Lattice dynamics metals

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. 

Hohlfeld, J., Wellershoff, S.-S., Giidde, J., Conrad, U., Jahnke, V. and Matthias, E. (2000) Electron and lattice dynamics following optical excitation of metals. Chem. Phys., 251, 237-258. 

Acknowledgement. I would like to thank Drs. H. D. Fair. Jr., H. J. Prask, J. Sharma and D. A. Wiegand (Explosives Laboratory, FRL), and Dr. S. K. Deb (Cyanamid, Stamford) for critical reading and suggestions regarding the manuscript. I would also hke to acknowledge many discussions on the lattice dynamics of the metal pseudohalides with Dr. S. Trevino (Explosives Laboratory, FRL) and Prof. S. S. Mitra (University of Rhode Island) and their permission to quote and depict (Fig. 6) unpublished results. 

A.I. Kolesnikov, V.E. Antonov, V.K Fedotov, G. Grosse, A.S. Ivanov F.E. Wagner (2002). Physica B, 316-317, 158-161. Lattice dynamics of high pressure hydrides of the Group Vl-Vni transition metals. 

Core-polarisation and conduction-electron polarisation effects can be studied as can exchange polarisation of diamagnetic atoms in magnetic hosts. The lattice dynamics of the metal lattice are examined via the temperature dependence of the /-factor. Many metals approximate closely to the Debye model, and a Debye temperature has some significance. Impurity doping can... 

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]. 

Other metal systems studied include IrSu2 and PtSn2 which have the CaFa lattice [23. Recoil-free fraction and lattice dynamical studies have been made on SnAs, SnSb, SnTe, and SnPt [237] and on NbaSn [238,239]. 

Detailed measurement of the recoil-free fraction in germanium metal [8] has since been reinterpreted [11] using a different lattice-dynamical model. 

Some lattice-dynamical calculations for nickel metal have been made [12]. 

A number of recoil-free fraction and lattice-dynamical studies have been made on gold metal [90, 91]. The resonance in gold microcrystals of mean diameter 20 and 6 nm shows a greater recoil-free fraction in the smaller crystals corresponding to an increase in the effective Debye temperature from... 

Room-temperature-stable jS-NaNa is rhombohedral, space group [66], with one formula unit per primitive unit cell so that structurally it is among the simplest of the metal azides. This has made NaNa the logical starting material for lattice-dynamic studies of inorganic azides. Unfortunately, single crystals of sufficient size for CNIS studies have not been grown, so dispersion-curve measurements have not been performed. Nevertheless, the lattice dynamics are partially determined as summarized in Table V. 

Because of the isomorphous structures of the four compounds and their phase instabilities, they are an interesting set of compounds for detailed lattice-dynamic calculations. However, despite their relative simplicity with respect to other metal azides, their structure, with eight atoms per primitive unit cell, presents a formidable calculational problem. With compounds of this complexity it is imperative that dispersion-curve data be available to test lattice-dynamic models, and, thus far, this has been possible only for KN3. 

The principal techniques employed in the study of molecular vibrations and lattice dynamics are Raman, infrared (absorption and reflection), and neutron scattering. Numerous publications detail the theory and applications of the techniques [102,113]. Data for metal azides were obtained by a concerted use of all the techniques, and a brief discussion of their complementary character follows. 

The loss of three-dimensionality in the higher temperature regime is not a consequence of internal sample geometry—the fibers are macroscopic. For example, the specific heat of the boron/aluminum composite contains the cubic term and conforms to the mixture principle for bulk metallic ingredients. Moreover, experiments performed previously and discussed elsewhere [ ] demonstrate the dominance of a quadratic term in the low-temperature specific heat of a fiberglass-cloth-reinforced resin. The tendency to lower-order dimensionality is presumably a property of the lattice dynamics of the polymeric chains and rings characteristic of the resin matrix. 

Elastic constants measured as a function of temperature are available for most of the lanthanides in polycrystalline form (Rosen, 1967, 1968) and for Tb, Dy, Ho and Er single crystals (Palmer, 1970 Palmer and Lee, 1973 and du Plessis, 1976). For a summary of the elastic properties of the lanthanides reference can be made to Taylor and Darby (1972, section 2.4) and to ch. 8, section 9. If a suitable lattice dynamical model were devised, we should be able to calculate Cl from first principles. This was done for Gd, Dy and Er metals (Sundstrom, 1968), but at the time of these calculations, elastic constants were available only for polycrystalline samples at a few fixed temperatures. Nevertheless the results obtained did indicate that Lounasmaa s (1964a) interpolation idea was reasonable. With the elastic constant data available today it should be possible to calculate Cl for the entire region of interest, although this appears not to have attracted much attention, presumably because the uncertainty involved in separating off the contributions in experimental heat capacity results makes comparison with theory unrewarding as far as Cl is concerned. 

The lattice vibrations of molecular solids have received brief consideration in reviews dealing with the infrared spectra of these solids (Dows, 1963,1965, 1966). ThereviewbySchnepp (1969) provides a good summary of the field. A recent review by Venkataraman and Sahni (1970) of the lattice dynamics of complex crystals contains much subject matter related to the present review. A number of good reviews are available on the lattice motions of ionic, covalent, and metallic solids (Mitra and Gielisse, 1964 Martin, 1965 Cochran and Cowley, 1969). 

In the case of the Pt(lOO) surface the interaction potential is derived from semiempirical quantum chemical calculations of the interactions of a water molecule with a 5-atom platinum cluster [35]. The lattice of metal atoms is flexible and the atoms can perform oscillatory motions described by a single force constant taken from lattice dynamics studies of the pure platinum metal. The water-platinum interaction potential does not only depend on the distance between two particles but also on the projection of this distance onto the surface plane, thus leading to the desired property of water adsorption with the oxygen atoms on top of a surface atom. For more details see the original references [1,2]. This model has later been simplifled and adapted to the Pt(lll) surface by Berkowitz and coworkers [3,4] who used a simple corrugation function instead of atom-atom pair potentials. 

For the assignment of the different vibrational peaks to certain hydrogen sites a simple lattice dynamical model was used. The frequencies of localized hydrogen vibrations in metals are obtained by solving the eigenvalue problem... 

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