Miroslawa Rak

Kinetic Monte Carlo study of crystal growth from solution

A study of both surface micromorphology and growth kinetics of the (001) face of a crystal growing from solution is performed on the basis of Monte Carlo simulations taking into account surface diffusion. Special attention is paid to growth simulations performed for layer-by-layer growth mechanism. An influence of the size of two-dimensional array describing crystal surface on simulation results is also discussed. The presented results show that the size of the surface array affects both growth mechanism and growth rate. The simulation results are confronted with predictions of crystal growth theories. The influence of surface diffusion on growth process is compared with some results reported for vapor growth, and it is found that for solution growth, the influence is much weaker. An implementation of fast simulation algorithm with explicit growth time is presented. It is revealed that calculations of the average crystal growth rate using time proportional to the number of events fail in the case of the perfect face growing at low supersaturations.

Growth units concentration during crystal growth from solution

The BCF differential diffusion equation is solved and the growth units concentration at the surface is found. The analysis of the growth units concentration distribution gives information regarding the transport processes and adsorption phenomena as well as it indicates that the BCF expression for the growth rate is strongly limited to low values of supersaturation.

Transient surface supersaturation after crystal submersion (I)

The time dependent BCF equation is analytically solved for transient growth conditions occurring just after placing crystal in supersaturated solution. Thus the time dependences of surface concentration and surface supersaturation are found. The obtained results show that the higher bulk supersaturation the sooner the steady state is reached. The characteristic time necessary to reach the steady state, may be shorter or greater than the relaxation time for leaving the surface adsorption layer.

Modification of the step distance approximation

The modification of Cabrera and Levine formula which describes step distance on crystal surface is proposed. Replacing of bulk supersaturation by theoretically calculated surface supersaturation makes the so modified Cabrera and Levine approximation usable for both low and high supersaturations. In the case of middle values of supersaturations which are most frequently used in crystal growth practice, the modified approximation gives better results than other approximations.

Effect of step-distance approximations on growth unit concentration

In most papers concerning theory of crystal growth the distance between turns of the growth spiral (step distance) is described by Cabrera and Levine approximation. However, other approximations of this distance are proposed in literature. The effect of the applied step distance approximations on the dependences of growth units concentration and crystal growth rate versus supersaturation are analyzed in this paper. The results of calculations show that the Cabrera and Levine approximation may be used for very low supersaturations only.

Structures of impurity defects in KDP and their influence on the quality of crystals

On the basis of crystal chemical analysis and modeling KDP structure, the mechanism of incorporation of bivalent ions (Ni2+, Co2+, Fe2+, Mn2+) of radii 0.75 Å < r < 1.1 Å and trivalent ions (Al3+, Fe3+, Mn3+, Y3+, La3+) in KDP crystals is analyzed. For the considered bivalent (Me2+) and trivalent (Me3+) impurity ions, formation of two types of defect centers is revealed: isolated centers formed by trivalent impurity ions and Ni2+ ions; chains of bivalent impurity ions, oriented at an angle of 60° - 70° or even more to the [001] direction. The formation energy of Me2+ centers is much greater than that of Me3+ centers. This fact and crystal chemical analysis of structure deformations confirm stronger lattice strains generated by Me2+ ions in KDP structure. The different influence of Me2+ and Me3+ ions on surface morphology of KDP faces is presented. The effect of Me3+ ions is supposed to be due to the adsorption while the influence of Me2+ ions depend mainly on their incorporation in crystal structure (structural mechanism of impurity influence).© (2003) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Transient surface supersaturation after crystal submersion: II

In our earlier papers, we solved the time-dependent equation of Burton, Cabrera and Frank for transient state conditions occurring immediately after submersion of a crystal surface in supersaturated solution. As a result, the expression for the transient surface supersaturation was found and discussed. In this paper we present an approximation of that expression. The approximation enables a simple estimation of the time required to attain the steady-state value of the surface supersaturation.

Analysis of some limitations of Monte Carlo crystal growth simulations

Monte Carlo simulations with the use of a new, efficient algorithm have been performed for a wide range of supersaturation values. The influence of both the method of calculation of the average growth rate and the size of an array on the simulation results are analyzed. It is revealed that calculations of the average growth rate without the use of explicitly defined growth time lead to systematic errors and inconsistency with observed growth process, especially at low supersaturations. On the other hand, the size of an array affects not only value of the average growth rate but also operating growth mechanism. Therefore, the average growth rate increases non-linearly with increasing size of an array, tending to a constant value. This effect has been observed for growth of a perfect face as well as for growth of a face consisting steps.

Growth mechanism of KAP crystals: surface morphology of the (010) face

The surface morphology of the (010) face of KAP crystals growth from aqueous solution at low supersaturations (0.03 divided by 0.04) was investigated by the optical and electron microscopy using the gold decoration technique. The variety of growth patterns has been revealed: macroscopic hillocks, shallow hillocks, microscopic hillocks and numerous 2D nuclei. The macroscopic hillocks and smaller polygonal hillocks are formed by a group of cooperating dislocations or by a single dislocation. The density of observed shallow hillocks is higher than the dislocation density. The results reveal that, at low supersaturations, growth of the (010) face occurs by combined spiral and 2D nucleation mechanisms. The influence of low concentrations of organic additives on surface morphology of the (010) face has also been studied. The additives stimulate 2D nucleation and they increase the spread velocity of steps. The growth promoting effect of impurities is discussed in terms of the above data.

Monte Carlo model of crystal growth with solvation

A new modified Monte Carlo model of crystal growth is presented. The modification takes into account solvation and desolvation of growth units. The simulation results for growth on flat crystal surface are presented. The solvation effect changes the surface morphology as compared to the one simulated without solvation, but the growth rate seems to be practically unchanged.