6.3 Phonon DOS and harmonic thermodynamics

These are unexecuted teaching inputs and starting models. Original diagrams are schematics, not calculated results. Validate version-specific syntax, licensed or authorized data, numerical convergence and the scientific model before using this workflow.

6.3.1 Model, units and provenance

PW cutoffs and energies use Ry, common force output uses Ry/bohr, and pressure uses kbar. Geometry cards state their coordinate units. Different executables have distinct grammars and time-unit conventions.

Shared inputs, conventions and evidence

Original schematic: Phonon DOS and harmonic thermodynamics. No numerical results are claimed.

6.3.2 Unexecuted inputs and explicit deltas

Use the accompanying instructions to identify the parent calculation and placement of every delta; a snippet is not automatically a standalone input. Preserve all blank-line and file-provenance requirements.

6.3.2.1 Input block 1

&INPUT
 flfrc='si.fc', asr='crystal', dos=.true.,
 nk1=24, nk2=24, nk3=24,
 fldos='si.phdos', deltaE=1.0
/

6.3.3 Worked investigation

6.3.3.1 Intuition and prerequisites

Harmonic thermodynamics integrates all vibrational modes, so a path plot is insufficient. Use the converged Si force constants from 6.2. matdyn.x supplies the phonon DOS; numerical integration of free energy, entropy and heat capacity is a clearly identified external analysis step. Harmonic heat capacity is not thermal conductivity, which requires additional scattering physics.

6.3.3.2 Original DOS input and analysis definition

See input block 1 above.

6.3.3.3 Checks, pitfalls and exercise

Imaginary modes invalidate ordinary stable-harmonic free-energy formulas; do not silently take absolute frequencies or delete an unstable region. Exact Γ translations occupy zero measure in the continuum integral, but a coarse discrete integration needs careful treatment. Converge both the original force-constant q mesh and the dense integration mesh. At high temperature a stable harmonic cell tends toward 3Nk_B heat capacity; this is a useful normalization check, not evidence that anharmonic effects vanish.

Exercise: calculate free-energy differences between two nearby volumes and outline a quasiharmonic volume-minimization workflow. Explain why thermal expansion requires volume-dependent phonons and why a single-volume harmonic DOS is insufficient. Report per-cell, per-atom or molar normalization explicitly in every exported column.