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ISSN 2522-1841 (Online) ISSN 0005-2531 (Print)
UDC 544.344.015.3: 546.71'81 '86/24
3D ANALYTICAL MODELING OF CRYSTALLIZATION SURFACES OF THE MnTe-SnTe-Sb2Te3 SYSTEM
E.N.Orujlu1, A.N.Mammadov1'2, M-B.Babanly1
institute Catalysis and Inorganic Chemistry, NAS of Azerbaijan 2Azerbaijan Technical University
elnur.oruclu@yahoo.com asif1947a@gmail. com
Received 25.12.2020 Accepted 27.01.2021
An analytical method was used for 3D modeling of crystallization surfaces of the MnTe-SnTe-Sb2Te3 system based on the existing data of boundary systems and a small number of experimental DTA-measurements. All analytical dependencies temperatures on composition for liquidus of the binary and three-system were obtained using the 2D and 3D options of the OriginLab software. The obtained results allowed us to visualize the crystallization surfaces of the phases based on initial components of the MnTe-SnTe-Sb2Te3 system as a separate form and in one graph.
Keywords: 3D analytical modeling, liquidus surfaces, MnTe-SnTe-Sb2Te3 system, topological insulators.
doi.org/10.32737/0005-2531-2021-2-94-100 Introduction
Tetradymite-type layered ternary phases of
the quasi-binary AIV (AVn) Te-B 2V Te3 (AIV = Ge,
Sn, Pb; AVn = Mn; B 2 = Sb, Bi) systems have
been intensively studied as three-dimensional topological insulating materials [1-5]. Among them manganese contained layered phases have especially gained substantial attention since MnBi2Te4 and other ternary manganese-bismuth tellurides possess both topological insulating (TI) and magnetic properties at the same time [6-14]. The relationship between magnetism and TI behavior has dramatically inspired great attention in recent years due to their potential prospects to realize many exotic topological phenomena, including quantum anomalous Hall Effect, topological axion insulators, etc. More recent investigations indicated to the existence of layered chalcogenide MnSb2Te4 which is a structural analog of the well-known MnBi2Te4, is an antiferromagnetic semiconductor with a trivial energy gap [15-17]. In this connection, layered manganese antimony (or bismuth) tellurides and phases based on them with partial substitution of manganese with other elements can be a platform for experimental visualization of many elusive topological quantum effects.
VII
, V '
JV _
The phase relationship in the MnTe-SnTe-Sb2Te3 system was studied by us using powder XRD, DTA, and SEM results of the equilibrated alloys. In this work, an analytical method was used for 3D modeling of crystallization surfaces of the MnTe-SnTe-Sb2Te3 system based on the data of boundary systems and a small number of experimental DTA measurements. All analytical dependencies were obtained using the "analysis" option of the OriginLab software.
Modeling technique
An analytical method was used for the 3D modeling of crystallization surfaces of the MnTe-SnTe-Sb2Te3 system. The method was successfully tested in several works up to now [18-23]. The temperature dependences of the crystallization surface were determined as a form of function (1) for the three-component MnTe-SnTe-Sb2Te3 system:
T=f(x, y). (1)
Here x - is the mole fraction of MnTe: y=x(Sb2Te3/[x(Sb2Te3)+ x(SnTe)] and y - is relative mole fraction of Sb2Te3 in MnTe-SnTe-Sb2Te3 system.
The obtained analytical expressions for ternary MnTe-SnTe-Sb2Te3 and its boundary systems are listed in Tables 1 and 2. All analyt-
ical dependences were presented in the form used by the OriginLab software.
The modeling process was carried out in the following order. Firstly, the temperature dependences of the compositions were determined as T = f (x) and T = f (y) for the liquidus of each boundary system. Next, T=f (x, y) function was defined based on experimental results of the MnTe-SnTe-Sb2Te3 system.
Results and discussion
Binary boundary systems. The boundary systems of the investigated system have been carefully studied. The phase equilibria of the MnTe-Sb2Te3 system was investigated using powder X-ray diffraction and Differential Thermal Analysis methods in [24]. The system is featured with the formations of 2 intermediate compounds, MnSb2Te4 and MnSb4Te7, which melts peritectically at 920 and 901 K respectively. There are significant solid-solubility fields based on both ternary compounds and starting Sb2Te3. Similarly, the SnT--Sb2Te3 system is also featured by the formation of the two ternary SnSb2Te4 and SnSb4Te7 compounds that melt peritectically at 868 and 866 K respectively. Besides, the system has homogeneity areas
based on both starting and intermediate compounds. However, the SnTe-MnTe system is characterized by a wide range of solid solutions based on SnTe and MnTe [25].
The phase diagrams of the boundary SnTe-MnTe, MnTe-Sb2Te3 and SnTe-Sb2Te3 systems and their analytical dependences for liquidus curves are shown in Table 1(eq.1-10). Analytical dependencies were determined using the "analysis" option of the OriginLab software. As can be seen in Figure 1, obtained analytical dependence approximates the liquidus curve of the compound of the MnTe-Sb2Te3 system with sufficient accuracy.
MnTe-SnTe-Sb2Te3 system. The analytical dependences for 3D modeling of the liqui-dus surfaces of the MnTe, SnTe, and Sb2Te3 phases are given in Table 2 (equations 11-14). These equations allowing us to visualize the crystallization surfaces separately (Figure 5) and on one graph of all phases (Figure 6).
The crystallization surfaces of phases based on initial components of the MnTe-SnTe-Sb2Te3 system are visualized in Figure 6, where the 3D phase diagram of the system is viewed from the side of the MnTe-Sb2Te3 system, from top to bottom.
X,MnTe
Fig. 1. Dependence of the liquidus temperatures of the MnTe compound on the composition in the MnTe-Sb2Te3 system: curve - polynomial, symbols - experimental results taken from [24].
Table 1. Phase diagrams and analytical dependencies of their liquidus curves of the SnTe-MnTe, MnTe-Sb2Te3, and SnTe-Sb2Te3 systems (equations are presented in computer variation)_
Phase diagram
Region
Equations: T,K=f(x)
Eq.N.
liquidus (Mn ht), x=x(MnTe)=0.93-1
1250+186*x
liquidus (MnTe ht,it1, it2, rt ), x=x(MnTe)=0.255-0.93
-190+6990*x-12819*xA2+ 10983*xA3-3521*xA4
curve pip2 x=x(MnTe)=0.2-0.255
652,64+1944,85*x-3515.15*xA2
curve p2e x=x(MnTe)=0.154-0.25
746,13+1384.7*x-3051,84*xA2
40 60
mol% Sb2Te3
Fig. 2. Phase diagram of the MnTe-Sb2Te3 system [24].
liquidus (ß-Sb2Te3) x=x(MnTe)=0-0.154
893-9,907*x-188.66*xA2
Liquidus (a-SnTe), x=x(Sb2Te3)=0-0.55
1080,6-614,3*x +190,9*xA2+ 409,2*xA3
Liquidus (ß-Sb2Te3, x=x(Sb2Te3)=0.61-1
40 60 mol% Sb2Te3 Fig. 3. Phase diagram of the SnTe-Sb2Te3 system.
729,92+316,92*x-153,85*xA2
Liquidus (Mn ht),, x=x(MnTe)=0.9R1
928+544*x
Liquidus (MnTe ), x=x(MnTe)=0.25-0.91
1272-2444*x+ 10388*xA2-14994*xA3 +7390*xA4
Liquidus (a-SnTe), x=x(MnTe)=0-0.25
1070+237*x-390*xA2
40 60 mol% MnTe Fig. 4. Phase diagram of the SnTe-MnTe system [25].
10
1
2
3
4
5
6
7
8
9
Table 2. Analytical dependencies for crystallization surfaces of phases based on initial components of the MnTe-SnTe-Sb2Te3 system
Liquidus surface, region T,K=f(x,y); x=x(MnTe); y= x(Sb2Tes/[x(Sb2Tes)+ x(SnTe)]; x,=mole fractions MnTe,SnTe,Sb2Te3 Eq. N
(Mn ht), x=x(MnTe)=0.91-1; 0.93-1; y=0-1 (1250+186*x)*y+(928+544*x)*(1-y) 11
liquidus (MnTe ht,it1, it2,rt ), x=x(MnTe)= 0.245-0.91; y=0-1 (-190+6990*x-12819*xA2+10983*xA3-3521*xA4)*y+(1272-2444*x+10388*xA2-14994*xA3+7390*xA4)*(1-y) 12
liquidus (a-SnTe), x=x(MnTe)= 0-0.29; y=0-0.56 (1080.6 -614.3*y+190.9*yA2+409.2*yA3)*(1-x)A(-0.112) 13
liquidus (ß- Sb2Te3), x=x(MnTe)= 0-0.295; y=0.33-1 (729.92+316.92*y-153.85*yA2)*(1-x)A0.04 14
T,K
Fig. 5. 3D model of crystallization surface of phase based on MnTe, visualized by the equation (12) Table 2.
Fig. 6. Multi-3D model of crystallization surfaces of phases based on (Mn ht), (MnTe ht, it1, it2, rt), a-SnTe and p-Sb2Te3 in the MnTe-SnTe-Sb2Te3 system, visualized by equations 11-14 in Table 2.
Conclusion
An analytical method was used for 3D modeling of crystallization surfaces of the MnTe-SnTe-Sb2Te3 system based on the data of boundary systems and a small number of experimental DTA-measurements. The obtained analytical dependences of the liquidus temperatures on the composition allowed us to visualize the crystallization surfaces of phases based on initial components of the MnTe-SnTe-Sb2Te3 system as a separate form and in one graph. All analytical dependences were obtained using the 2D and 3D analytical options of the OriginLab software. Matrices in the form of 100x100 = 10.000 and 50x50 = 2500 tabular data can be used for choosing the optimal values of the composition and temperature for the synthesis of binary alloys, as well as alloys of the MnTe-SnTe-Sb2Te3 system.
Acknowledgement
This work has been carried out within the framework of the international joint research
laboratory "Advanced Materials for Spintronics and Quantum Computing" (AMSQC) established between the 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 - Grant № EIF-GAT-5-2020-3(37)-12/02/4-M-02.
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MnTe-SnTe-Sb2Te3 SiSTEMiNDO KRiSTALLA§MA SOTHLORiNiN 3D ANALiTiK MODELLO§DiRlLMOSi
E.N.Oruclu, A.N.Mamm3dov, M.B.Babanli
MnTe-SnTe-Sb2Te3 sisteminin kanar ikili sistemlarinin faza diaqramlari va seçilmiç bir neça tarkibin DTA naticalarina asasan ûçlû sistemin kristallaçma sathlarinin 3D modellaçdirilmasi ûçûn analtik asililiqlar mûayyanlaçdirilmiçdir. Asliliqlarin tayini ûçûn OriginLab proqramimn 2D va 3D modellaçdirma funksiyalarindan istifada olunmuçdur. Tayin edilmiç temperatur-tarkib analitik asililiqlari vasitasi ila MnTe-SnTe-Sb2Te3 sisteminin fazalarinin kristallaçma sathlarinin 3D görüntüsünü alinmiçdir.
Açar sözlar: 3D analitik modelh§dirm3, kristalla§dirma ssthlsri, MnTe-SnTe-Sb2Te3 sistemi, topoloji izolyatorlar.
3D АНАЛИТИЧЕСКОЕ МОДЕЛИРОВАНИЕ КРИСТАЛЛИЗАЦИОННЫХ ПОВЕРХНОСТЕЙ
СИСТЕМЫ MnTe-SnTe-Sb2Te3
Э.Н.Оруджлу, А.Н.Мамедов, М.Б.Бабанлы
Для трехмерного моделирования поверхностей кристаллизации системы MnTe-SnTe-Sb2Te3 использовался аналитический метод на основе имеющихся данных граничных систем и небольшого количества экспериментальных ДТА-измерений. Аналитические зависимости температур от составов для ликвидусов исследуемой тройной системы и граничных бинарных систем получены с использованием 2D и 3D функции программы OriginLab. Полученные результаты позволили визуализировать поверхности кристаллизации фаз системы MnTe-SnTe-Sb2Te3.
Ключевые слова: трехмерное аналитическое моделирование, поверхности ликвидуса, система MnTe-SnTe-Sb2Te3, топологические изоляторы.
