CC BY
17
62 AZERBAIJAN CHEMICAL JOURNAL № 2 2023 ISSN 2522-1841 (Online)
ISSN 0005-2531 (Print)
UDC 546.81.24/87.24
3D MODELING OF PHASE DIAGRAM OF THE TERNARY SnTe-PbTe-Bi2Te3 SYSTEM
A.LAghazade1, V.I.Babanly2, I.M.Gojayeva\ E.N.Orujlu3, A.N.Mammadov1'4
1M.Nagiyev Institute of Catalysis and Inorganic Chemistry, Ministry of Science and Education
of the Republic of Azerbaijan 2French-Azerbaijani University 3Azerbaijan State Oil and Industry University 4Azerbaijan Technical University
aytenagazade94@gmail. com
Received 26.12.2022 Accepted 02.02.2023
For the SnTe-PbTe-Bi2Te3 system, an analytical model of the temperature-composition dependencies of the crystallization surfaces of the SnTe, PbTe, Bi2Te3, compounds and the ternary PB(Sn)Bi2Te4, Pb(Sn)Bi4Te7, PB(Sn)Bi6Te10 phases formed on based on them was developed and visualized using the 3D analytical function of OriginLab software. The analytical multi-3D model of the phase diagram of the SnTe-PbTe-Bi2Te3 system allows drawing a three-dimensional image of the phases in equilibrium from different angles, obtaining 2D projections, and tabulating the coordinates of the phase diagram. These coordinates as form of matrices - 100x100 = 10.000 and 50x50 = 2500 tabular data create chance for selecting optimal composition and temperature values for the synthesis of alloys, and crystal growth.
Keywords: SnTe-PbTe-Bi2Te3 system, 3D analytical modeling, thermodynamics, topological insulator.
doi.org/10.32737/0005-2531-2023-2-62-68
Introduction
Layered metal chalcogenides have attracted increasing research interest around the globe in the past year's thanks to rich electronic characteristics as well as potential application capabilities in various technological fields. Te-tradymite-like layered antimony and bismuth chalcogenides with a complex crystal lattice are of special interest to researchers for obtaining thermoelectric materials with low thermal conductivity and newly revealed topological insulating properties, for example, ternary-layer compounds in the pseudo-binary AIVBVI-A2VB3VI systems (AIV=Ge, Sn, Pb; AV=Bi, Sb; BVI=Te, Se) [1-10]. From this perspective, the study of phase relationships in multi-component systems, in particular constructing accurate phase diagrams of correlated systems is essential and important [10-12].
The construction of three-dimensional objects representing the surfaces and phase regions of the ternary system T-x-y diagram is the fundamental design principle. The use of 3D computer models of T-x-y diagrams makes it possible to take into account various variants of
the geometric structure of the studied systems. The process of obtaining an ideal model can be long, and additional refinement, as well as experiments, may be required. However, you can be sure that there are no methodological errors in the computer model caused by incorrect interpretation of the experiment and which are detected when constructing phase diagrams using traditional methods [13, 14].
Analytical modeling of phase diagrams of multicomponent systems is carried out in multivariate form [15, 16]. Multivariate modeling is the representation of two or more parameters in one graph. This modeling can be done in two and three dimensional form. Modeling is carried out using the coordinates of known phase diagrams of boundary systems of a multi-component system and a small number of DTA measurements of samples taken from some cross-sections of the system. Firstly, analytical expressions for liquidus surfaces in boundary systems are determined. Then, based on the experimental measurements of the multicompo-nent system, the analytical expressions of the liquidus and stratification surfaces are obtained. Based on these final equations obtained in the
form of polynomial equations, it is possible to obtain a three-dimensional visual description of the system in computer programs such as OriginLab. The variables in the initial graph when placing several surfaces in one graph should be selected in such an interval that all the equations are located in the selected interval. At present, using this method, the stratification surfaces of liquidus and liquid alloys of many ternary systems have been visualized with analytical expressions.
In this paper, we report the results of the 3D modeling of the phase diagram of the SnTe-PbTe-Bi2Te3 system. The phase relationship in the SnTe-PbTe-Bi2Te3 system was studied by us using powder XRD, DTA, and SEM results of the equilibrated alloys [17, 18]. An isothermal section, a liquidus surface projection, and several isopleths were constructed, and the primary crystallization fields of all phases, the types, and coordinates of non- and monovariant equilibria were determined. The analytical model of the phase diagram, in particular, the 3D visualization of the crystallization surface of the phases creates a chance for choosing the optimal conditions for obtaining solid phases by crystallization of liquid alloys of the studied system. For this purpose, literature data on boundary systems and a small number of experimental DTA measurements were used. All analytical dependencies were obtained using the "analysis" option of the OriginLab software.
Modeling technique
The three-dimensional modeling of crystallization surfaces in the SnTe-PbTe-Bi2Te3 system was done using the analytical method that was already successfully tested in [19-22]. In order to determine the temperature-composition dependence expressions of the crystallization surfaces, the analytical equation given below is used:
T=f(x, y) (1)
In this equation, x represents the mole fraction of Bi2Te3 and y=(SnTe/[x(SnTe)+x(PbTe)] where y represents the relative mole fraction
ratio of SnTe and PbTe in ternary SnTe-PbTe-Bi2Te3 system.
The overall modeling process is fulfilled in two stages. At the first stage, the temperature dependences on the composition are determined by T=f (x) and T=f (y) for the liquidus surfaces of both binary boundary systems. Then, T=f (x, y) expressions were determined based on previously found analytical functions and DTA data of synthesized samples in the SnTe-PbTe-Bi2Te3 concentration triangle.
All obtained analytical expressions for the binary boundary, as well as ternary SnTe-PbTe-Bi2Te3 systems are listed in Tables 1 and 2, respectively. The equations are written in the form used by the OriginLab software.
Results and discussion
Binary boundary systems. The literature information about boundary binary systems of the investigated system were adopted from [23-25]. According to PXRD (Powder X-ray Diffraction) and DTA (Differential Thermal Analysis), the existence of four tetradymite-type layered ternary compounds, Sn2Bi2Te5, SnBi2Te4, SnBi4Te7, SnBi6Te10 was confirmed. However, the first compound is not reflected in the constructed phase diagram in [23]. The existence of only three tetradymite-type layered ternary compounds, namely PbBi2Te4, PbBi4Te7, and PbBi6Te10 was confirmed according to our results in the PbTe-Bi2Te3 system [24]. The SnTe-PbTe system is characterized by the formation of continuous series of solid solutions with a tetradymite-like structure [25].
In order to model the crystallization surfaces of the boundary systems, the liquidus surfaces of both systems were divided into several parts, and as can be seen from Table 1, analytical expressions were determined for each of them separately including liquidus and solidus surfaces. The correctness of obtained analytical expressions was checked for one liquidus surface of the SnTe-Bi2Te3 system as an example in Figure 1. It is seen that the obtained analytical dependence approximates the liquidus surface of the SnTe-Bi2Te3 system with high accuracy.
1100-1 10501000950900850800750700
Equation y = Intercept + B1
Plot T,K
Weight No Weighting
Intercept 1079,95823 ± 0,22
B1 -516,26845 ± 1,59
B2 296,81114 ± 2,360
Residual Sum 0,05122
R-Square (CO 1
Adj. R-Square 0,99999
-0,1
0,0
—r~
0,1
0,2 0,3 0,4 Xliq (Bi2Te3)
—I—
0,5
0,6 0,7
Fig. 1. Parameters of the analytical modeling of the liquidus of Bi2Te3 for SnTe-Bi2Te3 system.
Table 1. Phase diagrams and analytical dependencies of liquidus and solidus surface of the PbTe-Bi2Te3 and SnTe-Bi2Te3 systems_
Phase diagram
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 pip2, 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
solidus ß-Bi2Te3, x=0.88-1
760+100*x
40 60 mol%
Fig. 2. Phase diagram of the system PbTe-Bi2Te3124|._
solidus ß-Bi2Te3, x=0.88-0.91
-9155+23100*x-13333*xA2
1
2
3
4
5
6
7
8
40 60 mo/% Bi2Te3 Fig. 3. Phase diagram of the system SnTe-Bi2Te3 [23].
Bi2Te3-SnTe. liquidus a-SnTe, x=0-0.648 1080-516*x+297*xA2 9
liquidus pip2p3. x=0.58-0.82 760+374*x-308*xA2 10
liquidus p3e, x=0.82-0.9 596.6+677.5*x-437.5*xA2 11
liquidus ß-Bi2Te3, x=0.86-1 569+529*x-238*xA2 12
solidus a-SnTe, x=0-0.18 1080-1654*x+ 730*x:2+10863*xA3 13
solidus a-SnTe, x=0.12-0.18 111+7835*x-20109*xA2 14
solidus ß-Bi2Te3, x=0.88-1 760+100*x 15
solidus ß-Bi2Te3, x=0.88-0.91 -50207+118150*x-68333*xA2 16
Table 2. Analytical dependencies of the surface of the phases SnTe-PbTe-Bi2Te3 system
Phase number in Fig. 5. T,K=f(x,y); x(Bi2Te3), y=x(SnTe)/[x(SnTe)+x(PbTe)] xj=mole fractions SnTe, PbTe, Bi2Te3 Eq.N.
1 -(1197-351*x-276,7*xA2-26,8*xA3)*(1-y)+(1079-211,33*x-189,7*xA2-102,1*xA3)*y+16*y*(1-y); x=0-0.625, y=0-1 17
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=0-0.158, y=0-1;(446+4325*x-10545*xA2)*(1-y)+ (443,5+2065*x)*y, x=0.046-0.168, y=0-1; 18
5 (760+374*x-308*xA2)*y+(694,5+593,7*x-518,5*xA2)*(1-y), x=0.625-0.71, y=0-0.95; 19
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; 20
7 (546+592*x-280*xA2)*(1-y)+(731+130*x)*y,x=0.8R0.875, y=0-1 21
9 ( -12550+26300*x), x=0.5-0.51, y=0-1 22
10 (-16942+26300*x), x=0.667-0.677, y=0-0.8; 23
11 (-19125+26300*x), x=0.75-0.759, y=0-1 24
12 (-13642+34100*x-20000*xA2). x=0.9-0.97, y=0-1 25
SnTe-PbTe-Bi2Te3 system. The analytical dependences for 3D modeling of the liquidus and solidus surface of the different phases in the SnTe-PbTe-Bi2Te3 system are listed in Table 2 (equations 17-25). By using these analytical equations, the phase surfaces can be visualized separately (Figure 4) or on a single graph that includes all phases (Figure 5).
The crystallization surfaces of all phases in the SnTe-PbTe-Bi2Te3 system are visualized in Figure 5, where the 3D dimensional phase diagram of the system is viewed from the side of the PbTe-Bi2Te3 system, from top to bottom. In order to understand the crystallization processes in the system, the model may be used to display not only the liquidus and solidus surfaces
but also additional surfaces and phase areas by rotation of 3D figures, x-y projections, etc. Some phase regions in the subsolidus area are shown in this figure as well. It should be noted that the crystallization surface of Sn2Bi2Te5 compound near to the boundary systems was not detected in this figure. However, this compound and related heterogeneous areas may also exist in the subsolidus. Besides, this modeling technique allows us to obtain matrices in the form of 100 □ 100 = 10.000 and 50D50 = 2500 tabular data that can be used for choosing the optimal composition and temperature values for the synthesis of alloys or crystal growth process.
Fig. 4. 3D visualization of the surface of crystallization of solid solutions (PbTe)y(SnTe)(i_y)(Bi2Te3)x in the ternary system SnTe-PbTe-Bi2Te3 according to the eq.(17).
Fig. 5. 3D visualization of the SnTe-PbTe-Bi2Te3 phase diagram from the side of the PbTe-Bi2Te3 system:
1 - Liquid surface of solid solutions based on a (PbTe) and a (SnTe);
2 - Solidus surface of solid solutions based on a (PbTe) and a (SnTe);
3 - Solid solution area based on a (PbTe) and a (SnTe)
4 - Plane obtaining peritectic compounds PbBi2Te4 and SnBi2Te4 ;
5 - Plane of crystallization of peritectic compounds by area p1p2p4p5.
6 - Plane of crystallization of peritectic compounds by area p2p5p3p6e1e2.
7 - Liquid surface of solid solutions based on p-Bi2Te3.
8 - Heterogeneous mixture of phases PbBi2Te4, SnBi2Te4, a(PbTe), a(SnTe).
9-11 - Planes perpendicular to the plane of obtaining peritectic phases Pb(Sn)Bi2Te4, Pb(Sn)Bi4Te7, Pb(Sn)Bi6Te10 12 - Solidus surface of solid solutions based on p-Bi2Te3.
Conclusion
In this work, 3D modeling and visualization of liquidus and solidus surfaces of different phases of the SnTe-PbTe-Bi2Te3 system were performed. The obtained analytical dependences of the liquidus temperatures on the composition made it possible to visualize the crystallization surfaces of the SnTe, PbTe, Bi2Te3, Pb(Sn)Bi2Te4, Pb(Sn)Bi4Te7, Pb(Sn)Bi6Teio phases separately and all on one graph. All analytical dependences were obtained using the 2D and 3D analytical options of the OriginLab software. Obtained matrices in the form of 100x100 = 10.000 and 50x50 = 2500 tabular data can be used for choosing the optimal composition and temperature values for the synthesis of binary alloys, as well as alloys of the ternary system.
Acknowledgment
The work was supported by the Azerbaijan Science Foundation - Grant № AEF-MCG-2022-1(42)-12/10/4-M-10.
References
1. Viti L., Coquillat D., Politano A., Kokh K.A., Ali-yev Z.S., Babanly M.B., Tereshchenko O.E., Knap W., Chulkov E.V., Vitiello M.S. Plasma Wave Terahertz Detection Mediated by Topological Insulators Surface States. Nano Lett. 2016. V. 16. P. 8087.
2. Li R., Liu G., Jing Q., Wang X., Wang H., Zhang J., Ma Y. Pressure-induced superconductivity and structural transitions in topological insulator SnBi2Te4. J. Alloys and Compounds. 2022. V. 900. P. 163371.
3. Shevelkov A.V. Chem. aspects of thermoelectric materials engineering. Russ. Chem. Rev. 2008. V. 77. P. 1-19.
4. Gelbstein Y., Ben-Yehuda O., Pinhas E., Edrei T., Sadia Y., Dashevsky Z., Dariel M.P. Thermoelectric Properties of (Pb,Sn,Ge)Te-Based Alloys. J. Electron. Mater. 2009. V. 38. P. 1478-1482.
5. Kuropatwa B.A, Kleinke H. Thermoelectric Properties of Stoichiometric Compounds in the (SnTe)x(Bi2Te3)y System. Z. anorg. allg. Chem. 2012. V. 638. No 15. P. 2640-2647.
6. Shvets I.A., Klimovskikh I.I., Aliev Z.S., Babanly M.B., Sánchez-Barriga J., Krivenkov M., Shikin A.M., Chulkov E.V. Impact of stoichiometry and disorder on the electronic structure of the PbBi2Te4-xSex topological insulator. Phys. Rev. B. 2017. V. 96. P. 235124-7.
7. Vergniory M.G., Menshchikova T.V., Silkin I.V., Koroteev Yu.M., Eremeev S.V., Chulkov E.V. Electronic and spin structure of a family of Sn based ternary topological insulators. Phys. Rev. B. 2015. V. 92. P. 045134.
8. Zhou X-S., Deng Y., Nan C-W, Lin Y-H. Transport properties of SnTe-Bi2Te3 alloys. J. Alloys Compd. 2003. V. 352. No 1-2. P. 328-332.
9. Shelimova L.E., Karpinski O.G., Konstantinov P.P., Avilov E.S., Kretova M.A., Zemskov V.S. Crystal Structures and Thermoelectric Properties of Layered Compounds in the ATe-Bi2Te3(A = Ge, Sn, Pb) Systems. Inorg. Mater. 2004. P. 451.
10. Seidzade A.E., Orujlu E.N., Babanly D.M. Imam-aliyeva S.Z., Babanly M.B. Solid-Phase Equilibria in the SnTe-Sb2Te3-Te System and the Thermodyna-mic Properties of the Tin-Antimony Tellurides. Russ. J. Inorg. Chem. 2022. V. 67. P. 683-690.
11. Babanly M.B., Chulkov E.V., Aliev Z.S., Shevelkov A.V., Amiraslanov I.R. Phase Diagrams in Materials Science of Topological Insulators Based on Metal Chalcogenides. Russ. J. Inorg. Chem. 2017. V. 62. P. 1703-1729.
12. Mamedov F.M., Babanly D.M., Amiraslanov I.R., Tagiev D.B., Babanly M.B. Physicochemical Analysis of the FeSe-Ga2Se3-In2Se3 System. Russ. J. Inorg. Chem. 2020. V. 65. No 11. P. 1747-1755.
13. Lutsyk V.I., Vorob'eva V. Verification of Phase Diagrams by Three-Dimension Computer Models. Mod Chem Appl. 2017. V. 5. No 1. P. 215.
14. Vorob'eva V., Zelenaya A., Lutsyk V. Analysis of the geometric features of T-x-y diagrams with melt immiscibility for silicate systems. JPCS.
2021. V. 1791. P. 012121-8.
15. Tagiyev D., Manafov M., Mammadov A. Kimyada informasiya texnologiyalannin tatbiqi. Baki: Elm n9§riyyati. 2018. 358 s.
16. Bhadeshia H.K.D.H. Mathematical models in materials science. Mater. Sci. Technol. 2008. V. 24. No 2. P. 128-136.
17. Aghazade A.I., Orujlu E.N., Babanly M.B. Experimental investigation of solid-phase equilibria in the SnTe-PbTe-Bi2Te3 system. Mezhdunarodnaya nauchnaya kon-ferenciya "Kinetika i mekhanizm kristallizacii. Kris-tallizaciya i materialy novogo pokoleniya", Ivanovo. 2021. P. 229-230. 2021. P. 229-230.
18. Aghazade A.I. Phase relations and characterization of solid solutions in the SnBi2Te4-PbBi2Te4 and SnBi4Te7-PbBi4Te7 systems. J. Azerb. Chem.
2022. V. 3. P. 75-80.
19. Yusibov Yu. A., Mamedov A.N., Babanly M.B. et al. Experimental Study and 3D Modeling of the Phase Diagram of the Ag-Sn-Se System. Russ. J. Inorg. Chem. 2018. V. 63. P. 1622.
20. Ahmadov E.J., Mammadov A.N., Guliyeva S.A., Babanly M.B. Modeling of phase diagram of the
system BiI3-Bi2S3-Bi2Te3. New Materials, Compounds and Applications. 2021. V. 5. No 1. P. 511.
21. Imamaliyeva S.Z., Alakbarzade G.I., Mamedov A.N., Babanly M.B. Modeling the phase diagram of the Tl9TbTe6-Tl4PbTe3-TlgBiTe6 system. J. Azerb. Chem. 2021. V. 2. P. 6-12.
22. Orujlu E.N., Mammadov A.N., Babanly M.B. 3D analytical modeling of crystallization surfaces of the MnTe-SnTe-Sb2Te3 system. J. Azerb. Chem. 2021. 2. P. 94-100.
23. Seidzade A.E., Orujlu E.N., Aliev Z.S., Babanly M.B. New investigation of phase equilibria in the
SnTe-Bi2Te3 system, 10 Rostocker International Conference: "Thermophysical Properties for Technical Thermodynamics", Rostock, Germany. 2021. P. 134.
24. Gojayeva I.M., Babanly V.I., Aghazade A.I., Orujlu E.N. Experimental reinvestigation of the PbTe-Bi2Te3 pseudo-binary system. J. Azerb. Chem. 2022. V. 1. No 2. P. 47-53.
25. Volykhov A.A., Yashina L.V., Shtanov V.I. Phase Relations in Pseudobinary Systems of Germanium, Tin, and Lead Chalcogenides. Inorg. Mater. 2006. V. 42. No 6. P. 596-604.
UÇLU SnTe-PbTe-Bi2Te3 SISTEMININ FAZA DIAQRAMININ 3D MODELLO§DIRILMOSI
A.i.Agazad3, V.i.Babanh, i.M.Qocayeva, E.N.Oruclu, A.N.Mammadov
SnTe-PbTe-Bi2Te3 sisteminda SnTe, PbTe, Bi2Te3 birlaçmalarinin va onlann asasinda эшэ1э galan ûçlû Pb(Sn)Bi2Te4, Pb(Sn)Bi4Te7, Pb(Sn)Bi6Teio fazalann kristallaçma sathlarinin temperatur-tarkib asililiqlannin analitik modeli içlanmiç va OriginLab kompüter proqraminin 3D funksiyasindan istifada etmakla vizuallaçdmlimiçdir. SnTe-PbTe-Bi2Te3 sisteminin faza diaqraminin analitik multi-3D modeli tarazliqda olan fazalann ûç ôlçûlû görüntüsünu müxtalif bucaqlardan tartib etmaya, 2D proyeksiyalanni almaga va faza diaqraminin koordinatlarini cadvallaçdirmaya imkan verir. Bu koordinatlar matris formasi kimi - 100x100 = 10.000 va 50x50 = 2500 cadval malumatlari arintilarin sintezi va kristal böyümasi ûçûn optimal tarkib va temperatur qiymatlarinin seçilmasina imkan yaradir.
Açar sözlzr: SnTe-PbTe-Bi2Te3 sistemi, 3D analtik modelh§dirm3, termodinamika, topoloji izolyator.
3D МОДЕЛИРОВАНИЕ ФАЗОВОЙ ДИАГРАММЫ ТРОЙНОЙ СИСТЕМЫ SnTe-PbTe-Bi2Te3
А.И.Агазаде, В.И.Бабанлы, И.М.Годжаева, Э.Н.Оруджлу, А.Н.Мамедов
Аналитическая модель температур-состав зависимостей поверхностей кристаллизации SnTe, РЬТе, Bi2Te3 и тройных фаз на их основе РЬ^п)В^Те4, Pb(Sn)Bi4Te7, РЬ^п)В^Тею в системе SnTe-PbTe-Bi2Te3 была разработана и визуализирована с помощью 3Д функции компьютерной программы OriginLab. Аналитический многомерный 3Д модель фазовой диаграммы системы SnTe-PbTe-Bi2Te3 позволяет построить трехмерное изображение равновесных фаз под разными углами, получить двумерные проекции и табулировать координаты фазовой диаграммы. Эти координаты в виде матриц - 100х100 = 10000 и 50х50 = 2500 табличный данный создают возможность выбора оптимальных значений состава и температуры для синтеза сплавов и роста кристаллов.
Ключевые слова: система SnTe-PbTe-Bi2Te3, трехмерное аналитическое моделирование, термодинамика, топологический изолятор.
