โ Scribed by L. Jansen; F.W. de Wette
No coin nor oath required. For personal study only.
On the theory of transitions in molecular crystals*)
Many molecular crystals exhibit transitions of first or second order at low temperatures. The best known examples of such transitions are found with the crystals of the hydrogen and ammonium halides. In general the phenomena are extremely complex 1).
Most of the theoretical attempts to explain these transitions have been applied to this kind of crystals. Whereas Pauling3) and Fowler3) explained these transitions in terms of the onset of free rotation of the molecules as temperature rises, it has later been found from observations on nuclear magnetic resonance 4) that in most cases the molecules do not rotate freely above the transition temPerature. This corroborates 1 ~ r e n k e l's 5) theory in which transitions were explained as changes in the orientational order of the molecules.
A second group of molecular crystals exhibiting transitions is formed by some diatomic molecules such as N 2, CO and 02. It is the purpose of this letter to outline a theoretical analysis of transition phenomena in crystals of this second group.
Nitrogen and carbon monoxide crystallize in two allotropic modifications, called a and ft. The crystal structure of the a-form is face centered cubic (f.c.c.) ; the/~-form is a hexagonal close packed lattice (h.c.p.) 6) 7). The f.c.c, lattice is stable at the lowest temperatures; at higher temperatures a transition occurs to the h.c.p, lattice.
As in the case of the hydrogen and ammonium halides, the transitions in the crystals of nitrogen and carbon monoxide are due to orientational effects. This follows from the fact that the heavy rare gases neon, argon, krypton and xenon, which also crystallize at the lowest temperatures in the f.c.c, structure, do not exhibit a transition to the h.c.p, lattice. It has been shown 8) that the orientational forces in the crystals of nitrogen and carbon monoxide at absolute zero constitute about 15 % of the total crystal energy. It can then be assumed that the spherically symmetric part of the interaction restricts the possible crystal structures of these diatomic molecules to either the cubic or hexagonal close packed lattice, but that the preference for one of these two structures is determined primarily by orientational forces. The most important deviations from spherical symmetry in the interaction field of crystalline nitrogen and carbon monoxide are caused by quadrupole orientation effects and by the anisotropy in the London forces s). The preferred orientations of the molecular axes are different for the two types of forces. As a result the orientational energy due to anisotropy in the London forces is even positive in the f.c.c, lattice at absolute zero, whereas the quadrupole interaction energy is strongly negative. On this basis it can be expected that the transition temperature increases with increasing values of the quadrupole moments. On the other hand, the correlation between transition temperature and anisotropy in the London forces should be the inverse.
In the following table the quadrupole moment Q, anisotropy in the polarizability 7, transition temperature Ttr'a-~l and transition heat AH are listed for crystals of nitrogen, carbon monoxide and oxygen.
Oxygen has been included in the table because it shows the same trend as CO and N 2 with respect to the dependence of Tt, on Q and 7. However, it apparently does not crystallize in a f.c.c, lattice at the lowest temperatures (it may deviate too much from the ideal concept of a molecular crystal).
It seems plausible to assume that the analysis of these transitions may be based on an interaction potential between the molecules which consists of a spherically symmetric part, a term referring to quadrupole orientations and a contribution
๐ SIMILAR VOLUMES
A semi-empirical theory of radiative transitions of trapped electrons in polar crystals is developed using a model in which the crystal is considered to consist of a large number of harmonic oscillators all having the same frequency co and which are coupled to the impurity centre by a coupling linea