Kinetics of Mixed Crystal K2(SO4, CrO4) Growth from Aqueous Solution

The investigation of crystal growth kinetics and phase equilibria in the system K₂SO₄–K₂CrO₄–H₂O was carried out using the method for the determination of the saturation temperature and the growth rate by microscopic observation of the seed crystal behaviour. The kinetics of mixed crystal growth can be characterized by the expression V = 450.24σ^1,6,2, where σ is the value of effective supersaturation of the solution calculated by taking into account the specific features of the phase equilibria diagram. Use of this criterion allows the control of the rate of delta crystal growth from solutions of variable composition.     

Kinetic studies on the influence of temperature and growth rate history on crystal growth

Crystallization experiments of sucrose were performed in a batch crystallizer to study the effect of temperature and growth rate history on the crystal growth kinetics. In one of the growth methods adopted, the isothermal volumetric growth rate (R_V) is determined as a function of supersaturation (S) at 35, 40 and 45 ºC. In the other, crystals are allowed to grow at constant supersaturation by automatically controlling the solution temperature as the solute concentration decreased. Using the latter method R_V is calculated as the solution is cooled. The obtained results are interpreted using empirical, engineering and fundamental perspectives of crystal growth. Firstly, the overall activation energy (E_A) is determined from the empirical growth constants obtained in the isothermal method. The concept of falsified kinetics, widely used in chemical reaction engineering, is then extended to the crystal growth of sucrose in order to estimate the true activation energy (E_T) from the diffusion‐affected constant, E_A. The differences found in the isothermal and constant supersaturation methods are explained from the viewpoint of the spiral nucleation mechanism, taking into account different crystal surface properties caused by the growth rate history in each method. Finally, the crystal growth curve obtained in the batch crystallizer at 40 ºC is compared with the one obtained in a fluidized bed crystallizer at the same temperature. Apparently divergent results are explained by the effects of crystal size, hydrodynamic conditions and growth rate history on the crystallization kinetics of sucrose. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The crystallisation of chromite-magnesiochromite spinels from a calcium magnesium aluminosilicate glass: Nucleation,crystal growth and final crystal sizes

The crystallisation of chromite-magnesiochromite spinels was studied from a calcium magnesium aluminosilicate glass (a simulated slag) containing 3 to 12 percent total iron oxides and 0.3 to 1.5 percent chromium(III) oxide, at temperatures from 1400° to 700 °C. – Spinel crystallisation occurred in glasses with 3–7 percent FeO and 0.7–1.1 percent Cr₂O₃. At temperatures 1100 °C and above, the nucleation was rapid and crystal numbers very high, at FeO contents above 3 percent and Cr₂O₃ contents above 0.7 percent; at 1056° and 1000 °C however, the crystal numbers reached some optimum values but then decreased as clinopyroxene crystals grew onto and enveloped the spinel microcrystals. In these glasses, the crystal lengths varied with growth time according to the relation, l_t = 2 k_g t^α = R_g1 t^α, where α = 0.7–1.0: this time dependence was a compromise between a relation for dendritic growth and one for facetted growth. The growth rates generally increased about five to seven times for 160 °C temperature rise: the energy of activation for the spinel crystal growth was then estimated as 180 ± 60 kJ mole⁻¹. – No spinel crystals were observed in glasses with more than 7 percent FeO content, only clinopyroxene crystals. Probably, these latter had nucleated rapidly and grown onto spinel microcrystals, while the spinel microcrystals were still of < 0.1 μm size.     

Kinetics of crystal growth of strontium tungstate from solutions in sodium tungstate melts by continuous cooling

The crystallisation kinetics of strontium tungstate from unstirred saturated solutions in sodium tungstate melts was studied by continuous cooling from initial crystallisation temperatures T₀ = 1000° to 800°C to room temperature at cooling rates R_T = 0.67° to 3.3°C min⁻¹. The main crystal growth was diffusion rate-controlled; the final crystal growth was rate-controlled by the development rate of excess solute concentration. The estimated diffusion rate constant (k_D) values increased with cooling rates and initial crystallisation temperatures. They are higher than the rate constants for diffusion-controlled growth of calcium tungstate from sodium tungstate melts, but very much smaller than those for strontium tungstate from lithium chloride melts.     

“Crystallization E.M.F.” Investigation in the lithium niobate pulling process from the melt

E.M.F. in the lithium niobate crystal-melt system as a function of pulling and rotation rates, crystal diameter and orientation was determined. Total E.M.F. is a sum of thermo-E.M.F. and “crystallization E.M.F.” Δφ. The logarithmic approximation Δφ = Δφ₀ In (1 + /v₀), where v is a growth rate, Δφ₀ = 3.9 mV, v₀ = 1.9 mm/h is adequate. The Δφ magnitude is independent within the experimental error on the rotation rate and crystal orientation, whereas it is slightly increasing along with the diameter increase. Some existing models of electric phenomena accompanying crystal growth are discussed and a new model based on charge carrier injection into solid during growth is proposed.     

Polymorphic single crystal ↔ single crystal transformations in Rb0.975Cs0.025NO3

The crystal growth morphology of modifications IV, III, II, and I during the IV ↔ III ↔ II ↔ I polymorphic transformations in Rb_0.975Cs_0.025NO₃ has been investigated by optical microscopy. The equilibrium temperatures between phases IV and III (T ₀ = 393 ± 0.5 K), III and II (T ₀ = 421 ± 0.5 K), and II and I (T ₀ = 497 ± 0.5 K) of the crystal studied have been determined. It is established that these transformations are of the single crystal ↔ single crystal type and occur with the formation and growth of new-crystal nuclei in crystalline matrices.     

An effective growth method to improve the homogeneity of relaxor ferroelectric single crystal Pb(In1/2Nb1/2)O3‐ Pb(Mg1/3Nb2/3)O3‐PbTiO3

Compositional segregation usually has negative effects on the growth of solid solution ferroelectric single crystals of Pb(In_1/2Nb_1/2)O₃‐Pb(Mg_1/3Nb_2/3)O₃‐PbTiO₃ (abbr. PIN‐PMN‐PT or PIMNT). A modified Bridgman method was adopted in this work to control the segregation and improve the compositional homogeneity significantly. The characteristic of this work is to use multiround growths and gradient composition raw materials in order to keep the PbTiO₃ concentration constant during the crystal growth. As an example, the two‐round growth of ternary PIN‐PMN‐PT single crystal is conducted in the same Pt crucible with gradient raw materials, where the first‐round boule was used as the seed crystal for the second‐round growth. Our results show that the as‐grown (Ф80 mm × 270 mm) PIN‐PMN‐PT crystals exhibit higher phase transition temperatures (T_c∼180 °C, T_r/t∼110 °C) and larger coercive field (E_c∼5–5.5 kV/cm), which are much better than the performances of Pb(Mg_1/3Nb_2/3)O₃‐PbTiO₃ crystals, and similar dielectric and piezoelectric performances (ε∼5000, tanδ∼1.25%, d₃₃∼1500 pC/N, k_t∼60%). And about 85 percent of the crystal boule grown by the two‐round growth technique could maintain its compositions around the morphotropic phase boundary.     

Optical defects in barium—strontium niobate single crystals

The distributions of edge dislocations and residual mechanical stresses in Ba_xSr_1-xNb₂O₆ (BSN) crystals are investigated and the explanation of the nature of the “growth column” is proposed. The “growth column” is a defect zone going through all of the crystal and usually repeating in its cross-section the contour of the seed crystal. The “growth column” boundary is the closed contour with extremely high edge dislocation density. These dislocations are connected with thermal stresses due to seed-melt contact or abrupt crystal widening. Under proper crystal seeding and widening conditions one can obtain the BSN crystals with dislocation densities less than 10 cm⁻² and without the “growth column”. The method of chemico-mechanical polishing of BSN crystals not forming a defect layer on the surface of the crystals have been developed. The high temperature diffusion annealing is shown to eliminate the growth striae in BSN crystals.     

Differential thermal analysis studies on the crystallization of strontium tungstate melts. Variation of rate constants with crystallization temperatures and cooling rates

Kinetics of strontium tungstate crystallization from sodium tungstate melts were studied in platinum crucibles (by DTA) by continuous cooling from initial crystallization temperatures T₀ = 800° to 1000° to below the eutectic temperature at cooling rates R_T = 0.67° to 3.3° min⁻¹. Heterogeneous nuclei first formed slowly onto metal platinate particles within the solution during induction periods (t ); the main crystal growth then started after the development of some exces solute concentration (ΔC ) at the induction temperature (T ). The actual growth after t was diffusion rate-controlled. The diffusion rate-constants (k_Dt) for growth after the induction periods along the major axis were estimated; the increased with T₀ and R_T. These values were higher than those for diffusion-controlled crystal growth of strontium tungstate from sodium tungstate melts in alumina crucibles but much smaller than the real diffusion rate-constants (k_Dl)_real.     

The Crystallisation of Aluminium Trihydroxide (Gibbsite) from Sodium Hydroxide Solution Onto Fine Seeds: Physico-chemical Studies on the Internal Structure and Agglomeration of Different Crystal Fractions

A batch of Bayer gibbsite crystals (particle size range 3 to 70 μm) was prepared by crystal growth onto fine seeds (1 to 3 μm) from sodium hydroxoaluminate/sodium hydroxid-solution. The internal structures and seed agglomeration of different fractions were examined by optical microscopy, infra-red spectrophotometry, thermal analysis and chemical dissolution analysis. These physico-chemical studies confirmed that crystal growth occurs with some seed agglomeration in the early stages, followed by growth onto the ‘agglomerates’. The agglomerated seeds contents (X) were as follows: for fraction DiD (l₀ = 6.3 μm), X = 0.44; for fraction Gi C (l₀ = 20 μm), X = 0.41; for fraction Gi B (l₀ = 38 μm), X = 0.31 and for fraction Gi A (l₀ = 55 μm), X = 0.24.     

Optimierung von Kristallisationsparametern beim Zonenschmelzen aus Temperatur-Feld-Berechnungen

The distribution of temperature in the crystal during the growth process decides the crystal perfection and first of all depends on the external conditions: on the nature and geometry of heater arrangement and on the enviroment of the crystal („atmosphere”︁, crucible, pull-respectivly hold rods a.s.o.). – A mathematical model is presented by which it's possible to calculate the distribution of temperature in the crystal on the basis of these external conditions. The efficiency of the theoretical model is discussed and evaluated by means of the special arrangement of vertical zone levelling. Important crystallization parameters are determined by use of the mathematical model for the growth of monocrystals of the Bi_1−xSb_x mixed crystal system through zone levelling.     

Characterization of large‐sized Nd:YAG single crystals grown by horizontal directional solidification

Nd³⁺‐doped Y₃Al₅O₁₂ single crystals have been grown by the horizontal directional solidification (HDS) method in different thermal zone. The Grashof (G_r), Prandtl (P_r), Marangoni (M_a) and Rayleigh (R_a) numbers of melt in HDS system have been discussed for our experimental system to understand the mechanism of melt flow patterns and concentration gradient of dopant. The concentration gradient of Nd³⁺ ions was explained with melt flow processes during crystal growth in different thermal zone, and results indicated that high growth temperature will be helpful for uniformity of dopant in HDS‐grown single crystal. The main microscopic growth defects such as bubbles and irregular inclusions in HDS‐grown Nd:YAG crystals were observed, and the causes were discussed as well. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Precipitation of Barium Chromate with Slow Development of Supersaturation. Kinetics of the Crystal Growth

Slow barium chromate precipitation was studied in well-stirred solutions — final concentration 0.002 mole 1⁻¹ — at 20°C at mixing rates varying from 0.2 to 2 · 10⁶ mole 1⁻¹ sec⁻¹; the kinetics of the crystal growth process were studied by chemical analysis and by optical microscopy. The crystal growth started after induction periods; regular growth then took place on the nuclei formed during these periods. For the main growth, up to about seventy percent precipitation time, growth rates at any time depended on the (residual excess solute concentrations in solution)². Immediately after the induction periods, crystal lengths varied with growth time according to the relation, for the main growth, crystal lengths varied with growth time according to a more complex relation, where k_l is the rate constant for surface growth, R_c is the rate of development of metal salt concentration and K is a constant that depends on the number of precipitate crystals. After some growth time τ = τ^*, when l_τ = l_τ*, all fresh solute added to the solution was utilised immediately and was deposited onto the growing crystals; then, for the final thirty percent precipitation, crystal lengths varied with growth time according to the relation, .     

CVD Processes with Direct and Indirect Incorporation

Indirect incorporation via adsorption, surface diffusion, and reaction at half crystal sites can be treated by the BCF theory of layer-by-layer growth in simple cases of CVD, even if there is strong surface coverage by adsorbed species. I that case, however, the parallel path by direct reactive incorporation of atoms into half crystal sites from the gas phase may play an important role. In any case, direct incorporation becomes the sole possibility for (normal) growth if the surface fraction y_k of half crystal sites (kinks) becomes I. The continuous transition from singular faces (y_k = 0) to half crystal faces (y_k = l) is covered by a simplified analytical expression and can be included into an overall circuit representation of stationary CVD processes which holds for in-situ doping, too. The model results in a good compromise between the conventional BCF treatment and Chernovs treatment of CVD surface processes.     

Morphology of β-BaB2O4 (BBO) Crystals in Relation to its Structure and Growth Conditions

β-BaB₂O₄ (BBO) crystals with well-defined morphology have been grown from Na₂O solutions using the top seeded solution growth (TSSG) method. The crystal morphology in relation to its structure and growth conditions has been studied in detail on the basis of crystallography and crystal chemistry. It is found that the morphological characteristics are related to the orientations of structural unit (B₃O₆)^3— anion rings in the crystal. On the other hand, the growth parameters may greatly affect the appearance of faces of the crystal, but the crystals still generally take trigonal in outline and have a diagnostic character of point group 3m. The observed morphology is in disagreement with BFDH and PBC analyses and is explained from the incorporation of the growth units on the faces and facets. Since the incorporation rates of the growth units are different on different faces, the boule habits with well-defined morphology are formed.     

The Precipitation of Strontium and Lead Sulphates from Aqueous Solution. Kinetics of the Crystal Growth

The precipitation of strontium and lead sulphates from well-stirred supersaturated aqueous solutions, of initial solute concentrations C₀ = 0.001 to 0.020 M and C₀ = 0.0002 to 0.003 M respectively, was studied at 20° and 40°C by chemical analysis and optical microscopy. Nucleation occurred during induction periods and continuous regular growth then took place onto the nuclei formed during these periods. Crystallisation was complete after 4 to 48 hr. The crystal growth was rate-controlled by the rate of deposition of metal salt ions onto the growing crystal surfaces. This rate (dC/dt), at any growth time, then depended on both the overall surface area (A_t) and on the residual excess solute concentration (ΔC_t) in solution according to the relation while the growth rate (dα/dt), expressed in terms of degree of crystallisation, was . The rate constants (k_α) for the crystal growth of strontium and lead sulphates at 20°C were 22 and 4200 sec⁻¹ M⁻² respectively — that is, greatest for the salt with least cation hydration –; these constants increased 4 to 6 times for 20°C temperature rise. The rate-determining process for the metal salt deposition was probably the ion dehydration.     

An Exponential-Hyperbolic Crystal Growth Rate Model

A new exponential-hyperbolic size-dependent crystal growth rate function G (L) = G_m (e^aL–b)/(e^aL – c) is proposed. The model has been examined in detail for the direct determination of size-dependent crystal growth rates from the cumulative number oversize distribution of continuous Mixed-Suspension Mixed-Product Removal (MSMPR) crystallizers using both simulated and realistic data, both for systems that hold and that violate McCabe's Δ law, respectively. It is show that direct fitting of cumulative number oversize distribution data using the proposed model gives an improved estimation of effective crystal growth rates over the whole size range during MSMPR crystallization compared with previous models tested.     

The precipitation of barium chromate from aqueous solution (with rapid mixing): Kinetics of the crystal growth

The kinetics of precipitation of barium chromate from well-stirred aqueous solutions of initial solute concentrations C₀ = 0.0001 to 0.0010 M (supersaturations 8 to 80) was studied at 25 °C by conductivity measurements and chemical analysis. Nucleation occurred during induction periods and regular crystal growth then took place onto the crystallites formed during the induction periods. The crystal growth was rate-controlled, in this range, by the rate of deposition of metal salt ions onto the growing crystal surfaces. This rate, at any time, then depended on both the overall surface area (A_t) and on the residual excess solute concentration (ΔC_t) in solution according to the relation, the growth rate expressed in terms of degree of crystallisation was then The rate constant (K_α) for the crystallisation of barium chromate at 25 °C was 1.5 10⁶ sec⁻¹ M⁻².     

In situ observation of β‐BaB2O4 microcrystal growth in glass matrix

The morphological evolution and growth mechanism of β‐BaB₂O₄ microcrystal in Li₂B₄O₇‐BaB₂O₄ glass (Li₂O‐B₂O₃‐BaO) matrix were investigated by optical in situ observation method. And the crystallization temperature T_c has been examined by differential thermal analysis (DTA). It demonstrates that homogeneous distribution of hexagonal shaped BBO microcrystals with size up to several tens of microns is typical when temperature is much higher than T_c, however, heterogeneous nucleation occurs when annealing temperature is close to T_c. For the latter case, crystal clusters that consist of several microcrystal grains are obvious. When the crystals in one specific cluster grows larger, crystal motion occurs in glass matrix while their orientation and symmetrical shape keep nearly no changes. Additionally, the BBO microcrystal has been determined to grow nearly in linear with time, which suggests a mechanism of interface‐controlled growth. Furthermore, the activation energy of BBO crystal growth in glass matrix is calculated which is around 2.4 eV. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the conduction mechanism and thermoelectric phenomena in In6S7 layer crystals

In the present paper, measurements of the electrical conductivity and Hall coefficient on single crystal of In₆S₇, grown by a new crystal growth technique, were done. The crystal was found to be of n-type conductivity. The low conductivity sample showed as the most striking feature an exponential increase of the Hall mobility with temperature. This effect was explained by assuming a mixed conduction and different scattering mechanisms for electrons and holes in the same temperature range. Also we have made thermoelectric power measurements to support this assumption. An energy gap of 0.64 eV was found.