Faceted Crystal Growth Research Articles

Developing centimeter-sized CuZr-based metallic glass composites via multi-element microalloying

A multi-element microalloying strategy has been implemented to manipulate the microstructure of CuZr-based bulk metallic glass composites (BMGCs) and, in turn, to improve their mechanical properties. It is found that microalloying with a combination of Ti, Hf, Co, Ni and/or Nb/Sn can effectively refine the austenitic B2–CuZr phase, resulting in finely dispersed B2 crystallites embedded in the BMG matrix while enlarging the sizes of BMGCs. Particularly, an optimum BMGC, i.e., Cu40.75Zr42Al4Ag5Sn0.75Co0.5Ti5Hf1Ni1, can be made by copper-mold casting in the range of diameter from 6.5 to 13.5 mm, much wider than those of BMGCs obtained from microalloying with merely one or two elements. Meanwhile, this centimeter-sized BMGC possesses good mechanical properties with a fracture strength as high as 1960 MPa and a compressive plastic strain up to 6.8 %. Our results demonstrate that multi-element microalloying would reduce the driving force for nucleation of B2 by lowering the melting entropy, and slow down the B2-growth kinetics by promoting faceted crystal growth while retarding multi-component diffusion, both accounting for the making of centimeter-sized BMGCs that contain finely dispersed B2 crystallites in the glass matrix.

Numerical modeling of faceted crystal growth using a lattice Boltzmann-phase field model with a new interfacial energy function

A lattice Boltzmann-phase field model is proposed to study faceted crystal growth in a supersaturated solution, taking into account a new anisotropic interfacial energy function to reproduce the facet characteristics. In this model, a flow field solver and a concentration field solver are coupled with the phase field equation to study faceted crystal growth with fluid convection and solute transfer. Qualitative and quantitative comparisons are carried out with the experimental observation and theoretical analysis of snowflakes to demonstrate the validity and accuracy of the present numerical method. Then crystallization of sodium chloride in a supersaturated solution is investigated in a 3D space at a constant temperature. The results show that the initial supersaturation, solute depletion rate, and solution flow can greatly change the faceted crystal growth by affecting solute transport and distribution. The mechanism of the formation of morphologies and interface velocity evolution is studied and concluded, which shows that the present model has instructional significance for studying and understanding the regulation mechanism of faceted crystal growth.

Filamentous crystal growth in organic liquids and selection of crystal morphology

Filamentous crystals such as whisker crystals are often seen not only in metallic liquids, but also in organic liquids and solutions. They are interesting as reinforce materials. However, it remains challenging to induce filamentous crystals due to an incomplete understanding of the mechanisms behind their formation. In this paper, we investigate filamentous crystal growth in viscous organic liquids. It is found that filamentous crystals grow via an extraordinary dynamical path, where the molecules locally evaporate to bubbles and then redeposite to the tip of growing crystalline filaments. We also succeeded in controlling whether filamentous or faceted crystal growth is selected by inducing or suppressing the bubbles.

Physics of double faceted crystal growth in solidification processes

The existence of solidification growth fronts having intersecting facets (double faceted) has recently been observed in silicon experiments of horizontal ribbon growth. This study investigates the physics of such configurations from a continuum perspective by analyzing the variation of temperature at locations where a facet intersects another facet or a free surface. The temperature distribution and gradients are obtained theoretically for different configurations and material properties. The theoretical formulations show that the intersection point of two facets is colder than the surrounding interface temperatures and thus could be a nucleation site. The analysis also shows that there is a supercooled liquid (below the interface temperatures) in front of the intersection point. However, this is only the case for materials that have a solid conductivity less than the liquid conductivity such as silicon. It is also shown, to the extent that continuum assumptions remain valid, that the temperature gradients can approach infinity at either the intersection point between two facets or the intersection of a facet with a free surface, depending on the material properties and configurations. The theoretical predictions in the vicinity of these points are validated using a finite element numerical solution that accounts for thermal transport, liquid convection, and solidification kinetics. This shows that the physical behavior of a double facet formation can be theoretically predicted informing further experimental, continuum numerical, and molecular dynamic investigations of the phenomenon.

Impact of hydrodynamics on growth and morphology of faceted crystals

The growth of faceted crystals occurs often in nature and industry, involving often the presence of flow. The growth of faceted crystals is the result of interface kinetics and diffusion phenomenon. The present paper presents a front tracking interface model based on a cellular automaton approach for the simulation of faceted crystal growth. The current model takes into account the interface kinetics and solute transport by diffusion and convection. The propagation of kinks is modelled by differentiating two growth velocities, one normal and one lateral at each face. The positions of the crystal corners are shifted according to growth of adjacent faces. The hydrodynamics is computed with a two-phase model using a penalty method to model the presence of growing obstacles (the crystals). This model was applied in 2D to the growth of hexagonal Fe2Al5 crystals, so called top dross particles, in a saturated liquid at constant temperature. Qualitative comparison was made between simulation and experimental observation of crystal shape and size. The growth rate was found to be strongly influenced by the flow hydrodynamic induced kinetics.

Solid state single crystal growth of three-dimensional faceted LaFeAsO crystals

Solid state single crystal growth (SSCG) is a crystal growth technique where crystals are grown from a polycrystalline matrix. Here, we present single crystals of the iron pnictide LaFeAsO grown via SSCG using NaAs as a liquid phase to aid crystallization. The size of the as-grown crystals are up to 2 × 3 × 0.4 mm3. Typical for this method, but very uncommon for crystals of the pnictide superconductors and especially for the oxypnictides, the crystals show pronounced facets caused by considerable growth in c direction. The crystals were characterized regarding their composition, structure, magnetic, and thermodynamic properties. This sets the stage for further measurements for which single crystals are crucial such as any c axis and reciprocal space dependent measurements.

High dimensional population balances for the growth of faceted crystals: Combining Monte Carlo integral estimates and the method of characteristics

A numerical scheme is proposed for the solution of population balance equations that describe the growth of faceted crystals. Therefore, two issues are discussed. First, a numerical scheme for solution of high dimensional population balance equations is proposed. The scheme is based on Monte Carlo integration for the integral distribution properties (number, area, volume) combined with the method of characteristics. Samples’ points are initially obtained from an arbitrary probability distribution via the Metropolis–Hastings algorithm. The evolution of these sample points is subsequently computed using the method of characteristics, while the sample points themselves are the basis of the Monte Carlo integration of the population to obtain e.g. total crystal volume to close the mass balance. The theoretical background of the Monte Carlo integration allows us to estimate the error introduced in the mass balance depending on a particular choice of sampling points. The effectiveness of the scheme is verified for an analytically solvable 3-dimensional population. That case study is also employed to demonstrate that an adequate choice of the probability distribution for the generation of the initial sample points can improve the accuracy without increasing the computational effort. The second issue that must simultaneously be considered comprises the disappearance of faces during growth. Such conditions create a constraint for each face distance, measured from a chosen origin, which, prior to the disappearance of that face, had freely evolved according to its growth rate. This constraint is defined for general faceted crystals, and a procedure is proposed to correct the growth rate so that the constraint can be maintained in dynamic simulations. The application of this procedure is demonstrated in a second case study that simulates a 7-dimensional population balance equation.

Quantitative Modeling of Faceted Ice Crystal Growth from Water Vapor Using Cellular Automata

We describe a numerical model of faceted crystal growth using a cellular automata method. The model was developed for investigating the diffusion-limited growth of ice crystals from water vapor, when the surface boundary conditions are determined primarily by strongly anisotropic molecular attachment kinetics. We restricted our model to cylindrically symmetric crystal growth with relatively simple growth morphologies, as this was sufficient for making quantitative comparisons between models and ice growth experiments. Overall this numerical model appears to reproduce ice growth behavior with reasonable fidelity over a wide range of conditions. More generally, the model could easily be adapted for other material systems, and the cellular automata technique appears well suited for investigating crystal growth dynamics when strongly anisotropic surface attachment kinetics yields faceted growth morphologies.

Measurements of surface attachment kinetics for faceted ice crystal growth

We present new measurements of the growth rates of faceted ice crystals in the temperature range −40<T<−2°C, from which we infer the surface attachment coefficients for the two principal facets. Our data are well described by a polynucleation model, allowing a determination of the molecular step energy as a function of temperature for both facets. These results are a substantial improvement over previous work, and we present an analysis showing that the inconsistencies seen in prior measurements could be explained by systematic errors associated with diffusion effects and substrate interactions. These data provide new insights into the surface attachment kinetics governing ice crystal growth, and they suggest new avenues for examining ice growth behavior using molecular dynamics simulations. Knowledge gained by a detailed case study of ice may in turn lead to a greater general understanding of the fundamental physics underlying crystal growth dynamics.

Topological colloids

Smoke, fog, jelly, paints, milk and shaving cream are common everyday examples of colloids, a type of soft matter consisting of tiny particles dispersed in chemically distinct host media. Being abundant in nature, colloids also find increasingly important applications in science and technology, ranging from direct probing of kinetics in crystals and glasses to fabrication of third-generation quantum-dot solar cells. Because naturally occurring colloids have a shape that is typically determined by minimization of interfacial tension (for example, during phase separation) or faceted crystal growth, their surfaces tend to have minimum-area spherical or topologically equivalent shapes such as prisms and irregular grains (all continuously deformable--homeomorphic--to spheres). Although toroidal DNA condensates and vesicles with different numbers of handles can exist and soft matter defects can be shaped as rings and knots, the role of particle topology in colloidal systems remains unexplored. Here we fabricate and study colloidal particles with different numbers of handles and genus g ranging from 1 to 5. When introduced into a nematic liquid crystal--a fluid made of rod-like molecules that spontaneously align along the so-called 'director'--these particles induce three-dimensional director fields and topological defects dictated by colloidal topology. Whereas electric fields, photothermal melting and laser tweezing cause transformations between configurations of particle-induced structures, three-dimensional nonlinear optical imaging reveals that topological charge is conserved and that the total charge of particle-induced defects always obeys predictions of the Gauss-Bonnet and Poincaré-Hopf index theorems. This allows us to establish and experimentally test the procedure for assignment and summation of topological charges in three-dimensional director fields. Our findings lay the groundwork for new applications of colloids and liquid crystals that range from topological memory devices, through new types of self-assembly, to the experimental study of low-dimensional topology.

Simulated rhythmic growth of targeted single crystal by polymer phase-field model

The novel phase field model with the “polymer characteristic” was established based on a nonconserved spatiotemporal Ginzburg–Landau equation TDGL model. Especially, we related the parameters of crystal temperature with the TDGL model. Moreover, the diffusion equations were discretized according to the diffusion coefficient of every lattice site in various crystal growth faces, and the shape of lattice was selected based on the real proportion of the unit cell dimensions. Spatiotemporal growth of stripped single crystals during isochronous decoration has been investigated theoretically based on this phase field model. Two dimensional numerical calculations were performed to elucidate the faceted single crystal growth including the stripped lozenge-shaped and hexagonal single crystals. Our simulated patterns were in good agreement with the experimental morphologies, and the physical origin of polymer single crystal growth was discussed.

Faceted growth rate estimation of potash alum crystals grown from solution in a hot-stage reactor

This paper developed a methodology to estimate 3D faceted crystal growth rates from 2D images obtained on-line from a single 2D camera. The cooling crystallisation experiment of potash alum was conducted in a small hot stage reactor. The promising results obtained provided a valuable alternative for the accurate estimation of faceted crystal growth rates, which are crucial to the performance of morphological population balance modelling and model-based control of crystal shape and size.

Evolution of morphology and composition in three-dimensional fully faceted strained alloy crystals

Alloy structures such as core-shell particles, heteroepitaxial multilayers and nanowires have received a lot of attention in recent years due to their applications in logic, energy storage and optoelectronics. In typical growth conditions, the surfaces of these structures are usually faceted i.e. they adopt low-energy singular crystalline orientations. For alloy systems, the growth law for a fully faceted structure requires the specification of the normal velocity of each facet, the incorporation rate of each alloy component on the surface, and the exchange of surface atoms with the bulk. The latter process requires consideration of both surface segregation and possibly bulk material transport. By using only fundamental concepts of thermodynamics, we derive the governing equations for the growth of strained and fully faceted two-component crystals in regimes where surface material transport may be governed by surface-attachment limited kinetics or surface diffusion limited kinetics. In both cases we derive a very compact form for the surface mass fluxes from chemical potentials that account for the constraint stemming from the fact that while the growth rate of each alloy component can vary along the surface (as governed by the individual chemical potentials), their sum should remain constant along the facet and should be equal to the growth velocity of the facet. Within our approach, the dynamics of surface segregation and other important features of faceted crystal growth that lead to compositional patterning such as a kinetic barrier for exchange of alloy components between different facets emerge in a very natural fashion.

Growth of 1‐D TiO2 Nanowires on Ti and Ti Alloys by Oxidation

The growth of titania nanowires by a simple metal oxidation process was investigated for both commercially pure α‐Ti and Ti alloys including Ti64 and β‐Ti under a limited supply of oxygen. The effects of processing variables including heat treatment temperature, gas flow rate, and process duration on the growth of nanowires were explored. Similarities and differences in the growth of nanowires on pure Ti versus Ti alloys were observed. While the growth window in terms of temperature and flow rate is narrow in pure Ti, the window is much wider in the alloys. However, the trend towards high temperature is similar in all the samples promoting faceted oxide crystal growth rather than nanowires.

Simulated morphological landscape of polymer single crystals by phase field model

The novel phase field model with the "polymer characteristic" was established based on a nonconserved spatiotemporal Ginzburg-Landau equation (TDGL model A). Especially, we relate the diffusion equation with the crystal growth faces of polymer single crystals. Namely, the diffusion equations are discretized according to the diffusion coefficient of every lattice site in various crystal growth faces and the shape of lattice is selected based on the real proportion of the unit cell dimensions. Spatiotemporal growth of syndiotactic polypropylene single crystals during isothermal crystallization has been investigated theoretically based on this phase field model. Two dimensional numerical calculations are performed to elucidate the faceted single crystal growth including square, rectangular, lozenge-shaped, and hexagonal single crystals. Our simulated patterns are in good agreement with the experimental morphologies, and the physical origin of polymer single crystal growth is discussed.

In situ observation and analysis of faceted crystal growth process in REBCO superconductive oxide

To clarify the nucleation and growth process of 123 crystals, growth of faceted RE123 (REBa2Cu3O7−X, RE=Nd, Sm, Gd, Y) crystals was observed in situ on MgO(100) by using high temperature optical microscope with zoom lens. RE123 crystals nucleated and grew at each undercooling (ΔT=13–50K). Growth rate (u) and incubation time (tinc) for nucleation were obtained from the relationship between the position of faceted interface and time (t). u increased with increasing ΔTr2, where ΔTr=ΔT/Tp, Tp was peritectic temperature. Nucleation rate (Iv) was obtained from the relationship between the number of nucleated crystals (n) and time. Iv increased with increasing of exp(-B/ΔTr2), where B was a constant. Both u and Iv under a fixed ΔT increased with increasing Tp: u(Nd123)>u(Sm123)>u(Gd123) and Iv(Nd123)>Iv(Sm123)>Iv(Gd123) for Tp(Nd123)>Tp(Sm123)>Tp(Gd123) in Ar–1%O2 atmosphere.

Manipulation of crystal shape by cycles of growth and dissolution

AbstractA method for the manipulation of crystal shape by using cycles of growth and dissolution is presented, representing a unique process‐based solution to an important product quality concern. Using 3‐D shape evolution models for faceted crystal growth and dissolution, results are reported for cycling both an illustrative crystal system, as well as a physical plate‐like system. The results show that crystal shape can be manipulated by cycling when the relative growth and dissolution rates are anisotropic, which can be caused by differences in growth mechanism, asymmetry in super/undersaturation, and by the use of surface active additives. Since this method of crystal shape enhancement uses the existing liquid solution, it could be a valuable alternative to the traditional methods which often require changes in the chemical nature of the solution, for example, by changing solvent. © 2007 American Institute of Chemical Engineers AIChE J, 2007

Tailoring of crystal surface morphology by induced spatiotemporal oscillations of temperature

This paper presents the model for pattern formation in the course of stable (unfaceted) and unstable (faceted) crystal growth from the vapor phase, which is influenced by the rapid spatiotemporal variations of the substrate and film temperature. In the model, such variations result from the interference heating of a substrate by weak pulsed laser beams. The ensuing form of the temperature field perturbation from the ground state is fairly generic and simple, and thus it may as well serve to model other situations. In the stable case the surface relaxational dynamics is influenced by surface diffusion transport of adatoms from the hot to the cold regions of a substrate; this leads to the accumulation of mass in the cold regions and depletion in the hot regions. In the unstable case the underlying faceting instability coupled to the directed diffusion transport leads to the formation of the stationary hill-and-valley structure, where the hills may terminate sharply or have the rough tops. The characteristic lateral scale of this structure increases as the wavelength of the temperature nonuniformity decreases, but the coarsening rate of the transients decreases. By effectively redistributing adatoms through the enhanced, spatially inhomogeneous diffusion the mechanism also delays the onset of the spatiotemporal chaos as the growth rate increases. These scenarios are modeled using the framework of the classical continuum theory of the morphological evolution, enriched with the recently developed regularization method for the ill-posed, unstable evolution partial differential equation (PDE), and coupled to the concept of the spatiotemporal oscillatory surface temperature as the "tailoring force" for the evolution dynamics. A mass-conserving finite volume method is developed that is capable of the accurate computation of the large-slope solutions of the unstable, strongly nonlinear, sixth order evolution PDE for the surface height.

Faceted Crystal Growth of Silicon from Undercooled Melt of Si-20 mass%Ni Alloy

Two-dimensional faceted crystal growth of silicon from undercooled melt of Si-20 mass%Ni alloy was experimentally investigated, in which a droplet sample from 10 to 100 mg was undercooled on a single-crystal sapphire and growing crystals were observed in situ. Observed crystals were classified according to the shapes of square, wedge and irregular shapes. The growth velocity was measured for different undercooling conditions. The growth velocity of square shaped crystals was about half times smaller than that of wedge shaped crystals. The growth of square shaped crystals is regarded to be two-dimensional and it is compared with the results of two-dimensional phase-field simulations. Growth velocity in both is in good agreement and the linear kinetic coefficient is estimated to be 0.002 m/sK.

Effects of surfactants on crystallization of ethylene glycol distearate in oil-in-water emulsion

Ethylene glycol distearate (EGDS) was forced to crystallize as thin platelet in order to obtain a pearlescent effect. This was possible by performing a cooling surface crystallization in oil-in-water emulsion with the presence of an emulsifier. Under stagnant conditions, nucleation events and growth of faceted crystals in the oil phase were in situ monitored under microscope. After a first primary nucleation of dendritic crystals, a second population of faceted crystals arose by secondary nucleation and seemed to be the prevailing population. In a stirred vessel, the platelet shape of EGDS crystals was driven by the surfactant choice. Only a non-ionic surfactant, located at the liquid interface was supposed to interact with EGDS during the development of the crystals favouring a platelet habit. The nature of the interaction was not yet established. Moreover, the mastery of the platelet shape was lost when the amount of non-ionic surfactant relatively to the EGDS was decreased. This underlined the importance of the non-ionic surfactant for the obtaining of desired shape. The different physical qualities of crystals produced allowed us to confirm relationships between EGDS particle features with their effect of pearlescence of a cold pearl blend.