Homogeneous Crystal Nucleation Research Articles

Molecular dynamics study of homogeneous crystal nucleation in amorphous silicon

We successfully simulated homogeneous crystal nucleation in well-relaxed amorphous silicon by using molecular dynamics. The critical nucleus size evaluated by structural parameters such as potential energy, ring statistics, and bond-angle deviation, amounted to about 30–50 atoms. The shape of nucleus was nearly spherical. The results agree with the experimental data very well.

Homogeneous nucleation of colloidal melts under the influence of shearing fields

We study the effect of shear flow on homogeneous crystal nucleation, using Browniandynamics simulations in combination with an umbrella sampling-like technique. Thesymmetry breaking due to shear results in anisotropic radial distribution functions. Thehomogeneous shear rate suppresses crystal nucleation and leads to an increase of the size ofthe critical nucleus. These observations can be described by a simple, phenomenologicalextension of classical nucleation theory. In addition, we find that nuclei have a preferentialorientation with respect to the direction of shear. On average the longest dimension of anucleus is along the vorticity direction, while the shortest dimension is preferablyperpendicular to that and slightly tilted with respect to the gradient direction.

Crystal nucleation of colloidal suspensions under shear.

We use Brownian dynamics simulations in combination with the umbrella sampling technique to study the effect of shear flow on homogeneous crystal nucleation. We find that a homogeneous shear rate leads to a significant suppression of the crystal nucleation rate and to an increase of the size of the critical nucleus. A simple, phenomenological extension of classical nucleation theory accounts for these observations. The orientation of the crystal nucleus is tilted with respect to the shear direction.

Dense Liquid Precursor for the Nucleation of Ordered Solid Phases from Solution

A line of recent theories and simulations have suggested that the nucleation of protein 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. In this review, I discuss experimental tests 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 recent results on the kinetics of homogeneous 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 mechanismas a superposition of fluctuations along the order parameters density and structure. Depending on whether the system is above or below its liquid−liquid coexiste...

A study on the variations in the density of nucleated particles with the maximum crystallization rate and with the corresponding temperature, by using differential scanning calorimetry

An analysis is carried out on two procedures which have been proposed for the determination of the temperature dependence of homogeneous crystal nucleation rates in glassy solids by using differential scanning calorimetry (DSC) measurements. The first procedure is based upon the hypothesis that the density of nucleated particles will increase monotonically as the reciprocal of the temperature corresponding to the maximum crystallization rate increases. The second procedure is based on the observation that the maximum crystallization rate increases as the corresponding temperature grows. The validity of both procedures is assessed for glassy solids by considering two specific crystal growth models.

A molecular dynamics study of homogeneous crystal nucleation in liquid nitrogen

The crystal nucleation of nitrogen is studied by molecular dynamics. Using the umbrella sampling technique, we are able to determine the free energy barrier of nucleation and the structure of the critical nucleus formed under typical experimental supercoolings. In agreement with Ostwald’s ‘step rule’, nucleation is shown to proceed into an orientationally disordered cubic phase instead of the thermodynamically stable hexagonal β phase. We also give an account of the system size dependence of the free energy profiles so obtained.

Details of Structure Formation During the Induction Period of Spinodal-Type Polymer Crystallization

An unexpected type of primary crystal nucleation is described, involving spinodal decomposition (SD) type microphase separation due to the orientation fluctuations of rigid segments prior to crystal nucleation. This type of mechanism was found by the present authors about 10 years ago, and recently, it was theoretically revealed by Olmsted et al. to be one of three types of primary crystal nucleation: the well-known homogeneous crystal nucleation directly from the liquid–crystal coexistence domain, which occurs at higher temperatures above the binodal temperature T b , crystal nucleation after binodal microphase separation between T b and spinodal temperature T s , and that after SD below T s . The detailed experimental results for the spinodal-type crystal nucleation, especially the temperature dependence of characteristic wavelength in SD, are explained as well.

On the thermodynamics of homogeneous crystal nucleation

A correct phenomenological consideration is given to the change in the Gibbs thermodynamic potential in the course of crystal nucleation. It is proved that this process is described by two activation barriers.

First interactive simulations of cirrus clouds formed by homogeneous freezing in the ECHAM general circulation model

A physically based parameterization for the nucleation and initial growth of ice crystals in cirrus clouds at low (<238 K) temperatures prevailing in the upper troposphere and in the tropopause region is implemented in the ECHAM general circulation model (GCM). With this model we performed the first interactive simulations of cirrus clouds in a global climate model. As homogeneous ice crystal nucleation requires relative humidities with respect to ice of 140–170% at these temperatures, we abandoned the saturation adjustment scheme previously used to compute the properties of cirrus clouds in GCMs. The comparison with relative humidity data taken on commercial aircraft showed that ECHAM reproduces the frequency distribution of supersaturation with respect to ice in cloud‐free regions well especially if high values of the subgrid‐scale vertical velocity are assumed. On the other hand, the higher frequency of occurrence of high supersaturations in the model may point to heterogeneous freezing as the missing mechanism for ice formation. We found that homogeneous freezing may be limited by the number of hygroscopic aerosols present. However, as the ice water content remains the same for the natural and present‐day aerosol scenarios the longwave radiation does not change. Thus anthropogenic aerosol and precursor emissions have only a small effect on cirrus formed by homogeneous freezing. Aircraft emissions of sulfate aerosols are not likely to be important for cirrus formation. Aircraft soot emissions may be important if the soot particles nucleate ice more efficiently than by homogeneous freezing.

Nucleation studies and crystal growth of (NH 4)H 2PO 4 doped with thiourea in supersaturated aqueous solutions

The metastable zone width studies were carried out for various temperatures for supersaturated aqueous solutions of ammonium dihydrogen orthophosphate added with 1 mol% of thiourea. The metastable zone width is increased with the addition of thiourea. The induction period was studied and various critical nucleation parameters were calculated based on the classical theory for homogeneous crystal nucleation. The induction period is increased with the increase of thiourea addition. The critical nucleation parameters vary with increase in doping concentration. The results are reported and discussed. The crystals were grown for various doping concentrations of thiourea and the morphological changes are discussed.

Nucleation of protein crystals: critical nuclei, phase behavior, and control pathways

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.

Homogeneous crystal nucleation in short polyethylenes

The homogeneous nucleation of the solid from the melt is studied in low molecular weight (MW) polyethylene samples with a narrow MW distribution and average carbon numbers in the range 38≤ n≤144. The measurements employ scanning calorimetry on both emulsified and non-emulsified samples, and low- and high-angle X-ray diffraction. The shortest polyethylenes show undercoolings agreeing well with those of monodisperse n-alkanes of similar chain lengths. The longer samples extrapolate smoothly between the undercoolings measured for monodisperse alkanes and high-MW polyethylenes with n≥654. The results support the earlier conclusions that any transition from a full-molecule nucleation to a ‘bundle’ nucleation must occur well below n≈25. The absence of significant features around n=120 where chain folding is expected to set in, implies that it may not occur at the nucleation stage, or may have no significant contribution to the nucleation energetics.

Intratubular crystallization of calcium oxalate in the presence of membrane vesicles: An in vitro study

Since urine spends only a few minutes in the renal tubules and has a low supersaturation with respect to calcium oxalate (CaOx), nucleation of CaOx crystals in the kidneys is most probably heterogeneous. We have proposed that membranes of cellular degradation products are the main substrate for crystal nucleation. The purpose of our study was to determine the site of membrane-mediated crystal nucleation within the renal tubules and the required lag time, factors that determine whether crystallization results in crystalluria or nephrolithiasis. Nucleation of CaOx was allowed to occur in five different artificial urine solutions with ionic concentrations simulating urine in proximal tubules (PTs), descending (DLH) and ascending (ALH) limbs of the loop of Henle, distal tubules (DTs), and collecting ducts (CDs). A constant composition crystallization system was used. Experiments were run for two hours with or without the renal tubular brush border membrane (BBM) vesicles. The addition of BBM significantly reduced the nucleation lag time and increased the rate of crystallization. The average nucleation lag time decreased from 84.6 +/- 43.4 minutes to 24.5 +/- 19 minutes in PTs, from 143.6 +/- 29 to 70.2 +/- 53.4 minutes in DLH, from 17.6 +/- 8.6 minutes to 0.625 +/- 0.65 minutes in DTs and from 9.54 +/- 3. 03 minutes to 0.625 +/- 0.65 minutes in CDs. There was no nucleation in the ALH solution without BBM for two hours. CaOx dihydrate (COD) was common in most solutions. Calcium phosphate (CaP) also nucleated in the DLH and CD solutions. In the absence of membrane vesicles, there was no crystallization in any of the solutions within the time urine spends in the renal tubules. As a result, homogeneous nucleation of crystals anywhere within the nephron appears unlikely. However, BBM-supported nucleation is possible in the DTs as well as CDs. A high crystallization rate in CDs would promote rapid crystal growth and aggregation, resulting in crystal retention within the kidneys and development of nephrolithiasis.

Molecular Dynamics Simulations of Nucleation Process from Supercooled Liquid Pt with EAM Potentials

The homogeneous nucleation process induced by supercooling liquid Pt has been studied by means of molecular dynamics employing the embedded-atom method for the potential energy. The process was simulated by cooling an equilibrated liquid to a low temperature, while structure analysis was performed during the subsequent time evolution of the system under constant temperature and pressure conditions. In order to investigate the effects of degree of supercooling and cooling rate on crystallization, cooling temperature was varied from 900 to 1300 K and three processes at different cooling rates were studied. The results proved that certain degree of supercooling is necessary for homogeneous nucleation of crystals due to the existence of a free energy barrier in forming critical nuclei from supercooled liquid, as described by the classical theory of homogeneous nucleation. The scale of the degree of supercooling has much effect on the incubation period of homogeneous nucleation and nucleation rate. The crystallization towards fcc and hcp phases takes place in all homogeneous nucleation processes from liquid in our simulations. The progression of crystallization is sensitive to cooling rate. A very high cooling rate has been found to prolong incubation period, decrease nucleation rate, thus suppress crystallization. This may be associated with the phenomenon that high cooling rate prohibits the rearrangement of atoms towards forming a crystal lattice at high temperatures during the early stage of cooling.

Thermodynamics and kinetics of homogeneous crystal nucleation studied by computer simulation

Crystal nucleation is numerically simulated in the Lennard-Jones model. By isobaric cooling and isothermal compression of a liquid, we succeeded in fully crystallizing a large number of systems containing up to 10 000 atoms. We assessed thermodynamic data (density, enthalpy, and chemical potential) of the crystalline as well as the (metastable) liquid phase for considerably larger ranges of pressure and temperature than published so far. Using these data, we were able to confront our simulation results with classical nucleation theories without the need to recognize a critical cluster during the simulations. One of the findings is that in our experiments the steady-state nucleation regime was almost never reached. Careful analysis resulted in an estimate of the time-dependent effects in the nucleation rate, during which the nucleation rate grows from zero to its steady-state value. This way we were able to determine the values of the steady-state nucleation rate, which are consistent with independent estimates for both the preexponential factor and the nucleation barrier. In most previous experimental and simulation studies by other research groups, preexponential factors have been found that are orders of magnitude too large or too small. Our investigations show that an important factor in this discrepancy could be due to an underestimation of time-dependent nucleation effects.

Control of protein crystal nucleation around the metastable liquid-liquid phase boundary.

The capability to enhance or suppress the nucleation of protein crystals opens opportunities in various fundamental and applied areas, including protein crystallography, production of protein crystalline pharmaceuticals, protein separation, and treatment of protein condensation diseases. Herein, 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 (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 polyethylene glycol on the phase diagram and the nucleation kinetics. The control mechanism does not require changes in the protein concentration, acidity, and ionicity of the solution. The effects of the two additives on the phase diagram strongly depend on their concentration, which provides opportunities for further tuning of nucleation rates.

Character of change in the work of nucleation of β-quartz, diamond, and aluminum hydride (α-AlH 3) crystals in homogeneous media

The model for homogeneous nucleation of covalent crystals has been developed, which considers the nuclei ranging from n to n×10 2 atoms and uses the noncontinuous calculations. The critical size of a nucleus depends stepwisely on the supersaturation. The mass crystallization processes are to yield product of stable condition in the wide ranges of supersaturation. The process and product change drastically on the borders of the ranges. The local minimums in the relationship between the free energy of nucleus and its size are evidently observed. Such stable nuclei are the building units which can condense to form the new phase.

Nucleation studies in supersaturated aqueous solutions of KH2PO4 doped with KBr and K2Cr2O7

Induction periods were measured for various supersaturated aqueous solutions of potassium dihydrogen orthophosphate doped separately with potassium bromide and potassium dichromate by the direct vision method. Various critical nucleation parameters were calculated based on the classical theory for homogeneous crystal nucleation and the results are reported and discussed. The critical nucleation parameters increased with increase in doping concentration for both the dopants considered.

Nucleation studies in supersaturated aqueous solutions of urea and thiourea doped with inorganic dopants

Induction periods were measured for various supersaturated aqueous solutions of urea doped separately with NH4NO3 and NaNO3 and thiourea doped separately with NaCl and KCI by the direct vision method. Based on classical theory for homogeneous crystal nucleation various critical nucleation parameters were calculated and the results are reported and discussed. In all the cases, the critical nucleation parameters increased with increase in doping concentration.

A generalized classical nucleation theory for rough interfaces: application in the analysis of homogeneous nucleation in silicate liquids

Computer simulations as well as a recent in situ small-angle X-ray scattering study of the nucleation process have shown evidences in favor of the presence of atomic scale surface roughness of the nuclei, especially at low temperatures and/or at early stages of their development. In this article we have introduced a generalized version of the classical theory of homogeneous nucleation in order to incorporate the effect of finite surface roughness of the critical nuclei. The surface roughness has been taken into account by treating the surface of the nuclei as a self-similar fractal with a fractal dimension 3⩾ d s⩾2. The energetic consequences of the increased surface area due to its fractal character have been shown to be sufficient to explain the long-standing discrepancy between the experimentally observed temperature dependence of homogeneous nucleation rates and corresponding theoretical predictions based on classical theory. This rough-interface theory has been tested against the literature data on homogeneous nucleation of crystals in a number of glass-forming silicate liquids.