Direct calculation of the lattice Green function with arbitrary interactions for general crystals

Area of Science:

• Solid State Physics
• Materials Science
• Computational Materials Science

Background:

• Accurate computation of lattice defect geometries is crucial for understanding material properties.
• Existing methods struggle to efficiently couple local defect displacements with long-range elastic strain.

Purpose of the Study:

• To develop an efficient and accurate method for calculating the lattice Green function for general crystals.
• To enable precise modeling of various lattice defects, including point defects, dislocations, and grain boundaries.

Main Methods:

• Extended a method for Bravais lattices to calculate the lattice Green function from the force-constant matrix for general crystals.
• Incorporated new terms to account for optical modes and loss of inversion symmetry.
• Separated poles and discontinuities in reciprocal space for controlled numerical accuracy.

Main Results:

• Demonstrated an efficient and accurate calculation of the lattice Green function for crystals with arbitrary bases.
• Showcased the method's applicability to systems with optical modes and broken symmetry.
• Verified the algorithm's general applicability in 2D and 3D for complex crystal structures.

Conclusions:

• The developed method provides a robust and efficient way to compute lattice Green functions.
• This enables more accurate and computationally feasible simulations of lattice defects in diverse crystalline materials.
• The approach is broadly applicable to various crystal symmetries and unit cell complexities.