Shape of steps on the (010) face of orthorhombic lysozyme crystals

An attempt is made to explain the shape of the curved steps at the (010) face of orthorhombic lysozyme crystals and to determine the density, the rate of formation, and the velocity of kinks. The interpretation is performed in terms of the concepts developed in studies on the crystallization of long-chain polymers within the Frank model. It is demonstrated that this model is incorrectly generalized to the case of high kink densities. A algorithm for determining the coordinates of the growth front in images obtained with atomicforce microscopes is proposed and implemented.     

Dependence of the step velocity on its length on the (010) face of the orthorhombic lysozyme crystal

The length of a two-dimensional critical nucleus has been measured, and the Gibbs-Thomson formula has been experimentally verified on orthorhombic lysozyme crystals. The step velocity was found to be independent of its length. The critical length initiating the step motion can be determined by a low density of kinks on a step, and not the critical-nucleus size. The invalidity of the Gibbs-Thomson formula in this case is discussed.     

Determination of individual rate constants of reaction and diffusion steps from over-all crystal growth coefficient

A universal method, being a solution of the problem formulated independently by NÝVLT and GARSIDE in 1971 is proposed. The method makes it possible — having at one's disposal the experimental growth rate constant — to determine individual rate constants of the main steps of the process of crystal growth i.e., the diffusion step and the surface integration step and thus indicate the step controlling the whole process of crystal growth. Experimental data on crystal growth of MgSO₄ and ZnSO₄ were evaluated.     

Solubility of tetragonal and orthorhombic lysozyme crystals under high pressure

Two-beam interferometry was applied to measure lysozyme solubility under high pressure. This rapid method allowed determination of one data point within 3 h. The solubility of tetragonal lysozyme crystals was determined as a function of temperature at 0.1, 50, and 100 MPa, and that of orthorhombic crystals was measured at 0.1 and 100 MPa. The solubility of tetragonal crystals increased with pressure; however, that of orthorhombic crystals decreased. In both cases, the enthalpy and entropy of dissolution decreased with pressure.     

Electrocrystallization of silver: Growth kinetics of screw-dislocation-free (100) crystal faces

At given conditions, especially at higher supersaturation, the growth rate of a close packed, perfect crystal face depends on the formation rate of two-dimensional nuclei and on the propagation rate of the monoatomic layers. This multinuclear multilayer growth as well as the advancement rate of growth steps have been studied experimentally on electrocrystallization of silver. The advancement rate of mono- and polyatomic growth steps has been measured on screw dislocation-free (100) crystal faces. For low overvoltages a linear dependence of the rate on overvoltage has been found. A strong influence of the surface condition of the crystal face — “fresh” or “aged” on the step advancement rate has been established. It was also found that on a “fresh” surface mono- and polyatomic steps advance with the same rate. The average monoatomic step spacing of the polyatomic step has been determined. The kinetic constants of the step growth rate are established and a conclusion regarding the mechanism of electrolytic deposition of silver is drawn. The initial current—time curves were recorded on applying potentiostatic pulses on a perfect crystal face. The shape of these curves coincides very well with those theoretically calculated for the cases of multinuclear growth. On the basis of the theoretical dependences, one can determine from these curves the formation rate J of two-dimensional nuclei at a given overvoltage η since the rate of step advancement is known. A linear dependence of log J on 1/η has been established. The values of the pre-exponential term in Volmer's equation and the specific edge energy of the two-dimensional nucleus have been determined. The surface condition of the crystal face influences strongly also the process of two-dimensional nucleation.     

In situ atomic force microscopy studies of surface morphology,growth kinetics,defect structure and dissolution in macromolecular crystallization

Surface morphologies of thaumatin, catalase, lysozyme and xylanase crystals were investigated using in situ atomic force microscopy. For thaumatin, lysozyme and xylanase crystals, growth steps having a height equal to the unit cell parameter were produced both by screw dislocations and two-dimensional nuclei. Growth of catalase crystals proceeded in alternating patterns exclusively by two-dimensional nucleation and the successive deposition of distinctive growth layers, each having a step height equal to half the unit cell parameter. The shapes of islands on successive layers were related by 2-fold rotation axes along the 〈0 0 1〉 direction. Experiments revealed that step bunching on crystalline surfaces occurred either due to two- or three-dimensional nucleation on the terraces of vicinal slopes or as a result of uneven step generation by complex dislocation sources. Growth kinetics for thaumatin and catalase crystals were investigated over wide supersaturation ranges. Strong directional kinetic anisotropy in the tangential step growth rates in different directions was seen. From the supersaturation dependencies of tangential step rates and the rates of two-dimensional nucleation, the kinetic coefficients of the steps and the surface free energy of the step edge were calculated. Adsorption of impurities which formed filaments on the surfaces of catalase and thaumatin crystals was recorded. Cessation of growth of xylanase and lysozyme crystals was also observed and appeared to be a consequence of the formation of dense impurity adsorption layers. Crystal growth resumed upon scarring of the impurity adsorption layer and clearing of the crystal surface with the AFM tip. Adsorption of three-dimensional clusters, which consequently developed into either properly aligned multilayer stacks or misaligned microcrystals was recorded. For catalase crystals, incorporation of misoriented microcrystals as large as 50×3×0.1 μm³ produced elastic deformations in growth layers of ≈0.6%, but did not result in the defect formation. Etching experiments on catalase crystals revealed high defect densities.     

Uncertainties in crystallization of hen‐egg white lysozyme: reproducibility issue

The reproducibility of biomacromolecular crystallization (tetragonal and orthorhombic lysozyme crystals) was studied by monitoring the evolution of protein concentration during the crystallization process using Mach‐Zehnder interferometer. It was found that formation of both tetragonal and orthorhombic crystals exhibited poor reproducibility. When the crystallization occurred under isothermal conditions, the protein concentration in the solution varied differently in different experiments under identical conditions (for both types of crystals). Moreover, in the case of orthorhombic lysozyme crystallization (under either isothermal or thermal gradient conditions), it is clear that the crystals could not be always readily formed. When formation of tetragonal lysozyme crystals was conducted at a temperature gradient condition, however, the evolution of concentration was reproducible. The phenomena found in this study revealed that biomacromolecular crystallization can be uncertain, which is probably caused by the process of nucleation. Such uncertainties will be harmful for the efforts of screening crystallization conditions for biomacromolecules. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effects of purification on the crystallization of lysozyme

We have additionally purified a commercial lysozyme preparation by cation exchange chromatography, followed by recrystallization. This material is 99.96% pure with respect to macromolecular impurities. At basic pH, the purified lysozyme gave only tetragonal crystals at 20°C. Protein used directly from the bottle, prepared by dialysis against distilled water, or which did not bind to the cation exchange column had considerably altered crystallization behavior. Lysozyme which did not bind to the cation exchange column was subsequently purified by size exclusion chromatography. This material gave predominately bundles of rod-shaped crystals with some small tetragonal crystals at lower pHs. The origin of the bundled rod habit was postulated to be a thermally dependent tetragonal ↔ orthorhombic change in the protein structure. This was subsequently ruled out on the basis of crystallization behavior and growth rate experiments. This suggests that heterogeneous forms of lysozyme may be responsible. These results demonstrate three classes of impurities: (1) small molecules, which may be removed by dialysis; (2) macromolecules, which are removable by chromatographic techniques; and (3) heterogeneous forms of the protein, which can be removed in this case by cation exchange chromatography. Of these, heterogeneous forms of the lysozyme apparently have the greatest affect on its crystallization behavior.     

Nonstoichiometry in steps on AB crystals (II). Extended treatments

Concentrations of atoms with different numbers of nearest neighbours, and of the kink and non-kink positions between atoms in step fronts, have been calculated by two treatments. The results differ in the general case, but agree in cases with extreme nonstoichiometry as well as in nearly stoichiometric cases. With respect to the relevance of the model calculations, further investigations are necessary on step reconstructions, on the positions of stability limits of AB compounds in terms of step nonstoichiometry, and on the possibility of roughening transitions in connection with step nonstoichiometry. With increasing nonstoichiometry in the steps, neighbouring kink positions, and the corresponding neighbour-kink atoms become increasingly important. In contrast to this, the concentrations of double kink positions become smaller, and they vanish in the extreme cases where the PBC-directed steps consist merely of A, or of B neighbour-kink atoms. These concentrations are negligible in the extended model calculations at sufficiently low temperatures, together with concentrations of triple and further multiple kink positions.     

Anisotropy in the growth rates of silicon deposited by reduction of silicon tetrachloride

The Si epitaxial growth on the {111} facet using the SiCl₄-H₂ process has shown a rapid lateral growth rate with remarkable anisotropy. This phenomenon can be explained in terms of Kossel's model which is modified by taking the surface migration process of adatoms into consideration. In the case of insufficient supply of Si adatoms, the lateral growth rate does not depend on kink density due to the predominant attachment rate of adatoms to kink; the number density of migrating adatoms to kinks is rate-limiting for the lateral growth rate. In the case of sufficient supply of Si adatoms, however, the density of kinks is rate-limiting for the lateral growth rate. The faceted surface morphology reveals that a uniform distribution of pyramidal hills becomes more pronounced at lower temperatures. It is shown that the density of pyramids increases with increasing supply rate of material gas and decreasing temperature, and that the interpyramidal distance is governed by the surface migration length and the minimum density of adatoms for nucleus formation. The lateral growth rate seems to depend on the inter-pyramidal distance. following the diffusion equation for adatoms on the facet.     

Direct AFM observations of impurity effects on a lysozyme crystal

Impurity effects on the growth of tetragonal lysozyme crystals have been studied using in situ atomic force microscopy. Commercially available hen egg white lysozyme was characterized by sodium dodecyl sulfate polyacrylamide gel electrophoresis with silver staining, and purified by re-crystallization and successive high pressure liquid chromatography. On the (1 1 0) crystal surface, there was no significant difference in morphology between crystals grown in commercial and in purified solutions. On the (1 0 1) surface, however, a large number of small particles were found when the crystal was grown in the commercial solution, while the surface grown in the purified solution was quite smooth. Among the typical residual impurities contained in commercial lysozyme, only covalently bound lysozyme dimer yielded such particles. From measurements of particle separation and an estimate of the critical nucleation size, we infer that the particles reduced the step velocity according to the mechanism described by Cabrera et al. [N. Cabrera, D.A. Vermilyea, in: R.H. Doremus et al. (Eds.), Growth and Perfection of Crystals, 1958, P. 393].     

Self-assembly of apoferritin molecules into crystals: thermodynamics and kinetics of molecular level processes

Aside from the biological, biomedical and materials importance of ferritin and apoferritin, the self-assembly of these molecules into crystals is of interest because it is a suitable model for protein crystallization and aggregation that impact many fundamental and applied fields. We use the atomic force microscope in-situ, during the crystallization of apoferritin to visualize and quantify at the molecular level the processes responsible for crystal growth. We image the configuration of the incorporation sites, “kinks”, on the surface of a growing crystal. We show that the kinks are due to thermal fluctuations of the molecules at the crystal-solution interface. This allows evaluation of the free energy of the intermolecular bond φ = 3.0 k_BT = 7.3 kJ/mol. The crystallization free energy, extracted from the protein solubility, is − 42 kJ/mol. Thermodynamics analyses based on these two values suggest that the main component in the crystallization driving force is the entropy gain of the waters bound to the protein molecules in solution and released upon crystallization. Furthermore, we determine the characteristic frequency of attachment of individual molecules into the kinks at one set of conditions. We show that the macroscopic step growth velocity, scaled by the molecular size, equals the product of independently determined kink density and attachment frequency, i.e., these are the molecular-level parameters for crystallization. Finally, we show that although new crystal layers are generated by intrinsically stochastic surface nucleation, for crystals > 200 μm layer generation predominantly occurs at the crystal edges. Numerical simulations of the concentration fields in the solution allow us to assign this localization to higher interfacial concentration at the edges. As the steps propagate to cover the crystal face, step density waves, or bunches, develop and may lead to non-uniformity and lower quality and utility of the growing crystal.     

Nature of impurities during protein crystallization

Crystallography Reports - Lysozyme crystal growth was studied using reagents of different purity of three trademarks— Seikagaku Corporation (sixfold recrystallized lysozyme), Sigma-Aldrich...     

Nonlinear dynamics of layer growth and consequences for protein crystal perfection

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, Pe_k, i.e., the relative weight of bulk transport and interface kinetics in the control of the growth process, governs the step bunching dynamics. Since Pe_k 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.     

Crystalline quality of lysozyme crystals grown in agarose and silica gels studied by X-ray diffraction techniques

The crystalline quality of hen egg white lysozyme (HEWL) crystals grown in agarose gels and in silica gels has been characterized by measuring resolution and mosaic spread. These crystals have been compared to solution grown ones. A quasi-plane-wave X-ray topography study has also been done on some crystals. The study concerns triclinic, monoclinic, orthorhombic and tetragonal forms of HEWL. One observes that the resolution is not really changed by gelling the growth medium, even for rather high gel contents (agarose 0.5% wt/wt). On the contrary, mosaicity, characterized through reflection profile recordings allows to differentiate crystals grown by different techniques: agarose gel grown crystals are, on average, better than solution grown ones but the best crystals are obtained in silica gel. X-ray topography confirms this result.     

Desymmetrization of the polyhedral crystal shape of tetragonal lysozyme due to face-growth rate fluctuations

We have studied the desymmetrization of the polyhedral crystalline shape of tetragonal lysozyme crystals due to the growth rate differences of the equivalent {1 0 1} planes. Using atomic force microscopy, we have observed the evolution of the multifaceted structures composed of four equivalent {1 0 1} faces during growth. In our growth condition, lateral step flow, where a large density of dislocations acts as a source of steps, is the dominant growth mechanism. The measured step flow velocities are almost independent of the separation between the neighboring steps, revealing that the local face normal growth rate is determined by the local step density. By tracing the motion of the vertex surrounded by the {1 0 1} faces, we have found that the desymmetrization of the crystalline shape is due to the large fluctuation of the local face normal growth rate, which is comparable in magnitude to the average growth rate.     

PVT法氮化铝晶体铝面、氮面生长对比分析

在氮气环境下用PVT方法生长氮化铝过程中,氮面和铝面由于表面化学性质不同,生长的主要化学反应速度存在差异。原子在生长表面的迁移能力不同造成单晶表面生长方式差异较大。在基本相同条件下(生长温度、生长温差、生长气压、类似的籽晶、同一台生长设备)进行了铝、氮面氮化铝单晶晶体生长。为了更明显地表现铝氮面的差异,将同一片籽晶分为两半,翻转其中一半让铝氮面同时生长。铝面生长较好的区域形成了明显的晶畴,而氮面生长时生长较好的部分出现了明显的生长台阶,并出现了晶畴边界被生长台阶湮灭的生长现象,进一步通过AFM观测到铝面生长台阶平整但被缺陷所阻隔,晶畴发育明显为各晶畴独立生长。氮面生长台阶没有铝面规则但连续性较强,在原来晶畴边界位置也出现了连续的生长台阶(或台阶簇)。所以籽晶质量不高时氮面生长更容易提高晶体质量,后续的XRD测量结果也证明了氮面生长后的晶体质量明显高于铝面生长的晶体质量。     

Orthorhombic Pbcn SnO2 nanowires for gas sensing applications

Pure monocrystalline orthorhombic SnO₂ nanowires decorated and non-decorated with cassiterite SnO₂ nanoclusters are analyzed and compared with pure monocrystalline cassiterite SnO₂. We corroborate the coexistence of both, cassiterite and orthorhombic phases, having a higher growth speed for the cassiterite one, in the obtained nanowires by the evaporation/condensation technique. For both phases, the building blocks are the [SnO₆]^8? octahedron which are forming chains of edge-sharing octahedral along the [0 0 1] direction for the cassiterite phase, while in the orthorhombic phase, chains run in a zigzag fashion and contains four octahedra on each unit of chain instead of two previously reported for orthorhombic material obtained at high pressure conditions as Pbcn SnO₂ orthorhombic structure. Results obtained reveal singular structural characteristics of these synthesized orthorhombic nanowires.     

Growth of USb2 single crystals and their structural perfection

USb₂ single crystals were grown by three methods; I — Chemical vapour transport with iodine as transporting reagent, II — Crystallization from U Sb liquid solution, III — Crystallization from U Sb Sn liquid solution. The morphology of growth and results of X-ray topography examination of crystal surface are given.     

The dependence of surface morphology of GaSb- and AlxGa1–xSb epitaxial layers on the conditions of LPE growth

The present work shows the dependence of surface morphology of the GaSb and Al_xGa_1–xSb epitaxial layers on the conditions of LPE growth. It is found that for LPE growth at 500 °C a supersaturation of 5—10 °C and a cooling rate of 0.24—0.4°C/min for GaSb epitaxial layers and 0.8—1.2 °C/min for Al_xGa_1–xSb epitaxial layers is necessary to obtain a flat and smooth surface.