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.

The structural properties of ${\mathrm{BiMnO}}_3$ were determined from neutron powder diffraction data as a function of temperature and magnetic field. The structure at all temperatures was found to be centrosymmetric with space group $C2∕c$, which is incompatible with ferroelectricity. At $T_C\simeq 100\mathrm{K}$, we observed the onset of a large magnetoelastic strain, proportional to the square of the magnetization. We interpret this structural rearrangement, together with the previously observed magnetodielectric anomalies, due to the need to optimize the partially frustrated magnetic interactions.

The vibrational dynamics of a permanently densified silica glass is compared to the one of an $\alpha$-quartz polycrystal, the silica polymorph of the same density and local structure. The combined use of inelastic x-ray scattering experiments and ab initio numerical calculations provides compelling evidence of a transition, in the glass, from the isotropic elastic response at long wavelengths to a microscopic regime as the wavelength decreases below a characteristic length $\xi$ of a few nanometers, corresponding to about 20 interatomic distances. In the microscopic regime the glass vibrations closely resemble those of the polycrystal, with excitations related to the acoustic and optic modes of the crystal. A coherent description of the experimental results is obtained assuming that the elastic modulus of the glass presents spatial heterogeneities of an average size $a\sim \xi /2\pi$.