Isothermal stress and elasticity tensors for ions and point dipoles using Ewald summations

The isothermal stress tensor and isothermal elasticity tensor for systems of point charges and of nonpolarizable point dipoles are derived from the strain derivatives of the free energy. For the case of point dipoles, it is shown that the angular dependence of the interaction potential gives rise to additional contributions to the stress and elasticity tensors not recognized previously.

Figure 1

Deformation sequence assuming point dipoles do not rotate when the system is strained: (a) reference state, (b) after shear strain by angle $\theta$, (c) after counter-clockwise rotation by angle $\theta$, and (d) after final shear strain by angle $\theta$.

Figure 2

Deformation sequence assuming point dipoles rotate according to Eq. (39): (a) reference state, (b) after shear strain by angle $\theta$, (c) after counter-clockwise rotation by angle $\theta$, and (d) after final shear strain by angle $\theta$.