Different Approach to Thermodynamic Description of Bi-Te Binary System

Abstract

The aim this work was the reinvestigation of phase equilibria in Bi-Te system. The as-cast and long-time equilibrated alloys of Bi-Te binary system were analysed by scanning electron microscopy, X-ray diffraction (XRD) and differential thermal analysis (DTA) methods. The primary solidified phases were identified for as-cast samples. The existence of the four intermetallic phases: Bi₂Te₃, BiTe, Bi₂Te, Bi₇Te₃ was confirmed. Three of them melt incongruently in peritectic reactions. The model parameters of all phases in this system were assessed by optimization using available data by Calphad method. The stabilisation of these phases in other ternary systems was discussed taking into consideration its future application in thermodynamic description of Ag-Bi-Te ternary system.

1 Introduction

The Peltier effect in a thermocouple incorporating bismuth telluride, Bi₂Te₃ was observed more than 60 years ago.¹ From that time this compound has been extensively used in the construction of different thermoelectric modules.² The performance of these modules depends on the number of factors which are combined in the thermoelectric figure of merit, ZT, where Z is defined as α²σ/λ, (α is the Seebeck coefficient, σ is the electrical conductivity and λ is the thermal conductivity). Optimizing ZT is a nontrivial task because the variables in ZT, despite of separate expression are in fact coupled to each other. From the beginning the optimization of the charge carrier concentration and reduction of the lattice component of the thermal conductivity, λ_L were achieved through the use of solid solutions of bismuth telluride with the isomorphous compounds antimony telluride and bismuth selenide.³ The enhanced scattering of phonons in these solid solutions is not usually accompanied by a reduction in the mobility of the charge carriers. It has been found that Bi₂Te₃-based alloys have the relatively highest ZT near room temperature (~300 K). Such alloys used in solid-state devices dominate the market for temperature control in optoelectronics. Peltier cooling is also more and more attractive particularly in small systems to eliminate greenhouse-gas refrigerants. Since thermoelectric technology will be greatly enhanced by improving Bi₂Te₃, numerous attempts have been made to discover better materials which requires the knowledge of the stability of phases in Bi-Te system.

At the beginning the inconsistency in Bi-Te phase diagram was observed, especially in solid-liquid equilibria in the Bi-rich part of the system. To explain such a discrepancy in experimental data Brebrick⁴ concluded that a continuous sequence of ordered phases formed as Bi_mTe_n, can be interpreted as solid solutions without arbitrary choice of m and n. He also suggested⁴ that the bismuth layers of Bi₄Te₅ may arise from antistructure defects of tellurium atoms which must lead to a homogeneity region in the compounds. Brebrick⁴ also suggested the existence of two different versions of phase diagrams for the Bi-Te system. The first metastable phase diagram, corresponding to differential thermal analysis (DTA) and solid state synthesis conditions with extensive regions of solid solution. The equilibrated second one, requires the synthesis of intermetallic compounds. Next, Anderson⁵ proposed to describe the crystal structure of solid phases in Bi-Te system as the structures built by the ordered repetition of a common hexagonal sub-cell along c-axis with a minimum adjustment of atomic positions with composition. Such a repetition of a set of sub-cells differs in compositions but are structurally closely related. The stoichiometry of compounds obtained from such repetition can be additionally affected by probable replacement of Bi by Te at a level of 1 at.%. Consequently, Bos et al.⁶ examining the series of alloys in range from Bi to Bi₂Te₃ derived the crystal structures as an ordered stacking of Bi₂Te₃ and Bi₂ building blocks. All phases in the bismuth tellurides together with terminal solution of (Bi) can be recognized as homologous series of (Bi₂)_m(Bi₂Te₃)_n type: Bi₂Te₃ (m:n = 0:3), Bi₄Te₅ (m:n = 1:5), Bi₆Te₇ (m:n = 2:7), Bi₈Te₉ (m:n = 9:3), BiTe (m:n = 1:2), Bi₄Te₃ (m:n = 3:3), Bi₂Te (m:n = 2:1), Bi₇Te₃ (m:n = 15:6), and Bi (m:n = 3:0). The existence of Bi₁₀Te₉ (m:n = 6:9) has been additionally predicted.^{7, 8}

In order to analyse the experimentally obtained liquidus projection and isothermal section at the 523 K of the Bi-In-Te ternary system Chen and co-workers⁹ proposed the simplification of the Bi-Te system by grouping the undetermined binary phases between Bi and Bi₂Te₃ as a (Bi₂)_m(Bi₂Te₃)_n phase.

The p-T-x literature data of Bi-Te phase system up to the year 1994, with special attention to Russian publications, had been reviewed by Chizevskaya et al.¹⁰ and the T-x diagram was assessed. The characteristics of Bi₂Te₃ solid- liquid and solid-gas transitions were analysed. Additionally, the crystal data of existing detected phases were summarized together with thermodynamic functions. Chizevskaya et al.¹⁰ using cubic spline analysis¹¹ combined with thermodynamic rules critically assessed the parts of liquidus line starting from crystallization points of solid compounds.

Based on the DSC results and morphology difference of scanning electron microscopy/back scattered electron (SEM/BSE) images of samples annealed in different temperatures Mao et al.¹² put forward the Bi-Te phase diagram. They assumed that the single solid solution denoted as β phase represents the superstructure of the (Bi₂)_n(Bi₂Te₃)_m homologous series. Additionally, Mao et al.¹² had taken into consideration compounds Bi₄Te₃ and Bi₂Te modelled as the intermetallic compounds, i.e. line compounds. But the proposed thermal stability ranges of Bi₂Te and Bi₄Te₃ compounds are very narrow, 30 and 20 K, respectively. It should be emphasised that such stability ranges are rather unusual.

In 2008 the thermodynamics and topology of bismuth-tellurium system were critically reviewed by Mao et al.¹² and Gierlotka.¹³ They both emphasized that the phase diagram of Bi-Te system had several versions that did not agree. The observed inconsistency of the phase equilibria concentrates in Bi-Bi₂Te₃ part of compositions in which a layered structure of solid phases was determined.

Coupling their experimental results with the literature thermodynamic and topological data Mao et al.¹² assessed the Bi-Te binary system using Calphad (calculation of phase diagrams) technique. In their approach, the β phase was described by the two sublattice (Bi)₂(Bi,Te)₃ model. It seems that the stoichiometric ratio of β phase can be recognized as phase BiTe which composition deviating from stoichiometric ratio to higher Bi content as the temperature decreases.

All other telluride phases Mao et al.¹² modeled as the stoichiometric compounds and the liquid solution as a substitutional solution. The lack of detectable mutual solubility in terminal solutions of Bi and Te was neglected in phase modelling.

Considering Mao’s¹² work, Gierlotka¹³ took into consideration the thermodynamic data of Bi₂Te₃ phase determined at 298 K by Howlett et al.¹⁴, Boncheva-Mladenova et al.¹⁵, Vecher et al.¹⁶, Wagman et al.¹⁷ and Sidorko et al.¹⁸ In his reassessment of Bi-Te system¹³ the possible clustering in liquid phase^19,20,21,22 was taken into account, and consequently the liquid solution was modelled as the associate liquid solution.²³ According to Brebrick results²⁴ the narrow homogeneity range (59.7 and 60.2 Te at.%) of Bi₂Te₃ compound was described by Wagner-Schottky model.²⁵

In 2015 Kifune et al.²⁶ found that the boundary of the compound homologous series is Bi₈Te₃ (27.3 at.% Te) single phase instead of the Bi₇Te₃ (30.0 at.% Te) phase in the Bi-rich boundary.^{6, 27} Using Rietveld method, the homologous phase is a four-dimensional superstructure of space group $R\overline{3}m.$ This experimental data do not correspond to the data presented by Mao et al.¹² and in Gierlotka’s¹³ assessments as well.

In turn, Babanly et al.²⁸ observed the existence of stable Bi₁₄Te₆ compound and Bi₂Te, BiTe, and Bi₂Te₃ compounds with restricted range of homogeneity (non-stoichiometric). The boundaries between the intermediate phases in the Bi-Te system were determined via electromotive force (EMF) method²⁸ and agree with the data derived from physicochemical analysis.²⁹ It seems that these results confirm stability of Bi₂Te and BiTe phases in the low temperature range. The existence of the compounds Bi₂Te₃, BiTe, Bi₂Te and Bi₁₄Te₆ was also confirmed in the study of Bi-Te-I system by Babanly’s group.³⁰ Very similar result was obtained by Prokhorenko et al.³¹ in the range of 495–550 K using thermal titration method.^{32, 33} Prokhorenko et al.³¹ noticed that intermediate variable-composition Bi₂Te₃, BiTe, Bi₂Te, and Bi₁₄Te₆ phases form in the partial ternary Bi-Ag₂Te-Bi₂Te₃ system. The triangulation of the ternary Ag₂Te-Bi-Bi₂Te₃ system within a temperature range of 300–600 K agrees well with the literature data of Babanly et al.^{28, 30}

The conclusions of experimental work from Babanly et al.^{28, 30} and Prokhorenko et al.³¹ also do not agree with data presented by Mao et al.¹² According to these results²⁸ it seems that the addition of third element to bismuth tellurides can stabilize them as solid compounds. To obtain the thermodynamic description of Ag-Bi-Te and Bi-Te-I systems agreeing with their results, it is necessary to assess the Bi-Te phase diagram with binary phases where the stability was confirmed in ternaries.^{28, 30, 31} Taking into account the results of the analysis of Ag-Bi-Te system^{28, 31} the stabilisation of binary tellurides can be expected with Ag addition in ternary Ag-Bi-Te alloys.

Consequently, the aim of the present work is the analysis of phase equilibria in Bi-Te system and optimization of model parameters of phases in this system to be next applied in Ag-Bi-Te ternary system description by Calphad method. The compositions of the six Bi-Te alloys were selected to enable the identification of the phases: Bi₂Te₃, BiTe, Bi₂Te, Bi₇Te₃. The phase BiTe corresponds to the β phase in the assessments of Mao et al.¹² and Gierlotka.¹³ The Bi₁₄Te₆ phase corresponds to the stoichiometry of the Bi₇Te₃ phase which was described by Glazov et al.²⁰ and by Chizhevskaya et al.¹⁰ The annealing temperatures were selected below the liquidus temperature for the Bi-Te two-component system based on the work of Chizhevskaya et al.¹⁰

2 Materials and Experimental Methods

The Bi-Te alloys were prepared from high purity metals: Bi 99.997 wt.% (Alfa Aesar, USA) and Te 99.9999 wt.% (Alfa Aesar, USA). The theoretical composition of alloy samples (no. 1–6) are given in Table 1. The weighed amounts of pure metals (~2 g) were sealed in quartz tube under vacuum and then fused and molten in furnace at 700 °C for 24 h to mix together, followed by water quenching. Additionally, intermetallic phase Bi₂Te of stoichiometric composition was prepared by the same procedure as above, with different melting temperature–600 °C.

Table 1 Constitution of Bi-Te alloys and heat treatment parameters, as a process temperature and an annealing time for equilibrated alloys

Due to the relatively high evaporation rates of bismuth and tellurium,^{21, 24, 34,35,36} to avoid a significant change in the chemical composition of the alloys samples during the sealing process in quartz ampoules, each of the elements was added with a slight excess: ~ 80 mg, and ~ 60 mg for bismuth and tellurium, respectively.

Next, the samples were weighed again to control the possible mass loss during the sample preparation according to the relatively high tellurium partial pressure at operation temperatures.^{12, 37} After synthesis the samples were isothermally equilibrated at the chosen temperatures according to the following procedure: The as-cast weighed Bi-Te alloy samples (~1 g) were sealed in quartz tubes under vacuum again and then annealed below the solidus. The appropriate temperatures were applied for individual alloys to achieve equilibrium (Table 1). It is well known that the bulk samples of layered Bi-Te phases obtained by melting of pure components do not reach an equilibrium state even after a long period 84–125 days of thermal annealing.^{27, 29, 37} Due to very low diffusion rates between layers the non-equilibrium phase constitution obtained by cooling from liquid solution only changes slightly during further heat treatment. Based on older literature data (details in the discussion) and the latest experimental investigations of Mao et al.¹² it was decided in the current work to equilibrate Bi-Te alloys isothermally for 30 and 60 days at appropriate temperatures. After long-term annealing, the samples were quenched into iced water to maintain high-temperature phase composition. The annealed samples were cut into parts for the different examinations.

The obtained microstructure was observed by scanning electron microscopy (SEM) (Hitachi, SU-70, Japan, with electron microprobe ThermoScientific, with ZAF correction). For qualitative and quantitative analysis, the EDX (Energy Dispersive X-ray Spectroscopy) method was applied. Four samples (Bi60Te40, Bi68Te32, Bi80Te20 and the Bi₂Te phase sample) were additionally analysed using FEI Quanta 3D FEG-SEM scanning electron microscope with an EDAX APOLLO energy dispersion x-ray spectrometer. The phase constitution of studied alloys was determined by x-ray Powder Diffraction (XRD) method using Rigaku Japan MiniFlex II x-ray Diffractometer with Cu-Kα radiation.

DTA measurements were performed with the use of DSC/DTA Pegasus 404 F1 (Netzsch, Germany) scanning calorimeter with a DTA probe. The samples were sealed in evacuated silica tubes and placed at the DTA sensor in a platinum crucible. An empty evacuated silica tube of similar mass was used in a second platinum crucible as a reference. No traces of Te evaporation were observed at inner surface of quartz tubes after measurements. The thermal analysis was carried out in cycles with heating rates of 2 as well as 5 and 10 deg/min (for specified sample compositions). The compositions of all alloys in atomic percent used in our studies are presented in the Table 1.

3 Results

Table 1 summarizes chemical composition, weight loss during casting, and the isothermal equilibration parameters: temperature and an annealing time of the alloys for the Bi-Te two-component system. After melting process, the mass loss was generally below 1% (Table 1), this was not only due to Te evaporation but also to partial sticking of samples to the glass surface of the silica tube (above 1% mass loss of sample 4). So, after synthesis the composition of Bi-Te alloys remained unchanged in the experimental error range. Also, no significant evaporation of sample components was observed during isothermal annealing.

Tables 2 and 3 present the XRD, EDX results for as-cast and annealed Bi-Te alloys (Table 1). Bi₂Te₃ as the primary phase was observed for alloys samples: Bi30Te70, Bi40Te60, Bi45Te55, on the back-scattered electron image (BEI) micrograph, while BiTe as primary phase was determined for alloys Bi60Te40, Bi68Te32, Bi80Te20 (Fig. 2).

Table 2 Experimental results (XRD, EDX data) for as-cast alloy samples

Table 3 Experimental results (XRD, EDX data) for annealed alloy samples

Annealed alloys samples with the following compositions: Bi60Te40, Bi68Te32, Bi80Te20 and the Bi₂Te phase sample (Table 3) were also analysed on the SEM FEI Quanta 3D FEG-SEM microscope. The detected primary phases in the listed alloys are consistent for both series of measurements.

The DTA results of alloys no. 1-6 and phase Bi₂Te are shown in Table 4 for three different heating rates: 2, 5, 10 deg/min. Some data of the second heating cycle was also shown. From the cooling cycle data at different rates significant undercooling of liquid samples was determined. As an example, the onset data of liquidus points of different samples cooled with the different rates are shown in Table 4. DTA results for 2 deg/min first heating cycle are shown in Fig. 1.

Table 4 DTA results for annealed samples and Bi₂Te as-cast phase for cycles of different heating rates: 2, 5 and 10 deg/min

Fig. 1

DTA results for 2 deg/min heating rate. The first heating cycle was shown

Figure 2 and 3 show BEI micrographs of as-cast and annealed Bi-Te alloys. Detected phases are identified in the images. BEI micrograph of as-cast (non-equilibrated) alloy Bi30Te70 (no. 1) of the composition 70 at.% Te is shown in Fig. 2(a). The microstructure consists of: light elongated lamellar grains of Bi₂Te₃ phase, dark narrow areas around the Bi₂Te₃ plates which are tellurium phase, and needle-shaped solidified liquid phase of eutectic composition. The composition of the brightest phase Bi₂Te₃ was measured to be 66.29 at.% Te and that of the dark narrow areas of (Te) phase is 98.76 at.% Te.

Fig. 2

Back-scattered electron image micrographs of Bi-Te as-cast alloys: (a) Bi30Te70 alloy showing Bi₂Te₃+eutectic+(Te) microstructure; (b) Bi40Te60 alloy showing Bi₂Te₃+eutectic microstructure; (c) Bi45Te55 alloy showing BiTe+Bi₂Te₃+(Bi) three-phase microstructure; (d) Bi60Te40 alloy showing BiTe+Bi₂Te+(Bi) three-phase microstructure; (e) Bi68Te32 alloy showing BiTe+Bi₂Te+(Bi) three-phase microstructure; (f) Bi80Te20 alloy showing BiTe+Bi₇Te₃+(Bi) three-phase microstructure; (g) phase Bi₂Te with Bi67Te33 composition showing BiTe+Bi₂Te+(Bi) three-phase microstructure (image of FEI Quanta 3D FEG-SEM electron microscope)

Fig. 3

BEI micrographs of Bi-Te of annealed alloys: (a) Bi30Te70 alloy showing Bi₂Te₃ + Te+post-eutectic mixture microstructure; (b) Bi40Te60 alloy of Bi₂Te₃ one-phase microstructure; (c) Bi45Te55 alloy of BiTe one-phase microstructure; (d) Bi60Te40 alloy showing BiTe+Bi₂Te two-phase microstructure; (e) Bi68Te32 alloy showing Bi₂Te one-phase microstructure; (f) Bi80Te20 alloy showing Bi₇Te₃+(Bi) microstructure

Figure 2(b) is BEI micrograph of as-cast alloy no. 2 with the atomic composition of Bi40Te60. The structure is composed of mixed eutectic grains and the remainder are elongated grains of the Bi₂Te₃ phase with different shades of grey resulting from different orientations. The composition of the grey grains of Bi₂Te₃ phase is 61.78 at.% Te.

In Figure 2(c–g) the BEI micrographs of as-cast alloys no. 3-7 with the compositions: Bi45Te55, Bi60Te40, Bi68Te32, Bi80Te20, Bi67Te33 are shown. All these alloys have three distinct areas. The bright matrix is (Bi) phase (Fig. 2c–g). The amount of Te in the phase (Bi) was determined as 3.68 and 0.78 at.% Te for Bi45Te55 and Bi60Te40 samples, respectively. For the other alloys (Bi68Te32, Bi80Te20, Bi67Te33) no trace of Te was observed in (Bi) phase.

Figure 2(c) shows dark elongated grains of Bi₂Te₃ phase with the composition 59.32 at.% Te and grey precipitates of BiTe phase with composition 44.26 at.% Te. In Fig. 2(d), (e), (g) the darkest elongated lamellar grains are the BiTe phase, and the grey interphase regions are the Bi₂Te phase. The compositions of BiTe are 49.02, 45.80 and 40.94 at.% Te, and of Bi₂Te are 38.14, 34.53, 34.07 at.% Te for samples no. 4, 5 and Bi₂Te phase, respectively. The different shades of grey observed for Bi₂Te sample correspond to different crystal orientations of the grains. The situation is similar for the Bi₂Te₃ phase in Figure 3(b) for the equilibrated alloy with the composition Bi40Te60. The microstructure of as-cast Bi80Te20 (no. 6) alloy consists of the bright (Bi) phase, the dark lamellar grains of BiTe phase and the grey precipitates of Bi₇Te₃ phase (Fig. 2f). The composition of tellurium for BiTe, and Bi₇Te₃ phases was determined as 43.93 and 30.23 at.%, respectively. The primary solidified phases identified from microstructures (Fig. 2(a–g) are shown in last column in Table 2.

The BEI micrograph of annealed alloy of composition Bi30Te70 (no. 1) equilibrated at 390 °C during 60 days is shown in Figure 3(a). Its two-phase microstructure is composed of large light lamellar grains of the Bi₂Te₃ phase with average chemical composition of 38.3 at.% Bi (61.7 at.% Te). The image does not show the fine eutectic as in as-cast alloy but a mixture of dark areas of almost pure tellurium (Te) (~100 at.% Te) phase with the light grains of Bi₂Te₃ compound can be observed. In Figure 3(b) the BEI micrograph of alloy no. 2 with the composition of Bi40Te60 equilibrated at 480 °C for 30 days is shown. The microstructure is single phase with Bi₂Te₃ phase of composition 38.6 at.% Bi (61.4 at.% Te) with different shades of grey resulting from different grain orientations.

In Figure 3(c) the BEI micrograph of annealed alloy no. 3 (composition of Bi45Te55) equilibrated over 30 days at 480 °C is shown. Its microstructure consists of single-phase lamellar grains arranged in different orientations which are the BiTe phase with chemical composition 42.6 at.% Bi (57.4 at.% Te). They also have different shades of grey. The phases (Bi) and Bi₂Te₃ observed in as-cast alloy sample disappeared after annealing.

The next BEI micrograph shows the microstructure of alloy no. 4 (Bi60Te40) after 60 days of equilibration at 390 °C (Fig. 3d). It consists of three-phases: the bright pure bismuth phase (Bi) (~100 at.% Bi), lamellar grains with different shades of grey, which are the BiTe phase with average chemical composition 55.9 at.% Bi (44.1 at.% Te), and the Bi₂Te phase which forms lighter precipitates at grain boundaries (33.5 at.% Te). The grains of BiTe phase are much larger than in as-cast microstructure and the (Bi) phase is still present. So, it seems that in this sample the equilibration was not finished during annealing process. The presence of (Bi) phase in samples annealed at low temperature and did not reach equilibrium was described in literature.

In Figure 3(e) the BEI micrograph of alloy Bi68Te32 (no. 5) equilibrated at 240 °C over 60 days is presented. It is evident that this no longer a 3-phase microstructure as the as-cast alloy. Instead, it is the single-phase structure of Bi₂Te with the average chemical composition of 65.9 at.% Bi (34.1 at.% Te). The micrograph of alloy Bi80Te20 (no. 6) annealed at 240 °C over 60 days is shown in Figure 3(f). The two-phase microstructure is composed of the bright bismuth (Bi) phase (~100 at.% Bi) and a dark-grey areas assigned to Bi₇Te₃ phase with Bi content of 70 at.% (30 at.% Te), which is the microstructure of a ripened hypereutectic.

Figure 4 presents compiled normalized XRD diffractograms of annealed alloys no. 1-6. The number of phases in diffractograms for Bi30Te70, Bi40Te60, Bi45Te55, Bi68Te32, Bi80Te20 annealed alloys coincides with number of phases in micrographs from SEM analysis and EDX results. Diffractogram of Bi60Te40 alloy indicates two phases: BiTe and Bi₂Te.

Fig. 4

X-ray powder diffraction pattern of annealed alloy samples no. 1-6: (a) no. 1-Bi30Te70, (b) no. 2-Bi40Te60, (c) no. 3-Bi45Te55, (d) no. 4-Bi60Te40, (e) no. 5-Bi63Te32, (f) no. 6–Bi80Te20. Bi₂Te₃(1) is represented by chart no. 01-076-2813, Bi₂Te₃(2) by chart no. 01-085-0439, BiTe(1) by chart no. 01-075-1095 and BiTe(2) is represented by chart no. 01-083-1749. (For representation of the references to colour in this figure legend, the reader is referred to the web version of this article)

3.1 The Assessment of Bi-Te Phase System

As was mentioned previously, taking into accountg data obtained in present work the following phases are considered in this work: liquid, rhombohedral_A7 (Bi), hexagonal_A8 (Te), Bi₂Te₃, β(BiTe), Bi₂Te, and Bi₇Te₃ (Bi₁₄Te₆).

The Gibbs free energies of pure elements ${G}_{i}^{0}(T)={G}_{i}(T)-{H}_{i}^{SER}(298)$ are the following functions of temperature (Eq 2):

$$G_{i}^{0} \left( T \right) = a + bT + cT\ln T + dT^{2} + eT^{ - 1} + fT^{3} + iT^{4} + jT^{7} + kT^{ - 9}$$

(1)

The $G_{i}^{0} (T)$ functions are referred to the enthalpy values $H_{i}^{SER} (298)$ of the standard element reference SER at 298.15 K and 1 bar as recommended by SGTE Group¹.³⁸ The reference states are pure elements Bi and Te with rhombohedral_A7 and hexagonal_A8 structure, respectively. The expression Eq 2 may be used for several temperature ranges, with different set of coefficients (a, b, c, d, e, f, i, j, k) in each. The ${G}_{i}^{0}(T)$ functions are taken from thermodynamic database SGTE Unary TDB v.5³⁸ for pure elements.

3.2 Rhombohedral_A7 (Bi) and Hexagonal_A8 (Te) Terminal Phases

Experimental information does not indicate mutual solubility of Bi and Te. So, both phases were described as pure elements and their Gibbs energies were taken from the unary elements database.³⁸

3.3 Bi₇Te₃ and Bi₂Te Phases

These phases are modelled as the line compounds. Their heat capacity has not been determined yet, therefore their Gibbs energy is described according to the Neumann-Kopp rule:

$$G_{Bi:Te}^{{Bi_{m} Te_{n} }} = A + BT + m \cdot^{0} G_{Bi}^{{{\text{rom}}}} + n \cdot^{0} G_{Te}^{{{\text{hex}}}}$$

(2)

where T is an absolute temperature, A and B are adjustable parameters. Numbers m and n are the stoichiometric parameters. Functions $^{0} G_{Bi}^{{{\text{rom}}}}$ (GHSERBI) and $^{0} G_{Te}^{{{\text{hex}}}}$ (GHSERTE) are Gibbs energies of pure Bi and Te in their SER reference state, respectively.

3.3.1 β(BiTe) Phase

β(BiTe) phase is treated as the phase with homogeneity range extending to Bi-rich side of compound. In order to describe the off-stoichiometric phase compositions, the anti-site atoms were introduced in the model. Therefore the Bi_0.4(Bi, Te)_0.6 model as in earlier assessments¹² and¹³ was used to describe this homogeneity range. The Gibbs energy of this model (for one mole of atoms) has the following form:

$$\begin{aligned} ^{0} G_{{Bi:Bi,Te}}^{{Bi_{{0.4}} Te_{{0.6}} }} & = y_{{Bi}}{^{0}} G_{{Bi:Bi}}^{{Bi_{{0.4}} Te_{{0.6}} }} + y_{{Te}}{^{0}} G_{{Bi:Te}}^{{Bi_{{0.4}} Te_{{0.6}} }} + 0.6 \cdot RT\left( {y_{{Bi}} \ln y_{{Bi}} + y_{{Te}} \ln y_{{Te}} } \right) \\ & \quad + y_{{Bi}} y_{{Te}} \sum\limits_{i} {^{i}} L_{{Bi:Bi,Te}}^{{Bi_{{0.4}} Te_{{0.6}} }} \left( {y_{{Bi}} - y_{{Te}} } \right)^{i} \\ \end{aligned}$$

(3)

where ${}^{0}G_{Bi:Bi}^{{Bi_{0.4} Te_{0.6} }}$ and ${}^{0}G_{Bi:Te}^{{Bi_{0.4} Te_{0.6} }}$ represent the Gibbs energies of Bi and Bi_0.4Te_0.6, respectively.

3.3.2 Bi ₂ Te ₃ Phase

Gibbs free energy of binary stoichiometric Bi₂Te₃ compound is described by Wagner-Schottky defect model.²⁵ The model describes the composition range as a function of various defects. In this case the anti-site atoms defect describes very small homogeneity range of Bi₂Te₃ intermetallic compound as (Bi,Te)₂(Bi,Te)₃, which is in agreement with considerations by Xu et al.³⁹ and Hashibon and Elsässer.⁴⁰ Then Gibbs free energy is:

$$\begin{aligned} ^{0} G^{{Bi_{2} Te_{3} }} & = y_{{Bi}}^{{\left( 1 \right)}} y_{{Bi}}^{{\left( 2 \right)}} \;^{0} G_{{Bi:Bi}}^{{Bi_{2} Te_{3} }} + y_{{Te}}^{{\left( 1 \right)}} y_{{Te}}^{{\left( 2 \right)}} \;^{0} G_{{Te:Te}}^{{Bi_{2} Te_{3} }} + y_{{Bi}}^{{\left( 1 \right)}} y_{{Te}}^{{\left( 2 \right)}} \;^{0} G_{{Bi:Te}}^{{Bi_{2} Te_{3} }} \\ & \quad + y_{{Te}}^{{\left( 1 \right)}} y_{{Bi}}^{{\left( 2 \right)}} \,^{0} G_{{Te:Bi}}^{{Bi_{2} Te_{3} }} + ^{{id}} G_{m}^{{Bi_{2} Te_{3} }} + ^{{ex}} G_{m}^{{Bi_{2} Te_{3} }} \\ \end{aligned}$$

(4)

where ${}_{{}}^{0} G_{i:j}^{{Bi_{2} Te_{3} }}$ (i, j = Bi, Te) is the Gibbs energy of end-member compounds when element i occupies sublattice (1), and element j occupies sublattice (2), $y_{i}^{s}$ is fraction of element i in sublattice s (s = (1), (2))⁴¹. The Gibbs energy of ideal mixing is:

$$^{{id}} G_{m}^{{Bi_{2} Te_{3} }} = RT\left\lfloor {2\left( {y_{{Bi}}^{{\left( 1 \right)}} \ln y_{{Bi}}^{{\left( 1 \right)}} + y_{{Te}}^{{\left( 1 \right)}} \ln y_{{Te}}^{{\left( 1 \right)}} } \right) + 3\left( {y_{{Bi}}^{2} \ln y_{{Bi}}^{{\left( 2 \right)}} + y_{{Te}}^{{\left( 2 \right)}} \ln y_{{Te}}^{{\left( 2 \right)}} } \right)} \right\rfloor$$

(5)

${}^{ex}G_{m}^{{Bi_{2} Te_{3} }}$ is the excess Gibbs energy of Bi₂Te₃ phase described by the parameters:

$$L_{i:i,j}^{{{\text{Bi}}_{2} Te_{3} }} = L_{j:i,j}^{{Bi_{2} Te_{3} }} = L_{*:i,j}^{{Bi_{2} Te_{3} }}$$

(6)

$$L_{i,j:i}^{{Bi_{2} Te_{3} }} = L_{i,j:j}^{{Bi_{2} Te_{3} }} = L_{i,j:*}^{{Bi_{2} Te_{3} }}$$

(7)

3.4 Liquid Phase

The liquid phase was described by an associate solution model,²³ which has been successfully previously adopted.¹³ The liquid phase is assumed to have three species (i.e., Bi, Te and Bi₂Te₃). The Gibbs energy of the liquid is written as:

$$\begin{gathered} {}^{0}G_{m}^{L} = y_{Bi} {}^{0}G_{Bi}^{L} + y_{Te} {}^{0}G_{Te}^{L} + y_{{Bi_{2} Te_{3} }} {}^{0}G_{{Bi_{2} Te_{3} }}^{L} \hfill \\ \quad \quad \;\; + RT\left( {y_{Bi} \ln y_{Bi} + y_{Te} \ln y_{Te} + y_{{Bi_{2} Te_{3} }} \ln y_{{Bi_{2} Te_{3} }} } \right) + {}^{ex}G_{m}^{L} \hfill \\ \end{gathered}$$

(8)

where y_i is a molar fraction of species i (i = Bi, Te and Bi₂Te₃) in liquid phase, ${}^{0}G_{i}^{L}$ is a Gibbs energy of pure liquid species i. Excess Gibbs energy of liquid is denoted as ${}^{ex}G_{m}^{L}$, and T is an absolute temperature and R is a gas constant.

The expression of excess Gibbs energy of liquid has the form:

$$\begin{aligned} {}^{{ex}}G_{m}^{L} & = y_{{Bi}} y_{{Bi_{2} Te_{3} }} \sum\limits_{{i = 0}}^{{n_{1} }} {{}^{i}L_{{Bi,Bi_{2} Te_{3} }}^{L} \left( {y_{{Bi}} - y_{{Bi_{2} Te_{3} }} } \right)^{i} } \\ & \quad + y_{{Bi_{2} Te_{3} }} y_{{Te}} \sum\limits_{{i = 0}}^{{n_{2} }} {{}^{i}L_{{Bi_{2} Te_{3} ,Te}}^{L} \left( {y_{{Bi_{2} Te_{3} }} - y_{{Te}} } \right)^{i} } \\ & \quad + y_{{Bi}} y_{{Te}} \sum\limits_{{i = \,0}}^{{n_{3} }} {{}^{i}L_{{Bi,Te}}^{L} \left( {y_{{Bi}} - y_{{Te}} } \right)^{i} } \\ \end{aligned}$$

(9)

where $n_{1} ,\,n_{2} ,\,n_{3}$ are respectively the degrees of the Redlich-Kister polynomial and parameters ${}^{i}L_{{Bi(Te),Bi_{2} Te_{3} }}^{L}$ are functions of temperature, in general like (1). To optimize this system the model parameters of liquid and Bi₂Te₃ phases were taken from Gierlotka¹³ despite this description resulting in an inverted miscibility gap at T > 1587 °C. Considering the gas phase in thermodynamic calculations it is easy to show that this inverted miscibility gap occurs when the gas phase is the stable phase. Taking into account the available experimental information of this work together with reported data in literature the thermodynamic model parameters of Bi₇Te₃, Bi₂Te and BiTe were evaluated.

The results of the assessment obtained in the present work are presented in Tables 5 and 6. The phase diagram of Bi-Te system calculated from the present assessment is shown in Fig. 5.

Table 5 The optimized parameters of the Bi-Te system

Table 6 The invariant reactions in the Bi-Te system calculated from present assessment

Fig. 5

Bi-Te phase diagram calculated from present assessment. The phase BiTe is modelled as β phase in [12] and [13]. Tie-lines are blue.

4 Discussion

In the present discussion of the phase stability in Bi-Te system the data obtained for two ternary systems were also taken into consideration. Having in mind the future thermodynamic description of Ag-Bi-Te ternary system, the silver addition to Bi-Te phases is reviewed first.

Babanly et al.²⁸ reported the temperature evolution of EMF results obtained in several phase fields of Ag-Bi-Te system α′-Ag₂Te + Bi₂Te, α′-Ag₂Te + BiTe, and α′-Ag₂Te + BiTe + Bi₂Te₃. They used the electrochemical cell:

$$\left( {-} \right) \, Ag \, \left( {solid} \right) \, \left| { \, Ag_{4} RbI_{5} \left( {solid} \right) \, } \right| \, \left( {Ag - Bi - Te} \right) \, \left( {solid} \right) \, \left( + \right)$$

(10)

for which as a solid electrolyte the solid superionic conductor Ag₄RbI₅ was used in relatively narrow temperature range 30–130 °C. The EMF measured in three-phase fields were reproduced upon repeated heating cycles of cells within the range of experimental errors. It means that the electrochemical cell (10) worked reversibly in the experimental temperature range which confirmed the stability of all three phases used as working electrode. Concluding, Babanly et al.²⁸ observed the existence of stable Bi₁₄Te₆ compound and Ag-, Bi₂Te-, BiTe-, and Bi₂Te₃-base solid solutions, which they denoted α, β, γ, and δ, respectively. The Bi₂Te₃-base solubility did not exceed 1 at.% Ag, which is consistent with Brebrick results.²⁴ The solubility of silver in the γ-BiTe and β-Bi₂Te phases was obtained up to ~ 2 at.% Ag at 230 °C. The boundaries between the solid solutions of intermediate phases in the Bi-Te system determined via EMF²⁸ agree with the data from physicochemical analysis.²⁹ It seems that these results have confirmed the stability of Bi₂Te and BiTe phases at low temperatures.

Very similar result was obtained by Prokhorenko et al.³¹ using electrochemical cell:

$$\left( {-} \right) \, Ag \, \left| { \, AgI \, } \right| \, glass \, Ag_{2} GeS_{3} |K\left( + \right),$$

(11)

where cell electrodes K are the equilibrated three-phase alloys in the Ag₂Te-Bi-Bi₂Te₃ region (Fig. 6), and (AgI | glass Ag₂GeS₃) is a two-layers membrane with Ag⁺ ion conductivity. In such cell design the two-layers ion-selective membrane blocks the electron current in the electrochemical cell (11).⁴⁴ The temperature dependences of EMF values of cell (11) were studied in the range of 220–280 °C using the titration method.⁴⁵

Fig. 6

The 3-phase fields of ternary Ag₂Te-Bi-Bi₂Te₃ system proposed by Prokhorenko et al.³¹. (a) pseudo-binaries between compounds (b), (c) the isopleths (Ag)–bismuth telluride. (d) Sample alloy compositions of the 3-phases electrode K of the experimental cells were superimposed³¹.

Also in this work, the obtained EMF results were reproduced upon repeated heating cycles of cells within the experimental error range. Such results confirm the stability of ternary phase fields in this system. Concluding, Prokhorenko et al.³¹ noticed that Bi₂Te₃, BiTe, Bi₂Te, and Bi₁₄Te₆ phases of intermediate variable-composition form in the ternary Bi-Ag₂Te-Bi₂Te₃ system (Fig. 6). In their work,³¹ the thermodynamic properties of saturated solid solutions of the Bi₁₄Te₆, Bi₂Te, BiTe, and Bi₂Te₃ phases in the Ag₂Te-Bi-Bi₂Te₃ system were determined using the EMF method.^{33, 45, 46} The three-phase scheme of the ternary Ag₂Te-Bi-Bi₂Te₃ system within a temperature range of 300-600 K agrees well with the data of Babanly et al..^{28, 32}

The existence of the compounds Bi₂Te₃, BiTe, Bi₂Te and Bi₁₄Te₆ has been also confirmed by Babanly’s group³⁰ in the study of Bi-Te-I system. Besides the DTA and the XRD methods the thermodynamic properties in this system were also analysed by the measurements of electromotive forces of concentration cells with glycerine + KI saturated solution with small BiI₃ addition as the electrolyte. As a result of this study, the series of isopleths, isothermal section of the phase diagram at 300 K and a projection of the liquidus surface were constructed.³¹

In this work, Bi₂Te₃, BiTe and Bi₂Te compounds were synthesized by melting stoichiometric amounts of the corresponding pure, high grade elements under vacuum in quartz ampoules. Bismuth tellurides were synthesized by heating samples to ~ 900 K followed by slow cooling and annealing at temperatures below the corresponding peritectic reactions for 500–800 h. From the EMF measurements the set of partial molar functions of bismuth in ternary alloys have been calculated as a function of temperature.³¹

It should be emphasized that in both analyses of ternary systems²⁸ and³¹ the phase Bi₄Te₃ was not confirmed and the stable Bi₂Te compound was observed at room temperature.

In present work, the comparison of the results of the EDX and XRD analyses for as-cast alloys no. 3, 4 (with chemical composition Bi45Te55, Bi60Te40, respectively), Bi₂Te phase sample and annealed sample no. 4 (Bi60Te40 at.%) differ slightly, which may mean that one of the phases did not occur in a relevant volume in the alloys or that it was too little for the XRD equipment to detect. This confirms the unregular phase distribution in the as-cast alloys during fast cooling in cold water. Generally, the solidification of primary phases (Tab. 2) agrees with the solidification sequence according to the calculated phase diagram (Fig. 5).

Large grains of the primary phase Bi₂Te₃ and fine eutectic structure are visible in the sample of as-cast alloy no. 1 with the composition Bi30Te70 (Fig. 2a). The microstructure of the alloy with the Bi40Te60 composition studied by Zu et al.⁴⁷ looks very similar to as-cast alloy sample in this work. Whereas in this work, the microstructure of the as-cast sample no. 2 (Bi40Te60) practically does not contain the eutectic structure. It indicates a good agreement of the experimental alloy composition with the composition of the Bi₂Te₃ intermetallic compound.

The cooling rate has a significant impact on the degree of supercooling of the alloy, and on the phase crystallization sequence in a relevant alloys.^{48, 49} The tendency to undercooling is greater when the solidification rate is increased. Huang et al.⁴⁸ investigated the peritectic reactions for the alloy with the atomic composition Bi60Te40. The cooling rate range was from 41.4 to 6·10⁵ deg/min, which shows that the lower cooling value according to Huang et al.⁴⁸ was in fact quite high. Experimental results from the work⁴⁸ which indicate the crystallization of the metastable phases: Bi₄Te₅, Bi₄Te₃, is a consequence of strong tendency to undercooling the alloys in Bi-Te system.⁴⁹

Glatz³⁷ studied alloys from the Bi-Te system and concluded that the eutectic on the bismuth side (266 °C) can be eliminated in the alloy with the atomic composition Bi56Te44 by equilibrating it at 300 °C for 180 days, while the equilibration at 250 °C for 90 days does not eliminate the eutectic reaction. For samples with a Te content greater than 40 at.%, which were equilibrated at 400 °C for 39 days, and at 300 °C for 180 days, the traces of Bi eutectic were still observed.³⁷ The data from Glatz’s work³⁷ are consistent with the results obtained for the annealed alloy Bi60Te40 (Table 4, Fig. 4) in the present work – the eutectic is still present in this sample.

The (Bi) and Bi₈Te₃, (Bi) and Bi₈Te₃, Bi₈Te₃ phases were obtained in three equilibrated alloys with compositions Bi90Te10, Bi80Te20, Bi73Te27, respectively, by annealing them at 220 °C for 150 days during the studies carried out by Kifune et al.²⁶ The Bi₈Te₃ phase probably corresponds to the Bi₇Te₃ phase, which appears in the few studies as one of the intermetallic phases in Bi-Te system.^{6, 7, 10} However, this probably indicates that there is also a certain range of non-stoichiometry of this phase, which has not been included in the representation of the Bi-Te phase diagram prepared by Chizhevskaya et al.¹⁰ Additionally, the results of the sample with the composition Bi80Te20²⁶ are consistent with the results of the present work: at this chemical composition of the Bi-Te binary system the two-phase alloy was detected.

X-ray powder diffraction pattern of annealed alloy samples no. 1–6 shown in Figure 4 present quite similar patterns to each other. This is due to the fact that the Bi₇Te₃, Bi₂Te, BiTe, Bi₂Te₃ phases are composed of the same structural units in different configurations of the atom layers: Te(1)Bi(1)Te(2)Bi(1)Te(1) (this layer cluster is only in Bi₂Te₃) and Bi(2)Bi(2).^{6, 12, 27, 49,50,51,52}

Invariant reactions between the equilibrium phases are easier to observe during DTA analysis with low heating rates, e.g. 2 and 5 deg/min, which were also applied in the present work. The experimental DTA results are shown as diamond symbols in the proposed variant of the Bi-Te binary system (Fig. 5). Additionally, the DTA results were compared with the data of other researchers: Mao et al.¹² Brebrick,²⁴ Glatz,³⁷ Strassburger.⁴² The experimental data of the present work do not coincide with the Bi-Te system proposed by Mao et al.¹² The Bi₄Te₃ phase does not occur in the equilibrated samples in present work (Table 4), and it was not recorded in the DTA measurements. The compound Bi₄Te₃, as well as Bi₄Te₅, Bi₆Te₇, Bi₈Te₉ phases are considered to be the metastable phases.^{8, 27}

In addition, the samples of alloys (a–d) in Mao et al. work (Table 1 in¹²) were annealed for 30 days, which seems to be an insufficient period of time to reach the equilibrium in Bi-Te alloys.³⁷ It is also unlikely that the proposed β solution will exist in the Bi-Te binary system, as covalent-ionic interactions in intermetallic compounds do not allow for the formation of a structure with such a wide homogeneity range. Similar conclusions were obtained in the work of Stasova.⁵⁰ Basing on the XRD studies,⁵⁰ the presence of two intermetallic compounds in the binary system, Bi₂Te and BiTe, was confirmed. The BiTe phase was already obtained from very slow cooling, while the Bi₂Te phase required homogenizing equilibration. That observation was also confirmed by the results obtained in present study, where the following phases occurred in the unequilibrated sample of the Bi₂Te composition: BiTe and (Bi) (Table 2, Fig. 2g).

The present experimental DTA data and the similar data of Brebrick,³⁴ Glatz³⁷ and Strassburger⁴² show very good agreement with the liquidus of the Bi-Te system developed by Chizhevskaya et al.¹⁰ The only doubts are the points in the temperature range 260–390 °C for alloy no. 4 with the composition Bi60Te40. It is possible that the solubility of Bi in β(BiTe) phase is probably higher. To solve this problem some additional analyses are requested. On the other hand, the results for alloy no. 4 with the composition Bi60Te40 annealed at 265 °C confirm the presence of the Bi eutectic as in Glatz’s work.³⁷ Therefore, for the alloys with similar compositions, it is necessary to equilibrate the samples over a 6 months period or longer.

After completion of the present work the latest topological data of Bi-Te system were published.⁴³ Hasanova et al.⁴³ proposed the new version phase diagram of Bi-Te system based on the study of long-term annealed samples of the bismuth-rich part of diagram studied by DTA, XRD, and SEM methods. To ensure homogeneous distribution of the elements in the samples, they were quenched from liquid state (430 °C) after alloying by dropping ampoules into water + ice mixture. Depending on the tellurium content the alloys were annealed at different temperatures for 43 days and then all samples were kept at 100 °C for 1 day. For comparison, they⁴³ synthesized several alloys of selected compositions by the traditional fusion method and annealed them under similar conditions.

Additionally, to the above used methods, the EMF study of concentration cell relative to Bi electrode with morpholine formate as an electrolyte was also performed. In the refined version of the phase diagram seven intermetallic compounds, Bi₂Te₃, Bi₄Te₅, Bi₈Te₉, BiTe, Bi₄Te₃, Bi₂Te, and Bi₇Te_3, with practically stoichiometric compositions were reported. All compounds, except Bi₂Te₃, melt incongruently in peritectic reactions. The EMF results were used to determine the partial molar thermodynamic functions of Bi in the alloys. Unfortunately, no BEI micrographs of annealed samples and no heating/cooling rate of DTA analysis were published. Anyhow, the results of experiments of Hasanova et al.⁴³ confirm that the Bi-Te system description with β-phase¹² and¹³ seems to be wrong.

5 Conclusions

At the end, the following conclusions can be drawn:

• Scanning electron microscopy (SEM), X-ray diffraction (XRD) and differential thermal analysis (DTA) methods used to analyse the as-cast and equilibrated alloys of Bi-Te binary system confirmed the presence of the four intermetallic phases: Bi₂Te₃, β(BiTe), Bi₂Te and Bi₇Te₃. The presence of these phases suggests that the phase relations proposed in the descriptions of the binary system by Mao et al.¹² and Gierlotka¹³ differ from the present study. Also, the primary solidified phases were identified from as-cast samples (Table 2).

• The model parameters of phases in Bi-Te system were assessed by optimization of available data by Calphad method. The thermodynamic assessments of Bi-Te system were compared taking also into account the latest experimental data of Hasanova et al.⁴³ The new optimized model parameters of Bi-Te system can form the basis for the design of thermoelectric materials based on bismuth and tellurium, especially with silver addition.

• The stability of intermetallic Bi_nTe_m phases in ternary systems was discussed. The phase sequence of Bi₂Te₃, β(BiTe), Bi₂Te, and Bi₇Te₃ (Bi₁₄Te₆) compounds in Bi-Te system is mentioned.