The thermodynamics of crystal lattices

In previous papers by Misra(1) and by Born and Misra(2) lattice sums of the type required in discussing the stability of a cubic crystal of the Bravais type in which the forces are central have been calculated. In the investigation of the thermodynamic properties of crystals a more general type of lattice sum occurs, which involves the phases of the waves. In the present paper a method of calculating these sums is developed and tables are computed.

[1]  M. Born.  The thermodynamics of crystal lattices , 1943, Mathematical Proceedings of the Cambridge Philosophical Society.

[2]  Max Born,et al.  On the stability of crystal lattices IX. Covariant theory of lattice deformations and the stability of some hexagonal lattices , 1942, Mathematical Proceedings of the Cambridge Philosophical Society.

[3]  S. C. Power.  On the stability of crystal lattices VII. Long-wave and short-wave stability for the face-centred cubic lattice , 1942, Mathematical Proceedings of the Cambridge Philosophical Society.

[4]  C. Coulson,et al.  Momentum distribution in molecular systems , 1941, Mathematical Proceedings of the Cambridge Philosophical Society.

[5]  R. Fürth.  On the stability of crystal lattices , 1941, Mathematical Proceedings of the Cambridge Philosophical Society.

[6]  M. Born,et al.  The stability of crystal lattices. III , 1940, Mathematical Proceedings of the Cambridge Philosophical Society.

[7]  E. Kellermann.  Theory of the vibrations of the sodium chloride lattice , 1940, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[8]  R. Fürth,et al.  The Stability of Crystal Lattices , 1940, Mathematical Proceedings of the Cambridge Philosophical Society.

[9]  M. Born,et al.  On the stability of crystal lattices. IV , 1940, Mathematical Proceedings of the Cambridge Philosophical Society.

[10]  M. Born.  Thermodynamics of Crystals and Melting , 1939 .

[11]  J. Kirkwood.  Statistical Mechanics of Fluid Mixtures , 1935 .

[12]  L. P. Hunter.  The Variation with Temperature of the Principal Elastic Moduli of NaCl near the Melting Point , 1942 .

[13]  P. P. Ewald.  Die Berechnung optischer und elektrostatischer Gitterpotentiale , 1921 .

[14]  O. Stern.  Über eine Methode zur Berechnung der Entropie von Systemen elastisch gekoppelter Massenpunkte , 1916 .