• A. N. Mamedov Dr. Sci. (Chem.), Full Professor, Head of the laboratory ICICh; tel.: +(994) 503372845, e-mail:
  • N. Ya. Ahmedova postgraduate student, Azerbaijan Technical University; e-mail:
  • N. B. Babanly Ph.D., Associate Professor of Gazakh Branch of Baku State University; e-mail:
  • E. I. Mamedov Dr. Sci. (Chem.), Full Professor, Head of the Department of Chemistry, Azerbaijan Technical University; e-mail:
Keywords: thermodynamics, copper-lead-selenium, liquidus of lead selenide, vapor pressure of selenium, 3D modeling


From the condition that the chemical potentials of the components of the AB compound
are equal in the equilibrium liquid and solid phases, taking as pure liquid components as the standard
state, equations are obtained for calculating and modeling of partial excess thermodynamic functions,
of the pressure-temperature-composition diagram and liquidus surfaces of the binary compound in
the ternary system A–B–C. The equations obtained are tested on the Cu–Pb–Se system in the liquidus
region of the PbSe compound. It is shown that the vapor phase mainly consists of two atomic molecules
of selenium Se2. For the liquidus regions PbSe(p-type)-Se and PbSe(n-type)-Pb, the following
dependences are obtained, respectively:
lg Se p 2 (Pa) = [–1281 + 5624(1000/T) – 9190(1000/T)2 + 6648(1000/T)3 – 1797(1000/T)4] – 10.35 xCu
2 ;
lg Se p 2 (Pa) = [2026 – 8778(1000/T) + 14247(1000/T)2 – 10259(1000/T)3 + 2759(1000/T)4] – 8.36 xCu
2 .
For the thermodynamics calculation and modeling of surface crystallization PbSein the ternary system
Cu -Pb-Se is obtained dependence:
T = [ + ( - x ) Gexs (xl )] / [ . - . ln x ( - Cu
PbSe Se Se 110693 1 0 35D 25 695 8 31 1 xSe )]
Where DGexs l
, = –76057 + 335550,738хSe – 2,41759E6хSe
2 + 7,33249E6хSe
3 – 9,7868E6 хSe
4 + 4,69725E6хSe
3D visualization of the obtained analytical dependencies is carried out with the help of a computer
program OriginLab2017.


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1. Shelimova L. E., Tomashik V. N., Grytsiv V. I. Diagrammy sostoyaniya v poluprovodnikovom materialovedenii (sistemy na osnove khal'kogenidov Si,Ge, Sn, Pb): spravochnik [Diagrams of State in Semiconductor Materials Science (Systems Based on Chalcogenides Si, Ge, Sn, Pb): Handbook]. Moscow, Nauka Publ., 1991, 368 p.
2. West A. R. Solid State Chemistry and its Applications / 2nd edition. Wiley, 2014, 584 p.
3. Li C. C., Drymiotis F, Liao L. L., Dai M. J., Liu C. K., Chen C. L., Chen Y. Y., Kao C. R., Snyder G. J. Energy Conversion and Management, 2015, vol. 98, pp. 134—137. DOI: 10.1016/j.enconman.2015.03.089
4. Gierlotka, W., Łapsa, J. Fitzner, K. J. Phase Equilib. Diffus., 2010, vol. 31, no. 6, pp. 509—517. DOI: 10.1007/ s11669—010—9791—8
5. Fabrichnaya O., Savinykh G., Schreiber G. CALPHAD, 2014, vol. 44, pp. 133–137.
6. Asadov S. M., Mamedov A. N., Kulieva S. A. Inorganic Materials, 2016, vol. 52, no. 9, pp. 876—885. DOI: 10.1134/S0020168516090016
7. Ibragimova F. S., Tagiev E. R., Babanly N. B., Mamedov A. N. Condensed Matter and Interphases, 2016, vol. 18, № 4, pp. 550-557. Available at: t_18_4_2016_013.pdf (in Russ.)
8. Mamedov A. N., Salimov Z. E., Mashadiyeva L. F., Babanly M. B. // American Chemical Science Journal, 2016, vol. 10(2), pp. 1-5. DOI: 10.9734/ACSJ/2016/21808
9. Yusibov Yu. A., Alverdiev I. Dzh., Ibragimova F. S., Mamedov A. N., Tagiev D. B., Babanly M. B. Russ. J. Inorg. Chem., 2017, vol. 62, no. 9, pp. 1223–1233. DOI: 10.1134/S0036023617090182
10. Mamedov A. N., Tagiev E. R., Aliev Z. S., Babanly M. B. Inorganic Materials, 2016, vol. 52, no. 6, pp. 543–545. DOI: 10.1134/S002016851606008X
11. Babanly M B, Yusibov Yu. A. Elektrokhimicheskie metody v termodinamike neorganicheskikh sistem [Electrochemical Methods in the Thermodynamics of Inorganic Systems]. Baku, ELM Publ., 2011, 306 p. (in Russ.)
12. Babanly M. B., Yusibov Y. A., Babanly N. B. The EMF Method with Solid-State Electrolyte in the Thermodynamic Investigation of Ternary Copper and Silver Chalcogenides / Electromotive Force and Measurement in Several Systems. / Ed. by S. Kara. Intechweb.Org, 2011, pp. 57-78.
13. Nesmeyanov A. N. Davlenie para khimicheskikh elementov [The Vapor Pressure of Chemical Elements]. Мoscow, Izdatel'stvo Akademii Nauk SSSR Publ., 1961, 396 p. (in Russ.)
14. Novoselova A. V., Pashinkin A. S. Davlenie parov letuchikh khal'kogenidov metallov [Vapor Pressure of Volatile Metal Chalcogenides]. Moscow, Nauka Publ., 1978, 112 p. (in Russ.)
15. Abrikosov N. X., Shelimova L. E. Poluprovodnikovye materialy na osnove soedinenii AIVVVI [Semiconductor Materials on the Basis of Compounds AIVВVI]. Nauka Publ., 1975, 195 p. (in Russ.)
16. Glazov V. M., Pavlova L. M. Khimicheskaya termodinamika i fazovye ravnovesiya [Chemical Thermodynamics and Phase Equilibrium]. Moscow, Metallurgiya Publ., 1988, 560 p. (in Russ.)
17. Morachevsky A. G., Voronin G. F., Heiderich V. A., Kutsenok I. B. Elektrokhimicheskie metody issledovaniya v termodinamike metallicheskikh sistem [Electrochemical Methods of Investigation in the Thermodynamics of Metallic Systems]. Moscow, Akademkniga Publ., 2003, 334 p. (in Russ.)
18. Morachevsky A. G., Sladkov I. B. Termodinamicheskie raschety v metallurgii. Spravochnik [Thermodynamic Calculations in Metallurgy. Handbook]. Moscow, Metallurgiya Publ., 1985, 137 p. (in Russ.)
19. Putilov K. A. Termodinamika [Thermodynamics]. Moscow, Nauka Publ., 1971, 376 p. (in Russ.)
20. Fiziko-khimicheskie svoistva poluprovodnikovykh veshchestv. Spravochnik [Physico-Chemical Properties of Semiconductor Substances. Handbook]. / Eds. by A. V. Novoselova, V. B. Lazarev, Мoscow, Nauka Publ., 1979, 338 p. (in Russ.)
21. Baza dannykh. Termicheskie konstanty veshchestv [Database. Thermal Constants of Substances]. / V. S. Iorish and V. S. Yungman, Institut teplofiziki ekstremal'nykh sostoyanii RAN. Khimicheskii fakul'tet MGU Publ., 2006 (in Russ.)
22. Hampel C. A. Rare Metals Handbook. Reinhold Publishing Corp., London, 1961, pp. 469–518.
23. Sealy B. J., Crocker A. J. J. Materials Science, 1973, vol., 8, pp. 1737-1747.
24. Mamedov A. N., Ibragimova F. S., Babanly N. B., Yusibov Yu. A. XXI International Conference on Chemical Thermodynamics in Russia (RCCT–2017). 26-30 June, 2017, Akademgorodok, Novosbirsk, p. 285.
25. ASM Alloy Phase Diagrams Center. / Eds. by P. Villars, H. Okamoto and K. Cenzual. ASM International, Materials Park, OH, USA, 2006—2016.
How to Cite
Mamedov, A. N., Ahmedova, N. Y., Babanly, N. B., & Mamedov, E. I. (2018). THERMODYNAMIC CALCULATION AND 3D MODELING T-x-y AND P (Se2) -T-x DIAGRAMS IN THE SYSTEM Cu-Pb-Se ON LIQUIDUS PbSe. Condensed Matter and Interphases, 20(1), 84-92.