Isothermal and adiabatic elastic constants from virial fluctuations

Area of Science:

• Computational Materials Science
• Condensed Matter Physics
• Solid-State Chemistry

Background:

• Calculating elastic constants for periodic systems is crucial for understanding material properties.
• Traditional methods involve complex second derivatives of potential energy, posing computational challenges.

Purpose of the Study:

• To derive new expressions for elastic constants that simplify calculations.
• To explicitly include boundary contributions in elastic constant derivations.
• To reformulate the Born term using first derivatives of potential energy.

Main Methods:

• Derivation of analytical expressions for isothermal and adiabatic elastic constants.
• Expressing the potential-dependent part using atomic group energies.
• Reformulating the Born term using atomic group virials.
• Validation through molecular-dynamics simulations of crystalline argon and silicon.

Main Results:

• New expressions for elastic constants were derived, incorporating boundary contributions.
• The Born term was successfully reformulated using first derivatives of potential energy.
• Molecular-dynamics simulations confirmed good agreement between the new and original Born term formulations for argon and silicon.
• The new Born term formulation showed slower convergence but yielded comparable elastic constant values.

Conclusions:

• The derived expressions offer a computationally efficient alternative for calculating elastic constants.
• The reformulated Born term provides a valid and potentially simpler approach for elastic constant calculations.
• The findings are validated by simulation data for representative crystalline materials.