Methods of Calculating Phonon Frequencies

The following sections are included:

• Introduction

• Crystal Hamiltonian and normal modes of vibration

• Calculation of phonon modes using ab initio theory

  • Frozen phonon approach

  • Planar force constant method

  • Linear response method

  • Calculation of elastic constants and mode Grüneisen constant

• Calculation of phonon modes using an adiabatic bond charge model

  • The C-type matrix within the BCM

  • The Coulomb interaction

  • The central short-range interaction

  • Keating's bond-bending interaction

  • Relationship between BCM force constant matrices and Born-von Kármán force constant matrices

  • Relationship between short-range force constants and Madelung energy