Elastic interaction of point defects in cubic and hexagonal crystals

The elastic interaction of two point defects in cubic and hexagonal structures has been considered. On the basis of the exact expression for the tensor Green’s function of the elastic field obtained by the Lifschitz–Rozentsveig for a hexagonal medium, an exact formula for the interaction energy of two point defects has been obtained. The solution is represented as a function of the angle of their relative position on the example of semiconductors such as III-nitrides and α-SiC. For the cubic medium, the solution is found on the basis of the Lifschitz–Rozentsveig Green’s tensors corrected by Ostapchuk, in the weak-anisotropy approximation. It is proven that the calculation of the interaction energy by the original Lifschitz–Rozentsveig Green’s tensor leads to the opposite sign of the energy. On the example of the silicon crystal, the approximate solution is compared with the numerical solution, which is represented as an approximation by a series of spherical harmonics. The range of applicability of the continual approach is estimated by the quantum mechanical calculation of the lattice Green’s function.     

具有立方晶系结构的多晶体材料的弹性常数——Y弹性常数

提出了一个新的物理参量“Ｙ弹性常数”,并阐述了其物理含义.并将其应用于具有立方晶系结构的多晶体材料,推导了立方晶系结构的多晶体材料的Ｙ弹性常数,通过算例与具有立方晶系结构的多晶体材料的X射线弹性常数进行了比较.运用这个Ｙ弹性常数进一步推导出的多晶体材料整体的机械弹性常数的表达式与Krner的研究结果完全符合. 关键词： Y弹性常数 立方晶系 多晶体材料     

Propagation of elastic waves in hexagonal piezoelastic crystals

The propagation of elastic waves in an arbitrary direction through a hexagonal piezoelectric crystal is investigated. Orientational relations are obtained in analytic form for the effective elastic moduli and the piezoelectric and dielectric constants, and also for the basic parameters of the elastic waves: the phase velocity, electromechanical coefficient, and the divergence between the displacement vector and the energy flux. Expressions are given for the directions in which the electromechanical coefficient takes an extremal value, and the basic parameters are calculated for cadmium sulfide.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 101–105, May, 1977.     

Theories of elastic properties and elastic waves of equal phase velocities in crystals

A survey is made of pairs of heteronormal planar elastic waves, which can propagate in an unlimited crystal medium and have equal theoretical values of the phase velocity, using Voigt elastic moduli. Such pairs are chosen for which it is possible that the theoretical equality of velocities will be disturbed when using another theory of the elastic properties of crystals with generally different tensors of material constants (for example Kuvshinskij J. V., Aero E. L.: Fiz. tv. tela5 (1963), 2591). In such a case, a comparison of the measured velocities of a suitable pair of waves can help to decide between the two theories. Pairs of waves are found for 12 non-piezoelectric crystal classes. Among such pairs it is easy to find pairs of waves of the same properties for piezoelectric crystal classes.     

Electron paramagnetic resonance of Dy3+ in cubic ZnSe and Tm3+ in hexagonal CdS single crystals

Electron paramagnetic resonance has been observed for Dy³⁺ in ZnSe and Tm³⁺ in CdS. For Dy³⁺ doped ZnSe, an isotropic spectrum was observed having well resolved hyperfine lines due to ¹⁶¹Dy and ¹⁶³Dy. The g value obtained was 6.577 ± 0.002 and ¹⁶¹A was 191 ± 1 × 10⁴ cm^?1 and ¹⁶³A was 265 ± 3 × 10^?4 cm^?1. The agreement of the observed g value to g(τ₆) = 6.667 and the point-charge calculations suggest that Dy³⁺ occupies an interstitial (II) site with no local charge compensation. For Tm³⁺ doped in hexagonal CdS, an axial spectrum consistent with g_⊥ = 0, g_∥ = 10.722 ± 0.007, D = 2.57 GHz (crystal field splitting) and ¹⁶⁹A = 1207 ± 5 × 10^?4cm^?1. The large g_∥ value indicates that the Tm ion exits in the trivalent state. This is in reasonable agreement with previous reports of the non-Kramer's state of Tm³⁺.     

Temperature dependence of the second-order elastic constants of cubic crystals

A simplified phenomenological theory of the temperature dependence of the second-order elastic constants of crystals is considered. The temperature dependences of the second-order elastic constants are calculated for a series of cubic crystals with various types of predominant chemical bonding. Satisfactory agreement between the calculation results and experimental data is obtained. Fiz. Tverd. Tela (St. Petersburg) 41, 235–240 (February 1999)     

Effect of cubic hydrostatic compression on the elastic properties of single crystals of halides of sodium and potassium

Experimental studies (by the ultrasonic pulse method) and theoretical investigations (with the model of polarizable ions) were made of changes in the elastic moduli of single crystals of NaCl, NaBr, NaI, KCl, KBr, and KI in cubic hydrostatic compression in the pressure range up to 10⁸ Pa at a temperature of 298°K. The experimental unit and method of measurement are described. Theoretical values of the derivatives of the elastic moduli with respect to pressure are presented for the compounds studied and are compared with existing empirical data.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 71–75, October, 1985.     

Cuspidal edges for elastic wave surfaces for cubic crystals

The paper deals with a detailed numerical study of the sections of the inverse and ray velocity surfaces for cubic crystals. The figures for the sections of the inverse and ray surfaces by the (001) and (110) planes have been plotted for over 65 crystals and from these, the nature of the cuspidal edges has been discussed. Typical graphs of the inverse and ray surfaces have been given. The parameters characterising the dimensions of the cusps have been tabulated. It is shown that the A-15 compounds exhibit very unusual and interesting wave surfaces at temperatures below superconducting critical temperatures.     

Energy estimates of twinning processes in cubic single crystals

The role of twinning processes giving rise to the fragmentation and rotation of a structure caused by single-crystal deformation, as well as the joining of grains during the manufacturing of optical ceramics, is investigated. Models describing the twins in the single crystals under study, which are formed by rotating a cubic lattice about the threefold symmetry axis through an angle of 60°, are constructed. The twin formation energies are estimated.     

Magnetic properties and phase transitions in hexagonal DyMnO3 single crystals

DyMnO₃ single crystals of hexagonal modification were grown for the first time by zone melting, and their anisotropic magnetic properties were studied in detail. At T ～ 7 K, a small uncompensated magnetic moment (～1 μ_B per formula unit) is shown to occur along the hexagonal axis. At temperatures 7–45 K, a transition from the purely antiferromagnetic state to a state with uncompensated magnetic moment was revealed; the transition is induced by a magnetic field H parallel to the c axis. This transition seems to be due to a ferrimagnetic ordering of the moments of Dy cations located in nonequivalent crystallographic positions.     

Vibronic structure and the anisotropy of excitons in cubic LiH single crystals

The shape of one-phonon sidebands of exciton in LiH is studied both in reflection and edge luminescence spectra. The main structure of the shape is found to reflect the phonon density of states. This fact is interpreted as a result of a high anisotropy of the exciton band.     

The optical constants of single crystals of hexagonal selenium

The optical constants of single crystals of hexagonal selenium in the region of the intrinsic absorption edge in polarized light were investigated. The absorption edge for light polarized normal to the optical axis of the crystal is displaced towards longer wavelengths. The absorption maximum of hexagonal selenium for a wavelength of 0·6 is interpreted as the maximum corresponding to interaction between neighbouring chains and in connection with this the position of the absorption edge of different modifications of selenium is discussed.

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In conclusion the author wishes to thank Dr. E. Klier and R. Kuel for valuable discussions and advice. He thanks laboratory assistants J. Ontl and O. Kundrátová for help in the work.     

Tensor tomography of residual stresses of hexagonal single crystals

A method for determining residual stresses in elongated transparent blanks of hexagonal single crystals the optical axis of which is directed along the crystal is proposed. It is assumed that the residual deformation tensor is of thermal character and is characterized by a fictitious temperature. Characteristic parameters of polarized light have been measured by the tomographic method in the plane orthogonal to the single crystal axis.     

The Eshelby factor for cubic crystals with arbitrary elastic anisotropy

The Eshelby factor for cubic crystals has been calculated for arbitrary anisotropy. One of the two integrations needed could be performed analytically. An expansion up to 4th order in the anisotropy and exact results for special cases are also given.     

Polarisation of the IR luminescence of cubic ZnS single crystals

The polarization of the IR luminescence of oriented ZnS crystals has been measured. None of the three main emission bands shows measurable polarization after excitation with polarized or unpolarized light. This result supports centers with symmetryT _d because they do not require any selection rules for the polarization of optical dipole transitions.     

Damage studies in cubic ZnSe single crystals grown from melt

A microscopy study of the morphology of the damage produced by TEA-CO₂ laser pulses in cubic ZnSe single crystals grown from melt is presented. The observed bulk filamentary damage consists of relatively uniformly distributed elementary damaged zones, located at specific sites where absorbing inclusions could exist. Transmission electron microscopy and laser ion mass spectroscopy investigations revealed the absorbing inclusions to be thin graphite foils, originating from the crucible used for crystal growth.     

The elastic behaviour of InBi single crystals

Ultrasonic wave velocities have been measured by the pulse echo technique at 15MHz in single crystals of InBi grown by zone-melting. The elastic stiffness constant set has been computed from the velocity data by a least-mean-squares procedure. The elastic behaviour of this metallic compound is quite different in kind from that of the semiconducting III-V crystals; the volume compressibility does not follow Keyes' generalisation for the other III-V compounds. The elastic properties of InBi have been found to show the characteristics of a layer-like crystal with weak interlayer binding; this finding is illustrated by the linear compressibilities and by a compilation of cross-sections of the wave velocity and Young's modulus surfaces. The Debye temperature is 115°K.     

Molecular forces and elastic constants of polyethylene single crystals

Polyethylene has an orthorhombic lattice for which nine elastic constants exist; they are obtained in terms of the intra- and intermolecular forces. Constants involved in the 6-12 Lennard-Jones potential approximating the London dispersion type of van der Waals' forces are obtained by computing the crystal potential energy and comparing it with the cohesive energy. First and second nearest-neighbor interactions are considered to establish relationship between the elastic constants and the interaction constants. The latter are obtained in terms of the C—C bond, stretching, bending, and repulsive force constants and the L-J potential constants. A limited type of central force assumption is applied. Values of Young and shear moduli are obtained along the three axes. The value along the chain compares with the experimentally determined and calculated values for oriented polyethylene. Young's modulus along the lateral direction is of the order of Young's modulus of bulk polyethylene, showing that intermo-lecular forces are the ones that determine the Young modulus of bulk polyethylene.