Local bond average for the thermally driven elastic softening of solid specimens

It has long been a puzzle regarding the atomistic origin of the thermally driven elastic softening of a solid specimen since the pioneering works of Anderson in 1966 and Watchman in 1961. Here we present an analytical solution developed from the perspective of the local bond average. It is shown that the thermally driven elastic softening of crystals can be directly related to the geometric and energetic response of the representative bonds or their average of the given specimen to the temperature variation. Reproduction of the experimental results of Ag, Au, MgO, Mg2SO4, Al2O3, KCl, Si, Ge and diamond crystals has been realized giving rise to information on the mean atomic cohesive energy without involving any hypothetical parameters used in classical thermodynamics or in continuum mechanics.