  An analytical solution has been developed clarifying that the thermally
driven elastic softening of crystals can be directly related to the length and
strength of the representative bonds of the crystal and to the response of the
bonding identities to the change of temperature. Reproduction of the
experimental results Ag, Au, MgO, Mg2SO4, Al2O3, and KCl derived mean atomic
cohesive energy of the specimen may evidence the validity of the proposed
approach without involving parameters using in classical thermodynamics.
