Empirical determination of thermal expansion in insulators with no experimental input

Abstract

The localized-continuum model of thermal expansion which was applied to insulators in the previous paper is further refined by empirical means to allow the calculation of thermal expansion in insulating materials with no input other than the chemical formula. Estimation of the Madelung constants is made by using the empirical methods of Kapustinsky and Templeton while the atomic nearest-neighbour distances are estimated by using atomic radii tables. Approximate values of repulsive exponents are obtained by using an empirical scaling rule and a table of monovalent repulsive exponents. The Debye temperature is approximated by a simple formula involving the estimated parameters of the interatomic potential. Using this approach, thermal expansion is estimated in a group of binary and complex ternary materials and a group of complex salts. The agreement with experiment is generally good, although the elimination of experimental input appears to increase the probable error in the calculations by 15% to 20%. The results indicate that this approach is capable of predicting with reasonable accuracy the thermal expansion in a wide range of insulating materials with no experimental input and no adjustable parameters. The limitations of this method for certain cases is also discussed.