Experimental reinvestigation and thermodynamic description of Bi-Te binary system

Calphad 60 (2018) 81–89

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Experimental reinvestigation and thermodynamic description of Bi-Te binary system ⁎

Cun Mao1, Mingyue Tan1, Ligang Zhang , Di Wu, Weiming Bai, Libin Liu

T

⁎

School of Materials Science and Engineering, Central South University, Changsha 410083, PR China

A R T I C L E I N F O

A B S T R A C T

Keywords: Phase diagram Bi-Te Thermodynamic calculation CALPHAD

The Bi-Te phase diagram was determined by equilibrium alloy method, combined with electron probe microanalysis (EPMA), X-ray diffraction (XRD) and thermal analysis (DSC). The experimental result shows that there is a β-phase with a large composition range at low temperature, while Bi2Te and Bi4Te3 are relatively stable in the solid-liquid region. A consistent phase diagram that covers the experimental findings has been achieved. Based on the new experimental phase diagram, coupling with the reported thermodynamic data, the thermodynamic optimization of the Bi-Te binary system was carried out with the help of CALPHAD approach. A group of reasonable thermodynamic parameters was obtained.

1. Introduction With the emergence of the energy crisis, research and development of applicable thermoelectric materials for waste heat recovery and power generation have drawn increasing interest in the past decade [1–4]. Among the most suitable materials, the Bi-Te alloys are wellknown commercial materials for good thermoelectric properties at room temperature. However, the low ZT is still limiting its wide applications. Numerous efforts have been made to improve their thermoelectric performance [5–8]. The performance of Bi-Te alloys is strongly associated with the crystallographic structure, thermodynamic stability and phase transformation of Bi-Te compounds which can be readily extracted from the phase diagram and thermodynamic database of Bi-Te system [9–11]. Thus, the construction of reliable phase diagram and the understanding of phase transformation in Bi-Te alloys are of importance to tune the chemical composition and phase constitution of Bi-Te alloys, so as to advance the exploration of novel thermoelectric materials. Although phase relations of Bi-Te system have been studied experimentally for several times, however, a phase diagram which can cover all available experimental results compatibly has not been achieved yet. The contradictions were concentrated on the identification of stable intermetallic compounds and the types and temperatures of relevant invariant reactions. Hansen's early work [12] described the Bi-Te phase diagram into the combination of two simple eutectic reactions separated by a ridge like solid-solution phase (then dominated as β phase by Brown and Lewis ⁎

1

[13]) in the central part. Accordingly, the β phase can be introduced by both eutectic reactions of L→Bi + β and L→Te + β at 266 °C and 413 °C, respectively. The detected invariant temperatures were then verified and agreed by other researchers [14,15]. Hansen's work was consolidated by Brown and Lewis [13], as shown in Fig. 1(a). Based on the evidence of X-ray diffraction, they measured the solidus of β, which indicated the β phase exhibited a broad solid solubility from 32 to 60 at % Te. The minerals Hedleyite (Bi7Te3), Wehrlite (BiTe) and Tellurbismuth (Bi2Te3) were suggested to be described into the single solidsolution β phase due to their close structural similarity as well as the progressive changes in the cell dimensions with change of composition [13]. However, the single β phase description hardly convinced the crystallgraphic scientists especially Glatz [14], and he employed both DTA and metallography to corroborate X-ray measurements in the region of β. It was conducted that congruent melting Bi2Te3 is stable as a single phase over a very narrow composition range and is separated from a bismuth-rich peritectic β-phase by a narrow two-phase field. Noticeably, a peritectic reaction L + Bi2Te3→β at 562 °C was identified and several enthalpic effects were detected [14]. From then on, thermal analysis was widely applied to determine the thermodynamic stability of compounds with specific stoichiometric ratios. The measured DTA readings were correlated with a series of peritectic reactions to form different compounds, which gave rise to an updated phase diagram compiled by Glazov et al. [16]. As shown in Fig. 1(b), four stable compounds, namely Bi7Te3, Bi2Te, BiTe, and Bi2Te3 were present in Glazov's phase diagram. The degenerated solidus of stoichiometric Bi2Te3 and Bi7Te3 as well as the convex solidus of Bi2Te and BiTe，

Corresponding authors. E-mail addresses: [email protected] (L. Zhang), [email protected] (L. Liu). These authors contributed equally to this work and should be considered co-first authors.

https://doi.org/10.1016/j.calphad.2017.11.007 Received 30 July 2017; Received in revised form 24 November 2017; Accepted 29 November 2017 0364-5916/ © 2017 Elsevier Ltd. All rights reserved.

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Fig. 1. Bi-Te phase diagram assessed by (a) Brown and Lewis [13], (b) Glazov et al. [16], (c) Okamoto and Tanner [17].

annealed below the solidus, appropriate temperatures are applied for different alloys to achieve equilibrium more completely (see Table 1). After long-term annealing, the alloys were quenched into ice water to preserve the high-temperature microstructure. The microstructure was observed by scanning electron microscopy(SEM) (FEI Quanta 250). Chemical composition of phases was detected by electron probe microanalysis (EPMA) (JXA-8800R, JEOL, Japan) equipped with OXFORD INCA 500 wave dispersive X-ray spectrometer(WDS). X-ray Powder Diffraction (XRD) was employed to identify the phase constitution of samples. It was performed on a Rigaku D-max/2550VB + X-ray diffractometer using a Cu Ka radiation. Differential Scanning Calorimetry & Thermo-Gravimetric Analysis(DSC/TGA) was adopted to determine the invariant temperatures in alloys. It was carried out on Netzsch 449C under Ar-atmosphere with a heating rate of 10 K/min. In consideration of the volatility of Tellurium, each sample was put into the alumina cup with a lid.

which have a homogeneous range, deviated from the smooth solidus in the region from 27 to 60 at% Te in the phase diagram depicted by Brown [13]. In the latest phase diagram compiled by Okamoto and Tanner [17], as shown in Fig. 1(c), more newly-synthesized compounds were included, so that the smooth solidus in Brown's phase diagram was approximately substituted by a succession of peritectic steps. However, the one-to-one mapping between peritectic temperatures and formed stoichiometric compounds had not been clarified. The tie-lines between solid phases and liquid phase were far beyond clearly outlined. Therefore, the Okamoto's compilation was indeed a compromised result. Due to the undetermined phase diagram of Bi-Te system and complicated structure-composition-energetic relationship of relevant intermetallic compound, we revised the Bi-Te phase diagram. 2. Experimental details The Bi-Te binary phase diagram was studied by discerning the phase constitution and microstructure evolution of key alloy samples with different compositions. The nominal compositions of alloy samples #1#12 are given in Table 1. The alloys were prepared from high purity Bi (99.99 wt%) pieces and pulverized Te (99.99 wt%). The weighed raw materials were sealed in quartz tubes under the protection of inert argon gas and then melted at 700 °C for 2 h followed by water quench. The as-cast samples were subjected to microstructure observation and phase composition analysis. According to former experiment of Bi-Te system [14], the composition of same sample will change after annealed due to the volatility of Tellurium. We thus determined the compositions of each sample before and after annealing by chemical analysis. The compositions of as-cast samples barely deviate from the nominal ones shown in Table 1, while after annealed, about 1–2 at% tellurium lost. In order to conduct a phase diagram more precisely, actual compositions were taken into consideration for annealed sample analysis. The as-cast samples were sealed in evacuated quartz tubes again and

3. Experimental results and analysis 3.1. As-cast microstructure Fig. 2(a)-(f) illustrate the as-cast microstructure of alloys #3-#8, respectively. The dark phase shows a lenticular shape and distributes randomly, indicating it is the primary phase. The light phase serves as a matrix, which solidified from the residual liquid. The EPMA to the central part of the primary laths determined different compositions in individual samples. Increased with alloy composition, the Te content at the central lath also shows an increasing tendency. More importantly, there is inhomogeneous composition distribution of primary laths in individual samples. The EPMA detected decreasing composition profiles of Te from the inner part to the boundary for the cross-section of the primary laths. Taking alloy #4 as an example (Fig. 2(b)), the content of Te was detected as 47 at% in the central part of the lath and gradually 82

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Table 1 Equilibrium phase constitution of Bi-Te alloys. `

Nominal composition (at%) Bi

Te

1

90

10

2

75

25

3

70

30

4

65

35

5

60

40

6

55

45

7

50

50

8

45

55

9

40

60

10

35

65

11

30

70

12

25

75

a

70

30

b

65

35

c

62

38

d

60

40

Heat treatment

220 °C 90 days 220 °C 90 days 220 °C 60 days 320 °C 60 days 320 °C 60 days 400 °C 40 days 400 °C 40 days 400 °C 40 days 400 °C 40 days 320 °C 60 days 320 °C 60 days 320 °C 60 days 320 °C 30 days 375 °C 30 days 420 °C 30 days 450 °C 30 days

Actual composition after annealed (at%)

Composition of phase (at%)

Phase constitution

Bi

Te

Bi

Te

90.24

9.76

75.34

24.66

71.12

28.88

99.60 73.52 99.70 73.49 71.12

0.40 26.47 0.30 26.51 28.88

(Bi) β (Bi) β β

66.05

33.95

66.05

33.95

β

62.17

37.83

62.17

37.83

β

56.65

43.34

56.65

43.34

β

52.82

47.18

52.82

47.18

β

47.69

54.31

41.76

58.24

35.68

64.32

30.37

69.63

25.90

74.10

71.48

28.52

66.32

33.68

63.31

36.69

61.85

38.15

41.36 47.02 40.88 46.77 0.20 40.35 0.18 40.13 0.21 39.98 99.30 66.76 99.12 * 99.25 57.13 99.40 *

58.64 52.98 59.12 53.23 99.80 59.87 99.82 59.87 99.79 60.02 0.70 33.24 0.88 * 0.75 42.87 0.60 *

Bi2Te3 β Bi2Te3 β (Te) Bi2Te3 (Te) Bi2Te3 (Te) Bi2Te3 (Bi) Bi2Te (Bi) β (Bi) Bi4Te3 (Bi) β

Notes: * Chemical composition of the phase is inhomogeneous.

features and composition distribution give evidence of that the continuous solidus form a broad solid solution β phase, which corresponds to the primary lenticular phases in our experiments. It is noteworthy that there is a subtle distinction in the microstructure of the alloy #8 in

decreased to 27 at% at the boundary. And the composition profile in Fig. 3(a) illustrate this variation more visually. The one in contrast is the matrix. It was identified as Bi-rich solid solution in all samples, which unanimously contains 1–2 at% Te. All these microstructural

Fig. 2. SEM/BSE images of as-cast samples: (a) #3 Bi70Te30; (b) #4 Bi65Te35; (c) #5 Bi60Te40; (d) #6 Bi55Te45; (e) #7 Bi50Te50; (f) #8 Bi45Te55.

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Fig. 3. Line scan to primary phase in as-cast samples (a) #4 Bi65Te35, (b) #8 Bi45Te55.

The SEM/BSE image of alloy #8 (Fig. 4(h)) demonstrates another twophase equilibrium. The dark lenticular phase was determined to be Bi2Te3 under EPMA and XRD. The light matrix was measured with a chemical composition of Bi-53 at% Te. Noticeably, the microstructures of the alloys #3-#7 shown in Fig. 4(c)-(g) unanimously turned into homogeneous morphologies after annealing, which illustrates alloys #3-#7 are located in a single-phase region. Those single-phase microstructures are against the Bi-Te phase diagram compiled by Glazov et al. [16], and Okamoto et al. [17], but are more aligned with the β phase determined by Brown and Lewis [13]. As shown in Fig. 4, (Bi), Bi2Te3, and β phases are indexed in individual alloys samples. Since some reflection peaks of Bi, Bi2Te3, and β are overlapped at 2θ = 24°, 38°, they can’t be used to tell one from another. Thus, (Bi), Bi2Te3 and β phases were determined by the peaks symbolled in solid disc, open square and solid pentagram, respectively. With the decreasing of Te content, the reflection peaks (00 m) and (10 n) were continuously right shifting, which indicates that the

comparison with those of other samples. As illustrated in Fig. 2(f), the primary lath contains two types of domains in different colors, leading to a peritectic-like morphology. The dark gray domains which hold a homogeneous composition of Bi2Te3 are surrounded by the gray second phase. The scan line set to illustrate the peritectic reaction in sample #8 is shown in Fig. 3(b). This peritectic reaction can be also traced from the as-cast microstructure of the alloy #7 (Fig. 2(e)). 3.2. Low-temperature annealed microstructure Fig. 4 and Fig. 5 compare the equilibrium microstructural images and XRD patterns of eight annealed alloys. As depicted in Fig. 4(a), (b), the microstructure of alloy #1 and alloy #2 show the same two-phase equilibrium, which is evidenced by the same compositions under EPMA detection and same indexed phases in XRD. The light phase was detected as approximate pure Bi, and the average composition of dark phase was determined to be about Bi-27 at% Te, as shown in Table 1.

Fig. 4. SEM/BSE images of annealed alloy samples #1-#8: (a) #1 Bi90.2Te9.8; (b) #2 Bi75.3Te24.7; (c) #3 Bi71.1Te28.9; (d) #4 Bi66.0Te34.0; (e) #5 Bi62.2Te37.8; (f) #6 Bi56.7Te43.3; (g) #7 Bi52.8Te47.2; (h) #8 Bi45.7Te54.3.

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microstructure of alloy #8. However, it is strange that in the heating curves of alloys #3-#5, as shown in the enlarged view in Fig. 6, other than the endothermic peaks assigned to solidus and liquidus, several weak endothermic effects were detected between the temperatures of solidus and liquidus. According to [16,17], the series peritectic reactions were introduced to account for these DSC effects (shown in Fig. 1(b), (c)). By doing so, two phase microstructures should have been observed under SEM in low-temperature annealed samples. Unfortunately, the homogenous solid solution phase in Fig. 4(c)-(g) obviously cannot account for it. If we admitted that the transformations were originated from the solid-state transformation of β only, the endothermic peaks should be presented in the entire temperature range. However, it violated from our experimental finding either. Fig. 5. X-ray powder diffraction patterns of annealed alloy samples #1-#8: (a) #1 Bi90.2Te9.8; (b) #2 Bi75.3Te24.7; (c) #3 Bi71.1Te28.9; (d) #4 Bi66.0Te34.0; (e) #5 Bi62.2Te37.8; (f) #6 Bi56.7Te43.3; (g) #7 Bi52.8Te47.2; (h) #8 Bi45.7Te54.3.

3.4. High-temperature annealed microstructure To clarify the controversial points mentioned above, four alloy samples were prepared and annealed at different high temperatures. The specific chemical composition of alloy samples and corresponding annealing temperatures are shown in Fig. 7 by red solid circles. Additionally, the four dash lines in Fig. 7 correspond to the four endothermic effects at 312 ℃, 343 ℃, 420 ℃, 440 ℃ we found in DSC, as shown in the enlarged view in Fig. 6. Each sample was encapsulated in a quartz tube backfilled with Ar gas and heat-treated at different temperatures for 30 days, followed by quenching in iced water. Scanning electron microscopy (SEM) with backscatter electron (BSE) imaging were used to microstructure observation, and Electron probe microanalysis (EPMA) was employed for local compositional analysis. The backscattered electron (BSE) images of four samples annealed at different temperatures were depicted in Fig. 7. Two-phase microstructures were obtained for these samples. The light matrix phase in each sample is Bi-based solid solution dissolved with a small content of Te, while it is noteworthy that the morphologies and compositions of the dark phases for different alloys have obvious difference. For the microstructures of samples annealed at 320 °C and 420 °C (a, c), the dark phases in Fig. 7(a, c) are multilaterals with regular shape, of which the chemical composition distributions are all homogeneous. Under the EPMA detection, the chemical constituents of dark phases in these two samples were determined to be approximately Bi-33.3 at% Te and Bi42.9 at% Te, respectively. However, as illustrated in the

variation of chemical composition leads to a little change of the unit cell, but hardly introduces a reconstructive transformation in β phase. The XRD pattern exhibits structure similarity of these annealed alloys. Combined with the microstructures analysis, the experimental findings of annealed samples demonstrate there is a solid solution phase β with a broad composition range being equilibrium with Bi and Bi2Te3. According to the equilibrium composition of two-phase alloys, we determined the solid solubility of β phase ranges from 27 at% Te to 53 at % Te. 3.3. Thermal analysis by DSC Fig. 6 shows typical DSC profiles obtained by heating measurements. And the thermogravimetric curves of all samples are almost horizontal, which indicates the compositions of those samples are still reliable. In the heating curves of annealed alloys #3-#8, the first endothermic signal and the last peak correspond to the start and completion of melting of each sample, i.e., the solidus and liquidus temperatures, respectively. A sharp endothermic signal which appeared at 560 °C in 54.3 at% Te alloy was caused by the peritectic reaction of L + Bi2Te3→β. This peritectic reaction, which was detected by Glatz [14] and Brebrick [15,18] before, also evidenced from the as-cast

Fig. 6. DSC heating curves of alloy samples #3-#8: (a) #3 Bi71.1Te28.9; (b) #4 Bi66.0Te34.0; (c) #5 Bi62.2Te37.8; (d) #6 Bi56.7Te43.3; (e) #7 Bi52.8Te47.2; (f) #8 Bi45.7Te54.3; and enlarged view for alloys #3#5.

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Fig. 7. Composition and annealing temperature of high-temperature annealed alloy samples (a, b, c, d); SEM/BSE images of these samples. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article).

microstructures of samples annealed at 375 °C and 450 °C (b, d), the dark phase with the irregular shape has the obvious variety of contrast. The EPMA detected decreasing composition profiles of Te from the inner part to the boundary for the irregular phase, which is like the primary crystal of the as-cast structure. Therefore, it can be inferred that there could be several phases with relatively stable structure between the liquidus and solidus. The stability of these phases at hightemperature can response to several weak endothermic effects in the heating curve of some samples mentioned above.

Table 2 Crystallographic data of phases in Bi-Te system. Phase

(Bi) (Te) Bi2Te3 Bi2Te Bi4Te3 β

4. Discussion and results of phase diagram

Prototype

As W Bi2Te3 * Bi4Se3 *

Pearson symbol

hR6 cI2 hR5 hP9 hR7 *

Space group

R-3m(166) Im-3m(229) R-3m(166) P-3m1(164) R-3m(166) *

Lattice parameters a(Å)

b(Å)

c(Å)

4.546 4.453 4.388 4.49 4.451 *

4.546 4.453 4.388 4.49 4.451 *

11.862 5.905 30.488 18.09 41.89 *

Refs.

[17] [19] [20] [21] [22]

Notes: * Information of this part is not clear.

The updated Bi-Te phase diagram is shown in Fig. 8. Experimental data in this work are highlighted in red and compared with some reported ones in literature [12,14,15] (in blue). Temperatures in our experiment are from DSC analysis (symbolled as red inverted triangles) and compositional analysis of annealed alloys (symbolled as red points). Those weak endothermic effects between solidus and liquidus at 312 ℃, 343 ℃, 420 ℃, 440 ℃ correspond to the invariant reactions related to Bi2Te and Bi4Te3 respectively. The crystallographic data of phases included in this Bi-Te phase diagram are concluded in Table 2. To better understand the Bi-Te phase diagram, it is necessary to refer to the specificity of crystal structure belong to this binary system. In 1973, Anderson [23] proposed an infinitely adaptive series to describe the existence of a class of crystalline materials with specific structural characteristics. The structures in such a series are built by the ordered repetition of sub-units and can readily interconvert with a minimum of adjustment of atomic positions. In an infinitely adaptive series, changes in chemical composition are accompanied neither by forming a progression of phases nor by forming disordered nonstoichiometric solid solutions. The modulated structure analysis done

by Bos et.al. [24] shows that in the composition range of β phase, each preparation has its own superstructures, which is a classic example of an infinitely adaptive series, while only the certain chemical compositions: Bi2Te and Bi4Te3 can be adequately described using the supercells shown in Fig. 9. The other prepared compositions cannot be described using this structural sketch but do belong to the (Bi2)n(Bi2Te3)m homologous series. Coincidentally, these two certain chemical compositions are close to the EMPA results of regular dark phases in hightemperature annealed samples. With this, we know that the single β phase actually belongs to the infinitely (Bi2)n(Bi2Te3)m homologous series. In the composition range of β phase, each preparation has its own superstructures, so the highly structural similarity of these structures exhibited the characteristics of solid solution, which is explained by our experimental results of low-temperature annealed samples. In this series, certain compositions such as Bi2Te and Bi4Te3 have relatively structural stability at certain temperature ranges, which could contribute to the structural change discontinuously occurring above the solidus. This point can be evidenced by not only our DSC results and morphology difference of SEM/BSE images of samples annealed in different temperatures, but also the pioneers' investigations. In view of phase diagram, in order to fully represent our experimental discoveries without any violation of Gibbs phase law, a updated phase diagram is presented in Fig. 8.

5. Thermodynamic calculations The thermodynamic assessment of the binary Bi-Te system was done by the CALPHAD method. The Gibbs energy functions of elements Bi and Te are taken from the SGTE (Scientific Group Thermodata Europe) database of pure elements [25] (Fig. 10). The liquid phase was modeled as a substitutional solution phase based on random mixing of the constituent atoms. The Gibbs energy of the liquid phase was expressed with the following equation:

Fig. 8. Experimentally determined Bi-Te binary phase diagram compared with data reported in Ref. [12,14,15]. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article).

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Fig. 9. Schematic diagram of crystal structure of BiTe system with specific composition.

G Bi2 Te3 = a + bT + cTln (T ) + dT 2 + eT 3 + fT −1 where a , b , c , d , e and f are the parameters to be optimized according to the thermochemical experimental data [26,27], such as the heat capacity, and formation enthalpy. For Bi2Te and Bi4Te3, due to a lack of the heat capacities of these phases, the molar Gibbs free energy is expressed for each of the intermetallic compounds, according to the Neumann–Kopp rule:

GmBimTen =

m 0 SER n 0 SER GBi + GTe + A + BT m+n m+n

where m and n are the stoichiometric coefficients of the compound SER SER and 0GTe are the molar Gibbs free energies for the pure BimTen; 0GBi components Bi and Te in their Standard Element Reference (SER) states, Rhombohedral_A7 for Bi and Hexagonal_A8 for Te. The parameters A and B are to be optimized in the present work. As we described before, the β-phase can be built by orderly stacking the sub-units Bi and Bi2Te3 along c-axis. β-phase is therefore treated as Bi0.4(Bi, Te)0.6 to describe the stacking of the two atomic clusters as the composition change. The Gibbs energy expression is as the following:

Fig. 10. Calculated phase diagram of the Bi-Te system compared with experimental data in this work.

liquid liquid G liquid = xBi GBi + xTe GTe + RT (xBilnxBi + xTelnxTe ) n liquid i + xBi xTe ∑ iLBi , Te (xBi − xTe ) i=0

G β = yBi GBiβ : Bi + yTe GBiβ : Te+0.6RT (yBi lnyBi + xTelnxTe )

where xBi and xTe are the mole fractions of the pure elements Bi, Te, liquid liquid respectively. GBi and GTe are from SGTE pure elements database [25]. i liquid LBi, Te is the interaction parameter for rhom(Bi), and hex(Te), which liquid is formulated as iLBi , Te = a + bT , and the coefficients a and b are the thermodynamic parameters will be optimized. Bi2Te3, a small homogeneity, is treated as a stoichiometric compound in the present work. Since the heat capacity of Bi2Te3 has been studied before, the molar Gibbs energy is expressed as:

n

+ yBi yTe

∑ jLBiβ :Bi,Te (yBi − yTe ) j j=0

β GBi:Bi

β where and GBi:Te represent the Gibbs energies of Bi and Bi2Te3, respectively. yBi and yTe are the site fractions of Bi and Te in the second sublattice, respectively. The thermodynamic model parameters for the binary system Bi-Te are evaluated based on the experimental information of this work and the reported thermochemical experimental data [26–29].

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Table 3 The optimized parameters of the Bi-Te system. Phase

Evaluated parameters

Liquid phase, Model (Bi, Te)1

0 liquid LBi, Te =−40546 + 9.47T 1 liquid LBi, Te = 4973−2.84T G Bi2 Te3=−31307 + 108.21T-22.33Tln(T)−4.98

Bi2Te3 phase, Model Bi0.4Te0.6

× 10−3 × T2 + 5.252 × 10–11 × T3 + 17080T−1

Bi2Te phase, Model Bi0.667Te0.333

Rohm G Bi2 Te = −14821 + 1.8T + 0.67 0GBi + 0.33

Bi4Te3 phase, Model Bi0.571Te0.429

Rohm G Bi 4 Te3 = −18858 + 3.5T + 0.57 0GBi + 0.43

β phase, Model Bi0.4(Bi, Te)0.6

Fig. 12. Calculated activity of Bi in liquid at 863 K in comparison with experimental data [28].

0 Hex GTe

0 Hex GTe β Rohm GBi:Bi = 2.8T + 0GBi β Bi GBi:Te = 780 + G 2 Te3 0 β LBi : Bi, Te = −9698 + 3.6T 1 β LBi : Bi, Te

= + 8088 −1.0T

Table 4 The invariant reactions in the Bi-Te system. Reaction

Liquid ↔ (Bi) + β Bi2Te ↔ Liquid + β Liquid + β ↔ Bi2Te Bi4Te3 ↔ Liquid + β

Liquid + β ↔ Bi4Te3 Liquid + Bi2Te3 ↔ β

Liquid↔ Bi2Te3 + (Te)

T/°C

Te at%

Ref.

1

2

3

266 263 312 314 343 343 420

2.40 3.14 33.3 33.3 9.3 9.2 42.9

0.0 0.0 6.6 6.6 36.2 36.1 19.1

27.0 27.9 33.3 33.5 33.3 33.3 42.9

430 440 446 560

42.9 21.8 21.6 43.6

19.1 44.2 44.1 60.0

42.9 42.9 42.9 53.0

551 414 414

43.6 90.7 91.2

60.0 60.0 60.0

53.4 100 100

[12] Cal. Exp. Cal. Exp. Cal. Exp. [14] Cal. Exp. Cal. Exp. [14] Cal. Exp. Cal.

Fig. 13. Calculated mixing Enthalpy of liquid at 863 K in comparison with experimental data [29].

Bi2Te3 conducted by Zurhelle et al. [26] and Feng et al. [27], activity of Bi in liquid at 863 K conducted by Feutelais et al. [28], and mixing enthalpies of liquid at 863 K conducted by Morgan et al. [29]). 6. Conclusion Reinvestigation of the Bi-Te binary system performed using equilibrium alloy method has been updated by EPMA-WDS results, XRD analysis, and thermal analysis (DSC). A solid solution with a large composition range (β phase) was observed at low temperature. Two relative stable phases: Bi2Te and Bi4Te3 were found in the solid-liquid region. A self-consistent Bi-Te phase diagram has been put forward. According to the new experimental phase diagram, based on existing thermodynamic data, CALPHAD method was applied in the thermodynamic optimization of the Bi-Te binary system. And a group of reasonable thermodynamic parameters were obtained.

Notes: Exp.: experimental finding Cal.: calculation result.

Prime novelty statement The phase relations in the Bi-Te system have been systematically investigated, and the region of β phase which is full of controversy and divergence before was confirmed and explained. A consistent experimental phase diagram of Bi-Te system that covers all our experimental findings was built. A set of self-consistent thermodynamic parameters for Bi-Te was obtained. All authors have participated sufficiently in this work to take public responsibility for it and approve it for publication. Fig. 11. Calculated heat capacity of Bi2Te3 in comparison with experimental data [26,27].

Acknowledgements This work was supported by the National Natural Science Foundation of China [grant numbers 51501229, 51371200, 51671218].

The optimized thermodynamic parameters and the calculated invariant equilibria are given in Table 3 and Table 4, respectively. The present modeling agrees well with the experimental data of the present work. The activity of Bi in liquid at 863 K, calculated mixing enthalpies of liquid at 863 K and heat capacity of Bi2Te3 are presented in Figs. 11–13, respectively. The present calculated thermochemical data are consistent with the literatures reported ones (heat capacity of

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