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CHEMICAL PROBLEMS 2023 no. 4 (21) ISSN 2221-8688 353
UDC 544.344.015.3: 546.81'86'23
MULTI-3D MODELING OF PHASE DIAGRAM OF PbTe-Bi2Te3-Sb2Te3 SYSTEM
A.I. Aghazade1, S.M. Rustamova3, I.M. Gojayeva1, E.N. Orujlu2, D.M. Babanly12,
A.N. Mammadov1'3
11nstitute of Catalysis and Inorganic Chemistry ofMSE Azerbaijan Republic, AZ1143, H. Javid Ave. 113, Baku, Azerbaijan 2 Azerbaijan State Oil and Industry University, French - Azerbaijani University, AZ 1010, Azadlyg Ave. 20, Baku, Azerbaijan
3Azerbaijan Technical University, AZ1073, H. Javid Ave. 25, Baku, Azerbaijan e-mail: [email protected]
Received 12.07.2023 Accepted 04.09.2023
Abstract. Using the analytical option of the Origin Lab computer program, the analytical dependences of the liquidus temperature on the composition for the PbTe-Bi2Te3, PbTe-Sb2Te3, Bi2Te3-Sb2Te3 boundary systems of the PbTe-Bi2Te3-Sb2Te3 ternary system were determined. Based on these dependencies and thermal analysis data of the ternary system, the analytical model of the temperature-composite dependence of the crystallization surfaces of PbTe, Sb2Te3, Bi2Te3 compounds and PbBi2Te4, PbBi4Te7, PbBi6Te10phases in the PbTe-Bi2Te3-Sb2Te3 system was determined. The resulting equations made it possible to visualize the phase diagram of the PbTe-Bi2Te3-Sb2Te3 system from the side of the PbTe-Bi2Te3 in 3D coordinates. The analytical model of the phase diagram of the PbTe-Bi2Te3-Sb2Te3 system allowed constructing a three-dimensional image of equilibrium phases from different angles, to obtain two-dimensional projections and to tabulate the coordinates of the phase diagram.
Keywords: PbTe-Bi2Te3-Sb2Te3 system, 3D analytical modeling, phase diagram, liquidus, solidus. DOI: 10.32737/2221-8688-2023-4-353-360
1. Introduction
One of the main problems of materials science is the design of new functional materials and the expansion of their existence horizons by optimizing the desired properties and new prospects for application in various fields. In recent years, a lot of theoretical and experimental work has been done to create the thermoelectric materials, which are considered as main method to solve the problems of fuel use and energy harvesting [1-3]. Lead tellurides-based alloys are the most successfully applied thermoelectric materials used in the production of similar materials [4,5]. Also, tetradymite-type layered Bi2Te3-based alloys are classic low-temperature thermoelectric materials, and recently, their electrical and thermal properties have been enhanced through nanostructuring [6,7].
As the information on topological
insulators increased [8, 9], layered bismuth and antimony chalcogenides were also proven to host topological surface states [10-12]. Ongoing research in this field revealed that tetradymite-like ternary compounds formed in AIV —BV -Te systems (AIV-Ge, Sn, Pb; BV-Sb, Bi) systems including AIVBV2Te4, AIVBV4Tey, AIVBV6Te10 are also three-dimensional topological insulators [13-21]. The creation of new multicomponent functional materials is possible based on the phase equilibria data of the corresponding systems. The desired properties can be achieved by substituting appropriate elements in these materials via the formation of solid solutions [22-25].
The main principle of building a three-dimensional (3D) computer model of a T-x-y diagram of a ternary system is the construction of three-dimensional images of its surfaces and
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CHEMICAL PROBLEMS 2023 no. 4 (21)
phase regions. It may take a lot of time and additional experiments to create the ideal model. However, the computer model does not contain the methodological errors detected during the construction of phase diagrams using traditional methods [26].
The phase relationship in the PbTe-Bi2Te3-Sb2Te3 system was studied by using
powder XRD, DTA, and SEM results of the equilibrated alloys [27,28]. In this research, the analytical method was used for 3D modeling of crystallization surfaces of the PbTe-Bi2Te3-Sb2Te3 system based on the data of boundary systems and a small number of experimental DTA measurements.
2. Modeling Technique
The analytical method, tested in [29-31], Sb2Te3 system. For 3D modeling of was used for the three-dimensional modeling of crystallization surfaces of phases the following crystallization surfaces in the PbTe-Bi2Te3- equation was used:
Ti(i-2-3)=yTi(i-2) (xi)+(1->0Ti(i.3) (xi)+axi(i-xi)2y(i-y)
(1)
Here y=x2/(x2+x3), y=x3/(x2+x3), x1, x2 and x3— are mole fraction of 1, 2, 3 components; T1(1-2) and T1(1-3) - are liquidus temperatures for boundary binary systems 1-2 and 1-3. The parameter a1 is determined from the experimental data of the ternary system PbTe-Bi2Te3-Sb2Te3.
Modeling is made in the following order. First, the temperature dependences on the composition T = f (x) and T = f (y) were
determined for the liquidus of boundary binary systems. Next, based on the experimental data of the PbTe-Bi2Te3-Sb2Te3 ternary system, the function T = f (x,y) is defined, where: x-=x(PbTe): y=x(Bi2Te3)/[ x(Sb2Te3)+ x(Bi2Te3)]; xi - molar fractions of PbTe, Bi2Te3, Sb2Te3 compounds. To determine the boundaries of immiscibility of liquid alloys, the asymmetric version of the model of regular solutions
And the thermodynamic condition for internal stability
(2)
(32AG0/3x2)p,T=-2*(a+b*xA2+2*b*x *(x- i)+b*x*(3*x-i))+8.3i*T/(i -x)+8.3i*T/x (3)
were used. The obtained analytical expressions for the PbTe-Bi2Te3-Sb2Te3 ternary system and its boundary binary systems are given in Tables
1 and 2. The analytical dependencies are given in the form used by the Origin Lab computer program.
2.1. Boundary binary systems
The boundary sides of the analyzed system were studied. According to PXRD (Powder X-ray Diffraction) and DTA (Differential Thermal Analysis) data, the existence of three PbBi2Te4, PbBi4Te7, and PbBi6Teio tetradymite-like layered ternary compounds was confirmed. All listed ternary compounds melt by peritectic reactions at 864, 856, and 851 K, respectively [32]. According to [33-35], two members of nPbTe-mSb2Te3 homologues series, namely, PbSb2Te4 and PbSb4Te7 are formed in the PbTe-Sb2Te3
system, while further studies [35-39] show that earlier reported Pb2Sb6Te11 compound is stable only in a small temperature range and decomposes by solid-phase reaction. The Bi2Te3-Sb2Te3 system is characterized by the formation of continuous solid solutions with a tetradymite-like structure [21].
Here and throughout the text, the following notation is adopted: a-is solid solutions based on PbTe; P-is solid solutions based on Bi2Te3 and Sb2Te3.
Table 1. Phase diagrams and analytical dependencies for liquidus Bi2Te3, PbTe-Sb2Te3, and Sb2Te3-Bi2Te3 systems (equations are
and solidus surfaces of the PbTe-jresented in computer variation).
Phase diagrams
System, region x=x(Bi2Te3)
Equations: T,K=f(x) x=x(Bi2Te3)
Eq. N.
Bi2Te3-PbTe. liquidus a-PbTe, x= 0-0.62
1198-288.4*x-1224*xA2+1321*xA3
liquidus p1p2, x=0.62-0.7
694.5+593.7*x-518.5*xA2
liquidus p2p3e, x=0.7-0.825
776.4+264,5*x-215.4*xA2
liquidus ß-Bi2Te3, x=0.85-1
654+354*x-148*xA2
solidus a-PbTe, x=0-0.18
1198-238*x-20458* xA2+63470*xA3
solidus a-PbTe, x=0.12-0.18
473+4510*x-13000*xA2
Fig. 1. Phase diagram of PbTe-Bi2Te3 [32] system
solidus ß-Bi2Te3, x=0.88-1
760+100*x
solidus ß-Bi2Te3, x=0.88-0.91
-9155+23100*x-13333*xA2
4
10
Bi2Te3- Sb2Te3. x=x(Bi2Te3)=0-1 liquidus
895-35*x+15*x*(1-x)
x=x(Bi2Te3)=0-1 solidus
895-35*x-15*x*(1-x)
40 60 Bi.Te,, mol%
Fig. 2. Phase diagram of Bi2Te3-Sb2Te3 [20] system
12
13
Sb2Te3-PbTe liquidus a-PbTe x=x(PbTe)=0.38-1
653+539*x+5.8*xA2
liquidus p4e2, x= x(PbTe)=0.36-0.38
765+250*x
liquidus ß-Sb2Te3 x=x(PbTe)=0-0.36
895-46*x-180*xA2
solidus ß-Sb2Te3 x=x(PbTe)=0-0.08
895-650*x+1875*xA2
Fig. 3. Phase diagram of Sb2Te3-PbTe [39] system
solidus ß-Sb2Te3 x=x(PbTe)=0.05-0. 1
555+5750*x-25000*xA2
solidus a-PbTe x=x(PbTe)=0.96-1
58828+113775*x-53750*xA2
solidus a-PbTe x=x(PbTe)= 0.96-0.94
446+4325*(1-x)-10545*(1-x)A2
14
15
16
17
18
19
20
5
6
7
8
9
2.2.System PbTe-BiiTe3-SbiTe3
Analytical dependencies of the 3D Sb2Te3 system are given in Table 2 (equations
modeling of the phases of the PbTe-Bi2Te3 - 21-28).
Table 2. Analytical dependencies of the phases of the PbTe-Bi2Te3-Sb2Te3 system.
Phase number in Fig. 4. T,K=f(x,y); x=x(PbTe): y= x(Bi2Te3)/[ x(Sb2Te3)+ x(Bi2Te3)]; xi-mole fractions of the PbTe, Bi2Te3, Sb2Te3 Eq.N.
1 (1197-351*(1-x)-276.7*(1-x)A2-26.8*(1-x)A3)*y+ (653+539*x+5.8*xA2)*(1-y)+70*y*(1-y)*(1-x) x=0-0.625, y=0-1 21
2 (1197-1465,3*x+9728*xA2-91304*xA3)*(1-y)+(1079-1923,1*x+5841,7*xA2-6624,48*xA3)*y-48*y*(1-y), x=0.842-1, y=0-i; (446+4325*x-10545*xA2)*(1 -y)+ (443,5+2065*x)*y, x=0.954-0.832, y=0-1 22
5 694.5+593.7*(1-x)-518.5*(1-x)A2)*y+(765+250*x)*(1-y) +70*y*(1-y)*(1-x) x=0.625-0.71, y=0-0.95 23
6 (776,4+264,5*x-215,4*xA2)*(1-y)+(596,6+677,5*x-437,5*xA2)*y, x=0.695-0.875, y=0-1 24
7 (546+592*x-280*xA2)*(1-y)+(731+130*x)*y, x=0.8R0.875, y=0-1 25
9 (629,6+421,9*(1-x)-190,5*(1-x)A2)*y+(895-46*x-180*xA2)*(1- y)+ 70*y*(1-y)*(1-x); y=0-1 26
11 (-13642+34100*x-20000*xA2). x=0.9-0.97, y=0-1 27
12,13,14 12550+26300*x; 9542-26300*x;-5975+26300*x 28
According to the numbers of the indicated fragments of the phase diagram of the PbTe-
Bi2Te3-Sb2Te3 system, T,K=f(x,y) are visualized in Fig 4:
Fig. 4. 3D view of the phase diagram of the PbTe-Bi2Te3-Sb2Te3 system from the side of the PbTe-
Bi2Te3 system.
1- Liquid surface of solid solutions based on a-PbTe;
2- Solidus surface of solid solutions based on a-PbTe;
3- Solid solution based on a-PbTe;
4- Plane obtaining peritectic PbBi2Te4 compound
5- Liquidus surface of the peritectic PbBi2Te4 compound;
6- Liquidus surface of peritectic PbBi4Te7 and PbBi6Te10 compounds;
7- Liquidus surface of the peritectic Pb2Bi6Te11 compound;
8- Liquid surface of solid solutions based on P-Bi2Te3;
9- Liquid surface of solid solutions based on P-Bi2Te3 and P-Sb2Te3;
10- Solid solution based on P-Bi2Te3 and P-Sb2Te3;
11- Solidus surface of solid solutions based on P-Bi2Te3 and P-Sb2Te3;
12-14- Planes perpendicular to obtaining peritectic phases PbBi2Te4, PbBi4Te7, PbBi6Te10;
15- Heterogeneity areas of solid solutions based on a-PbTe-+ PbBi2Te4;
16- Heterogeneity area of PbBi2Te4 + PbBi4Te7 phase;
17- Heterogeneity area of PbBi4Te7 + PbBi6Te10 phase;
18- Heterogeneity area of PbBi6Te10+ solid solutions based on P-Bi2Te3 and P-Sb2Te3.
3. Conclusion
The use of 3D modeling made it possible to determine the analytical dependences of integral and partial thermodynamic properties depending on the mole fractions of all components in the entire concentration range (xi=0^1) in the 300-1250 K temperature range.
Based on obtained data, the homogeneity areas of stable solid solutions and the areas of the formation of ternary compounds and the multiphase diagram of the PbTe-Sb2Te3-Bi2Te3 system in three-dimensional space were determined. Analytical dependences, in the form of 3D model, according to the analytical option
of the Origin Lab program, contain, respectively, 100x100 = 10,000 and 50x50 = 2500 tabular data in the form of matrices that can be used for choose the optimal values of the composition, and temperature for the synthesis of PbTe, Bi2Te3, Sb2Te3 binary compounds and three-component phases in the PbTe-Bi2Te3 -Sb2Te3 system.
The obtained 3D model of the phase diagram also makes it possible to better understand the crystallization processes in the system via visualization of liquidus and solidus surfaces.
Acknowledgment
The work was supported by the Azerbaijan Science Foundation - Grant № AEF-MCG-2022-1(42)-12/10/4-M-10.
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МУЛЬТИ-3Б МОДЕЛИРОВАНИЕ ФАЗОВОЙ ДИАГРАММЫ СИСТЕМЫ
РЬТе-Б12Тез-8Ь2Тез
1 3 1 2 12
А.И. Агазаде , С.М. Рустамова , И.М. Годжаева , Э.Н. Оруджлу , Д.М. Бабанлы ' ,
А.Н. Мамедов1'3
1 Институт Катализа и Неорганической Химии, Пр. Г.Джавида, 113, А21143 Баку, Азербайджан 2Азербайджанский Государственный Университет Нефти и Промышленности, Французско-Азербайджанский Университет Пр. Азадлыг, 20, А21010 Баку, Азербайджан 3Азербайджанский Технический Университет, Пр. Г.Джавида, 25, А21073 Баку, Азербайджан
Аннотация: С помощью аналитической опции компьютерной программы OriginLab определены аналитические зависимости температуры ликвидуса от состава для граничных систем РЬТе^2Те3, РЬТе-8Ь2Те3, В^Те3-8Ь2Те3 тройной системы РЬТе-В^Те3-8Ь2Те3. На основании этих зависимостей и данных термического анализа тройной системы построена аналитическая модель поверхностей кристаллизации соединений РЬТе, 8Ь2Те3, В^Те3 и фаз РЬВ^Те4, PbBi4Te7, РЬВ^Тею в системе РЬТе-В^Те3-8Ь2Те3. Полученные уравнения позволили визуализировать фазовую диаграмму системы РЬТе-В^Те3-8Ь2Те3 со стороны РЬТе-В^Те3 в трехмерных координатах. Аналитическая модель фазовой диаграммы системы РЬТе-В^Те3-8Ь2Те3 позволяет представить трехмерное изображение равновесных фаз с разных ракурсов, получить двумерные проекции и табулировать координаты фазовой диаграммы.
Ключевые слова: система РЬТе-В^Те3-8Ь2Те3, трехмерное аналитическое моделирование, фазовая диаграмма, ликвидус, солидус.
РЬТе-Б12Те3-8Ь2Те3 SiSTEMiNiN FAZA DÍAQRAMININ МиЬИ^ MODELLЭ§MЭSi
АХ Agazadэ1, S.M. Rustэmova1, i.M. Qocayeva1' E.N. Огис1и2, D.M. ВаЬапИ1'2,
А.^ Mэmmэdov1'3
1 Kataliz уэ Qeyri-йzvi Ктуа ^ЫШШ, И.Сау1ёрг., 113, А21143 ВаЬ, Azэrbaycan 2Azэrbaycan Dovlэt ЫеА уэ Sэnaye Universiteti, Azэrbaycan-Franslz Universiteti, Azadllqрг., 20, А21010 ВаЬ, Azэrbaycan
3Azэrbaycan Техткл Universiteti, И.Сау1ёрг., 25, А21073 ВаЬ, Azэrbaycan
Хи^э: OriginLab kompйter proqrammm апаШк variantmdan istifadэ etmэklэ РЬТе-В^Те3-8Ь2Те3 й?1й sisteminin PbTe-Bi2Te3, РЬТе-8Ь2Те3, Bi2Te3-Sb2Te3 sэrhэd sistemlэri й?йп likvidus 1ешрега1игипип tэrkibdэn апаШк aslllllqlaп тйэууэп edilmi§dir. Ви aslhhqlar vэ й?1й sistemin termiki analizi mэlumatlaп эsasmda PbTe-Bi2Te3-Sb2Te3 sistemindэ РЬТе, Sb2Te3, Bi2Te3 ЬЫэзтэЬйшп vэ PbBi2Te4, PbBi4Te7, PbBi6Telo fazalaпшn kristaПa§ma sэtЫэriшn analitik modeli ^Ьпт^к. А1тап tэnliklэr PbTe-Bi2Te3-Sb2Te3 sisteminin faza diaqramlшn PbTe-Bi2Te3 tэrэfdэn mйxtэlif bucaqlardan й^б^йШ tэsvirini qurmaga, ikiбl5йlй proyeksiyalaпш эЫэ etmэyэ vэ faza diaqrammm кооМтаЙапш cэdvэПэ§dirmэyэ imkan verir. А^аг sozlэr: PbTe-Bi2Te3-Sb2Te3 sistemi, 3D modeПэ§dirmэ, faza diaqraml, likvidus, solidus.
