The thermodynamic approach to the structure analysis of crystals

In a previous paper [Khachaturyan, Semenovskaya & Vainshtein (1979). Soy. Phys. Crystallogr. 24, 519- 524], the thermodynamic formulation of the procedure of crystal structure determination from the intensity array of X-ray reflections was proposed. This approach requires the introduction of analogues of such thermodynamic functions as the free energy, entropy, temperature and so on, and it is reduced to the solution of the specific 'kinetic equation'. It was shown that the equilibrium state of the system is described by the distribution of the scattering substance density which at low temperature corresponds to the true structure of the crystal. The problem of crystal structure determination is thus reduced to determination of the equilibrium distribution of the scattering substance. The Önsager equation formalism was applied to derive 'kinetic equations' describing the relaxation of the system to its equilibrium state. The test of the proposed procedure exemplified by the solution of the 'kinetic equation' to determine the crystal structure of l-proline, C₅H₉NO₂, with 32 atoms per unit cell is considered.