Thermally driven elastic weakening of crystals
  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. 
Chang Q. Sun