A unified theoretical and computational framework for inelastic neutron scattering in anharmonic and disordered crystals

We present a unified theoretical and computational framework for analyzing inelastic neutron scattering (INS) in disordered anharmonic crystals. By enhancing the classical Green’s function method with modern theoretical derivations and validating the results using density functional perturbation theory (DFPT), we derive a generalized Lorentzian expression for the INS cross-section. This formulation explicitly incorporates phonon linewidths and frequency shifts resulting from anharmonic interactions and lattice defects. The framework is applied to simulate temperature-dependent scattering behavior in SrTiO₃, with results benchmarked against published experimental data. This approach offers a practical tool for interpreting INS spectra and guiding lattice dynamics studies in structurally complex materials.