A phase field model with electric current

A diffuse interface model is presented for the solidification or melting of a pure single crystal that includes the effect of an applied electric current. A coupled set of differential equations modelling the evolution of the phase, the temperature and the current density are derived by applying principles of non-equilibrium thermodynamics. An asymptotic analysis shows that as the diffuse interfacial region tends to zero thickness, classical results are recovered. For this model classical results mean that Joule heating and the Thomson effect in the bulk phases and the Peltier effect at the interface are included. A one-dimensional numerical solution is presented and compared to an analytical solution verifying the model and asymptotic analysis. This phase field model is relevant for solid–liquid phase changes occurring in pure metallic and semi-conductor materials.     

On the electrochemical behaviour of undercooled melts and glasses

The electrochemical behaviour of undercooled melts and glasses is considered in detail. First the thermodynamic properties of the corresponding phases are calculated and then the temperature course of the emf and of other thermodynamic functions of a galvanic cell in which the net reaction is: undercooled melt (glass)→crystal, are determined. Some additional problems concerning the electrochemistry of amorphous electrodes are analyzed, e.g. hydrogen overvoltage upon hydrogen evolution on crystalline or amorphous electrodes of a given metal. Several variants are discussed for the possible experimental realization of a galvanic cell in which the emf is determined by the difference in the chemical potentials of the undercooled melt (or the glass) and the crystal, i.e. of a galvanic cell with a vitreous and a crystalline electrode made of one and the same electronic conductor or of a bipolar cell with an amorphous and a crystalline electrolyte, etc. An attempt is made to estimate the interal electric (Galvani) potential at the melt/crystal interface by using data for the difference of the Peltier coefficient between the respective phases.The analysis of the electrochemical behaviour of vitreous, liquid and crystalline electrodes is performed on the basis of formal thermodynamics and in terms of classical model approaches. It is shown how to determine by electrochemical measurements the main thermodynamic parameters of glasses which are considered as frozen-in non-equilibrium systems.     

A new method of studying anisotropy of crystals

A new method is proposed of studying the anisotropy in crystal wafers cut out in respective orientations. For this purpose the TWYMAN effect, discovered in 1905 in the processing of optical glass, is used. It is shown that this effect, the physical nature of which is described in detail in another work of ours, is in force also with crystal wafers which bend to a strictly spherical surface in an isotropic state and to a characteristic ellipsoid surface in an anisotropic state. In the latter state a definite ratio exists of the large to the small axis of the ellipsoid, characterising the anisotropy of a given orientation.     

Piezoelectricity Effect Detector

An apparatus for the detection of the piezoelectricity effect in non-conducting crystals is described. It is possible to mark the crystal resonance frequency and show the resonance curve on the oscilloscope, both with or without mechanical contact between the crystal and electrodes. For the urotropine crystals the section of the surface of the longitudinal piezoelectric effect with (110) plane was determined without mechanical contact.     

Steroid motor: dynamics of cholesteric helix induction in the nematic droplet

A nematic liquid crystal can be converted into a cholesteric phase by a chiral dopant, and the cholesteric pitch can be changed by its photochemical transformations [1]. For the first time we investigate the dynamics of the cholesteric phase induction using seven steroids (vitamin D isomers and related compounds) as chiral dopants. Here we report the new effect of rotation of a rod-like steroid crystal (0.1-1 mm length) when it is placed at the surface of a nematic drop and its dissolution course was followed with a polarizing microscope. For all the compounds univocal correspondence was noticed between the crystal rotation direction, the helicity of the molecular steroid ring system [2] and the sign of the cholesteric macrohelix determined by the Cano-Grandjean method [3]. No rotation was observed in the isotropic phase.     

Study of Formation,Phase Behavior,and Microdroplet Size of a Polyurethane-based Polymer-dispersed Liquid Crystal

Using calorimetry and scanning electron microscopy, we have investigated the formation process and phase behavior of a polyurethane-based polymer-dispersed liquid crystal system. We have measured the kinetics and energetics of the cure process during which liquid crystal microdroplets form by phase separation from the matrix as it cross-links. The greatest degree of cure occurs for samples cured at 375 K. For a given cure temperature, the heat of cure decreases more or less linearly with increasing liquid crystal concentration due to a dilution effect. The time constant for the cure process decreases rapidly with increasing temperature but is much less sensitive to liquid crystal content.

Samples cured below 375 K are apparently not fully phase separated, but subsequent treatment at higher temperatures evidently increases the degree of cure. The highest nematic-isotropic transition temperatures were achieved for liquid crystal concentrations above 40 volume percent. The nematic isotropic transition enthalpy, ΔH_NI, is a measure of the amount of liquid crystal contained in the microdroplets. A model has been developed which explains the linear increase of ΔH_NI with increasing liquid crystal concentration.

Optimum microdroplet formation occurs at 375 K, but only for liquid crystal concentrations below about 53 volume percent. At higher concentrations a reversed phase (“polymer ball”) morphology is seen. For the lower concentrations droplet size increases linearly with LC content. Droplet number density decreases with increasing droplet size in rough agreement with a simple model.     

Die Bedeutung mechano-elektrischer Erscheinungen für die Bestimmung der Oberflächenenergie von Kristallen

Using the method of crystal cleaving a calculation of the surface free energy of mica is given. For this an effective elastic stiffness constant is introduced, this taking into consideration the electrostatic charging of the crystal surface. For measuring the charges arising from the cleaving of the crystal a special experimental equipment is used. Microgeometry and mechano-exoelectronic flow are determined. With sufficient high vacuum the latter becomes the main process of stabilizing instable electric crystal surfaces. The electrostatic charging only little affects the values of measured surface energies. The deformation, however, of layers near the surface gives a larger effect. Considering this deformation a surface free energy of 380 erg · cm⁻¹ for mica is given.     

石英晶体板非线性高频振动的拓展伽辽金法分析

针对考虑几何和材料非线性的石英晶体板厚度剪切振动和弯曲振动的方程组,利用扩展伽辽金法对该方程组进行转化和求解,分别获得了强烈耦合的厚度剪切振动模态和弯曲振动模态的频率响应关系,绘制了不同振幅比和不同驱动电压影响下的频率响应曲线图。数值计算结果表明可以选取石英晶片的最佳长厚比尺寸来避免两种模态的强烈耦合。驱动电压的变化将引起石英晶体谐振器厚度剪切振动频率的明显改变,必须将振动频率的漂移值控制在常用压电声波器件的允许值之内。扩展伽辽金法对石英晶体板非线性振动方程组的求解为非线性有限元分析和偏场效应分析奠定了基础。     

The Analysis of Growth Kinetics in Liquid Phase Electroepitaxy (LPEE) of binary systems

Growth kinetics of binary systems in liquid phase electroepitaxy (LPEE) is analysed in terms of one-dimensional forced diffusion with initial and boundary conditions reflecting the features of various modifications of LPEE. Electromigration of a solute in the melt and the Peltier effect at the interface between liquid and solid phases induced by electric current are taken into account. Three LPEE modifications are considered here. The first modification is when liquid phase is constantly riched due to dissolution of the semiconductor cathode. The second one-when liquid phase is constantly riched from vapour phase by controlled vapour pressure. The third one-when any source of the melt enrichment is absent. This consideration is limited by the assumption that the deviation of the solution heighs or convection doesn' affect the steady-state temperature at the interfaces between solid and liquid phases. The obtained expressions for growth rate show that quantitative results of the epitaxial growth are closely connected with a concrete method of LPEE realization.     

Thermal radiation and low-temperature-vapour growth of HgI2 crystal in production furnace

Heat exchanges in a sealed ampoule in the LTVG (low temperature vapour growth) furnace have been modelled in order to compute temperature fields and control the growth of HgI₂ crystals from vapour phase at low temperatures. We use a coupled conductive-radiative model to determine the shapes of the source and the crystal at different equilibrium states (i.e. without growth rate). The model involves conductivity anisotropy in the crystal and radiative exchanges between grey and diffuse surfaces (source and crystal interfaces, Pyrex walls), which are considered as opaque. Internal buoyancy effect is not taken into account as the pressure inside the ampoule is very small. The source temperature is fixed. For different undercoolings, i.e. for different cold finger temperatures, the “equilibrium” isotherm between the source/gas and crystal/gas interface has been numerically obtained. This “equilibrium” isotherm, which is associated with the stop of the growing process, gives a crystal shape. This shape is compared with experimental results given by the ETH-Zürich group. The model would permit a better understanding and control of the future HgI₂ crystal growth experiment. The computations are performed using a finite element package (FIDAP).     

Determination of Mass Transfer Coefficients for Crystal Growth of Nitrate Salts

In this paper, the crystal growth of sodium nitrate and potassium nitrate from aqueous solutions, in a perfectly stirred batch crystallizer, has been studied considering the effect of temperature, supersaturation degree, and the size of seed crystal growth rate. The mass transfer coefficients obtained correlated with Re, Sc and NL dimensionaless numbers. Supersaturation curve determination using a 0.5 mW He-Ne laser, connected to an automated data acquisition system, was the first stage of the study. The supersaturation and saturation curves were closely parallel with average DT value of 4.1 and 6.8 °C for KNO₃ and NaNO₃ respectively. For the growth kinetics order, unit values were found for both salts, with diffusion as a controlling stage.     

Effect of orientation on the microstructure of nickel‐based crystalline superalloys

The effect of crystal orientation on the microstructure of a nickel‐based crystalline superalloys during directional solidification was explored. Differently oriented crystals with [001] and [011] orientations were fabricated with seeding technique. The results showed that primary dendrite arm spacings decreased simultaneously with the increase of misroientation. The primary dendrites arrange in lines in [011] single crystal. For [001] oriented crystals, the size of γ′ phase increased with the increasing of misorientation. However, it was observed that the size of γ′ decreased with large misorientation for [011] orientated growth. Meanwhile, more γ′ in [011] crystals tended to be triangular. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Crystallographic defects in epitaxial layers of cadmium sulphide

Thin epitaxial films of CdS deposited in high vacuum on ionic single crystal substrates have been studied by transmission electron microscopy. The (100), (110) and (111) faces of NaCl and the (111) face of BaF₂ were used as substrate surfaces. Both cubic sphalerite and hexagonal wurtzite structure films have been produced. The orientations of the sphalerite structure films were (100) and (110) and were produced on substrate faces having the same two orientations. The wurtzite structure films were in (0001) orientation and grew on (111) oriented substrate faces. For a fixed rate of deposition both the number and type of defects found in the films appear to be dependent upon the growth temperature and the crystal structure. Annealing the films at a high temperature has been tested as a means for reducing their defect content and the effect is very different for the two crystal structures. A reduction in the defect content of the wurtzite structure films is induced but no change in the crystal structure occurs. In contrast to this, the sphalerite structure films undergo a progressive phase transformation to the wurtzite stucture while at the same time losing a high proportion of their defects.     

The X-ray method for the determination of damaged layer thickness of the Si crystal surface

In this paper the X-ray section topograph method was used for determination of damaged layer thickness of silicon crystal surface. For measurements such reflections should be chosen for which the “margine” effect is very sharp. It was used the fact that in the ranges of strong perturbances the approximation of kinematic theory could be applied.     

Spatial distribution of piezoinduced change in the optical pathlength in lithium niobate crystals

For the first time, the “indicative” surfaces of the constants of the piezooptic effect and their stereographic projections have been constructed with due regard for crystal elasticity for lithium niobate crystals described by the symmetry class 3m. The comparative analysis of these surfaces and the corresponding surfaces of the true piezooptic effect has been performed.     

Explanation of some peculiarities of crystal morphology deduced from the BFDH law

The morphological variety of crystal habits is due to differences in relative growth rates of faces of which the crystal is composed. For equilibrium, the growth rates of faces are proportional to the distances from the centre of the crystal to the respective hkl faces. According to the BFDH law, such distances are inversely proportional to the interplanar distances, therefore the observed crystal faces are those with the largest interplanar distances. This paper tries to explain some peculiarities of the crystal morphology deduced from the BFDH law and shows that the crystal geometry influences morphological importance of faces and because of crystal geometry, the faces of the largest interplanar distances are not necessarily the largest faces in the BFDH morphology.     

Analyses of Crystal Shape Monitoring of LEC-Grown InP Crystals by using a Disc Approximation Approach

This paper analyzes crystal shape monitoring for automatic diameter control (ADC) during the liquid encapsulated Czochralski (LEC) growth of InP crystals. The crystal diameter (shape) is monitored numerically (diagrammatically) by using a disc approximation approach based on precise weight and pulling length measurements. The error in the diameter calculation based on the approximation is estimated to be sufficiently small for practical use. The monitoring accuracy was investigated for crystal bodies with nearly flat growth interfaces, and for their shoulder portions with largely convex growth interfaces. For the straight body portions, the accuracy depended on diameter, d, and improved from ±15% for d=10 mm to ±3% for d=50mm. For the shoulder portions, the diameter was monitored with nearly the same accuracy. This method has therefore made it possible to monitor the growing crystal visually in real time, and was applied to the growth of <111> InP crystals with a cone angle of less than 39° and a smooth appearance to avoid twinning.     

Stability of faceted growth forms from melts and in the presence of impurities

Transition from regular polyhedron to skeleton shape for crystals growing from melts is considered. This transition is due to the lower undercooling in central parts of facets as compared with vertexes. It is the growth rate anisotropy which withstands to that undercooling inhomogeneity. For very strong anisotropy the stability criterion is determined as the crystal size above which the undercooling in the centers of facets approaches zero. For arbitrary anisotropy the stability criterion presents the relationship between crystal size and small distortion of facets.     

Behavior of a nematic liquid crystal in oscillatory flow at weak surface anchoring

The effect of the surface viscosity on the orientational dynamics of a nematic liquid crystal in an oscillatory flow has been studied. For the shear and the Poiseuille flows, the approximate analytical solutions of the nematodynamic equations are obtained at small flow amplitudes. The frequency range of the oscillatory flow is determined, in which the surface viscosity strongly affects the optical response of a nematic layer. The results obtained are compared with the data of direct numerical simulation of the nematodynamic equations and the method for the experimental determination of surface viscosity is proposed.     

Externe Kristalljustierung für die Lang-Topographie

In dependence on crystal altitude, Bragg angle and distance focus-crystal the necessary accuracy of crystal adjustment is calculated on condition that with illumination of the full crystal height the Kα-doublet is separable. In this connection a critical crystal altitude for the Lang-topography is stated, which requires a faultless adjustment of the net plane. For the real altitude of crystal resp. film adequate demands for adjustment are derived. A simple diffractometer device for external crystal adjustment if described and the attainable accuracy is indicated.