Elemental surface phonons

The first mention of surface phonons is due to Lord Rayleigh (1885), who predicted the existence of a surface acoustic mode with a sound velocity lower than in the bulk. He proved this result, using elasticity theory, by representing the semi-infinite sofid by a continuous and isotropic medium (Landau and Lifehitz, 1967). Considering an infinitesimal volume element, he wrote a Fourier component of its displacement u q, co), in the following form ... 

The data for surface phonon dispersion determined either experimentally or theoretically for adsorbed covered systems is reported and compared with the surface phonon dispersion of the corresponding bare system. The data is organised according to the electrical properties of the material firstly metals, secondly elemental semiconductors and insulators, and finally compound semiconductors, oxides and salts. The reported systems are collected in Table I. 

This chapter has given an introduction to vibrations at bare elemental surfaces, namely, surface phonons. Owing to the low energy of surface phonons, thermal excitations at surfaces nearly always include a significant thermal population of surface phonons. Consequently, the thermal properties are closely linked to phonon properties. 

In the case of Cu(l 11) face, the Au adatom presents almost similar phonon modes for both the in-plane directions (solid and dashed line in Figure 3) at 0.7THz, which can be compared with that of Cu adatom on the same surface (1. ITHz). There is now again a shift to lower frequencies, due to the different mass of the two elements. The DOS at the perpendicular to the surface direction ( thick dashed line in Figure 3) shows a main peak at 1.7 THz, which appears in energetically lower position, compared with that of Cu adatom (3.2 THz) ... 

Figure 15.8 shows the thermal scheme of one detector there are six lumped elements with three thermal nodes at Tu T2, r3, i.e. the temperatures of the electrons of Ge sensor, Te02 absorber and PTFE crystal supports respectively. C), C2 and C3 are the heat capacity of absorber, PTFE and NTD Ge sensor respectively. The resistors Rx and R2 take into account the contact resistances at the surfaces of PTFE supports and R3 represents the series contribution of contact and the electron-phonon decoupling resistances in the Ge thermistor (see Section 15.2.1.3). 

To proceed further, three major approximations to the theory are made [44] First, that the transition operator can be written as a pairwise summation of elements where the index I denotes surface cells and k counts units of the basis within each cell second, that the element is independent of the vibrational displacement and, third, that the vibrations can all be treated within the harmonic approximation. These assumptions yield a form for w(kf, k ) which is equivalent to the use of the Bom approximation with a pairwise potential between the probe and the atoms of the surface, as above. However, implicit in these three approximations, and therefore also contained within the Bom approximation, is the physical constraint that the lattice vibrations do not distort the cell, which is probably tme only for long-wavelength and low-energy phonons. 

P. H. Dederichs, H. Schober, D. J. Sellmyer, Phonon States of Elements Electron States and Fermi Surface of Alloys, in Metals Phonon States Electron States and Fermi Surfaces , Vol 13a, p. 458. (K.-H. Hellwege, J. L. Olsen, Eds.), Springer-Verlag, and Landolt-Bomstein, Berlin, 1981. 

The effective mass ratios measured are of the order of one. The deformation potential coupUng constants vary between 0.5 x 10 K and 3.8 x 10 K. That deduced from the temperature dependence is 10 K. From the band structure for LaAg it was conjectured that the phase transition in the LaAgIn compounds could be due to a nesting feature of the Fermi surface, which gives large electron-phonon matrix elements for the observed M-point phonons (Knorr et al. 1980, Niksch et al. 1987). 

Complete dispersion curves along symmetry directions in the Brillouin zone are obtained from calculated force constants. Calculations of enharmonic terms and phonon-phonon interaction matrix elements are also presented. In Sec. IIIC, results for solid-solid phase transitions are presented. The stability of group IV covalent materials under pressure is discussed. Also presented is a calculation on the temperature- and pressure-induced crystal phase transitions in Be. In Sec. IV, we discuss the application of pseudopotential calculations to surface studies. Silicon and diamond surfaces will be used as the prototypes for the covalent semiconductor and insulator cases while surfaces of niobium and palladium will serve as representatives of the transition metal cases. In Sec. V, the validity of the local density approximation is examined. The results of a nonlocal density functional calculation for Si and... 

The precoverage of the surface of elemental metals by contaminants like oxygen, sulphur, carbon (SO2, CO) degrades their H adsorption, absorption and desorption properties drastically. The contamination can interfere in different steps in the sorption process The contaminating species themselves are chemisorbed, induce reconstruction and alter the electronic properties and the phonon spectra of the substrate surface. Thus sticking coefficient, chemisorption energy, vibrational properties and surface mobility of H2 and H are affected and dissociation and recombination are often made impossible. 

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