It is important to note that the experiment selectively probes the Fe atoms, and other elements in the sample do not contribute to the recorded signal. In an NRIXS experiment, short pulses of synchrotron X-rays excite fluorescent radiation from the Fe sublattice, and this fluorescence is recorded in a short time window between pulses. The configuration of a sample for a high-pressure NRIXS experiment in a diamond cell is shown in Figure 15. Dobrzynski and Leman (1969) developed a frequency-moment representation of the surface phonons, and calculated their contribution to the heat capacity. The theory referred to above is in reasonable agreement with the experiments. (1965)) and metals (Pb, In Novotny and Meincke (1973)). The excess heat capacity (above the bulk value) has been measured for ionic solids (NaCl Barkman et al. Nishiguchi and Sakuma (1981) made an accurate study of the vibrations of a small elastic sphere. This has been recognised by Burton (1970), Chen et al. The discrete nature of the low frequency part of the vibrational spectrum means that we must write out explicitly the first terms in the partition function when T < ∼ ( d 0 / d ) θ D, instead of applying the usual integral approximation. q > 2 Π / d With ω D = C q D ∼ 2 π C / d 0 where d 0 is the diameter of an atom, we get ω min ∼ ( d 0 / d ) ω D. In a small particle, of diameter d, it is unphysical to consider wavelengths larger than d, i.e. In the bulk, ω = C q where C is a sound velocity. In particular, there is a lowest eigenfrequency ω min which can be estimated crudely as follows.

In a very small sample, on the other hand, the eigenfrequencies form a discrete spectrum. The bulk material has a phonon density of states which is quasicon-tinuous and varies as ω 2 for small ω. GÖRAN GRIMVALL, in Thermophysical Properties of Materials, 1999 3.4 Small particles From these data, the signatures for the α phases and β phases are seen to be very similar, whereas the c phases and r phases show behavior qualitatively similar to that shown by the cubic and hexagonal modifications of boron nitride that also have zinc blende and rhombohedral structures, respectively. The results of these simulations are shown in Figure 17. In this procedure, they considered a cluster of carbon and nitrogen atoms in the stoichiometric ratio 3:4 terminated by hydrogen at the outer boundaries and applied the process to four proposed crystal structures: an α phase and β phase analogous to the α- Si 3N 4 and β-Si 3N 4 structures, a cubic zinc blende structure (C–C 3N 4) with one carbon vacancy per unit cell, and a rhombohedral phase (r-C 3N 4) comparable to a graphite-like layered structure with carbon vacancies all modifications have been proposed as stable or metastable crystals. Theoretical calculations of the vibrational density of states of carbon nitride were carried out by Widany and coworkers using a nonorthogonal tight-binding molecular dynamics simulation procedure based on density function.

Debye wave vector 2d