Emergence of glassy features in halomethane crystals

Both structural glasses and disordered crystals are known to exhibit anomalous thermal, vibrational, and acoustic properties at low temperatures or low energies, what is still a matter of lively debate. To shed light on this issue, we studied the halomethane family ${\mathrm{CBr}}_n{\mathrm{Cl}}_{4-n}$ ($n=0,1,2$) at low temperature where, despite being perfectly translationally ordered stable monoclinic crystals, glassy dynamical features had been reported from experiments and molecular dynamics simulations. For $n=1,2$ dynamic disorder originates by the random occupancy of the same lattice sites by either Cl or Br atoms, but not for the ideal reference case of ${\mathrm{CCl}}_4$. Measurements of the low-temperature specific heat ($C_p$) for all these materials are here reported, which provide evidence of the presence of a broad peak in Debye-reduced $C_p\left(T\right)/T^3$ and in the reduced density of states ($g\left(\omega \right)/{\omega }^2$) determined by means of neutron spectroscopy, as well as a linear term in $C_p$ usually ascribed in glasses to two-level systems in addition to the cubic term expected for a fully ordered crystal. Being ${\mathrm{CCl}}_4$ a fully ordered crystal, we also performed density functional theory (DFT) calculations, which provide unprecedented detailed information about the microscopic nature of vibrations responsible for that broad peak, much alike the “'boson peak” of glasses, finding it to essentially arise from a piling up (at around $3–4$ meV) of low-energy optical modes together with acoustic modes near the Brillouin-zone limits.

Figure 1

(a) Debye-reduced specific heat $C_p/T^3$ for the monoclinic crystals of ${\mathrm{CBr}}_2{\mathrm{Cl}}_2$ (open blue circles), ${\mathrm{CBrCl}}_3$ (solid red circles), and ${\mathrm{CCl}}_4$ (open black squares). The peak position is marked by arrows and the corresponding Debye cubic coefficients $C_D$ obtained from the fits in the panel (b) are shown by horizontal dashed lines (same colors). Earlier published data for ${\mathrm{CCl}}_4$ are also shown by solid green stars [52], solid pink stars [53], and open blue stars [51]. (b) Our specific-heat data, with symbols as in panel (a), but plotted at the lowest temperatures as $C_p/T$ vs. $T^2$. The curves are fitted in the appropriate range to a quadratic polynomial (see text). The obtained coefficients are shown in Table 1.

Figure 2

Normalized specific-heat data referred to $C_D$ values, scaled to the height $[(C_p-C_D)/T^3){]/[(C_p-C_D)/T^3)]}_{\max }$ and shifted to the position of the peak to show the universal shape for the three halomethanes, ${\mathrm{CCl}}_4$ (black empty squares), ${\mathrm{CBrCl}}_3$ (full red circles), and ${\mathrm{CBr}}_2{\mathrm{Cl}}_2$ (blue empty circles), for several structural glasses as glycerol [70] (pink line) and deuterated ethanol (green dots), orientational glass of deuterated ethanol [19] (continuous green line), and several ordered crystalline phases of glycerol [70] (pink circles) and ethanol (green circles) [19].

Figure 3

(a) Vibrational spectrum as measured using TOSCA spectrometer at 10 K (red) with the calculated quantity at the crystal $\mathrm{\Gamma }$-point (black sticks) (see text). (b) Low-frequency vibrational spectra as measured using MARI spectrometer in the reduced form $g\left(\omega \right)/{\omega }^2$, for the monoclinic phases of ${\mathrm{CCl}}_4$ (black empty squares), ${\mathrm{CBrCl}}_3$ (full red circles), and ${\mathrm{CBr}}_2{\mathrm{Cl}}_2$ (blue empty circles). Dashed lines are a guide to the eye.

Figure 4

(a) Dispersion relations for $\mathrm{C}{}^{35}\mathrm{Cl}_3{}^{37}\mathrm{Cl}$ obtained from DFT. (b) Vibrational density of states calculated from the dispersion relations (black for the three acoustic branches plus the first three optical branches and red for the contributions of all branches) and experimental as measured from inelastic neutron scattering using the MARI spectrometer (black squares). (c) Relation dispersions in the low-energy range for the acoustic branches (black) and the first three optical branches (blue).

Figure 5

Experimental specific-heat data (black squares) at the lowest temperatures plotted as normalized $(C_p/T^3)/{(C_p/T^3)}_{\max }$ vs. $T$ for the monoclinic phase of ${\mathrm{CCl}}_4$. Solid lines correspond to DFT calculated contributions for the reference case of $\mathrm{C}{}^{35}\mathrm{Cl}_3{}^{37}\mathrm{Cl}$: black curves shows the contribution of the acoustic plus the three low-energy optical branches, red curve shows the contributions of the rest of optical branches, and blue curve correspond to the total (acoustic and optical) contributions of the phonons to the specific heat. Horizontal dotted line corresponds to the normalized Debye value. Inset: Experimental specific-heat data at the lowest temperatures plotted as normalized $(C_p/T^3)/{(C_p/T^3)}_{\max }$ vs. $T/T_{\max }$ for ${\mathrm{CCl}}_4$ (black squares), ${\mathrm{CBrCl}}_3$ (red circles), and ${\mathrm{CBr}}_2{\mathrm{Cl}}_2$ (blue circles).