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Shear flow alters the rate at which crystals nucleate from solution, yet the underlying mechanisms remain poorly understood. To fill this knowledge gap, we explore the response to shear of dense liquid clusters, which may serve as crystal nucleation precursors. Solutions of the protein lysozyme were sheared in a Couette cell at rates from 0.3 to 200 s−1 for up to seven hours. The cluster size and total population volume were characterized by dynamic light scattering. We demonstrate that shear rates greater than 10 s−1 applied for longer than one hour reduce the volume of the cluster population. The likely mechanism of the observed response involves enhanced partial unfolding of the lysozyme molecules, which exposes hydrophobic surfaces between the constituent domains to the aqueous solution. We show that disruption of the intramolecular S-S bridges does not contribute to the mechanism of response to shear. The decrease of the cluster population volume with increasing shear rate or shear time implies that nucleation could be inhibited at moderate shear rates.

We use atomic force microscopy to explore the mechanisms of crystal growth of the protein lumazine synthase. We find that at moderate supersaturations, the only mechanism of layer generation on the (0 0 1) face is via landing of ∼100 nm large dense objects. After landing on the crystal surface, the objects flatten and yield stacks of steps. These steps merge continuously with each other and with the underlying lattice. These observations allow us to conclude that the dense objects are not microcrystals nucleated in the solution, but are droplets of the dense liquid phase. Dynamic light scattering revealed the presence of dense liquid droplets, which are metastable with respect to the solution, have a finite lifetime of several seconds, radii of 50–200 nm, and consist of 10 2 –10 4 molecules. Under the influence of the periodic field of the crystal upon landing on the crystal surface, these droplets stabilize and transform into stacks of crystalline layers, whose spreading results in crystal growth. Since crystals of this protein do not have dislocations, and two-dimensional (2D) nucleation of new layers does not occur, likely because of high barriers, the sedimentation and structuring of metastable droplets of protein-rich liquid is the only mechanism providing for crystal growth.

Summary of recent results on fundamental issues in crystal growth from non-stoichiometric solutions, development of steps with low kink density and influence of turbulence on step bunching.

We investigated the effects of the constant electric fields from 2.0 to 6.0 kV cm −1 on the nucleation of ferritin, apoferritin and lysozyme crystals. For this, supersaturated solutions of the three proteins were held between electrodes separated by 1.0 cm in batch and sitting drop geometries without contact between electrodes and solutions. The nucleation rate was characterized by the number of crystals appearing after a certain time (1–3 days). We show that in sitting drop arrangements, weak electric fields ( −1 ) either suppress or have no effect on the nucleation rate of ferritin and apoferritin, while electric fields of 5 or 6 kV cm −1 reproducibly enhance crystal nucleation of both proteins. Electric fields of all tested strengths consistently enhance lysozyme crystal nucleation. All batch experiments showed no effect of the electric field on the nucleation rates. Since the solutions contain high electrolyte concentrations and are conductive, the electric field strengths within them are negligible. We show that the electric field causes solution stirring with rates of up to 100 μm s −1 , depending of the field strength. Thus, our observations indicate that at slow solution flow rates, the rates of nucleation of ferritin and apoferritin crystal are suppressed, while faster stirring enhances crystal nucleation of these proteins. All solution flow rates enhance lysozyme crystal nucleation. Our results suggest that solution convection may strongly affect nucleation, and that for some systems, an optimal convection velocity, leading to fastest nucleation, exists.

A line of recent theories and simulations have suggested that the nucleation of crystals might, under certain conditions, proceed in two steps: the formation of a droplet of a dense liquid, metastable with respect to the crystalline state, followed by ordering within this droplet to produce a crystal. Here, experimental tests are discussed of the applicability of this mechanism to the nucleation of ordered solid phases: crystals, or linear, planar, branched, or otherwise ordered aggregates, of proteins and small-molecule materials from solution. The main arguments stem from results on the kinetics of homogenous nucleation of crystals of the protein lysozyme. These results indicate that under a very broad range of conditions the nucleation of lysozyme crystals occurs via a modification of the theoretically postulated mechanism—as a superposition of fluctuations along the order parameters density and structure. Depending on whether the system is above or below its liquid–liquid coexistence line, a density fluctuation may never or may selectively lead to the formation of a dense liquid droplet; in the former case the high-density region, the “quasi-droplet”, is metastable also with respect to the dilute solution. In both cases, the molecules contained in the high-density region may attain an ordered arrangement, i.e., a structure fluctuation is superimposed on the density fluctuation and a crystalline nucleus obtains. This outlook on the nucleation of ordered solids from dilute phases suggests that the rate of nucleation can be controlled either by shifting the phase region of the dense liquid phase, or by facilitating the structure fluctuations within a dense liquid droplet or quasi-droplet. Results from literature indicate that the proposed two-step nucleation mechanism and the related tools for nucleation control may be applicable to the formation of crystalline and non-crystalline ordered solid phases of other, protein and non-protein materials, from solution.

We have developed a real-time phase-shifting interferometer capable of imaging of interfacial morphology with a depth resolution of ∼25 A and lateral resolution of ∼0.5 μm across a field of view of 2×2 mm 2 . The method employs a phase-shifting algorithm employing five interferograms and image processing that yield a three dimensional digital representation of the surface relief. The time resolution of imaging is 0.1 s. This method is applied in situ to the (1 0 1) face of potassium dihydrogen phosphate crystals growing from an aqueous solution. We image the formation and evolution of solution-flow induced step bunches and determine their characteristic wavelength to be λ c =45 μm. This wavelength is within the range predicted by a stability theory based on balance between the diffusion interaction between steps and capillarity. The found value suggests that step–step interactions are the likely major factor for instability.

We investigated the homogeneous nucleation and subsequent evolution of polymers of sickle cell hemoglobin (HbS) using differential interference contrast (DIC) microscopy. The same technique was employed to determine the liquid–liquid separation boundaries for a variety of conditions in solution of sickle cell and normal human hemoglobin. The HbS polymers were also imaged using atomic force microscopy. We found that the location of Liquid–Liquid phase boundary under conditions that mimic those in the erythrocytes is consistent with previous determinations of the spinodal for this phase transition. Increasing the ionic strength shifts this phase boundary to significantly lower temperatures and Hb concentrations. We also found that the nucleation of individual HbS fibers indicates that the process is random and follows statistics similar to those established for nucleation of crystals or liquid droplets from vapors.

We have studied the nucleation of crystals of the model protein lysozyme using a novel technique that allows direct determinations of homogeneous nucleation rates. At constant temperature of 12.6°C we varied the thermodynamic supersaturation by changing the concentrations of protein and precipitant. We found a broken dependence of the homogeneous nucleation rate on supersaturation that is beyond the predictions of the classical nucleation theory. The nucleation theorem allows us to relate this to discrete changes of the size of the crystal nuclei with increasing supersaturation as (10 or 11)→(4 or 5)→(1 or 2). Furthermore, we observe that the existence of a second liquid phase at high protein concentrations strongly affects crystal nucleation kinetics. We show that the rate of homogeneous nucleation of lysozyme crystals passes through a maximum in the vicinity of the liquid–liquid phase boundary hidden below the liquidus (solubility) line in the phase diagram of the protein solution. We found that glycerol and polyethylene glycol (PEG), which do not specifically bind to proteins, shift this phase boundary and significantly suppress or enhance the crystal nucleation rates, although no simple correlation exists between the action of PEG on the phase diagram and the nucleation kinetics. This provides for a control mechanism which does not require changes in the protein concentration, or the acidity and ionicity of the solution. The effects of the two additives on the phase diagram strongly depend on their concentration and this provides opportunities for further tuning of nucleation rates.

We used chromatographic, static and dynamic light scattering techniques, and atomic force microscopy (AFM) to study the structure of the protein species and the protein–protein interactions in solutions containing two apoferritin molecular forms, monomers and dimers, in the presence of NaAc buffer and CdSO 4 . The sizes and shapes of the monomers and dimers, separated by size-exclusion chromatography, were determined by dynamic light scattering and AFM. While the monomer is an apparent sphere with a diameter corresponding to previous X-ray crystallography determinations, the dimer shape corresponds to two, bound monomer spheres. Static light scattering was used to characterize the interactions between solute molecules of monomers and dimers in terms of the second osmotic virial coefficients. The addition of even small amounts of Cd 2+ causes attraction between the monomer molecules. Furthermore, we found that the second virial coefficient and the protein solubility do not noticeably depend on temperature in the range from 0°C to 40°C. This suggests that the enthalpy for crystallization of apoferritin is close to zero, and the gain of entropy is essentially constant in this temperature range. We also found that in solutions of the apoferritin dimer, the molecules attract even in the presence of acetate buffer only, indicating a change in the surface of the apoferritin molecule. In view of the repulsion between the monomers at the same conditions, this suggests that the dimers and higher oligomers form only after partial unfolding of some of the apoferritin subunits. These observations suggest that aggregation and self-assembly of protein molecules or molecular subunits may be driven by forces other than those responsible for crystallization in the protein solution.

Using the atomic force microscope (AFM) in-situ during the crystallization of a model protein, we investigate the elementary processes of crystal growth at the molecular level. We show that the density of the incorporation sites (kinks) on growth steps propagating on the surface (i) is the same as at equilibrium, and (ii) does not depend on the macroscopic step orientation since during growth the steps consist of segments along the dense crystallographic directions. Observation (i) allows evaluation of the bond energy between molecules in the crystal as 3.2 k B T . Furthermore, we determine the frequency of attachment of molecules at the kinks and show that step motion is fully described by this frequency and the kink density. We monitor the formation of point defects and show that, unlike in semiconductors, they are caused by incorporation of impurity particles and therefore are nonequilibrial. The point defects replicate in subsequent layers due to the strain they cause. We demonstrate that using single-molecule manipulation with the AFM tip the defects can be “healed” to restore the regular lattice.

Ribonuclease, insulin, cytochrome C, myoglobin and ovalbumin were introduced into solutions from which ferritin and lysozyme crystals were grown. These measurements were also performed for the ferritin dimers trapped by growing ferritin crystals. The crystals were later dissolved in a pure solvent, the impurity concentrations were measured by high performance liquid chromatography and the effective impurity distribution coefficient, K, was evaluated relative to the initial concentrations of ferritin or lysozyme. The density of impurity species in crystal relative to its density in mother solution were used to calculate volumetric distribution coefficient, k. These distribution coefficients was found to exceed unity (k>1) in terrestrial condition for all impurity species, except for insulin and cytochrome C lysozyme. For ferritin dimers, K=4, k=1.8×103. Crystals grown in space under the otherwise identical conditions incorporated lower amounts of all of these impurities, majority of them below the detection limit. The lower impurity incorporation obtained in stagnant solution may be partially due to more difficult impurity supply through the impurity depletion zone arising around the growing crystals at k>1 in the absence of buoyancy driven convection or stirring. Analytical estimates of the depletion zone show reasonable agreement with measurements for ferritin dimers. Step bunching and other flow-dependent surface processes may also contribute to lower distribution coefficient.

In situ high-resolution optical interferometry of lysozyme crystal growth reveals that under steady external conditions, the local growth rate R, vicinal slope p and step velocity are not steady but fluctuate by several times their average values. The variations in p, which is proportional to the local step density, indicate that these fluctuations occur through the dynamic formation of step bunches. Our previous work with unstirred solutions has shown that the fluctuation amplitude of R increases with supersaturation and crystal size (Vekilov et al., Phys. Rev. E 54 (1996) 6650). Based on scaling arguments and numerical simulations, we have argued that the fluctuations are the response of the coupled bulk transport and nonlinear interface kinetics to finite amplitude perturbations provided by the intrinsically unsteady step generation. In this paper, we emphasize the recently discovered spatio-temporal correlation between the sequence of moving step bunches and striations (compositional variations) in the crystal, visualized by polarized-light microscopy. Hence, these unsteady kinetics have detrimental effects on the perfection of the crystals, and means to reduce and eliminate them should be sought. To this end, based on the above conclusion as to the mechanism of the kinetic unsteadiness, we accelerated the bulk transport towards the interface by forced solution flow. We found that this results in lower fluctuation amplitudes. This observation confirms that the system-dependent kinetic Peclet number, Pek, i.e., the relative weight of bulk transport and interface kinetics in the control of the growth process, governs the step bunching dynamics. Since Pek can be modified by either forced solution flow or suppression of buoyancy-driven convection under reduced gravity, this model provides a rationale for the choice of specific transport conditions to minimize the formation of compositional inhomogeneities. Interestingly, on further increase of the solution flow velocities >500 μm/s, the fluctuation amplitudes in R increased again, while the average growth rate decreased. At low supersaturations, this leads to growth cessation. The growth instability, deceleration and cessation were immediately reversible upon reduction of the flow velocity. When solutions, intentionally contaminated with ∼1% of covalent lysozyme dimer were used, these undesirable phenomena occurred at about half the flow rates required in pure solutions. Thus, we conclude that enhanced convective supply of impurities to the interface causes an increase in step-bunching related defects, growth deceleration and, in some cases, cessation. Finally, we correlate the “slow protein crystal growth” to step bunch formation. We show that in the absence of significant step density variations, the kinetic coefficient for step propagation is as high as 4×10−3 cm/s, which is 1–2 orders of magnitude higher than the previously determined, apparent values for any protein.

Crystals of tetragonal hen egg white lysozyme (HEWL) grown on a series of space missions and their terrestrial counterparts were analyzed by gel electrophoresis and X-ray diffraction. The crystals were produced by vapor-diffusion and dialysis methods. The microgravity and terrestrial grown HEWL crystals were found to have effective partitioning coefficients (K eff ) for an oxidatively formed covalent dimer impurity (MW 28 K) of 2 and 9, respectively, i.e. the latter contain 4.5 times more dimers. The microgravity grown crystals allowed the collection of 24% more useful reflections and improved the resolution from 1.6 to 1.35 A. Other improvements were also noted including lower isotropic B-factors of 16.9. versus 23.8 A 2 for their terrestrial counterparts. High-resolution laser interferometry was applied quantitatively to evaluate the influence of dimer impurity on growth kinetics. It is shown that the growth of the (1 0 1) face from solution into which I % dimers were introduced decelerates with increasing solution flow rate and the growth stops at a flow rate of about 0.2 mm/s. This effect occurs faster than in ultrapure solutions. The covalently bound dimers essentially increase the amplitudes of the striation-inducing growth rate fluctuations. The effect is ascribed to the enhanced transport of growth inhibiting HEWL dimer to the interface. Theoretical analysis shows that a stagnant solution around a growing crystal is strongly depleted with respect to impurity by about 60% for the measured growth parameters as compared to the solution bulk. Thus, a crystal in microgravity grows from essentially purer solution than the ones in the presence of convection flows. Therefore, it traps less stress inducing impurity and should be more perfect. For crystal/impurity systems where K eff is small enough microgravity should have an opposite effect.

We have experimentally studied the effects of solution flow on the growth kinetics of the protein lysozyme. To this end, we have expanded our interferometry setup by a novel crystallization cell and solution recirculation system. This combination permits monitoring of interface morphology and kinetics with a depth resolution of 200 A at bulk flow rates of up to 2000 micron/s. Particular attention was paid to the prevention of protein denaturation that is often associated with the pumping of protein solutions. We found that at bulk flow rates it less than 250 microns/s the average growth rate and step velocity, R(sub avg) and upsilon(sub avg) increase with increasing it. This can be quantitatively understood in terms of the enhanced, convective solute supply to the interface. With high-purity solutions, it u greater than 250 microns/s lead to growth deceleration, and, at low supersaturations sigma, to growth cessation. When solutions containing approx. 1% of other protein impurities were used, growth deceleration occurred at any u greater than 0 and cessation in the low sigma experiments was reached at about half the it causing cessation with pure solution. The flow-induced changes in R(sub avg) and upsilon(sub avg) including growth cessation, were reversible and reproducible, independent of the direction of the u-changes and solution purity. Hence, we attribute the deceleration to the convection-enhanced supply of impurities to the interface, which at higher flow rates overpowers the effects of enhanced interfacial solute concentration. Most importantly, we found that convective transport leads to a significant reduction in kinetics fluctuations, in agreement with our earlier expectations for the lysozyme system. This supports our hypothesis that these long-term fluctuations represent an intrinsic response feature of the coupled bulk transport-interfacial kinetics system in the mixed growth control regime.

Recently, much progress has been made in understanding the nucleation and crystallization of globular proteins, including the formation of compositional and structural crystal defects. Insight into the interactions of (screened) protein macro-ions in solution, obtained from light scattering, small angle X-ray scattering and osmotic pressure studies, can guide the search for crystallization conditions. These studies show that the nucleation of globular proteins is governed by the same principles as that of small molecules. However, failure to account for direct and indirect (hydrodynamic) protein interactions in the solutions results in unrealistic aggregation scenarios. Microscopic studies of numerous proteins reveal that crystals grow by the attachment of growth units through the same layer-spreading mechanisms as inorganic crystals. Investigations of the growth kinetics of hen-egg-white lysozyme (HEWL) reveal non-steady behavior under steady external conditions. Long-term variations in growth rates are due to changes in step-originating dislocation groups. Fluctuations on a shorter timescale reflect the non-linear dynamics of layer growth that results from the interplay between interfacial kinetics and bulk transport. Systematic gel electrophoretic analyses suggest that most HEWL crystallization studies have been performed with material containing other proteins at percent levels. Yet, sub-percent levels of protein impurities impede growth step propagation and play a role in the formation of structural/compositional inhomogeneities. In crystal growth from highly purified HEWL solutions, however, such inhomogeneities are much weaker and form only in response to unusually large changes in growth conditions. Equally important for connecting growth conditions to crystal perfection and diffraction resolution are recent advances in structural characterization through high-resolution Bragg reflection profiling and X-ray topography.

Interferometric microscopy was used to investigate the growth morphology and kinetics of {110} and {101} faces of tetragonal lysozyme crystals. Solutions were prepared from as-received Sigma and Seikagaku material, and Seikagaku lysozyme further purified by cation exchange liquid chromatography under salt-free conditions. The protein composition of the solutions was characterized by sodium dodecyl sulphate (SDS) electrophoresis with silver staining. We found that on crystals smaller than about 150 μm, 2D nucleation sites were randomly distributed over the faces. With increasing crystal size, surface nucleation became restricted to facet edges and, eventually, to facet corners. This reflects the higher interfacial supersaturation at these locations. However, on some crystals, we observed 2D nucleation at preferred non-corner sites presumably associated with defects. Upon abrupt temperature decreases, dislocation step sources formed on faces that previously had none. Within groups of dislocations, the dominating step source changed frequently. Depending on the activity of the dislocation groups, growth rates of different crystals differed by up to a factor of five during the same experiment. On facets with dislocation step sources, step generation by 2D nucleation became dominant above a critical supersaturation σ∗. In the absence of dislocations, nucleation-induced growth set in at σ < σ∗. In solutions with higher impurity concentrations, the density of the steps generated by 2D nucleation was higher and σ∗ was lower. Hence, it appears that impurity adspecies are active in surface nucleation. The presence of less than 1% of protein impurities with molecular weight (MW) ≥ 30 kD had significant effects on the crystallization kinetics. Step motion was impeded even at high σ, presumably through blocking of kink sites. In solutions without these high MW impurities, facets containing step sources did not grow below σ = ln(C / Csat) < 0.5. In the less pure solutions such a “dead zone” was not observed. Hence, it appears that in lysozyme dead zones are caused by non-protein impurities. In growth from the highly purified material no growth sector boundaries were visible, in contrast to the as-received lysozyme, and striae formation on growth temperature changes appeared drastically reduced.

A model for the evolution of facet morphologies in growth from solutions is presented. The numerical model links, for the first time, bulk transport of solute and impurities in a solution growth cell with microscopic interfacial kinetics processes. The macroscopic transport is dealt with as in the 2D model [H. Lin, F. Rosenberger, J.I.D. Alexander and A. Nadarajah, J. Crystal Growth 151 (1995) 153] of a crystallization cell used for lysozyme in our laboratory. The microscopic kinetics is incorporated through a meso-scale continuum model of growth step motion in response to the interfacial concentration distributions. Local growth step velocities are linearly interpolated from the values obtained at the grid points of the bulk transport simulation. Experimentally determined kinetics and transport coefficients are employed. We find that the facets remain macroscopically flat, in spite of the lower nutrient and impurity concentrations in the facet center regions. This stabilization is achieved through the formation of a microscopic depression in the facet, with nonuniform vicinal slope (step density). If the step density in the facet center exceeds a certain value, no further stabilization results on further steepening, and the facet loses its macroscopic morphological stability. This loss of morphological stability depends sensitively on the value of the steps' kinetic coefficient. For pure lysozyme-precipitant solutions, we obtain microscopic depressions with a higher slope at the facet center than at the edge. However, with an impurity that impedes step kinetics and is preferentially incorporated into the crystal, the simulations produce microscopic facet depressions with higher slope at the edge. Impurity depletion at the interface, due to low initial concentration and/or slow diffusion leads to mixed shapes, and eventually to shapes typical of growth from pure solution. Quantitative agreement with facet morphologies observed on lysozyme crystals [P.G. Vekilov and F. Rosenberger 158 (1996) 540] is obtained, assuming overlap of the steps' diffusion fields.

The growth morphology and kinetics of crystal facets were investigated by in-situ high-resolution optical interferometry, using tetragonal lysozyme as a model system. The protein composition of the growth solutions was characterized by high pressure liquid chromatography and gel electrophoresis. In relatively pure solutions, the facets exhibited depressions with lower vicinal slope at their edges. In solutions with ≤ 1% of protein impurities, that were found to be incorporated into the crystal, the depressions in the facets had higher vicinal slope at the edges. These deviations from planarity increased with crystal size and growth rate. This indicates that transport-induced nonuniformities in the nutrient and impurity concentrations cause these microscopic shapes. Quantitative accounts of both interface shapes are possible only if one assumes strong overlap of the coupled volume and surface diffusion fields of growth steps. From this we conclude that the characteristic surface diffusion length of ad-molecules on lysozyme 110 facets is of order 1 μm or ∼ 200 molecule diameters. The values obtained for the average step (tangential) velocities in the lower purity solutions suggest that the impurities affect growth kinetics through their adsorption at kink sites.

Laser Michelson interferometry was applied to study the elementary growth mechanism of protein crystals. The results for the (101) face of tetragonal lysozyme show that for supersaturations σ higher than 1.6, growth proceeds by two-dimensional nucleation. However, at lower supersaturations growth is governed by dislocation sources. The observed non-linearity of the step velocity versus supersaturation dependence for supersaturations up to 1.2 is proved to be due to strong impurity effects. At σ < 0.4 the crystal surface is covered with macrosteps. The effective step kinetic coefficient for the studied face is determined: β = 2.8 × 10−6 m/s. The applicability of general crystal growth principles and theories to protein crystallization is thus illustrated.

The elementary processes of electrochemical growth of cubic faces of silver single crystals were investigated after the so-called capillary method by means of in situ laser Michelson interferometry. Data were obtained about the motion of dislocation generated steps during electrocrystallization from a stagnant solution. It was proved that step motion proceeds after the direct incorporation mechanism, with bulk diffusion field overlap, leading to deviation from linearity in the step velocity/overvoltage dependence at higher hillock slopes. The true value of the step kinetic coefficient for the studied face was determined: β = 1.2 cm/s. In acidified solutions β is much smaller: β = 0.17 cm/s. Interferometric measurements of hillock slope versus overvoltage dependencies allowed us to determine the Burgers vectors of the leading growth dislocation sources. The free surface energy of the step riser was determined without any additional suppositions: for pH ≅ 5 it was 130 erg/cm 2 and for pH ≅ 1 it was 110 erg/cm 2 .

Michelson interferometry combined with X-ray topography was applied to study growth morphology and kinetics of the (101) ADP face in a flowing solution. Step velocity was measured as a function of different parameters. The data reveal a step-step interaction at average distances of the order of ≈ 1 μm. This interaction is interpreted in the terms of surface diffusion. Parameters of step motion and adsorption on the surface are determined. Azimuthal growth anisotropy is related to crystal structure. A formula giving the azimuthally anisotropic hillock slope versus supersaturation on a complex dislocation source plus experimental dependencies of the hillock slope on the supersaturation for various dislocation sources enabled us to determine the free surface energy of the step riser α = 29 erg/cm2 and the Burgers vector of the growth sources. “Quantization” of the measured hillock slopes in the whole supersaturation region supposes identical structure of the dislocation sources of equal strength.

In-situ Michelson interferometry was applied to study the (101) ADP face in the temperature ( T ) interval 29–67 °C. The slopes of the growth hillock on one and the same dislocation source were independent of T . The surface diffusion model is valid for all the temperatures studied. The effective activation energy for step propagation was 65 kJ/mol for T T #62; 40°C. This is explained by the splitting up of nonelementary steps, existing at low T to give unitary height steps at higher T . Thus the free energy of this surface structure phase transition is Δ = 18 kJ / mol . The anisotropy of the growth features is connected to the crystal structure through the “jump” distance in different directions. The activation energy for adsorption of the ADP particles on the surface is determined as E ad = 35 kJ / mol .

Michelson interferometry and X-ray topography were applied to study the growth kinetics on dislocation sources with changing structure. To vary the size of the critical two-dimensional nucleus ϱ c independent of supersaturation, the experiments were carried out under two different pH values of the mother solution. Different Cr 3+ concentrations were added to observe impurity effects. It is shown that the dislocation source consists of parallel dislocations and splits if the distance between a pair of dislocations d does not satisfy the condition d πϱ c . On the contrary, dislocations that follow the above condition always form a joint growth source. Different types of R (σ) curves appear if the growth source activity changes. Due to the Gibbs-Thomson effects, the growth source activity drops when it approaches the crystal edge. If no other dislocations are present on the studied face, its growth is governed by the adjacent prism face - “dependent growth”. A formula to describe it is proposed.

X-ray topography and laser Michelson interferometry combined with a two-thermostat interswitchable growth system were applied to study the (101) ADP face in undersaturated solutions. The movement of existing step patterns proved to be symmetrical with respect to growth and dissolution. The limiting undersaturation for the appearance of a dislocation etchpit (α∗=0.5%) allowed us to estimate the Burgers vector/effective free surface energy ratio for one of the dislocation sources: b /α=5.3x10 -8 J -1 m 3 . Etching of micro-defects and of colloid size particles present in the crystal was observed. Dissolution and regeneration of the crystal edges show a strong step diffusion field overlap. The (100) ADP face surface layer dissolves in a slightly supersaturated solution, presumably due to excess stress. Etching of vicinal boundaries was observed and the existence of a limiting undersaturation for it helped us to propose a new model of sectorial boundaries.