Growth and melting of metallic nanoclusters in glass: A review of recent investigations

The mechanisms of nucleation and growth and the solid-to-liquid transition of metallic nanoclusters embedded in sodium borate glass were recently studied in situ via small-angle X-ray scattering (SAXS) and wide-angle X-ray scattering (WAXS). SAXS results indicate that, under isothermal annealing conditions, the formation and growth of Bi or Ag nanoclusters embedded in sodium borate glass occurs through two successive stages after a short incubation period. The first stage is characterized by the nucleation and growth of spherical metal clusters promoted by the diffusion of Bi or Ag atoms through the initially supersaturated glass phase. The second stage is named the coarsening stage and occurs when the (Bi-or Ag-) doping level of the vitreous matrix is close to the equilibrium value. The experimental results demonstrated that, at advanced stages of the growth process, the time dependence of the average radius and density number of the clusters is in agreement with the classical Lifshitz-Slyozov-Wagner (LSW) theory. However, the radius distribution function is better described by a lognormal function than by the function derived from the theoretical LSW model. From the results of SAXS measurements at different temperatures, the activation energies for the diffusion of Ag and Bi through sodium borate glass were determined. In addition, via combination of the results of simultaneous WAXS and SAXS measurements at different temperatures, the crystallographic structure and the dependence of melting temperature T _m on crystal radius R of Bi nanocrystals were established. The experimental results indicate that T _m is a linear and decreasing function of nanocrystal reciprocal radius 1/R, in agreement with the Couchman and Jesser theoretical model. Finally, a weak contraction in the lattice parameters of Bi nanocrystals with respect to bulk crystals was established. The text was submitted by the authors in English.     

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.     

Investigation of metastable zone width of ammonium oxalate aqueous solutions

The metastable zone width of pure ammonium oxalate aqueous solutions, as represented by maximum supercooling ΔT_max, is investigated as functions of cooling rate R and saturation temperature T₀ by the polythermal method. The experimental results are discussed by using two recently advanced approaches: (1) self‐consistent Nývlt‐like approach based on a power‐law relationship between nucleation rate J and maximum supersaturation lnS_max, and (2) a novel approach based on the relationship between J and lnS_max described by the classical three‐dimensional nucleation theory. Analysis of the experimental data revealed that both approaches describe the experimental data on metastable zone width by the polythermal method reliably and provide useful information about the physical processes and parameters involved in nucleation kinetics. The values of various physical quantities predicted by both of these approaches are reasonable for a fairly‐soluble compound. A careful examination of the data on ΔT_max as a function of T₀ obtained by polythermal method and from density measurements showed that ΔT_max has a slight tendency to decrease with increasing saturation temperature T₀. The values of lnS_max at saturation temperature 303 K suggest that the metastable zone width of ammonium oxalate aqueous solutions is determined by primary nucleation in the polythermal method and by secondary nucleation during density measurements. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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 (R,S)- and (R)-mandelic acid in an unseeded cooling batch crystallizer

The objective of this work is to determine the nucleation and growth kinetics of (R,S)-mandelic acid ((R,S)-MA) and (R)-mandelic acid ((R)-MA) in aqueous solutions using an unseeded cooling crystallization process. To obtain the nucleation and growth kinetics, the solubility, metastable zone limits, and supersaturation were measured by in-situ attenuated total reflection Fourier transform infrared (ATR-FTIR) spectroscopy and focused beam reflectance measurement (FBRM). The nucleation rate and growth rate parameters were determined by a nonlinear optimization algorithm. The effects of initial concentration and cooling rate on supersaturation and the nucleation rate are also discussed.     

Nucleation velocity of NaPO3 melts

The time τ for visible crystallization of NaPO₃ melts is measured in the whole range of undercoolings from the melting temperature T_m to the temperature of vitrification T_g. It is shown that the time τ, needed for the appearance of a visible crystallization at high supersaturations is determined by the linear growth rate, whereas the rate of heterogeneous nucleation is the main factor, determining the experimentally measured time τ at low supersaturations. The specific surface energy σ at the melt-crystal interface is calculated from the data on nucleation velocity in the vicinity of T_m and the temperature dependences of both heterogeneous and homogeneous nucleation velocity for NaPO₃ melts are constructed. It is concluded that at normal cooling rates only nucleation, initiated by active crystallized cores could be observed for NaPO₃.     

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 alkaline-earth metal molybdates and tungstates from lithium chloride melts by continuous cooling. Nucleation mechanism and kinetics and induction periods

Calcium, strontium and barium molybdate (and tungstate) solutions in lithium chloride melts were crystallised in alumina and in platinum crucibles; saturated solutions were cooled from initial temperatures 700° to 800°C down to room temperature at cooling rates 40° to 200°C hr⁻¹. The nucleation and early crystal growth were investigated by chemical and differential thermal analysis and by optical microscopy studies. Crystallisation occurred through heterogeneous nucleation at low supersaturations. Heterogeneous nuclei formed slowly onto metal aluminate (and platinate) particles within the solution during induction periods from < 0.2 to 14 hr. The main growth surge then started and few new nuclei were formed. The nucleation probably terminated at times just after the times for maximum rate of formation of nuclei. Then, at any temperature, the induction periods (t ) varied inversely with cooling rate and with the rate (R_c) of development of excess solute concentration according to the relation, The parameters k₁ were related to the rate constants (k_n) for the heterogeneous nucleation. These constants in turn probably dependend on the free energy for formation of critical heterogeneous nuclei and thence on some nucleator vs solute surface energy ‘wetting’ function. The k₁ and k_n values at any temperature decreased in the order : they increased from 2 to 4 times for 100°C rise in temperature.     

Antisolvent crystallization of aqueous ammonium dihydrogen phosphate solutions by addition of acetone at different rates

Results of an investigation of in situ measurements of laser‐beam intensity I_s and I_m transmitted through aqueous ammonium dihydrogen phosphate (ADP) solutions saturated at 30 °C and water, respectively, and temperature T_s of solution and T_m of water during feeding of antisolvent acetone at different rates R_A, using an indigenously designed experimental setup, are presented and discussed. It was found that: (1) for the measurement of MSZW, defined as the maximum volume fraction of acetone content Δx_max in the solution, obtained from temperature measurements are more reliable than transmitted laser‐beam intensity measurements for solutions, (2) two minima ΔT_min1 and ΔT_min2 associated with endothermic reactions, separated by a maximum ΔT_max due to exothermic reactions appear in the plots of temperature difference ΔT = T_s−T_m against acetone feeding time t, and (3) in the ΔT(t) plots there are time intervals Δt of constant rates R_T of increase in ΔT of aqueous ADP solutions, and these values of R_T increase linearly with acetone feeding time rate R_A. The experimental data on the observed dependence of MSZW on antisolvent feeding rate R_A, the appearance of minima ΔT_min1 and ΔT_min2 and maximum ΔT_max and their dependence on R_A, and the relationship between R_T and R_A are discussed from consideration of processes of nucleation and growth of crystallites.     

Numerical modeling of frequency influence on the electromagnetic stirring of semiconductor melts

Alternating magnetic fields can be used in order to increase the level of convection and to mix the doped semiconductor alloys. A numerical analysis of the electromagnetic induced convection in GaInSb semiconductor melts is performed by using the software package CrysVUn. The magnetic field parameters are varied in order to obtain a maximum efficiency of the induced convection with a minimum quantity of the heat released in the melt. The influence of the electrical current frequency on the convection intensity is analyzed for samples with various radii (R = 0.5 – 3cm). Numerical procedure is validated by comparing the numerical results obtained in mercury samples with the experimental data given from the literature, which show a maximum stirring for a magnetic skin depth δ = 0.2R , in the case of a mercury sample with the radius R = 10 cm. This maximum corresponds to a shielding parameter R _ω = 40. Our numerical results show that the value of the shielding parameter for which the convection intensity reaches the maximum depends on the sample radius and increases when the sample radius increases. The results of this analysis are important in the case of samples with small radius, when a good mixing of the melt can be obtained for frequencies much lower than those corresponding to a shielding parameter R_ω = 40. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dislocation Structure of Epitaxial Ferrite-Spinel Films

The dislocation structure of ferrite-spinel films obtained on the (001) plane of magnesium oxide has been studied. For the films of Mn and Mg Mn ferrites there has been found the formation of a cellular dislocation structure, complex dislocation clusters, for the Li ferrite the twinning. Experimental data are compared with the predictions of the theory of relaxation of internal stresses in heteroepitaxial structures. It has been shown that in the Li → Mn → Mg Mn ferrite the energy at the interface of magnesium ferrite and oxide ranges from 64 to 9 mJ · m⁻², the absolute magnitude of lattice mismatch at a synthesis temperature being 10.328 to 3.451 × 10⁻³ and the critical thickness of a continuous film 0.02–0.1 μm. The formation of three-dimensional islets-nuclei hinders the obtaining of pseudomorphous continuous films. The critical radius (R_cr) of a pseudomorphous islet in the same series of ferrites is 0.2–1.1 μm. For Li ferrite R_exp > R_er, for Mg Mn R_exp < R_er, that determines the prevailing types of defects. The process of relaxation of thermal stresses is associated with the overcoming of interaction barriers by dislocations and largely dependent on the film composition and temperature.     

Mechanism of nucleation and growth of crystals under α → β transformation of tin

This article presents data on the mechanism underlying the nucleation and growth of α-Sn crystals in mono- and polycrystal β-Sn tin. It is demonstrated that the low temperature deformation and thermocycling (subjection to the cyclic changes of temperature) of the samples of tin (99.9995% Sn) brings to the increase in the α-Sn crystal nuclestion rate. Kinetics of the nucleation is characterised by the presence of the non-steady State period t_n. On analysing the temperature dependencies of the rate of the α-Sn centre growth obtained for the planes (100), (001) and (110) it was shown that the mechanism of movement of the interphase boundary depends on the value of the motive force ΔF.     

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)     

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.     

Facet Formation in Garnet Crystals

Formation of {110} and {211} type facets in rare-earth aluminium garnet crystals grown along different crystallographic directions is analyzed and it is shown that D/2R parameter (where D is the crystal diameter and R is the curvature radius of spherical growth interface) may be used to characterize the number of originating facets and their configuration in crystals.     

On the growth of one spherical precipitate in an isotropic infinite matrix

The growth of one spherical precipitate in an isotropic infinite matrix is treated solving the diffusion equation of the “stationary solution”, i.e. assuming ∂c/∂t = 0, for the general case that the diffusion constant D depends on concentration c. The influence of the resistance of the interface p = p(R) on the growth is considered, too (R radius of the precipitate). It could be shown that the growth law of the particle R ∼ t^1/2 holds even foreach D = D(c) used, but it depends sensitively on p = p(R) applied.     

The Precipitation of Sparingly-Soluble Alkaline-Earth Metal and Lead Salts with Slow Development of Supersaturation (Slow Anion and Hydroxyl Ion Addition): Kinetics of Nucleation and Induction Periods

Barium and lead sulphate and chromate precipitations were studied at 20° to 95°C at precipitation rates varying from 10⁻³ to 10⁻⁷ ion l⁻¹ sec⁻¹: the supersaturation was developed by slow direct addition of anion to metal nitrate solution and by neutralisation of equivalent metal salt in excess acid solution. Slow heterogeneous nucleation occurred onto particles dispersed within the aqueous solution. The nucleation rate at any time was Where k_n is the rate constant for heterogeneous nucleation, N_∞ is the maximum number of potential nuclei, n_t is the number of nuclei after time t, I. P_t is the ionic product (C_mt)(C_mt) and 2π is the number of metal salt ions in the critical nucleus, generally eight. Crystal growth started after induction periods (t̄) at times just after the times for maximum rate of formation of nuclei. The induction periods (t̄) for precipitations from solutions of initial cation concentration ^cM₀ varied with precipitation rate (R) according to the relation, where γ = π/(π + 1) and k₁ (the unit reciprocal induction period) = . Nucleation rate constants for different precipitations were estimated from the k₁ values and are tabulated. For slow precipitations by direct anion addition, the rate constants were lower for precipitation from solution of the salt of greater solubility. The rate constants for slow precipitation of metal chromates from acid solution were far lower than those for slow precipitation by direct chromate addition. Rate constants decreased somewhat with rise in precipitation temperature.     

Interfacial stability and grain diameter of the metal phase of directionally solidified Al-Si-type eutectics

The morphology of the solid-liquid interface and the metal phase grain diameter of Al—Si-type eutectics (Al—Si, Ag—Si, Ag—Ge, Zn—Ge) were investigated in the range of a growth rate R = 0.2 … 20 mm/h and of a temperature gradient at the solid-liquid interface G = 2 … 25 K/mm. Three types of interfacial morphologies depending on the G/R ratios were found out. The G/R ratio of the transition from a planar to a nonplanar solid-liquid interface corresponds to the critical G/R|_c ratio, which can be calculated by the criterion of the constitutional undercooling. The grain diameter of the metal phase depends on growth parameters as follows: d_K ∼ R^—rG^—g with r = 0.33 … 0.43 and g = −0.37 … 0.03.     

Kinetic investigations within the transition region from polyhedral to skeletal growth mode (III). Growth kinetics of the basal face of zinc single crystals and its edge under diffusion conditions

The growth kinetics of the basal face and its edge of zinc single crystals grown from zinc vapours in the presence of argon at pressures 5 – 250 Torr has been investigated simultaneously. The alterations of the crystal size R and the length of the basal edge a with time t have been measured at constant temperature and supersaturation. It is shown that the R²(t) and a²(t) dependences change their initial shape into linear at one and the same moment. It is established that the transition from a kinetic to a diffusion regime can be determined both by the kinetic critical size R_k and by the kinetic critical size a_k. It is found also that in the kinetic regime the lateral growth rate of the basal edge is higher than the normal growth rate of the {0001} face. During the growth in a diffusion regime the R²(t) and a²(t) curves of a given single crystal become parallel, due to the isotropic character of the transport processes of the material. The rate determining role of the diffusion in the parent phase on the growth of the basal face and its edge is demonstrated.     

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.