Abstract
The vibrational density of states (VDOS) of solids in the low-energy regime controls the thermal and transport properties of materials, such as heat capacity, heat conduction, free energy and entropy. In α-Cristobalite, the low-frequency part of vibration density of states (VDOS) has many common features with the Boson peak in silica glass of matched densities. Recent theoretical work reported that anharmonic phonon–phonon interactions were critical for the low-frequency part of VDOS in α-Cristobalite. Therefore, it is urgent to identify the role of different anharmonic interactions from first principles. In this paper, we focus on the main peak of the low-frequency part of VDOS in α-Cristobalite. Calculated by our own developed codes and first principles, we find that the quartic anharmonic interaction can increase the frequency of the peak, while the cubic anharmonic can reduce the frequency and change the shape of the peak. Meanwhile, the anharmonic interactions are critical for the temperature effect. Therefore, we calculated the temperature-dependent property of the peak. We find that the frequency of the peak is directly proportional to the temperature. The atomic displacement patterns of different temperatures also confirm the above conclusion. All our calculations converged well. Moreover, our basic results agree well with other published results. Finally, we highlight that our codes offer a general and reliable way to calculate the VDOS with temperature.
Highlights
The vibrational spectra of solids play important role in thermodynamics physics [1,2], where the low-energy vibrational spectra are described by the Debye model as proportional to phonon frequency squared [3,4]
We developed the codes to use the phonon Green function method to calculate the vibrational density of states (VDOS)
We culated the low-frequency part of the VDOS with increasing temperature, which shows calculated the low-frequency part of the VDOS with increasing temperature, which shows that the frequency of the main peak at low-frequency part increases in direct proportion that the frequency of the main peak at low-frequency part increases in direct proportion to to temperature
Summary
The vibrational spectra of solids play important role in thermodynamics physics [1,2], where the low-energy vibrational spectra are described by the Debye model as proportional to phonon frequency squared [3,4]. Boson peak is an anomaly in VDOS (vibration density of states) that appears in glasses upon normalizing the VDOS g(ω) by the Debye law ω2 [5]. In 2014, in some ordered crystals, for example, α-Cristobalite, α-Quartz, Coesite, the low-frequency part of VDOS had many common features with Boson peak in silica glass [19,20,21]. According to the published experiments, for α-Cristobalite and silica glass with matched densities, the DOS of silica glass appeared as the smoothed counterpart of DOS of the corresponding crystal, which illustrates that two systems have the same number of the excess states relative to the Debye model, the same number of states in the low-energy region, and the same specific heat. A recent theoretical paper reported that anharmonic phonon–phonon interactions are critical for the low-frequency part of
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