The study of the Pb–Se–Te phase diagram: Part 2 – The thermodynamic assessment of the Se–Te and Pb–Se–Te systems
Introduction
Pb–Se–Te ternary system is important system for the development of materials for thermoelectric applications which can significantly extend the development of green energy resources and allow significant savings in the energy consumption. The thermoelectric materials can directly convert the waste heat into energy. They are usually used in specific applications as the efficiency of most of these devices is small. It can be described by so called Figure of Merit zT, which characterizes the efficiency of the materials. For zT = 3.0 which is value higher that most of current devices can reach and ΔT = 400 K the power generation efficiency is approx. 25%, which is comparable to traditional heat engines [1]. Nevertheless, they are still exploited in specific niches covering extreme situations and special applications. E.g., the radioisotope thermoelectric generators (RTGs) have long been used as power sources in satellites and space probes, such as Apollo 12, Voyager 1 and Voyager 2 [2], they are also used in modern refrigeration as well as in electric power generation (e.g. exploiting the waste exhaust heat in automobiles) because their simplicity (no moving parts), reliability, and the eco-friendliness compensate their relatively high cost and low efficiency (typically only about 10%).
The constituent Pb–Se, Pb–Te binary and Pb–Se–Te ternary systems are important directly for the development of thermoelectric materials. The binary subsystems have been intensively examined [[3], [4], [5], [6], [7], [8], [9]] and their phase diagrams provide fundamentally important information for materials design and development [[10], [11], [12], [13]]. However, there are only limited phase equilibria experimental studies of the Pb–Se–Te system which are oriented mostly on PbSe–PbTe quasi binary system and liquidius surface [[14], [15], [16], [17]] with exception of the study [18], where two isothermal sections at 350 and 500 °C for the entire compositional range were established. The data [[14], [15], [16], [17]] were used by several authors for the modelling of liquidus and solidus of above-mentioned quasibinary system, using various theoretical approaches [[19], [20], [21], [22], [23]].
Selenium-tellurium alloys have been extensively used for their good optical properties. They perform well as optical recording media, photoreceptors for laser printers and Se–Te glasses yield some improvements in comparison to pure Se glasses. From the point of view of this study the thermoelectric materials of our interest contain Se and Te and therefore reliable theoretical assessment of the Se–Te binary subsystem is needed to be able to assess higher order systems containing these elements, both aforementioned Pb–Se–Te and Ag–Se–Sn–Te. The alloys based on these systems are expected to have good thermoelectric properties.
Thermodynamic assessments of the Se–Te system have been carried out in the past [24,25] to provide its phase diagrams, but their accuracy does not seem satisfactory. Therefore, a thermodynamic re-assessment of this system, which could be used for the thermodynamic description of higher order systems, is needed.
The thermodynamic assessment of Pb–Se–Te ternary system using the new Se–Te description is presented in this paper. To our knowledge there has not been done any CALPHAD assessment of this ternary system so far. These two assessments will be used for the development of databases allowing the prediction of phase diagrams and thermodynamic properties of perspective thermoelectric materials.
Section snippets
Se–Te system
Experimental data for the Se–Te phase diagram were measured by Pellini and Vio [26], Lanyon [27], Kimata [28] and Kotkata et al. [29] using thermal analysis. This system tends to supercool hence the measurements are rather dispersed. Ghosh et al. [24] pointed out that results provided by Kimata [28] do not agree with other results, so they were not used in the optimization in this work. The complete solid-state solubility suggested by experimental data agrees with results obtained by Grison [30
Thermodynamic models
The CALPHAD [11,41] method was used for thermodynamic modelling and calculation of phase diagrams for both studied systems. The calculations were performed using ThermoCalc and PANDAT software, which solve the minimization problem using the least squares method. The Gibbs energies are described relative to the stable element reference (SER) state. SER state is the state of the element at 298.15 K and 105 Pa. The molar Gibbs energy of a phase α (shown for the binary system for the
Se–Te system
The calculated phase diagram of the Se–Te system superimposed with the available experimental data is shown in Fig. 2. The agreement with the data obtained by Pellini and Vio [26], Kotkata et al. [29] and Lanyon [27] is good. Neither the solidus nor the liquidus data measured by Kimata [28] were used for the optimization, because the proposed temperatures are too low compared with other experimental data. The solidus and liquidus experimental data are scattered due to the aforementioned
Conclusion
The Se–Te system was re-assessed using an associate model resulting in a very good agreement with the experimental measurements of phase diagram and enthalpies of mixing in both liquid and solid phase. The maximum calculated fraction of the SeTe associate in the liquid phase is approximately 0.31, which is consistent with the rather wide V-shape of the enthalpy of mixing curve. Slightly worse agreement was reached in the chemical potentials of both elements in the liquid phase, but an issue of
Data availability statement
The thermodynamic dataset is available and will be presented on request.
Declaration of competing interest
Here we declare that the authors have no known conflict of interests with respect to the work published.
Acknowledgements
The authors acknowledge the financial support of the Czech Science Foundation No. 18-25660J, the Ministry of Science and Technology of Taiwan (MOST 107-2923-E-007-005-MY3), and the project of the Brno University of Technology (FSI-S-20-6313). We also thank prof. A. Dinsdale for a fruitful discussion.
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