Lattice dynamical information

RMC has recently been extended to study not just structure but atom dynamics. The ability to extract phonon and lattice dynamical information from total scattering data has been under debate for some time, with the consensus ultimately being that incomplete, but potentially highly useful, lattice dynamical information can be obtained directly from total scattering data. RMC has recently been shown to be useful for extracting that information." ... 

We have discussed the basic procedures how to obtain a Mossbauer spectrum. However, a spectrum like fig. 6 contains only lattice dynamical information via Yq and allows to determine from W. Yet, our interest lies in electronic roicture properties. To understand how those are reflected in a Mossbauer spectrum we have first to discuss hyperfine interactions. Before entering this topic a few final words on dealing with a Mossbauer spectrum are appropriate. 

Much of the Pt Mossbauer work performed so far has been devoted to studies of platinum metal and alloys in regard to nuclear properties (magnetic moments and lifetimes) of the excited Mossbauer states of Pt, lattice dynamics, electron density, and internal magnetic field at the nuclei of Pt atoms placed in various magnetic hosts. The observed changes in the latter two quantities, li/ (o)P and within a series of platinum alloys are particularly informative about the conduction electron delocalization and polarization. 

Material response in THz frequency region, which corresponds to far- and mid-infrared electromagnetic spectrum, carries important information for the understanding of both electronic and phononic properties of condensed matter. Time-resolved THz spectroscopy has been applied extensively to investigate the sub-picosecond electron-hole dynamics and the coherent lattice dynamics simultaneously. In a typical experimental setup shown in Fig. 3.5, an... 

This technique, besides allowing determination of the Lamb-Mossbauer factor, provides direct access to the density of phonon states for the probe isotope in a solid. It thus provides information about lattice dynamics that is excluded by the limitations of Mossbauer spectroscopy. This technique could be valuable in investigations of adsorption with the adsorbing element as the probe and showing the modifications brought about by the adsorbate on the dynamic properties of the probe. 

This is undertaken by two procedures first, empirical methods, in which variable parameters are adjusted, generally via a least squares fitting procedure to observed crystal properties. The latter must include the crystal structure (and the procedure of fitting to the structure has normally been achieved by minimizing the calculated forces acting on the atoms at their observed positions in the unit cell). Elastic constants should, where available, be included and dielectric properties are required to parameterize the shell model constants. Phonon dispersion curves provide valuable information on interatomic forces and force constant models (in which the variable parameters are first and second derivatives of the potential) are commonly fitted to lattice dynamical data. This has been less common in the fitting of parameters in potential models, which are onr present concern as they are required for subsequent use in simulations. However, empirically derived potential models should always be tested against phonon dispersion curves when the latter are available. 

Infrared light is absorbed through vibrations of the atoms or rotations of the molecular system. IR spectra give information on lattice dynamics, bond strengths, coordination, and polyhedral linkage in complex structures. 

Lattice dynamics in bulk perovskite oxide ferroelectrics has been investigated for several decades using neutron scattering [71-77], far infrared spectroscopy [78-83], and Raman scattering. Raman spectroscopy is one of the most powerful analytical techniques for studying the lattice vibrations and other elementary excitations in solids providing important information about the stmcture, composition, strain, defects, and phase transitions. This technique was successfully applied to many ferroelectric materials, such as bulk perovskite oxides barium titanate (BaTiOs), strontium titanate (SrTiOs), lead titanate (PbTiOs) [84-88], and others. 

In contrast, neutron spectroscopy is a more powerful probe, its results are directly proportional to the phonon density of states (DOS) (see Fig. 2) which can be vigorously calculated by lattice dynamics (LD) and molecular dynamics (MD). Applying these simulation techniques provide an excellent opportunity for constructing and testing potential functions. Because optical selection rules are not involved, INS measures all modes (IR/Raman measure the modes at the Brillouin Zone (BZ) q = 0, see Fig. 2) and is particularly suitable for studying disordered systems (or liquids). It hence provides direct information on the hydrogen bond interactions in water and ice. 

In most cases, the crystal potential is not known a priori. The usual procedure is to introduce some model potential containing several parameters, which are subsequently found by fitting the calculated crystal properties to the observed data available. This procedure has the drawback that the empirical potential thus obtained includes the effects of the approximations made in the lattice dynamics model, which is mostly the harmonic model. It is very useful to have independent and detailed information about the potential from quantum-chemical ab initio calculations. Such information is available for nitrogen (Berns and van der Avoird, 1980) and oxygen (Wormer and van der Avoird, 1984), and we have chosen the results calculated for solid nitrogen and solid oxygen to illustrate in Sections V and VI, respectively, the lattice dynamics methods described in Sections III and IV. Nitrogen is the simplest typical molecular crystal as such it has received much attention from theorists and... 

Rather less information is available for the oxide derivatives of tin(Il). The crystal structure of black, tetragonal SnO is known [63], and was referred to in Chapter 14.1 in the discussion of the nuclear quadrupole moment. The Mossbauer parameters are given in Table 14.4 together with those for SnS, which has a considerably distorted NaCl lattice [64], SnSe (isostructural with SnS) [65], and SnTe, which has a cubic NaCl lattice [66]. Application of high pressure to SnO causes the formation of some Sn02 and tin metal [67]. A detailed lattice dynamical study of SnS between 60 and 320 K has shown evidence for a Karyagin effect [68]. 

It is intended for this chapter to be a brief introduction to surface lattice dynamics and to some of the kinds of information that one is able to obtain about the electronic and vibrational properties of surfaces through high-resolution helium atom scattering. Such information is critical to the understanding of many aspects of surface chemistry and to the design of novel materials with specifically desired properties. 

It is the measurement, in a representative number of directions in the Brillouin zone, of the coy(q) and its variation with temperature and pressure which provides the most direct information on the interatomic forces. The forces are inferred by adjusting the frequencies calculated from a crystal model with assumed interatomic interactions to achieve agreement with measured vibrational frequencies obviously, the more frequencies measured, the better the test of the assumed force model. These aspects of lattice-dynamic studies are discussed in some detail in the Appendix. It should be emphasized, however, that almost without exception crystal force models have been obtained in a... 

Vibrational spectroscopy has been applied to the study of molecular structure and physical properties of conjugated polyfurans <92CPL(l9l)419, 93JCP(98)769, 93SM(57)4467>. Vibrational spectra provide simultaneous and selective information on the structure of a polymer and on its charge distribution. Interpretation of experimental data is performed with the assistance of lattice dynamics calculations. 

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