Phonon density of states for ZnO (Rocksalt)

D(ω) [10¹⁵ s/rad m^-3]
	ω [10¹² rad/s]

The lattice constant of ZnO in the rocksalt structure is 4.28 Å. There are four zinc atoms and four oxygen atoms in the conventional unit cell so the atomic density is $n= 8/(4.28\times 10^{-10})^3 = 1.02\times 10^{29}$ 1/m³. Every atom has three degrees of freedom so there are $3n = 3.06\times 10^{29}$ modes/m³. The integral of the phonon density of states over all frequencies should be $3n$.

This phonon dispersion relation was calculated using Quantum ESPRESSO. The details of the calculation including the input and output files can be found here.

ω [rad/s] D(ω) [s rad^-1m^-3]
0.00E+00 0.00E+00 1.88E+11 3.48E+10 3.77E+11 1.39E+11 5.65E+11 3.13E+11 7.53E+11 5.57E+11 9.42E+11 8.70E+11 1.13E+12 1.25E+12 1.32E+12 1.71E+12 1.51E+12 2.23E+12 1.70E+12 2.82E+12 1.88E+12 3.48E+12 2.07E+12 4.21E+12 2.26E+12 5.01E+12 2.45E+12 5.88E+12 2.64E+12 6.82E+12 2.83E+12 7.83E+12 3.01E+12 8.91E+12 3.20E+12 1.01E+13 3.39E+12 1.13E+13 3.58E+12 1.26E+13 3.77E+12 1.39E+13 3.96E+12 1.54E+13 4.14E+12 1.69E+13 4.33E+12 1.84E+13 4.52E+12 2.01E+13 4.71E+12 2.18E+13 4.90E+12 2.35E+13 5.09E+12 2.54E+13 5.27E+12 2.73E+13 5.46E+12 2.93E+13 5.65E+12 3.13E+13 5.84E+12 3.35E+13 6.03E+12 3.57E+13 6.22E+12 3.79E+13 6.40E+12 4.02E+13 6.59E+12 4.27E+13 6.78E+12 4.51E+13 6.97E+12 4.77E+13 7.16E+12 5.03E+13 7.35E+12 5.30E+13 7.53E+12 5.57E+13 7.72E+12 5.85E+13 7.91E+12 6.14E+13 8.10E+12 6.44E+13 8.29E+12 6.74E+13 8.48E+12 7.05E+13 8.67E+12 7.37E+13 8.85E+12 7.69E+13 9.04E+12 8.02E+13 9.23E+12 8.36E+13 9.42E+12 8.70E+13 9.61E+12 9.06E+13 9.80E+12 9.42E+13 9.98E+12 9.78E+13 1.02E+13 1.02E+14 1.04E+13 1.05E+14 1.05E+13 1.09E+14 1.07E+13 1.13E+14 1.09E+13 1.17E+14 1.11E+13 1.21E+14 1.13E+13 1.25E+14 1.15E+13 1.30E+14 1.17E+13 1.34E+14 1.19E+13 7.05E+14 1.21E+13 8.84E+14 1.22E+13 6.03E+14 1.24E+13 3.91E+14 1.26E+13 4.12E+14 1.28E+13 4.33E+14 1.30E+13 4.54E+14 1.32E+13 4.76E+14 1.34E+13 4.98E+14 1.36E+13 5.21E+14 1.38E+13 5.44E+14 1.39E+13 5.68E+14 1.41E+13 5.92E+14 1.43E+13 6.17E+14 1.45E+13 6.42E+14 1.47E+13 6.68E+14 1.49E+13 6.94E+14 1.51E+13 7.20E+14 1.53E+13 7.47E+14 1.54E+13 7.75E+14 1.56E+13 8.03E+14 1.58E+13 8.31E+14 1.60E+13 8.60E+14 1.62E+13 8.89E+14 1.64E+13 9.19E+14 1.66E+13 9.49E+14 1.68E+13 1.03E+15 1.70E+13 1.12E+15 1.71E+13 1.21E+15 1.73E+13 1.28E+15 1.75E+13 1.34E+15 1.77E+13 1.39E+15 1.79E+13 1.43E+15 1.81E+13 1.47E+15 1.83E+13 1.52E+15 1.85E+13 1.57E+15 1.86E+13 1.63E+15 1.88E+13 1.71E+15 1.90E+13 1.88E+15 1.92E+13 2.10E+15 1.94E+13 2.30E+15 1.96E+13 2.45E+15 1.98E+13 2.54E+15 2.00E+13 2.59E+15 2.02E+13 2.59E+15 2.03E+13 2.68E+15 2.05E+13 2.82E+15 2.07E+13 2.97E+15 2.09E+13 3.13E+15 2.11E+13 3.35E+15 2.13E+13 3.77E+15 2.15E+13 4.09E+15 2.17E+13 4.28E+15 2.19E+13 4.43E+15 2.20E+13 4.75E+15 2.22E+13 4.98E+15 2.24E+13 4.62E+15 2.26E+13 4.78E+15 2.28E+13 4.94E+15 2.30E+13 5.12E+15 2.32E+13 5.32E+15 2.34E+13 5.53E+15 2.35E+13 5.78E+15 2.37E+13 6.07E+15 2.39E+13 6.42E+15 2.41E+13 6.82E+15 2.43E+13 7.28E+15 2.45E+13 7.82E+15 2.47E+13 9.82E+15 2.49E+13 1.02E+16 2.51E+13 1.01E+16 2.52E+13 9.91E+15 2.54E+13 1.03E+16 2.56E+13 1.09E+16 2.58E+13 1.16E+16 2.60E+13 1.26E+16 2.62E+13 1.36E+16 2.64E+13 1.41E+16 2.66E+13 1.39E+16 2.67E+13 1.30E+16 2.69E+13 1.18E+16 2.71E+13 1.12E+16 2.73E+13 1.06E+16 2.75E+13 9.94E+15 2.77E+13 9.44E+15 2.79E+13 9.29E+15 2.81E+13 8.87E+15 2.83E+13 8.56E+15 2.84E+13 8.33E+15 2.86E+13 8.24E+15 2.88E+13 8.10E+15 2.90E+13 7.87E+15 2.92E+13 7.65E+15 2.94E+13 7.41E+15 2.96E+13 7.20E+15 2.98E+13 6.33E+15 3.00E+13 6.08E+15 3.01E+13 5.94E+15 3.03E+13 5.81E+15 3.05E+13 5.67E+15 3.07E+13 5.53E+15 3.09E+13 5.39E+15 3.11E+13 5.25E+15 3.13E+13 5.11E+15 3.15E+13 4.97E+15 3.16E+13 6.00E+15 3.18E+13 4.90E+15 3.20E+13 4.78E+15 3.22E+13 4.64E+15 3.24E+13 4.49E+15 3.26E+13 4.31E+15 3.28E+13 4.10E+15 3.30E+13 3.85E+15 3.32E+13 3.58E+15 3.33E+13 3.27E+15 3.35E+13 2.94E+15 3.37E+13 2.37E+15 3.39E+13 1.45E+15 3.41E+13 1.31E+15 3.43E+13 1.18E+15 3.45E+13 1.06E+15 3.47E+13 9.55E+14 3.48E+13 8.54E+14 3.50E+13 7.63E+14 3.52E+13 6.81E+14 3.54E+13 6.09E+14 3.56E+13 5.45E+14 3.58E+13 4.91E+14 3.60E+13 4.45E+14 3.62E+13 4.09E+14 3.64E+13 3.83E+14 3.65E+13 3.65E+14 3.67E+13 3.56E+14 3.69E+13 3.57E+14 3.71E+13 3.65E+14 3.73E+13 3.73E+14 3.75E+13 3.82E+14 3.77E+13 3.90E+14 3.79E+13 3.99E+14 3.81E+13 4.08E+14 3.82E+13 4.16E+14 3.84E+13 4.25E+14 3.86E+13 4.34E+14 3.88E+13 4.77E+14 3.90E+13 5.89E+14 3.92E+13 7.28E+14 3.94E+13 8.96E+14 3.96E+13 1.09E+15 3.97E+13 1.31E+15 3.99E+13 1.58E+15 4.01E+13 1.91E+15 4.03E+13 2.24E+15 4.05E+13 2.51E+15 4.07E+13 2.73E+15 4.09E+13 2.90E+15 4.11E+13 3.01E+15 4.13E+13 3.10E+15 4.14E+13 3.18E+15 4.16E+13 3.26E+15 4.18E+13 3.34E+15 4.20E+13 3.42E+15 4.22E+13 3.49E+15 4.24E+13 3.50E+15 4.26E+13 3.51E+15 4.28E+13 3.52E+15 4.29E+13 3.55E+15 4.31E+13 3.59E+15 4.33E+13 3.64E+15 4.35E+13 3.70E+15 4.37E+13 3.76E+15 4.39E+13 3.84E+15 4.41E+13 3.92E+15 4.43E+13 4.00E+15 4.45E+13 4.08E+15 4.46E+13 4.15E+15 4.48E+13 4.22E+15 4.50E+13 4.29E+15 4.52E+13 4.35E+15 4.54E+13 4.50E+15 4.56E+13 4.71E+15 4.58E+13 4.81E+15 4.60E+13 4.79E+15 4.62E+13 4.67E+15 4.63E+13 4.57E+15 4.65E+13 4.49E+15 4.67E+13 4.40E+15 4.69E+13 4.33E+15 4.71E+13 4.28E+15 4.73E+13 4.22E+15 4.75E+13 4.17E+15 4.77E+13 4.12E+15 4.78E+13 4.06E+15 4.80E+13 4.01E+15 4.82E+13 3.96E+15 4.84E+13 3.91E+15 4.86E+13 3.87E+15 4.88E+13 3.82E+15 4.90E+13 3.77E+15 4.92E+13 4.11E+15 4.94E+13 4.31E+15 4.95E+13 4.13E+15 4.97E+13 3.60E+15 4.99E+13 3.20E+15 5.01E+13 2.92E+15 5.03E+13 2.68E+15 5.05E+13 2.49E+15 5.07E+13 2.33E+15 5.09E+13 2.23E+15 5.10E+13 2.15E+15 5.12E+13 2.08E+15 5.14E+13 2.01E+15 5.16E+13 1.94E+15 5.18E+13 1.88E+15 5.20E+13 1.86E+15 5.22E+13 1.85E+15 5.24E+13 1.85E+15 5.26E+13 1.87E+15 5.27E+13 1.90E+15 5.29E+13 1.92E+15 5.31E+13 1.94E+15 5.33E+13 1.96E+15 5.35E+13 1.96E+15 5.37E+13 1.96E+15 5.39E+13 1.94E+15 5.41E+13 1.93E+15 5.43E+13 1.93E+15 5.44E+13 1.93E+15 5.46E+13 1.95E+15 5.48E+13 1.98E+15 5.50E+13 2.01E+15 5.52E+13 2.05E+15 5.54E+13 2.08E+15 5.56E+13 2.12E+15 5.58E+13 2.15E+15 5.59E+13 2.20E+15 5.61E+13 2.29E+15 5.63E+13 2.38E+15 5.65E+13 2.46E+15 5.67E+13 2.54E+15 5.69E+13 2.61E+15 5.71E+13 2.67E+15 5.73E+13 2.73E+15 5.75E+13 2.79E+15 5.76E+13 2.84E+15 5.78E+13 2.90E+15 5.80E+13 2.95E+15 5.82E+13 3.01E+15 5.84E+13 3.08E+15 5.86E+13 3.15E+15 5.88E+13 3.22E+15 5.90E+13 3.30E+15 5.91E+13 3.37E+15 5.93E+13 3.45E+15 5.95E+13 3.55E+15 5.97E+13 3.66E+15 5.99E+13 3.75E+15 6.01E+13 3.82E+15 6.03E+13 3.94E+15 6.05E+13 4.03E+15 6.07E+13 4.08E+15 6.08E+13 4.09E+15 6.10E+13 4.06E+15 6.12E+13 4.00E+15 6.14E+13 3.95E+15 6.16E+13 3.91E+15 6.18E+13 3.88E+15 6.20E+13 3.85E+15 6.22E+13 3.82E+15 6.24E+13 3.73E+15 6.25E+13 3.60E+15 6.27E+13 3.48E+15 6.29E+13 3.38E+15 6.31E+13 3.28E+15 6.33E+13 3.20E+15 6.35E+13 3.21E+15 6.37E+13 3.23E+15 6.39E+13 3.25E+15 6.40E+13 3.28E+15 6.42E+13 3.32E+15 6.44E+13 3.36E+15 6.46E+13 3.41E+15 6.48E+13 3.47E+15 6.50E+13 3.53E+15 6.52E+13 3.60E+15 6.54E+13 3.65E+15 6.56E+13 3.67E+15 6.57E+13 3.68E+15 6.59E+13 3.66E+15 6.61E+13 3.63E+15 6.63E+13 3.57E+15 6.65E+13 3.50E+15 6.67E+13 3.44E+15 6.69E+13 3.43E+15 6.71E+13 3.42E+15 6.72E+13 3.40E+15 6.74E+13 3.39E+15 6.76E+13 3.38E+15 6.78E+13 3.37E+15 6.80E+13 3.36E+15 6.82E+13 3.34E+15 6.84E+13 3.33E+15 6.86E+13 3.32E+15 6.88E+13 3.31E+15 6.89E+13 3.29E+15 6.91E+13 3.28E+15 6.93E+13 3.27E+15 6.95E+13 3.25E+15 6.97E+13 3.24E+15 6.99E+13 3.23E+15 7.01E+13 3.23E+15 7.03E+13 3.22E+15 7.05E+13 3.22E+15 7.06E+13 3.22E+15 7.08E+13 3.22E+15 7.10E+13 3.22E+15 7.12E+13 3.23E+15 7.14E+13 3.23E+15 7.16E+13 3.25E+15 7.18E+13 3.27E+15 7.20E+13 3.31E+15 7.21E+13 3.36E+15 7.23E+13 3.41E+15 7.25E+13 3.48E+15 7.27E+13 3.55E+15 7.29E+13 3.64E+15 7.31E+13 3.74E+15 7.33E+13 3.93E+15 7.35E+13 4.01E+15 7.37E+13 3.89E+15 7.38E+13 3.64E+15 7.40E+13 3.63E+15 7.42E+13 3.60E+15 7.44E+13 3.55E+15 7.46E+13 3.48E+15 7.48E+13 3.39E+15 7.50E+13 3.35E+15 7.52E+13 3.30E+15 7.53E+13 3.26E+15 7.55E+13 3.21E+15 7.57E+13 3.17E+15 7.59E+13 3.13E+15 7.61E+13 3.08E+15 7.63E+13 3.04E+15 7.65E+13 3.00E+15 7.67E+13 2.96E+15 7.69E+13 2.92E+15 7.70E+13 2.89E+15 7.72E+13 2.88E+15 7.74E+13 2.97E+15 7.76E+13 3.07E+15 7.78E+13 3.14E+15 7.80E+13 3.18E+15 7.82E+13 2.89E+15 7.84E+13 2.79E+15 7.86E+13 2.69E+15 7.87E+13 2.60E+15 7.89E+13 2.52E+15 7.91E+13 2.44E+15 7.93E+13 2.36E+15 7.95E+13 2.30E+15 7.97E+13 2.23E+15 7.99E+13 2.17E+15 8.01E+13 2.12E+15 8.02E+13 2.13E+15 8.04E+13 2.16E+15 8.06E+13 2.20E+15 8.08E+13 2.24E+15 8.10E+13 2.29E+15 8.12E+13 2.35E+15 8.14E+13 2.41E+15 8.16E+13 2.49E+15 8.18E+13 2.58E+15 8.19E+13 2.65E+15 8.21E+13 2.67E+15 8.23E+13 2.65E+15 8.25E+13 2.59E+15 8.27E+13 2.51E+15 8.29E+13 2.49E+15 8.31E+13 2.44E+15 8.33E+13 2.37E+15 8.34E+13 2.27E+15 8.36E+13 2.15E+15 8.38E+13 2.11E+15 8.40E+13 2.09E+15 8.42E+13 2.07E+15 8.44E+13 2.06E+15 8.46E+13 2.05E+15 8.48E+13 2.04E+15 8.50E+13 2.02E+15 8.51E+13 2.01E+15 8.53E+13 1.99E+15 8.55E+13 1.98E+15 8.57E+13 1.96E+15 8.59E+13 1.95E+15 8.61E+13 1.93E+15 8.63E+13 1.92E+15 8.65E+13 1.90E+15 8.67E+13 1.88E+15 8.68E+13 1.86E+15 8.70E+13 1.84E+15 8.72E+13 1.80E+15 8.74E+13 1.74E+15 8.76E+13 1.67E+15 8.78E+13 1.59E+15 8.80E+13 1.50E+15 8.82E+13 1.40E+15 8.83E+13 1.28E+15 8.85E+13 1.16E+15 8.87E+13 1.03E+15 8.89E+13 8.83E+14 8.91E+13 7.27E+14 8.93E+13 5.78E+14 8.95E+13 5.08E+14 8.97E+13 4.43E+14 8.99E+13 3.81E+14 9.00E+13 3.23E+14 9.02E+13 2.70E+14 9.04E+13 2.20E+14 9.06E+13 1.75E+14 9.08E+13 1.33E+14 9.10E+13 9.58E+13 9.12E+13 6.24E+13 9.14E+13 3.30E+13 9.15E+13 1.15E+13 9.17E+13 3.98E+12 9.19E+13 7.82E+12 9.21E+13 1.42E+13 9.23E+13 2.26E+13 9.25E+13 3.28E+13 9.27E+13 4.49E+13 9.29E+13 5.90E+13 9.31E+13 7.49E+13 9.32E+13 9.27E+13 9.34E+13 1.13E+14 9.36E+13 1.34E+14 9.38E+13 1.58E+14 9.40E+13 1.83E+14 9.42E+13 2.11E+14 9.44E+13 2.40E+14 9.46E+13 2.71E+14 9.47E+13 3.04E+14 9.49E+13 3.39E+14 9.51E+13 3.76E+14 9.53E+13 4.15E+14 9.55E+13 4.56E+14 9.57E+13 5.18E+14 9.59E+13 6.11E+14 9.61E+13 7.34E+14 9.63E+13 8.87E+14 9.64E+13 1.07E+15 9.66E+13 1.28E+15 9.68E+13 1.53E+15 9.70E+13 1.80E+15 9.72E+13 2.11E+15 9.74E+13 5.93E+15 9.76E+13 3.96E+15 9.78E+13 4.20E+15 9.80E+13 4.44E+15 9.81E+13 4.68E+15 9.83E+13 4.94E+15 9.85E+13 5.21E+15 9.87E+13 5.62E+15 9.89E+13 5.72E+15 9.91E+13 5.46E+15 9.93E+13 5.23E+15 9.95E+13 5.02E+15 9.96E+13 4.83E+15 9.98E+13 4.66E+15 1.00E+14 4.49E+15 1.00E+14 4.34E+15 1.00E+14 4.32E+15 1.01E+14 4.30E+15 1.01E+14 4.29E+15 1.01E+14 4.28E+15 1.01E+14 4.27E+15 1.01E+14 4.29E+15 1.02E+14 4.35E+15 1.02E+14 4.46E+15 1.02E+14 4.60E+15 1.02E+14 4.78E+15 1.02E+14 4.99E+15 1.02E+14 5.23E+15 1.03E+14 4.70E+15 1.03E+14 4.52E+15 1.03E+14 4.38E+15 1.03E+14 4.30E+15 1.03E+14 4.27E+15 1.04E+14 4.25E+15 1.04E+14 4.23E+15 1.04E+14 4.20E+15 1.04E+14 4.17E+15 1.04E+14 4.14E+15 1.05E+14 4.11E+15 1.05E+14 4.08E+15 1.05E+14 4.05E+15 1.05E+14 4.01E+15 1.05E+14 3.98E+15 1.05E+14 4.00E+15 1.06E+14 4.18E+15 1.06E+14 4.37E+15 1.06E+14 4.55E+15 1.06E+14 8.71E+15 1.06E+14 4.76E+15 1.07E+14 4.20E+15 1.07E+14 3.69E+15 1.07E+14 3.22E+15 1.07E+14 2.79E+15 1.07E+14 2.40E+15 1.08E+14 2.06E+15 1.08E+14 1.75E+15 1.08E+14 1.48E+15 1.08E+14 1.25E+15 1.08E+14 1.06E+15 1.09E+14 9.10E+14 1.09E+14 7.81E+14 1.09E+14 6.63E+14 1.09E+14 5.57E+14 1.09E+14 4.62E+14 1.09E+14 3.79E+14 1.10E+14 3.03E+14 1.10E+14 0.00E+00