Multiphonon scattering formula of dynamic structure factors for classical Debye solids.

Area of Science:

• Condensed Matter Physics
• Materials Science
• Statistical Mechanics

Background:

• Understanding the dynamic structure factor S(k,ω) is crucial for characterizing lattice dynamics in solids.
• Previous models often simplified or neglected multiphonon contributions, limiting accuracy at higher wave-numbers.
• Thermal diffuse scattering (TDS) plays a significant role in neutron and X-ray scattering experiments.

Purpose of the Study:

• To develop a semianalytic formula for the dynamic structure factor S(k,ω) applicable to classical Debye solids.
• To incorporate multiphonon thermal diffuse scattering (TDS) up to infinite order across the entire k-ω range.
• To investigate the transition of scattering spectra with increasing wave-number (k).

Main Methods:

• Construction of a semianalytic formula for S(k,ω) using Gaussian approximations for multiphonon displacement correlations.
• Analysis of the formula's behavior in different regimes: hydrodynamic (k→0), large-k limit, and at Bragg points.
• Verification of the theory using zeroth-order and second-order frequency-moment sum rules.

Main Results:

• The formula accurately describes the transition from sharp one-phonon peaks to diffuse spectra (umklapp and multiphonon continuum) as k increases.
• Analytic properties confirm the approach to ideal-gas spectra at large k.
• A 1/ω divergence in S_TDS(k,ω) at Bragg points leads to logarithmic enhancement of the static structure factor S_TDS(k).

Conclusions:

• The developed formula provides a comprehensive description of dynamic structure factors in Debye solids, including complex multiphonon effects.
• The results offer valuable insights for interpreting scattering data and understanding lattice dynamics.
• The theory shows good agreement with sum rules, validating its accuracy.