Physics of the Solid State
Volumes and Issues
Home » Physics of the Solid State » Year 2024, issue 11 » Article p. 1880
<<<>>>
Melting criteria for classical and quantum crystals
Russian version
Magomedov M. N. 1
1Institute for geothermal problems and renewable energy – branch of the joint Institute of high temperatures of the Russian Academy of Sciences, Makhachkala, Russia
Email: mahmag4@mail.ru
PDF
It was shown that the Lindemann ratio (L) can be calculated by means of the delocalized criterion of melting for classical crystals, i. e. those with a melting point (Tm) greater than the Debye temperature (Theta): Tm/Theta>1.5. It was shown that for classical single-component crystals, the L value is determined only by the crystal structure. Calculations for various structures of classical crystals showed good agreement with the estimates of other authors. A generalization of the Lindemann relation was obtained for the case of quantum single-component crystals, i. e. for which Tm/Theta<0.4. It was shown that for quantum crystals, the Lindemann ratio is determined not only by the crystal structure, but also by the function Theta/Tm. Therefore, when moving from the classical to the quantum domain, the Tm(Theta) function changes its functional dependence. It was shown that for quantum crystals, the L value decreases with increasing pressure along the melting line. For quantum nanocrystals, the L value increases with an isobaric decrease in the size of the nanocrystal. At the same time, the more noticeably the shape of the quantum nanocrystal deviates from the energy-optimal shape, the greater the sized increase in the Lindemann ratio. A generalization of the delocalized criterion of melting was obtained for the case of quantum single-component crystals. Keywords: melting, delocalization, Debye temperature, quantum crystal, nanocrystal, hydrogen, helium.
  1. J.H. Bilgram. Phys. Rep. 153, 1, 1--89 (1987). DOI: 10.1016/0370-1573(87)90047-0
  2. Q.S. Mei, K. Lu. Prog. Mater Sci. 52, 8, 1175--1262 (2007). DOI: 10.1016/j.pmatsci.2007.01.001
  3. G. de With. Chem. Rev. 123, 23, 13713--13795 (2023). DOI: 10.1021/acs.chemrev.3c00489
  4. F.A. Lindemann. Phys. Z. 11, 14, 609--612 (1910)
  5. J.J. Gilvarry. Phys. Rev. 102, 2, 308--316 (1956). DOI: 10.1103/PhysRev.102.308
  6. J.J. Gilvarry. Phys. Rev. 103, 6, 1700--1704 (1956). DOI: 10.1103/PhysRev.103.1700
  7. J.N. Shapiro. Phys. Rev. B 1, 10, 3982--3989 (1970). DOI: 10.1103/PhysRevB.1.3982
  8. S.A. Cho. J. Phys. F. Met. Phys. 12, 6, 1069--1083 (1982). DOI: 10.1088/0305-4608/12/6/008
  9. T. Matsuura, H. Suzuki, K.I. Takano, F. Honda. J. Phys. Soc. Jpn. 79, 5, 053601 (2010). DOI: 10.1143/JPSJ.79.053601
  10. M.M. Vopson, N. Rogers, I. Hepburn. Solid State Commun. 318, 113977 (2020). DOI: 10.1016/j.ssc.2020.113977
  11. V.V. Goldman. J. Phys. Chem. Solids 30, 4, 1019--1021 (1969). DOI: 10.1016/0022-3697(69)90301-1
  12. N.P. Gupta. Solid State Commun. 13, 1, 69--71 (1973). DOI: 10.1016/0038-1098(73)90069-0
  13. R.K. Crawford. Melting, vaporization and sublimation. In "Rare Gas Solids", Eds. M.L. Klein, J.A. Venables. Academic Press, New York (1977) Vol. 2, P. 663--728
  14. R.K. Singh, D.K. Neb. Phys. Status Solidi B 126, 1, K15--K18 (1984). DOI: 10.1002/pssb.2221260153
  15. P. Mohazzabi, F. Behroozi. J. Mater. Sci. Lett. 6, 404--406 (1987). DOI: 10.1007/BF01756777
  16. S.S. Batsanov. Russ. J. Phys. Chem. A 83, 11, 1836--1841 (2009). DOI: 10.1134/S0036024409110053
  17. C. Domb. II Nuovo Cimento (1955--1965) 9, (Suppl 1), 9--26 (1958). DOI: 10.1007/BF02824224
  18. R. Guardiola, J. Navarro. J. Phys. Chem. A 115, 25, 6843--6850 (2011). DOI: 10.1021/jp1111313
  19. S.T. Chui. Phys. Rev. B 41, 1, 796--798 (1990). DOI: 10.1103/PhysRevB.41.796
  20. I. Loa, F. Landgren. J. Phys.: Condens. Matter 36, 18, 185401 (2024). DOI: 10.1088/1361-648X/ad1e08
  21. M.N. Magomedov. Tech. Phys. Lett. 33, 10, 837--840 (2007). DOI: 10.1134/S1063785007100094
  22. M.N. Magomedov. Phys. Met. Metallogr. 105, 2, 116--125 (2008). DOI: 10.1134/S0031918X08020038
  23. D.S. Sanditov. J. Exp. Theor. Phys. 115, 1, 112--124 (2012). DOI: 10.1134/S1063776112060143
  24. D.S. Sanditov, B.S. Sydykov. Tech. Phys. 59, 5, 682--685 (2014). DOI: 10.1134/S1063784214050272
  25. M.N. Magomedov. Phys. Met. Metallogr. 74, 4, 319--321 (1992)
  26. A.G. Chirkov, A.G. Ponomarev, V.G. Chudinov. Tech. Phys. 49, 2, 203--206 (2004). DOI: 10.1134/1.1648956
  27. G.M. Poletaev, M.D. Starostenkov. Phys. Solid State 51, 4, 727--732 (2009). DOI: 10.1134/S106378340904012X
  28. M.N. Magomedov. Crystallogr. Rep. 62, 3, 480--496 (2017). DOI: 10.1134/S1063774517030142
  29. M.N. Magomedov. Phys. Solid State 66, 2, 221--233 (2024). DOI: 10.61011/PSS.2024.02.57919.241
  30. M.N. Magomedov. Tech. Phys. 55, 9, 1373--1377 (2010). DOI: 10.1134/S1063784210090227
  31. M.N. Magomedov. Tech. Phys. 65, 10, 1659--1665 (2020). DOI: 10.1134/S1063784220100138
  32. T. Soma, H. Matsuo. J. Phys. C: Solid State Phys. 15, 9, 1873--1882 (1982). DOI: 10.1088/0022-3719/15/9/010
  33. N.T.T. Hang. Commun. in Phys. 24, 3, 207--215 (2014). DOI: 10.15625/0868-3166/24/3/4070
  34. L.V. Sang, V.V. Hoang, D.T.N. Tranh. Eur. Phys. J. D 69, 208 (2015). DOI: 10.1140/epjd/e2015-60153-1
  35. H. Li, R. Xu, Z. Bi, X. Shen, K. Han. J. Electron. Mater. 46, 7, 3826--3830 (2017). DOI: 10.1007/s11664-016-5070-8
  36. G.L. Pollack. Rev. Mod. Phys. 36, 3, 748--791 (1964). DOI: 10.1103/RevModPhys.36.748
  37. Cryocrystals, Eds. B.I. Verkin, A.F. Prikhod'ko. Naukova Dumka, Kiev (1983). 526 p. (in Russian)
  38. M. Nielsen. Phys. Rev. B 7, 4, 1626--1635 (1973). DOI: 10.1103/PhysRevB.7.1626
  39. D.A. Young, M. Ross. J. Chem. Phys. 74, 12, 6950--6955 (1981). DOI: 10.1063/1.441058
  40. V. Diatschenko, C.W. Chu, D.H. Liebenberg, D.A. Young, M. Ross, R.L. Mills. Phys. Rev. B 32, 1, 381--389 (1985). DOI: 10.1103/PhysRevB.32.381
  41. M. Dusseault, M. Boninsegni. Phys. Rev. B 95, 10, 104518 (2017). DOI: 10.1103/PhysRevB.95.104518
  42. T.R. Prisk, R.T. Azuah, D.L. Abernathy, G.E. Granroth, T.E. Sherline, P.E. Sokol, J. Hu, M. Boninsegni. Phys. Rev. B 107, 9, 094511 (2023). DOI: 10.1103/PhysRevB.107.094511
  43. H.H. Sample, C.A. Swenson. Phys. Rev. 158, 1, 188--199 (1967). DOI: 10.1103/PhysRev.158.188
  44. E.C. Heltemes, C.A. Swenson. Phys. Rev. 128, 4, 1512--1519 (1962). DOI: 10.1103/PhysRev.128.1512
  45. P.A. Whitlock, D.M. Ceperley, G.V. Chester, M.H. Kalos. Phys. Rev. B 19, 11, 5598--5633 (1979). DOI: 10.1103/PhysRevB.19.5598
  46. H.R. Glyde. "Helium, Solid". P. 1--11. [Online]. http://www.physics.udel.edu/ glyde/Solid_H13.pdf
  47. C.A. Burns, E.D. Isaacs. Phys. Rev. B 55, 9, 5767--5771 (1997). DOI: 10.1103/PhysRevB.55.5767
  48. I.J. Zucker. Proc. Phys. Soc. 77, 4, 889--900 (1961). DOI: 10.1088/0370-1328/77/4/311
  49. J. De Boer. Physica 14, 2-3, 139--148 (1948). DOI: 10.1016/0031-8914(48)90032-9
  50. B. Grabowski, L. Ismer, T. Hickel, J. Neugebauer. Phys. Rev. B 79, 13, 134106 (2009). DOI: 10.1103/PhysRevB.79.134106
  51. C. Freysoldt, B. Grabowski, T. Hickel, J. Neugebauer, G. Kresse, A. Janotti, C.G. Van de Walle. Rev. Mod. Phys. 86, 1, 253--305 (2014). DOI: 10.1103/RevModPhys.86.253
  52. D.D. Satikunvar, N.K. Bhatt, B.Y. Thakore. J. Appl. Phys. 129, 3, 035107 (2021). DOI: 10.1063/5.0022981
  53. M. Borinaga, I. Errea, M. Calandra, F. Mauri, A. Bergara. Phys. Rev. B 93, 17, 174308 (2016). DOI: 10.1103/PhysRevB.93.174308

Подсчитывается количество просмотров абстрактов ("html" на диаграммах) и полных версий статей ("pdf"). Просмотры с одинаковых IP-адресов засчитываются, если происходят с интервалом не менее 2-х часов.

Дата начала обработки статистических данных - 27 января 2016 г.

Publisher:

Ioffe Institute

Institute Officers:

Director: Sergei V. Ivanov

Contact us:

26 Polytekhnicheskaya, Saint Petersburg 194021, Russian Federation
Fax: +7 (812) 297 1017
Phone: +7 (812) 297 2245
E-mail: post@mail.ioffe.ru