New method for reducing the general formula for lattice specific heat to the Einstein and Nernst-Lindemann approximations

Canadian Journal of Physics

Volumn 81, Issue 8, 2003, Pages 1015-1036

  Irons, F E ^a  

^a UNIVERSITY OF NEW SOUTH WALES   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; LATTICE CONSTANTS; OSCILLATIONS; THERMAL EFFECTS;

DEBYE FORMULA; NERNST-LINDEMANN FORMULA;

SPECIFIC HEAT;

EID: 0345548515     PISSN: 00084204     EISSN: None     Source Type: Journal    
DOI: 10.1139/p03-069     Document Type: Article

References (74)

1. A. Einstein. Ann. Phys. 22, 180 (1907); 22, 800 (1907); For an English translation, see A. Einstein. The collected papers of Albert Einstein. Vol. 2. The Swiss years: Writings, 1900-1909. Translated by A. Beck. Princeton University Press, Princeton. 1989. Docs. 38 and 42. M.J. Klein. Science, 148, 173 (April 1965); A. Pais. "Subtle is the Lord..." The science and the life of Albert Einstein. Clarendon Press, Oxford. 1982. Chapt. 20.
2. A. Einstein. Ann. Phys. 22, 180 (1907); 22, 800 (1907); For an English translation, see A. Einstein. The collected papers of Albert Einstein. Vol. 2. The Swiss years: Writings, 1900-1909. Translated by A. Beck. Princeton University Press, Princeton. 1989. Docs. 38 and 42. M.J. Klein. Science, 148, 173 (April 1965); A. Pais. "Subtle is the Lord..." The science and the life of Albert Einstein. Clarendon Press, Oxford. 1982. Chapt. 20.
3. A. Einstein. Ann. Phys. 22, 180 (1907); 22, 800 (1907); For an English translation, see A. Einstein. The collected papers of Albert Einstein. Vol. 2. The Swiss years: Writings, 1900-1909. Translated by A. Beck. Princeton University Press, Princeton. 1989. Docs. 38 and 42. M.J. Klein. Science, 148, 173 (April 1965); A. Pais. "Subtle is the Lord..." The science and the life of Albert Einstein. Clarendon Press, Oxford. 1982. Chapt. 20.
4. A. Einstein. Ann. Phys. 22, 180 (1907); 22, 800 (1907); For an English translation, see A. Einstein. The collected papers of Albert Einstein. Vol. 2. The Swiss years: Writings, 1900-1909. Translated by A. Beck. Princeton University Press, Princeton. 1989. Docs. 38 and 42. M.J. Klein. Science, 148, 173 (April 1965); A. Pais. "Subtle is the Lord..." The science and the life of Albert Einstein. Clarendon Press, Oxford. 1982. Chapt. 20.
5. A. Einstein. Ann. Phys. 22, 180 (1907); 22, 800 (1907); For an English translation, see A. Einstein. The collected papers of Albert Einstein. Vol. 2. The Swiss years: Writings, 1900-1909. Translated by A. Beck. Princeton University Press, Princeton. 1989. Docs. 38 and 42. M.J. Klein. Science, 148, 173 (April 1965); A. Pais. "Subtle is the Lord..." The science and the life of Albert Einstein. Clarendon Press, Oxford. 1982. Chapt. 20.
6. H.P. Myers. Introductory solid state physics. 2nd ed. Taylor and Francis, London. 1997. Sect. 5.1; J. Kestin and J.R. Dorfman. A course in statistical thermodynamics. Academic Press, New York. 1971. Sect. 9.2.
7. H.P. Myers. Introductory solid state physics. 2nd ed. Taylor and Francis, London. 1997. Sect. 5.1; J. Kestin and J.R. Dorfman. A course in statistical thermodynamics. Academic Press, New York. 1971. Sect. 9.2.
8. R. Resnick and D. Halliday. Basic concepts in relativity and early quantum theory. 2nd ed. John Wiley and Sons, New York. 1985. p. 311.
9. A. Pais. "Subtle is the Lord..." The science and the life of Albert Einstein. Clarendon Press, Oxford. 1982. p. 394.
10. P. Debye. Ann. Phys. 39, 789 (1912).
11. M. Born and Th. von Kármán. Phys. Z. 13, 297 (1912).
12. W. Nernst and F. Lindemann. Z. Elektrochem. 17, 817 (1911).
13. W. Nernst. The theory of the solid state. University of London Press, London. 1914. pp. 43-66.
14. L. Boltzmann. Theoretical physics and philosophical problems. D. Reidel, Dordrecht. 1974. p. 132. Also of interest are the comments on p. 48.
15. S.G. Brush. Statistical physics and the atomic theory of matter from Boyle and Newton to Landau and Onsager. Princeton University Press, Princeton. 1983. p. 52.
16. L. Boltzmann. Akad. Wissen. Wien. Sitzungsber. 74, 553 (1876); L. Boltzmann. Lectures on gas theory. Translated by S.G. Brush. University of California, Berkeley. 1964. Footnote on pp. 330-331.
17. L. Boltzmann. Akad. Wissen. Wien. Sitzungsber. 74, 553 (1876); L. Boltzmann. Lectures on gas theory. Translated by S.G. Brush. University of California, Berkeley. 1964. Footnote on pp. 330-331.
18. F. Richarz. Ann. Phys. 48, 708 (1893); F.C. Brown. The physics of solids. W.A. Benjamin, New York. 1967. p. 176.
19. F. Richarz. Ann. Phys. 48, 708 (1893); F.C. Brown. The physics of solids. W.A. Benjamin, New York. 1967. p. 176.
20. A. Einstein. Ann. Phys. 34, 170 (1911).
21. R. Becker. Theory of heat. 2nd ed. Springer-Verlag, Berlin. 1967. pp. 245-251; S.B. Palmer and M.S. Rogalski. Advanced university physics. Gordon and Breach, Luxembourg. 1996. Sect. 49.3.
22. R. Becker. Theory of heat. 2nd ed. Springer-Verlag, Berlin. 1967. pp. 245-251; S.B. Palmer and M.S. Rogalski. Advanced university physics. Gordon and Breach, Luxembourg. 1996. Sect. 49.3.
23. R. Fowler and E.A. Guggenheim. Statistical thermodynamics. Cambridge University Press, Cambridge. 1960. p. 131.
24. R. Courant. Differential and integral calculus. 2nd ed. Blackie and Son, London. 1956. Vol. 1. pp. 126-128.
25. M. Born and K. Huang. Dynamical theory of crystal lattices. Clarendon Press, Oxford. 1956. Fig. 4, p. 43.
26. R. Resnick and D. Halliday. Basic concepts in relativity and early quantum theory. 2nd ed. John Wiley and Sons, New York. 1985. p. 312.
27. A. Cezairliyan, A.C. Anderson, D.W. Bonnell et al. Specific heat of solids. Edited by C.Y. Ho. Hemisphere Publishing, New York. 1988. p. 79.
28. H.P. Myers. Introductory solid state physics. 2nd ed. Taylor and Francis, London. 1997. Fig. 5.2, p. 107.
29. P.M. Morse. Thermal physics. 2nd ed. W.A. Benjamin Inc., New York. 1969. See caption to Fig. 20-2, p. 284.
30. M. Born and K. Huang. Dynamical theory of crystal lattices. Clarendon Press, Oxford. 1956. p. 43.
31. J.S. Blakemore. Solid state physics. 2nd ed. Cambridge University Press, Cambridge. 1985. p. 123.
32. J.R. Waldram. The theory of thermodynamics. Cambridge University Press, Cambridge. 1985. p. 109.
33. J.R. Waldram. The theory of thermodynamics. Cambridge University Press, Cambridge. 1985. See the caption to Fig. 10.3, p. 110.
34. Y. Rocard and C.R.S. Manders. Thermodynamics. Sir Isaac Pitman & Sons, London. 1961. p. 591.
35. P. Debye. Ann. Phys. 39, 789 (1912). Table I; H.P. Myers. Introductory solid state physics. 2nd ed. Taylor and Francis, London. 1997. Fig. 5.3, p. 108.
36. P. Debye. Ann. Phys. 39, 789 (1912). Table I; H.P. Myers. Introductory solid state physics. 2nd ed. Taylor and Francis, London. 1997. Fig. 5.3, p. 108.
37. D.E. Gray. (Editor) American Institute of Physics handbook. 3rd ed. McGraw-Hill, New York. 1972. pp. 4-115 and 4-116.
38. A. Guinier and R. Jullien. The solid state: from superconductors to superalloys. English translation by W.J. Duffin. Oxford University Press, Oxford. 1989. pp. 12-13.
39. D. Bohm. Quantum theory. Prentice-Hall, Englewood Cliffs, N.J. 1951. p. 20.
40. A. Einstein. Ann. Phys. 35, 679 (1911); For an English translation, see A. Einstein. The collected papers of Albert Einstein. Vol. 3. The Swiss years: Writings, 1909-1911. Translated by A. Beck. Princeton University Press, Princeton. 1993. Doc. 21, for quotation see p. 370.
41. A. Einstein. Ann. Phys. 35, 679 (1911); For an English translation, see A. Einstein. The collected papers of Albert Einstein. Vol. 3. The Swiss years: Writings, 1909-1911. Translated by A. Beck. Princeton University Press, Princeton. 1993. Doc. 21, for quotation see p. 370.
42. M. Born. Physics in my generation. Springer-Verlag, New York. 1969. p. 58.
43. A. Einstein. The collected papers of Albert Einstein. Vol. 3. The Swiss years: Writings 1909-1911. Translated by A. Beck. Princeton University Press, Princeton. 1993. Doc. 27. p. 437.
44. M. Planck. Philos. Mag. 28, 60 (1914). For quotation, see p. 68.
45. R.M. Eisberg. Fundamentals of modern physics. John Wiley & Sons, New York. 1961. p. 64.
46. R.M. Eisberg. Fundamentals of modern physics. John Wiley & Sons, New York. 1961. p. 68; A. Holden. The nature of solids. Columbia University Press, New York. 1965. pp. 22-23; D. Halliday and R. Resnick. Physics. Part 2. 3rd ed. Extended version. John Wiley & Sons, New York. 1986. pp. 1097-1099.
47. R.M. Eisberg. Fundamentals of modern physics. John Wiley & Sons, New York. 1961. p. 68; A. Holden. The nature of solids. Columbia University Press, New York. 1965. pp. 22-23; D. Halliday and R. Resnick. Physics. Part 2. 3rd ed. Extended version. John Wiley & Sons, New York. 1986. pp. 1097-1099.
48. R.M. Eisberg. Fundamentals of modern physics. John Wiley & Sons, New York. 1961. p. 68; A. Holden. The nature of solids. Columbia University Press, New York. 1965. pp. 22-23; D. Halliday and R. Resnick. Physics. Part 2. 3rd ed. Extended version. John Wiley & Sons, New York. 1986. pp. 1097-1099.
49. A. Einstein. The collected papers of Albert Einstein. Vol. 3. The Swiss years: Writings 1909-1911. Translated by A. Beck. Princeton University Press, Princeton. 1993. Doc. 26. p. 410.
50. M. Blackman. Proc. R. Soc. A, 148, 365 (1935); 148, 384 (1935); 149, 126 (1935); J.K. Roberts. In Heat and thermodynamics. 3rd ed. Blackie and Son, London. 1940. pp. 435-437.
51. M. Blackman. Proc. R. Soc. A, 148, 365 (1935); 148, 384 (1935); 149, 126 (1935); J.K. Roberts. In Heat and thermodynamics. 3rd ed. Blackie and Son, London. 1940. pp. 435-437.
52. M. Blackman. Proc. R. Soc. A, 148, 365 (1935); 148, 384 (1935); 149, 126 (1935); J.K. Roberts. In Heat and thermodynamics. 3rd ed. Blackie and Son, London. 1940. pp. 435-437.
53. M. Blackman. Proc. R. Soc. A, 148, 365 (1935); 148, 384 (1935); 149, 126 (1935); J.K. Roberts. In Heat and thermodynamics. 3rd ed. Blackie and Son, London. 1940. pp. 435-437.
54. F. Reiche. The quantum theory. Methuen and Co., London. 1924. pp. 36-37.
55. M. Blackman. In Handbuch der physik. Vol. VII. Edited by S. Flügge. Springer-Verlag, Berlin. 1955. pp. 325-382. See p. 327.
56. J. Mehra and H. Rechenberg. The historical development of quantum theory. Vol. 1. Part 1. Springer-Verlag, New York. 1982. pp. 131-132.
57. A. Einstein. The collected papers of Albert Einstein. Vol. 3. The Swiss years: Writings 1909-1911. Translated by A. Beck. Princeton University Press, Princeton. 1993. Doc. 21, p. 370 and Doc. 26, p. 409.
58. M.J. Klein. Science, 148, 173 (April 1965), see p. 178.
59. J.K. Fink. Int. J. Thermophys. 3, 165 (1982). For quotation, see p. 167.
60. D.K. Barkan. Walther Nernst and the transition to modern physical science. Cambridge University Press, Cambridge. 1999. For quotation, see p. 204.
61. M. Blackman. In Handbuch der physik. Vol. VII. Edited by S. Flügge. Springer-Verlag, Berlin. 1955. pp. 325-382, see p. 327; J.K. Roberts. In Heat and thermodynamics. 3rd ed. Blackie and Son, London. 1940. Footnote on p. 429.
62. M. Blackman. In Handbuch der physik. Vol. VII. Edited by S. Flügge. Springer-Verlag, Berlin. 1955. pp. 325-382, see p. 327; J.K. Roberts. In Heat and thermodynamics. 3rd ed. Blackie and Son, London. 1940. Footnote on p. 429.
63. W. Nernst. Z. Elektrochem. 17, 265 (1911). See Table 3.
64. A. Einstein. The collected papers of Albert Einstein. Vol. 3. The Swiss years: Writings 1909-1911. Translated by A. Beck. Princeton University Press, Princeton. 1993. Table on p. 408.
65. J.S. Blakemore. Solid state physics. 2nd ed. Cambridge University Press, Cambridge. 1985. p. 121.
66. W. Nernst. The theory of the solid state. University of London Press, London. 1914. p. 31.
67. J. de Launay. In Solid state physics. Vol. 2. Edited by F. Seitz and D. Turnbull. Academic Press, New York. 1956. p. 233.
68. F. Seitz. The modern theory of solids. McGraw-Hill, New York. 1940. p. 110.
69. H.P. Myers. Introductory solid state physics. 2nd ed. Taylor and Francis, London. 1997. p. 121.
70. A. Cezairliyan, A.C. Anderson, D.W. Bonnell et al. Specific heat of solids. Edited by C.Y. Ho. Hemisphere Publishing, New York. 1988. p. 25.
71. R.H. Silsbee and J. Dräger. Simulations for solid state physics. Cambridge University Press, Cambridge. 1997. The average of the two curves in Fig. 5.4, p. 100.
72. M. Born and K. Huang. Dynamical theory of crystal lattices. Clarendon Press, Oxford. 1956. p. 81.
73. F.C. Brown. The physics of solids. W.A. Benjamin, New York. 1967. The broken curve in Fig. 6-8, p. 170.
74. J.S. Blakemore. Solid state physics. 2nd ed. Cambridge University Press, Cambridge. 1985. p. 121.