Инд. авторы: Drebushchak V.A.
Заглавие: Thermal expansion of solids: review on theories
Библ. ссылка: Drebushchak V.A. Thermal expansion of solids: review on theories // Journal of Thermal Analysis and Calorimetry. - 2020. - ISSN 1388-6150. - EISSN 1572-8943.
Внешние системы: DOI: 10.1007/s10973-020-09370-y; РИНЦ: 43235648; РИНЦ: 45529079; SCOPUS: 2-s2.0-85078785350; WoS: 000510102300003;
Реферат: eng: The coefficient of thermal expansion of a solid can be derived from (1) anharmonicity of atomic vibrations; (2) lattice dynamics; (3) equation of state by G. Mie; (4) equation of state by E. Gruneisen; and (6) potential of interatomic interaction. Only the last theory in this list provides us with the equation describing correctly all features in the thermal expansion: (1) proportionality between thermal expansion and heat capacity; (2) various values of "plateau" for the coefficient of thermal expansion at temperatures close to Debye temperature; and (3) acceleration of the thermal expansion in the vicinity of melting point.
Ключевые слова: LATTICE; TEMPERATURE; DEGREES-K; PRESSURE-DEPENDENCE; THERMODYNAMIC PROPERTIES; ISOTHERMAL COMPRESSIBILITY; HEAT-CAPACITY; EQUATION-OF-STATE; Thermal expansion; Interatomic potential; Heat capacity; Gruneisen; Anharmonicity; GRUNEISEN-PARAMETER; SODIUM;
Издано: 2020
Цитирование: 1. Wallace DC. Thermodynamics of crystals. New York: Wiley; 1972. 2. Filby JD, Martin DL. The specific heats below 30 K of lithium metal of various isotopic compositions and of sodium metal. Proc R Soc Lond A. 1963;276:187–203. 10.1098/rspa.1963.0202. DOI: 10.1098/rspa.1963.0202 3. Martin DL. The specific heat of sodium from 20 to 300 K: the martensitic transformation. Proc R Soc Lond A. 1960;254:433–43. 10.1098/rspa.1960.0030. DOI: 10.1098/rspa.1960.0030 4. Archer DG. Enthalpy increment measurements for NaCl (cr) and KBr (cr) from 4.5 K to 350 K. Thermodynamic properties of the NaCl + H2O system. J Chem Eng Data. 1997;42:281–92. 10.1021/je960224q. DOI: 10.1021/je960224q 5. Ditmars DA, Plint CA, Shukla RC. Aluminum. I. Measurement of the relative enthalpy from 273 to 929 K and derivation of thermodynamic functions for Al (s) from 0 K to its melting point. Int J Thermophys. 1985;6:499–515. 10.1007/BF00508893. DOI: 10.1007/BF00508893 6. Desai PD. Thermodynamic properties of titanium. Int J Thermophys. 1987;8:781–94. 10.1007/BF00500794. DOI: 10.1007/BF00500794 7. Kraftmakher YA. Modulation method for studying thermal expansion. In: Peggs ID, editor. Thermal expansion, vol. 6. Boston: Springer; 1978. p. 155–64. 10.1007/978-1-4615-9086-6_14. DOI: 10.1007/978-1-4615-9086-6_14 8. Bedford RE, Bonnier G, Maas H, Pavese F. Recommended values of temperature on the international temperature scale of 1990 for a selected set of secondary reference points. Metrologia. 1996;33:133–54. 10.1088/0026-1394/33/2/3. DOI: 10.1088/0026-1394/33/2/3 9. Janz GJ, Allen CB, Bansal NP, Murphy RM, Tomkins RP. Physical properties data compilations relevant to energy storage. II. Molten salts: data on single and multi-component salt systems. NSRDS-NBS 61, Part II. Washington: Government printing office; 1979. 10. Wang K, Reeber RR. High temperature thermal expansion of alkali halides. J Phys Chem Solids. 1995;56:895–900. 10.1016/0022-3697(95)00015-1. DOI: 10.1016/0022-3697(95)00015-1 11. Losee DL, Simmons RO. Thermal-expansion measurements and thermodynamics of solid krypton. Phys Rev. 1968;172:944–57. 10.1103/PhysRev.172.944. DOI: 10.1103/PhysRev.172.944 12. Cooper RF. The thermal expansion of solids. Phys Educ. 1976;11(4):284–90. 10.1088/0031-9120/11/4/003. DOI: 10.1088/0031-9120/11/4/003 13. Kasap S, Málek J, Svoboda R. Thermal properties and thermal analysis: Fundamentals, experimental techniques and application. In: Kasap S, Capper P, editors. Springer handbook of electronic and photonic materials. 2nd ed. Leipzig: Springer; 2017. p. 425–51. 10.1007/978-3-319-48933-9_19. DOI: 10.1007/978-3-319-48933-9_19 14. Fermi E. Molecole e cristalli. Bologna: Zanichelli; 1934. 15. Fermi E. Moleküle und Kristalle. Leipzig: Barth; 1938. 16. Фepми Э. Moлeкyлы и кpиcтaллы. Mocквa: Гoc. изд. Инocтpaннoй литepaтypы; 1947. 17. Fermi E. Molecules, crystals, and quantum statistics. New York: Benjamin; 1966. 18. Maradudin AA. Thermal expansion and phonon frequency shifts. Physica status solidi (b). 1962;2:1493–507. 10.1002/pssb.19620021107. DOI: 10.1002/pssb.19620021107 19. Bicknese V. The thermal expansion of a face-centered cubic lattice with central two-body interactions. Physica. 1965;31:1473–85. 10.1016/0031-8914(65)90114-X. DOI: 10.1016/0031-8914(65)90114-X 20. Kittel C. Introduction to solid state physics. 8th ed. New York: Wiley; 2005. 21. Levy RA. Principles of solid state physics. New York: Academic Press; 1968. 22. Sirdeshmukh DB, Sirdeshmukh L, Subhadra KG. Micro-and macro-properties of solids: thermal mechanical and dielectric properties. Heidelberg: Springer; 2006. 23. Frenkel AI, Rehr JJ. Thermal expansion and X-ray-absorption fine-structure cumulants. Phys Rev B. 1993;48:585–8. 10.1103/PhysRevB.48.585. DOI: 10.1103/PhysRevB.48.585 24. Fornasini P, Beccara S, Dalba G, Grisenti R, Sanson A, Vaccari M, Rocca F. Extended X-ray-absorption fine-structure measurements of copper: local dynamics, anharmonicity, and thermal expansion. Phys Rev B. 2004;70:17430112(12). 10.1103/PhysRevB.70.174301. DOI: 10.1103/PhysRevB.70.174301 25. Hung NV, Fornasini P. Anharmonic effective potential, correlation effects, and EXAFS cumulants calculated from a Morse interaction potential for fcc metals. J Phys Soc Jpn. 2007;76:084601(7). 10.1143/JPSJ.76.084601. DOI: 10.1143/JPSJ.76.084601 26. Hung NV, Rehr JJ. Anharmonic correlated Einstein-model Debye–Waller factors. Phys Rev B. 1997;56:43–6. 10.1103/PhysRevB.56.43. DOI: 10.1103/PhysRevB.56.43 27. Haug J, Chassé A, Schneider R, Kruth H, Dubiel M. Thermal expansion and interatomic potentials of silver revealed by extended X-ray absorption fine structure spectroscopy using high-order perturbation theory. Phys Rev B. 2008;77:184115(14). 10.1103/PhysRevB.77.184115. DOI: 10.1103/PhysRevB.77.184115 28. Born M. Atomtheorie des festen Zustandes (Dynamik der Kristallgitter). 2nd ed. Leipzig: Springer; 1923. 29. Born M, von Kármán T. Über Schwingungen in Raumgittern. Physik Z. 1912;13:297–309. 30. Kellermann EW. Theory of the vibrations of the sodium chloride lattice. Philos Trans. 1940;238A:513–48. 10.1098/rsta.1940.0005. DOI: 10.1098/rsta.1940.0005 31. Fletcher GC. The thermal expansion of solids. Aust J Phys. 1959;12:237–47. 10.1071/PH590237. DOI: 10.1071/PH590237 32. Fürth R. On the equation of state for solids. Proc R Soc Lond A Math Phys Sci. 1944;183:87–110. 10.1098/rspa.1944.0023. DOI: 10.1098/rspa.1944.0023 33. Fletcher GC. Anharmonicity and the thermal expansion of solids. Aust J Phys. 1961;14:420–31. 10.1071/PH610420. DOI: 10.1071/PH610420 34. Powell DGM, Fletcher GC. Thermal expansion and other properties of sodium chloride. Aust J Phys. 1965;18:205–18. 10.1071/PH650205. DOI: 10.1071/PH650205 35. Mie G. Zur kinetischen Theorie der einatomigen Körper. Ann Phys. 1903;316(8):657–97. 10.1002/andp.19033160802. DOI: 10.1002/andp.19033160802 36. Connell LF, Martin HC. Concerning reported discrepancies between X-ray and macroscopic measurements of thermal expansion of some alkali halides. Acta Cryst. 1951;4:75–6. 10.1107/S0365110X51000234. DOI: 10.1107/S0365110X51000234 37. Simmons RO, Balluffi RW. Measurement of equilibrium concentrations of vacancies in copper. Phys Rev. 1963;129:1533–44. 10.1103/PhysRev.129.1533. DOI: 10.1103/PhysRev.129.1533 38. Fouchaux RD, Simmons RO. Measurements of thermal expansion and thermal equilibrium defects in silver chloride. Phys Rev. 1964;136:A1664–74. 10.1103/PhysRev.136.A1664. DOI: 10.1103/PhysRev.136.A1664 39. Kovács I, El Sayed H. Point defects in metals. J Mater Sci. 1976;11:529–59. 10.1007/BF00540934. DOI: 10.1007/BF00540934 40. Schwalbe LA. Equilibrium vacancy concentration measurements in solid argon. Phys Rev B. 1976;14:1722–32. 10.1103/PhysRevB.14.1722. DOI: 10.1103/PhysRevB.14.1722 41. Grüneisen E. Über die thermische Ausdehnung und die spezifische Wärme der Metalle. Ann Phys. 1908;331:211–6. 10.1002/andp.19083310611. DOI: 10.1002/andp.19083310611 42. Grüneisen E. Über die thermische Ausdehnung der Metalle. Ann Phys. 1910;338:33–64. 10.1002/andp.19103381104. DOI: 10.1002/andp.19103381104 43. Grüneisen E. Über den Einfluß von Temperatur und Druck auf Ausdehnungskoeffizient und spezifische Wärme der Metalle. Ann Phys. 1910;338:65–78. 10.1002/andp.19103381105. DOI: 10.1002/andp.19103381105 44. Einstein A. Die Plancksche Theorie der Strahlung und die Theorie der spezifischen Wärme. Ann Phys. 1907;327:180–90. 10.1002/andp.19063270110. DOI: 10.1002/andp.19063270110 45. Grüneisen E. Theorie des festen Zustandes einatomiger Elemente. Ann Phys. 1912;344(12):257–306. 10.1002/andp.19123441202. DOI: 10.1002/andp.19123441202 46. Grüneisen E. Zustand des festen Körpers. In: Henning F, editor. Thermische Eigenschaften der Stoffe. Berlin: Springer; 1926. p. 1–59. 10.1007/978-3-642-99531-6_1. DOI: 10.1007/978-3-642-99531-6_1 47. Nernst W, Lindemann FA. Spezifische Wärme und Quantentheorie. Zeitschrift für Elektrochemie und angewandte physikalische Chemie. 1911;17:817–27. 10.1002/bbpc.19110171809. DOI: 10.1002/bbpc.19110171809 48. Debye P. Zur Theorie der spezifischen Wärmen. Ann Phys. 1912;344:789–839. 10.1002/andp.19123441404. DOI: 10.1002/andp.19123441404 49. Slater JC. Note on Grüneisen’s constant for the incompressible metals. Phys Rev. 1940;57:744–6. 10.1103/PhysRev.57.744. DOI: 10.1103/PhysRev.57.744 50. Miki H. Grüneisen’s parameter and the depth of isostatic compensation. J Phys Earth. 1952;1:19–20. 10.4294/jpe1952.1.19. DOI: 10.4294/jpe1952.1.19 51. Dugdale JS, MacDonald DK. The thermal expansion of solids. Phys Rev. 1953;89:832–4. 10.1103/PhysRev.89.832. DOI: 10.1103/PhysRev.89.832 52. Gilvarry JJ. The Lindemann and Grüneisen laws. Phys Rev. 1956;102:308–16. 10.1103/PhysRev.102.308. DOI: 10.1103/PhysRev.102.308 53. Knopoff L, Shapiro JN. Comments on the interrelationships between Grüneisen’s parameter and shock and isothermal equations of state. J Geophys Res. 1969;74:1439–50. 10.1029/JB074i006p01439. DOI: 10.1029/JB074i006p01439 54. Mulargia F. Is the common definition of the Mie-Grüneisen equation of state inconsistent? Geophys Res Lett. 1977;4:590–2. 10.1029/GL004i012p00590. DOI: 10.1029/GL004i012p00590 55. Wruk N, Pelzl J, Saunders GA, Hailing T. Elastic constants, acoustic mode vibrational anharmonicity and Grüneisen parameters of hexahalometallate crystals. J Phys Chem Solids. 1985;46:1235–42. 10.1016/0022-3697(85)90125-8. DOI: 10.1016/0022-3697(85)90125-8 56. Quareni F, Mulargia F. The validity of the common approximate expressions for the Grüneisen parameter. Geophys J Int. 1988;93:505–19. 10.1111/j.1365-246X.1988.tb03877.x. DOI: 10.1111/j.1365-246X.1988.tb03877.x 57. Harrison WA, Wills JM. Interionic interactions in simple metals. Phys Rev B. 1982;25:5007–17. 10.1103/PhysRevB.25.5007. DOI: 10.1103/PhysRevB.25.5007 58. Vasil’ev AN, Buchel’nikov VD, Georgius RS, Ilyushin AS, Savchenko YI. Striction of antiferromagnetic transition and magnetic Grüneisen parameter of α-Mn. JETP Lett. 1990;52:401–4. 59. Vočadlo L, Poirer JP, Price GD. Grüneisen parameters and isothermal equations of state. Am Miner. 2000;85:390–5. 10.2138/am-2000-2-319. DOI: 10.2138/am-2000-2-319 60. Marini A. The Grüneisen parameter for aluminum in the temperature range 0.3–1.1 K. J Low Temp Phys. 2003;133:313–9. 10.1023/A:1026039409111. DOI: 10.1023/A:1026039409111 61. Hofmeister AM, Mao HK. Redefinition of the mode Grüneisen parameter for polyatomic substances and thermodynamic implications. PNAS. 2002;99:559–64. 10.1073/pnas.241631698. DOI: 10.1073/pnas.241631698 62. Sindhu S, Menon CS. Generalized Grüneisen parameters and low temperature limit of lattice thermal expansion of cadmium and zirconium. Pramana. 2006;67:535–40. 10.1007/s12043-006-0014-0. DOI: 10.1007/s12043-006-0014-0 63. Tolpadi S. Volume and temperature variation of Gruneisen constant. J Phys F Metal Phys. 1974;4:2138–44. 10.1088/0305-4608/4/12/008. DOI: 10.1088/0305-4608/4/12/008 64. Boehler R, Ramakrishnan J. Experimental results on the pressure dependence of the Grüneisen parameter: a review. J Geophys Res B. 1980;85:6996–7002. 10.1029/JB085iB12p06996. DOI: 10.1029/JB085iB12p06996 65. Nie CH. Volume and temperature dependence of the second Grüneisen parameter of NaCl. Phys Status Solidi B. 2000;219:241–4. 10.1002/1521-3951(200006)219:2%3c241:AID-PSSB241%3e3.0.CO;2-6. DOI: 10.1002/1521-3951(200006)219:2<241::AID-PSSB241>3.0.CO;2-6 66. Pandya CV, Vyas PR, Pandya TC, Gohel VB. Volume variation of Gruneisen parameters of fcc transition metals. Bull Mater Sci. 2002;25:63–7. 10.1007/BF02704597. DOI: 10.1007/BF02704597 67. Cui GL, Yu RL. Volume and pressure dependence of Grüneisen parameter γ for solids at high temperatures. Phys B. 2007;390:220–4. 10.1016/j.physb.2006.08.034. DOI: 10.1016/j.physb.2006.08.034 68. Bell PM. Status of the Grüneisen constant. EOS Trans Am Geophys Union. 1981;62:649. 10.1029/EO062i035p00649-02. DOI: 10.1029/EO062i035p00649-02 69. Anderson OL. The Grüneisen ratio for the last 30 years. Geophys J Int. 2000;143:279–94. 10.1046/j.1365-246X.2000.01266.x. DOI: 10.1046/j.1365-246X.2000.01266.x 70. Sadovnikov SI, Gusev AI. Thermal expansion, heat capacity and phase transformations in nanocrystalline and coarse-crystalline silver sulfide at 290–970 K. J Therm Anal Calorim. 2018;131:1155–64. 10.1007/s10973-017-6691-8. DOI: 10.1007/s10973-017-6691-8 71. Tripathy H, Rai AK, Hajra RN, Shanthi NV, Subramanian R, Saibaba S. High-temperature thermophysical properties of 18Cr–9Ni–2.95Cu–0.58Nb–0.1C (mass%) austenitic stainless steel. J Therm Anal Calorim. 2018;131:2749–61. 10.1007/s10973-017-6792-4. DOI: 10.1007/s10973-017-6792-4 72. Pet’kov VI, Dmitrienko AS, Bokov AI. Thermal expansion of phosphate–sulfates of eulytite structure. J Therm Anal Calorim. 2018;133:199–205. 10.1007/s10973-017-6676-7. DOI: 10.1007/s10973-017-6676-7 73. Pet’kov VI, Lavrenov DA, Kovalsky AM. Synthesis, characterization and thermal expansion of the zinc-containing phosphates with the mineral-like framework structures. J Therm Anal Calorim. 2019. 10.1007/s10973-019-08624-8. DOI: 10.1007/s10973-019-08624-8 74. Kutin AM, Shiryaev VS, Plekhovich AD, Plekhovich SD. Calorimetric and volumetric functions of AsxSe1−x (x = 0.3–0.5) glasses and their model representation. J Therm Anal Calorim. 2019. 10.1007/s10973-019-08491-3. DOI: 10.1007/s10973-019-08491-3 75. Ito H, Kawada K, Akimoto SI. Thermal expansion of stishovite. Phys Earth Planet Int. 1974;8:277–81. 10.1016/0031-9201(74)90094-6. DOI: 10.1016/0031-9201(74)90094-6 76. Suzuki I. Thermal expansion of periclase and olivine, and their anharmonic properties. J Phys Earth. 1975;23:145–59. 10.4294/jpe1952.23.145. DOI: 10.4294/jpe1952.23.145 77. Matsui T, Manghnani MH. Thermal expansion of single-crystal forsterite to 1023 K by Fizeau interferometry. Phys Chem Miner. 1985;12:201–10. 10.1007/BF00311289. DOI: 10.1007/BF00311289 78. Chopelas A. Thermal expansion, heat capacity, and entropy of MgO at mantle pressures. Phys Chem Miner. 1990;17:142–8. 10.1007/BF00199665. DOI: 10.1007/BF00199665 79. Bouhifd MA, Andrault D, Fiquet G, Richet P. Thermal expansion of forsterite up to the melting point. Geophys Res Lett. 1996;23:1143–6. 10.1029/96GL01118. DOI: 10.1029/96GL01118 80. Gartvich Y, Galkin V. Ni olivine: thermal behavior of liebenbergite. J Therm Anal Calorim. 2019;136:2333–9. 10.1007/s10973-018-7859-6. DOI: 10.1007/s10973-018-7859-6 81. Kane G. The equation of state of frozen neon, argon, krypton, and xenon. J Chem Phys. 1939;7:603–14. 10.1063/1.1750498. DOI: 10.1063/1.1750498 82. Murphy GW, Rice OK. Corresponding states in the frozen rare gases. J Chem Phys. 1946;14:518–25. 10.1063/1.1724186. DOI: 10.1063/1.1724186 83. Peterson OG, Batchelder DN, Simmons RO. Measurements of X-ray lattice constant, thermal expansivity, and isothermal compressibility of argon crystals. Phys Rev. 1966;150:703–11. 10.1103/PhysRev.150.703. DOI: 10.1103/PhysRev.150.703 84. Batchelder DN, Losee DL, Simmons RO. Measurements of lattice constant, thermal expansion, and isothermal compressibility of neon single crystals. Phys Rev. 1967;162:767–75. 10.1103/PhysRev.162.767. DOI: 10.1103/PhysRev.162.767 85. Trefny JU, Serin B. Specific heat of solid xenon. J Low Temp Phys. 1969;1:231–40. 10.1007/BF00628411. DOI: 10.1007/BF00628411 86. Jones JE. On the determination of molecular fields—II. From the equation of state of a gas. Proc R Soc Lond A. 1924;106:463–77. 10.1098/rspa.1924.0082. DOI: 10.1098/rspa.1924.0082 87. Brewer L. The cohesive energies of the elements. https://escholarship.org/content/qt08p2578m/qt08p2578m.pdf (1977). Accessed 28 Aug 2019. 88. Ferreira AG, Lobo LQ. The sublimation of argon, krypton, and xenon. J Chem Thermodyn. 2008;40:1621–6. 10.1016/j.jct.2008.07.023. DOI: 10.1016/j.jct.2008.07.023 89. Novikova SI. Thermal expansion of solids. Moscow: Izdatel’stvo Nauka; 1974 (in Russian). 90. Bokov OG. Calculation of the thermal expansion and compressibility of crystals of the inert gases. J Struct Chem. 1981;22:540–4. 10.1007/BF00784087. DOI: 10.1007/BF00784087 91. Mohazzabi P, Behroozi F. Simple classical calculation of thermal expansion for rare-gas solids. Phys Rev B. 1987;36:9820–3. 10.1103/PhysRevB.36.9820. DOI: 10.1103/PhysRevB.36.9820 92. Mohazzabi P, Behroozi F. Vibrational energy as a function of interatomic distance in rare-gas solids. A universal relationship. Phys Status Solidi B. 1988;149:495–501. 10.1002/pssb.2221490210. DOI: 10.1002/pssb.2221490210 93. Mohazzabi P, Behroozi F. Thermal expansion of solids: a simple classical model. Eur J Phys. 1997;18:237–40. 10.1088/0143-0807/18/3/019. DOI: 10.1088/0143-0807/18/3/019 94. Drebushchak VA, Turkin AI. Relationship between heat capacity and thermal expansion derived from the Lennard–Jones potential. J Therm Anal Calorim. 2001;65:745–53. 10.1023/A:1011903510977. DOI: 10.1023/A:1011903510977 95. Drebushchak VA. Heat capacity of solids. Novosibirsk: Novosibirsk State University; 2013 (in Russian). 96. Tilford CR, Swenson CA. Thermal expansions of solid argon, krypton, and xenon above 1 K. Phys Rev B. 1972;5:719–32. 10.1103/PhysRevB.5.719. DOI: 10.1103/PhysRevB.5.719 97. Holste JC, Swenson CA. Experimental thermal expansions for solid neon, 2–14 K. J Low Temp Phys. 1975;18:477–85. 10.1007/BF00116138. DOI: 10.1007/BF00116138