increasing atomic number, measurement of pCs(g) generated by decomposing antimonide compounds has been the common method of determining their thermodynamic properties.79,89,90,127,128 Several of these looked only at the decomposition of Cs3Sb or CsSb and so cannot be used to determine enthalpies and Gibbs energies of formation from the elements. The results of Voronin et al. are the only ones that can be used.79 Table 7 lists ΔH° and ΔG° for the cesium antimonides; the same concerns over uncertainty described for Table 6 apply. Sommer et al. measured the enthalpy of formation of Cs3Sb using direct-reaction calorimetry;129 their value of −101 kJ/mol is considerably different from that in Table 7. E

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Figure 3. Cesium−antimony phase diagram. Reprinted with permission from ref 294. Copyright 1992 ASM International (www.asminternational. org).

Table 7. Thermodynamic Properties of Cesium Antimonides (kJ/mol)79 Cs3Sb7

CsSb2

CsSb

Cs5Sb4

Cs2Sb

Cs3Sb

temp (K)

ΔH°

ΔG°

ΔH°

ΔG°

ΔH°

ΔG°

ΔH°

ΔG°

ΔH°

ΔG°

ΔH°

ΔG°

298.15 301.54 301.54 400 500 600 700 800 900

−287 −287 −293 −293 −293 −293 −293

−268 −267 −267 −259 −251 −243 −234

−96 −98 −98 −98 −98 −98

−88 −88 −88 −85 −82 −78

−84 −84 −86 −86 −86 −86 −86 −86

−74 −74 −74 −70 −66 −62 −58 −54

−412 −412 −425 −425 −425 −425 −425 −425

−355 −354 −354 −331 −307 −283 −259 −236

−153 −153 −157 −157 −157 −157 −157

−125 −125 −125 −114 −104 −93 −82

−198 −198 −204 −204 −204 −204 −204 −204 −204

−160 −159 −159 −145 −130 −115 −100 −85 −70

Mg3Sb2. On this basis, they calculated ΔG° between 988 and 1203 K (Mg(l) and Sb(l) reference state):

Shchukarev et al. later used acid-solution calorimetry to determine ΔH°298 = −334.7 kJ/mol.132 The relatively high melting point of Mg3Sb2 (1501 K), coupled with the lower vapor pressure of metals in this group, makes EMF measurements a preferred means of obtaining ΔG° for this compound. Three EMF studies have been reported, all using a magnesium reference electrode and a molten chloride electrolyte. Eremenko and Lukashenko experimented at lower temperatures (673−923 K)133,134 and were able to calculate ΔG° directly from their data. However, these results show a positive entropy of formation of Mg3Sb2 from the elements, an improbable result. Zabdyr and Moser (912−1016 K) determined the activities of magnesium in molten alloys saturated with Mg3Sb2,132 along with the EMF of the solid compound, but the scatter in the results with solid Mg3Sb2 makes their data unusable for ΔG° calculations. The only EMF study producing reliable results is that of Rao and Patil (980− 1250 K),135 who also determined aMg in liquid alloys in equilibrium with solid Mg3Sb2, along with the EMF of solid

ΔG° (kJ/mol) = − 364.845 + 0.132T

(5)

This translates to ΔH°298 = −378.998 kJ/mol, in reasonable agreement with the results of direct determinations.131,132 Ustimov et al. determined the concentrations of magnesium and antimony dissolved in molten lead in equilibrium with Mg3Sb2 at 595 K102 and calculated ΔG° for the compound as a function of temperature. Their results are substantially different from those of Rao and Patil and not consistent with experimental measurements of ΔH°. Thermodynamic optimizations of the Mg−Sb system include those of Jönsson and Ågren,136 Balakumar and Medraj,137 and Paliwal and Jung.138 The results demonstrate that optimization is not an exact science; calculated values of ΔH°298 for Mg3Sb2 from the three results are −276, −490, and −292 kJ/mol, respectively. Better experimental results for this system would be desired, in particular heat-capacity measurements for both F

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Figure 4. Calcium−antimony phase diagram. Reprinted with permission from ref 294. Copyright 1992 ASM International (www.asminternational. org).

forms of Mg3Sb2. A more accurate experimental determination of ΔH° would also be desirable. Four stable compounds are currently thought to exist in the Ca−Sb system (Figure 4):139 CaSb2, Ca11Sb10, Ca5Sb3, and Ca2Sb. This is controversial, since previous phase diagrams showed a much different system, with compounds CaSb, CaSb3, and Ca3Sb2. As a result, much of the current thermodynamic database is focused on ΔH° and ΔG° determinations for calcium antimonide compounds which may not exist. These include the following: • Direct-reaction calorimetry determination of ΔH°923 for Ca3Sb2 (−669 kJ/mol) by Kubaschewski and Walter.131 The plot of ΔH° against the mole fraction of calcium in the system suggests that Ca3Sb2 is the only stable compound in the system. • Acid-solution calorimetry determination of ΔH°298 for Ca3Sb2 (−477 kJ/mol) by Shchukarev et al.33 • Calculation of ΔG° for Ca3Sb2 from phase equilibria between the solid and Ca and Sb dissolved in molten lead, reported by Ustimov et al.102 According to this work, the entropy of formation of Ca3Sb2 from the elements is positive, an unlikely result. • Polarimetric studies (molten nitrate and chloride electrolytes, antimony cathode) that determined ΔG° at 433 and 800 K for CaSb3, CaSb, Ca5Sb3, Ca3Sb2, and Ca7Sb4, reported by Klebanov et al.140 • Determination of ΔG° for Ca3Sb2 by equilibrating with molten silver and calcium carbide (1273−1573 K) and determining the activity of calcium and antimony, performed by Min and Sano.130 According to the current phase diagram, the melting point of Ca11Sb10 (1396 K) is

the highest in the system, but Min and Sano claim to have maintained solid Ca3Sb2 at 1573 K or higher. More recent thermodynamic data for the Ca−Sb system include those of Zaitsev et al.,83,84 who used the Knudsen-cell/ mass spectrometry approach to determine the vapor pressures of calcium and antimony in equilibrium with liquid solutions and solid compounds (Ca5Sb3 and Ca11Sb10) between 933 and 1669 K. On the basis of the results, ΔG° was calculated for the two compounds. For 5Ca(l) + 3Sb(l) ⇄ Ca5Sb3(s) ΔG° (kJ/mol) = − 919.280 + 0.0342T

(6)

For 11Ca(l) + 10Sb(l) ⇄ Ca11Sb10(s) ΔG° (kJ/mol) = − 21884.4 − 0.04357T

(7)

This implies an enthalpy of formation for Ca11Sb10 of −1042 kJ/mol of atoms, a highly unlikely result. The highly positive entropy of formation also seems questionable. The implied enthalpy of formation for Ca5Sb3 from eq 6 equals −877 kJ/ mol when solid calcium is used as the reference state and −21791 kJ/mol for Ca11Sb10; this can be compared with values obtained at 1078 K by Bouhajib et al. using direct-reaction calorimetry (−688 and −2289 kJ/mol, respectively).63 The most recent study of the system is the EMF investigation of Poizeau et al.141 A good deal more information is needed on the system, including confirmation of the phase diagram, heatcapacity measurements, and reliable investigations of all four compounds. The only thermodynamic investigation of strontium antimonides is that of Shchukarev et al.,32 who used acidsolution calorimetry to determine ΔH°298 for SrSb (−195.0 kJ/ mol), Sr3Sb2 (−570.3 kJ/mol), and Sr2Sb (−326.3 kJ/mol). G

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Table 8. Experimental and Modeled Standard Enthalpies of Formation for Rare-Earth Antimonides ΔH°298 (kJ/mol) direct-reaction calorimetry

molten-salt EMF −199152

La4Sb3 La5Sb3 La2Sb CeSb2

−26358 −209145 −770145 −256145 −276146 −261146 −21758 −832146 −853146 −294146 −379147

CeSb

−253147

Ce4Sb3

−817

Ce5Sb3 Ce2Sb

−870147 −309147

PrSb2

−29156

PrSb

−252

Pr4Sb3

−84056

Pr5Sb3

−89656

Pr2Sb

−19856

NdSb2

−27255

NdSb

−24655

Nd4Sb3

−79755

Nd5Sb3

−86055

SmSb2 SmSb Sm4Sb3 Sm5Sb3 Sm2Sb

−268 −244148 −826148 −896148 −306148

compd ScSb YSb Y5Sb3 Y3Sb LaSb2 LaSb

−292160 −296160

ΔH°298 (kJ/mol)

vapor-pressure measurement

modelpredicted

−26877

−19266 −68866 −24466 −30066 −23666

−982 −1108159 −394159 159

molten-salt EMF

Gd16Sb39

−429057

GdSb

−274161

Gd4Sb3

−24057 −20558 −81257

Gd5Sb3

−88057

−1135158

TbSb DySb

−23458 −22859

−238150

Dy4Sb3

−78059

Dy5Sb3

−84459

−1015158

66

−23475

147

56

−784 −82466 −28266 −28866 −314172 −22866 −238172 −76366 −837172 −80066 −27666 −357172 −27666 −293171 −21866 −257171 −73566 −840171 −77666 −896171 −26766 −306171 −26766 −272171 −21266 −247171 −71466 −812171 −76066 −862171 −28266 −20266 −67966 −72066 −24966

compd

direct-reaction calorimetry

−266

77

−25977

148

−26777

−251151 −253157

HoSb ErSb2

−237149

ErSb

−222149

Er5Sb3

−800149

−221157

TmSb2 TmSb Tm5Sb3 Lu3Sb Lu5Sb3 LuSb LuSb2

−18758

−238163

vapor-pressure measurement

−26277

modelpredicted −429066 −4332170 −19266 −242170 −65166 −822170 −68866 −909170 −18866 −18666 −241168 −63066 −754168 −67266 −797168 −18266 −21666 −225163 249166 −17866 −223163 −229166 −64866 −664163 −710166 −21366 −228163 −17666 −226163 −64066 −668163 −22866 −230167 −63266 −692167 −17466 −231167 −21066 −239167

• MSb2 (Y, La, Ce, Pr, Nd, Sm, Eu, Tb, Dy, Ho, Er, Tm, Yb, Lu) • M5Sb3 (Sc, Y, La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu) • M4Sb3 (Y, La, Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Yb) • M3Sb (Y, Tm, Lu) • M11Sb10 (Eu, Yb) Most of the thermodynamic studies of rare-earth antimonides have been performed by one of four groups. The first is a group at the University of Genoa, who used an isoperibol calorimeter to perform direct-reaction measurements of ΔH°300 for numerous compounds.55−57,59,62,143−149 Chua and Pratt also used direct-reaction calorimetry to determine ΔH° for ScSb, YSb, LaSb, and LuSb;58 comparison of their results with those of the Genoa group shows sporadic agreement.

Kubaschewski and Villa used direct-reaction calorimetry to determine ΔH° for Ba3Sb2 (−732 kJ/mol).142

6. GROUP 3: RARE-EARTH ELEMENTS AND ACTINIDES The antimonide compounds of the rare-earth elements are unique in two ways. The first is their stability; several of these compounds have melting points above 2000 K. The second is the degree to which the phase diagrams of the elements with antimony are known, despite the minimal practical significance of the compounds to date. Most of the compounds in these systems belong to one of seven common stoichiometries: • MSb (Sc, Y, La, Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu) • M2Sb (Sc, La, Ce, Pr, Nd, Sm) H

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Two groups in the former Soviet Union used EMF studies to determine ΔG° and ΔH° for a series of antimonide compounds in this group. Both groups used a molten LiCl−KCl electrolyte and similar temperature ranges. The group at Ural Polytechnic Institute used an intermetallic compound of the rare-earth element with a known ΔG° as the reference electrode,150−156 while the group at Moscow State University used the element itself as a reference.157−163 The advantage of the Ural Polytechnic approach is the lack of intermediate compounds with a composition between those of the electrode and the compound being measured, eliminating potential interference; the advantage of the Moscow State approach is the greater certainty in the value of ΔG° (0 J/mol) for the reference. The greater stability of these antimonides recommends the use of EMF measurements for determining ΔG°. The last group to investigate the thermodynamics of rareearth antimonides is Viksman and Gordienko at the Ukranian Academy of Sciences.77,78,164 This group measured the vapor pressures of Sb(g) and the metallic element released by decomposing antimonides at temperatures ranging between 1800 and 2300 K. Schiffman and Franzen performed a similar study of decomposing CeSb.75 The use of studies such as this to determine ΔG° and ΔH° as a function of temperature requires the availability of accurate thermodynamic data for Sb(g), which as pointed out in a previous are not available. In addition, the only published high-temperature heat capacities for rare-earth antimonides are estimates.165 As a result, the vapor-pressure measurements are the least useful of the existing data for calculating the thermodynamic properties of compounds in this group. Model-calculated values of thermodynamic properties for rare-earth antimonides include ΔH° values determined using the Miedema approach66 and enthalpies and Gibbs energies of formation obtained from phase-diagram optimization in the Ce−Sb, Dy−Sb, Er−Sb, Gd−Sb, Lu−Sb, Nd−Sb, Pr−Sb, and Tm−Sb systems.166−172 Table 8 compares the enthalpies of formation of rare-earth compounds (converted to 298 K reference states) reported by the various groups. While the models predict ΔH° with reasonable accuracy in many cases, the variance with experimental results in others is such that it is not a reliable substitute for missing data. Enthalpies of formation obtained from EMF results tend to be much more negative than those obtained by calorimetric techniques. Table 9 lists standard Gibbs energies of formation at 298 K of compounds in this group, obtained from the EMF studies.150−152,157−162 Results calculated from the optimization studies are also included.166−172 The results are comparable, but the discrepancy of ΔH°298 values obtained using this approach from others in Table 8 suggests caution. No high-temperature measurements of compound heat capacities have been reported in the group. Wallace and coworkers determined Cp for LaSb and PrSb between 7 and 300 K;11,173 S°298 is 88.8 J/(mol K) for LaSb and 105.1 J/(mol K) for PrSb. The lack of high-temperature heat-capacity data is a particular concern in these systems, given the unusually high melting points of these compounds. Thermodynamic studies of actinide-series antimonide compounds are comparatively rare. Lebedev et al. used EMF cells (molten salt, 808−950 K) to determine the activity of plutonium in PuSb2, thorium in ThSb2, and uranium in USb2.174−176 Low-temperature heat-capacity measurements have been made for PuSb,177 USb2,178 and USb;7,179 S°298 is 107.23 J/(mol K) for PuSb and 141.45 for USb2. Direct-

Table 9. Standard Gibbs Energies of Formation of Lanthanide Antimonide Compounds compd Ce2Sb Ce4Sb3 CeSb CeSb2 Dy5Sb3 Dy4Sb3 DySb DySb2 Er5Sb3 ErSb

ErSb2 GdSb Gd4Sb3 Gd5Sb3 Gd16Sb39 HoSb

ΔG°298 (kJ/mol)

ref

compd

−330.6 −793.4 −228.2 −292.5 −793.5 −752.9 −237.7 −240.2 −248.0 −648.9 −661.5 −225.3 −219.5 −218.8 −233.2 −220.5 −269.6 −240.1 −977.3 −810.9 −1077.9 −889.8 −4329.6 −246.4 −249.0

172 172 172 172 168 168 150 168 150 166 169 162 166 169 166 169 157, 161 170 158 170 158 170 170 171 157

La4Sb3 La5Sb3 La2Sb LaSb LaSb2 Lu3Sb Lu5Sb3 LuSb

LuSb2 Nd2Sb Nd5Sb3 Nd4Sb3 NdSb NdSb2 Pr2Sb Pr5Sb3 Pr4Sb3 PrSb PrSb2 ScSb TmSb2 TmSb Tm5Sb3

ΔG°298 (kJ/mol)

ref

−1012.2 −1146.0 −410.5 −290.4 −94.4 −568.0 −680.8 −232.5 −232.8 −225.8 −233.5 −285.2 −831.7 −784.7 −239.0 −269.0 −291.7 −854.9 −803.2 −246.6 −277.7 −199.4 −225.3 −111.8 −661.9

159 159 159 160 160 167 167 163 162 167 167 171 171 171 171 171 171 171 171 171 171 152 169 169 169

reaction calorimetry experiments by Baskin and Smith at 698 or 798 K produced enthalpies of formation for USb (−138.4 kJ/ mol), U3Sb4 (−451.8), and USb2 (−347.3).180 The direct reaction proceeds slowly for the formation of antimonides, lowering confidence in the accuracy of the results.

7. GROUP 4 A number of antimonide compounds have been discovered for elements in this group. These include the following: • TiSb2, TiSb, Ti6Sb5, Ti5Sb3, Ti5Sb2, Ti3Sb, and Ti4Sb • ZrSb2, Zr3Sb2, Zr5Sb3, Zr2Sb, and Zr3Sb • HfSb2, Hf5Sb9, HfSb, Hf5Sb3, and Hf3Sb However, a lack of uses or interesting properties has resulted in little interest in thermodynamic research. Shchukarev et al. used combustion calorimetry to determine ΔH°298 for TiSb (−281.2 kJ/mol).35 Nothing else has been reported. 8. GROUP 5 Again, several antimonide compounds have been reported for the three elements in this group. A15 compounds, including V3Sb, Nb3Sb, and Ta3Sb, were considered good superconductors until about 1990; since that time, very little interest has been expressed in these systems. Goncharuk and co-workers performed EMF studies on the V−Sb system (molten chloride electrolyte, vanadium reference; 703−853 K).181,182 Their results generated values of ΔG°775 and ΔH°775 for VSb2 (−46.2 kJ/mol, −54.3 kJ/mol). Murray et al. attempted to study the decomposition of solid Ta3Sb (1367−1556 K) and NbSb2 (990−1160 K) by Knudsen effusion.68 Kinetic limitations and uncertainty over the thermodynamics of Sb4 and Sb2 vapor make both results suspect. I

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Figure 5. Chromium−antimony phase diagram. Reprinted with permission from ref 294. Copyright 1992 ASM International (www. asminternational.org).

Figure 6. Manganese−antimony phase diagram. Reprinted with permission from ref 294. Copyright 1992 ASM International (www. asminternational.org).

J

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9. GROUPS 6 AND 7 Although antimonides are known for all six elements in this group, only the Cr−Sb and Mn−Sb systems are the subject of substantial study. Both chromium and manganese antimonides have ferrimagnetic or ferromagnetic properties that have potential uses in electronic devices. In addition, the Cr−Sb and Mn−Sb systems each have only two stable compounds: CrSb and CrSb2, Mn2Sb and MnSb. The solid-solution range for Mn2Sb is Mn-rich and does not appear to include the actual 2:1 ratio at 298 K.183 The assessed Cr−Sb and Mn−Sb phase diagrams are shown in Figures 5 and 6. The heat capacity of CrSb was first measured over the 298− 463 K range by Schimpff.13 Since then, Grønvold and coworkers have reported more accurate measurements for CrSb (300−950 K) and CrSb2 (5−991 K).1,25 The transition of CrSb from the antiferromagnetic to the paramagnetic state at 684.6 K has an enthalpy of transition of 6.33 kJ/mol and makes determination of a, b, and c values for the common heatcapacity expression (Cp = a + bT + cT−2) infeasible. CrSb2 engages in a similar transition at 274 K; S°298.15 for this compound is 114.9 J/(mol K). Between 298 and 991 K, Cp,CrSb2 (J/(mol K)) = 77.120 + 0.0175T + 63358T−2. No direct measurements of ΔH° have been made for either compound; Miedema’s model was used to estimate −18 kJ/mol for CrSb and −18 kJ/mol for CrSb2.67 The lack of ΔH° measurements for chromium antimonides is made up for by four separate investigations of ΔG°, all using

thermodynamic properties does not seem advisable. Direct measurement of ΔH° for this compound would be desirable, as would measurement of low-temperature heat capacities. The existence of low-temperature heat-capacity measurements for CrSb2 makes it possible to judge the relative accuracy of the ΔG° measurements.1 Using the values for S°T for solid antimony obtained here, a value of ΔS° of 19.44 J/(mol K) is calculated at 850 K, which compares best with the experimental Table 12. Thermodynamic Properties of CrSb2

Table 10. Experimentally Determined Thermodynamic Properties for CrSb ref

ΔG°850 (kJ/mol)

ΔH°850 (kJ/mol)

ΔS°850 (J/(mol K))

184 185, 186 96 188

−15.980 −17.400 −17.240 −15.730

−3.140 5.770 4.100 5.810

15.10 27.28 25.10 24.18

ref

ΔG°850 (kJ/mol)

ΔH°850 (kJ/mol)

ΔS°850 (J/(mol K))

−19.500 −21.340 −21.090 −21.210

−12.130 −3.890 −9.000 −11.080

8.62 20.50 13.81 13.81

Cp (J/(mol K))

HT − H298 (kJ/mol)

S°T (J/(mol K))

ΔH°T (kJ/mol)

ΔG°T (kJ/mol)

300 350 400 450 500 550 600 650 700 750 800 850 900 950 991.3

82.34 83.97 85.43 86.52 87.02 87.11 87.27 87.78 88.70 89.78 90.87 92.04 93.13 94.43 95.43

0.152 4.309 8.545 12.846 17.185 21.540 25.899 30.271 34.685 39.149 43.660 48.233 52.864 57.834 61.755

115.39 128.19 139.53 149.65 158.78 167.10 174.67 181.66 188.23 194.38 200.19 205.72 21.103 216.39 220.40

−14.910 −14.116 −13.226 −12.281 −11.318 −10.365 −9.439 −8.534 −7.623 −6.699 −5.767 −4.812 −3.839 −2.568 −1.734

−15.007 −15.151 −15.370 −15.694 −16.114 −16.650 −17.259 −17.935 −18.712 −19.530 −20.414 −21.337 −22.352 −23.402 −24.305

results of Goncharuk and Lukashenko.185,186 As a result, ΔG°850 from this study is combined with the heat-capacity results to generate a table of thermodynamic properties for CrSb2, provided as Table 12. The rapidly changing values of ΔH° and ΔS° as a function of temperature suggest that confirmation of the heat-capacity measurements would be of some interest. In addition to measuring the heat capacities of chromium antimonides, Grønvold and co-workers also measured the heat capacities of Mn2.10Sb and Mn2Sb (5−1000 K).3,183 From the low-temperature results, S°298.15 for Mn2.10Sb is 123.55 J/(mol K). The high-temperature heat capacity of stoichiometric Mn2Sb shows the effect of a magnetic transition at 546 K and further distortion over the 546−746 K range. As a result, a, b, and c calculation is not recommended. No measurements of heat capacity for MnSb have been reported. ΔH° was determined for MnSb (−50.2 kJ/mol) by Shchukarev et al.,36 using combustion calorimetry. Miedema’s model was also used to estimate ΔH° for MnSb (−70 kJ/mol) and Mn2Sb (−105 kJ/mol).67

Table 11. Experimentally Determined Thermodynamic Properties for CrSb2 184 185, 186 96 188

temp (K)

EMF measurements against a chromium cathode. Three of these investigations took advantage of the low melting point of the KCl−LiCl eutectic to use a molten-salt electrolyte;96,184−186 Vecher and co-workers used a solid-electrolyte (CaF2) cell instead.187,188 The experimental temperatures are for the most part above 684 K, eliminating the magnetic transformation of CrSb as a concern. Tables 10 and 11 compare the results of the four investigations at 850 K. The ΔG° values are reasonably similar, but ΔH° and ΔS° vary considerably. The positive values of ΔH° and ΔS° seem unlikely; Goncharuk and Lukashenko ascribe this result to magnetic disordering within CrSb.185 Goryacheva performed a CALPHAD-type assessment for the Cr−Sb system,184 which generated optimized values of ΔH° (−1.076 kJ/mol) and ΔS° (3.42 J/(mol K)) for CrSb. However, these values differ by so much from the experimentally determined results that calculation of reliable

Table 13. Calculated Thermodynamic Properties of MnSb2

K

temp (K)

ΔG° (kJ/mol)

ΔH° (kJ/mol)

temp (K)

ΔG° (kJ/mol)

ΔH° (kJ/mol)

300 350 400 450 500 546.5 550 600

−43.79 −44.52 −45.24 −46.15 −47.05 −48.05 −48.14 −49.36

−40.09 −39.42 −38.76 −37.82 −36.89 −35.52 −35.43 −34.12

650 700 750 800 850 900 950 1000

−50.71 −52.06 −53.23 −54.40 −56.22 −58.04 −59.60 −61.15

−33.08 −32.04 −31.50 −30.96 −30.66 −30.35 −32.37 −34.40

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Figure 7. Iron−antimony phase diagram. Reprinted with permission from ref 294. Copyright 1992 ASM International (www.asminternational.org).

The only ΔG° measurements for manganese antimonides are those of Eremenko et al.,190 who performed EMF measurements (673−833 K) against solid Mn using a molten KCl−LiCl electrolyte. From these results, ΔG°753 and ΔH°753 for MnSb are −38.4 and −26.8 kJ/mol, respectively; for Mn2Sb the values are −53.6 and −31.4 kJ/mol. Table 13 shows calculated values of ΔH° and ΔG° for stoichiometric Mn2Sb, calculated on the basis of the experimental results of Eremenko et al. and Askheim and Grønvold.183,190 The values are highly suspect and should be used with caution. The only molybdenum antimonide is Mo3Sb7.191 Mart et al. measured the vapor pressure of Sb2 and Sb4 generated by decomposition between 824 and 1060 K. Applying the Gibbs energies of formation of Sb4(g) listed in Table 2 to the results generates the following expression for the Gibbs energy of formation of Mo3Sb7 from solid molybdenum and antimony: ΔG° (kJ/mol) = − 87.020 + 0.0348T

the research database is for the antimonides of cobalt, iron, and nickel. The Fe−Sb phase diagram (Figure 7) shows two stable compounds: stoichiometric FeSb2 and ε, an iron-excess (FeSb) solid solution whose composition ranges roughly between those of Fe0.58Sb0.42 and Fe0.52Sb0.48. The Curie point of ε is somewhere between 484 and 510 K. Heat-capacity measurements in the system have been reported for FeSb2 (5−1021 K),4 Fe0.54Sb0.46 (310−1080 K),28 and “Fe3Sb2” (800−1500 K), which may be iron-saturated ε.21 The low-temperature data for FeSb2 result in S°298.15 = 108.70 J/(mol K), and from the hightemperature data Cp,FeSb2 (J/(mol K)) = 103.16 − 0.06643T − 859659T −2 + 682000T 2

(8)

(9)

The results of Espeleta et al.21 show a heat capacity for ε that is virtually unchanged with temperature; this differs considerably from the results of Perring et al.28 The heat-capacity data provided by Perring et al. are stated as J/(mol K) of “FeSb”. However, calculation of ΔCp for the formation of ε from the elements based on this assumption results in large negative values, an unlikely result for a phase with minimal stability. Presuming that the equations provided by Perring et al. are actually meant to represent J/(mol K) of Fe0.46Sb0.54 rather than FeSb results in much more defensible values of ΔCp. As a result, this approach has been used to determine the thermodynamic properties of FeSb. The heat capacity reported by Perring et al. is given per mole of atoms:

These results vary from those calculated by Mart et al. using different values for the thermodynamic properties of Sb4(g).191 Measured heat capacities for Mo3Sb7 would be useful.

10. GROUPS 8−10 The metal−antimony phase diagrams of the nine elements in this group have few common aspects. All nine elements form a stable MSb2 compound, and most form a stable monoantimonide solid solution as well. Practical interest in these compounds is limited, although the thermoelectrical properties of MSb3 compounds formed by some elements in this group have encouraged further research. M−Sb phase diagrams have been published for six of the elements in this group (Co, Fe, Ni, Pd, Pt, Rh), and thermodynamic investigations have been performed in five of the systems. As might be expected, most of L

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Table 14. Thermodynamic Properties of FeSb2

Cp, ε (J/(mol K)) = 64.33 − 0.131T + (130.28 × 10−6) 2

T − 945051T

−2

temp (K)

(298.15−510 K)

= 46.86 − 0.0240T + 14.10 × 10−6T 2 − 2564050T −2 (510−1080 K)

300 350 400 450 500 550 600 650 700 750 800 850 900 903.9 903.9 950 1000 1021.2

(10)

Three investigations directly measured the enthalpies of formation of ε and FeSb2: • Körber and Oelsen,192,193 direct-reaction calorimetry (1873 K) • Predel and Vogelbein,49 metal-solution calorimetry (1090 K, ε only) • Boa et al.,194 metal-solution calorimetry (1065 K) Predel and Vogelbein determined ΔH°298 values for ε of 2.999 kJ/mol (Fe0.55Sb0.45) and −0.045 kJ/mol (Fe0.57Sb0.43); this compares with −5.020 kJ/mol reported by Körber and Oelsen and with −5.100 kJ/mol by Boa et al. (Fe0.55Sb0.45). The values of ΔH°298.15 reported for FeSb2 are −15.060 kJ/mol (Körber and Oelsen) and −35.400 kJ/mol (Boa et al.). Two groups have used EMF techniques to determine Gibbs energies of formation in the Fe−Sb system using a molten KCl−LiCl electrolyte: Geiderikh et al. (673−973 K)96,195,196 and Zabdyr and Fitzner (FeSb2 only, 647−851 K).197 Dynan and Miller used Knudsen-cell effusion to measure the vapor pressure of Sb4 + Sb2 at 893 K,72 and Richter and Ipser used an isopiestic technique to measure vapor pressures between 1000 and 1290 K.300 Within the limits of experimental error, the results of all four studies are in agreement within the ε composition range. ΔH° values for ε reported by Geiderikh et al. (−5.021 kJ/mol at 830 K) and Dynan and Miller (−3.350 to −4.140 kJ/mol at 893 K) are in the same range as those of the direct measurements. The indirectly determined values of ΔH°FeSb2 are more divergent (−28.870 kJ/mol by Geiderikh et al., −36.400 by Dynan and Miller, −19.780 by Zabdyr and Fitzner). Combining the heat-capacity results of Grønvold et al. for FeSb2 and the entropy of antimony selected here results in a calculated ΔS°830 of −8.50 J/(mol K); this compares with values obtained by Geiderikh et al. (−7.53 J/(mol K) at 830 K), Dynan and Miller (−17.57 J/(mol K) at 893 K), and Zabdyr and Fitzner (2.76 J/(mol K)). Numerous investigators have calculated thermodynamic parameters for ε and FeSb2 as part of a CALPHAD-style optimization of the binary Fe−Sb system or ternary systems.55,166,198 For the standard Gibbs energy of formation of FeSb2 ΔG° (kJ/mol) = − 30.186 + 0.00921T

ΔH°T (kJ/mol)

ΔG°T (kJ/mol)

108.19 121.62 132.53 142.25 151.02 159.02 166.42 173.31 179.80 185.96 191.85 197.53 203.02 203.45 203.45 208.38 213.64 215.84

−23.104 −22.838 −22.547 −22.301 −22.135 −22.065 −22.095 −22.225 −22.447 −22.754 −23.133 −23.572 −24.058 −24.098 −63.681 −64.238 −64.740 −64.936

−20.285 −19.837 −19.430 −19.058 −18.709 −18.373 −18.040 −17.700 −17.348 −16.976 −16.583 −16.164 −15.719 −15.683 −15.683 −13.274 −10.584 −9.435

148 4178 8263 12.388 16.547 20.745 24.991 29.296 33.672 38.133 42.694 47.370 52.177 52.558 52.558 57.131 62.248 64.470

temp (K)

Cp (J/(mol K))

HT − H298 (kJ/mol)

ΔH°T (kJ/mol)

ΔG°T (kJ/mol)

300 350 400 450 500 510 550 600 650 700 750 800 850 900 903.9 903.9 950 1000 1080

52.36 53.28 53.54 53.97 54.99 55.29 56.37 57.82 58.77 59.39 59.79 60.04 60.20 60.30 60.32 60.32 60.40 60.50 60.71

97 2.743 5.414 8.100 10.821 11.372 13.687 16.680 19.757 22.899 26.095 29.337 32.622 35.949 36.210 36.210 39.318 42.730 48.288

−10.401 −10.256 −10.107 −10.009 −9.969 −9.966 −9.892 −9.809 −9.770 −9.799 −9.913 −10.120 −10.427 −10.838 −10.875 −31.458 −31.977 −32.578 −33.685

−12.055 −12.341 −12.650 −12.974 −13.306 −13.373 −13.643 −13.988 −14.338 −14.689 −15.034 −14.370 −15.689 −15.987 −16.009 −16.009 −15.238 −14.342 −12.841

The thermodynamic values for FeSb2 listed in Table 14 rely on the Gibbs-energy measurements of Geiderikh et al. and the heat-capacity measurements of Grønvold et al.4,195 The results of Geiderikh et al. have also been used to calculate thermodynamic properties for FeSb (Table 15), along with the adjusted heat-capacity data of Perring et al.28 The level of uncertainty is greater for the values in Table 15, due to the impact of changing stoichiometry and the need for confirmation of the heat-capacity measurements. The Co−Sb system (Figure 8) is similar to Fe−Sb. The β phase is a CoSb solution, with a stoichiometry range centered around the 1:1 ratio.294 The solubility range of β at lower temperatures is controversial.204 γ is CoSb2, with a solid-state transformation and a possible metal-excess solid-solution region. An additional compound is δ (CoSb3). Heat-capacity measurements have been reported for β (13−330 and 310−

(11)

(12)

(see ref 166), and ΔG° (kJ/mol) = − 35.400 + 0.0144T

79.82 81.25 82.13 82.83 83.56 84.41 85.47 86.76 88.23 90.17 92.32 94.78 97.55 97.78 97.78 100.65 104.07 105.62

S°T (J/(mol K))

Table 15. Thermodynamic Properties of ε (FeSb)

(see refs 198 and 199) ΔG° (kJ/mol) = − 36.585 + 0.0138T

Cp HT − H298 (J/(mol K)) (kJ/mol)

(13)

(see ref 55). The variation is considerable, although the enthalpies of formation are reasonably consistent with those measured by Boa et al. and by Dynan and Miller.72,194 None of the optimizations seem to make use of the existing heat-capacity data for the two antimonide phases, and the linear ΔG° expressions assume that ΔCp is a constant. M

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Figure 8. Cobalt−antimony phase diagram. Reprinted with permission from ref 294. Copyright 1992 ASM International (www.asminternational. org).

1080 K)9,28 and CoSb2 (800−1236 K);21 Kalishevich et al. report S°298 = 69.6 J/(mol K) for stoichiometric CoSb. Enthalpies of formation in the system were directly determined by Körber and Oelsen (direct-reaction calorimetry,

1073 K),192,193 and Predel and Vogelbein (molten-tin dissolution calorimetry, 1060 K)49 and estimated by Niessen et al.201 Gibbs-energy determinations include EMF studies by Geiderikh and Gerasimov (molten-salt cell, 770−980 K)200 and by Malkin and Pokidyshev (molten salt, 900−1000 K).202 Ipser and co-workers measured activities in β at 1173 K using an isopiestic technique203 and later expanded the approach to a wider temperature range (1108−1364 K).299 Zhang et al.

Table 16. Measured and Estimated Enthalpies of Formation of Cobalt and Nickel Antimonides compd

temp (K)

ΔH° (kJ/mol)

ref

β (CoSb)

850

γ (CoSb2)

298 1000 873 850

δ (CoSb3)

298 873 850

−33.5 −32 −41.8 −53.5 −31.1 −40 −47.7 −33 −55.2 −82.0 −51 −58.6 −32 −58.6 −61 −66.1 −40 −64.6 −77 −68 −95 −63 −78

96, 200 201 192, 193 49 202 204 96, 200 201 192, 193 49 204 96, 200 200 192, 193 204 192, 193 201 49 205 204 205 204 204

873 NiSb

Ni3Sb NiSb2

298 800 873 800 873 873

Table 17. Thermodynamic Properties of CoSb

N

temp (K)

Cp (J/(mol K))

HT − H298 (J/mol)

ΔH°T (J/mol)

ΔG°T (J/mol)

300 350 400 450 500 550 600 650 700 700 750 800 850 900 903.9 903.9 950 1000 1080

48.29 48.34 49.40 50.57 51.12 51.79 52.63 53.68 54.96 54.96 56.48 58.25 60.28 62.58 62.77 62.77 65.15 67.99 73.11

89 2.536 5.023 7.539 10.081 12.653 15.263 17.920 20.635 20.635 23.420 26.287 29.249 32.320 32.564 32.564 35.512 38.839 44.479

−34.472 −34.555 −34.648 −34.771 −34.928 −35.117 −35.332 −35.565 −35.805 −36.258 −35.199 −34.279 −33.470 −32.749 −32.696 −52.488 −51.925 −51.300 −50.286

−36.920 −37.321 −37.710 −38.086 −38.446 −38.789 −39.114 −39.419 −39.707 −39.707 −38.692 −37.821 −37.068 −36.414 −36.367 −36.367 −34.862 −33.268 −30.850

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Figure 9. Nickel−antimony phase diagram. Reprinted with permission from ref 294. Copyright 1992 ASM International (www.asminternational. org).

performed a CALPHAD-style optimization of the system,204 obtaining results similar to some of the experimentally obtained values. Table 16 compares measured and predicted enthalpies of formation for the three cobalt antimonides; as can be seen, the disagreement is considerable. However, the results of Geiderikh and Gerasimov show sufficient internal consistency to justify adoption. Table 17 shows calculated values of the enthalpy and Gibbs energy of formation for CoSb, obtained using the results of Geiderikh and Gerasimov and the heat-capacity measurements of Perring et al.,28 corrected as previously described. The Gibbs energies of formation can be compared with the result determined at 1173 K by Hanninger et al. (−37.4 kJ/mol).299 Additional heat-capacity measurements in the system would be desirable, especially for CoSb2 and CoSb3. The Ni−Sb phase diagram (Figure 9) is more complicated than that of Fe−Sb or Co−Sb. As before, the monoantimonide is a solid solution with a substantial range, and the diantimonide NiSb2 has minimal nonstoichiometry and a congruent decomposition temperature. Ni and Sb also form a series of lower antimonide solid solutions, with nominal Ni3Sb, Ni7Sb3, and Ni5Sb2 stoichiometries. As is the case with Co−Sb, heat-capacity measurements in the system are rare, limited to measurements of Ni5Sb2 (800−1500 K)21 and NiSb (310− 1080 K).28 Enthalpies of formation were investigated or estimated by the same groups that studied the Co−Sb system.49,192,193,201 The results from both experimental investigations suggest that the enthalpies of formation of NiSb2, Ni3Sb, Ni7Sb3, or Ni5Sb2 from NiSb and elemental nickel or antimony are very close to zero. However, specific determinations of ΔH° for these other compounds are ambiguous at best. Two phase-diagram optimizations have

also been reported.205,206 Table 16 includes reported values of ΔH° for NiSb in addition to those for cobalt antimonides. Komarek and co-workers used an isopiestic technique to measure activities of antimony in the NiSb field between 975 Table 18. Heat-Capacity Coefficients for PGM Antimonides (J/(mol K)) compd

temp (K)

a

b × 10−3

PdSb PdSb2 β-Pd3Sb α-Pd3Sb PtSb2

463−873 473−775 473−1173 1213−1275 373−873

44.75 61.51 63.25 134.85 70.55

16.818 35.89 52.14 10.362

c × 105

ref

−44.12

17, 109 17, 109 17, 109 109 17, 109

and 1375 K;203,207 Huang et al. performed similar experiments at 1173 K.208 None of these results are sufficient to calculate the thermodynamic properties of nickel antimonides, although the optimization results can be used to predict these properties. While the phase diagrams for platinum-group-metal (PGM)−antimony systems are well-known,209 thermodynamic information about them is not. The specific heats of PdSb (463−873 K), PdSb2 (473−873 K), and Pd3Sb (473−1273 K) were measured by Poppema and Jaeger using drop calorimetry. The results were similar to those predicted by the Neumann− Kopp law.16,109 This was not the case for PtSb2 (373−873 K), also studied by Poppema and Jaeger.17,109 Heat-capacity expression coefficients are summarized in Table 18. Lowtemperature heat-capacity results include those of Kundrotas and Dargys for PtSb2 (4.2−300 K).10 Darby et al. measured the enthalpies of formation at 298 K (molten-tin solution calorimetry) of PdSb (−94.930 kJ/mol) and PdSb 2 (−116.828 kJ/mol).210 A CALPHAD optimization of the O

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Figure 10. Copper−antimony phase diagram. Reprinted with permission from ref 294. Copyright 1992 ASM International (www.asminternational. org).

Pd−Sb system by Han and Li calculated ΔH° values of −95.314 and −112.572 kJ/mol for these compounds, respectively.211 Otherwise, nothing about the thermodynamic properties of these compounds is known.

results for Ag3Sb (250−600 K,27 123−573 K14), AuSb2 (423− 723 K,216 423−623 K,26 373−723 K,64 250−630 K27), Cu2Sb (373−673 K,14 290−463 K,13 800−1500 K21), and Cu3Sb (373−573 K,14 290−463 K13). It is not certain if the lower temperature results for “Cu2Sb” are for the η or δ phase, since both were obtained before the phase diagram was fully determined. The same concern applies to the results for Cu3Sb and to measurements on “ε” (Cu0.81Sb0.19) reported by Wallbrecht et al.27 The measurements of Wallbrecht et al. for Ag0.9Sb0.1 are outside the stoichiometry range for ξ. Kleppa used molten-tin solution calorimetry to determine enthalpies of formation in the Ag−Sb, Au−Sb, and Cu−Sb systems at 723 K.43,45,46 Biltz and Haase used direct-reaction calorimetry to determine ΔH° for Cu3Sb at 298 K,38 and other direct measurements of ΔH° for AuSb2 have been reported by Biltz et al. (direct-reaction calorimetry, 298 K),217 Jena and Bever (molten-tin calorimetry, 623 K),40 Anres et al. (directreaction calorimetry, 916 K),64 and Hayer and Castanet (metalsolution calorimetry, 298 K).218 Measurements of ΔG° in the three systems are limited to EMF studies using a molten-salt electrolyte. Vecher and Gerasimova looked at Cu−Sb alloys (Cu electrode, 643−883 K),219 determining ΔH° and ΔG° for Cu2Sb. Results in the Cu−Sb system were also reported by Wetscher and Gerassimow (Cu electrode, 673−873 K).220 The Ag−Sb system was studied by Lukashenko et al. (Ag electrode, 573−673 K),221 Verduch and Wagner (Sb electrode, 473−648 K),93 and Weibke and Efinger (Sb electrode, 673−773 K);94 Weibke and Efinger looked at ξ compositions as well as ε. Weibke and Schrög (Sb electrode, 585−626 K) looked at twophase Au−Sb alloys.95 Given the limited results and the lack of low-temperature data, the most popular way of determining thermodynamic

11. GROUP 11 Antimony is often found in nature in mineral phases with copper, gold, and/or silver, and this was the original source of interest in antimonide compounds with these metals. More recently, the development of lead-free solders has resulted in numerous alloys containing these elements,212,213 making the thermodynamic characterization of these systems more significant. As a result, much more is known about the properties of antimonide phases in the three systems, and numerous reviews have been published.212,214,215 The Cu−Sb phase diagram (Figure 10) is the most complex of the three. It includes an extensive Cu-base solid solution, as well as six intermetallic phases. Only two of the intermetallic phases are stable at room temperature. η is a metal-excess Cu2Sb, stable below 858 K; δ is nominally Cu9Sb2, stable below 735 K. Other phases stable over smaller temperature ranges include γ (Cu11Sb2; 673−761 K), ζ (Cu3.3Sb; 513−663 K), ε (Cu3Sb; 633−719 K), and β (Cu3Sb; 713−956 K). (Different letters were assigned to the phases by Teppo and Taskinen.215) The Ag−Sb phase diagram features two intermetallic phases. ε (Ag0.744−0.780Sb0.220−0.256, nom. Ag3Sb) is stable below 836 K, and ξ (Ag0.910−0.839Sb0.090−0.161, nom. Ag6Sb) is stable below 974 K. Only one intermetallic compound exists in the Au−Sb system; AuSb2 is a line compound, stable below 732 K. None of the reported heat-capacity measurements in the Ag−Sb, Au−Sb, and Cu−Sb systems use low enough temperatures to calculate compound entropies. These include P

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properties for intermetallic phases in the Ag−Sb, Au−Sb, and Cu−Sb systems has been optimization using existing thermodynamic data and the phase boundaries in the accepted phase diagrams. Three such optimizations have been published which include the Ag−Sb system;222−224 four include the Au− Sb system,214,223,225,226 and three others the Cu−Sb system.212,215,227,228 Tables 19 and 20 compare the reported standard enthalpies and Gibbs energies of formation of intermetallic phases in the three systems from both experimental and modeling determinations. In the Ag−Sb systems, the optimization results of Oh et al. and Zoro et al. are similar and likely the most accurate. The enthalpies of formation of AuSb2 calculated by optimization are more negative than those determined experimentally, although the difference is not substantial; the values proposed by Liu et al. might be slightly more accurate.225 For the Cu−Sb system, recommendations are harder to suggest. The optimization results of Teppo andTaskinen refer to a phase diagram missing a stable phase; the results of Liu et al. are more complete, but treat the Gibbs energy of formation of δ (Cu9Sb2) as a constant with respect to temperature, which may not be accurate. The optimization results of Gierlotka and Jendrzejczyk-Handzlik are probably the most accurate.228 What all three optimizations demonstrate is the minimal stability of the copper antimonides.

Table 19. Experimental and Estimated Thermodynamic Properties of Gold and Silver Antimonides method

ΔH° (kJ/mol)

optimization

−28.51222

−28.51 − 0.0257 T

EMF calorimetry (723 K) optimization optimization optimization

−49.4994 −6.1543

−49.49 + 0.0475 T

compd Ag6Sb (ξ)

Ag3Sb (ε)

AuSb2

EMF calorimetry (723 K) EMF EMF optimization optimization calorimetry (273 K) calorimetry (723 K) calorimetry (363 K) calorimetry (298 K) EMF (600 K) optimization (298 K) optimization (298 K) optimization (298 K) optimization (298 K) optimization (298 K)

ΔG° (kJ/mol)

−1.36224 −0.48223 8.05222

−1.36 − 0.0305T −0.48 − 0.0280T 8.05 − 0.0291T

−6.67221 −1.8443

−6.67 − 0.0216T

−19.5894 −6.6493 −1.35224 −1.65223 −13.0540

−19.58 + 0.00135T −6.64 − 0.0194T −1.35 − 0.0181T −1.65 − 0.0153T

−9.4145 −14.68217 −5.40218 −20.00 −16.23214 95

−19.09214 −16.61223 −14.82225 −16.23226

−20.00 + 0.191T −6.55 + 0.00697T 0.00062T ln T −6.55 + 0.00697T 0.00062T ln T −17.17 + 0.0208T 0.00186T ln T −16.29 + 0.0384T 0.00491T ln T −16.66 + 0.0163T 0.0014T ln T

12. GROUP 12 Zinc and cadmium antimonides are semiconductors, which has led to a higher level of interest in these compounds than other antimonides. The Zn−Sb phase diagram (Figure 11) is the most complex of the three and the most controversial.229 All of the compounds in the system have a small solid solubility range, and the number of crystalline forms of Zn4Sb3 and their transition temperatures is still not certain.212,230 It is thought that the true stoichiometry of this phase might be Zn6Sb5 or Zn13Sb10;295 since the existing thermodynamics presume the Zn4Sb3 formula, it will be used here. The only stable phase in the Cd−Sb system is the stoichiometric compound CdSb; metastable Cd3Sb2 and Cd4Sb3 (Cd13Sb10) have been the object of some interest.231,296 There is no stable mercury antimonide. The only subambient measurement of heat capacities in the two systems is that of Danilenko et al. (55−300 K),8 who determined S°298 for CdSb (72.254 J/(mol K)) and ZnSb (70.037 J/(mol K)). High-temperature measurement of Cp is limited to the results of Caillat et al. (Zn4Sb3, 298−650 K) and Schimpff (ZnSb, 292−463 K).13,232 Direct measurements of ΔH° in the two systems were made by Biltz and Haase (CdSb and Cd3Sb2, aqueous-solution calorimetry),38 Skoropanov et al. (CdSb, molten-tin solution calorimetry),51 Oelsen and Middel (ZnSb, direct-reaction calorimetry),233 Shchukarev et al. (ZnSb and Zn3Sb2, acid-solution calorimetry),34 and Stolyarova (ZnSb, direct-reaction calorimetry).234 Most of the direct measurements of ΔG° in the two systems use EMF cells with molten-chloride electrolytes and cadmium or zinc electrodes, but the relative volatility of elemental Cd and Zn makes the use of vapor-pressure measurement possible as well. EMF studies in the Cd−Sb system include those of Goncharuk and Lukashenko (493−593 K),235 Zabdyr (640− 710 K),236 Vinokurova et al. (655−803 K),231 Seltz and coworkers (666−719 K),237,238 Ö lander (acetic acid electrolyte, 523 K),239 Kutsenok et al. (aqueous sulfate electrolyte, 293− 348 K),240 and Klebanov et al. (493−623 K).241 Measurements of the vapor pressure of Cd(g) generated by decomposing CdSb include those of Silvestri (dew-point technique, 560−721

+ − − − −

Table 20. Experimental and Estimated Thermodynamic Properties of Copper Antimonides compd

method

ΔH° (kJ/mol)

γ (Cu17Sb3)

calorimetry (723 K) optimization optimization optimization optimization optimization optimization optimization optimization optimization optimization calorimetry (723 K) EMF (773 K) EMF (775 K) optimization optimization calorimetry (773 K) EMF (773 K) EMF (775 K) optimization optimization optimization

−0.2746 −2.68212 −0.208215 −2.845227,228 −1.20215 −5.83228 −4.72212 −2.31215 −5.513227,228 4.94212 −5.283227,228 0.64046 0.920220 1.05219 0.438212 1.800228 −4.2346 −4.5220 −4.60219 −4.35212 −5.04215 −4.753227,228

δ (Cu4Sb) ς (Cu10Sb3)

ε (Cu3Sb) β (Cu3Sb)

η (Cu2Sb)

ΔG° (kJ/mol) −2.68 − 0.0018T −0.208 − 0.00494T −2.845 − 0.00155T −1.20 − 0.00423T −5.83 + 0.00114T −4.72 − 0.00169T −2.31 − 0.00465T −5.513 − 0.00005T 4.94 − 0.00094T −5.283 − 0.00083T 0.920 − 0.00972T 1.05 − 0.00995T 0.438 − 0.00898T 1.800 − 0.0106T −4.50 − 0.00369T −4.60 − 0.00383T −4.35 − 0.00389T −5.04 − 0.00289T −4.753 − 0.0033T Q

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Figure 11. Zinc−antimony phase diagram. Reprinted with permission from ref 294. Copyright 1992 ASM International (www.asminternational.org).

K),76 Borg (Knudsen effusion, 549−652 K),70 and Evseeva et al. (Knudsen effusion, 543−650 K).242 The literature up to 1980 was reviewed by Ansara and Bernard.243 In the Zn−Sb system, EMF studies include those of Lukashenko and co-workers (600−773 K),133,244−246 DeWitt and Seltz (753−993 K),247 Zabdyr (515−823 K),248 and Goryacheva and Geiderikh (glycerol electrolyte, 380−480 K).249 The vapor pressure of zinc generated by decomposing ZnSb was measured by Hirayama (Knudsen effusion, 658−745 K).74 Thermodynamic optimizations of the system were reported by Zabdyr,250 Liu et al.,212 Li et al.,230 and Liu and Tedenac;251 only the first two are consistent with the current phase diagram. Table 21 compiles reported data for the enthalpies and Gibbs energies of formation of cadmium and zinc antimonides from the solid elements. For CdSb and ZnSb, the results are in good agreement, with the exception of acid-solution calorimetry measurements for ZnSb.34 Using the low-temperature heatcapacity results to calculate ΔS°298 yields values of −24.961 (CdSb) and −17.012 (ZnSb) J/(mol K), which are more negative than the values predicted from the ΔG° expressions in Table 21. For other zinc antimonides, the compiled data are more scattered, with the optimization results in particular differing from many of the experimentally obtained values. Some of this may result from confusion over which antimonide phase was stable at a given temperature during experiments; lack of precise data for the phase diagram may also play a role. As a result, no recommended thermodynamic values are tabulated. Reliable high-temperature heat-capacity data for all the solid compounds would be especially useful for resolving these issues.

13. GROUP 13 Although there are few stable antimonide compounds in this group, they are the best known (and most studied) of the entire collection. AlSb, GaSb, and InSb are semiconductors, widely used in infrared detectors and guidance systems and thermal imaging equipment. Their thermodynamic properties have been extensively studied and previously reviewed.103,252,253 As a result, a complete review is not needed here. Figure 12 shows the In−Sb phase diagram, which is similar to the Al−Sb and Ga−Sb phase diagrams. It features a single congruently melting monoantimonide, with no solid solubility range or phase changes. The B−Sb system has no stable compound; BSb has been prepared only under high pressure or as thin films. There are three stable thallium antimonides: TlSb2, a high-thallium (∼Tl11Sb) solid solution, and TlSb, stable only between 464 and 468 K. Very little is known about them. The number of calculations of the thermodynamic properties of AlSb generated by modeling or optimization is greater than the number of experimental determinations. However, the experimental and predicted results vary considerably. The most reliable experimental results are heat-capacity measurements. Two low-temperature studies produced virtually identical values of S°298 (64.2 and 63.9 J/(mol K)).6,254 The results of three high-temperature Cp measurements are also very similar.19,20,255 Table 22 includes S°T for AlSb, calculated using the results of Yamaguchi et al. and Malkova et al.6,255 Using the entropy for the elements calculates entropies of formation for AlSb of −9.87 J/(mol K) at 298.15 K and −13.92 J/(mol K) at 800 K. Two experimental determinations of ΔH° have been made for AlSb: Martosudirdjo and Pratt (precipitation calorimetry from molten tin, 527 K)47 and Yamaguchi et al. (solution R

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mol, 107 −81.26 kJ/mol, and −50.0 kJ/mol. 106 Finally, thermodynamic optimizations have produced still more estimates of ΔH°298.15: −48.96 kJ/mol,259 −49.58 kJ/mol,260 −81.26 kJ/mol,137 −73.50 kJ/mol,261 and −65.8 kJ/mol.106 Obviously, this is not a settled issue. Several of the estimating techniques have produced values of ΔG° as well as ΔH° for AlSb, and these can be used to calculate entropies of formation: −33.1 J/(mol K)107 and −31.69 J/(mol K)137 at 800 K and −36.15 J/(mol K) at 298.15 K.261 The experimental measurements of ΔG° also produced values of ΔS° at 773 K (−26.78 J/(mol K))258 and at 800 K (−14.39 J/ (mol K)).256 Only the latter of these is similar to that calculated using the heat-capacity measurements in Table 22. As a result, the EMF measurements of Samokhval and Vecher seem like the best choice to use along with the heat-capacity results to calculate ΔH° and ΔG° for AlSb. These calculated values are listed in Table 22. Whether they are more accurate than the long list of other recommended values is uncertain, but they may be more consistent. The only low-temperature measurement of Cp for GaSb is that of Piesbergen,254 which established S°298 = 76.06 J/(mol K). Above-ambient measurements include those of Kochetkova and Rezukhina (293−1000 K),262 Cox and Pool (298−985 K),19 Yamaguchi et al. (800−991 K),12,22 Lichter and Sommelet (298−985 K),20 and Malkova et al. (298−798 K).255 The results of the last two investigations are nearly identical and are used in Table 23 to calculate S°T for the compound. On the basis of these values and the entropies of elemental antimony tabulated in Table 1, ΔS°298.15 = −10.19 J/ (mol K). Direct measurements of ΔH° for GaSb were made by Sharifov et al. (direct-reaction calorimetry, 298 K),61 Schottky and Bever (molten-tin solution calorimetry, 298 K),50 and Yamaguchi et al. (molten-tin solution calorimetry, 773 K).39 A first-law calculation yields ΔH°298 for all three studies: −44.78, −41.59, and −45.33 kJ/mol, respectively. The review of Vasil’ev and Gachon recommended a value of −42.0 kJ/mol.106 Direct measurements of ΔG° for GaSb have been made by using an EMF cell and by measuring the vapor pressure of Sb4 generated by the decomposing compound. The EMF study (molten-salt electrolyte, Ga electrode, 380−460 K) calculated ΔG°298 = −41.00 kJ/mol and ΔS°298 = −10.88 J/(mol K).263 Vapor-pressure results reported in 1959 determined ΔG°900 = −23.91 kJ/mol and ΔS°900 = −39.19 J/(mol K) for formation from Ga(l) and Sb(s); this compares to ΔS°900 = −31.19 calculated using the data in Tables 1 and 2.86 More recent vapor-pressure measurements determined a constant value of ΔS° = −31.08 J/(mol K) at temperatures below the melting point of antimony.85 Two phase-diagram assessments have been performed for the Ga−Sb system;103,105 from these, calculated values of ΔG°298 equal to −44.54 and −38.53 kJ/ mol, respectively, were determined (ΔH°298 = −41.35 and −41.79 kJ/mol, and ΔS°298 = −10.70 and −10.95 J/(mol K)). The values listed in Table 23 are derived from the heat-capacity measurements of Piesbergen and Malkova et al.254,255 and the enthalpy of formation measured by Schottky and Bever.50 These seem to provide the most consistency with other estimates of ΔG°. Piesbergen’s low-temperature investigation is also the only source of experimentally obtained results for S°298 for InSb (86.18 J/(mol K)).254 Five comprehensive high-temperature heat-capacity measurements have been reported;12,19,20,22,23,255 again, the results of Lichter and Sommelet and Malkova et al. agree within 1%. Table 24 lists entropy values for InSb using

Table 21. Experimental and Estimated Thermodynamic Properties of Cadmium and Zinc Antimonides (Reference State (Cd,Zn)(s), Sb(s)) compd CdSb

ZnSb

αZn4Sb3

Zn4Sb3 (δ)

αZn3Sb2

βZn3Sb2

method

ΔH° (kJ/mol)

ΔG° (kJ/mol)

EMF EMF EMF EMF EMF vapor pressure vapor pressure vapor pressure calorimetry assessment EMF phase diagram EMF EMF EMF EMF EMF vapor pressure calorimetry calorimetry optimization optimization optimization EMF EMF EMF optimization optimization optimization optimization

−10.44 −20.66 (293 K)240 −7.782239 −7.49236 −8.42237 −2.15 (553 K)242

−10.44 + 0.00312T −20.66 + 0.0197T −7.782 + 0.00074T −7.49 + 0.00056T −8.42 + 0.00055T

optimization optimization EMF EMF EMF optimization optimization calorimetry optimization optimization optimization EMF EMF EMF

235

−6.8670

−6.86 + 0.00030T

−13.96234

−13.96 + 0.0129T

−6.2838 −6.67243 −17.29244 −18.41247 −15.68246 −19.10245 −16.46248 −21.80249 −17.15133 −19.0074

−6.67 + 0.000837T −23.80 + 0.00109T −18.41 + 0.00318T −15.68 − 0.00016T −19.10 + 0.00452T −16.46 + 0.00062T −21.80 + 0.00640T −17.15 + 0.00209T −19.00 + 000440T

−12.80234 −74.4734 −22.918230 −22.976251 −22.485212 −41.72245 −32.97246 −36.96248 −65.646230 −65.571251 −54.11212 −51.44212

−22.918 + 0.00927T −22.976 + 0.00883T −22.485 + 0.010T −41.72 − 0.0136T −32.97 − 0.0273T −36.96 − 0.0200T −65.646 + 0.00210T −65.571 + 0.0143 T −54.11 −51.44 − 0.0035T

−23.744230 −51.485251 −54.787247 −74.900249 −5.32248 −25.21212 −30.439251 −200.8234 −29.51212 −27.750230 −25.717251 −6.94248 −0.213247 −13.14245

−23.744 − 0.133T −51.485 − 0.0051T −91.665 − 0.00682T −74.900 + 0.0322T −5.32 − 0.0612T −25.21 − 0.0137T −30.439 −0.0101T −29.51 − 0.0169T −27.750 − 0.0250T −25.717 − 0.0172T −6.94 − 0.0388T −0.213 − 0.0513T −13.14 − 0.0338T

calorimetry in molten gallium, 773 K).6 Vecher and co-workers published two EMF studies of ΔG° for AlSb, one using a CaF2 solid electrolyte (778−895 K)256,257 and the other a moltenchloride electrolyte (663−889 K).258 Using eq 2, the literature heat capacity of aluminum, and the heat capacity of AlSb reported by Malkova et al.,255 the experimental results can be used to calculate ΔH°298 values of −49.91 kJ/mol,47 −57.53 kJ/ mol,6 −51.52 kJ/mol,256 and −62.78 kJ/mol.219 The phase diagram has been combined with measured activities in the liquid to produce other estimates: −65.8 kJ/mol,253 −82.0 kJ/ S

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Figure 12. Indium−antimony phase diagram. Reprinted with permission from ref 294. Copyright 1992 ASM International. (www.asminternational. org).

Table 22. Thermodynamic Properties of AlSb

Table 23. Thermodynamic Properties of GaSb

temp (K)

C°P (J/(mol K))

S° (J/(mol K))

ΔH° (kJ/mol)

ΔG° (kJ/mol)

temp (K)

C°p (J/(mol K))

S° (J/(mol K))

ΔH° (kJ/mol)

ΔG° (kJ/mol)

298.15 300 400 500 600 700 800 900 903.9 903.9 933.6 933.6 1000 1100 1200 1300 1330

46.45 46.49 48.39 49.66 50.69 51.60 52.45 53.27 53.30 53.30 53.54 53.54 54.06 54.84 55.61 56.37 56.59

63.90 64.19 77.85 88.79 97.94 105.82 112.77 118.99 119.22 119.22 120.95 120.95 124.65 129.83 134.64 139.12 140.41

−51.156 −51.162 −51.436 −51.738 −52.152 −52.713 −53.438 −54.338 −54.376 −74.168 −74.474 −85.268 −85.888 −86.756 −87.547 −88.262 −88.462

−48.218 −48.200 −47.168 −46.067 −44.895 −43.642 −42.298 −40.852 −40.794 −40.794 −39.692 −39.692 −36.429 −31.441 −26.376 −21.249 −19.701

298.15 300 302.9 302.9 400 500 600 700 800 900 903.9 903.9 981

48.49 48.52 48.56 48.56 49.98 51.24 52.43 53.59 54.72 55.85 55.89 55.89 56.75

76.06 76.36 76.83 76.83 90.53 101.82 111.26 119.43 126.66 133.17 133.42 133.42 138.03

−41.587 −41.593 −41.604 −47.195 −47.542 −47.760 −47.917 −48.050 −48.178 −48.308 −48.313 −68.105 −68.215

−38.549 −38.531 −38.510 −38.510 −35.627 −32.600 −29.539 −26.456 −23.356 −20.240 −20.115 −20.115 −16.013

Table 24. Thermodynamic Properties of InSb

the values for the elements and the heat-capacity measurements of Piesbergen and Malkova et al. The calculated entropy of formation at 298.15 K is −17.04 J/(mol K). Enthalpies of formation of InSb have been measured by direct-reaction calorimetry (−28.450 kJ/mol at 298.15 K)54 and by molten-tin solution calorimetry (−29.789 kJ/mol at 78 K,41,42 −36.000 at 723 K,44 −29.035 at 275 K,50 and −34.100 at 298.1539). Several investigators used EMF measurements to determine ΔG° for solid InSb: • Nikol’skaya et al. (molten-chloride electrolyte, 663−763 K)96,264

temp (K)

C°p (J/(mol K))

S° (J/(mol K))

ΔH° (kJ/mol)

ΔG° (kJ/mol)

298.15 300 400 429.78 429.78 500 600 700 800

49.86 49.90 51.68 52.10 52.10 52.97 54.05 55.04 55.99

86.21 86.51 101.13 104.86 104.86 112.81 122.56 130.97 138.38

−30.400 −30.395 −30.546 −30.629 −33.891 −34.072 −34.314 −34.560 −34.822

−25.321 −25.280 −23.463 −22.915 −22.915 −21.073 −18.416 −15.722 −12.995

• Terpilowski and Trzebiatowski (molten-bromide electrolyte, 638−765 K)265 T

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• Abbasov and Mamedov (KCl in glycerol electrolyte,

this review due to their properties being similar to those of previously discussed compounds. Sb2S3 is known either as antimonite or as stibnite.275−277 It has a negligible solid solubility range and melts somewhere between 819 and 832 K. As a naturally occurring antimony mineral and a ferroelectric semiconductor, it has attracted considerable interest and has an extensive history of thermodynamic research.276,277 Most of the database consists of heat-capacity and ΔH° measurements and is not always in agreement. The most recent low-temperature study is that of Gurevich et al. (21−338 K);277 this used a lower starting temperature than previous studies and produced more reliable results. One controversy in the study of Sb2S3 is the claim of a solid-state transformation at 310−320 K;276 this transformation has been observed in some calorimetric studies, but the difference between the high- and low-temperature structures has not been described. Gurevich et al. observed no such transition and suggested that previous claims were the result of “structural defects” in the samples used by others. The calculation of thermodynamic properties for Sb2S3 made here presumes that this is correct; however, a better explanation of the differing results would be of value. The value of S°298.15 obtained by Gurevich et al. is 176.68 J/(mol K). Several high-temperature Cp measurements for Sb2S3 have been reported.276−279 There is disagreement in the results, possibly due to the enthalpy of sublimation of the compound. As a result, the data above 600 K are somewhat suspect. Gurevich et al. found that the results of Seal et al. matched most closely with their low-temperature data and were able to produce a smooth curve of heat capacity against temperature by slightly changing the constant value in the high-temperature heat-capacity expression:

663−763 K)266 • Vassiliev et al. (molten-chloride electrolyte, 640−800 K)267 Adjusted to 298.15 K using the entropies of the elements and that for InSb, the results of these measurements produce entropies of formation of −13.38, −18.45, −25.26, and −16.01 J/(mol K), respectively. Three assessments using the In−Sb phase diagram and measured activities in the liquid solutions have also been used to calculate thermodynamic properties for InSb.103,104,225 ΔS°298.15 calculated from these results to be equal to −16.02, −17.98, and −15.94 J/(mol K), respectively. Some of these are close to the experimentally obtained value of −17.04 J/(mol K), but none are close enough to achieve internal consistency. Values of ΔH°298.15 obtained from the EMF studies and optimizations range between −29.185 and −37.571 kJ/mol.104,264 Given the scatter of the experimentally obtained data, the value of ΔH°298.15 recommended by Vasil’ev and Gachon (−30.400 kJ/mol) seems like an appropriate choice. Table 24 lists the thermodynamic properties of InSb, calculated using this recommendation and the heat-capacity measurements of Piesbergen and Malkova et al.254,255 The value of ΔG° for solid InSb at the melting point (800 K) is −12.995 kJ/mol; the range of values calculated from other results goes from −10.322 to −21.044 kJ/mol.104,260,266,268

14. GROUP 14 The only element in this group that forms a stable intermetallic phase with antimony is tin. The tin−antimony phase diagram is controversial; the most current experimental results suggest that there are two stable intermetallic phases. The first is a sold solution known as β, with the ambient-temperature composition range Sn0.372−0.53Sb0.47−0.628.269 The second is the stoichiometric Sn3Sb2, stable to 596 K. Other assessments of the system disagree, particularly concerning the stability of Sn3Sb2.227,270 The thermodynamic properties of β (often described as SnSb) were first determined by thermodynamic optimization of the phase diagram, presuming a stable Sb2Sn3 compound.271 Subsequently, Badawi and Eid used direct-reaction calorimetry to determine the enthalpies of formation of β across the composition range; values range from −2.200 kJ/mol (XSb = 0.550) to −3.724 kJ/mol (XSb = 0.433) at 298.15 K and from −2.324 to −3.970 kJ/mol at 483.15 K.272 More recently, Vasil’ev measured the Gibbs energies of formation of various β2 compositions via an EMF cell using a molten-salt electrolyte.273 The most negative values of ΔG° occurred at approximately XSb = 0.531 (Sn15Sb17). At this composition, ΔG° (kJ/mol) = −4.741 + 0.002813T for the formation of Sn0.469Sb0.531 from solid antimony and liquid tin. Optimizations have also been performed by Chen et al.227,269 and by Kroupa and Vizdal.270

Cp,Sb2S3 = 166.82 − 0.0031T + 645000T −2 − 911T −0.5 (14)

Seal et al. have reviewed the existing database for measurements of Gibbs energy and enthalpy of formation of stibnite.278 Several measurements have been reported for the ratio of H2S to H2 in equilibrium with Sb2S3 and elemental antimony. The partial pressure of S2 in equilibrium with Sb2S3 and Sb has also been measured, and this can be used to calculate ΔG° and ΔH° for the compound. Two experimental measurements of ΔH° have also been reported: Johnson et al.279 using fluorine combustion calorimetry and Bryndzia and Kleppa275 using direct-reaction calorimetry. ΔH°298.15 values calculated from these results show extensive disagreement, ranging from −129.7 to −205.0 kJ/mol. The experimental measurements of ΔH° are less exothermic than those calculated from gas-equilibration results. Seal et al. used the p S 2 measurements to calculate the Gibbs energy of formation of Sb2S3 as a function of temperature; their results generate a value of S°298.15 of 182.0 J/(mol K), different from that measured by Gurevich et al.277 As a result, a table of recommended thermodynamic values for this compound is not generated here. Performing the hydrogen-reduction experiments described earlier (which date between 1902 and 1952) using more accurate measuring techniques might address the discrepancies. The database for solid Sb2Se3 is much smaller. The only subambient study is the heat-capacity measurements (53−300 K) reported by Zhdanov,280 S°298.15 = 212.96 J/(mol K). Pashinkin et al. recently measured the above-ambient (350−

15. GROUPS 15 AND 16 Antimony forms no stable compounds with the other group 15 elements (As, Bi, N, P), but it does form stable Sb2M3 compounds with selenium, sulfur, and tellurium. Two other marginally stable intermetallic phases exist in the Sb−Te system:274 δ (Sb0.633−0.836Te0.164−0.367) and γ (Sb0.510−0.589Te0.411−0.490). While these are technically chalcogenide compounds rather than antimonides, they are included in U

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Metal-solution calorimetry has been used to determine ΔH° for Sb2Te3 by Howlett et al. (bismuth solvent, 623 K) and Vecher et al. (tin solvent, 700 K).52,288 Vecher et al. provide a value of −60.665 kJ/mol, without providing a temperature; Howlett et al. list −56.481 kJ/mol at 273.15 K. EMF techniques have also been used to measure ΔG° for Sb2Te3: Gerasimov and Nikol’skaya (molten-salt electrolyte, 653−693 K),96,289 Semenkovich and Melekh (molten-salt electrolyte, 530−560 K),284 and Mallika and Sreedharan (yttria-stabilized zirconia, 588−722 K).290 Boncheva-Mladenova et al. measured the partial pressures of Sb4 and Te2 generated by decomposition (697−819 K).69 The most recent data for the compound result

600 K) heat capacity, improving on previous results of Blachnik and Schneider:281,282 Cp,Sb2Se3 (J/(mol K)) = 125.01 + 0.0177T − 360000T −2 (15)

Measurements of the total vapor pressure over solid Sb2Se3 are difficult to use, since the vapor generated is a mixture of several species;172,283 however, Semenkovich and Melekh Table 25. Thermodynamic Properties of Sb2Se3 temp (K)

C°p (J/(mol K))

S° (J/(mol K))

ΔH° (kJ/mol)

ΔG° (kJ/mol)

298.15 300 400 494.3 494.3 500 600 700

126.24 126.32 129.84 132.29 132.29 132.42 134.63 136.67

212.96 213.75 250.61 278.69 278.69 279.77 303.71 324.19

−127.594 −127.593 −127.577 −127.335 −146.211 −146.385 −149.180 −151.684

−126.044 −126.035 −125.520 −125.023 −125.023 −124.778 −120.187 −115.154

Table 27. Thermodynamic Properties of Sb2Te3

performed an EMF study (molten-chloride electrolyte, 430− 485 K),284 and Howlett et al. used solution calorimetry in molten bismuth (623 K) to determine ΔH°273.15.52 The calculated enthalpies of formation at 298.15 K resulting from the two studies (−134.7 and −127.6 kJ/mol, respectively) are roughly similar; however, ΔS°298.15 calculated from the EMF study (−16.7 J/(mol K)) is significantly different from that calculated using the ambient-temperature entropies of Sb2Se3 and the elements (−5.2 J/(mol K)). As a result, the heatcapacity results of Zhdanov and Pashinkin et al. are combined with the enthalpy of formation reported by Howlett et al. to calculate the thermodynamic properties of Sb2Se3 listed in Table 25. The low-temperature heat-capacity work of Zhdanov yielded S°298.15 for Sb2Te3 of 246.42 J/(mol K).285 High-temperature heat-capacity measurements for the solid phase have been reported by Howlett et al.,52 Medzhidov,286 and Pashinkin et al.;287 according to the latter

These values are consistent with the low-temperature data of Zhdanov. Table 26. Recalculated Thermodynamic Properties of Sb2Te3 at 298.15 K

Boncheva-Mladenova et al. (vapor pressure)69 Ghosh et al. (CALPHAD)291 Mallika and Sreedharan (EMF)290 Gerasimov and Nikol’skaya (EMF)289 Semenkovich and Melekh (EMF)284 Vecher et al. (molten-tin calorimetry)288 Howlett et al. (molten-bismuth calorimetry)52

ΔG° (kJ/mol)

−52.7

−52.9

0.62

−54.9 −87.8 −56.6

−46.8 −76.9 −59.2

−27.3 −36.79 8.60

−58.3

−61.8

11.75

S° (J/(mol K))

ΔH° (kJ/mol)

ΔG° (kJ/mol)

298.15 300 400 500 600 700

128.65 128.70 131.50 134.30 137.10 139.90

248.55 248.71 266.29 282.62 297.35 310.56

−56.638 −56.636 −56.750 −57.375 −58.574 −60.375

−59.201 −59.217 −60.072 −60.842 −61.433 −61.776

16. CONCLUSIONS AND RECOMMENDATION For the most part, thermodynamic information on the antimonide phase is generated on a need-to-know basis, so the largest database is for antimonides of interest for electronic applications. This is likely to continue, despite recent interest in their potential for battery applications. For the most part, thermodynamic research with antimonides presents no extraordinary experimental challenges and requires only the need for data for a particular system. CALPHAD-style modeling using antimonide phase diagrams and the increasing reliability of thermodynamic predictions made using firstprinciples calculations may eventually make the need for experimental measurements obsolete.

(16)

ΔH° (kJ/mol)

C°p (J/(mol K))

from a CALPHAD assessment by Ghosh et al.291 Table 26 compares listed values of ΔH° and ΔG° from these various sources, recalculated at 298.15 K using the heat capacity of antimony given in eq 2 and the heat-capacity expression developed by Paskinkin et al. (eq 14).287 The results of Mallika and Sreedharan differ significantly from those of the others. Recalculated entropies of formation are also provided in Table 26; the value calculated from the results of Zhdanov and S°298.15 for antimony from Table 1 equals 6.47 J/(mol K).285 The experimental results of Gerasimov and Nikol’skaya show the best internal consistency. Table 27 lists recommended thermodynamic values for Sb2Te3, based on the experimental results of Gerasimov and Nikol’skaya and the heat-capacity measurements of Pashinkin et al. The optimization of the Sb−Te system performed by Ghosh et al. also included estimated values of ΔG° for the δ and γ phases.291 Both of these phases are marginally stable, and their existence and solubility regions are controversial.274

Cp,Sb2Te3 (J/(mol K)) = 120.3 + 0.028T (300−700 K)

investigator

temp (K)

ΔS° (J/(mol K))

AUTHOR INFORMATION Corresponding Author

−60.7

*E-mail: [email protected].

−56.5

Notes

The author declares no competing financial interest. V

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Biography

(24) Glazov, V. M.; Lyusternik, V. E.; Pavlova, L. M.; Pashinkin, A. S. Dokl. Phys. Chem. (Engl. Transl.) 1997, 352, 43; Dokl. Akad. Nauk SSSR 1997, 352, 490. (25) Grønvold, F.; Haraldsen, H. Rev. Chim. Miner. 1976, 13, 516. (26) Itagaki, K. Nippon Kinzoku Gakkishi 1976, 40, 1038. (27) Wallbrecht, P. C.; Blachnik, R.; Mills, K. C. Thermochim. Acta 1981, 45, 189. (28) Perring, L.; Kuntz, J. J.; Bussy, F.; Gachon, J. C. Intermetallics 1999, 7, 1235. (29) Morozova, M. P.; Bol’shakova, G. A.; Lukinykh, N. L. J. Gen. Chem. USSR (Engl. Transl.) 1959, 29, 3112; Zh. Obshch. Khim. 1959, 29, 3144. (30) Morozova, M. P.; Getskina, L.; Golomolzina, M. J. Gen. Chem. USSR (Engl. Transl.) 1959, 27, 1812; Zh. Obshch. Khim. 1959, 27, 1746. (31) Shchukarev, S. A.; Morozova, M. P.; Bortnikova, M. M. J. Gen. Chem. USSR (Engl. Transl.) 1958, 28, 3315; Zh. Obshch. Khim. 1958, 28, 3289. (32) Shchukarev, S. A.; Morozova, M. P.; Kan, K.-I. J. Gen. Chem. USSR (Engl. Transl.) 1957, 27, 1803; Zh. Obshch. Khim. 1957, 27, 1737. (33) Shchukarev, S. A.; Morozova, M. P.; Li, M.-H. J. Gen. Chem. USSR (Engl. Transl.) 1959, 29, 3109; Zh. Obshch. Khim. 1959, 29, 3142. (34) Shchukarev, S. A.; Morozova, M. P.; Sapozhnikov, Yu. P. J. Gen. Chem. USSR (Engl. Transl.) 1956, 26, 321; Zh. Obshch. Khim. 1956, 26, 321. (35) Shchukarev, S. A.; Morozova, M. P.; Li, M.-H. J. Gen. Chem. USSR (Engl. Transl.) 1959, 29, 2427; Zh. Obshch. Khim. 1959, 29, 2465. (36) Shchukarev, S. A.; Morozova, M. P.; Stolyarova, T. A. J. Gen. Chem. USSR (Engl. Transl.) 1961, 31, 1657; Zh. Obshch. Khim. 1961, 31, 1773. (37) Shchukarev, S. A.; Volf, E.; Morozova, M. P. J. Gen. Chem. USSR (Engl. Transl.) 1954, 24, 1887. (38) Biltz, W.; Haase, C. Z. Anorg. Allg. Chem. 1923, 129, 141. (39) Yamaguchi, K.; Takeda, Y.; Kameda, K.; Itagaki, K. Mater. Trans., JIM 1994, 35, 596. (40) Jena, A. K.; Bever, M. B. Trans. Met. Soc. AIME 1968, 242, 1453. (41) Jena, A. K.; Bever, M. B.; Banus, M. D. Trans. Met. Soc. AIME 1967, 239, 725. (42) Jena, A. K.; Bever, M. B.; Banus, M. D. Trans. Met. Soc. AIME 1967, 239, 1232. (43) Kleppa, O. J. J. Phys. Chem. 1956, 60, 846. (44) Kleppa, O. J. J. Am. Chem. Soc. 1955, 77, 897. (45) Kleppa, O. J. J. Phys. Chem. 1956, 60, 858. (46) Kleppa, O. J. J. Phys. Chem. 1956, 60, 852. (47) Martosudirdjo, S.; Pratt, J. N. Thermochim. Acta 1974, 10, 23. (48) Predel, B.; Ruge, H. Thermochim. Acta 1972, 3, 411. (49) Predel, B.; Vogelbein, W. Thermochim. Acta 1978, 24, 155. (50) Schottky, W. F.; Bever, M. B. Acta Metall. 1958, 6, 320. (51) Skoropanov, A. S.; Mechkovskii, L. A.; Vecher, A. A. Russ. J. Phys. Chem. (Engl. Transl.) 1976, 50, 1669; Zh. Fiz. Khim. 1976, 50, 2800. (52) Howlett, B. W.; Misra, S.; Bever, M. B. Trans. Met. Soc. AIME 1964, 230, 1367. (53) Schneider, A.; Klotz, H. Naturwissenschaften 1959, 46, 141. (54) Schneider, A.; Klotz, H.; Stendel, J.; Strauss, G. Pure Appl. Chem. 1961, 2, 13. (55) Boa, D.; Hassam, S.; Kra, G.; Kotchi, K. P.; Rogez, J. CALPHAD: Comput. Coupling Phase Diagrams Thermochem. 2008, 32, 227. (56) Borzone, G.; Borsese, A.; Zanicchi, G.; Ferro, R. J. Therm. Anal. 1982, 25, 433. (57) Borzone, G.; Fornasini, M. L.; Parodi, N.; Ferro, R. Intermetallics 2000, 8, 189. (58) Chua, K. S.; Pratt, J. N. Thermochim. Acta 1974, 8, 409. (59) Ferro, R.; Borzone, G.; Cacciamani, G. Thermochim. Acta 1988, 129, 99.

Mark E. Schlesinger is Professor of Metallurgical Engineering at the Missouri University of Science and Technology, Rolla, MO. His research interests include high-temperature thermochemistry, metals extraction processes, and recycling technology. He is also the author of the monograph Aluminum Recycling and a coauthor of Extractive Metallurgy of Copper (4th and 5th eds.).

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