Role of Disorder in the Thermodynamics and Atomic Dynamics of Glasses

We measured the density of vibrational states (DOS) and the specific heat of various glassy and crystalline polymorphs of ${\mathrm{SiO}}_2$. The typical (ambient) glass shows a well-known excess of specific heat relative to the typical crystal ($\alpha$-quartz). This, however, holds when comparing a lower-density glass to a higher-density crystal. For glassy and crystalline polymorphs with matched densities, the DOS of the glass appears as the smoothed counterpart of the DOS of the corresponding crystal; it reveals the same number of the excess states relative to the Debye model, the same number of all states in the low-energy region, and it provides the same specific heat. This shows that glasses have higher specific heat than crystals not due to disorder, but because the typical glass has lower density than the typical crystal.

Figure 1

The density of states (a)–(b) and the reduced density of states (c)–(d) of ambient and densified silica glass. The solid and the open circles refer to the NRAIXS and IXS data, respectively. The solid lines show the Debye levels for the DOS (a)–(b) and reduced DOS (c)–(d). The area of the filled region of the DOS above the Debye parabola in (a)–(b) gives the number of the excess states. The entire area of the filled region in (a)–(b) gives the number of all states within the same energy ranges. The filled areas in (c)–(d) show the same energy regions for the reduced DOS. (e)–(f) The measured specific heat (symbols) and the specific heat calculated from the corresponding DOS (solid lines). The horizontal lines in (e)–(f) show the Debye levels for the specific heat.

Figure 2

The density of states (a)–(c) and the reduced density of states (d)–(f) of $\alpha$-cristobalite, $\alpha$-quartz, and coesite. (g)–(i) The measured specific heat (symbols) of $\alpha$-cristobalite (from Refs. [25, 26]), $\alpha$-quartz, and coesite and the specific heat calculated from the corresponding DOS (solid lines). The symbols, solid lines, and the filled regions have the same meaning as in Fig. 1.

Figure 3

Comparison of the density of states (a), (d) and the reduced density of states (b),(e) obtained with the NRAIXS technique, and of the specific heat (c),(f) for ambient silica glass and $\alpha$-quartz (a)–(c), and for densified silica glass and $\alpha$-cristobalite (d)–(f). The experimental data for the specific heat of $\alpha$-cristobalite in (f) are those from Refs. [25, 26].

Figure 4

Comparison of the density of states (a),(d) and the reduced density of states (b),(e) obtained with the NRAIXS, and of the specific heat (c),(f) for ambient silica glass and $\alpha$-cristobalite (a)–(c), and for densified silica glass and $\alpha$-quartz (d)–(f). The solid lines in (a)–(b), (d)–(e) show the modified DOS (a), (d) and reduced DOS (b),(e) of $\alpha$-cristobalite (a)–(b) and $\alpha$-quartz (d)–(e) calculated allowing for the finite size of the Brillouin zone (see text). The arrows in (a)–(b), (d)–(e) emphasize the shift of the peaks in the DOS and reduced DOS of glasses relative to those of crystals. The experimental data for the specific heat of $\alpha$-cristobalite in (c) are those from Refs. [25, 26].