Book•
Acoustic Fields and Waves in Solids
01 Jan 1973-
TL;DR: In this article, the authors apply the material developed in the Volume One to various boundary value problems (reflection and refraction at plane surfaces, composite media, waveguides and resonators).
Abstract: This work, part of a two-volume set, applies the material developed in the Volume One to various boundary value problems (reflection and refraction at plane surfaces, composite media, waveguides and resonators). The text also covers topics such as perturbation and variational methods.
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01 Jan 2011TL;DR: In this article, the authors present basic tools for elasticity and Hooke's law, effective media, granular media, flow and diffusion, and fluid effects on wave propagation for wave propagation.
Abstract: Preface 1. Basic tools 2. Elasticity and Hooke's law 3. Seismic wave propagation 4. Effective media 5. Granular media 6. Fluid effects on wave propagation 7. Empirical relations 8. Flow and diffusion 9. Electrical properties Appendices.
2,007 citations
TL;DR: In this paper, the authors present the best known elasticity data for silicon, both in depth and in a summary form, so that it may be readily accessible to MEMS designers.
Abstract: The Young's modulus (E) of a material is a key parameter for mechanical engineering design. Silicon, the most common single material used in microelectromechanical systems (MEMS), is an anisotropic crystalline material whose material properties depend on orientation relative to the crystal lattice. This fact means that the correct value of E for analyzing two different designs in silicon may differ by up to 45%. However, perhaps, because of the perceived complexity of the subject, many researchers oversimplify silicon elastic behavior and use inaccurate values for design and analysis. This paper presents the best known elasticity data for silicon, both in depth and in a summary form, so that it may be readily accessible to MEMS designers.
1,741 citations
Book•
02 Feb 2004TL;DR: The role of stress in mass transport is discussed in this article, where the authors consider anisotropic and patterned films, buckling, bulging, peeling and fracture.
Abstract: 1. Introduction and overview 2. Film stress and substrate curvature 3. Stress in anisotropic and patterned films 4. Delamination and fracture 5. Film buckling, bulging and peeling 6. Dislocation formation in epitaxial systems 7. Dislocation interactions and strain relaxation 8. Equilibrium and stability of surfaces 9. The role of stress in mass transport.
1,562 citations
Book•
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TL;DR: In this article, the elastodynamics and its simple solutions of dynamic ray tracing are discussed. But they do not consider the effect of the propagation speed of the ray on the propagation.
Abstract: Preface 1. Introduction 2. The elastodynamics and its simple solutions 3. Seismic rays and travel times 4. Dynamic ray tracing. Paraxial ray methods 5. Ray amplitudes 6. Ray synthetic seismograms Appendix. Fourier transform, Hilbert transform and analytical signals References Index.
1,206 citations
TL;DR: Crystal14 as discussed by the authors is an ab initio code that uses a Gaussian-type basis set: both pseudopotential and all-electron strategies are permitted; the latter is not much more expensive than the former up to the first second transition metal rows of the periodic table.
Abstract: The capabilities of the Crystal14 program are presented, and the improvements made with respect to the previous Crystal09 version discussed. Crystal14 is an ab initio code that uses a Gaussian-type basis set: both pseudopotential and all-electron strategies are permitted; the latter is not much more expensive than the former up to the first-second transition metal rows of the periodic table. A variety of density functionals is available, including as an extreme case Hartree–Fock; hybrids of various nature (global, range-separated, double) can be used. In particular, a very efficient implementation of global hybrids, such as popular B3LYP and PBE0 prescriptions, allows for such calculations to be performed at relatively low computational cost. The program can treat on the same grounds zero-dimensional (molecules), one-dimensional (polymers), two-dimensional (slabs), as well as three-dimensional (3D; crystals) systems. No spurious 3D periodicity is required for low-dimensional systems as happens when plane-waves are used as a basis set. Symmetry is fully exploited at all steps of the calculation; this permits, for example, to investigate nanotubes of increasing radius at a nearly constant cost (better than linear scaling!) or to perform self-consistent-field (SCF) calculations on fullerenes as large as (10,10), with 6000 atoms, 84,000 atomic orbitals, and 20 SCF cycles, on a single core in one day. Three versions of the code exist, serial, parallel, and massive-parallel. In the second one, the most relevant matrices are duplicated, whereas in the third one the matrices in reciprocal space are distributed for diagonalization. All the relevant vectors are now dynamically allocated and deallocated after use, making Crystal14 much more agile than the previous version, in which they were statically allocated. The program now fits more easily in low-memory machines (as many supercomputers nowadays are). Crystal14 can be used on parallel machines up to a high number of cores (benchmarks up to 10,240 cores are documented) with good scalability, the main limitation remaining the diagonalization step. Many tensorial properties can be evaluated in a fully automated way by using a single input keyword: elastic, piezoelectric, photoelastic, dielectric, as well as first and second hyperpolarizabilies, electric field gradients, Born tensors and so forth. Many tools permit a complete analysis of the vibrational properties of crystalline compounds. The infrared and Raman intensities are now computed analytically and related spectra can be generated. Isotopic shifts are easily evaluated, frequencies of only a fragment of a large system computed and nuclear contribution to the dielectric tensor determined. New algorithms have been devised for the investigation of solid solutions and disordered systems. The topological analysis of the electron charge density, according to the Quantum Theory of Atoms in Molecules, is now incorporated in the code via the integrated merge of the Topond package. Electron correlation can be evaluated at the Moller–Plesset second-order level (namely MP2) and a set of double-hybrids are presently available via the integrated merge with the Cryscor program. © 2014 Wiley Periodicals, Inc.
1,172 citations
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TL;DR: In this article, the Schroedinger perturbation theory is extended to the boundary value problems of guided electromagnetic waves in cylindrical structures containing inhomogeneous, anisotropic, dissipative media.
Abstract: The Schroedinger perturbation theory is extended to the boundary value problems of guided electromagnetic waves in cylindrical structures containing inhomogeneous, anisotropic, dissipative media. A general variational principle, which reduces to existing restricted forms valid for nondissipative media, is also formulated. These approximation methods evolve in a unified manner from the eigenvalue formulation of Maxwell's equations wherein the wave numbers are the eigenvalues of a linear operator. The properties of the media are restricted only by the requirement that they be independent of the axial coordinate. Perturbation of the backward wave is considered and the condition for nonreciprocal waveguides is stated. Modification of the perturbation method for application to gyrotropic media is outlined and it is indicated that convergence of the perturbation terms is improved in those media, such as the plasma and semiconductor, which permit a Taylor expansion of the susceptibility tensor in powers of the external field. Two specific examples, whose exact solutions are known, are included to illustrate the application.
53 citations
TL;DR: In this article, general formulas for the electrical admittance of a piezoelectric crystal, in terms of its resonant frequencies and static and motional capacitances, are derived and applied to the investigation of the effect of electrode shape on the spectrum of resonances and the capacitance ratio of the crystal.
Abstract: In the present paper general formulas for the electrical admittance of a piezoelectric crystal, in terms of its resonant frequencies and static and motional capacitances, are derived and applied to the investigation of the effect of electrode shape on the spectrum of resonances and the capacitance ratio of the crystal. Particular attention is given in two cases of practical importance, namely, small piezoelectric coupling and thin crystal plates.
51 citations
TL;DR: In this article, the first-order and second-order magnetoelastic effects in yttrium iron garnet (YIG) have been studied using a pulsed ultrasonic technique and have been interpreted using finite-deformation magneto-elastic theory.
Abstract: First-order and second-order (in strain) magnetoelastic effects in yttrium iron garnet (YIG) have been studied using a pulsed ultrasonic technique and have been interpreted using finite-deformation magnetoelastic theory. Small-amplitude plane-wave modes in 100g, 110g, and 111g directions in uniformly magnetized, homogeneously deformed cubic single crystals have been analyzed including first-order and second-order magnetoelastic coupling. First-order and second-order magnetoelastic constants have been completely determined for YIG. The second-order "morphic" effect has been analyzed and completely evaluated for YIG in terms of 8 "morphic" constants. Experimental results are described which agree with finite-deformation magnetoelastic theory and disagree with small-strain theory.
34 citations