T.A. Land

Recovery of surfaces from impurity poisoning during crystal growth

Growth and dissolution of crystal surfaces are central to processes as diverse as pharmaceutical manufacturing,, corrosion, single-crystal production and mineralization in geochemical and biological environments,. Impurities are either unavoidable features of these processes or intentionally introduced to modify the products. Those that act as inhibiting agents induce a so-called ‘dead zone’, a regime of low supersaturation where growth ceases. Models based on the classic theory of Cabrera and Vermilyea explain behaviour near the dead zone in terms of the pinning of elementary step motion by impurities,. Despite general acceptance of this theory, a number of commonly investigated systems exhibit behaviour not predicted by such models. Moreover, no clear microscopic picture of impurity–step interactions currently exists. Here we use atomic force microscopy to investigate the potassium dihydrogen phosphate {100} surface as it emerges from the dead zone. We show that traditional models are not able to account for the behaviour of this system because they consider only elementary steps, whereas it is the propagation of macrosteps (bunches of monolayer steps) that leads to resurrection of growthout of the dead zone. We present a simple physical model of this process that includes macrosteps and relates characteristics of growth near the dead zone to the timescale for impurity adsorption.

An in-situ AFM investigation of canavalin crystallization kinetics

We present the results of an in-situ atomic force microscopy investigation of the kinetics of canavalin crystal growth. The results show that, depending on the supersaturation, growth occurs on steps of one growth unit in height generated either by simple and complex screw dislocation sources, 2D nucleating islands, or macroclusters which sediment onto the surface before spreading laterally as step bunches. The step velocity of canavalin at three different pHs (pH = 7.0, 7.7 and 8.0) varies linearly with concentration and gives a kinetic coefficient β which depends strongly on pH, with β ≈ 2.6 × 10−3 cm s−1 at pH 7.3 to β ≈ 5.8 × 10−4 cm s−1 at pH 8.0. Analysis of the velocity of single steps versus that of step bunches created by macroclusters, as well as the occurrence of 2D nucleation on broad terraces, constrains the length scale for diffusion to be of the order of 1 mm. A simple diffusion analysis is presented which indicates that surface diffusion rather than bulk diffusion is the controlling mechanism of solute transport to the steps. A demonstration of step homogenization with an exponential time dependence for step pair decay is presented, and is found to be in qualitative agreement with predictions of the models of Schwoebel and Shipsey and Ehrlich and Hudda [R.L. Schwoebel. E.J. Shipsey, J. Appl. Phys. 37 (1966) 3682; G. Ehrlich, F.G. Hudda, J. Chem. Phys. 44 (1966) 1039]. showing that the behavior of the system is consistent with a model of surface-diffusion controlled growth coupled with an up-step diffusion bias. The relationship between step speed and terrace width during step homogenization was investigated quantitatively using the model of Gilmer et al. [G.H. Gilmer, R. Ghez, N. Cabrera, J. Crystal Growth 8 (1971) 79]. The best fit to the data is obtained with a surface diffusion length of 0.4–0.9 μm, and leads to estimates for values of the activation energy for adsorption to the terrace Ead, and for incorporation at the step Einc, of 0.27 and <0.1 eV, respectively. The results of this analysis are compared to those obtained from interferometric measurements on NH4H2PO4 (ADP), a common inorganic crystal, for which the kinetic coefficient is three orders of magnitude larger. The comparison indicates that the main reason for this difference is the slow adsorption rate to the surface for canavalin as compared to ADP.

The effect of dislocation cores on growth hillock vicinality and normal growth rates of KDP {1 0 1} surfaces

We present results from atomic force microscopy measurements on KDP {1 0 1} faces which show that over the range of supersaturations, 3% ≤ σ ≤ 30%, the terrace widths on vicinal growth hillocks formed by dislocations are nearly independent of both supersaturation and dislocation structure, in contradiction to the predictions of simple BCF models. The data also show that, for Burgers vectors in excess of one unit step height, the dislocations generate hollow cores in accordance with theoretical predictions. Both analytical and numerical analyses are presented, which show that a model that takes into account the effect of these cores on the period of step rotation predicts a dependence of slope on supersaturation and Burgers vector, which is in good agreement with the experimental results. These calculations also show that the effect of the core perimeter on the step transit time dominates the effect of reduced step velocity due to stresses near the core. Consequently, a simple analytical expression can be used to describe the slope even in the case of anistropic step kinetics. Finally, the results are used to explain the reproducible character of macroscopic growth rates and to rescale data on growth rate as a function of temperature and supersturation onto a single curve.

The evolution of growth modes and activity of growth sources on canavalin investigated by in situ atomic force microscopy

In situ atomic force microscopy has been used to investigate the evolution of growth modes and the activity of dislocation sources as a function of supersaturation during canavalin crystal growth. The results presented here show that, depending on the supersaturation, growth occurs on monomolecular steps generated either by simple or complex screw dislocation sources, 2D nucleating islands, or macroclusters that sediment onto the surface before spreading laterally as step bunches. We have observed the process of an individual dislocation source generating new steps which can be used to directly measure the critical length necessary for steps to advance. The activity of various dislocation sources are investigated as a function of supersaturation. A comparison of fundamental materials parameters for canavalin and a variety of other systems show systematic scaling. The kinetic coefficient decreases as the molecular complexity increases and the supersaturation at which 2D nucleation is observed increases with step free energy.

Mechanisms of protein and virus crystal growth: An atomic force microscopy study of canavalin and STMV crystallization

The evolution of surface morphology and step dynamics during growth of rhombohedral crystals of the protein canavalin and crystals of the cubic satellite tobacco mosaic virus (STMV) have been investigated for the first time by in situ atomic force microscopy. These two crystals were observed to grow by very different mechanisms. Growth of canavalin occurs on complex vicinal hillocks formed by multiple, independently acting screw dislocations. Small clusters were observed on the terraces. STMV on the other hand, was observed to grow by 2D nucleation of islands. No dislocations were found on the crystal. The results are used to determine the growth mechanisms and estimate the fundamental materials parameters. The images also illustrate the important mechanism of defect incorporation and provide insight to the processes that limit the growth rate and uniformity of these crystals.

Oriented liquid inclusions in KDP crystals

We describe a particular type of defect in KDP that consists of oriented chains of liquid inclusions. Using optical microscopy and X-ray topography we show that these inclusions are not directly formed by dislocations. The results of in situ atomic force microscopy show that hollow channels are stable during growth and that they can be caused by inclusion of foreign particles.

Using atomic force microscopy to investigate solution crystal growth

Publisher Summary Over the past 10 years, the atomic force microscope (AFM) has become a common tool for investigating the growth of crystal surfaces from solutions. This chapter describes the basic operation of the AFM and present examples of its application to crystal growth science. The dynamic range of the AFM makes it possible to access features with sizes from tens of nanometers to tens of microns. Operation of the AFM is possible in different environments including air, vacuum, vapor (including H2O), and solution. The choice of environment clearly depends on the objectives of the experiment. The majority of AFM studies on crystal surfaces have been performed either ex situ in air at room temperature or in situ in solution in the vicinity of room temperature. Despite the many reasons why in situ imaging is more desirable than ex situ imaging for investigating solution crystal growth physics, a simple analysis shows that many crystal systems simply grow too rapidly to allow for in situ operation. By increasing the super saturation, one can unambiguously monitor the transition to 2D nucleation using the AFM. The chapter provides examples of 2D nucleation on calcite, canavalin, and satellite mosaic tobacco virus (STMV).

A Study of Potassium Dihydrogen Phosphate (KDP) Crystal Surfaces by XPS

Potassium dihydrogen phosphate KH2PO4 (KDP) is a transparent dielectric material best known for its nonlinear optical and electro-optical properties (Refs. 1 and 2). Because of its nonlinear optical properties, it has been incorporated into various laser systems for harmonic generation and optoelectrical switching. In addition, KDP is particularly suitable for use in large-aperture laser systems such as that located at the National Ignition Facility (NIF) because it can be grown as a single crystal to large size (Refs. 3 and 4). Despite the importance of this material, surface composition and surface electronic structure data were found to be nonexistent. X-ray photoemission spectroscopy was thus used to characterize the composition and surface structure of (100) and (101) native crystals.

Growth Morphology of Vicinal Hillocks on the {101} Face of KH 2 PO 4 : Evidence of Surface Diffusion

The growth morphologies of vicinal hillocks on KH 2 PO 4 {101} surfaces have been investigated using atomic force microscopy. Both 2D and spiral dislocation growth hillocks are observed on the same crystal surface at supersaturations of ∼5 %. Growth occurs on monomolecular 5 A steps both by step-flow and through layer-by-layer growth. The distribution of islands on the terraces demonstrate that surface diffusion is an important factor during growth. Terraces that are less than the diffusion length do not contain any islands. This, together with the length scale of the inter island spacing and the denuded zones provide an estimate of the diffusion length. In situ experiments at very low supersaturation (∼0.1 %) show that growth is a discontinuous process due to step pinning. In addition, in situ images allow for the direct determination of the fundamental growth parameters a, the step edge energy, and β, the kinetic coefficient.