Effets isotopiques et propriétés thermodynámiques en phase condensée. I

✍ Scribed by I. Prigogine; R. Bingen; J. Jeener

• Publisher: Elsevier Science
• Year: 1954
• Weight: 587 KB
• Volume: 20
• Category: Article
• ISSN: 0031-8914
• DOI: 10.1016/s0031-8914(54)80053-x

✦ Synopsis

The zero point energy of solid isotopic mixtures is discussed and their properties are compared with those of the pure isotopes. The case of a one-dimensional chain of molecules is considered in some detail because the calculations may then be performed in a rigourous way. An extension of the results to real three-dimensional crystals will be worked out in a subsequent paper. Only harmonic oscillators are considered. It is shown that the zero point energy increases steadily with the number of couples of first neighl~ours between molecules of different masses. The zero point energy is lowest for the pure isotopes and highest for the ordered lattice ABAB ..... Also its value for a random distribution of the isotopes is higher than that for the pure isotopes. The stable state at 0°K always requires a separation into pure isotopes.

Differences in masses, i.e. isotopic effects, may give positive deviations from R a o u 1 t s law without any effect of the statistics. The results obtained indicate the possibility of pure quantum transitions in the phase diagram due to isotopic effects at sufficiently low temperatures. These transitions are quantum analogues of order-disorder transitions. The differences in the zero point energies due to different spatial distributions of the isotopes are small, however, so that these effects can only appear at extremely low temperatures. They are much smaller than the effects calculated by Prigogine and Philippot which are related to volume changes on mixing and thus to the anharmonicity of the motion of the molecules.