The origin in thermodynamic stability of paracrystals

Abstract

Statistical mechanical methods have been used to explore the fluctuations in the lattice spacing which can be measured by X-ray diffraction. The total variance can be divided into three parts. Only one of these, the inter-crystal variance of the average lattice spacing can be related to the well known statistical mechanical fluctuations of small homogeneous systems. The other two components of the total variance must be related to inhomogeneities caused by immobile defects trapped within the lattice during its formation. These defects have the equilibrium concentration and distribution for the crystal size and thermodynamic conditions which existed at the time of their formation. The immobility of these defects prevents their concentration from decreasing as is required for a crystal to grow under equilibrium condition. Conversely if the crystal is already large and the strain energy around a defect is greatly increased by a chemical transformation, the immobility of the defects may cause the crystal to split up into microparacrystalline domains (mPC’s). Consequently the size of these mPC’s is fixed by the concentration and distribution of defects which existed at their formation.