Experimental Study of the Tl4PbTe3-Tl9TbTe6-Tl9BiTe6 Section of the Tl-Pb-Bi-Tb-Te System

The aim of the present study was to determine the phase relations in the Tl4PbTe3-Tl9TbTe6-Tl9BiTe6 section of the Tl-Pb-Bi-Tb-Te system. Based on a set of the methods of the physicochemical analysis (differential thermal analysis, powder X-ray diffraction method as well as microhardness measurements), the phase diagram of the Tl4PbTe3-Tl9TbTe6 boundary system, some isopleth sections, liquidus and solidus surfaces projections, as well as isothermal sections at 840 and 860 K, were plotted. Unlimited solid solutions with the Tl5Te3 structure (δ-phase) were found in the system, which are of interest as a thermoelectric materials.


Introduction
Presently, great interest has devoted to the chalcogenides of heavy metals as prospective functional materials which found applications in the wide range of devices such as computer memories, chemical sensors, photo-detectors, solar cells, thermoelectric and optical devices, and ionic sensors [1][2][3][4] . Some of them expected as a good candidates for use in the spintronic devices 5, 6 . The rare-earth materials, including chalcogenides, have been intensively investigated owing to their promising functional properties [7][8][9][10][11] . Tl 5 Te 3 compound crystallizes in tetragonal structure (Sp. gr.I4/mcm, a = 8.930; c = 12.598 Å, z=4) 12,13 . The formula Tl 5 Te 3 can thus be rewritten as Tl 16 [TlTe 3 ] 4 . The thallium atoms on the 4c site can be partially or fully replaced by other elements, resulting in a group of ternary compounds: Tl 4 A IV Te 3 and Tl 9 B V Te 6 -type (A IV -Sn, Pb; B V -Sb, Bi) [14][15][16][17] . Above-stated compounds possess a good thermoelectric performance [18][19][20][21] whereas Tl 9 BiTe 6 found to have excellent thermoelectric properties with extremely low thermal conductivity at room temperature 18 . As it was shown by authors of the Ref. 21  New structural analogs of Tl 5 Te 3 with common formula Tl 9 LnTe 6 (Ln-Ce, Nd, Sm, Gd, Tb, Tm) were found in the 23,24 . Later, the crystal structure, thermoelectric and magnetic properties of a number Tl 9 LnTe 6 -type compounds were determined by H.Kleinke and co-workers 25,27 .
The design and development of novel methods for controlled synthesis and growth of large single crystals require detailed studies of respective phase diagrams [28][29][30] . On the other hand, the improvement of thermoelectric performance can be achieved by introduction of the heavy metals into the crystal lattice 31 . With this aim, we presented the results of the study of phase relations for a number of systems including the Tl 5 Te 3 compound and its structural analogs [32][33][34][35] . The formation of unlimited solid solutions was found for all these systems.
In this paper, we continued to study similar systems and presented the results of the study of the phase relations in the Tl 4 PbTe 3 -Tl 9 TbTe 6 -Tl 9 BiTe 6 section of the Tl-Pb-Bi-Tb-Te system.
The initial compounds of above-mentioned system were studied in a number of papers. Tl 4 PbTe 3 and Tl 9 BiTe 6 melt congruently at 893 K 15  According to Ref. 38 , the boundary system Tl 4 PbTe 3 -Tl 9 BiTe 6 is quasi-binary and characterized by the formation of unlimited solid solutions (δ-phase) with Tl 5 Te 3 -structure.
Other boundary system Tl 9 TbTe 6 -Tl 9 BiTe 6 was shown to contain a continuous series of solid solutions with a Tl 5 Te 3 tetragonal structure, but not quasi-binary due to the incongruent melting of Tl 9 TbTe 6 compound 32 .
All synthesis were carried out in previously cleaned and dried quartz ampoules. Taking into account the high toxicity of thallium and its compounds, we used protective gloves at all times when working.
Stoichiometric amounts of the starting components were put into silica tubes of about 20 cm in length and diameter of about 1.5 cm and sealed under a pressure of 10 -2 Pa. Tl 4 PbTe 3 and Tl 9 BiTe 6 were synthesized by direct synthesis of elemental components in a resistance furnace at 920 K followed by cooling in the switched-off furnace.
The synthesis of Tl 9 TbTe 6 was carried out at 1000 K in the graphitized ampoule in order to avoid the interaction between the terbium and quartz. Then the intermediate ingot of Tl 9 TbTe 6 was powdered in an agate mortar, thoroughly mixed, pressed into a pellet and annealed at 750 K during ~700 h.
The ampoules were shaken during all the heating process in order to help the complete mixing of all the elements.
We used the differential thermal analysis (DTA) and X-ray diffraction (XRD) in order to control the purity of synthesized compounds. Only one thermal effect was observed for Tl 9 BiTe 6 (830 K) and Tl 4 PbTe 3 (893 K), while two peaks for Tl 9 TbTe 6 compound which are relevant to the peritectic reaction at 780 K and its liquidus at 1110 K. These data agree with the literature data 13,17,33 . The X-ray patterns showed that the desired compounds Tl 4 PbTe 3 , Tl 9 TbTe 6 and Tl 9 BiTe 6 formed as pure phases.
The multicomponent alloys of the Tl 4 PbTe 3 -Tl 9 TbTe 6 -Tl 9 BiTe 6 section were prepared by melting of previously synthesized ternary compounds. After thermal treatment at 1000 K for 24-36 h, the samples were slowly cooled (20-30 K per hour) down to 750 K and annealed within 1000 h in order to complete the homogenization.

Methods
We used the DTA and XRD methods, as well as microhardness measurements to analyze the samples of the Tl 4 PbTe 3 -Tl 9 TbTe 6 -Tl 9 BiTe 6 section.
The temperatures of the thermal effects were determined using a NETZSCH 404 F1 Pegasus differential scanning calorimeter within room temperature and ~1400 K at a heating rate of 10 K.min -1 and accuracy of ±2 K. The phase composition of the powdered samples was identified by powder X-ray diffraction Bruker D8 diffractometer with CuK α radiation within 10°≤ 2θ ≤ 70° at room temperature. The unit cell parameters of intermediate alloys were calculated by indexing of powder patterns using Topas V3.0 software. An accuracy of the crystal lattice parameters is shown in parentheses (Table 1). Microhardness measurements were done with a microhardness tester PMT-3, the typical loading being 20 g and accuracy about 20 MPa.

Results and Discussion
The character of the phase relations along the Tl 4 PbTe 3 -Tl 9 TbTe 6 -Tl 9 BiTe 6 section is established based on combined analysis of experimental results and literature data on boundary systems Tl 4 PbTe 3 -Tl 9 BiTe 6 38 and Tl 9 TbTe 6 -Tl 9 BiTe 6 33 ( Fig.1-6).

Tl 4 PbTe 3 -Tl 9 TbTe 6 boundary section
The results of DTA, XRD and microhardness measurements for starting compounds and some intermediate alloys of the Tl 4 PbTe 3 -Tl 9 TbTe 6 section are presented in Table 1. This section (Fig.1) is characterized by the formation of    unlimited solid solutions (δ-phase) with Tl 5 Te 3 -structure. However, it is a non-quasi-binary section of the Tl-Pb-Tb-Te quaternary system due to the peritectic character of melting of the Tl 9 TbTe 6 compound. This leads to the crystallization of TlTbTe 2 compound in a wide composition interval and to the formation of L+TlTbTe 2 two-phase and L+TlTbTe 2 +δ three-phase areas. Due to a narrow interval of temperatures, the area L+TlTbTe 2 +δ is not fixed experimentally and shown by a dashed line. The dependences of microhardness on composition have a flat maximum which is typical for systems with unlimited solid solutions (Fig.1b) 39 .  The XRD powder patterns for some alloys of the Tl 4 PbTe 3 -Tl 9 TbTe 6 section as well as Tl 5 Te 3 are presented in Fig.2. Powder diffraction patterns of Tl 4 PbTe 3 , Tl 9 TbTe 6 and also intermediate alloys are single-phase and have the diffraction patterns qualitatively similar to Tl 5 Te 3 with slight reflections displacement from one compound to another. For example, we present the powder diffraction patterns of alloys with composition 20, 50 and 80 mol% Tl 9 TbTe 6 . Parameters of the tetragonal lattice of solid solutions obey the Vegard's law (Table 1, Fig.1c) 40 .

Isopleth sections of the phase diagram
We plotted some isopleth sections, in order to construct a complete T-x-y diagram. Figs.3a-c present the isopleth sections Tl 9 TbTe 6 -[A], Tl 9 BiTe 6 -[B] and Tl 4 PbTe 3 -[C] of the Tl 4 PbTe 3 -Tl 9 TbTe 6 -Tl 9 BiTe 6 concentrations area, where A, B, and C are equimolar alloys from the respective boundary system as shown in Fig.4.
According to Fig.3a, b, the Tl 4 PbTe 3 -[C] and Tl 9 BiTe 6 -[B] sections are characterized by primary crystallization of the δ-phase from the melt over the entire concentration interval.
In contrast to the above-mentioned sections, along the Tl 9 TbTe 6 -[A] section, the direct crystallization of the δ-phase from the melt occurs only in the interval <60 mol% Tl 9 TbTe 6 . In the Tl 9 TbTe 6 -rich concentration area, the more refractory phase of TlTbTe 2 first crystallizes from the melt. Then a monovariant peritectic process L+TlTbTe↔δ occurs (Fig.3c), as a result of which a three-phase region L+TlTbTe 2 +δ should form on the phase diagram. However, according to DTA data, we were unable to fix this region, which is apparently associated with the narrowness of the temperature interval of the above-stated peritectic reaction. Therefore, this region is indicated by the dotted line (Fig. 3b). The crystallization of all alloys is completed by the formation of δ-phase. The TlTbTe 2 phase is completely consumed in the peritectic reaction L+TlTbTe 2 ↔δ, and the remaining excess of the melt crystallizes into the δ-phase.
The XRD powder patterns for selective alloys on polythermal sections confirmed the formation of continuous solid solutions with the Tl 5 Te 3 -structure.

The liquidus and solidus surfaces projections
Projection of liquidus of the Tl 4 PbTe 3 -Tl 9 TbTe 6 -Tl 9 BiTe 6 section consists of two fields of the primary crystallization of TlTbTe 2 and δ-solid solutions. These fields are separated by a monovariant peritectic curve L+TlTbTe 2 ↔δ (ab curve). The solidus projection (dashed lines) consist of one surface corresponding to the completion of the crystallization of the δ-phase.

Isothermal sections at 860 and 840 K
Both sections are consist of areas of L-, TlTbTe 2 and δ-phases (Fig.5). In alloys with composition <60 mol% Tl 9 TbTe 6 in the two-phase L+δ region the directions of the tie-lines on the studied composition plane. It should be noted that comparison of the isopleth sections (Fig.3) and isothermal sections (Fig.5) shows that the directions of the connodes in the two-phase region L+δ deviate from the T-x plane and constantly vary with temperature. Isothermal sections at 860 and 840 K clearly confirm this.

Conclusion
At the first time, a self-consistent scheme of the phase relations in the Tl 4 PbTe 3 -Tl 9 TbTe 6 -Tl 9 BiTe 6 section of the Tl-Pb-Bi-Tb-Te system is obtained. The T-x diagrams of boundary system Tl 4 PbTe 3 -Tl 9 TbTe 6 , some isopleth sections, an isothermal section at 860 and 840 K, as well as liquidus and solidus surface projections, are plotted. It was shown, that studied system is characterized by the formation of the continuous field of δ-solid solutions with the Tl 5 Te 3 structure. Obtained experimental results can be used for choosing the composition of solution-melt for the growth of the high-quality crystals of δ-phase which are of interest as thermoelectric materials.

Acknowledgment
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).