Phonon focusing and phonon conduction in hexagonal crystals in the boundary-scattering regime

McCurdy, A. K.

doi:10.1103/physrevb.9.466

Cited by 51 publications

(17 citation statements)

References 20 publications

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“…It is instructive to compare the critical values of Payton's parameter, derived from the exact equation [5], with Musgrave's approximation and two well-defined geometrical conditions which also provide approximations, one of which has been employed by McCurdy et al [8,9]. A tabulation of such comparisons for a wide range of possible anisotropies is presented.…”

Section: §1 Introductionmentioning

confidence: 99%

“…McCurdy et al [8,9] have made extensive surveys of crystalline elastic properties with the same application in mind. They re-derive and apply the criteria of Musgrave [4] and, furthermore, obtain from consideration of a sextic equation sufficient conditions for the existence of inflexions asymmetrically disposed with respect to a direction non-coincident with a symmetry axis.…”

Section: §1 Introductionmentioning

confidence: 99%

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Criteria for elastic waves in anisotropic media — a consolidation

Musgrave

Payton

1984

J Elasticity

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The geometry relating to the tangent plane at a stationary point on a surface has been used to re-examine various criteria for the existence of parabolic points (inflexions in 2D-sections) on the outermost sheet of the slowness surface for elastic waves in anisotropic media.Previous results obtained by the authors, exact [4,5], and approximate [6], are related in detail. Further approximations, based on geometrical properties, are derived; one of these proves equivalent to a sufficient condition first applied by McCurdy [8].Numerical investigation shows that, over a wide range of anisotropy, the simply applied approximate criterion of [6] is sufficient and within the accuracy of observation of the elastic stiffnesses. §1. IntroductionIn the study of elastic waves in anisotropic media, the geometry of the slowness surface has proved fundamental [1,2].When a spatial pattern of phase is defined on a plane boundary (for example, by the incidence of a plane wave), the waves consistent with this pattern are determined by the intersections, real or imaginary, of a straight line with the sagittal section of the slowness surface. (Note. The sagittal plane contains the normal to the boundary and the slowness determining the phase pattern upon it. The definition thus includes both the concept of the plane of incidence for reflexion-refraction problems and that of the reference plane [3] as used in discussions of surface and interface waves). Clearly, the presence or absence of non-convex regions on the outer slowness sheets occasions significant differences in the possible configurations of intersection. Thus, within the bounds of anisotropy consistent with positive definite strain energy, a variety of possible sets of waves compatible with the given phase pattern occurs.The particular case of elastic waves with normals contained in planes of 2 or m material symmetry has been the subject of considerable study, owing to its relative tractability. It is well known [2] that the equation of the section of the slowness surface by such planes factorises to a quadratic (an ellipse) and a quartic representing a curve of two sheets which, in the case of known physical materials, are non-intersecting.Criteria for the existence of inflexions about symmetry axes in the outer quartic sheet were first given by Musgrave [4] in the form of simple inequalities involving elastic stiffnesses. More recently, Payton [5] presented the theory for inflexions occur-269

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Section: §1 Introductionmentioning

confidence: 99%

Section: §1 Introductionmentioning

confidence: 99%

Criteria for elastic waves in anisotropic media — a consolidation

Musgrave

Payton

1984

J Elasticity

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“…The first data on phonon focusing in cadmium sulphide have been reported by McCurdy [4,5], and the detail 2D calculation of the focusing directions in this crystal has been fulfilled in the following [6] to check the streamer breakdown theory based on the phonon streams. It has been revealed that there are unusual, in comparison with the literature data, properties in STA mode to possess directions of infinite focusing in CdS.…”

Section: Phonon Focusing Onsetmentioning

confidence: 99%

Khatkevich's theory for acoustic axes in 6mm piezoelectric CdS

Zubrytski¹

2007

J. Phys.: Conf. Ser.

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Abstract. The simplest derivation of Khatkevich's equation based on Fedorov's mathematics is presented here in view of recent confusions on the subject discussed in the literature. In the development of Khatkevich's theory of acoustic axes the general equation is extended by introducing into consideration piezoelectric interaction. It is shown that the linear piezoelectric effect doubles the order of equation for the degenerated roots in hexagonal media in comparison with that obtained at taking into account pure elasticity only. Method is provided for control of phonon focusing anisotropy by investigation of acoustic axes in the piezoelectric medium. Examples of equilibrium dynamics of the acoustic axes for phonon modes in the temperature range from 4.2 to 500 K in CdS and of the phonon focusing factor in ZnO are supplied.

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“…They are elementary except for the off-axis triplication, which is algebraically more involved. For this case, several authors proposed simpler but approximate triplication conditions (McCurdy, 1974;Musgrave, 1979;Musgrave and Payton, 1984;Alshits and Chadwick, 1997;Thomsen and Dellinger, 2003). Among these conditions, the condition proposed by Thomsen and Dellinger (2003) is particularly interesting, because it is far simpler than the other approximations, and provides an insight into which parameters control the off-axis triplication.…”

Section: Introductionmentioning

confidence: 99%

Approximate Conditions for the Off-Axis Triplication in Transversely Isotropic Media

Vavryčuk¹

2004

Studia Geophysica et Geodaetica

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The presented approximate formulas yield a critical value of anisotropy parameter σ, for which an incipient off-axis SV-wave triplication occurs in transversely isotropic media. The formulas are simple but approximate the exact solution with a high accuracy. The best results are obtained using the third-order approximation, which yields accuracy at least 30 times higher than the formulas presented by Thomsen and Dellinger (2003

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Phonon focusing and phonon conduction in hexagonal crystals in the boundary-scattering regime

Cited by 51 publications

References 20 publications

Criteria for elastic waves in anisotropic media — a consolidation

Criteria for elastic waves in anisotropic media — a consolidation

Khatkevich's theory for acoustic axes in 6mm piezoelectric CdS

Approximate Conditions for the Off-Axis Triplication in Transversely Isotropic Media

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