On the validity of using the Debye model to quantitatively correlate the shear modulus with vibrational properties in cubic metals

The relationship between the shear modulus and the flexibility volume has been examined using molecular dynamics simulations in fifteen cubic metallic elements over a range of temperatures. We have observed a universal correlation, and identified the applicability range in which this correlation is quantitatively consistent with the prediction based on the Debye model. Deviation is observed for high modulus metals, and its origin is discussed in terms of the Debye assumptions regarding the vibrational mean squared displacement and the phonon density of states.