Elastic effects due to lattice strain modify the local equilibrium condition at the solid-solid interface compared to the classical dendritic growth. Both, the thermal and the elastic fields are eliminated by the Green's function techniques and a closed nonlinear integro-differential equation for the evolution of the interface is derived. In the case of pure dilatation, the elastic effects lead only to a trivial shift of the transition temperature while in the case of shear transitions, dendritic patterns are found even for isotropic surface energy.
The microsegregation and dendritic growth mode of Al-5wt%Cu alloy was investigated. In the early solidification stage, the crystal growth mode of interrupted growth and periodic boundary trapping will happen, which results in the segregationless dendritic grains. Microsegregation only exists at the final solidification stage with extremely tiny residual melt fraction. In the tiny residual melt zone, the diffusion of solute from the enriched boundary layer to the residual melt and the convergence of enriched boundaries produce the final microsegregation.
Ice crystals growing in highly supersaturated air at temperatures near -5 C exhibit a distinctive, nonplanar dendritic morphology that has not been previously documented or explained. We examine this structure and identify its most prominent features in relation to the ice crystal lattice. Developing a full 3D numerical model that reproduces this robust morphology will be an interesting challenge in understanding diffusion-limited crystal growth in the presence of highly anisotropic surface attachment kinetics.
Gravity-induced buoyancy, inevitable in most solidification processes, substantially alters the dynamics of crystal growth, such that incorporating fluid flow in solidification models is crucial to understand and predict key aspects of microstructure selection. Here, we present a multi-scale Dendritic Needle Network (DNN) model for directional solidification that includes buoyant flow in the liquid, and apply it to a range of alloys and growth conditions. After a brief presentation of the model, we study the selection of stable primary dendrite arm spacings in Al-4at.%Cu and in Ti-45at.%Al all…
The evolution of solidification microstructures in ternary metallic alloys is investigated by adaptive finite element simulations of a general multicomponent phase-field model. A morphological transition from dendritic to globular growth is found by varying the alloy composition at a fixed undercooling. The dependence of the growth velocity and of the impurity segregation in the solid phase on the composition is analyzed and indicates a smooth type of transition between the dendritic and globular growth structures.
The Kruskal-Segur approach to selection theory in diffusion-limited or Laplacian growth is extended via combination with the Zauderer decomposition scheme. This way nonlinear bulk equations become tractable. To demonstrate the method, we apply it to two-dimensional crystal growth in a potential flow. We omit the simplifying approximations used in a preliminary calculation for the same system [T. Fischaleck, K. Kassner, EPL 81, 54004 (2008)], thus exhibiting the capability of the method to extend mathematical rigor to more complex problems than hitherto accessible.
Atom probe tomography (APT) analysis of chemically pure nanofilms of zero-valent iron (Fe(0), or ZVI) and their thermal oxide nano-overlayers reveals the presence of dendritic iron oxide features that extend from the oxide nano-overlayer surface into the ZVI bulk. The dendrites are observed by APT to be in the 5 nm x 10 nm size range and form quickly under natural atmospheric conditions. Their growth into the ZVI lalyer is, within the limit of our three-month long study, self-limiting (i.e. their initial growth appears to quickly discontinue). The atomistic views presented here shed first ligh…
A thin-interface phase-field model of electrochemical interfaces is developed based on Marcus kinetics for concentrated solutions, and used to simulate dendrite growth during electrodeposition of metals. The model is derived in the grand electrochemical potential to permit the interface to be widened to reach experimental length and time scales, and electroneutrality is formulated to eliminate the Debye length. Quantitative agreement is achieved with zinc Faradaic reaction kinetics, fractal growth dimension, tip velocity, and radius of curvature. Reducing the exchange current density is found …
Sub-monolayer physical layer deposition of Zn on Ag(111) substrate at room temperature is investigated using Auger electron spectroscopy, low energy electron diffraction and scanning tunneling microscopy. We identified an original Zn highly-anisotropic structure in the shape of finger-like inserted dendrite in front of Zn monolayer growth. On the basis of STM observations, a mechanism of inserted dendritic growth and a mechanism of its transition to layered growth are proposed.
We present a mathematical formulation of a multiscale model for solidification with convective flow in the liquid phase. The model is an extension of the dendritic needle network approach for crystal growth in a binary alloy. We propose a simple numerical implementation based on finite differences and step-wise approximations of parabolic dendritic branches of arbitrary orientation. Results of the two-dimensional model are verified against reference benchmark solutions for steady, unsteady, and buoyant flow, as well as steady-state dendritic growth in the diffusive regime. Simulations of equia…
We report a scheme for very significantly accelerating growth of dendritic patterns in diverse liquids, making use of only a few hundred microwatts of laser power in the presence of an efficient absorber like carbon nanotubes (CNTs). The CNTs act as a heat source that drives dendritic growth; their anisotropy ensures a rich diversity of branched patterns. We rationalize the unprecedented speed of dendritic growth using a diffusion equation for the temperature field with an additional source term. Close to the heat source, the well-established microscopic solvability theory is seen to break dow…
Numerical Simulation of Dendritic crystal growth using phase field method and investigating the effects of different physical parameter on the growth of the dendrite
We present a first implementation of the Dendritic Needle Network (DNN) model for dendritic crystal growth in three dimensions including convective transport in the melt. The numerical solving of the Navier-Stokes equations is performed with finite differences and is validated by comparison with a classical benchmark in fluid mechanics for unsteady flow. We compute the growth behavior of a single equiaxed crystal under a forced convective flow. As expected, the resulting dendrite morphology differs strongly from the case of the purely diffusive regime and from similar two-dimensional simulatio…
We report the results of a new method of measuring the capillary length for the dendritic crystal growth of non-faceted materials. This method uses a nearly spherical crystal held near unstable equilibrium in an oscillating temperature field. For the growth of ammonium chloride crystals from aqueous solution, previous published estimates of the capillary length varied by over a factor of 20. With this new method, we find the product of the diffusion constant and capillary length $D d_0$ to be $0.78 \pm 0.07 \,\mathrm{μm^3/s}$, similar to that obtained for ammonium bromide crystals.
We present a quantitative benchmark of multiscale models for dendritic growth simulations. We focus on approaches based on phase-field, dendritic needle network, and grain envelope dynamics. As a first step, we focus on isothermal growth of an equiaxed grain in a supersaturated liquid in three dimensions. A quantitative phase-field formulation for solidification of a dilute binary alloy is used as the reference benchmark. We study the effect of numerical and modeling parameters in both needle-based and envelope-based approaches, in terms of their capacity to quantitatively reproduce phase-fiel…
We examine scaling in two-dimensional simulations of dendritic growth at low undercooling, as well as in three-dimensional pivalic acid dendrites grown on NASA's USMP-4 Isothermal Dendritic Growth Experiment. We report new results on self-similar evolution in both the experiments and simulations. We find that the time dependent scaling of our low undercooling simulations displays a cross-over scaling from a regime different than that characterizing Laplacian growth to steady-state growth.
We study the effect of fluid flow on three-dimensional (3D) dendrite growth using a phase-field model on an adaptive finite element grid. In order to simulate 3D fluid flow, we use an averaging method for the flow problem coupled to the phase-field method and the Semi-Implicit Approximated Projection Method (SIAPM). We describe a parallel implementation for the algorithm, using Charm++ FEM framework, and demonstrate its efficiency. We introduce an improved method for extracting dendrite tip position and tip radius, facilitating accurate comparison to theory. We benchmark our results for two-di…
We compare time-dependent solutions of different phase-field models for dendritic solidification in two dimensions, including a thermodynamically consistent model and several ad hoc models. The results are identical when the phase-field equations are operating in their appropriate sharp interface limit. The long time steady state results are all in agreement with solvability theory. No computational advantage accrues from using a thermodynamically consistent phase-field model.
Highly dendritic graphene crystals up to 0.25 mm in diameter are synthesized by low pressure chemical vapor deposition inside a copper enclosure. With their sixfold symmetry and fractal-like shape, the crystals resemble snowflakes. The evolution of the dendritic growth features is investigated for different growth conditions and surface diffusion is found to be the growth-limiting step responsible for the formation of dendrites. The electronic properties of the dendritic crystals are examined down to sub-Kelvin temperatures, showing a mobility of up to 6300 cm$^2$V$^{-1}$s$^{-1}$ and quantum H…
We present the second set of benchmark problems for phase field models that are being jointly developed by the Center for Hierarchical Materials Design (CHiMaD) and the National Institute of Standards and Technology (NIST) along with input from other members in the phase field community. As the integrated computational materials engineering (ICME) approach to materials design has gained traction, there is an increasing need for quantitative phase field results. New algorithms and numerical implementations increase computational capabilities, necessitating standard problems to evaluate their im…
Understanding over-limiting current (faster than diffusion) is a long-standing challenge in electrochemistry with applications in desalination and energy storage. Known mechanisms involve either chemical or hydrodynamic instabilities in unconfined electrolytes. Here, it is shown that over-limiting current can be sustained by surface conduction in nano pores, without any such instabilities, and used to control dendritic growth during electrodeposition. Copper electrode posits are grown in anodized aluminum oxide membranes with polyelectrolyte coatings to modify the surface charge. At low curren…
We investigate dendritic sidebranching during crystal growth in an undercooled melt by simulation of a phase-field model which incorporates thermal noise of microscopic origin. As a non-trivial quantitative test of this model, we first show that the simulated fluctuation spectrum of a one-dimensional interface in thermal equilibrium agrees with the exact sharp-interface spectrum up to an irrelevant short-wavelength cutoff comparable to the interface thickness. Simulations of dendritic growth are then carried out in two dimensions to compute sidebranching characteristics (root-mean-square ampli…
We develop a description of diffusion limited growth in solid-solid transformations, which are strongly influenced by elastic effects. Density differences and structural transformations provoke stresses at interfaces, which affect the phase equilibrium conditions. We formulate equations for the interface kinetics similar to dendritic growth and study the growth of a stable phase from a metastable solid in both a channel geometry and in free space. We perform sharp interface calculations based on Green's function methods and phase field simulations, supplemented by analytical investigations. Fo…
We simulate dendritic growth in directional solidification in dilute binary alloys using a phase-field model solved with an adaptive-mesh refinement. The spacing of primary branches is examined for a range of thermal gradients and alloy compositions and is found to undergo a maximum as a function of pulling velocity, in agreement with experimental observations. We demonstrate that wavelength selection is unambiguously described by a non-trivial crossover scaling function from the emergence of cellular growth to the onset of dendritic fingers, a result validated using published experimental dat…
We discuss a free boundary problem for two moving solid-liquid interfaces that strongly interact via the diffusion field in the liquid layer between them. This problem arises in the context of liquid film migration (LFM) during the partial melting of solid alloys. In the LFM mechanism the system chooses a more efficient kinetic path which is controlled by diffusion in the liquid film, whereas the process with only one melting front would be controlled by the very slow diffusion in the mother solid phase. The relatively weak coherency strain energy is the effective driving force for LFM. As in …
Magnetron sputtering has also been used to deposit thin films of some materials and it has significant technological importance. A modeling on deposition of epitaxial thin films of Yttrium Stabilized Zirconia (YSZ) was done the diffusion of adatom on the surface were studies. There exists a strong interaction of ions formed in the plasma during the sputtering process. Cu thin films were deposited on Si. Nanocomposite thin film of SiCN showed dendritic growth.
Strain can be used as an alternate way to tune the electronic properties of graphene. Here we demonstrate that it is possible to tune the uniform strain of graphene simply by changing the chemical vapor deposition growth temperature of graphene on copper. Due to the cooling of the graphene on copper system, we can induce a uniform compressive strain on graphene. The strain is analyzed by Raman spectroscopy, where a shift in the 2D peak is observed and compared to our ab initio calculations of the graphene on copper system as a function of strain.
Temperature dependent structural phase transitions of SrRuO3 thin films epitaxially grown on SrTiO3(001) single crystal substrates have been studied using high-resolution x-ray diffraction. In contrast to bulk SrRuO3, coherently strained epitaxial layers do not display cubic symmetry up to ~730 oC and remain tetragonal. Such behavior is believed to be induced by compressive strain between the SrRuO3 layer and SrTiO3 substrate due to lattice mismatch. The tetragonal symmetry during growth explains the single domain growth on miscut SrTiO3 substrates with step edges running along the [100] or [0…
We use atomistic simulations with an empirical potential (EAM) to study the elastic effects of heteroepitaxial islands on adatom diffusion. We measure the diffusion barrier on pure stressed substrate and near a misfit island, as well as the detachment barrier from islands of different size.
We present a novel hybrid computational method to simulate accurately dendritic solidification in the low undercooling limit where the dendrite tip radius is one or more orders of magnitude smaller than the characteristic spatial scale of variation of the surrounding thermal or solutal diffusion field. The first key feature of this method is an efficient multiscale diffusion Monte-Carlo (DMC) algorithm which allows off-lattice random walkers to take longer and concomitantly rarer steps with increasing distance away from the solid-liquid interface. As a result, the computational cost of evolvin…
We have investigated the formation of tungsten oxide nanowires under different CVD conditions. We find that exposure of oxidized tungsten films to hydrogen and methane at 900C leads to the formation of a dense array of typically 10 nm diameter nanowires. Structural and chemical analysis shows that the wires are crystalline WO3. We propose a chemically-driven whisker growth mechanism in which interfacial strain associated with the formation of tungsten carbide stimulates nanowire growth. This might be a general concept, applicable also in other nanowire systems.
Ductile fracture has been extensively studied in metals with weak mechanical anisotropy such as copper and aluminum. The fracture of more anisotropic metals, especially those with a hexagonal crystal structure (e.g. titanium), remains far less understood. This paper investigates the ductile fracture process in commercially pure titanium (CP-Ti) with particular emphasis on the influence of grain orientation and local state of strain on void growth. An experimental approach was developed to directly relate the growth of a void in three dimensions to its underlying grain orientation. Grain orient…
An efficient method for the simulation of strained heteroepitaxial growth with intermixing using kinetic Monte Carlo is presented. The model used is based on a solid-on-solid bond counting formulation in which elastic effects are incorporated using a ball and spring model. While idealized, this model nevertheless captures many aspects of heteroepitaxial growth, including nucleation, surface diffusion, and long range effects due elastic interaction. The algorithm combines a fast evaluation of the elastic displacement field with an efficient implementation of a rejection-reduced kinetic Monte Ca…
A numerical method for computation of heteroepitaxial growth in the presence of strain is presented. The model used is based on a solid-on-solid model with a cubic lattice. Elastic effects are incorporated using a ball and spring type model. The growing film is evolved using Kinetic Monte Carlo (KMC) and it is assumed that the film is in mechanical equilibrium. The strain field in the substrate is computed by an exact solution which is efficiently evaluated using the fast Fourier transform. The strain field in the growing film is computed directly. The resulting coupled system is solved iterat…
We report the interplay between In incorporation and strain relaxation kinetics in high-In-content InxGa1-xN (x = 0.3) layers grown by plasma-assisted molecular-beam epitaxy. For In mole fractions x = 0.13-0.48, best structural and morphological quality is obtained under In excess conditions, at In accumulation limit, and at a growth temperature where InGaN decomposition is active. Under such conditions, in situ and ex situ analysis of the evolution of the crystalline structure with the growth thickness points to an onset of misfit relaxation after the growth of 40 nm, and a gradual relaxation…
Cooperative growth of the structure units (SUs) in a 14H type long-period stacking ordered (LPSO) structure has been observed, and there is no obvious accumulation of transformation strain at the growth fronts. The atomic structures at this front are further characterized by Cs-corrected scanning transmission electron microscopy, and the partial dislocations associated SUs are uniquely defined based on the observations at different zone axes. It is found that the Burgers vectors of neighbouring partials are alternatively opposed so that the transformation strain is self-accommodated. Furthermo…
We present a detailed x-ray diffraction study of the strain in InAs/GaSb superlattices grown by molecular beam epitaxy. The superlattices were grown with either InSb or GaAs interfaces. We show that the superlattice morphology, either planar or nanostructured, is dependent on the chemical bonds at the heterointerfaces. In both cases, the misfit strain has been determined for the superlattice layers and the interfaces. We also determined how the magnitude and sign of this strain is crucial in governing the morphology of the superlattice. Our analysis suggests that the growth of self-assembled n…
Monolayer molybdenum disulphide (MoS$_2$) is a promising two-dimensional (2D) material for nanoelectronic and optoelectronic applications. The large-area growth of MoS$_2$ has been demonstrated using chemical vapor deposition (CVD) in a wide range of deposition temperatures from 600 °C to 1000 °C. However, a direct comparison of growth parameters and resulting material properties has not been made so far. Here, we present a systematic experimental and theoretical investigation of optical properties of monolayer MoS$_2$ grown at different temperatures. Micro-Raman and photoluminescence (PL) stu…
The subtle balance of electronic correlations, crystal field splitting and spin--orbit coupling in layered Ir$^{4+}$ oxides can give rise to novel electronic and magnetic phases. Experimental progress in this field relies on the synthesis of epitaxial films of these oxides. However, the growth of layered iridates with excellent structural quality is a great experimental challenge. Here we selectively grow high quality single--phase films of Sr$_2$IrO$_4$, Sr$_3$Ir$_2$O$_7$, and SrIrO$_3$ on various substrates from a single Sr$_3$Ir$_2$O$_7$ target by tuning background oxygen pressure and epita…
Strain engineering of perovskite oxide thin films has proven to be an extremely powerful method for enhancing and inducing ferroelectric behavior. In ferroelectric thin films and superlattices, the polarization is intricately linked to crystal structure, but we show here that it can also play an important role in the growth process, influencing growth rates, relaxation mechanisms, electrical properties and domain structures. We have studied this effect in detail by focusing on the properties of BaTiO$_{3}$ thin films grown on very thin layers of PbTiO$_{3}$ using a combination of x-ray diffrac…
We have studied the effect of the misfit on the equilibrium shape of three-dimensional pyramidal islands grown on a foreign substrate in the case of incomplete wetting (Volmer-Weber mode of growth). We have found that tensile islands have smaller aspect ratios compared with compressed islands owing to its better adhesion to the substrate. The average strains of consecutive layers decrease faster with thickness in compressed than in tensile islands. The strains decrease rapidly with thickness, with the consequence that above a certain height, the upper layers of the pyramid become practically u…
Crack advance from short or long pre-cracks is predicted by the progressive failure of a cohesive zone in a strain gradient, elasto-plastic solid. The presence of strain gradients leads to the existence of an elastic zone at the tip of a stationary crack, for both the long crack and the short crack cases. This is in sharp contrast with previous asymptotic analyses of gradient solids, where elastic strains were neglected. The presence of an elastic singularity at the crack tip generates stresses which are sufficiently high to activate quasi-cleavage. For the long crack case, crack growth resist…
Analytical treatments, formulated to predict the rate of the bainite transformation, define autocatalysis as the growth of the subunits at the bainite-austenite interface. Furthermore, the role of the stress-free transformation strain is often translated to a thermodynamic criterion that needs to be fulfilled for the growth of the subunits. In the present work, an elastic phase-field model, which elegantly recovers the sharp-interface relations, is employed to comprehensively explicate the effect of the elastic energy on the evolution of the subunits. The primary finding of the current analysi…
Experimental observations of the growth of more than one monolayer of Ge on Si(001) show a progression of effects beyond the (2xN) reconstruction which is seen at submonolayer coverages: a reduction in the value of N with coverage; formation of straight trenches of missing dimer vacancies; and formation of the (MxN) ``patch'' structure. We present tight binding calculations which investigate the energetics and geometries associated with these effects, and extend our earlier treatment of formation energies for reconstructions with different stoichiometries to the case of several layers of Ge. T…
First-principles full potential linearized augmented plane wave (FLAPW) calculations have been performed for lattice-mismatched common-atom III-V interfaces. In particular, we have examined the effects of epitaxial strain and ordering direction on the valence band offset in [001] and [111] GaSb/InSb and InAs/InSb superlattices, and found that the valence band maximum is always higher at the InSb side of the heterojunction, except for the common-anion system grown on an InSb substrate. The comparison between equivalent structures having the same substrate lattice constant, but different growth …
We present a first-principles analysis of the strain renormalization of the cation diffusivity on the GaAs(001) surface. For the example of In/GaAs(001)-c(4x4) it is shown that the binding of In is increased when the substrate lattice is expanded. The diffusion barrier ΔE(e) has a non-monotonic strain dependence with a maximum at compressive strain values (e < 0), while being a decreasing function for any tensile strain (e > 0) studied. We discuss the consequences of spatial variations of both the binding energy and the diffusion barrier of an adatom caused by the strain field around a heteroe…
A new phase field model of microstructural evolution is presented that includes the effects of elastic strain energy. The model's thin interface behavior is investigated by mapping it onto a recent model developed by Echebarria et al (Phys Rev E, 70:061604,2004). Exploiting this thin interface analysis the growth of solid state dendrites are simulated with diffuse interfaces and the phase field and mechanical equilibrium equations are solved in real space on an adaptive mesh. A morphological competition between surface energy anisotropy and elastic anisotropy is examined. Two dimensional simul…
The effect of stress-triaxiality on growth of a void in a three dimensional single-crystal face-centered-cubic (FCC) lattice has been studied. Molecular dynamics (MD) simulations using an embedded-atom (EAM) potential for copper have been performed at room temperature and using strain controlling with high strain rates ranging from 10^7/sec to 10^10/sec. Strain-rates of these magnitudes can be studied experimentally, e.g. using shock waves induced by laser ablation. Void growth has been simulated in three different conditions, namely uniaxial, biaxial, and triaxial expansion. The response of t…
Dendrite formation is a major obstacle, such as capacity loss and short circuit, to the next-generation high-energy-density lithium (Li) metal batteries. The development of successful Li dendrite mitigation strategies is impeded by an insufficient understanding of Li dendrite growth mechanisms. Li-plating-induced internal stress in Li metal and its effect on dendrite growth have been studied in previous models and experiments, while the underlying microcosmic mechanism is elusive. Here, we analyze the role of plating-induced stress in dendrite formation through first-principles calculations an…
The effect of hydrogen on the fracture behaviour of austenitic stainless steel has been investigated in the past [1][2]. It has been reported that fracture initiates by void formation at inclusions and regions of enhanced strain localisation [3]. There is experimental evidence that supports the fact that hydrogen influences void nucleation, growth and coalescence during material fracture [4]. This work investigates the effect of hydrogen on void growth and coalescence in austenitic stainless steel. The effect of hydrogen on void growth and coalescence for different stress triaxialities has bee…
