Study of the dissolution and growth of salt single crystals in inhomogeneous acoustic fields: I. A standing acoustic wave

The growth of the isolated (100) face of a KDP crystal at exposure of the phase boundary to the initial ultrasound field and a standing acoustic wave has been investigated. A significant growth response of this face, exposed to sound normally along the acoustic axis in the near zone of a piston-like half-wave vibrator with f = 20 kHz and tangentially in the pulsed two-frequency (f = 600 and 900 kHz) standing-wave mode, has been revealed. It is shown that the mechanisms of mass exchange enhancement in these acoustic modes are different. The results obtained show a fundamental possibility of controlling crystal growth and dissolution by varying the parameters of inhomogeneous acoustic field.     

Electrocrystallization of silver: Growth kinetics of screw-dislocation-free (100) crystal faces

At given conditions, especially at higher supersaturation, the growth rate of a close packed, perfect crystal face depends on the formation rate of two-dimensional nuclei and on the propagation rate of the monoatomic layers. This multinuclear multilayer growth as well as the advancement rate of growth steps have been studied experimentally on electrocrystallization of silver. The advancement rate of mono- and polyatomic growth steps has been measured on screw dislocation-free (100) crystal faces. For low overvoltages a linear dependence of the rate on overvoltage has been found. A strong influence of the surface condition of the crystal face — “fresh” or “aged” on the step advancement rate has been established. It was also found that on a “fresh” surface mono- and polyatomic steps advance with the same rate. The average monoatomic step spacing of the polyatomic step has been determined. The kinetic constants of the step growth rate are established and a conclusion regarding the mechanism of electrolytic deposition of silver is drawn. The initial current—time curves were recorded on applying potentiostatic pulses on a perfect crystal face. The shape of these curves coincides very well with those theoretically calculated for the cases of multinuclear growth. On the basis of the theoretical dependences, one can determine from these curves the formation rate J of two-dimensional nuclei at a given overvoltage η since the rate of step advancement is known. A linear dependence of log J on 1/η has been established. The values of the pre-exponential term in Volmer's equation and the specific edge energy of the two-dimensional nucleus have been determined. The surface condition of the crystal face influences strongly also the process of two-dimensional nucleation.     

Heat and mass transfer problems in solution growth of GaP crystals by the travelling solvent method (TSM)

The influence of the natural convection on the heat and mass transfer process during growth of GaP crystals from the solution is considered. The two-dimensional quasi-stationary thermodiffusive hydrodynamic problem for the GaP growth system by travelling solvent method (TSM), as a model, has been solved. Computation is given for the temperature and concentration field distribution in the solution. The picture of vortex configuration for different lengths of the liquid zone, the shape of the growing and dissolving interfaces and also the boundary layers thickness are obtained. The experimental dependence of the growth rate on the convection intensity observed mostly confirmed the calculation results.     

Heteroepitaxial growth of ZnS on GaP by the close-spaced technique

Heteroepitaxial growth of ZnS on GaP substrates was achieved with high growth rate by the close-spaced technique. Source temperatures were between 900 and 1150° C. The apparent enthalpy change of 36.6 kcal/mol obtained from the temperature dependence of the evaporation rate of source ZnS powder suggests that the material transport is carried out via the reaction between the source and hydrogen by diffusion and convection. The dependence of the growth rate on the substrate orientation is (100) > (111)Ga > (111)P, and the growth rates on these faces at a source temperature of 1000° C are about 1.6, 0.85, and 0.4 μm/min, respectively. The growth kinetics on the (111)Ga face are close to the mass transport limited case. The growth kinetics on the (111)P face are close to the surface reaction limited case, and that on the (100) face are almost the mass transport limited case. The surface morphology and X-ray analysis show that the crystal structure depends on the orientation of the substrate. The (0001) oriented α (hexagonal) modification of ZnS is obtained on the (111)Ga face, the (111) oriented β (cubic) modification on the (111)P face, and the (100) oriented β modification on the (100) face in the studied range of temperature.     

Kinetics of dissolution of potassium alum crystals in a flow cell in the presence of Fe++ cations

Dissolution rates of the {111} face of potassium alum crystals have been measured in situ in a flow cell. Dependence of the mass dissolution fluxes on the subsaturation and on the presence of Fe⁺⁺ cations has been studied. No influence of these cations over the concentration range 0–165 ppm on the dissolution kinetics has been observed. In addition, the dissolution process has been found to be of a purely diffusive character.     

Heat transfer and mass transport in a multiwafer MOVPE reactor: modelling and experimental studies

An improved detailed model for the calculation of the temperature distribution in a multiwafer Planetary Reactor™ has been developed. The temperature field of the reactor has been calculated in dependence of the reactor parameters for (Al,Ga)As growth as well as on the kind and the thickness of the wall and susceptor deposits. The amount of parasitic wall deposits can be minimized by a proper tuning of the reactor temperature distribution. Calculated GaAs growth rate profiles on 3 inch wafers show a strong dependence on the temperature field in the reactor and the amount of parasitic deposits. These predicted relationships have been used to optimize the reactor temperature distribution in order to minimize parasitic wall depositions. By this procedure a growth rate uniformity of < 1% on 3 inch wafers can be reproducibly achieved.     

Study of the growth mechanism in the ADP-type anion-doped crystals

A simultaneous simulation of the growth process in the A(K)DP-type anion-doped crystal and growing of this crystal from aqueous solution under controlled conditions has made it possible to analyse the mechanism of impurity influence on the growth rate of various crystal faces. The anisotropy of the face growth rate and the capture coefficient of various impurities by the faces have been determined by the difference in dissolution heats and in sizes of replacing ions. The increase in energy change, when the ion in a solution enters a crystal, causes an increase in the growth rate and the capture of impurities by the face with the largest change. Breaking of one of the joined faces and increased growth of another one resulted in forming of the new faces, i.e. in changing crystal morphology.     

Study of potassium titanyl phosphate (KTP) flux growth by holographic phase-contrast interferometric microphotography

This paper describes a special set of equipment we designed, which is suitable to be used to study the high temperature solution growth process by optical method. The variation regularities of the solid-liquid interface boundary layer in the potassium titanyl phosphate (KTP) crystal growth and dissolution process have been investigated by holographic phase-contrast interferometric microphotography. It has been found that under the condition of free convection, the relation between the thickness of the boundary layer and supersaturation is linear. Moreover, the variation of refractive index caused by the change of solute concentration in the boundary layer will form an exponential function of the distance from the crystal face.     

Atomic force microscopy study of lysozyme crystallization

Crystallization of lysozyme from solutions has been studied by the atomic force microscopy method. The surface morphology and the growth kinetics of several faces of the orthorhombic and monoclinic modifications of lysozyme crystals are considered. The surface images are obtained at molecular resolution. For the (010) face of orthorhombic lysozyme, the phenomenon of the surface reconstruction is established—doubling of the unit-cell parameter along the a-axis. The main growth parameters of lysozyme are determined—the kink density at steps, probabilities of the attachment and detachment of building blocks, the kink and step velocities, and the dependence of the fluctuation in the step position on time.     

Growth‐Sector Boundaries and Growth‐Rate Dispersion in Potassium Alum Crystals

Crystals of potassium alum, pure and slightly doped with Cr³⁺, were grown from aqueous solution by slow temperature lowering. In addition, short re‐dissolution periods were introduced in order to provoke growth defects and changes of growth rates. Crystal slices of about 1 mm thickness were studied by conventional LANG X‐ray diffraction topography using MoKα radiation. For Cr‐doped crystals, boundaries between {100}, {100} and {111} growth sectors appear by pronounced dynamical X‐ray topographic contrast similar to that of stacking faults. Re‐dissolution experiments provoke the formation of inclusions on {100} faces, followed by an increase of the {100} growth rate by the factor of about six, relative to the neighboured {111} faces. X‐ray topographs show that this increase is correlated with the formation of dislocations, which interestingly have pure‐edge character. During further growth these dislocations penetrate the {100}‐{111} growth sector boundary and vanish from the {100} face, which slows down and finally adopts its former growth rate before re‐dissolution.     

Crystallization kinetics of the borax decahydrate

The growth and dissolution rates of borax decahydrate have been measured as a function of supersaturation for various particle sizes at different temperature ranges of 13 and 50 °C in a laboratory-scale fluidized bed crystallizer. The values of mass transfer coefficient, K, reaction rate constant, k_r and reaction rate order, r were determined. The relative importances of diffusion and integration resistance were described by new terms named integration and diffusion concentration fraction. It was found that the overall growth rate of borax decahydrate is mainly controlled by integration (reaction) steps. It was also estimated that the dissolution region of borax decahydrate, apart from other materials, is controlled by diffusion and surface reaction. Increasing the temperature and particle size cause an increase in the values of kinetic parameters (K_g, k_r and K). The activation energies of overall, reaction and mass transfer steps were determined as 18.07, 18.79 and 8.26 kJmol⁻¹, respectively.     

Kinetics of dissolution and calcium sulphate growth on {111} faces of calcium fluoride crystals etched in sulphuric acid

The effect of temperature (20–100°C) and concentration of H₂SO₄ etching solutions on the etching behaviour of {111} faces of calcium fluoride crystals is investigated. Whisker growth of calcium sulphate is observed. Temperature of the etchant also has an effect on their formation. The kinetics of dissolution at the sites of dislocations and general dissolution have been studied. Studies on induction period and its dependence on the concentration of the acid and temperature are also described. It is observed that: (i) at low and high acid concentrations, the dissolution is diffusion controlled while it is predominantly reaction-rate controlled in the intermediate concentration range and (ii) the growth rate of calcium sulphate whiskers decreases with time and their induction period decreases with increase in the temperature of the solution. The implications are discussed.     

Kinetics of the exchanges at the solid–liquid interface during the dissolution process of gallium orthophosphate

Gallium orthophosphate is a piezoelectric material with an α-quartz structure. In order to manufacture bulk acoustic wave devices (BAW), controlled chemical dissolution is often used to reduce the thickness of the piezoelectric membranes. This paper presents the kinetics of the chemical exchanges, which occur at the solid–liquid interface during the chemical dissolution of GaPO₄ in phosphoric acid. Based on chemical composition of phosphoric acid solvent, the pure dissolution rate is determined. A strong anisotropy of chemical reactivity is formed. The dissolution rate is the lowest for the crystallographic z-plane (0 0 0 1) but this orientation is the most sensitive with respect to the proton concentration and the temperature. In accordance with the crystal growth rates, the nucleation at the interface for the (1 0 2 0) plane, named X-plane, is also the most rapidly dissolved. Assuming the activation energies corresponding to dissolution and to nucleation are like standard activation energies, the different values of the standard enthalpy variation are calculated. The most important variation is obtained for the z-plane (Δ_rH=−14.3 kJ/mol) and the lowest for the X-plane (Δ_rH=−5.4 kJ/mol).     

Thermal conductivity of glassy primary mono-hydroxylalcohols

Thermal conductivity κ(T) data for homologous series of primary mono-hydric alcohols – methanol, ethanol, 1-propanol, 1-butanol – within their molecular glass states are analyzed within the temperature region stretching from 2 K up to the glass transition T_g. Below 7 K κ(T) increases with the number of carbon atoms in the molecule. Furthermore, its temperature dependence exhibits a behavior akin to that predicted by the phenomenological model of soft potentials (SPM). The data are then rationalized in terms of the SPM parameters such as characteristic energy W and the parameter ¯С which measures the strength of the coupling of acoustic modes with two-level systems. The dependence of such parameters upon the molecular mass of the alcohol seems to agree with the SPM predictions. The parameters ¯С and W were used to calculate the boson peak energies. The values obtained agree well with literature data.     

Efficient solution of a batch crystallization model with fines dissolution

In this paper, an efficient and accurate numerical method is proposed for solving a batch crystallization model with fines dissolution. The dissolution of small crystals (fines dissolution) is useful for improving the quality of a product. This effectively shifts the crystal size distribution (CSD) towards larger crystal sizes and often makes the distribution narrower. The growth rate can be size-dependent and a time-delay in the dissolution unit is also incorporated in the model. The proposed method has two parts. In the first part, a coupled system of ordinary differential equations (ODEs) for moments and solute mass is numerically solved in the time domain of interest. These discrete values are used to get growth and nucleation rates in the same time domain. In the second part, the discrete growth and nucleation rates along with the initial CSD are used to construct the final CSD. The analytical expression for CSD is obtained by applying the method of characteristics and Duhamel's principle on the given population balance model (PBM). A Gaussian quadrature method, based on orthogonal polynomials, is used for approximating integrals in the ODE-system of moments and solute mass. The efficiency and accuracy of the proposed numerical method is validated by a numerical test problem.     

Investigation of the crystallization of the system KAl(Cr)(SO4)212 H2O under various conditions

The crystallization of the isomorphous system KAl(Cr)(SO₄)₂ · 12 H₂O under various conditions has been studied. It has been found that the rate of linear crystallization of the face (100) passes through a maximum on the interval of Cr³⁺ concentrations 0.02–0.08 g ions/l which is shifted to the right with increasing temperature. Under the same conditions, the equilibrium coefficient of distribution of the microcomponent D has been determined in single crystals. D decreases with the increase of the Cr³⁺ concentration and the crystallization temperature. These results can be explained with the formation of complexes of Cr³⁺ in the solution which decreases the active concentration of the ion and are selectively adsorbed on the face (100). At the same Cr³⁺ concentration (0.058 g ion/l), the temperature dependence of the rate of growth of the face (100), as well as the influence of supersaturation on the rate of growth of the faces (100) and (111), have been studied. The apparent activation energy of crystallization of the face (100) has been determined to be E = 11.2 Kcal. · mol⁻¹. The data obtained are compared with analogical results for pure KAl(SO₄)₂ 12 H₂O.     

Influence of phenol on the habit of sodium chloride crystals

The influence of phenol on the habit of sodium chloride crystals was studied quantitatively. At small concentrations the presence of phenol has no influence whatsoever on the growth rate of the (100) face. At greater concentrations this growth rate increases. Spiral growth was observed on the (100) face by surface dissolution. Phenol slows down the growth rate of the (111) face, the energy barrier being about 600 cal/mole. Roughening of this face is observed when crystallization takes place from pure solutions and in the presence of small amounts of phenol. At a phenol concentration of 0.065 mole/l the growth rates of the (100) and (111) faces become equal.     

The role of stress on initial stages of crystal growth

Crystallization in undercooled melts is accompanied by development of stress energy, due to the difference in volume of the new system as compared to the ambient phase. Therefore, the growth rate decreases with time. Here, the non-stationary differential equation is solved, accounting for the production of energy of stress deformation as well as for its reduction caused by relaxation. In this way the growth rate and the dependence of crystal size on time are obtained. The change of the growth rate is significant when new formed phase has composition different from the ambient phase, so that particles, creating the new phase can move much faster the main molecules of the matrix. A steady state is determined by the condition that the rate of stress energy production is equal the rate of stress energy consumption. The degree to which the stationary growth rate U_st is reduced as compared to the initial growth rate U_max is controlled mainly by the ratio of the self-diffusion coefficient of the building units to the diffusion coefficient of the building units creating the new phase. A clear break in the size versus time dependence of the growing crystal is seen.     

Marangoni Convective Effect during Crystal Growth in Space

GaSb:Te and GaInSb samples have been solidified under microgravity conditions during the D2 Spacelab mission. Experimental design and parameters are described. Analysis of the thermal data taken during the flight, associated to numerical simulations of heat transfer in the experiment, with the help of FIDAP, gave the experimental conditions (thermal gradients and growth rate). Quantitative chemical analyses of the samples show a chemical segregation characteristic of strong mixing in the melt during crystal growth. Silica crucibles with an internal screw thread groove on the inner wall were used in order to get dewetting of samples from the crucible. It was therefore supposed that Marangoni convection on the free surface associated to the groove might have been the source of convection. This hypothesis has been studied by numerical simulation using FIDAP and the velocity field obtained is in agreement with a strong perturbation of the solutal boundary layer ahead the solid-liquid interface. This can explain the observed chemical segregation.     

Oxygen and carbon transfer during solidification of semiconductor grade silicon in different processes

A model is established for comparing the solute distribution resulting from four solidification processes currently applied to semiconductor grade silicon: Czochralski pulling (CZ), floating zone (FZ), 1D solidification and electromagnetic continuous pulling (EMCP). This model takes into account solid–liquid interface exchange, evaporation to or contamination by the gas phase, container dissolution, during steady-state solidification, and in the preliminary preparation of the melt. For simplicity, the transfers are treated in the crude approximation of perfectly mixed liquid and boundary layers. As a consequence, only the axial (z) distribution can be represented. Published data on oxygen and carbon transfer give a set of acceptable values for the thickness of the boundary layers. In the FZ and EMCP processes, oxygen evaporation can change the asymptotic behaviour of the reference Pfann law. In CZ and in 1D-solidification, a large variety of solute profile curves can be obtained, because they are very sensitive to the balance between crucible dissolution and evaporation. The CZ process clearly brings supplementary degrees of freedom via the geometry of the crucible, important for the dissolution phenomena, and via the rotation rate of the crystal and of the crucible, important for acting on transfer kinetics.