Temperature dependence of the elastic and vibronic behavior of Si, Ge, and diamond crystals

The thermally induced softening of the elastic and vibronic identities in crystals and their correlations have long been a puzzle. Analytical solutions have been developed, showing that the detectable elastic and vibronic properties could be related directly to the bonding parameters, such as bond length and strength, and their response to the temperature change. Reproduction of measured T -dependent Young's modulus and Raman shift of Si, Ge, and diamond reveals that the thermally driven softening of the elasticity and the optical Raman frequency arises from bond expansion and vibration, with derived information about the atomic cohesive energy and clarification of their interdependence.