Abstract
Since the publication of Eucken’s „Energie und Wärmeinhalt“ [1] in 1929 our knowledge of the heat capacity of solids has increased tremendously, especially in the very low temperature region.
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General References
Eucken, A.: Energie und Wärmeinhalt, Bd. 8, Teil 1 im Handbuch der Experimentalphysik, Herausg. W. Wien u. F. Harms. Leipzig: Akademische Verlagsgesellschaft 1929.
Eucken, A.: An encyclopedic work on all aspects of heat capacity problems, including experimental techniques, results of experiment and theory, together with an extensive bibliography.
Einstein, A.: Die Plancksche Theorie der Strahlung und die Theorie der spezifischen Wärme. Ann. Phys. 22, 180–190 (1907).
Einstein, A.: Berichtigung zu: die Plancksche Theorie usw. Ann. Phys. 22, 800 (1907).
Einstein, A.: Eine Beziehung zwischen dem elastischen Verhalten und der spezifischen Wärme bei festen Körpern mit einatomigen Molekül. Ann. Phys. 34, 170–174 (1911).
Einstein, A.: The first of these papers is historically important as marking two great theoretical advances: the application of Planck’s quantum theory outside its original domain; and the explanation of the failure of the equipartition law as evidenced by atomic heat values for certain elements which are lower than that predicted by the law of Dulong and Petit.
Debye, P.: Zur Theorie der spezifischen Wärme. Ann. Physik 39, 789–839 (1912). — This paper contains Debye’s derivation of his T3 law for heat capacity at low temperatures. Besides being of historical interest, his conclusions remain valid, in a restricted temperature range, even in more detailed theories.
Born, M., u. T. v. Kármán: Über Schwingungen in Raumgittern. Phys. Z. 13, 297–309 (1912).
Born, M., u. T. v. Kármán: Zur Theorie der spezifischen Wärme. Phys. Z. 14, 15–21 (1913).
Born, M., u. T. v. Kármán: Über die Theorie der Verteilung der Eigenschwingungen von Punktgittern. Phys. Z. 14, 65–71 (1913).
The first and third of these papers laid the foundation of the lattice theory which has since been developed by many workers, especially Blackman (see reference [5]). In the second the T3 law is shown to follow from the lattice theory at very low temperatures.
Blackman, M.: The Theory of the Specific Heat of Solids. Repts. Progr. Phys. 8, 11–30 (1941). — A review of the experimental values of atomic heat at low temperatures, as compared with calculations based on Debye’s theory using elastic constants, and with the lattice theory as developed by Blackman and others. The apparent agreement with the Debye theory is shown in many cases to be largely fortuitous. References are included to Blackman’s original calculations of vibration spectra and to other calculations published up to 1940.
Born, M., and K. Huang: Dynamical Theory of Crystal Lattices. London: Oxford University Press 1954. — Discussion of the application of lattice theory to a variety of problems. Sect. 4 through 6 treat thermodynamical applications, including heat capacity. A review of the methods which have been devised to evaluate vibration spectra is included, with references.
Sommerfeld, A.: Zur Elektronentheorie der Metalle. Naturwiss. 15, 825–832 (1927). — Zur Elektronentheorie der Metalle auf Grund der FERMischen Statistik I. Allgemeines, Strömungs- und Austrittsvorgänge. Z. Physik 47, 1 – 32 (1928). — The first of these papers is a shorter summary of the results presented in detail in the second. Sommerfeld’s formulas for the electronic heat capacity appears for the first time in the latter, although a qualitative discussion on the basis of the temperature variation of a degenerate electron gas is given in the former.
Sommerfeld, A., u. H. Bethe: Elektronentheorie der Metalle. Handbuch der Physik, Bd. 24, Teil 2, S. 333–622. Berlin: Springer 1933. — Classical account of the electron theory of metals, including Sommerfeld’s free electron treatment and the applications of band theory as well.
Seitz, F.: The Modern Theory of Solids. New York and London: The McGraw-Hill Book Company, Inc. 1940. — A valuable text on many aspects of solid state theory. Chapter III is devoted to specific heat of simple solids, including a discussion of vibration spectra; Chapter IV sect. 27 treats the electronic heat capacity in non-transition metals and sect. 28, that in transition metals. The theory of the band approximation and approximation methods involved in band calculations are discussed in Chapters VIII and IX respectively and typical band structures in metals and other solids are described in Chapter XIII.
Eisenstein, J.: Superconducting elements. Revs. Mod. Phys. 26, 277–291 (1954). — A review of magnetic and calorimetric data on superconducting elements, with the data for each element discussed in some detail. A summarizing table includes the crystal structure, normal transition temperature, critical field at absolute zero and magnetic and calorimetric values of y.
Raynor, G. V.: The band structure of metals. Repts. Progr. Phys. 15, 173–248 (1952). — A comprehensive survey of theoretical calculations and experimental evidence on metallic band structures. Other types of data receive more attention than the electronic heat capacity.
Daunt, J. G.: The electronic specific heat of metals. In Progress in Low Temperature Physics, ed. C. J. Gorter, vol. 1, pp. 202–223. Amsterdam and New York: North-Holland Publishing Company and Interscience Publishers, Inc. 1955. — A detailed discussion of the relation of the band structure to the electronic heat capacity, including magnetic evidence from superconductive elements. Extensive references are appended.
Mott, N. F.: Recent advances in the electron theory of metals. In Progress in Metal Physics, vol. 3, pp. 76–114. London and New York: Pergamon Press Ltd. and Interscience Publishers, Inc. 1952. — A comprehensive survey of many aspects of the theory, including heat capacity.
Shiffman, C. A.: The Heat Capacities of the Elements below Room Temperature. Schenectady: General Electric Research Laboratory 1952.
Shull, D. R., and G. C. Sinke: The Thermodynamic Properties of the Elements in their Standard States. Midland, Michigan: The Dow Chemical Company 1955. — This and the previous reference tabulate values of the thermodynamic properties and include extensive lists of references. Those in reference [14] are especially conveniently arranged.
Serin, B.: The Magnetic threshold curve of superconductors. In Progress in Low Temperature Physics, ed. C. J. Gorter, vol. 1, pp. 138–150. Amsterdam and New York: North-Holland Publishing Company and Interscience Publishers, Inc. 1955. — The relation between the threshold curve and thermodynamic properties is discussed, with data on tin treated in detail.
Shoenberg, D.: Superconductivity. Cambridge: Cambridge University Press 1952. — In this text both experimental and theoretical aspects are discussed. Tables and graphs of data are included, with a detailed bibliography of recent work.
Nix, F. C., and W. Shockley: Order-disorder transformations in alloys. Rev. Mod. Phys. 10, 1–17 (1938).
Nakamura, T.: Statistical Mechanics of cooperative phenomena. Progr. Theor. Phys. 7, 241–254 (1952).
Kikuchi, R.: A theory of cooperative phenomena. Phys. Rev. 81, 988–1003 (1951).
Ter Haar, D.: Elements of Statistical Mechanics. New York: Rinehart & Company, Inc. 1954. Chapt. XIII, pp. 251–295. Cooperative phenomena.
Smoluchowski, R., editor: Phase Transformations in Solids. New York and London: John Wiley & Sons, Inc. and Chapman & Hall, Ltd. 1951. — Ter Haar gives a good account of the basic theory together with some applications. Nakamura and Kikuchi present detailed discussions of particular forms of the theory. The problem of order-disorder, both theoretical and experimental, is considered by Nix and Shockley. The last entry is a symposium in which a variety of cooperative phenomena are treated.
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Keesom, P.H., Pearlman, N. (1956). Low Temperature Heat Capacity of Solids. In: Flügge, S. (eds) Low Temperature Physics I / Kältephysik I. Encyclopedia of Physics / Handbuch der Physik, vol 3 / 14. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-39773-2_5
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