Phonon Properties of Silicon

Parameters for converged calculations

• Lattice constant = 10.34 Bohr
• xctype = "GGA_PBE"
• ngridk = "8 8 8"
• rgkmax = "7.0" (default)
• ngridq = "4 4 4"

Check Landolt-Börnstein tables for literature data.

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☛ Phonon density of states (DOS)

☛ Phonon-dispersion relations

☛ Zero-point energy

 Zero-point energy is 1.2060e-01 [eV]

☛ Vibrational free energies

☛ Vibrational entropy

☛ Heat capacity

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[Phonon frequencies and mode Grüneisen parameters]

Phonon frequencies (im cm$^{-1}$) and mode Grüneisen parameters

q-point $\omega_j({\bf q},a_0)$ $\gamma_j({\bf q},a_0)$ $\quad\gamma_{\rm expt}$ [REF] $\Gamma_{\rm LTO}$ 505 0.98 0.90 — 1.08 $X_{\rm TO}$ 448 1.52 0.90 — 1.51 $X_{\rm LA}$ 401 1.00 0.61 — 1.03 $X_{\rm TA}$ 143 -1.93 -3.69 — -1.08 $L_{\rm TO}$ 479 1.23 1.3 $L_{\rm LO}$ 401 1.62 0.9 $L_{\rm LA}$ 370 0.37 0.9 $L_{\rm TA}$ 109 -1.61 -2.74 — -1.15

[Linear thermal-expansion coefficient]

Linear thermal-expansion coefficient

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