Thin Crystal Plates Research Articles

High Resolution Electron Micrographs of Crystalline beta‐Cyclodextrine

AbstractThe electron microscopic picture of thin crystal plates of BCD, obtained at a magnification of 1.5 million, shows a linear structure with a periodicity of 14.5 A. At a magnification of 2 million, structural units, corresponding to cyclodextrin rings, can be observed.

Proposal of a Fabry-Perot-type interferometer for x-rays

A Fabry-Perot-type interference filter for x-rays is proposed, where thin crystal plates are used as Bragg reflectors at normal incidence. The plates are cut from a perfect silicon crystal leaving a thin gap which may be filled with an appropriate immersion liquid. The calculated resolution of the transmitted beam isE/ΔE≈5 × 107, corresponding toΔE≈4 ×10−4 eV. A possible layout of a high-resolution x-ray spectrometer based on Fabry-Perot-type interferometers is discussed.

Specific directions of plane elastic waves in thin LiTaO3and LiNbO3crystal plates

When plane clastic waves propagate in specific directions in an anisotropic medium, they can satisfy the conditions of pure longitudinal and transverse plane elastic waves. The purpose of this paper is to find all the specific directions in which pure elastic waves propagate in thin LiTaO3 or LiTaO3 crystal plates. The result, is that all the specific directions for pure plane elastic waves in thin LiTaO3 and LiNbO3 crystal plates have been thoroughly analysed.

Optical properties and electronic structure of UO2

The near normal incidence reflectivity of UO2 single crystals has been measured in the photon energy range from 0.03 eV to 13 eV. From the reflectivity spectrum the complex dielectric function ε (ω) =ε1(ω)+iε2(ω) has been derived by means of the Kramers-Kronig relation. In addition the absorption coefficient was determined from a direct transmission measurement on thin single crystal plates in the weakly absorbing spectral region below the absorption edge. An energy level scheme is proposed which allows a self-consistent assignment of the structure in ε2 with optical transitions between maxima in the density of states. The energy gap found at 2.1±0.1 eV is attributed to a 5f2→5f16deg transition. A crystal field splitting 10Dq=2.8 eV is derived for the 6d conduction states. Good agreement is obtained within this model with XPS measurements and a recent molecular cluster approximation. It disagrees with a previous interpretation of reflectivity data.

Helical magnetic structure in CrB 2

A cycloidal magnetic structure was discovered in CrB 2 by neutron diffraction using a thin single crystal plate prepared with natural boron. The propagation vector was determined to be τ = 0.285 τ 110. The magnetic moments of a magnitude of 0.5 ± 0.1μ B turn in the a−c plane.

TIME EFECTS IN 57Fe NMR IN YFeO3

The NMR of 57Fe has been studied in a thin single crystal plates of YFeO3 by spin echo and steady-state methods at the temperature range of 1.8-450 K. The observed signals undergo a change after the application of a weak magnetic DC field. The new state is unstable. The recovery time at 77 K is about 0.5 h and decreases with increasing temperature. Below 77 K these effects disappear. In the unstable state enhancement factor η is twice as large as before the field application. Spin echo signal does not increase but the amplitude of radiopulses required for the forming of spin echo signal decreases. This fact suggests that the volume of domain walls decreases. At 1.8 K some features characteristic for the phase transition were noticed.

A high-resolution X-ray topographical technique for thin flexible crystal plates

A new technique for high-resolution X-ray diffraction topography is described, which is specially applicable to the examination of thin crystal slices of large area in symmetric transmission. The crystal plate is slightly curved so that the whole area can selectively diffract a single wavelength from an X-ray beam divergent from a distant point source. For the case of symmetric transmission, image contrast is identical to that obtained from the conventional Lang technique. Resolution equivalent to that of the Lang technique is obtained in a small fraction of the exposure time. The method is restricted to materials in which the defect distribution is not strongly dependent on macroscopic strain. The method is illustrated by application to silicon crystals used in semiconductor device manufacture. Process-induced curvature can to some extent be compensated.

Flexural, Width-Shear, and Width-Twist Vibrations of Thin Rectangular Crystal Plates

Flexural, Width-Shear, and Width-Twist Vibrations of Thin Rectangular Crystal Plates

High-Frequency Vibrations of Crystal Surfaces, Plated with Electrodes

In a recent paper (M. C. Dökmeci, to be published in J. Math. Phys.), we established a variational theorem for linear piezoelectricity and then constructed a theory of piezoelectric crystal surfaces. This theory is now extended to include the effects of the elastic stiffness and inertia of the electrodes in crystal shells completely coated with electrodes on both faces. Each of the electrodes may have different thickness and material properties, and each is assumed to be perfectly conducting. Starting with the local equations of linear piezoelectricity and using an averaging procedure, we establish the two-dimensional dynamical theory of plated crystal surfaces for the case when the mechanical displacement and electric potential fields are taken to vary linearly with respect to the thickness coordinate. The interactions between the crystal shell and its electrodes are taken into account. Further, we study some special cases of practical importance such as very thin electrodes and crystal plates [cf. R. D. Mindlin, in Progress in Applied Mechanics (Macmillan, New York, 1963), p. 73, and H. F. Tiersten, Linear Piezoelectric Plate Vibrations (Plenum, New York, 1969)], and present the theorems of uniqueness in this theory. [Work supported by the U. S. Office of Naval Research.]

Extensional, Flexural, and Width-Shear Vibrations of Thin Rectangular Crystal Plates

An approximate one-dimensional theory is derived for thin crystal plates or bars with narrow rectangular cross section, and for cases in which the stiffness matrix of the crystal cij referring to the plate axes exhibits monoclinic symmetry. A set of five equations of motion is separated into two groups: the extensional, width-length flexural, and width-shear motion; and the transverse shear and width-twist motion. Closed form solutions of coupled extensional, flexural, and width-shear vibration are obtained for thin rectangular plates with free edges. Calculated resonant frequencies as a function of length-to-width ratio of the plate are compared with detailed measurements by Spears on +5° X-cut quartz plates. For the use in design, explicit algebraic formulas for predicting extensional and flexural frequencies are obtained in terms of elastic stiffnesses, density, and width-to-length ratio of the plates.

電析金膜の初期析出成長機構

The mechanism of initial formation and growth of Au plate crystals on Fe single crystals or polycrystals electrodeposited from hydrochloric auric chloride bath was examined by electron microscopy.The results obtained were as follows:(1) The population of nuclei or micro-particles of Au electrodeposited in the initial stage of deposition was about 3×1011cm-2. On further deposition, Au micro-crystals were connected one another by feather-like thin plate crystals and were formed into islandshaped or net-work structure.(2) The Au micro-particles of scores of Å in size gave a spotty diffraction ring pattern and the Au plate crystals gave distinctly arced or spotty arced diffraction pattern.(3) The stable coherency between the Au plate crystals and Fe substrate was formed when the surface coverage was about 80%. The coherency was as follows:(001)Fe//(001)Au [110] Fe//[010]Au}(4) The plate crystals at the stage of the surface coverage of 85% had many sub-grains of 150-400Å in diameter. With the progress of electrodeposition, the diameters of the sub-grains were increased.(5) In the plate crystals, there were some Au particles having crystal orientations different from those of the plate crystals.(6) In the plate crystals, there were observed many microtwins, which contributed to the relaxation of strain in Au plate crystals.

A qualitative X-ray diffraction study of the 205°K and 151°K phase transformations in praseodymium aluminate (PrAlO3)

PrAlO3 undergoes a first-order phase transformation at 205°K, and a second order transformation at 151°K. Single crystal X-ray measurements at 293°K, 172°K, and 135°K display the Laue symmetries \overline 3m, mmm, and 2/m respectively. With a specimen ground to a thin crystal plate, and mounted with minimal mechanical restraints, the 205°K transformation was single crystal to single crystal; the 151°K transformation was single crystal to twinned crystal. Both transformations were completely reversible with no sign of fatigue; the twinned crystal always transformed back to a single crystal. The true space group symmetries of the low temperature phases are masked by the effects of two types of domains on the observed intensities. The most probable space groups, expressed in unconventional orientations to preserve continuity with the ideal perovskite structure, are: at 293°K F\overline 32/c, α = 90°21′, V/8 = 53.56 Å3, at 172°K I112/m, γ = 90°, V/4 = 53.22 Å3, at 135°K I\overline 1, α = γ = 90°, β = 90°40′, V/4 = 53.02 Å3. To unravel the true symmetries it was necessary to solve all three crystal structures. The first order transformation is characterized by a shear of (0k0) planes along the rhombohedral [101] direction to form an orthogonal space lattice. The AlO6 groups are rotated into new orientations and Pr atoms are subjected to displacements which are normal to the shear direction. The Pr displacements lower the symmetry from orthorhombic to monoclinic even though the space lattice is orthogonal. The second order transformation is characterized by a shear of (00l) planes along ±[100] in the orthogonal space lattice to form twinned monoclinic space lattices. The AlO6 groups do not assume new orientations. The Pr displacements are increased, again in directions normal to the shear directions. Because of the Pr displacements the symmetry is triclinic even though the space lattice is monoclinic.

An optical lever for thickness determination of thin crystal plates

An accurate instrument is described which is suitable for thickness measurements on crystals in the range 1-100 μm. The optical lever principle is employed and the instrument is completely portable and self-contained. Crystal thickness may be determined to within 01 μm.

Infrarotdichroitische und sonstige infrarotspektroskopische Untersuchungen an Resorcin

The infra-red spectra of oriented polycrystalline layers from α- and β-resorcine and of thin single crystal plates from α-resorcine have been measured with polarized radiation. In addition we have studied the solution of resorcine in H 2O, the crystal spectrum of C 6H 4(OD) 2 and the solution of the latter in D 2O. The interpretation of the dichroic measurements is based on the known crystal structures. It is shown that applicability of the “oriented gas model” may be deduced from the absence of band splitting in the spectrum.

Infrared spectra of some scheelite structures

The infrared spectra of powdered samples of CaWO 4, CaMoO 4, PbWO 4 and PbMoO 4 have been recorded from 1000 to 60 cm −1. The spectra of thin single crystal plates of these specimens have also been recorded from 2000 to 1000 cm −1. All the infrared active fundamental modes have been assigned. Similarities and differences between the infrared and the previously reported Raman spectra are discussed in the light of intermolecular coupling between the modes and the frequency dependence upon the phonon wave vector.

Perturbation Solution of Plane Stress Problems in Anisotropic Elasticity

The problem on the approximate determination of the mean stress distribution across a thin crystal plate by the method of perturbation is considered. The plate is free from surface tractions and body forces, but is stressed under the action of prescribed self-equilibrating edge forces. The anisotropic elastic compliance matrix $S_{IJ} $ is written in the form $S_{IJ} = S_{IJ}^0 + \epsilon S_{IJ}^ * $, where $S_{IJ}^0 $, is the isotropic elastic compliance matrix nearest to $S_{IJ} $. A power series expansion in $ \epsilon $ is then assumed for the Airy stress function from which the stress components may be derived. The problem of the zeroth order in $ \epsilon $ is that of an isotropic plate. The perturbed problems satisfy nonhomogeneous differential equations and vanishing stress boundary values. The 7090/94 Ibsys Formac programming is used to handle some of the tedious algebraic and analytic routines involved in developing the perturbation solutions. Application of the perturbation method is carried out explicitly for a circular plate.

Curling of crystals of 2,5-di-t-butyl-1,4-dimethoxybenzene during growth

A further study has been made of the curling during growth of thin crystal plates of 2,5-di-t-butyl-1,4-dimethoxybenzene, and this behaviour has been related to the approximate structure of the compound deduced from its optical properties. It is suggested that the curling may be due to differential adsorption of the solvent on opposite faces of the plates.

Experimentelle Untersuchung der ?erenkov-Strahlung in optisch einachsigen Kristallen

The relative yields of Cerenkov radiation produced by theβ-rays of P32 by passing through a thin uniaxial crystal plate have been investigated experimentally with the aid of a fast coincidence and a linear gate circuit. Measurements were performed with electrons moving (a) parallel to the optic axis of the uniaxial crystal plate and (b) perpendicular to the optic axis. The experiment showed that the yield of Cerenkov radiation when the electrons moved parallel to the optic axis of the crystal was about 15% higher than in the case of the electrons moving perpendicular to it. This is in good accordance with theory.

Die Polarisation der Fluoreszenz organischer Szintillationskristalle bei Anregung durch?-Strahlen

The polarisation of the fluorescence spectra of the organic scintillation crystals naphthalene, anthracene, terphenyl, quaterphenyl and stilbene is measured by excitation with α-particles. The measurements are carried out with thin crystal plates of different crystallographic orientation and for different angles of incidence of α-particles. Careful experiments showed that the polarisation values of anthracene do not depend on the angle of incidence of α-particles. A simple model is proposed for explaining the results and the polarisation values are discussed and compared with corresponding values of UV-investigations of other authors.

Hole injection into CdS from Cu 2S

Diodes consisting of cuprous sulphide (Cu 2S) in contact with cadmium sulphide have been prepared by the evaporation of Cu 2S onto thin CdS plate crystals and current-voltage and electroluminescence measurements have been made on them. The forward characteristics are interpreted on the basis that up to a threshold voltage the electron current is primarily space-charge limited and the hole current is recombination limited in the CdS bulk; at the threshold voltage, the hole transit time becomes of the order of the hole lifetime and double injection currents occur, as predicted by Lampert; the Cu 2S-CdS barrier then mainly controls the current. On the basis of this theory, hole lifetimes lying between 1·0 and 2·0 × 10 −8 sec have been deduced for six specimens. Long wavelength electroluminescence under forward bias has been observed which is linear in current, in agreement with theory for transitions taking place via a deep state.