Crystal-solution Interface Research Articles

Quartz Crystal Microbalance Studies on Surface-Initiated DNA Hybridization Chain Reaction

The hybridization chain reaction (HCR), a type of nucleic acid amplification method, was studied by a quartz crystal resonator technique. We probed the properties of the boundary DNA layer with a thickness of the viscous penetration depth at the crystal-solution interface. According to the relationship between the change of resonant frequency and the mass adsorbed on the crystal surface, the kinetics of surface-initiated HCR was measured, as well as the viscosity and the shear modulus of H1/H2 solution with different concentrations near a solid substrate. This work provides a new method for study- ing nucleic acid reactions at solid surface and mechanistic insight for HCR-based amplification and biodetection. Keywords hybridization chain reaction; quartz crystal microbalance; DNA; viscosity; interface; penetration depth

The growth of benzophenone crystals by Sankaranarayanan–Ramasamy (SR) method and slow evaporation solution technique (SEST): A comparative investigation

Longest unidirectional〈100〉 benzophenone (BP) crystal having dimension of 1060mm length and 55mm diameter was grown by Sankaranarayanan–Ramasamy method. The growth rate was measured by monitoring the elevation of the crystal–solution interface at different temperatures. The high resolution X-ray diffraction and etching measurements indicate that the unidirectional grown benzophenone crystal has good crystalline perfection and less density of defects. The optical damage threshold of SEST and SR grown BP crystals has been investigated and found that the SR grown benzophenone crystal has higher laser damage threshold value than the conventional method grown crystal. Microhardness measurement shows that crystals grown by SR method have a higher mechanical stability than the crystals grown by SEST method. Dielectric permittivity and birefringence are high in SR grown crystal compared to SEST grown BP crystal. The UV–vis-NIR results show that SR method grown crystal exhibits 7% higher transmittance as against crystals grown by conventional method.

High temperature Raman spectroscopy study on the microstructure of the boundary layer around a growing LiB3O5 crystal

High temperature Raman spectroscopy has been applied to investigate in situ the microstructure of the high temperature solution near a LiB3O5 (LBO) crystal–solution interface. A preordering boundary layer was found around the interface. In the boundary layer, an isomerization reaction between 3-coordinated and 4-coordinated boron was observed. The reaction led to the formation of B3O7 triborate groups, the characteristic structural group involved in the LBO crystal. According to the mechanism, the growth habits of LBO crystal can be understood well.

Swimming Photochromic Azobenzene Single Crystals in Triacrylate Solution

Self-motion of a growing single crystal of azobenzene chromophore in triacrylate solution (TA) is investigated in relation to the solid-liquid phase diagram bound by the solidus and liquidus lines. Upon thermal quenching from the isotropic melt to the crystal + liquid gap, various single crystals develop in a manner dependent on concentration and supercooling depth. During the crystal growth, TA solvent is rejected from the growing faceted fronts, enriching with TA in close proximity to the crystal-solution interface. The concentration gradient that formed as the result of TA expulsion induces convective flows in the solution and generates spatial variability of surface tension usually responsible for Marangoni effect. Either or both of these phenomena may have contributed to the observed self-motion including swimming, sinking, and floating of the azobenzene rhomboidal crystal in TA solution. A stationary rhomboidal crystal is also shown to swim upon irradiation with the UV light because of a mechanical torque generated by the trans-cis isomerization. Judging from the sinking or floating behavior of the azobenzene crystal, it may be inferred that the nucleation occurs at the solution-air interface.

The role of magnesium in the growth of calcite: An AFM study

Abstract The mechanisms that determine the inhibition of calcite growth by magnesium have remained unclear and subject to controversy over decades. Although it has been long apparent that the inhibition mechanisms take place at the crystal-solution interface, the molecular phenomena occurring at calcite surfaces in contact with Mg-bearing solutions are still not completely understood. The main goal of this work is to contribute to further clarify those phenomena. With this aim, we carried out in situ atomic force microscopy (AFM) observations of the growth behaviour of calcite { 10 1 ¯ 4 } surfaces in contact with supersaturated aqueous solutions (β = 5) bearing different amounts of Mg (ranging from 0.05 to 4.00 mmol dm− 3). Under the conditions considered, growth occurred by monolayer spreading. Our observations revealed that only the first elementary growth layer advancing on the original calcite surfaces grow normally, showing characteristics nearly identical to the growth of pure calcite. However, subsequent monolayers behave differently. Thus, as soon as one of these monolayers reaches areas of the surface that have grown incorporating Mg and whose composition can consequently be described as MgxCa1-xCO3, the rate at which this step advances significantly decreases. Moreover, the step becomes progressively rougher. A clear relationship between the extent of the inhibition effect and the concentration of Mg in the aqueous solution exists. Furthermore, our observations allow us to conclude that each newly formed monolayer exerts a certain control on the development of the growth of subsequent monolayers. Such a control causes the reproduction of the nanotopographic features of the original surface, producing the so called “template effect”. This behaviour cannot be easily incorporated within the general framework of the currently accepted impurity crystal growth models, which are based on either the pinning of elementary step motion by impurities or changes in the solubility of the newly formed layers as a result of the incorporation of the impurity into the lattice of the growing crystal. We discuss our results on the basis of the solid solution–aqueous solution model and provide a complementary explanation for the development of “dead zones” in the case of the growth of calcite { 10 1 ¯ 4 } surfaces from divalent cation-bearing aqueous solutions.

Ion microprobe assessment of the heterogeneity of Mg/Ca, Sr/Ca and Mn/Ca ratios in <i>Pecten maximus</i> and <i>Mytilus edulis</i> (bivalvia) shell calcite precipitated at constant temperature

Abstract. Small-scale heterogeneity of biogenic carbonate elemental composition can be a significant source of error in the accurate use of element/Ca ratios as geochemical proxies. In this study ion microprobe (SIMS) profiles showed significant small-scale variability of Mg/Ca, Sr/Ca and Mn/Ca ratios in new shell calcite of the marine bivalves Pecten maximus and Mytilus edulis that was precipitated during a constant-temperature culturing experiment. Elevated Mg/Ca, Sr/Ca and Mn/Ca ratios were found to be associated with the deposition of elaborate shell features, i.e. a shell surface stria in P. maximus and surface shell disturbance marks in both species, the latter a common occurrence in bivalve shells. In both species the observed small-scale elemental heterogeneity most likely was not controlled by variable transport of ions to the extra-pallial fluid, but by factors such as the influence of shell organic content and/or crystal size and orientation, the latter reflecting conditions at the shell crystal-solution interface. In the mid and innermost regions of the P. maximus shell the lack of significant small-scale variation of Mg/Ca ratios, which is consistent with growth at constant temperature, suggest a potential application as a palaeotemperature proxy. Cross-growth band element/Ca ratio profiles in the interior of bivalve shells may provide more promising palaeo-environmental tools than sampling from the outer region of bivalve shells.

Reconstruction of time-dependent concentration gradients around a KDP crystal growing from its aqueous solution

Reconstruction of the steady three-dimensional concentration field from path-integrated two-dimensional data has been studied by the authors earlier. The extension of this approach to reconstruct three-dimensional unsteady concentration gradient field around a KDP crystal growing from its aqueous solution is examined in the present work. The experiments reported in the present work have been carried out in the mixed convection regime where inertial as well as buoyancy effects are significant. The crystal size is large enough to induce a time-dependent movement of convection currents in the growth chamber. Laser schlieren is used as the measurement technique for mapping the concentration gradients around the crystal. Projection data is in the form of a time sequence of schlieren images over an angular span of 0–360°. Images are recorded by rotating the growing crystal while the growth chamber is kept fixed. The time sequence recorded for one projection is uncorrelated to the next, creating an asynchronous data set. The technique proposed herein is an application of proper orthogonal decomposition to the image sequence. The method decouples the spatial and temporal components of the measured time-dependent data. The spatial modes, in turn, are ordered across all projections, thus facilitating three-dimensional reconstruction over the entire physical domain. The algorithm proposed integrates principles of tomography with proper orthogonal decomposition. It has been validated with simulated as well as experimental data. The results show that the first few modes contain much of the information of the time-dependent growth process. The differences in the nature of temporal fluctuations of the concentration gradient field in regions close to the growing crystal against those in the bulk are clearly revealed. The concentration gradient field is found to be purely unsteady near the crystal–solution interface, whereas the level of temporal fluctuations decreases as one moves towards the bulk of the solution. The reconstructed POD modes reveal an overall axisymmetry of the concentration gradients field in the growth chamber while a slight loss of symmetry was revealed in the vicinity of the growing crystal.

New concept of solute distribution around a diffusive crystal-solution interface of a binary Lennard-Jones mixture from the viewpoint of molecular dynamics

Directional crystallization from a binary mixture was performed by pseudo-NpT ensemble molecular dynamics. The initial crystal phase having a face-centered-cubic (fcc) structure grew toward the whole cell according to the temperature gradient in the universal cell. The growing crystal phase was not planar even though the solute molecules grew in two-dimensional coordinates because the solvent molecules disturbed the crystallization of the solute molecules at the diffusive crystal-solution interface. This represented the essential phenomenon of solute distribution during crystallization. Consequently, the growing crystal phase still contained solvent molecules having a liquid structure. The time change of the solute composition in the early phase of crystal growth showed an increase in solute composition as the time step proceeded. The resulting solute composition in this early phase was considered at different temperature gradients in the universal cell and it increased as the temperature of the initial crystal-solution interface increased. A new distribution coefficient model was proposed as a function of the difference between the local solute composition and bulk solute composition in the solution around the crystal-solution interface. The impurity-solvent distribution coefficient could be represented by the new model for faster growth of the lower temperature's initial interface. As regards a better distribution coefficient, there was found to be a very dilute solution phase over the crystal phase. The new variable "distribution rate" instead of the ambiguous variable "growth rate" was considered as a function of temperature gradient in the universal cell.

Crystal growth in porous materials—II: Influence of crystal size on the crystallization pressure

A thermodynamically consistent equation for the calculation of the pressure generated during crystal growth in porous materials is provided. The treatment makes use of an equation derived previously (paper I of this series) which is based on the chemical potentials of loaded and unloaded surfaces of confined crystals in porous materials. The influence of the crystal–solution interface on the chemical potentials is analyzed and a more general equation is derived that can be used to calculate the crystallization pressure considering both the degree of supersaturation of the solution and the effect of the curvature of the crystal–liquid interface. The present treatment is compared to other equations available in the literature and the different approaches are discussed in detail. It is shown that, for a given concentration of a pore solution, the crystallization pressure increases with crystal size. The equation is also applied to calculate equilibrium growth pressures assuming idealized pore geometries such as spherical and cylindrical pores with small entrances. It is shown that existing equations, e.g. Everett's equation [Trans. Faraday Soc. 57 (1961) 1541] can be derived as a special case from the more general treatment provided in this paper. The growth pressure of a crystal in a large pore increases with decreasing size of the pore entrance. Finally, a brief discussion on the particular problems of irregular pore geometries and highly anisotropic surface free energies of salts in porous building materials is provided.

Numerical simulation of liquid phase electro-epitaxial selective area growth

A computational model for semiconductor crystal growth on a partially masked substrate under simplified liquid phase electroepitaxy conditions is developed. The model assumes isothermal diffusional growth, which is enhanced by applied DC current through crystal-solution interface. A finite-difference, front-tracking method is used to numerically evolve the interface. Computed examples show strong influence of the electromigration on growth rates in vertical and lateral directions and the dependence of growth on electrical resistance of mask material, and on the wetting contact angle.

Rate-controlled calcium isotope fractionation in synthetic calcite

The isotopic composition of Ca (Δ 44Ca/ 40Ca) in calcite crystals has been determined relative to that in the parent solutions by TIMS using a double spike. Solutions were exposed to an atmosphere of NH 3 and CO 2, provided by the decomposition of (NH 4) 2CO 3, following the procedure developed by previous workers. Alkalinity, pH and concentrations of CO 3 2−, HCO 3 −, and CO 2 in solution were determined. The procedures permitted us to determine Δ( 44Ca/ 40Ca) over a range of pH conditions, with the associated ranges of alkalinity. Two solutions with greatly different Ca concentrations were used, but, in all cases, the condition [Ca 2+]>>[CO 3 2−] was met. A wide range in Δ( 44Ca/ 40Ca) was found for the calcite crystals, extending from 0.04 ± 0.13‰ to −1.34 ± 0.15‰, generally anti-correlating with the amount of Ca removed from the solution. The results show that Δ( 44Ca/ 40Ca) is a linear function of the saturation state of the solution with respect to calcite (Ω). The two parameters are very well correlated over a wide range in Ω for each solution with a given [Ca]. The linear correlation extended from Δ( 44Ca/ 40Ca) = −1.34 ± 0.15‰ to 0.04 ± 0.13‰, with the slopes directly dependent on [Ca]. Solutions, which were vigorously stirred, showed a much smaller range in Δ( 44Ca/ 40Ca) and gave values of −0.42 ± 0.14‰, with the largest effect at low Ω. It is concluded that the diffusive flow of CO 3 2− into the immediate neighborhood of the crystal-solution interface is the rate-controlling mechanism and that diffusive transport of Ca 2+ is not a significant factor. The data are simply explained by the assumptions that: a) the immediate interface of the crystal and the solution is at equilibrium with Δ( 44Ca/ 40Ca) ∼ −1.5 ± 0.25‰; and b) diffusive inflow of CO 3 2− causes supersaturation, thus precipitating Ca from the regions exterior to the narrow zone of equilibrium. The result is that Δ( 44Ca/ 40Ca) is a monotonically increasing (from negative values to zero) function of Ω. We consider this model to be a plausible explanation of most of the available data reported in the literature. The well-resolved but small and regular isotope fractionation shifts in Ca are thus not related to the diffusion of very large hydrated Ca complexes, but rather due to the ready availability of Ca in the general neighborhood of the crystal-solution interface. The largest isotopic shift which occurs as a small equilibrium effect is then subdued by supersaturation precipitation for solutions where [Ca 2+]>>[CO 3 2−] + [HCO 3 −]. It is shown that there is a clear temperature dependence of the net isotopic shifts that is simply due to changes in Ω due to the equilibrium “constants” dependence on temperature, which changes the degree of saturation and hence the amount of isotopically unequilibrated Ca precipitated. The effects that are found in natural samples, therefore, will be dependent on the degree of diffusive inflow of carbonate species at or around the crystal-liquid interface in the particular precipitating system, thus limiting the equilibrium effect.

Fabrication of SiGe bulk crystals with uniform composition as substrates for Si-based heterostructures

SiGe bulk crystal was grown by the multicomponent zone-melting method equipped with an in situ monitoring system of the position and the temperature at the crystal-solution interface. By utilizing the in situ monitoring system, an attempt was made to control the interface position at a fixed position during growth by balancing the growth rate and the pulling rate of the crystal. This led to realization of SiGe bulk crystal with Ge composition of 0.86±0.004 over 22 mm in length. However, as growth proceeds, development of small angle boundaries was evidenced by X-ray characterizations. This polycrystallization was found to be accompanied with appearance of deep-level emission in photoluminescence spectra. A preliminary result to grow SiGe with intermediate composition, which is important for Si-based heterostructures, was also performed.

A model of oscillatory zoning in solid solutions grown from aqueous solutions: Applications to the (Ba,Sr)SO4 system

Barite-celestite crystals can be synthesized from aqueous solutions during counter-diffusion in a gel column connecting two reservoirs. It is known that such crystals may exhibit oscillatory zoning, whereby the barium composition in the crystal fluctuates more or less regularly from the core of the crystal to its rim. We present here a simple model of oscillatory zoning in such binary solid solutions A1A2 grown from aqueous solutions. The model combines diffusive transport of the relevant ions with an autocatalytic growth process. The latter is formulated as a continuous growth in which the probability of finding a kink site on the growing surface depends on the chemical composition of that surface. Thus, an A1-rich surface favors the growth of A1 over A2, as long as A1 is present in the vicinity of the surface. Precipitation results in a local depletion of A1 in the aqueous solution, and the system may switch to a A2 growth mode, until diffusion replenishes the amount of A1, and so on. We use a dynamical equation for the molar fraction of component A1 in the crystal, which results from mass conservation across the rough crystal-solution interface. Linear stability analysis and direct numerical solutions show that the system exhibits oscillatory behavior. Using the barite-celestite system as a framework, the scaling is consistent with the experimental observations. We discuss the variety of zoning patterns and textures numerically obtained as the concentrations of reactants in the reservoirs vary. This model might help in understanding the formation of oscillatory zoning in hydrothermal environments.

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 B T = 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.

In-situ monitoring system of the position and temperature at the crystal–solution interface

We developed an in-situ observation system of the position and temperature at the crystal–solution interface grown under high temperature. A zone furnace of vertical type has an optical window made of quartz glass, and a sample in the furnace can be directly observed from outside through this window. Beam splitter made of an Si single crystal reflects the visible light comming from the sample, and the visible light image is observed using a CCD camera. Infrared light emitted from the sample penetrates the beam splitter, and the infrared image is monitored by an infrared CCD camera (thermoviewer). A growth process of a SiGe mixed crystal was chosen as a model system. Using the newly developed in-situ monitoring system, the position of the growth interface could be monitored with a spatial resolution of 300 μm. Temperature distribution around the growth interface could be determined with a spatial resolution of 230 μm and an accuracy of ±8°C.

Applications of morphological stability theory

Recent applications of morphological stability theory are reviewed. For growth of a binary alloy from the melt, the temperature-dependence of the solute diffusivity can have a significant effect on the critical wavelength at the onset of instability. The response of the interface velocity to an electrical current pulse has been calculated by a linear perturbation analysis. The effect of a parallel shear flow and anisotropic interface kinetics on the onset of instability during growth from a supersaturated solution has been analyzed. The kinetic anisotropy arises from a model of step motion in which the morphological instability corresponds to step bunching. Kinetic anisotropy causes traveling waves along the crystal-solution interface and an enhancement of morphological stability. A shear flow in the direction of the step motion promotes morphological instability, while flow in the opposite direction is stabilizing. Oscillatory (in time) shear flows can be studied by Floquet theory.

Growth of SixGe1-x (x \\fallingdotseq0.15) Bulk Crystal with Uniform Composition Utilizing in situ Monitoring of the Crystal-solution Interface

A new growth system, which allows in situ monitoring of the crystal-solution interface, was developed and applied to grow SixGe1-x (x\\fallingdotseq0.15) bulk crystal with uniform composition by the multicomponent zone-melting method. By utilizing the system, the dynamical change of the growth rate was evaluated from the nonlinear upward shift of the interface as a function of the growth time. Based on the monitoring, an attempt was made to balance the pulling rate of the ampoule with the growth rate of the crystal, which led to the suppression of the upward shift of the growth interface. Consequently, the compositional uniformity of the crystal in the growth direction was markedly improved.

Molecular-level thermodynamic and kinetic parameters for the self-assembly of apoferritin molecules into crystals

The self-assembly of apoferritin molecules into crystals is a suitable model for protein crystallization and aggregation; these processes underlie several biological and biomedical phenomena, as well as for protein and virus self-assembly. 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. To evaluate the governing thermodynamic parameters, 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 kBT=7.3 kJ/mol. The crystallization free energy, extracted from the protein solubility, is −42 kJ/mol. Published determinations of the second virial coefficient and the protein solubility between 0 and 40°C revealed that the enthalpy of crystallization is close to zero. Analyses based on these three values suggest that the main component in the crystallization driving force is the entropy gain of the water molecules bound to the protein molecules in solution and released upon crystallization. Furthermore, monitoring the incorporation of individual molecules in to the kinks, we determine the characteristic frequency of attachment of individual molecules at one set of conditions. This allows a correlation between the mesoscopic kinetic coefficient for growth and the molecular-level thermodynamic and kinetic parameters determined here. We found that step growth velocity, scaled by the molecular size, equals the product of the kink density and attachment frequency, i.e. the latter pair are the molecular-level parameters for self-assembly of the molecules into crystals.

The {1 0 4} cleavage rhombohedron of calcite: theoretical equilibrium properties

The character of the most important crystallographic forms of calcite crystal is quantitatively reviewed according to the Hartman and Perdok theory. Specific surface and edge energies of the cleavage {1 0 4} rhombohedron are calculated in the crystal–vacuum system by means of a semi-empirical potential function and following Stranski’s definition of the total surface energy of a finite crystal. A comparison is made between the calculated value and the experimental quantities entering the Dupré formula (specific crystal–solution interface energy, specific vapour–solution surface energy): the crystal–vacuum specific surface energy is proved to be quite reasonable, and for the first time, the specific crystal–solution adhesion energy for the {1 0 4} form is estimated.

Free convection and surface kinetics in crystal growth from solution

As a crystal grows from solution, there is ordinarily a boundary layer depleted in solute, which forms at the crystal–solution interface. When the normal to the growing crystal surface is oriented in any direction other than parallel to gravity, the boundary layer is set into motion by the force of buoyancy. Using a similarity transformation and a boundary layer approximation, we have solved the Navier–Stokes equation and the equation for convective diffusion for a crystal in the form of a flat plate growing with normal perpendicular to gravity. Parameters in the theory include solute concentration, c0, and diffusion coefficient, D; solution shear viscosity, μ, mass density, ρ, and logarithmic density derivative with respect to concentration, α; crystal solubility, cs, height, h, and linear growth rate, kG; the specific rate, k (sticking coefficient), of the reaction which transfers molecules from the solution to the crystal and the kinetic order, n, of this reaction; and the acceleration due to gravity, g. We find these parameters to be related by the equation log[1−Sh/a (Sc) 1/4(Gr) 1/4φ s1/4]=(1/n) log[a(5/4) n(D/hkc 0n−1)(Sc) 1/4(Gr) 1/4]+[(5/4−n)/n]log φs, where a=0.9, Sh=kGh/D, Sc=μ/ρD, Gr=gαh3ρ2/4μ2, and φs=(c0−cs)/c0. Given a knowledge of the solution physical properties, if Sh is measured as a function of φs and the results plotted in accord with the above equation, both n and k can be determined.