Crystallizaton Characteristics of the Alternating Tetrafluoroethylene-Ethylene Copolymer

The alternating tetrafluoroethylene-ethylene (TFE-E) copolymer has been studied with respect to its crystallization by using differential scanning calorimetry and optical microscopy. The value of the specific surface energy σ at the melt/crystal interface is calculated to be about 2 · 10⁻³ J/m². The nucleating activity Φ of TiO₂ particles introduced into TFE-E copolymer is estimated to be approximately 0.9. The temperature dependence of the nucleation rate and of the linear growth velocity are constructed in the whole region from the melting temperature T_m to the vitrification temperature T_g. The minimum cooling rate for the formation of a crystal-free TFE-E copolymer glass is calculated and its value amounts to 10⁴ K · min⁻¹.     

Induction periods and mechanism and kinetics of nucleation of barium tungstate crystal growth from sodium tungstate melts in platinum crucibles

Induction periods (t) and mechanism and kinetics of nucleation in barium tungstate crystallization from sodium tungstate melts in platinum crucibles were studied. A theoretical relation has been developed to express the dependence of t on the cooling rates (R_T) and the rate (R_c) of development of excess solute concentration. At any crystallization temperature the average rate-constant (k_n) for heterogeneous nucleation was related to R_c by (k_n/p)^1/(p+1) = 1/(tR_c^γ), where γ is a constant and p is the average number of particles in the critical nuclei. The critical temperature (T), critical supersaturation (S) and γ values were estimated.     

Elastic stress effects on critical cluster shapes

Crystallization of solids at planar solid–air surfaces was analyzed. Shape and size of clusters of the newly evolving phase are determined which correspond to the minimal work of cluster formation in nucleation. Both elastic field and surface energy terms are taken into consideration. This work is not restricted to the consideration of spherical interfaces cluster–ambient solid phase but allows, more general arbitrary shapes of the new phase. Application to crystallization of glassforming melts, gives additional support to the idea that differences in the degree of evolution of elastic strains in crystallization in the bulk and near external or internal surfaces of highly viscous glassforming melts in the vicinity of the temperature of vitrification T_g may be the origin for the preferential surface crystallization of glasses.     

Controlled crystallization and ionic conductivity of a nanostructured LiAlGePO4 glass–ceramic

A Li_1.5[Al_0.5Ge_1.5(PO₄)₃] glass composition was subjected to several crystallization treatments to obtain glass–ceramics with controlled microstructures. The glass transition (T_g), crystallization onset (T_x) and melting (T_m) temperatures of the parent glass were characterized by differential scanning calorimetry (DSC). The glass has a reduced glass transition temperature T_gr = T_g/T_m = 0.57 indicating the possibility of internal nucleation. This assumption was corroborated by the similar DSC crystallization peaks from monolithic and powder samples. The temperature of the maximum nucleation rate was estimated by DSC. Different microstructures were produced by double heat treatments, in which crystal nucleation was processed at the estimated temperature of maximum nucleation rate for different lengths of time. Crystals were subsequently grown at an intermediate temperature between T_g and T_x. Single phase glass–ceramics with Nasicon structures and grain sizes ranging from 220 nm to 8 μm were then synthesized and the influence of the microstructure on the electrical conductivity was analysed. The results showed that the larger the average grain size, the higher the electrical conductivity. Controlled glass crystallization allowed for the synthesis of glass–ceramics with fine microstructures and higher electrical conductivity than those of ceramics with the same composition obtained by the classical sintering route and reported in literature.     

Nucleation kinetics in deionized charged colloidal suspension

A systematic experimental study on the nucleation, crystallization and crystal-growth of one-component charged colloidal particles (122 nm diluted in pure water with densities between 0.5 μm⁻³ < n_p < 5 μm⁻³) is present by means of time resolved static light scattering spectroscopy revealing the heterogeneous and homogenous nature of the crystallization. The interactions between the charged colloidal particles are sufficiently strong to cause crystallization which described in terms of Debye-Hückel approximation. Crystallization starts always with the formation of compressed structurally heterogeneous precursor domains. The results show that the heterogeneous nucleation at the cell walls starts simultaneously with the homogeneous bulk nucleation and the rate density of the heterogeneous nucleation appears slightly higher. It has been also found that the overall crystallization consists of at least a two-step nucleation process involving formation of early stage nuclei or crystal precursor then followed by the main crystallization. The induction time, the number density of nuclei and the growth rate of crystals, is strongly dependent on particle concentration and on whether the nucleation are homogeneous in cell center or heterogeneous on cell walls.     

Kinetics of relaxation and crystallization of sodium metaphosphate glass

Kinetics of structural relaxation and crystallization of NaPO₃ glassforming melt is studied by means of thermal analyses. It is demonstrated that activation energy depends strongly on fictive temperature T_f. The dependence of the onset temperature T_o of the glass transition interval on the heating rate q⁺ is investigated for samples that were previously cooled down at a rate q⁻ of about 850 K/min. The dimensionless fragility F is a measure of the dependence of the activation energy for spatial rearrangement on the changes of structure. According to the present results F is large for NaPO₃ (i.e. phosphates are ‘fragile’ substances).     

A kinetic treatment of glass formation V: Surface and bulk heterogeneous nucleation

An analytical method is described for calculating the detailed distribution of crystallite sizes in a supercooled liquid, and the changes in this distribution as a function of temperature (time) while the liquid is cooled from above the melting point.This method, termed the analysis of crystallization statistics, is applied to the calculation of continuous cooling curves for anorthite and o-terphenyl as representative of inorganic and organic systems. In addition to homogeneous nucleation, bulk as well as surface heterogeneous nucleation are considered. The effects of distributions of heterogeneities with contact angles between 40 and 100° as well as overall concentrations of heterogeneities between 10³ and 10⁹ cm^?3 are considered. Heterogeneities with contact angles higher than about 100° are shown not to have an effect on the critical cooling rate for typical concentrations of heterogeneities.For liquids containing distributions of heterogeneities, the nucleation behavior is dominated by small concentrations of heterogeneities having small contact angles. Theoretical log (I_vη) versus (T_r³ΔT_r²)^?1 curves have been constructed for homogeneous nucleation + heterogeneous nucleation with a single type of heterogeneity and for homogeneous nucleation + heterogeneous nucleation with the heterogeneities distributed with regard to contact angle. In the former case, the curve is composed of two linear portions; and in the latter case, the curve shows pronounced curvature. The curvature reflects a continous change in the frequency of heterogeneous nucleation.Surface heterogeneous nucleation was assumed to originate at discrete surface heterogeneities and was shown to give rise to continuous cooling curves similar to those calculated for bulk heterogeneous nucleation.     

A Study of the Nucleation Kinetics,Linear Growth and the Overall Crystallization Kinetics of Meltspun Pd80Si20 Amorphous alloy

Nucleation kinetics, linear growth rate and overall isothermal crystallization kinetics of Pd Si amorphous alloy are studied by means of DSC and optical microscopy. It is found that both the histograms of the crystallite sizes and the DSC isotherms (resp. the time dependences of the degree of transformation α(t)) are best described by the model comprosing the simultaneous occurrence of two reactions of crystallization: heterogeneous as well as homogeneous non-stationary nucleation with subsequent three-dimensional growth in both cases. From the fit of the experimentally measured and the calculated according the model thus proposed distribution curves N_i(Φ) the stationary rates of heterogeneous and homogeneous nucleation, the number of quenched-in nucleation sites and the transient time lags of heterogeneous and homogeneous nucleation have been estimated. Using the values of these parameters kintic curves degree of transformation vs. time have been generated, which are closed to the exerimental x(t) curves obtained by means of DSC at isothermal conditions.     

Effect of supersaturation on the crystallization of phenylbutazone polymorphs

The article describes the effect of degree of supersaturation, σ, on the crystallization of specific polymorphs of phenylbutazone from its methanolic solution at 20 °C. At low initial supersaturation, σ ≤ 2.0, the fraction of the metastable α polymorph in the crystallized product exceeds that of the δ polymorph, while at σ ≥ 5.0, the fraction of the stable δ polymorph increases in the crystallized product. The results are explained by the effect of supersaturation on the relative rates of nucleation and crystal growth of the polymorphs. Furthermore, the mechanism of nucleation and crystal growth also change with supersaturation. Supersaturated methanolic solutions of phenylbutazone exhibit a critical temperature at which the nucleation rates of the polymorphs decrease drastically. This effect is partly explained by the decreased mobility of phenylbutazone molecules at lower temperatures. Nucleation is most rapid when the crystallization temperature is close to the transition temperature, T_t(α ⟷ δ), between the polymorphs, α and δ. The nucleation rate decreases as the temperature difference between T_t(α ⟷ δ) and the crystallization temperature increases. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

On the kinetic of crystallization of zinc oxalate (II). Determination of the specific surface energy at the crystal solution interface by kinetic studies

An apparatus based on turbidimetry was constructed for studying the kinetics of crystallization of sparingly soluble salts. The kinetics of crystallization of zinc oxalate was investigated at various supersaturations and pHs of the medium. The specific surface energy at the crystal-solution interface was determined from the induction periods of the S-shaped curves by means of the classical theory of nucleation. The calculations were made using the slope of the logarithmic dependence of I or τ, respectively, on supersaturation (equations 1 and 2) and the critical supersaturation which was also determined on the basis of kinetic data. Various values of σ were found for the different supersaturations. Different values for this quantity were also obtained when supersaturation was presented by the concentration ratio (S = C/C₀) or by the ratio of the product of the two ions concentrations in the supersaturated solution to that in the saturated one (S = ab/L_p). These σ values were lower than those obtained using the critical supersaturations at the two different solution pHs. For the present it is impossible to give a definite explanation of the results obtained. The experiments for determining the specific surface energy at the crystal-solution interface will be continued.     

A novel self‐consistent Nývlt‐like equation for metastable zone width determined by the polythermal method

Using a power‐law relation between three‐dimensional nucleation rate J and dimensionless supersaturation ratio S, and the theory of regular solutions to describe the temperature dependence of solubility, a novel Nývlt‐like equation of metastable zone width of solution relating maximum supercooling ΔT_max with cooling rate R is proposed in the form: ln(ΔT_max/T₀) = Φ + β lnR, with intercept Φ = {(1–m)/m }ln(ΔH_s/R_GT_lim) + (1/m)ln(f/KT₀) and slope β = 1/m. Here T₀ is the initial saturation temperature of solution in a cooling experiment, ΔH_s is the heat of dissolution, R_G is the gas constant, T_lim is the temperature of appearance of first nuclei, m is the nucleation order, and K is a new nucleation constant connected with the factor f defined as the number of particles per unit volume. It was found that the value of the term Φ for a system at saturation temperature T₀ is essentially determined by the constant m and the factor f. The value of the factor f for a solute–solvent system at initial saturation temperature T₀ is determined by solute concentration c₀. Analysis of the experiment data for four different solute‐water systems according to the above equation revealed that: (1) the values of Φ and m for a system at a given temperature depend on the method of detection of metstable zone width, and (2) the value of slope β = 1/m for a system is practically a temperature‐independent constant characteristic of the system, but the value of Φ increases with an increase in saturation temperature T₀, following an Arrhenius‐type equation with an activation energy E_sat. The results showed, among others, that solubility of a solute is an important factor that determines the value of the nucleation order m and the activation energy E_sat for diffusion. In general, the lower the solubility of a solute in a given solvent, the higher is the value of m and lower is the value of E_sat. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Kinetics of sodium fluosilicate precipitation

The formation of Na₂SiF₆ by discontinuous precipitation of dilute H₂SiF₆ with a 40% excess of an aqueous solution of NaCl under various conditions was studied. The values of induction time, number of crystals formed, their final size and their habit were determined during precipitation from solutions, whose initial supersaturation was 2 < S < 11. At S < 7–8 the crystals were formed by heterogeneous nucleation, whereas at S ≳ 7–8 homogeneous nucleation mechanism began to prevail. Once formed, the Na₂SiF₆ crystals were growing according to the screw-dislocation mechanism till they reached visible size; the corresponding values of kinetic order of nucleation and of the growth rate constant were g = 1.35 and k_g = 4.32 × 10⁻⁸ cm^2.05 sec⁻¹ g^−0.35, resp. The value of interfacial tension on the phase boundary Na₂SiF₆ crystal — saturated solution was determined (σ ∼ 52 erg/cm²). The resulting Na₂SiF₆ crystals conformed to log-normal distribution irrespective of conditions of precipitation. The dependence of the final size of crystals on supersaturation exhibited a maximum at S ∼ 6. Crystals of Na₂SiF₆ had a hexagonal habit, which was near to a spherical form at lower supersaturations, while dendritic crystals were formed at higher supersaturations.     

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)     

Crystallization of vitamin C in a continuous DT MSMPR crystallizer – Size independent growth kinetic model approach

The experimental results concerning continuous mass crystallization process in L(+)‐ascorbic acid – water system are presented and discussed. Influence of L(+)‐ascorbic acid concentration in a feeding solution and mean residence time of suspension in laboratory DT MSMPR crystallizer on product crystal size distribution as well as nucleation and growth kinetics were determined. Kinetic parameter values were evaluated on the basis of size–independent growth (SIG) kinetic model (McCabe's ΔL law). It was observed, that within the examined range of crystallizer productivity (120–1600 kg LAA crystals m^–3h^–1) crystal product population of mean size L_m from 0.2 to 0.3 mm and CV from 66.6 to 49% is withdrawn. Linear growth rate values present decreasing trend (from ca. 7 · 10^–8 to ca. 6 · 10^–8 m s^–1) with the productivity increase (assuming constant mean residence time of suspension τ = 900 s). Occurrence of secondary nucleation within the circulated and mixed suspension, resulting from crystal attrition and breakage, was observed. The parameter values in design equation connecting linear growth rate and suspension density with nucleation rate were determined. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Investigation of nucleation kinetics and crystal defects of HMX

The nucleation kinetics of HMX (cyclotetramethylene tetranitramine, C₄H₈N₈O₈) in γ‐butyrolactone was studied in cooling process by induction time method. The laser scattering method was used to measure the solubility data and metastable region of HMX in γ‐butyrolactone. The induction time was measured over a range of supersaturation at different temperatures. Then, the nucleation mechanism of HMX in γ‐butyrolactone was investigated by analysis the relationships between induction time and supersaturation. The results indicated homogeneous nucleation dominated at high supersaturation of S >1.35, while the heterogeneous nucleation dominated at low supersaturation of S < 1.35. The values of interfacial tension at different final temperatures were calculated to indicate the ability of HMX to be crystallized. The growth mechanism of HMX was investigated by the data fitting applying different growth mechanism models and identified as two‐dimensional nucleation‐mediated (2D) growth. Finally, the effects of supersaturation and temperature on the crystal defects were analyzed based on the nucleation kinetics. When the temperature is below 303.15K, homogeneous nucleation dominated the nucleation process at higher supersaturation. Fine HMX crystals with more defects were produced. On the contrary, heterogeneous nucleation mechanism dominated at lower supersaturation. large regular HMX crystals with fewer defects were formed when the temperature is above 318.15K.     

Calcium Oxalate Monohydrate Crystal Growth

The growth rate of calcium oxalate monohydrate seed representing aggregates of highly irregular crystals from solutions of the stoichiometric composition with I = 100 mol m⁻³ in the range of supersaturation Δc = 0.056 to 0.353 mol m⁻³ was measured at 37 °C by the constant composition method. The crystal growth rate decreased during the initial period of experiment, then reached a value constant over a considerable time and later increased again. The initial decrease of the growth rate resulted from crystal perfection whereas the later increase was caused by formation of new crystals by secondary nucleation. The supersaturation dependence of the kinetic growth rate satisfied the power law with the growth order equal to 2 and 4 at supersaturations lower and higher than about Δc = 0.150 mol m⁻³, respectively.     

Structural aspects of volume nucleation in silicate glasses

An interrelationship between parameters of short and intermediate range order in silicate glasses and the tendency to nucleate homogeneously in the volume is tested. Changes in the average coordination number and metal-oxygen distance of network modifying cations as well as changes in the concentration of constitutive silica tetrahedra accompanied with the crystallization of 18 stoichiometric glass compositions into their crystalline analogs are determined. The intermediate range structure of the glasses is investigated by configurational entropy and flow birefringence. The changes in structural parameters are analyzed in terms of the reduced glass transition temperature T_rg, which is negatively correlated with the maximal rate of volume nucleation. The results indicate that the short-range structure in stoichiometric glasses is, in general, very similar to the corresponding crystal structure but independent of the T_rg-scale and for this reason independent of nucleation properties. In contrast to the short range of the glass structure, birefringence induced by a forced flow above the glass transition temperature and configurational entropy are positively correlated with increasing T_rg. The results indicate increased structural order in the intermediate range for melts with a high supercool limit (T_rg < 0.58). It is concluded that this order phenomena may promote nucleation events and may help to explain the tendency to volume nucleation of silicate glasses with T_rg < 0.58.     

Precipitation of Strontium Sulphate

Precipitation of unseeded supersaturated aqueous solutions of SrSO₄ and growth of SrSO₄ crystals at the size of approximately 20 μm were studied. Within the examined range of supersaturations, i.e. S_a < 16, the nucleation in aqueous solutions is controlled by the heterogeneous nucleation mechanism. The induction period of precipitation depends on the rates of both the nucleation and growth of the formed nuclei. The growth of SrSO₄ crystals in supersaturated solutions at S ⪅ 5.6 is of the 2nd order with respect to the concentration and at temperatures 25 ÷ 45°C the process is controlled by the surface reaction mechanism. The number of crystals in the precipitated slurry is decreasing rapidly as a result of the Ostwald maturing.     

Observation of nucleation effect on crystallization in lithium aluminosilicate glass by viscosity measurement

The crystal nucleation effect in lithium aluminosilicate glasses was investigated by the viscosity measurement with aid of the fiber elongation method. The abrupt increase of viscosity due to the crystallization of glass was observed in viscosity-temperature curve but the minimum viscosity temperature (T_η) related with crystallization showed a strong dependence on the nucleation state such as nucleation temperature, nucleation time and heating rate. The results by viscosity agreed well with those of DTA. The nucleation effect on the microstructure of glass-ceramics was also discussed. Finally, the nucleation effect on the crystallization kinetics was approached quantitatively by calculating the crystal volume from viscosity value.