Thermal Expansion of Chemical Bonds

Using the bond-valence model, a relationship is developed between the thermal expansion of a chemical bond, its amplitude of thermal vibration and its force constant. An empirical expression found between bond valence and the force constants derived from vibrational spectroscopy allows all of these quantities to be predicted from either the expected or the observed bond valence. The thermal expansion predicted by these relations is in excellent agreement with the average expansion observed around cations in inorganic solids, but individual bonds are found to expand more or less than this depending on strains and constraints within the structure. Comparison between the theoretical and observed amplitudes of thermal vibration gives a quantitative measure of correlation between the thermal motions of atoms that form the bond. The theory also shows how the parameters used in calculating bond valences from bond lengths should be corrected for temperature.