Processes in phase boundary region during liquid phase growth

The behavior of components within the phase boundary region during liquid phase growth is the subject of the present article. Based on the supposition that the phase boundary is a structured region, repeating the periodicity of the substrate, the distribution of different components within the phase boundary is considered. Assuming that the value of the supersaturation at the upper end of the phase boundary defines the growth rate of the compound, a relation has been derived, concerning the extension of the phase boundary. The case of liquid phase epitaxial growth of GaAs is considered and an effort for evaluation of the phase boundary extension is undertaken. The linear dependence of the stationary growth rate on the cooling rate, predicted previously, is proved experimentally.     

Electron microscope observations of phase separation near spinodal boundary in a sodium borosilicate glass

Time evolution of volume fraction of the minor phase is studied in an alumina-doped sodium borosilicate glass inside the immiscible region. It is shown that such a study permits a distinction between the two mechanisms of phase separation; namely spinodal decomposition and nucleation and growth. For spinodal decomposition, the volume fraction decreases initially, whereas for nucleation and growth, it increases with heat-treatment time.     

On calculation of the transformation kinetics for models with the diffusional law of growth of new-phase precipitates

A method of calculation of the transformation kinetics for the geometric probability model with continuous nucleation and diffusional growth of new-phase precipitates is described. Previously, this method made it possible to calculate very exactly (with a level of error no greater than 0.00011) the evolution of the volume fraction of the non-transformed phase. It is shown that the upper bounds for the volume fraction of the nontransformed phase published recently for this model are much less accurate. The theoretical basis of the proposed calculation method is discussed.     

Autodoping during the deposition of epitaxial Silicon layers from the gas phase (I). Autodoping from the gas phase

The doping profile within the autodoping range of epitaxial layers deposited on lowresistance substrates, is considered the result of redistributing a substrate doping fraction through the substrate layer boundary, of incorporating a limited amount of dopants from the gas phase, originating from the preepitaxial process, and the result of incorporating dopants, externally admitted to the gas flow during the deposition. Assuming a special incorporation equilibrium to exist for the gas phase fraction of autodoping an analytic expression is derived, correlating the autodoping profile characteristic to the limited amount of dopants in the gas phase. The extent is discussed, to which the gas phase fraction of autodoping may be influenced by varying the deposition process.     

Inverse problem in the layer-by-layer growth model

The problem of finding structural features of growing structures for which a specified growth shape is allowable is considered within the model of layer-by-layer growth of tilings or packings and the generalization of this model to connectivity graphs. In particular, the problem of revealing growth shapes that are impossible for periodic structures is solved.     

Transient nucleation effects in glass formation

We extend to the non-isothermal case a numerical technique that was developed to treat transient homogeneous nucleation in a one-component system by modeling directly the reaction by which clusters are produced. Calculations are presented for the nucleation frequency during the quench and for the number of nuclei produced and the volume fraction transformed at the end of quench for different rates of cooling from the melt. Three model systems are considered: an alkali silicate which is a relatively good glass former, and two metallic glasses. These show a wide range of critical cooling rates for glass formation. In some systems transient effects are predicted to be critical for glass formation. A simple technique is presented for determining when transient effects are important based on a calculation using steady state nucleation frequencies and macroscopic growth velocities.     

Kinetics of Overall Phase Transition in Changing Size System

Kinetics of phase transition is studied for the more general case when the size of the system is assumed time dependent. In the three dimensional case typical examples in this respect could be connected with the solution of cosmological problems. In the two dimensional case could be the spreading and crystallization of undercooled water on oil or the experiments concerning phase transition in monolayers in a Lengmuir balance. The time dependence of the degree of overall transformation α(t) is formulated in a generalized form corresponding to above assumption. Explicit solutions are given for a constant rate of expanding (or shrinking) and for a constant acceleration of the size change of the system under the assumption that both nucleation rate I and linear growth rate G are constants. It is demonstrated that the process of phase transition proceeds much faster in a shrinking systems and is impeded in expanding ones. The reason for this effect is that parts of the new phase, formed in the initial parts of the system, are transferred into the diminishing volume (or surface). Thus the concentration of the new phase is mechanically increased.     

An X-ray scattering study of hydrogenated nanocrystalline silicon with varying crystalline fraction

Using X-ray diffraction (XRD) and small angle X-ray scattering (SAXS), we probed the nanostructural features of several PECVD grown nc-Si:H thin films with varying crystalline volume fraction. XRD results of a mixed phase film, 70% a-Si:H and 30% c-Si:H, show these crystallites have a preferred [220] orientation in the growth direction. Another film with approximately 90% c-Si also shows elongated grains, but with a preferred [111] orientation. The SAXS results also show an increase in scattering intensity when compared to the mixed phase material. In the mixed phase material, models show that the electron density fluctuations between the amorphous and crystalline phases are not enough to explain the measured SAXS scattering. Hydrogen clustered at the crystallite boundaries and in void regions of the a-Si phase must be included as well.     

Theoretical model of crystal growth shaping process

A theoretical investigation of the crystal growth shaping process is carried out on the basis of the dynamic stability concept. The capillary dynamic stability of shaped crystal growth processes for various forms of the liquid menisci is analyzed using the mathematical model of the phenomena in the axisymmetric case. The catching boundary condition of the capillary boundary problem is considered and the limits of its application for shaped crystal growth modeling are discussed.

The static stability of a liquid free surface is taken into account by means of the Jacobi equation analysis. The result is that a large number of menisci having drop-like shapes are statically unstable. A few new non-traditional liquid meniscus shapes (e.g., bubbles and related shapes) are proposed for the case of a catching boundary condition.     

Growth Kinetics of GaP Layers in Liquid Phase Electroeptiaxy (LPEE) from Limited and Unlimited Source

Growth kinetics of GaP layers in two LPEE modifications has been experimentally studied. In the first modification the vapour phase is employed as a source of crystallization. In the second case the losses of the solute during crystallization are not compensated. It has been found that growth kinetics can be treated in the frame work of the model where the growth rate is governed by mass-transport in liquid phase. It's shown that electromigration gives the main contribution to mass-transport at the considered experimental conditions. The quantitative estimations of the effective mass-transport parameters for phosphorus in gallium melt in the range 800 to 1050°C have been obtained.     

Peculiarities of Silicon Carbide Crystal Growth in Quasiclosed Volume

On the basis of the accomplished investigation is has been shown that in the known schemes for growing of SiC epitaxial layers from the gas phase in quasiclosed volume it takes place an excretion of the redundant silicon upon the front of crystallization, its accumulation in the gas phase up to the state of the saturation and its deposition upon the growing surface as drops. In this case the growth of the epitaxial layer takes place by the vapour-liquid-solid (VLS) mechanisms.     

Formation and properties of transition layers in epitaxial films

The current state of the problem of film-substrate transition layers in semiconductor epitaxial films is discussed. Reasons for the formation of a transition layer are considered: the influence of the substrate, the influence of the peculiarities of growth processes, and the influence of changes in the properties of the vapour phase over the growth surface. Estimates of the lattice mismatch, dislocation mobility, and impurity diffusion during growth are presented. The superimposition of size effects and the difference of estimates of a transition layer location according to data of electrophysical investigations are pointed out. Methods to remove transition layers are shown for cases of the homo- and heteroepitaxy of semiconductors.     

Electrical conductivity of new zinc phosphate glass/metal composites

Zinc phosphate–glass/metal composites have been successfully prepared. Glass with composition of 45 mol% ZnO–55 mol% P₂O₅ (ZP) has been filled with metallic powders (nickel and cobalt). The glass matrix thermal stability has been assessed by differential thermal analysis technique. The morphology has been examined by scanning electronic microscopy, showing almost homogenous composites. Comparison between the measured and calculated densities as a function of metallic content exhibits a good coherence and allows the estimation of porosity inside the composites. X-ray diffraction analysis has revealed that the ZP-matrix phase is amorphous when the temperature treatment is below the glass transition temperature T_g. However, the principal peaks observed in the case of the composites have been assigned to the metallic crystals of nickel or cobalt fillers. It has been found that the phosphate glass phase is not affected by the growing of the metallic network. The electronic conductivity measurements versus filler volume fraction have been investigated for the first time on phosphate–glass/metal composites. This study has shown the occurrence of a conducting transition at around 30% filler volume fraction. The obtained result has been interpreted on the basis of the statistical percolation theory frame.     

Growth mechanism of corundum crystals from cryolite (Na3AlF6) flux

Using the experimental data of the velocity versus supersaturation, υ(σ), relation and estimated values of liquid viscosity and density, flow velocity, and crystal density, the diameter of solute particles in solution in the growth of Al₂O₃ crystals from cryolite flux was estimated on the hard sphere model to be 11.8 Å. The step heights of single spiral layers on the (0001) face were measured by means of phase contrast microscopy and multiple-beam interferometry, which gave the values of 26 and 53 Å in two cases. Both values are in fair agreement in order of magnitude. It is suggested that the solute exists in the supersaturated solution in the form of culsters rather than ionic or molecular entities. Both from υ(σ) relation and diffusion coefficient values, the rate-controlling process in this case is considered to be volume diffusion through the unstirred boundary layer.     

Crystallization in solid solution-aqueous solution systems: Thermodynamic and kinetic approaches

A new phenomenological approach is proposed to describe the crystallization kinetics in solid solution-aqueous solution binary systems. The phase diagrams, equilibria, and quasie-quilibria are considered within this approach. The crystallization kinetics near the true equilibrium and the crystallization features at large deviations from equilibrium are discussed on this basis. Special attention is paid to possible interactions in a solution with a seed crystal placed in it. In particular, the interactions leading to the seed’s crystal growth or dissolution and to a possible exchange or metasomatic reactions are considered. In addition, the effect of the generated mismatch stress on the crystal growth rate and composition is analyzed.     

Crystallization kinetics of 1Na2O · 2CaO · 3SiO2 · glass monitored by electrical conductivity measurements

We investigated the kinetics of crystal nucleation, growth, and overall crystallization of a glass with composition close to the stoichiometric 1Na₂O · 2CaO · 3SiO₂. The nucleation and subsequent growth of sodium-rich crystals in this glass decreases the sodium content in the glassy matrix, drastically hindering further nucleation and growth. Compositional changes of the crystals and glassy matrix at different stages of the crystallization process were determined by EDS. These compositional variations were also monitored by electrical conductivity measurements, carried out by impedance spectroscopy, in glassy, partially, and fully crystallized samples. The electrical conductivity of both crystalline and glassy phases decreases with the increase of the crystallized volume fraction. Starting at a crystallized volume fraction of about 0.5, the crystalline phase dominates the electrical conductivity of the sample. This behavior was corroborated by an analysis of the activation energy for conduction. We show that electrical conductivity is highly sensitive and can indicate compositional shifts, changes in the spatial distribution of mobile ions in the glassy matrix. Conductivity measurements are thus a powerful tool for the investigation of complex heterogeneous systems, such as partially crystallized glasses and glass-ceramics.     

On normal kinetics in the case of some refractory and transition metals' crystallization

In given work the crystal growth kinetics connected with some refractory and transition metals is considered. For melts of Fe, Co, Ni, Cr, Zr, Ti, Ag, Cu, and Pb in the vicinity of melting temperatures the solid phase growth is described by means of a fluctuation theory applied for the macro-systems. By virtue of the “unlimited” and limited spectrum solid state particle concentration fluctuations' theory some effective kinetic coefficients have been estimated in the work. The effective kinetic coefficients are specific in the case of normal crystal growth kinetics. In the case of the crystallization of Fe, Co, Ni, Cr, Zr, Ti, Ag, Cu, and Pb-melts a comparison between two effective kinetic coefficients (based on the fluctuation theory and so-called equilibrium growth points density) has been realized. In most cases a satisfactory agreement between the effective kinetic coefficients has been observed.     

Conditions for metastable crystallization from undercooled melts

The limits of validity of Ostwald's rule of stages are investigated theoretically in the case of crystallization of undercooled melts. The treatment is within the limits of capillary theory. Two basic models are compared: (1) According to the first one (model A), the phase with lower energy of formation of critical nucleus is predominantly formed. In an enantiotropic-type phase diagram there is no region of homogeneous preferential formation of the low temperature phase. If the phase diagram is monotropic-type there is a certain temperature below which the metastable crystalline phase is preferentially formed. (2) The second assumption takes into consideration that the nature of extremely small phases is somewhat undefined. One certainly cannot determine whether, say 3-particle complex, is of phase 1 or of phase 2. Moreover, it is known that properties of extremely small clusters could be different from the corresponding volume phase. The main assumption is that there is a certain crucial size (n-particle complex) at which the nature of the two phases can be distinguished. Complex of the phase, which has lower chemical potential at the crucial size, will be formed first. According to the model, in the case of enantiotropic-type transition there is a critical temperature.     

Fluctuation mechanism of normal crystal growth during solidification of binary metallic melts

A recently published theory on the solidification of a one-component melt has been extended to the more complex case of binary systems. The theory is based on the model of a two-phase transitional zone existing between the crystalline phase and the melt. The concentration of solid state atoms within each mono-atomic layer of the transitional zone are assumed to fluctuate due to thermal fluctuations. A crystal growth law has been derived expressing the crystallization velocity in terms of probability functions describing these concentrations fluctuations. When certain restricting conditions concerning the atomic interaction energies within the transitional zone and the distribution of the atoms among the solid and liquid phases at supercooling are fulfilled the crystal growth law attains a simple form predicting for small supercoolings a growth rate proportional to supercooling (linear growth law), roughly proportional to physical parameter θ_AA, and with a weak dependence on another parameter Δ.