The boson peak is one of the important unresolved problems of glass, along with glass transition. This excitation peak universally exists around an energy ($E$) range of 2-5 meV for most of glasses with quite different hardness from oxide glasses to molecular glasses. Although it is known that the temperature variation of the peak intensity can be scaled by the Bose factor (harmonic oscillator approximation) and that the peak energy does not change with respect to the momentum transfer $Q$ (suggesting local excitation), the origin of the peak is still unclear.

Our group has been studying the boson peak for many years, mainly focusing on simple molecular glasses [1-3]. Molecular glasses aggregate through simple van der Waals interactions and so suitable for the collaboration with theoretical and molecular dynamics works. Although simple molecules crystallize readily upon cooling, we have prepared glasses at low temperatures ($<$ 5 K) by using a vapor-deposition (VD) method, whose cooling rate is faster than 10⁷ K/s. The most effective experimental tool to study boson peaks is inelastic neutron scattering (INS), which provides vibrational density of states. Another effective method is heat capacity ($C_p$) measurement. We use an adiabatic method to obtain absolute $C_p$ values accurately.

We have examined three VD glasses with different molecular structures; CCl₄ (tetrahedral, van der Waals), CS₂ (linear molecule, van der Waals) and water (dog-leg-shape, hydrogen bond). They are vitrified at 5 K with custom-made cryostats for VD samples [2,3] and measured in situ with BL14, AMATERAS at J-PARC, MLF and an adiabatic calorimeter at our laboratory.

Figure 1 shows the INS data for the three samples. For CCl₄ and CS₂, $S(Q,E)$ of the glassy sample was clearly larger than that of the crystalline states. As known in the previous studies, there was no $Q$ dependence of the peak energy and the peak intensity was enhanced at the second and third peaks of $S\left(Q\right)$. Figure 2 shows the heat capacities of the three samples. Apparently, excess heat capacities were observed in CCl₄ and CS₂. The curve in Fig. 2 was calculated through the density of states $G\left(E\right)$ which was calculated from $S(Q,E)$ by the established method [1-3]. During this calculation, the scale factor to link the neutron and calorimetric data was determined. The agreement between the experimental and calculated data was satisfactory except high temperature region where anharmonic effects become important. Figure 3 gives the “absolute value” of the density of states divided by squared energy. It should be noted that this value is obtained by combining the data of the INS and adiabatic calorimetry. The gray-shaded area, corresponding to the degrees of freedom related to the boson peak, is 0.48 for CCl₄ and 0.22 for CS₂. We have integrated $G\left(E\right)$ up to 15 meV to discuss the origin of the boson peak. Interestingly, there is no difference between the glassy and crystalline states, and the integrated $G\left(E\right)$ was about 6 for CCl₄ and 5 for CS₂, both corresponding to the sum of the translation and rotation degrees of freedom. The present result has indicated an important fact that there is no extra degrees of freedom for the boson peaks of molecular glasses.

References

• [1] O. Yamamuro et al., J. Chem. Phys. 105, 732 (1996).
• [2] O. Yamamuro et al., J. Chem. Phys. 106, 2997 (1997).
• [3] O. Yamamuro et al., J. Chem. Phys. 115, 9808 (2001).

Authors

• X. Wu, Y. Zhao, H. Akiba, Y. Ohmasa, M. Kofu, and O. Yamamuro