The DMDW code

DMDW: A set of tools to calculate Debye-Waller factors and other vibrational properties using dynamical matrices.



DMDW is a set of tools developed to calculate vibrational properties such as EXAFS and crystallographic Debye-Waller (DW) factors, vibrational free energies, phonon densities of state and other related quantities from dynamical matrices (i.e. the matrix of force constants or Hessian matrix) using the Lanczos recursion algorithm. DMDW provides an alternative to the correlated Einstein and Debye models. These semi-empirical models are unsatisfactory for several reasons:

  • There are typically many more independent DW factors in the XAFS MS path expansion than can be fit reliably to the available data.
  • They require separate fits to appropriate Debye or Einstein temperatures for each multiple-scattering path.
  • They typically ignore anisotropic contributions, and hence do not capture the detailed structure of the phonon spectra and associated DW factors.



Left: Dynamical matrix (in pole and continuous representations) and experimental phonon density of states.
Right: Correlated Debye, dynamical matrix and experimental near neighbor DW factor in Ge.




A detailed description of the methodology can be found in:

  • “Theoretical x-ray absorption Debye-Waller factors”, F. D. Vila, J. J. Rehr, H. H. Rossner and H. J. Krappe, Phys. Rev. B 76, 014301 (2007), DOI: 10.1103/PhysRevB.76.014301.
  • “Recursion method for multiple-scattering XAFS Debye-Waller factors”, A. V. Poiarkova and J. J. Rehr, J. Synchrotron Rad. 6, 313 (1999) DOI: 10.1107/S0909049599001685.