Thermodynamic integration at constant pressure from the nonlocal Einstein crystal

Area of Science:

• Thermodynamics
• Solid-state physics
• Computational materials science

Background:

• Estimating Gibbs free energy is crucial for predicting material properties and phase stability.
• Current methods can be computationally intensive or lack generality for complex crystalline structures.

Purpose of the Study:

• To develop and demonstrate a novel method for calculating the Gibbs free energy of periodic crystalline assemblies.
• To provide an efficient and accurate approach for thermodynamic calculations in materials science.

Main Methods:

• Utilizing thermodynamic integration at constant pressure.
• Employing a nonlocal Einstein crystal as a reference system.
• Applying the method to a two-dimensional harmonic crystal with hexagonal symmetry.

Main Results:

• The Gibbs free energy was successfully estimated for the d-dimensional crystalline assembly.
• An analytical derivation of the isobaric Gibbs function was achieved for the specific 2D hexagonal crystal model.
• The nonlocal Einstein crystal approach proved effective for thermodynamic integration.

Conclusions:

• The proposed thermodynamic integration method offers a viable route for Gibbs free energy calculations in crystalline materials.
• The analytical results for the 2D hexagonal system validate the general applicability of the method.
• This approach has implications for computational materials design and discovery.