Plane Of Cubic Crystals Research Articles

Informational coupling of photoinduced dichroism in the absorption bands of 𝑴𝑨-centers of coloration 𝑺𝒓𝑪𝒍𝟐 − 𝑴𝒆+ crystal

A method of obtaining a sample with two mutually perpendicular planes (001) and (110) from the SrCl2 crystal has been developed. Calculated information dependence of photoinduced dichroisms in different absorption bands of MA- coloring centers in SrCl2-Me+ crystals, if illumination and observation are carried out in the (001) and (110) planes.The performed calculations show that in some crystallographic planes of cubic crystals the action of linearly polarized light on an optically active absorption band may not lead to the occurrence of optical dichroism in this region, although it induces dichroism in other absorption bands of this color center, regardless of the degree of their optical activity. At the same time, these dichroisms are always opposite to each other.

The Sensitivity of Dislocation Rosettes to the Shape of a Berkovich Indenter on LiF and MgO Crystals

The peculiar effect observed under the indentation of the (001) plane of LiF and MgO single crystals, namely, the sensitivity of the form of dislocation rosettes to the shape of the indenter, is considered. It is shown that the dislocation rosettes being formed around Vickers indentations are symmetrical, while the rosettes around Berkovich indentations are asymmetrical, the edge arms of the dislocation rosettes are different with respect to their length, and the screw arms do not demonstrate such asymmetry. Also, an orientational effect is found under the penetration of a Berkovich indenter, thus, the form of the dislocation rosettes and length of the edge arms change at varying the orientation of the indenter relative to the crystallographic directions of the sample. It is also shown that the asymmetry of the dislocation rosettes is more pronounced on harder crystals and increases with the growth in the load on the indenter. The factors responsible for the anomaly in the development of the dislocation rosettes under nano- and microindentation of the (001) plane of cubic crystals by a Berkovich indenter are found.

Чувствительность дислокационных розеток к форме индентора Берковича на кристаллах LiF и MgO

A peculiar effect, namely, the sensitivity of the shape of dislocation rosettes to the indenter type under indentation of the (001) face of LiF and MgO single crystals has been revealed. It was shown that the dislocation rosettes forming around the Vickers indenter are symmetrical, while the rosettes around the Berkovich one are asymmetric, the edge beams of the dislocation rosettes vary in length, and the screw ones do not show such asymmetry. An orientation effect was found during the penetration of the Berkovich indenter: the shape of the dislocation rosettes and the length of the edge beams change with a change in the orientation of the indenter relative to the crystallographic directions of the sample. It was also shown that the asymmetry of dislocation rosettes is more visible on harder crystals and increases with load growth on the indenter. The factors responsible for the anomaly in the development of dislocation rosettes under indentation in nano and micro scale by the Berkovich indenter of the (001) plane of cubic crystals are established

Simultaneous determination of mean pressure and deviatoric stress based on numericaltensor analysis: a case study for polycrystalline x-ray diffraction of gold enclosed in amethanol–ethanol mixture

It is known that the {100} and {111} planes of cubic crystals subjected to uniaxial deviatoricstress conditions have strain responses that are free from the effect of lattice preferredorientation. By utilizing this special character, one can unambiguously and simultaneouslydetermine the mean pressure and deviatoric stress from polycrystalline diffraction data ofthe cubic sample. Here we introduce a numerical tensor calculation method based on thegeneralized Hooke’s law to simultaneously determine the hydrostatic component of thestress (mean pressure) and deviatoric stress in the sample. The feasibility of this methodhas been tested by examining the experimental data of the Au pressure markerenclosed in a diamond anvil cell using a pressure medium of methanol–ethanolmixture. The results demonstrated that the magnitude of the deviatoric stress is∼0.07 GPa at the mean pressure of 10.5 GPa, which is consistent with previous results of Austrength under high pressure. Our results also showed that even a small deviatoric stress(∼0.07 GPa) could yielda ∼0.3 GPa meanpressure error at ∼10 GPa.

Nonlinear coupling of surface and quasitransverse bulk modes in cubic crystals.

In crystals the speed of the surface acoustic wave mode may approach that of the lowest-speed quasitransverse bulk mode in some directions of propagation. Under these circumstances, it is possible for energy to be transferred from the surface mode to the bulk mode by nonlinear coupling. In the present paper we investigate the possibilities for mode coupling in the (001), (110), and (111) planes of cubic crystals. A condition is given for determining the range of propagation directions with significant coupling, and numerical results are provided for eight different crystals with a range of anisotropy ratios. It is shown that even for significant excitation amplitudes the coupling is negligible for most propagation directions in the aforementioned surface cuts.

Effects of harmonic phase on nonlinear surface acoustic waves in the (111) plane of cubic crystals.

Spectral evolution equations are used to perform numerical studies of nonlinear surface acoustic waves in the (111) plane of several nonpiezoelectric cubic crystals. Nonlinearity matrix elements which describe the coupling of harmonic interactions are used to characterize velocity waveform distortion. In contrast to isotropic solids and the (001) plane of cubic crystals, the nonlinearity matrix elements usually cannot be written in a real-valued form. As a result, the harmonic components are not necessarily in phase, and dramatic variations in waveforms and propagation curves can be observed. Simulations are performed for initially monofrequency surface waves. In some directions the waveforms distort in a manner similar to nonlinear Rayleigh waves, while in other directions the velocity waveforms distort asymmetrically and the formation of shocks and cusped peaks is less distinct. In some cases, oscillations occur near the shocks and peaks because of phase differences between harmonics. A mathematical transformation based on the phase of the matrix elements is shown to provide a reasonable approximation of asymmetric waveform distortion in cases where the matrix elements have similar phase.

Directional dependence of nonlinear surface acoustic waves in the (001) plane of cubic crystals.

Spectral evolution equations are used to perform analytical and numerical studies of nonlinear surface acoustic waves in the (001) plane of a variety of nonpiezoelectric cubic crystals. The basic theory underlying the model equations is outlined, and quasilinear solutions of the equations are presented. Expressions are also developed for a characteristic length scale for nonlinear distortion and a nonlinearity coefficient. A time-domain equation corresponding to the spectral equations is derived. Numerical calculations based on measured second- and third-order elastic constants taken from the literature are performed to predict the evolution of initially monofrequency surface waves. Nonlinearity matrix elements that indicate the coupling strength of harmonic interactions are shown to provide a useful tool for characterizing waveform distortion. The formation of compression or rarefaction shocks can be strongly dependent on the direction of propagation, and harmonic generation is suppressed or increased in certain directions.

Periodicity of linear and nonlinear surface acoustic wave parameters in the (111) plane of cubic crystals

Previous numerical and experimental studies of surface acoustic waves (SAWs) in the (111) plane of cubic crystals have shown that linear properties, including the wave speed and the direction of power flow, exhibit sixfold symmetry. However, recent measurements by Lomonosov and Hess of finite-amplitude SAW pulses propagating in opposite directions in the (111) plane of crystalline silicon have demonstrated that the same periodicity does not hold for the nonlinear distortion. Calculations based on a model for nonlinear SAWs in anisotropic media [Hamilton et al., J. Acoust. Soc. Am. 105, 639–651 (1999)] indicate that complex-valued nonlinearity matrix elements, which describe the coupling between harmonics, have sixfold symmetry in magnitude but only threefold symmetry in phase. As a result, pulses traveling in opposite directions exhibit different nonlinear phase shifting between harmonics that give rise to the distinctly different types of observed distortion. Threefold symmetry of nonlinearity is also predicted for other cubic crystals besides silicon. Additional computations show that the complex-valued eigenvalues and eigenvectors of the linearized equations (physically corresponding to the depth decay coefficients and component amplitudes, respectively) also have sixfold symmetry in magnitude but only threefold symmetry in phase. [Discussions with A. P. Mayer are gratefully acknowledged.]

Line focus acoustic microscopy to measure anisotropic acoustic properties of thin films

Propagation characteristics of surface acoustic waves on thin film coated elastic materials have been investigated by the use of an acoustic microscope with a line focus beam. Measurements were carried out for thin films of various thicknesses deposited on the (001) plane of cubic crystals. The phase velocities measured as functions of the angle of propagation display the anisotropy and confirm the advantage of directional measurement by the line focus acoustic microscope. Dispersion curves of surface waves propagating along the symmetry axes were obtained for various film thicknesses and frequencies. A systematic inversion of surface wave data based on a comparison of theoretical and experimental results has been used to obtain the thin film material constants.

Changes of the principal directions of electrical resistivity caused by a magnetic field

Magnetoresistance skewness effect (change of the principal directions of electrical resistivity) appears when a magnetic field of arbitrary direction is applied on the examined material. This effect is useful for the magnetoresistance coefficients determination. A complete investigation of the skewness effect requires additional experimental facilities, such as the rotation of the sample and the contact system, which in some cases are impossible or very difficult to obtain. In this work the importance of the (110) and (111) planes of cubic crystals for such measurements is shown. For this purpose the elements of the resistivity tensor in the systems of reference, used in these planes, are correlated with those in the basic system of the (001) plane.

Weak-field magnetoresistance skewness and galvanomagnetic measurements on the (001)-plane of n-type Ge single crystal

Weak-field galvanomagnetic measurements were carried out at room temperature on a (001)-circular flat sample of an n-type Ge single crystal using the Van der Pauw-Wasscher technique, with the magnetic field parallel and normal to the sample plane. Thus, the anisotropy which appears in the (001)-plane of cubic crystals due to the magnetic field is investigated and the existence of the magnetoresistance skewness effect is established experimentally. This effect allows the determination of all the galvanomagnetic coefficients in a simple way. The new result concerning Ge is the negative sign of the ρ1212 coefficient which is attributed to the reverse rotation of the magnetoresistance.

Elastic wave surfaces for the (111) plane of cubic crystals

The nature of inverse velocity surfaces as well as energy surfaces for elastic wave propagation in the (111) plane have been studied for a number of cubic crystals. The sections of inverse velocity surfaces by the (111) plane exhibit six-fold symmetry in all cases. Cuspidal edges are exhibited with a six-fold symmetry by both the slow transverse and fast transverse shear modes in the (111) plane, unlike the case of the (100) and (110) planes for which only the slow transverse shear mode exhibits cuspidal edges. The slow transverse mode energy surface exhibits cuspidal edges along % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaacbaGaa8hkai% qa-fdagaqeaiqa-fdagaqeaiaa-jdacaWFPaaaaa!3990! $$(\bar 1\bar 12)$$ direction or an equivalent symmetry direction. The inverse velocity surfaces of the A-15 compounds exhibit unusually large inflexions for the slow transverse mode, whereas their energy surfaces have large cuspidal edges which intersect each other resulting in common regions of cusps.

Weak field magnetoresistance skewness imposed by magnetic field

The effect of a magnetic field on any crystalline material is to introduce an anisotropy in the electric resistivity. This letter examines the anisotropy which appears in the (001) plane of cubic crystals. Compact formulas are developed which show that in general the extreme values of the resistivity occur in directions which differ from those of the crystallographic axes. We thus demonstrate the existence of magnetoresistance skewness, as defined in recent papers of Allgaier et al., but have analyzed the phenomenon from a point of view which is complementary to that employed in the earlier work.

Elastic Waves in {100}, {110}, and {111} Planes of Cubic Crystals

Elastic Waves in {100}, {110}, and {111} Planes of Cubic Crystals