Thermodynamic properties and Sn-Sb phase diagramкод для вставкиСкачать
Thermodynamic properties and Sn-Sb phase diagram/
20 Russian Journal of Physical Chemistry, Vol. 79, No. 1, 2005, pp. 20–28. Translated from Zhurnal Fizicheskoi Khimii, Vol. 79, No. 1, 2005, pp. 26–35. Original Russian Text Copyright © 2005 by Vasil’ev. English Translation Copyright © 2005 by Pleiades Publishing, Inc. INTRODUCTION Tin–antimony alloys and tin–antimony alloys doped with, for instance, indium are of interest for optoelec- tronics as an alternative to the CdTe–HgTe solid solu- tion. Exact data on the phase diagram, crystal structure, and thermodynamic properties of these alloys are nec- essary for the technology of obtaining semiconducting materials. The available data on the Sn–Sb system are contradictory. There are more than ten variants of the phase diagram of this system [1–14]. Each of these dif- fers from the others in some respect. The reason for this is the special properties of Sn–Sb alloys, namely, the low rate of chemical and phase transformations and the propensity to form metastable states. The question of the phase composition of Sn–Sb alloys therefore remains open in spite of the large number of works on this system. This is especially true of the central part of the diagram in which the β phase exists. We distinguish between three main points of view on the nature of the β phase. Some authors [10, 11, 13] believe it to have a continuous region of solid solutions of a complex conﬁguration which extends from 40 to 65 at. % Sb and to melt incongruently at 698 K ( 425°C ) and 65 at. % Sb. According to other authors [2, 5], there exist two different polymorphs of β phase solid solu- tions, low- and high-temperature. Lastly, it was shown in [5, 8, 14] that the β phase is a set of individual phases separated by heterogeneous mixtures rather than one solid solution, at least at room temperatures. Among the works on the Sn–Sb phase diagrams, we must mention that by Iwasé et al.  (Fig. 1), where the Sn–Sb system was studied by the differential thermal, X-ray phase, and microstructural analysis methods and by electrical resistance measurements using a large number (more than 100) of alloys. The authors of  suggested that there existed a broad region of β solid solutions in the system (43–56 at. % Sb) with a poly- morphic transition at 593–598 K ( 320–325°C ). The compositions of the boundary β phase solutions remain virtually unchanged from room to transition tempera- tures. According to , the Tammann triangles in the left part of the Sn–Sb phase diagram provide convinc- ing evidence of the absence of any intermediate phases between the solid solution of antimony in tin (Sn) and the left boundary of the β phase (43% at. % Sb). On the whole, the phase diagram reported in  differs insigniﬁcantly from than obtained in . The authors of , however, abandoned the suggestion of a polymorphic transition of the β phase but claimed the existence of an aerial Sn 3 Sb 2 phase, which had never A Complex Study of the Phase Diagram of the Sn–Sb System V. P. Vasil’ev Faculty of Chemistry, Moscow State University, Vorob’evy gory, Moscow, 119899 Russia E-mail: VVassiliev@veernet.ru Received December 23, 2003 Abstract —The Sn–Sb system was studied by the electromotive force method and the microstructural, X-ray diffraction, differential thermal, and microprobe analysis methods. Phenomenological crystal chemical models of the β phase were suggested. The models were based on hexagonal polymorph transformation into a quasi- cubic polymorph with a change in crystal symmetry corresponding to a second-order phase transition. The ther- modynamic properties of the system were optimized. CHEMICAL THERMODYNAMICS AND THERMOCHEMISTRY t °, C 600 500 400 300 200 100 Sn 20 40 60 80 Sb (Sn) (Sb) 246° 325° β 1 425° 320° β 2 1 2 3 4 Fig. 1. Phase diagram of the Sn–Sb system according to the ( 1 , 2 ) differential thermal analysis data  [( 1 ) cooling and ( 2 ) heating], ( 3 ) electrical resistance measurements, and ( 4 ) microstructural analysis data. RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY Vol. 79 No. 1 2005 A COMPLEX STUDY OF THE PHASE DIAGRAM OF THE Sn–Sb SYSTEM 21 been mentioned previously. They based their sugges- tion of the existence of Sn 3 Sb 2 solely on the differential thermal analysis data. Alloys with 10–35 at. % Sb gave a double thermal effect between 513 and 523 K. There was, however, no well-deﬁned boundary between these effects. The existence of a Sn 3 Sb 2 phase has not been substantiated by X-ray diffraction thus far. In , the Sn–Sb system was studied by the elec- trical conductivity and thermal and microstructural analysis methods. The regions of primary solid solu- tions of antimony in tin (0–9.8 at. % Sb) and tin in antimony (89.9–100 at. % Sb) were determined. The electrical conductivity curve maxima at 40.4, 49.4, and 55.4 at. % Sb corresponded to ordered phases. Two weak maxima at about 38.7 and 66.7 at. % Sb were also reported. The hypothesis of the discrete character of the β phase with the alternation of narrow homogeneous and heterogeneous regions was substantiated by the X-ray study of the structural parameters of the β phase in the region 42–62 at. % Sb in the Sn–Sb binary system and doped Sn–Sb (+2% In), Sn–Sb (+2% Cd), and Sn–Sb (+1% Te) alloys . For all these alloys, noticeable deviations from the Vegard linear law were observed. The composition dependences of the unit cell volume V cell ( x Sb ) contained regions where the unit cell volume remained constant. Such deviations were especially noticeable for the Sn–Sb and Sn–Sb (+2% In) sys- tems in the interval 50–55 at. % Sb, which was evi- dence of the possible existence of heterogeneous regions in the β phase. This experimental observation was ignored in more recent studies of the phase dia- gram of the Sn–Sb system and ternary systems deriv- ative from it. The Sn–Sb phase diagram in the concentration range 0–25 at. % Sb was studied in  by the differ- ential thermal and X-ray phase analysis methods. The authors did not observe a doublet of thermal effects between 515 and 523 K similar to that reported in . Nevertheless, a comparison of the X-ray patterns of the alloy containing 43.5 at. % Sb obtained at 293 and 573 K led them to suggest that the existence of an aerial Sn 3 Sb 2 phase was possible. The phase with 43.5 at. % Sb was identiﬁed as a face-centered cubic lattice of the NaCl type with the parameter ‡ = 0.613 nm. In , diffusion equilibrium between two pure metals (tin and antimony) was studied at 493 K. Only two intermediate phases of the compositions Sn 4 Sb 3 (42.86 at. % Sb) and Sn 3 Sb 4 (57.14 at. % Sb) were observed; these compositions coincided with the data obtained in  on boundary β phase solutions to within 1%. The purpose of this work was to obtain consistent data on the thermodynamic properties, structure, and phase diagram of the tin–antimony system using our own results obtained by the electromotive force method and the microstructural, X-ray phase, differential ther- mal, and microprobe analysis methods and the litera- ture data. THE X-RAY STRUCTURE AND MICROPROBE ANALYSIS DATA It follows from  that tin crystallizes in at least two modiﬁcations. The α polymorph has a diamond- like structure (space group Fd 3 m ), and the β polymorph has a distorted diamond-like structure ( I 4/ mmm ). The α ⇔ β transition occurs at 287 K ; β -tin has a tet- ragonal unit cell with the parameters a = 0.370 nm and c = 0.370 nm at 299 K. Antimony forms hexagonal arsenic-type crystals with six atoms per unit cell under normal conditions; the space group is P 6/ mmm . The equivalent rhombohe- dral cell (space group R m ) contains two antimony atoms. The hexagonal structure of antimony consists of corrugated layers linked with each other by covalent interactions between atomic planes (Fig. 2). The data on the crystal structure of Sn–Sb alloys taken from various sources are listed in Table 1. The structure of the β phase with various compositions can 3 0.133 c 0.200 c 0.133 c 0.200 c 0.133 c 0.200 c Fig. 2. Shubert projection of the hexagonal antimony cell ; Ò is the hexagonal cell parameter. 22 RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY Vol. 79 No. 1 2005 VASIL’EV be described as either hexagonal or rhombohedral packing. Changes in the hexagonal unit cell parameters from Sb hex to β -SnSb hex occur as a decrease in the Ò parameter from 1.127 (100 at. % Sb) to 1.06 nm (44 at. % Sb), the ‡ parameter remaining virtually con- stant ( ‡ = 0.431 ± 0.001 nm). Without taking into account superstructural reﬂec- tions from the β phase, it can conventionally be described in terms of a NaCl-type face-centered cubic lattice. Ignoring lattice distortions, the a parameter of such a lattice is 0.613 nm. An alloy of the composition 43.5 at. % Sb was stud- ied in  at 300 and 573 K to ﬁnd out whether or not the Sn 3 Sb 2 phase (40 at. % Sb) existed above 523 K. The authors determined the lattice cell parameter of this alloy at 573 K ( ‡ = 0.6130 nm) on the assumption that it was the high-temperature Sn 3 Sb 2 phase with a NaCl-type structure. The unit cell parameters obtained in  for the alloy with 45 at. % Sb at room tempera- ture and the unit cell parameter for the alloy with 43.5 at. % Sb at 573 K  virtually coincided on the assumption that the angle of the cubic unit cell was α = 90° in both structures. Our data on the β phase recalculated in the simpliﬁed approximation of the NaCl and CsCl structures yield parameters that exactly coincide with those reported in [12, 18, 20]. It becomes clear why the authors of  were unable to obtain the high-temperature diffractogram of the alloy containing 40.0 at. % Sb. The appearance of a substantial amount of melt at 573 K interferes with the recording of reliable X-ray patterns of this alloy. As X-ray analysis does not allow us to unambigu- ously distinguish between phases close in structure, we performed a phase analysis of a series of unannealed and annealed Sn–Sb alloys (a total of 25 samples) by the microprobe method. The results are listed in Tables 2 and 3. The measurements were performed for 5–10 points on a polished surface of each sample along its length. The diffusion layer between tin and anti- mony was measured separately. Tin and antimony pol- ished surfaces were brought into contact for two weeks at room temperature. The intermediate layer between pure metals was found to contain phases with 5.59 ± 1, 10.33 ± 1, and 43.92 ± 0.3 at. % Sb. All these data correspond to averaged compositions. MODEL DESCRIPTIONS OF THE β PHASE We suggested structural models of the β phase on the basis of the microprobe and X-ray data. Pure anti- mony and the β phase are structurally similar in many respects. Both crystallographic cells are rhombohedral of the R m type, and both structures can be described as hexagonal packings of periodically arranged six planes along the Ò direction. On the other hand, the β phase can be described as a face-centered quasi-cubic lattice of the NaCl type. Such a face-centered unit cell can also be represented as a rhombohedron with the α angle close to 60 °. 3 Table 1. Structure of tin–antimony alloys Structure typeSb, at. %Systema, nmc, nmα, degRefs. β-Sn (I4/mmm)0.020.3700.337–  (Fm3m) (distorted NaCl type) 43.51(0.613)– –  44.030.4311.06–  45.040.61389.7 (Fm3m) (distorted NaCl type) 50.030.43261.0693– * 40.4352– 59.87 30.86291.0656–  40.61389.7 (Pm3m)50.01(0.4315)– –  (Fm3m)55.040.6150– 89.18 P6/mmm60.030.4311.09–  Sb P6/mmm (Rm) 10030.43081.1274– * 30.43071.1273–  30.43261.1274–  40.45067– 57.11 Note:1, Cubic; 2, tetragonal; 3, hexagonal; and 4, rhombohedral system. * This work. 3 RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY Vol. 79 No. 1 2005 A COMPLEX STUDY OF THE PHASE DIAGRAM OF THE Sn–Sb SYSTEM 23 Table 2. Microprobe analysis of unannealed Sn–Sb alloys c 2 Possible phasesc 3 c 1 = 47.44, from 670 K 9.36 ± 0.5(Sn max )9.5 45.0 ± 1.4Sn 9 Sb 7 or Sn 17 Sb 15 43.75 or 46.87 53.73 ± 0.5Sn 15 Sb 17 53.12 56.49 ± 0.5Sn 7 Sb 9 56.25 c 1 = 49.96, from 670 K 8.7 ± 1.0(Sn max )9.5 44.98 ± 1.0Sn 9 Sb 7 or Sn 17 Sb 15 43.75 or 46.87 c 1 = 50.19, from 640 K 8.46 ± 1.0(Sn max )9.5 48.33 ± 1.0Sn 17 Sb 15 46.88 56.85 ± 0.6Sn 7 Sb 9 56.25 62.54 ± 0.6Sn 3 Sb 5 62.5 c 1 = 52.03, from 670 K 8.02 ± 1.0(Sn max )9.5 47.5 ± 0.7Sn 17 Sb 15 46.88 52.24 ± 0.9Sn 15 Sb 17 53.12 56.55 ± 0.5Sn 7 Sb 9 56.25 58.0 ± 1.4Sn 13 Sb 19 59.38 53.86 ± 0.9Sn 15 Sb 17 53.12 57.37 ± 1Sn 7 Sb 9 56.25 88.02 ± 0.5(Sb max )88.89 c 1 = 64.95, from 640 K 57.61 ± 1.0Sn 7 Sb 9 56.2 60.88 ± 0.3Sn 7 Sb 11 61.11 89.72 ± 0.8(Sb max )88.89 c 1 = 69.59, from 640 K 63.16 ± 1.0Sn 3 Sb 5 62.5 89.65 ± 1.0(Sb max )88.89 c 1 = 74.40, from 670 K 60.88 ± 0.5Sn 7 Sb 11 61.11 61.92 ± 0.8Sn 7 Sb 11 or Sn 3 Sb 5 61.11 or 62.5 88.42 ± 1.0(Sb max )88.89 Note:All the alloys were cooled from the speciﬁed temperatures in air; antimony contents (at. %): c 1 , in initial alloys; c 2 , analytic data; and c 3 , in possible phases; Sn max is the maximum sol- ubility of tin in antimony and Sb max is the maximum solu- bility of antimony in tin. Table 3. Microprobe analysis of annealed Sn–Sb alloys No.c 1 T anneal , Kc 2 c 3 198.0*67397.8 ± 0.8(Sb) 296.0*67395.5 ± 0.8(Sb) 394.0*67393.8 ± 0.8(Sb) 492.0*67391.3 ± 0.8(Sb) 590.00*67388.75 ± 0.8(Sb max ) 61.44 ± 0.5Sn 7 Sb 11 (61.11) 689.0067388.71 ± 0.5(Sb) 762.4250356.36 ± 0.5Sn 7 Sb 9 (56.25) 57.42 ± 0.5Sn 3 Sb 4 (57.14) 87 ± 3 (traces) (Sb max ) 861.1663361.17 ± 0.5Sn 7 Sb 11 (61.11) 959.3950354.46 ± 0.5β phase 55.76 ± 0.5Sn 4 Sb 5 (55.56) 57.66 ± 0.5Sn 3 Sb 4 (57.14) 1056.3050355.47 ± 0.5Sn 4 Sb 5 (55.56) 1153.1263352.68 ± 0.5Sn 17 Sb 19 (52.78) 1250.0850350.00 ± 0.5SnSb (50.00) 1346.8750346.94 ± 0.5Sn 17 Sb 15 (46.88) 1440.6050343.42 ± 0.5Sn 9 Sb 7 (43.75) 1540.00 5438.7 ± 1.0(Sn max ) 43.92 ± 0.5Sn 9 Sb 7 (43.75) 1637.5150343.15 ± 0.5Sn 9 Sb 7 (43.75) 41.9 (traces)Sn 19 Sb 13 (40.62)? Note:For each alloy, analyses were performed at nine points along ingot length (20 mm, ingot diameter was 5 mm). All the annealed alloys except 1–5 were quenched in water; alloys 1–5 were cooled in air; (Sb) denotes solid solutions of tin in antimony of various concentrations; for the denotations c 1 −c 3 , Sn max , and Sb max , see Table 2. 24 RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY Vol. 79 No. 1 2005 VASIL’EV Consider the model of a hexagonal lattice of the β phase (Fig. 3). The initial formation of the primary solid solution of tin in antimony occurs as statistical distribution of tin in the hexagonal lattice. Upon the attainment of the limiting saturation concentration (11.11 at. % Sn), ordering of the distribution of tin atoms occurs in the second and sixth layers (counting from the upper plane of the unit cell), but statistically, they only occupy one third of the sites in each layer (Fig. 3a). According to numerous differential thermal and microprobe analysis data, the limiting concentra- tion of the saturated solid solution of tin in antimony is also 11 ± 1.5 at. % Sn. The complete replacement of antimony atoms in the second and sixth layers results in the formation of the SnSb 2 structure. The replacement of antimony with tin in the mid- dle layer of the β phase unit cell can occur statistically continuously at elevated temperatures from 66.67 to 50 at. % Sb with the formation of the intermediate phases Sn 7 Sb 11 and Sn 4 Sb 5 (Figs. 3b, 3c). This homol- ogous series of phases based on hexagonal antimony manifests itself when solid solutions experience ordering. At a 1 : 1 ratio between Sn and Sb atoms, the hexagonal structure acquires features of a distorted NaCl-type structure. The distance between the (001) planes then becomes equal to 0.166Ò. Tin–antimony alloys with a NaCl-type structure can be formed in two ways. First, the atoms of both metals may be distributed statistically, and rock salt symmetry may remain unchanged on average. On the other hand, atoms of the two metals may alternate, that is, occupy different layers (ABCABC…) of the face-centered metal sublattice alternating along the body cell diago- nal. The crystal then acquires a rhombohedral shape and stretches or shrinks along the (111) axis. At elevated temperatures, the NaCl-type β phase forms a continuous series of solid solutions. Solid solu- tions experience ordering as the temperature decreases with the formation of intermediate phases that only dif- fer from each other by superstructural peculiarities. The crystal chemical models of such phases can be con- structed on the basis of the model of the unit cell of the SnSb (1 : 1) phase. The unit cell of the SnSb (1 : 1) superstructure with the parameter 2‡ consists of eight face-centered unit cells of the NaCl type (Fig. 4). Such a superstructural cell contains (8 × 8) 64 atoms, 32 tin and 32 antimony atoms. At a 1 : 1 ratio between the components, anti- mony and tin atoms alternate. The replacement of antimony with tin and tin with antimony only occurs along the central axes (I–IV) in each quarter of the superstructure unit cell. The replacement of antimony with tin occurs in the central plane (001) of the super- structure cell with the formation of the phases Sn 9 Sb 7 (43.75 at. % Sb) and Sn 17 Sb 15 (46.88 at. % Sb). (a) Sb Sn (b) (c) Fig. 3. Structural models of antimony and its alloys with tin: (a) saturated solid solution of tin in antimony (88.89 at. % Sb), (b) Sn 17 Sb 11 (61.11 at. % Sb), and (c) Sn 4 Sb 5 (55.56 at. % Sb). 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 I II III IV Sb Sn Fig. 4. Model of a superstructural phase of the NaCl type. RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY Vol. 79 No. 1 2005 A COMPLEX STUDY OF THE PHASE DIAGRAM OF THE Sn–Sb SYSTEM 25 The replacement of tin with antimony occurs only in the center of the cube of each of the eight simple unit cells with the formation of the phases Sn 15 Sb 17 (53.12 at. % Sb) and Sn 7 Sb 9 (56.25 at. % Sb). Such a replacement is only possible if the symmetry of trans- lation axes (I–IV) remains unchanged. The severe lim- itations speciﬁed above allow only a limited number of superstructural phases of the homologous series Sn 16 – n Sb 16 + n , where n = –2, –1, 0, 1, and 2, to be formed. The compositions of these phases were sub- stantiated by our microprobe data. The Sn 7 Sb 9 super- structural phase probably has a narrow homogeneity region from 56.25 to 57.14 at. % Sb (Sn 3 Sb 4 ). We do not exclude the possibility of the existence at room temperatures of the metastable phases Sn 3 Sb 2 (37.5 at. % Sb), Sn 19 Sb 13 (40.62 at. % Sb), and Sn 2 Sb 3 (62.5 at. % Sb). Table 4. Coefficients of the E(T) dependences for the liquid single-phase region and solid-phase heterogeneous regions of the Sn–Sb system Nox Sb a, mV b × 10 3 , mV/K l, K, mV × 10 2 , (mV) 2 Σ(T i –) 2 , K 2 T min –T max , K 10.1024–0.2274.6239710.533.050.04121572638–811 20.21070.04410.8640711.627.770.04123413638–811 30.30130.52717.8638709.1013.190.06118528638–811 40.31963.16124.0034723.2620.520.1492595655–811 50.43042.71628.8915747.3324.310.1026805678–811 60.45097.32125.2029725.225.600.1136331638–811 70.45968.65024.2876744.0426.710.26108513673–818 80.48038.70926.9326731.228.400.1827268681–787 90.499610.53626.5162752.2430.480.30 49961700–821 100.501910.38927.4922739.230.710.04 17968697–787 110.52038.28232.9658777.8033.920.0670247702–827 120.529212.72828.2117749.833.880.139475710–787 130.539911.23731.1061762.5134.950.2746807712–825 140.580812.90835.48 50 770.7 40.260.50 29053726–821 150.599211.90639.0443790.7342.780.1327154739–830 160.620316.02037.6331780.7145.390.8016932745–822 170.649512.48547.8236799.2850.700.1611527763–830 180.696211.92756.8726830.3959.15140262 798–913 190.800623.3066.016904.8383.035443893–919 200.88088.33 109.2 10891.50105.68211583872–913 210.919921.87112.311896.64122.58182985872–923 220.960546.21116.914898.14151.20193322872–923 S10.744– 59.58–46.3868637.4430.02643673592–682 0.696 S20.650– 61.63–52.6857637.3928.05832848592–682 0.599 S3'0.529269.972–70.1761613.3425.93411200589–638 S3''0.520371.455–76.2923624.2223.83410120592–659 S40.50194.21211.72108606.611.323211356589–627 S50.4803–11.72334.7358605.19.29179450589–623 T ε S 0 2 T Table 5. Coefficients of the E = a + bT + cT 2 + dT 3 dependences for heterogeneous regions l 1 + (β) and l 2 + (β) Regionx Sb abc × 10 3 d × 10 6 l , (mV) 2 T, K l 1 + (β)0.54–0.74–1337.525.71678–8.241184.088311830.01699–827 l 2 + (β)0.38–0.6279.58620.139822–1.21431.30095210.2589–697 S 0 2 26 RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY Vol. 79 No. 1 2005 VASIL’EV THE THERMODYNAMIC PROPERTIES AND PHASE DIAGRAM OF THE Sn–Sb SYSTEM The electromotive force method was our main tool for studying the Sn–Sb alloys. The electromotive force of electrochemical cells of the type (–)Sn Sn 2+ in salt melt Sn x Sb 1 – x (+) was measured in the concentration and temperature ranges 0.1 ≤ x Sb ≤ 0.96 and 589 ≤ T ≤ 830 K, respec- tively. Part of the experimental results were reported in [22, 23]. In this work, additional electromotive force measurements were performed for ﬁve alloys with x Sb = 0.3832, 0.4509, 0.4803, 0.5019, and 0.5292 in the tem- perature range 589–678 K. For these alloys, 716 mea- surement results were obtained for heterogeneous regions in the solid and liquid-solid states. The set of the coefﬁcients in the E(T) equations for the Sn–Sb sys- tem is given in Tables 4 and 5. The E(T) dependences are also shown in Fig. 5. The intersection points between straight lines 3–18 and curves L1 and L2 yield liquidus temperatures directly. Straight line 4–18 regions to the left of curves L1 and L2 describe supercooled alloys. Straight lines S1–S5 correspond to solid alloys, S1, S2, S4, and S5, to heterogeneous regions, and S3' and S3", to the homogeneous region of the β phase. The intersec- tion points between straight lines S1, S2, S3'', S4, and S5 and curves L1 and L2 give the peritectic reaction temperatures, and S3" gives the solidus temperature of the β phase for the alloy with 52.92 at. % Sb. Table 6 contains the temperatures found directly from these intersection points. It can be assumed that the change in the sign of the partial entropy of formation of solid β phase alloys of the series (S1–S3) and (S4, S5) [∆ = nF(∂E/∂T)] is related to a change in crystal symmetry. The β phase at elevated temperatures (starting with 643 K) has a homogeneity region from 50 to 55.56 at. % Sb. Close to 600 K , the hexagonal struc- ture transforms into quasi-cubic. We obtained the microstructure of this alloy annealed at 633 K and quenched in water. It contained well-discernible con- cretions of hexagonal crystals. The existence of the β phase with a composition close to 53 at. % Sb, which melts incongruently at 680 K, was substantiated by dif- ferential thermal analysis in studying ternary In–Sn–Sb alloys [24, 25]. The phase diagram shown in Fig. 6 was constructed on the basis of electromotive force and electrical resis- tance measurements and the differential thermal, X-ray phase, microstructural, and microprobe analysis data. In our view, the variant of the phase diagram reported in  with a broad region of β solid solutions from 47.7 to 65.2 at. % Sb is a metastable form of the crystallization of alloys of these compositions, which, when annealed for a long time, form a series of inter- mediate stoichiometric phases. The peritectic tempera- ture 597 K attributed to the Sn 3 Sb 2 phase (40 at. % Sb) in  in reality corresponds to the peritectic formation of the Sn 9 Sb 7 phase (43.75 at. % Sb). The existence of the Sn 3 Sb 2 aerial phase (40 at. % Sb) suggested in  has not been substantiated by any other researchers. We stress that the microprobe method is used to determine the local chemical composition of an alloy at a certain point. The quenched metastable phases present in a sample are then easily detected at room temperatures. The alloy with 40 at. % Sb annealed at 540 K and quenched in water did not contain even traces of the Sn 3 Sb 2 compound. The differential ther- S i 0 600 E, mV T, K 2 900 800 700 40 60 13 11 10 14 12 9 8 7 6 5 4 3 2 1 L1 S1 S2 S4 S5 L2 S3' S3'' 15 16 17 18 Fig. 5. Dependences E(T) for Sn–Sb alloys: (1–18) liquid alloys; L1 and L2, heterogeneous systems (liq + sol); and S1–S5, solid alloys. Table 6. Peritectic reaction temperatures Phase region Phasex Sb T, K S1SnSb 2 0.6667696.0 S2Sn 6 Sb 11 0.6111690.1 S3'β(Sn 15 Sb 17 )0.5312680.1 S3''β(Sn 17 Sb 19 ) (solidus)0.5278672.6 S4SnSb0.5000633.9 S5Sn 9 Sb 7 0.4375622.6 RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY Vol. 79 No. 1 2005 A COMPLEX STUDY OF THE PHASE DIAGRAM OF THE Sn–Sb SYSTEM 27 mal analysis of alloys with 10–50 at. % Sb performed in this work did not reveal the presence of a double ther- mal effect between 240 and 250°C similar to that described in . The phase with 61.11 at. % Sb was shown to exist by the electromotive force and micro- probe methods. It had a homogeneity region of ~1– 1.5% on the side of tin. The phase richer in antimony (66.67 at. % Sb) was only observed by the electromo- tive force method. When alloys containing 62 at. % Sb or more were slowly cooled, the SnSb 2 phase underwent peritectic decomposition with the formation of the phase with 61.11 at. % Sb, which was more stable under quenching conditions, and the solid solution of tin in antimony (Sb). THE OPTIMIZATION OF THE THERMODYNAMIC PROPERTIES OF THE Sn–Sb SYSTEM The optimization was performed with the inclusion of the calorimetric data on the heats of mixing [26–29], the results of electromotive force measurements , and our experimental E(T) dependences. The following description was obtained: ∆G(T, x)/R, K = x(1 – x)[–681.4821 – 108.3456(1 – 2x) + 146.9628(1 – 2x) 2 + 105.2240 (1 – 2x) 3 + 78.3754(1 – 2x) 4 ] + T[xlnx + (1 – x)ln(1 – x)] for liquid solutions, where x = x Sb and R = 8.31451 J/(mol K), and ∆G(T, x)/R, K = x(1 – x)(795.2333 – 1.015436T) + T[xlnx + (1 – x)ln(1 – x)] for antimony-based solid solutions. 400 0.20 0.4 0.6 0.8 1.0 600 800 1 2 3 4 5 6 7 590 515 519 600 597 623 634 680 697 x Sb T, K (Sb)(Sn) β 2 β 1           9 8 Fig. 6. Phase diagram of the Sn–Sb system constructed on the basis of the electromotive force (this work), differential thermal anal- ysis [1–3, 5, 6, 10–13], microstructural analysis [9, 11], and microprobe (this work and ) data; ∼ 600 K is the supposed tem- perature of the β 1 β 2 structural transition and (Sn) is the solidus line according to . Intermediate phases: (1) saturated solid solution of tin in antimony (88.89), (2) SnSb 2 (66.67), (3) Sn 7 Sb 11 (61.11), (4) Sn 3 Sb 4 (57.14), (5) Sn 4 Sb 5 (55.56), (6) Sn 15 Sb 17 (53.12), (7) SnSb (50.00), (8) Sn 17 Sb 15 (46.88), and (9) Sn 9 Sb 7 (43.75) (given in parentheses are antimony contents in at. %). 0.2 ∆ f G/R, K x Sb 400 1.0 0.8 0.4 0.6 0 0 –400 1 2 3 Fig. 7. Dependences of ∆ f G/R on the mole fraction of anti- mony for tin–antimony alloys at 605 K: (1) melts, (2) solid solution, and (3) compounds; standard states: liquid tin and solid antimony. 28 RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY Vol. 79 No. 1 2005 VASIL’EV The Gibbs energies of intermediate solid phases were calculated on the assumption that these phases were stoichiometric. The standard states of the ele- ments were liquid tin and solid antimony. Recalculation to the standard state was performed using the data from . The results were: ∆G(T, 0.666667)/R, K = –311.5340 + 0.025562T, ∆G(T, 0.6111)/R, K = –391.8849 + 0.104464T, ∆G(T, 0.53125)/R, K = –570.1572 + 0.33836T, ∆G(T, 0.5)/R, K = –540.2636 + 0.29897T, ∆G(T, 0.46875)/R, K = –483.8746 + 0.22056T. The phase stablest thermodynamically was Sn 15 Sb 17 (53.12 at. % Sb) (Fig. 7). According to the optimization results, liquid solu- tions of tin in antimony have ideal entropies of forma- tion; that is, these solutions are regular. In our view, the optimization of the Sn–Sb phase diagram performed in [13, 32] corresponds to a variant of its metastable state. To summarize, we performed complete analysis of the literature data on the phase diagram of the Sn–Sb system. We showed the possibility of the existence of metastable and stable β phase forms. For the ﬁrst time, crystal chemical models of the hexagonal and super- structural quasi-cubic β phase forms, whose intercon- version involved changes in crystal symmetry, was sug- gested. β-Phase solid solutions were shown to undergo ordering with the formation of homologous series of two symmetry types, hexagonal and quasi-cubic. The thermodynamic properties of the Sn–Sb system were optimized. A thermodynamically stable β phase close in its composition to Sn 15 Sb 17 (53.12 at. % Sb) was observed; this phase had a homogeneity region from 50 to 55.56 at. % Sb at elevated temperatures. ACKNOWLEDGMENTS The author thanks Prof. G.F. Voronin (Faculty of Chemistry, Moscow State University) and Prof. J.-K. Gachon (University Nancy-1, France) for their help with this work. REFERENCES 1.W. Reinders, Z. Anorg. Chem. 25, 113 (1900). 2.F. E. Gallagher, J. Phys. Chem. 10, 93 (1906). 3.R. S. Williams, Z. Anorg. Chem. 55, 12 (1907). 4.N. Konstantinov and W. A. Smirnov, Int. Z. Metal- lograﬁe 2, 154 (1912). 5.K. Iwasé, N. Aoki, and A. Osawa, Scientiﬁc Reports of Tohoku Imperial University 20, 353 (1931). 6.R. Blondel, Thése du Docteur (1936) (cited from ). 7.D. Hanson and W. T. Pelle-Walpolle, J. Inst. Met. 58 (1), 299 (1936). 8.K. Schubert, Z. Metallkd. 44, 457 (1953). 9.B. L. Eyer, J. Inst. Met. 88 (5), 223 (1960). 10.A. Stegher, Doctor–Ingenieurs Genehmigte Dissertation (Technischen Hochschule, Aachen, 1969). 11.B. Predel and W. Schwermann, J. Inst. Met. 99, 169 (1971). 12.W. P. Allen and J. H. Peperezko, Scr. Metall. Mater. 24 (11), 2215 (1990). 13.H. Ohtani, K. Okuda, and K. Ishida, J. Phase Equilib. 16 (5), 416 (1995). 14.P. J. T. L. Oberndorff, A. A. Kodentsov, V. Vuorinen, et al., Ber. Bunsen-Ges. Phys. Chem. 102 (9), 1321 (1998). 15.Termal Constants of Substances: A Handbook, Ed. by V. P. Glushko (VINITI, Moscow, 1971), Vol. 4 [in Rus- sian]. 16.K. Schubert, Kristallstrukturen Zweikomponentiger Phasen (Springer, Heidelberg, 1964; Metallurgiya, Mos- cow, 1971). 17.C. Barnett, J. Appl. Phys. 37, 1041 (1966). 18.G. Hägg and Hybinette, Philos. Mag. 12, 441 (1931). 19.G. Hägg and Hybinette, Philos. Mag. 20, 913 (1935). 20.E. G. Bowen and W. Morris, Philos. Mag. 12, 441 (1931). 21.H. Swanson and H. Fuyat, Natl. Bur. Stand. (U.S.), Circ. 539 3, 14 (1954). 22.V. Vassiliev, Y. Feutelais, M. Sghaier, and B. Legendre, J. Alloys Compd. 314, 197 (2001). 23.V. Vassiliev, M. Lelaurain, and J. Hertz, J. Alloys Compd. 247, 223 (1997). 24.B. Legendre, E. Dichi, and V. Vassiliev, Z. Metallkd. 92 (4), 328 (2001). 25.K. Lönberg, Metall. (Berlin) 22, 777 (1968). 26.F. E. Wittig and E. Gehring, Ber. Bunsen-Ges. Phys. Chem. 71 (4), 372 (1967). 27.A. Yazawa, T. Kawashima, and K. Itagaki, Nippon Kin- zoku Gakkaishi 32 (12), 1288 (1968). 28.F. Sommer, R. Luck, N. Rupf-Bolz, and B. Predel, Mater. Res. Bull. 18, 621 (1983). 29.M. Azzaoui, Thése du Docteur (Université Henri Poincaré, Nancy, 1995). 30.J. A. Yanko, A. E. Drake, and F. Hovorka, Trans. Electro- chem. Soc. 89, 357 (1946). 31.A. T. Dinsdale, CALPHAD: Comput. Coupling Phase Diagrams Thermochem. 15, 317 (1991). 32.B. Jonsson and J. Agren, Mater. Sci. Technol. 2, 913 (1986).