A. G. Every

Energies and spacings of point charges on a sphere

Numerical methods are in general required for the determination of the stable configurations of N point charges on a sphere. The stable configurations for N up to 50 have previously been ascertained and the authors extend the calculations for values up to 101. They report for the first time some remarkable global features of these configurations. They show that the minimum energy accurately follows a simple half-integral power law in 1/N over the full range they have investigated. This power law is explicable in terms of the idealization of mapping a planar Wigner lattice onto the surface of the unit sphere; the pair distribution functions of the larger-N configurations indicate predominant hexagonal coordination. The coefficients of the observed power law are closely straddled by values calculated on the basis of hexagonal and square Wigner lattices. This highly accurate description of the energy permits them to remark on the detailed deviations of the individual structures from the general trend. For N(30, they note that structures with N prime are relatively less stable, while structures with N equal to 6, 12, 32, 44, 48 and 60 seem more stable.

Secluded supersonic surface waves in germanium

Abstract A secluded supersonic SAW is known to exist in an isolated direction on the (001) surface of certain cubic crystals. This wave consists of two evanescent partial wave components and is not polarized in a symmetry plane. Calculations are reported on this mode, using germanium as an example, and it is found that this wave continues to exist for some surface orientations different from (001). A one dimensional family of nonsymmetrical supersonic SAW geometries is identified and it is found to be joined to the family of supersonic SAW polarized in the (1 1 0) symmetry plane.

Time-domain dynamic surface response of an anisotropic elastic solid to an impulsive line force

It is shown that the surface displacement response of a general anisotropic halfspace subjected to an impulsive line load can be obtained by purely algebraic means using a functional equivalence that exists between the time-space and Fourier domain dynamic Greens functions. Illustrative numerical results are presented for the silicon (111) surface that portray the role of bulk waves, surface waves (SAW) and pseudo-SAW.

Determination of the elastic constants of anisotropic solids

Abstract This article sets out to review the methods that are available for determining the elastic constants of anisotropic solids, with particular emphasis on techniques that involve the measurement of bulk acoustic wavespeeds. Some of the comparative advantages and disadvantages of the various methods are pointed out. In describing ultrasonic wave transmission, attention is given to the question of whether it is the phase or group velocity that is measured. Finally, the algorithms used for obtaining elastic constants from bulk acoustic wave phase and group velocity data are discussed.

Acoustic symmetry in phonon imaging

Phonon imaging with long-wavelength acoustic phonons provides a vivid means of exhibiting the acoustic symmetry of crystals. It is shown that piezoelectric stiffening of the elastic constants can bring about a reduction in this symmetry. Full details are provided of the acoustic symmetry for the 32 crystal classes with the piezoelectric effect excluded, and also with it taken into account.

Ballistic phonon imaging of diamond

Phonon imaging has been used to study the transport of ballistic phonons in diamond. The images that have been obtained display a number of sharp features. Some of these correspond to mathematical singularities or near singularities in bulk phonon focusing. Other structures are found to correspond to the channelling of transverse phonons close to the critical cone for mode conversion of transverse to longitudinal waves at the diamond surface. This channelling is mediated by longitudinal pseudo-surface waves at the diamond surface, and is extremely sharp because of the near isotropy of diamond and its exceptionally small effective Poissons ratio. The presence of these channelling structures signifies that the diamond surface is relatively flat on the scale of the dominant phonon wavelength ( approximately=200 AA) and that the bonding between the metal heater and detector films and the diamond substrate is mechanically weak.

A donor electron orbital for nitrogen in diamond

Abstract An orbital is proposed for the donor electron of substitutional nitrogen in diamond. It accounts for the quadrupole and the main hyperfine constants of the electron spin resonance spectrum reported by Smith et al. and Loubser and du Preez.

Formation of surface phonon focusing caustics in crystals

Abstract The effect of elastic anisotropy on surface phonon focusing in the (1 1 1) surface of cubic crystals is studied theoretically and experimentally. Calculations of the focusing factor for BaF2, NaCl, CaF2 and KCl are compared with anisotropic powder patterns created by laser-generated surface acoustic waves. Formation of a pair of caustics in 〈1 1 2 〉 directions with increasing anisotropy is observed. Conditions for caustics to appear on a (1 1 1) cubic crystal surface are expressed in terms of the elastic constant ratios.

Thermal Phonon Imaging

The development of phonon imaging by Northrop and Wolfe (1979,1980) arose from efforts to understand the dynamics of electron-hole droplets in semiconductors (Hensel and Dynes, 1979) and intensity measurements in ballistic heat pulse experiments (Ta-borek and Goodstein, 1979; Marx et al., 1978). Since its inception, phonon imaging has had a major impact on the field of phonon transport. It has led to the consolidation of earlier ideas on phonon focusing (Maris, 1971; McCurdy et al., 1970; Philip and Viswanathan, 1978; Rosch and Weis, 1976) and has opened up a broad new area of research. Over time it has emerged as a powerful tool that has found a range of applications in solid state physics, and significant progress has been made in its adaptation to particle detection.

Displacement field of a point force acting on the surface of an elastically anisotropic half-space

A ring integral expression is presented for the Green tensor pertaining to the static displacement field of a point force acting on the surface of an elastically anisotropic half-space. It is derived as the low-frequency limit of the dynamic Green tensor. The expression is suitable for rapid computations, and illustrative numerical results are presented for a semi-infinite (001) oriented silicon crystal. For surface displacements the Green tensor decomposes naturally into symmetric and antisymmetric parts. The ring integral for the symmetric part can be performed analytically, yielding an algebraic result. Simplifications brought about by material symmetry are discussed.