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5 "debye" - phonon spectra of fcc systems and heat capacity

"debye" calculates a variety of quantities related to the phonon spectrum and specific heat of fcc crystals with nearest neighbor interactions. It calculates from the Debye model, as well as from the lattice dynamic model, and compares the results with experimental heat capacity data for aluminum, copper, and lead. Neutron scattering data may also be displayed, for comparison with the model dispersion relations, for all three metals.

"debye" was programmed by Joerg Draeger, and derived in part from a problem developed by Doug Fitchen.

"debye" calculates the phonon dispersion relation for fcc crystals in the simplest possible model with a single adjustable force constant. The graph on the left shows the dispersion relation for wave vectors along the (110) axis in reciprocal space, with the force constant adjusted to give the low frequency slopes equal to the sound velocities in copper. The points are neutron data for copper: the agreement is remarkable. For lead, on the right, we display all of the symmetry drections and here we do not do so well.
. . .

"debye" samples the reciprocal space randomly, calculates the 3 phonon frequencies associated with each sampled point, and develops a density of modes histogram. The density of modes (in blue) may be displayed either in a linear plot (left) or a log/log plot (right). A density of modes given by the Debye model (in red) is shown for comparison.
. . .

From the density of states, the specific heat is calculated, is displayed, and can be compared with experimental data and with a Debye model calculation. In the log/log plot below, the wrong force constant was chosen for the numerical calculation (in blue). Should it be increased or decreased, and by what factor? For the Debye model (in red), the wrong lattice constant was chosen! Should it be larger or smaller, and by what factor?

Table of contents for Chapter 5 of Simulations for Solid State Physics

  1. Introduction
  2. Brillouin zone
  3. Dispersion relations
    1. Symmetry directions
    2. Force constants
    3. Comparison with neutron data
  4. Density of states
    1. From dispersion relations to density of states
    2. Resolution versus noise
    3. Van Hove singularities
    4. Superconducting tunneling
    5. Debye density of states
  5. Thermal energy
  6. Heat capacity
    1. Lead
    2. Copper and aluminum
  7. Summary
  8. Appendix: "debye" -- the program

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