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17Condensed Matter and Interphases (Kondensirovannye sredy i mezhfaznye granitsy)
Original articles
DOI: https://doi.org/10.17308/kcmf.2020.22/2961 ISSN 1606-867X
Received 22 June 2020 elSSN 2687-0711
Accepted 15 July 2020 Published online 30 September 2020
Thermodynamic investigation of the Bi2Se3-Bi2Te3 system by the EMF method
© 2020 G. S. Hasanovaa, A. I. Aghazadeb, Yu. A. Yusibova, M. B. BabanlybH
aGanja State University
425, H. Aliyev, Ganja AZ-2001, Azerbaijan
bInstitute of Catalysis and Inorganic Сhemistry, Azerbaijan National Academy of Sciences 113, H. Javid ave., Baku AZ-1143, Azerbaijan
Abstract
Binary and complex chalcogenides with a tetradimite-like layered structure are of great practical interest as topological insulators, thermoelectric, and optoelectronic materials. Their fundamental thermodynamic functions in combination with phase diagrams are important for the development and optimization of methods for the synthesis and growth of crystals. The work presents the results of a thermodynamic study of the starting compounds and solid solutions of the Bi2Se3-Bi2Te 3 system using the method of electromotive forces (EMF). Various modifications of this method are widely used to study binary and complex metal chalcogenides. Studies were carried out by EMF measurements of the concentration chains of the following type:
(-) Bi (solid) | ionic liquid + Bi3+ | Bi in the alloy (solid) (+) in the temperature range 300-450 K.
The pre-synthesized equilibrium Bi2Se3xTex alloys (x = 0; 0.6; 1.2; 1.8; 2.0; 2.4; 3.0) with a 0.5 at% excess tellurium were used as right electrodes. Ionic liquid (morpholine formate) with the addition of BiCl3 was used as the electrolyte. The acquired experimental data were processed by the Microsoft Office Excel 2003 computer program using the least-squares method and linear equations of the type E = a + bT were obtained. The obtained equations of the EMF temperature dependences were used to calculate the relative partial molar functions of bismuth in the alloys. The diagram of solid-phase equilibria of the Bi-Se-Te system was used to determine the equations of potential-forming reactions and the latter were used to calculate the standard thermodynamic functions of the formation and standard entropies of Bi2Se3, Bi2Te 3 compounds and Bi2Se3xTex solid solutions of the above compositions. The thermodynamic functions of the formation of Bi2Se3xTex solid solutions from the initial binary compounds were also calculated. The results correlate well with the structural data that suggests some ordering in the arrangement of selenium and tellurium atoms in the b-phase crystal lattice of the Bi2SeTe2 composition: selenium atoms predominantly occupy the central layer of the five-layer, and tellurium atoms are located in the two outer layers.
Keywords: bismuth selenides, bismuth telluride, solid solutions, EMF method, thermodynamic properties. Funding: The work has been carried out within the framework of the international joint research laboratory "Advanced Materials for Spintronics and Quantum Computing" (AMSQC) established between Institute of Catalysis and Inorganic Chemistry of ANAS (Azerbaijan) and Donostia International Physics Center (Basque Country, Spain) and partially supported by the Science Development Foundation under the President of the Republic of Azerbaijan, a grant ElF/MQM/Elm-Tehsil-1-2016-1(26)-71/01/4-M-33.
For citation: Hasanova G. S., Aghazade A. I., Yusibov Yu. A., Babanly M. B. Thermodynamic investigation of the Bi2Se3-Bi2Te3 system by the EMF method. Kondensirovannye sredy i mezhfaznye granitsy = Condensed Matter and Interphases. 2020;22(3): 310-319. DOI: https://doi.org/10.17308/kcmf.2020.22/2961
El Mahammad B. Babanly, e-mail: [email protected]
l@ ® I The content is available under Creative Commons Attribution 4.0 License.
1. Introduction
The Bi2Se3, Bi2Te 3 compounds, as well as solid solutions and composites based on them are of great interest as thermoelectric and optoelectronic materials [1-6]. Recent studies have shown that they are also topological insulators and are extremely promising for use in spintronics, quantum computers, and other high technology areas [7-12]. The introduction of magnetic elements into the crystal structure of these compounds led to the creation of a new class of innovative functional materials, i.e. magnetic topological insulators [13-16].
The thermodynamic functions of compounds and variable phases are their fundamental characteristics and, in combination with phase diagrams, form the basis for the synthesis and growth of crystals [17, 18]. Analysis of the reported data has shown that the thermodynamic properties of Bi2Se3 and Bi2Te 3 have been studied in many works by various methods [19-23]. Experimental studies of the thermodynamic properties of the Bi2Se3-Bi2Te3 solid solutions were carried out by the electromotive force (EMF) method in the temperature range of 670840 K [23]. An analysis showed that Bi2Te 3+Te and Bi2SexTe 3-x+Te alloys used as electrodes in the concentration cell contain a Te-based liquid solution in the indicated temperature range. According to the phase diagrams of the Bi-Te and Bi-Se-Te systems, the composition of this liquid phase varies with temperature, which should lead to a distortion of the EMF values, especially their temperature coefficient [24].
The aim of this work is the thermodynamic study of the initial compounds and solid solutions of the Bi2Se3-Bi2Te 3 system by the EMF method.
Various modifications of the EMF method are widely used to study binary and complex metal chalcogenides [25-33]. In high-temperature studies, as a rule, eutectic melts of alkali metal salts are used as an electrolyte. In the study of solid metal chalcogenides, it is advisable to make measurements at temperatures below solidus. For this purpose, the most suitable electrolytes were glycerol solutions of alkali metal salts, first used in [34] in the study of amalgam systems. In our recent studies [35, 36], an ionic liquid was successfully tested as a liquid electrolyte.
2. Experimental
To study the thermodynamic properties of the Bi2Se3-Bi2Te 3 system by the EMF method, the concentration cells of the following type
(-) Bi (solid) | ionic liquid + Bi3+ |
| Bi in the alloy (solid) (+) (1)
were assembled and their EMF in the temperature range 300-450 K were measured.
Elemental bismuth was used as the left electrode, and Bi2Se3-xTex equilibrium alloys (x = 0; 0.6; 1.2; 1.8; 2.0; 2.4; 3X0) with a 0.5 at% excess tellurium were used as the right electrodes.
The alloys of the right electrodes were synthesized by the melting of the previously synthesized and identified Bi2Se3, Bi2Te 3 compounds, and excess tellurium in evacuated (~ 10-2 Pa) quartz ampoules at 1000 K, followed by annealing at 750 K (500 h) and 400 K (20 h). The phase composition of the obtained alloys was confirmed by XRD.
Ionic liquid (morpholine formate) with the addition of BiCl3 was used as the electrolyte. Morpholine, formic acid, and anhydrous BiCl3 purchased from Alfa Aesar were used to produce the ionic liquid. The ionic liquid was obtained using the procedure described in [37]. The assembly of electrochemical cells of type (1) and the method for measuring EMF are described in detail in [27, 36].
The first equilibrium EMF values were obtained after maintaining the electrochemical cell at ~350 K for 40-60 hours; the subsequent values were obtained every 3-4 hours after a specific temperature was established. The EMF values were considered equilibrium if they did not differ from each other by more than 0.2 mV when measured repeatedly at a given temperature, regardless of the direction of the temperature change.
3. Results and discussion
The measurements showed that for each studied sample, the EMF value varied linearly with temperature (Fig. 1), and the EMF concentration dependence was a monotonic function. This confirms the phase diagram of the Bi2Se3-Bi2Te 3 system, according to which, it is characterized by the formation of a continuous series of solid solutions [38].
Fig. 1. Temperature dependencies of EMF for the alloys of the Bi2Se 3
Bi2Sei.;
Te • 4 ■
I 1.2* ^
Bi2Sei.2Te 1.8; 5 -
Bi2SeTe2; 6 ■
Bi2Seo.6Te 2.4; 7
2~~3 Bi2Te3 system. 1 Bi2Te3
Bi2Se3; 2 ■
Bi2Se2.4Teo.6;
The acquired experimental data were processed by the Microsoft Office Excel 2003 computer program using the least-squares method and linear equations of the type E = a + bT were obtained. The calculation steps for the Bi2Se24Te 06 sample are given in Table 1. The linear equations obtained during the calculations are shown in Table 2 in accordance with modern recommendations [26,27]:
E = a + bT ± t
d2 _ ^+sb(T - T)2
1/2
(2)
In equation (2), a and b are coefficients,_n is the number of pairs of values of E and T; T is the average temperature, K; t is Student's t-test, §E and 8b are dispersions of individual values of EMF and constant b. Given that the number of experimental points is n = 30, at a confidence level of 95 %, the Student test is t < 2 [26].
The obtained equations (Table 2) and known expressions [26]:
AGbî=- zFE
(3)
ASbî= ZF
dE
vdT;
= zF b
AHBi=-zF
E - T
dE_ dT
= -zFa
(4)
(5)
were used to calculate the partial molar Gibbs free energy, enthalpy, and entropy of bismuth in the alloys (Table 3).
As can be seen from Fig. 2, these partial molar functions continuously change with composition, which reflects the formation of a continuous series of solid solutions in the system.
To calculate the integral thermodynamic functions of Bi2SexTe 3-x solid solutions, we constructed a diagram of the solid-phase equilibria of the Bi-Se-Te system in the Bi2Se3-Bi2Te3-Te-Se composition range (Fig. 3) using the data from [38, 39]. According to [38], alloys of the Bi-Se and Bi-Te boundary systems in the composition range < 40 at% Bi consist of the two-phase mixtures Bi2Se3+Se and Bi2Te 3+Te accordingly. Another boundary Se-Te system
p
p
Table 1. Experimentally obtained data for temperature (T) and EMF (E) and data associated with the calculation steps for the Bi2Se24Te 06 sample
T, K l7 E,, mB T - T Ei (T - T) (T - T)2 E E, - E (E, - E)2
299.3 228.63 -74.26 -16978.83 5515.04 228.13 0.50 0.25
304.8 228.12 -68.76 -15686.29 4728.40 228.27 -0.15 0.02
311.7 228.71 -61.86 -14148.76 3827.07 228.45 0.26 0.07
316.2 228.95 -57.36 -13133.34 3290.55 228.57 0.38 0.14
320.6 228.23 -52.96 -12087.82 2805.11 228.69 -0.46 0.21
325.1 229.02 -48.46 -11099.07 2348.69 228.81 0.21 0.05
328.6 228.56 -44.96 -10276.82 2021.70 228.90 -0.34 0.11
334.8 228.11 -38.76 -8842.30 1502.60 229.06 -0.95 0.90
339.2 228.86 -34.36 -7864.39 1180.84 229.18 -0.32 0.10
343.5 229.17 -30.06 -6889.61 903.80 229.29 -0.12 0.01
348.4 230.13 -25.16 -5790.84 633.19 229.42 0.71 0.51
352.5 229.14 -21.06 -4826.45 443.66 229.53 -0.39 0.15
358.2 229.78 -15.36 -3530.19 236.03 229.68 0.10 0.01
364.7 229.22 -8.86 -2031.65 78.56 229.85 -0.63 0.39
368.8 230.23 -4.76 -1096.66 22.69 229.96 0.27 0.07
373.4 231.42 -0.16 -37.80 0.03 230.08 1.34 1.80
379.1 230.08 5.54 1273.88 30.65 230.23 -0.15 0.02
384.6 229.86 11.04 2536.89 121.81 230.37 -0.51 0.26
388.2 230.98 14.64 3380.78 214.23 230.47 0.51 0.26
394.3 230.13 20.74 4772.13 430.01 230.63 -0.50 0.25
402.4 230.82 28.84 6656.08 831.55 230.84 -0.02 0.00
407.5 231.47 33.94 7855.32 1151.70 230.98 0.49 0.24
414.1 230.86 40.54 9358.29 1643.22 231.15 -0.29 0.08
419.2 231.58 45.64 10568.54 2082.71 231.28 0.30 0.09
425.8 231.12 52.24 12072.94 2728.67 231.46 -0.34 0.11
431.6 232.07 58.04 13468.57 3368.25 231.61 0.46 0.21
435.5 231.32 61.94 14327.19 3836.15 231.71 -0.39 0.15
440.3 231.83 66.74 15471.56 4453.78 231.84 -0.01 0.00
444.7 232.27 71.14 16522.91 5060.43 231.96 0.31 0.10
449.8 231.78 76.24 17670.13 5812.03 232.09 -0.31 0.10
T = 373.56 E = 230.08
[39], as well as the Bi2Se3-Bi2Te 3 [38] system, is characterized by the formation of a continuous series of solid solutions. Therefore, in the diagram of solid-phase equilibria in the Bi2Se3-Bi2Te 3-Te-Se composition range, the a- and b-solid solutions are in the conode connection. Moreover, in the two-phase region a+b, the directions of the conodes will coincide with the ray lines from the bismuth angle of the concentration triangle.
On the other hand, according to the available data [40], the mixing heat of a-solid solutions
of the Se-Te system with an accuracy of ±1 kJ is zero, i.e. these solid solutions are close to ideal. Therefore, the entropy and Gibbs free energy of mixing the a-phase can be calculated by the following relations:
ASmx =-RT [In x + (1 - x )ln(1 - x)] (6)
AGmk = RT [ln x + (1 - x )ln(1 - x)] (7)
Taking into account the ray nature of the conode in the two-phase region a+b (Fig. 3),
Fig. 2. Composition dependences of the partial molar functions of bismuth in the Bi2Se3-Bi2Te 3 system at 298 K
Te
at% Se
Fig. 3. Diagram of solid-phase equilibria of the Bi-Se-Te system in the Bi„Se3-BLTe 3-Te-Se composition range
Table 2. Relations between the EMF and the temperature for type (1) cells for some samples of the Bi2Se3- Bi2Te 3 system in the 300-450 K temperature interval
Phase E, mV = a + bT ± t-dE(T)
Bi2Se3 241.08 + 0.0082T ± 2 0 33 + 5.4 10-6(T 373.53)2 _ 30 v 7 _ 1/2
Bi2Se2.4Te0.6 220.24 + 0.0263T ± 2 0.22 + 3.6 10-6(T 373.56)2 _ 30 _ 1/2
Bi2Se 1.8Te 1.2 195.02 + 0.0379T ± 2 a27 + 4.4 10-6(T 373.56)2 30 v _ 1/2
Bi2Se 1.2Te 1.8 180.17 + 0.0256T ± 2 0.22 + 3.7 10-6(T 373.56)2 _ 30 v 7 _ 1/2
Bi2SeTe2 175.56 + 0.0018T ± 2 r 02 1 — + 3.2 10-6(T - 376.17)2 _ 30 _ /2
Bi2Se0.6Te2.4 162.40 - 0,0117T ± 2 0.21 + 3.3 10-6(T 376.17)2 _ 30 v 7 _ 1/2
Bi2Te3 136.73 - 0.0133T ± 2 0.21 + 3.4 10-6(T 376.17)2 _ 30 v _ 1/2
Table 3. Partial molar functions of bismuth in the alloys of the Bi2Se3-Bi2Te 3 system at T = 298 K
Phase -AG Bi, kJ/mol -AHBi, kJ/mol AS Bi, J/(mol-K)
Bi2Se3 70.50 ± 0.08 69.78 ± 0.33 2.41 ± 0.87
Bi2Se2.4Te0.6 66.03±0.07 63.75±0.28 7.62±0.74
Bi2Se 1.8Te 1.2 59.73±0.07 56.45±0.30 10.98±0.81
Bi2Se 1.2Te 1.8 54.36±0.07 52.15±0.28 7.40±0.74
Bi2SeTe2 50.97±0.06 50.82±0.26 0.52±0.69
Bi2Se0.6Te2.4 46.00±0.06 47.01±0.27 -3.38±0.69
Bi2Te3 38.86±0.06 41.50±0.26 -7.71±0.70
the potential-forming reaction for any given composition of the b-phase should have the following form:
Bi + 1.5Se, Te = 0.5Bi2Se3 Te . (8)
1-y y 2 3-x x v '
In our case y = 0.2, 0.4, 0.6, 0.67, 0.8. For specific compositions, for example, x = 0.6, y = 0.2, this reaction has the following form:
Bi + 1.5Se0Je0, = (9)
According to reaction (9), for the b-phase of the Bi2Se24Te 06 composition, the standard thermodynamic functions of formation and the standard entropy can be calculated by the following relations:
AfG0 (Bi2 Se2.4 Te0.6) = 2AGBi + 3AGmix(Se0.8 Te0,), (10)
A fH0 (Bi2 Se24 Te06 ) = 2 A H Bi, A fS 0(Bi2Se24Te06) = = 2A S Bi + 2SB0i + 3ASmix(Se08Te0,),
50 (Bi2Se24Te06) = 2A 5 Bi + 2SBi + +3ASmix (Se0.8 Te0.2 ) + 2.4S0 (Se) + 0.6S0 (Te).
(11) (12)
(13)
The calculation results for the starting compounds and Bi2Se3-xTex solid solutions are presented in Table 4.
As can be seen from Table 4, for the initial compounds, our data are coherent with the
Table 4. Standard integral thermodynamic functions of alloys of the Bi2Se3-Bi2Te 3 system
Phase -AGo (298 K), kJ/mol -AH0 (298K), kJ/mol S0 (298K), J/(mobK) Ref.
Bi2Se3 141.0 ± 0.2 139.6 ± 0.7 245.1 ± 4.3 This work
141.1±1.1 142.5±2.0 [41]
143.6±0.4 145.0±4.0 [23]
151.6±2.0 153.5±6.5 [42]
140.2±3.0 240±8 [19-22]
Bi2Se2.4Te 0.6 135.8±0.2 127.5±0.6 272.0±3.0 This work
Bi2Se1.8Te 1.2 124.5±0.2 112.9±0.6 287.6±3.3 This work
Bi2Se1.2Te 1.8 113.7±0.2 104.3±0.6 284.6±3.2 This work
Bi2SeTe2 106.0±0.2 101.6±0.6 269.0±3.0 This work
Bi2Se0.6Te 2.4 95.7±0.2 94.0±0.6 263.2±3.1 This work
Bi2 Te3 76.9±0.2 79.2±0.6 254.2±3.0 This work
77.9±0.6 80.0±4.4 [43]
82.8 87.0 [42]
89.5±0.9 99.5±9.5 [23]
77.3±1.7 78.4±2.1 261.0±8.4 [20. 22]
75.3±1.7 78.6±0.2 251.0±8.4 [21]
results of [41, 43] acquired by the EMF method and recommended in modern handbooks [19-22]. Results [42] for both compounds are somewhat overestimated. It should also be noted that the data of [23] for Bi2Se3 are in agreement with our data, while for Bi2Te 3 they are somewhat overestimated.
By combining the standard thermodynamic functions of the formation of the b-phase of various compositions with the corresponding data for the initial binary compounds, we calculated the Gibbs free energy of the formation and the heat of the formation of b-solid solutions from binary compounds, i.e. thermodynamic mixing functions of Bi2Se3-Bi2Te 3 (Table 5).
Table 5. Thermodynamic functions of mixing of (Bi2Se3)1-y (Bi2Te3)y solid solutions (T = 298 K )
y -AG°mix, kC/mol -AH °mix, kC/mol
0.2 7.6±0.4 -3.1±1.2
0.4 9.1±0.4 -2.6±1.2
0.6 11.2±0.4 0.9±1.2
0.667 8.8±0.4 2.3±1.2
0.8 6.3±0.4 1.7±1.2
It is obvious that the data given in Table 5, characterize the substitution of selenium atoms by tellurium atoms in the Bi2Se3xTex crystal lattice
per 3 mole chalcogen. Therefore, for 1 mole of the solution, these values should be divided by 3. Fig. 4 shows the dependences of the heat and Gibbs free energy of mixing on the composition obtained in this way. As can be seen, the enthalpy of mixing in absolute value does not exceed 1 kJ/mol. In this case, the sign of this function changes from positive to negative in the composition range > 0.6. A similar change in a sign is also observed for the partial entropy of bismuth (Fig. 2). This, as well as the fact that the deepest negative AGmix values are observed for the b-phase with compositions x = 0.6-0.7, indicates the structural ordering in solid solutions of these compositions. This correlates well with structural data [38] suggesting some ordering in the arrangement of selenium and tellurium atoms composition in the crystal lattice of the b- phase of the Bi2SeTe2: selenium atoms predominantly occupy the central layer of the five-layer and tellurium atoms are located in the two outer layers.
A comparison of the data in Tables 4 and 5 with the results of [23] shows their general agreement. A more detailed analysis of data [23] is difficult since, in the temperature range of EMF measurements (670-840 K), a change in the liquid composition of the electrode of Bi2Te 3+Te (L) and Bi2SexTe 3-x+Te (L)
Fig. 4. Concentration dependences of the thermodynamic mixing functions of Bi2Se3 and Bi2Te3 during the formation of Bi2Se3_xTex solid solutions per 1 mol of chalcogen
alloys along the liquidus is inevitable. It means that the EMF temperature coefficient reflects not only the partial entropy of bismuth but also the change in the melt composition [24].
4. Conclusions
The Bi2Se3-Bi2Te 3 system was studied by analysing the EMF measurements of the concentration cells relative to the bismuth electrode in the temperature range 300-450 K. The obtained experimental data was used to calculate the partial thermodynamic functions of bismuth in the alloys. The diagram of solid-phase equilibria of the Bi-Se-Te system in the Bi2Se3-Bi2Te 3-Te-Se composition range was used to determine the potential-forming reactions and the latter were used to calculate the standard thermodynamic functions of the formation and standard entropies of the Bi2Se3, Bi 2Te 3, and Bi2SexTe 3-x solid solutions. The thermodynamic functions of mixing binary compounds during the formation of these solid solutions were calculated by combining these data. The analysis of these functions allowed us to make the conclusion about the ordered arrangement of selenium and tellurium atoms in the crystal lattice of solid solutions with Bi2Te2Se composition.
Acknowledgements
The work has been carried out within the framework of the international joint research laboratory "Advanced Materials for Spintronics and Quantum Computing" (AMSOC) established between Institute of Catalysis and Inorganic
Chemistry of ANAS (Azerbaijan) and Donostia International Physics Center (Basque Country, Spain) and partially supported by the Science Development Foundation under the President of the Republic of Azerbaijan, a grant EiF/MQM/ Elm-Tehsil-1-2016-1(26)-71/01/4-M-33.
Conflict of interests
The authors declare that they have no known competing financial interests or personal relationships that could have influenced the work reported in this paper.
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Information about the authors
Gunel S. Hasanova, Researcher, Ganja State University, Ganja,Azerbaijan; e-mail: gzeynalova1989@ gmail.com. ORCID iD: https://orcid.org/0000-0002-5610-7363.
Ayten I. Aghazade, Research Assistant, Institute of Catalysis and Inorganic Chemistry, Azerbaijan National Academy of Sciences; e-mail: [email protected]. ORCID iD: https://orcid. org/0000-0002-6072-1075.
Yusif A. Yusibov, DSc in Chemistry, Rector of Ganja State University, Ganja, Azerbaijan; e-mail: [email protected]. ORCID iD: https:// orcid.org/0000-0002-9172-3508.
MahammadB. Babanly, DSc in Chemistry, Deputy-Director of the Institute of Catalysis and Inorganic Chemistry, Azerbaijan National Academy of Sciences; e-mail: [email protected]. ORCID iD: https:// orcid.org/0000-0001-5962-3710.
All authors have read and approved the final manuscript.
Translated by Irina Charychanskaya
Edited and proofread by Simon Cox
