Статистико-термодинамический анализ влияния химического состава на изменение температур плавления галогенидов щелочных металлов

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Abstract

Предложена интерпретация зависимости температур плавления всего подкласса галогенидов щелочных металлов от химического состава, построенная на анализе изменения различных вкладов во внутреннюю энергию солей в расплавленной и кристаллической фазах с изменением суммы радиусов их катионов и анионов. Выражение для вычисления энергии жидкосолевых расплавов включает в себя вклад заряд-дипольных взаимодействий между ионами, который учитывается в работе на основе термодинамической теории возмущений с базисом в виде модели заряженных твердых сфер. Для энергии кристаллической фазы использованы формула Борна–Майера для электростатической части и формула Дебая для учета вклада колебаний. В рамках предложенного подхода дано объяснение причин более низких значений приведенных температур плавления галогенидов лития и натрия по сравнению с другими солями. Показано, что отклонения приведенных температур плавления галогенидов лития и натрия в зависимости от суммы ионных радиусов могут быть объяснены проявлением кулоновского и поступательного вкладов в энергию в расплавленном состоянии, а также вкладов Маделунга и Борна в кристаллической фазе.

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A. Г. Давыдов

Институт высокотемпературной электрохимии УрО РАН

Author for correspondence.
Email: A.Davydov@ihte.ru
Russian Federation, Екатеринбург

References

  1. Lantelme F., Groult H. Molten Salts Chemistry: From Lab to Applications. Elsevier, 2013. 592 p.
  2. Chang Y.A., Chen S., Zhang F., et al. // Prog. Mater. Sci. 2004. V. 49. P. 313. doi: 10.1016/s0079-6425(03)00025-2
  3. Chartrand P., Pelton A.D. // Metall. Mater. Trans. A. 2001. V. 32. P. 1397. doi: 10.1007/s11661-001-0229-0
  4. Xing X., Zhu Z., Dai S., Tanaka T. // Thermochim. Acta. 2001. V. 372. P. 109. doi: 10.1016/s0040-6031(01)00441-5
  5. Kapała J., Bochyńska M., Broczkowska K., Rutkowska I. // J. Alloys Compd. 2008. V. 451. P. 679. doi: 10.1016/j.jallcom.2007.04.085
  6. Gong W., Wu Y., Zhang R., Gaune-Escard M. // Calphad. 2012. V. 36. P. 44. doi: 10.1016/j.calphad.2011.11.001
  7. Kubíková B., Mlynáriková J., Beneš O., et al. // J. Mol. Liq. 2018. V. 268. P. 754. doi: 10.1016/j.molliq.2018.07.114
  8. Beneš O., Zeller Ph., Salanne M., Konings R.J.M. // J. Chem. Phys. 2009. V. 130. Article No. 134716. doi: 10.1063/1.3097550
  9. Aragones J.L., Sanz E., Valeriani C., Vega C. // J. Chem. Phys. 2012. V. 137. Article No. 104507. doi: 10.1063/1.4745205
  10. Dewan L.C., Simon C., Madden P.A., et al. // J. Nucl. Mater. 2013. V. 434. P. 322. doi: 10.1016/j.jnucmat.2012.12.006
  11. DeFever R.S., Wang H., Zhang Y., Maginn E.J. // J. Chem. Phys. 2020. V. 153. Article No. 011101. doi: 10.1063/5.0012253
  12. Wang H., DeFever R.S., Zhang Y., et al. // J. Chem. Phys. 2020. V. 153. Article No. 214502. doi: 10.1063/5.0023225
  13. Stillinger F.H. Equilibrium Theory of Pure Fused Salts. John Wiley & Sons, 1964. 108 p.
  14. Давыдов А.Г., Ткачев Н.К. // Расплавы. 2023. № 2. С. 167. doi: 10.31857/S0235010623020032
  15. Пригожин И., Дефэй Р. Химическая термодинамика. Новосибирск: Наука, 1966. 512 с.
  16. Укше Е.А. Строение расплавленных солей. Москва: Мир, 1966. 431 с.
  17. Ландау Л.Д., Лифшиц Е.М. Теоретическая физика. Т. 5. Статистическая физика. Ч. 1. Москва: Физматлит, 2013. 620 с.
  18. Blum L. Primitive Electrolytes in the Mean Spherical Approximation. Academic Press, 1980. 66 p.
  19. Hiroike K. // Mol. Phys. 1977. V. 33. P. 1195. doi: 10.1080/00268977700101011
  20. Solana J.R. Perturbation Theories for the Thermodynamic Properties of Fluids and Solids. CRC Press: Taylor & Francis Group, 2013. 400 p.
  21. Born M., Mayer J.E. // Z. Phys. 1932. V. 75. P. 1.
  22. Mayer J.E., Mayer M.G. Statistical Mechanics. John Wiley & Sons, 1940. 495 p.
  23. Магомедов М.Н. // ТВТ. 1992. Т. 30. С. 1110.
  24. Sirdeshmukh D.B., Sirdeshmukh L., Subhadra K.G. Alkali Halides: A Handbook of Physical Properties. Springer-Verlag, 2001. 299 p.
  25. Tosi M.P., Fumi F.G. // J. Phys. Chem. Solids. 1964. V. 25. P. 45. doi: 10.1016/0022-3697(64)90160-x.
  26. Ashcroft N.W., Mermin N.D. Solid State Physics. Harcourt College Publishers, 1976. 848 p.
  27. Batsanov S.S., Batsanov A.S. Introduction to Structural Chemistry. Springer Science + Business Media, 2012. 542p.
  28. Wilson J.N., Curtis R.M. // J. Phys. Chem. 1970. V. 74. P. 187. doi: 10.1021/j100696a034
  29. Fisher M.E. // J. Stat. Phys. 1994. V. 75. P. 1. doi: 10.1007/BF02186278
  30. Haynes W.M. CRC Handbook of Chemistry and Physics: 97th Edition. CRC Press: Taylor & Francis Group, 2017. 2643 p.

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2. Fig. 1. Experimental values ​​of the reduced melting temperatures of alkali metal halides Tₘ*=kBTₘε₀d/e² depending on the sum of the radii of cations and anions of individual salts d (a); as well as the values ​​of the reduced melting temperatures of lithium, sodium, potassium, rubidium and cesium halides, related to the melting temperatures of the corresponding alkali metal fluorides depending on the ratios of the sum of the radii of the ions of each salt to the sum of the radii of the ions of similar fluoride salts (b).

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3. Fig. 2. Results of calculations of the reduced internal energies of molten alkali metal halides ΔEliq*=ΔEliqε₀d/e² depending on the sum of the radii of cations and anions of individual salts d (a); as well as the values ​​of the reduced internal energies of molten lithium, sodium, potassium, rubidium and cesium halides, related to the internal energies of the corresponding alkali metal fluorides depending on the ratios of the sum of the radii of the ions of each salt to the sum of the radii of the ions of similar fluoride salts (b).

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4. Fig. 3. Results of calculations of the Coulomb contribution to the reduced internal energy of molten alkali metal halides ΔEq*=ΔEqε₀d/e² depending on the sum of the radii of cations and anions of individual salts d (a); as well as the values ​​of this contribution to the reduced internal energy of molten lithium, sodium, potassium, rubidium and cesium halides, related to the Coulomb contribution to the internal energy of the corresponding alkali metal fluorides depending on the ratios of the sum of the radii of the ions of each salt to the sum of the radii of the ions of similar fluoride salts (b).

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5. Fig. 4. Results of calculations of the translational contribution to the reduced internal energy of molten alkali metal halides ΔEtr*=ΔEtrε₀d/e² depending on the sum of the radii of the cations and anions of individual salts d (a); as well as the values ​​of this contribution to the reduced internal energy of molten lithium, sodium, potassium, rubidium and cesium halides, related to the translational contribution to the internal energy of the corresponding alkali metal fluorides depending on the ratios of the sum of the radii of the ions of each salt to the sum of the radii of the ions of similar fluoride salts (b).

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6. Fig. 5. Results of calculations of the charge-dipole contribution to the reduced internal energy of molten alkali metal halides ΔEc-d*= =ΔEc-dε₀d/e² depending on the sum of the radii of the cations and anions of individual salts d (a); as well as the values ​​of this contribution to the reduced internal energy of molten lithium, sodium, potassium, rubidium and cesium halides, related to the charge-dipole contribution to the internal energy of the corresponding alkali metal fluorides depending on the ratios of the sum of the radii of the ions of each salt to the sum of the radii of the ions of similar fluoride salts (b).

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7. Fig. 6. Results of calculations of the reduced internal energies of alkali metal halide crystals ΔEsol*=ΔEsolε₀d/e² depending on the sum of the radii of the cations and anions of individual salts d (a); as well as the values ​​of the reduced internal energies of lithium, sodium, potassium, rubidium and cesium halide crystals, related to the internal energies of the corresponding alkali metal fluorides depending on the ratios of the sum of the radii of the ions of each salt to the sum of the radii of the ions of similar fluoride salts (b).

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8. Fig. 7. Results of calculations of the Coulomb contribution (Madelung) to the reduced internal energy of alkali metal halide crystals ΔEM*=ΔEMε₀d/e² depending on the sum of the radii of the cations and anions of individual salts d (a); as well as the values ​​of this contribution to the reduced internal energy of lithium, sodium, potassium, rubidium and cesium halide crystals, related to the Coulomb contribution to the internal energy of the corresponding alkali metal fluorides depending on the ratios of the sum of the radii of the ions of each salt to the sum of the radii of the ions of similar fluoride salts (b).

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9. Fig. 8. Results of calculations of the repulsive contribution (Born) to the reduced internal energy of alkali metal halide crystals ΔEB*=ΔEBε₀d/e² depending on the sum of the radii of the cations and anions of individual salts d (a); as well as the values ​​of this contribution to the reduced internal energy of lithium, sodium, potassium, rubidium and cesium halide crystals, related to the Born contribution to the internal energy of the corresponding alkali metal fluorides depending on the ratios of the sum of the radii of the ions of each salt to the sum of the radii of the ions of similar fluoride salts (b).

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10. Fig. 9. Results of calculations of the vibrational contribution (Debye) to the reduced internal energy of alkali metal halide crystals ΔED*=ΔEDε₀d/e² depending on the sum of the radii of the cations and anions of individual salts d (a); as well as the values ​​of this contribution to the reduced internal energy of lithium, sodium, potassium, rubidium and cesium halide crystals, related to the Debye contribution to the internal energy of the corresponding alkali metal fluorides depending on the ratios of the sum of the radii of the ions of each salt to the sum of the radii of the ions of similar fluoride salts (b).

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