Alexander Virozub

Facetting during directional growth of oxides from the melt: coupling between thermal fields, kinetics and melt/crystal interface shapes

Implicit in most large-scale numerical analyses of crystal growth from the melt is the assumption that the melt/crystal interface shape and position are determined by transport phenomena. Although reasonable for many materials under a variety of growth conditions, this assumption is incorrect for a number of practical systems under realistic growth conditions. Specifically, the behavior of systems (e.g. certain oxides) which tend to develop facets along the melt/crystal interface is often affected both by transport phenomena and by interfacial attachment kinetics. We present a new modeling approach which accounts for interfacial kinetic effects during melt growth of large single crystals. The isotherm condition, typically employed at the melt/crystal interface, is replaced by an equation accounting for undercooling due to interface kinetics. A finite-element algorithm, designed to accommodate its numerical mesh to the appearance of facetted interfaces, is applied to this problem. Results are presented for the simulated directional growth of oxide slabs. The interplay between evolving thermal fields and anisotropic interface kinetics is investigated. In particular, the evolution of facets and the dependence of their size on growth conditions is explored. Trends reported here are in qualitative agreement with those appearing in the literature. Discrepancies between quantitative predictions of facet sizes using a theory (see Ann. Rev. Mater. Sci. 3 (1973) 397 and references within) and those calculated in this paper can, in a number of cases, be attributed to the simplifications on which this theory is based.

Three-Dimensional Simulations of Liquid Bridges between Two Cylinders: Forces, Energies, and Torques

We present numerical simulations of three-dimensional liquid bridges between two identical smooth and chemically homogeneous cylinders held at a fixed distance and angle one with respect to the other. Despite the limited range of parameters studied, an analysis of resultant forces, energies, and torques reveals a rich level of detail. For large enough separations between the cylinders, the bridges appear symmetric and stable in shape and are found to yield a negligible torque on the cylinders. The force of adhesion is found to be positive in this case (the cylinders are attracted one to the other). A reduction in the distance between the cylinders reveals different behavior depending on the particular value of the set of parameters considered. For example, it appears that while relatively low contact angle systems favor attractive (positive) forces and stable symmetric bridges for small separation distances, larger contact angles lead to the coexistence of stable asymmetric and (apparently) unstable symmetric solutions, mostly (and respectively) associated with near-zero and negative (repulsive) forces of adhesion. In addition, while the larger values of contact angles studied here (90 degrees, 110 degrees) are associated with barely detectable torques, smaller values of contact angle are found to be associated with torques acting to rotate cylinders into a position where they are parallel one with respect to the other.

Selecting finite element basis functions for computation of partially facetted melt/crystal interfaces appearing during the directional growth of large-scale single crystals

A finite element method capable of combining certain aspects of facetting in models of transport phenomena occurring within directional melt-growth systems was presented in Liu et al (1999 J. Crystal Growth 205 333). However, in certain cases this method suffers from difficulties most probably associated with the nature of the quadrilateral Lagrange biquadratic elements used in the analysis. This type of discretization yields a relatively low-order approximation of the melt/crystal interface crystallographic orientation which is also discontinuous at boundaries between elements. Here, two new finite element discretization techniques aimed at improving robustness of the method are presented and tested. In one case Lagrange cubic functions are used for representation of temperature and geometry, while in the other case Lagrange and Hermite cubic functions are used for calculations of temperature and geometry respectively. Both approaches provide a higher-order approximation of interface orientation, while in the case when Hermite functions are applied, an additional benefit in the form of a continuous (across element boundaries) interface orientation is achieved. Results from a number of tests show that both higher-order approximations provide a robust and efficient method for representation of geometry. In both cases, accuracy can be further increased with the aid of local mesh refinement in the vicinity of sharp corners on the interface. Finally, certain differences exist between the performances of these two methods. However, these seem (at this stage) minor compared to the benefits achieved relative to the previous lower-order approach.

Revisiting the quasi-steady state approximation for modeling heat transport during directional crystal growth. The growth rate can and should be calculated!

It is often feasible to use a quasi-steady-state (QSS) approach when analyzing heat transport in directional crystal growth systems. In such cases, it is common practice to approximate the growth velocity to be equal to the pull rate (the induced growth rate). The a priori unknown growth rate is needed for calculation of the rate of latent heat release during solidification. In this manuscript we propose and demonstrate the use of a modified QSS (MQSS) approach which allows for QSS analysis while taking into account, in a self-consistent manner, the calculated growth rate. The new method is shown to yield (for the model vertical gradient freeze system studied here) results which are in excellent agreement with those obtained from a fully transient model. This is achieved for all system parameter values considered in this manuscript, including those for which the standard QSS (SQSS) approach fails due to large deviations between the induced growth rate (the pull rate) and the actual, calculated growth rate. As expected, the SQSS approach is shown to yield satisfactory results when latent heat release is unimportant as well as in situations where the calculated growth rate is similar in value to the pull rate.

Radiative heat transport during the vertical Bridgman growth of oxide single crystals: slabs versus cylinders

Abstract Internal radiative heat transport in oxide crystals during their growth via the vertical Bridgman technique is known to promote severely deflected melt/crystal interface shapes. These highly curved interfaces are likely to encourage unwanted phenomena such as inhomogeneous distribution of impurities in the solidified crystalline material. Past computational analyses of oxide growth systems have mostly been confined to cylindrical geometries. In this letter a two-dimensional finite-element model, describing the growth of slab–shaped oxide crystals via the vertical Bridgman technique, is presented; internal radiative heat transport through the transparent crystalline phase is accounted for in the formulation. Comparison with calculations of cylindrical–shaped crystal growth systems shows a strong dependence of thermal fields and of melt/crystal interface shapes on the crystal geometry. Specifically, the interface position is strongly shifted toward the hot zone and its curvature dramatically increases in slab–shaped systems compared to what is observed in cylindrical geometries. This significant qualitative difference in interface shapes is shown to be linked to large quantitative differences in values of the viewing angle between the hot melt/crystal interface and the cold part of the crucible.

Human Milk Warming Temperatures Using a Simulation of Currently Available Storage and Warming Methods.

Human milk handling guidelines are very demanding, based upon solid scientific evidence that handling methods can make a real difference in infant health and nutrition. Indeed, properly stored milk maintains many of its unique qualities and continues to be the second and third best infant feeding alternatives, much superior to artificial feeding. Container type and shape, mode of steering, amount of air exposure and storage temperature may adversely affect milk stability and composition. Heating above physiological temperatures significantly impacts nutritional and immunological properties of milk. In spite of this knowledge, there are no strict guidelines regarding milk warming. Human milk is often heated in electrical-based bottle warmers that can exceed 80°C, a temperature at which many beneficial human milk properties disappear. High temperatures can also induce fat profile variations as compared with fresh human milk. In this manuscript we estimate the amount of damage due to overheating during warming using a heat flow simulation of a regular water based bottle warmer. To do so, we carried out a series of warming simulations which provided us with dynamic temperature fields within bottled milk. We simulated the use of a hot water-bath at 80°C to heat bottled refrigerated milk (60ml and 178 ml) to demonstrate that large milk portions are overheated (above 40°C). It seems that the contemporary storage method (upright feeding tool, i.e. bottle) and bottle warming device, are not optimize to preserve the unique properties of human milk. Health workers and parents should be aware of this problem especially when it relates to sick neonates and preemies that cannot be directly fed at the breast.