Cell Model and Elastic Moduli of Disordered Solids: Low Temperature Limit

The cell theory has been previously employed to compute the equation of state of a disordered condensed system. It is now generalized to include anisotropic stresses. We adopt the condition of affine deformation, transforming an originally spherical into an ellipsoidal cell. With a Lennard‐Jones n−m potential between non‐bonded centers, the formal expression for the deformational free energy is derived. It is to be evaluated in the limit of the linear elastic range. Since the bulk modulus in this limit is already known, it is convenient to consider a uniaxial deformation. To begin with, we restrict ourselves to the low temperature limit in the absence of entropy contributions. Young's modulus and Poisson's ratio then follow.