We compare the atomic dynamics of the glass to that of the relevant crystal. In the spectra of inelastic scattering, the boson peak of the glass appears higher than the transverse acoustic (TA) singularity of the crystal. However, the density of states shows that they have the same number of states. Increasing pressure causes the transformation of the boson peak of the glass towards the TA singularity of the crystal. Once corrected for the difference in the elastic medium, the boson peak matches the TA singularity in energy and height. This suggests the identical nature of the two features.

Using probe molecules with resonant nuclei and nuclear inelastic scattering, we are able to measure the density of states exclusively for collective motions with a correlation length of more than approximately 20 A. Such spectra exhibit an excess of low-energy modes (boson peak). This peak behaves in the same way as that observed by conventional methods. This shows that a significant part of the modes constituting the boson peak is of collective character. At energies above the boson peak, the reduced density of states of the collective motions universally exhibits an exponential decrease.

We measured the density of vibrational states (DOS) and the specific heat of various glassy and crystalline polymorphs of SiO 2 . The typical (ambient) glass shows a well-known excess of specific heat relative to the typical crystal (α-quartz). This, however, holds when comparing a lower-density glass to a higherdensity 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. DOI: 10.1103/PhysRevLett.112.025502 PACS numbers: 63.20.-e, 07.85.-m, 76.80.+y The low-temperature thermodynamic properties of glasses are accepted to be anomalously different from those of crystals due to the inherent disorder of the glass structure. At temperatures of ∼10 K, the specific heat of glasses shows an excess relativetothatofthecorrespondingcrystals.Theexcessspecific heat is related to a distinct feature in the spectrum of the atomic vibrations: At frequencies of ∼1 THz, glasses exhibit an excess of states above the Debye level of the acoustic waves, the socalled "boson peak." The excess of specific heat and the boson peak are universally observed for all glasses and by all relevant experimental techniques. However, the results still do not converge to a unified answer to how disorder causes these anomalies.Themajorityofthemodelsexplainthebosonpeakbyappealing tovarious glass-specific features. Theseincludelow-energy optical modes [1], onset of mechanical instability related to saddle points in the energy landscape [2] or to jamming [3][4][5], local vibrationalmodes of clusters [6] or locally favoured structures [7], librations [8] or other coherent motions [9] of molecular fragments, crossover of local and acoustic modes [10], quasilocal vibrations of atoms in an anharmonic potential [11], broadening of vibrational states in the Ioffe-Regel crossover regime [12], spatial variation of the elastic moduli [13], breakdown of the continuum approximation [14,15], and topologically diverse defects [16], to cite the most important ones.Alternatively, the boson peak is identified as the counterpart of the acoustic van Hove singularities of crystals, i.e., explained by the piling up of the vibrational states of the acousticlike branches near the boundary of the pseudoBrillouin zone [17][18][19][20].Diverging in explanations of the boson peak, all models agree that the excess states and the excess specific heat of

The presence of carbonates in inclusions in diamonds coming from depths exceeding 670 km are obvious evidence that carbonates exist in the Earth’s lower mantle. However, their range of stability, crystal structures and the thermodynamic conditions of the decarbonation processes remain poorly constrained. Here we investigate the behaviour of pure iron carbonate at pressures over 100 GPa and temperatures over 2,500 K using single-crystal X-ray diffraction and Mössbauer spectroscopy in laser-heated diamond anvil cells. On heating to temperatures of the Earth’s geotherm at pressures to ∼50 GPa FeCO3 partially dissociates to form various iron oxides. At higher pressures FeCO3 forms two new structures—tetrairon(III) orthocarbonate Fe43+C3O12, and diiron(II) diiron(III) tetracarbonate Fe22+Fe23+C4O13, both phases containing CO4 tetrahedra. Fe4C4O13 is stable at conditions along the entire geotherm to depths of at least 2,500 km, thus demonstrating that self-oxidation-reduction reactions can preserve carbonates in the Earth’s lower mantle.

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Nuclear inelastic scattering (NIS) spectra were recorded for a monocrystal of the spin-crossover complex [Fe(tptMetame)] (ClO (4))(2) (tptMetame = 1,1,1-tris([N-(2-pyridylmethyl)-N-methylamino]-methyl)ethane) at T = 30 K (low-spin state) and at room temperature (high-spin state) for different crystal orientations. The high energy resolution (0.65 meV) allowed us to resolve individual molecular vibrations which were unambiguously identified by density functional calculations. From the NIS spectra for the first time the angular-resolved iron-partial density of phonon states (PDOS) was extracted. The PDOS corroborates a vibrational entropy difference as driving force of the spin transition.

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Stankov, S.; Yue, Yuanzheng; Miglierini, M.; Sepiol, B.; Sergueev, I.; Chumakov, A. I.; Hu, L.; Svec, P.; Rüffer, R.