Polymorph selection during the crystallization of Yukawa systems

Using molecular-dynamics simulations, we study the crystallization of supercooled liquids of charge-stabilized colloidal suspensions, modeled by the Yukawa (screened-Coulomb) potential. By modifying the value of the screening parameter lambda, we are able to invert the stability of the body-centered cubic (bcc) and face-centered cubic (fcc) polymorphs and study the crystal nucleation and growth in the domain of stability of each polymorph. We show that the crystallization mechanism strongly depends on the value of lambda. When bcc is the stable polymorph (lambda=3), the crystallization mechanism is straightforward. Both kinetics and thermodynamics favor the formation of the bcc particles and polymorph selection takes place early during the nucleation step. When fcc is the stable polymorph (lambda=10), the molecular mechanism is much more complex. First, kinetics favor the formation of bcc particles during the nucleation step. The growth of the post-critical nucleus proceeds through the successive cross-nucleation of the stable fcc polymorph on the metastable hcp polymorph as well as of the hcp polymorph on the fcc polymorph. As a result, polymorph selection occurs much later, i.e., during the growth step, than for lambda=3. We then extend our findings established in the case of homogeneous crystal nucleation to a situation of practical interest, i.e., when a seed of the stable polymorph is used. We demonstrate that the growth from the (111) face of a perfect fcc crystal into the melt proceeds through the same mechanisms.     

Complete phase behavior of the symmetrical colloidal electrolyte

We computed the complete phase diagram of the symmetrical colloidal electrolyte by means of Monte Carlo simulations. Thermodynamic integration, together with the Einstein-crystal method, and Gibbs-Duhem integration were used to calculate the equilibrium phase behavior. The system was modeled via the linear screening theory, where the electrostatic interactions are screened by the presence of salt in the medium, characterized by the inverse Debye length, kappa (in this work kappasigma=6). Our results show that at high temperature, the hard-sphere picture is recovered, i.e., the liquid crystallizes into a fcc crystal that does not exhibit charge ordering. In the low temperature region, the liquid freezes into a CsCl structure because charge correlations enhance the pairing between oppositely charged colloids, making the liquid-gas transition metastable with respect to crystallization. Upon increasing density, the CsCl solid transforms into a CuAu-like crystal and this one, in turn, transforms into a tetragonal ordered crystal near close packing. Finally, we have studied the ordered-disordered transitions finding three triple points where the phases in coexistence are liquid-CsCl-disordered fcc, CsCl-CuAu-disordered fcc, and CuAu-tetragonal-disordered fcc.     

Homogeneous crystallization of the Lennard-Jones liquid. Structural analysis based on Delaunay simplices method

The crystallization process of a simple liquid upon slow cooling has been modeled by the Monte-Carlo method. The model contains 10,000 Lennard-Jones atoms in the model box with periodic boundary conditions. The model structure is investigated at different stages of crystallization using Delaunay simplices. The simplex belonging to one or another particular crystal structure was determined by the shape of the given simplex taking into account the shape of its neighboring simplices. Simplices typical of the fcc and hcp crystal structures, as well as of polytetrahedral aggregates, not typical of crystals, were studied. The analysis has shown that the “precursors” of a hcp structure are strongly dominating over the “precursors” of a fcc structure in liquid phase before the beginning of crystallization. When crystallization starts, small embryos of the fcc structure are observed; the simplices peculiar to hcp are present at that in great amount, but they are distributed over the sample more uniformly. As crystallization proceeds, the portion of the fcc phase grows faster than hcp. However, no unified crystal appears in our case of slow cooling of the model. A complex polycrystalline structure containing crystalline regions with multiple twinning, pentagonal prisms and elements of icosahedral structures arises instead.     

Zn-Mg合金的结构分析和Zn-Mg扩散体系的物相分布

分子动力学(MD)模拟常采用径向分布函数(RDF)、Honeycutt-Anderson (HA)键型指数法、原子团类型指数法(CTIM)表征物相的微观结构. 本文依据CTIM 理论, 对CTIM 进一步发展, 使CTIM 不仅能够表征bcc\fcc\hcp\非晶体, 也能表征其它晶系的晶体结构. 本文采用CTIM 完成Zn-Mg 合金标准晶体的结构表征和Zn-Mg扩散体系物相分布的分析. 结果表明: 合金组元的CTIM指数不仅反映了Mg₂₁Zn₂₅、MgZn₂、Mg₂Zn₁₁晶体结构的差异, 也说明了Mg₄Zn₇、MgZn₂晶体结构十分相近. Zn-Mg扩散体系两步法模拟后, 体系两端交替分布着hcp 与fcc 结构; 体系中部形成大量的非晶体; Zn原子端交替分布着hcp 与fcc 结构的界面区域主要是Zn12-C类原子.     

Formation and evolution of metastable bcc phase during solidification of liquid Ag: a molecular dynamics simulation study

On the basis of the quantum Sutton-Chen potential, the rapid solidification processes of liquid silver have been studied by molecular dynamics simulation for four cooling rates. By means of several analysis methods, the competitions and transitions between microstructures during the cooling processes have been analyzed intensively. It is found that there are two phase transitions in all simulation processes. The first one is from liquid state to metastable (transitional) body-centered cubic (bcc) phase. The initial crystallization temperature T(ic) increases with the decrease of the cooling rate. The second one is from the transitional bcc phase to the final solid phase. This study validates the Ostwald's step rule and provides evidence for the prediction that the metastable bcc phase forms first from liquid. Further analyses reveal that the final solid at 273 K can be a mixture of hexagonal close-packed (hcp) and face-centered cubic (fcc) microstructures with various proportions of the two, and the slower the cooling rate is, the higher proportion the fcc structure occupies.     

Molecular simulation of cross-nucleation between polymorphs

Recent experiments report that an early nucleating crystalline structure (or polymorph) may nucleate another polymorph. We use molecular dynamics simulations to model this phenomenon known as cross-nucleation. We study the onset of crystallization in a liquid of Lennard-Jones particles cooled at a temperature 22% below the melting temperature. We show that growth proceeds through the successive cross-nucleation of the metastable hexagonal close-packed (hcp) polymorph on the stable face-centered cubic (fcc) polymorph and of the stable fcc polymorph on the metastable hcp polymorph. This finding is in agreement with the experimental results which demonstrated that the cross-nucleation of a stable polymorph on a metastable polymorph is just as likely as the cross-nucleation of a metastable polymorph on a stable polymorph. We then extend our findings established in the case of the homogeneous crystal nucleation to a situation of practical interest, i.e., when a seed of the stable polymorph is used. By studying the crystal growth from the (111) plane of a perfect fcc crystal, we show that, again, growth proceeds through the cross-nucleation of the hcp and fcc structures.     

Melting and homogeneous crystallization of a Lennard-Jones system

Melting and homogeneous crystallization in a Lennard-Jones system of 10,976 atoms in a model box with periodic boundary conditions were investigated by the molecular dynamics method in an NVE ensemble. Crystal melting occurs by arbitrary generation and growth of local defects transformed into regions of a disordered phase. These defects gradually span the entire space of the sample, absorbing the residual islands of crystal. Homogeneous crystallization of a liquid starts with generation of crystal nuclei which grow into defective crystals. The resulting crystal varies in structure between different realizations of the model. Face-centered cubic (fcc) structures prevail. A hexagonal close packing (hcp) structure is present on the boundaries of fcc regions and arises from disordering in alternation of atomic planes. Multiple twinning of the fcc structure is observed, and aggregates with fivefold symmetry have been found.     

Polymorph selection during the crystallization of softly repulsive spheres: the inverse power law potential

Using hybrid Monte Carlo molecular simulations, we study crystallization from the melt of softly repulsive spheres interacting through an inverse power law potential. We work at fixed supercooling (i.e., at a temperature 25% below the melting temperature) and consider three systems, defined by different values for the inverse power exponent n: n = 5, n = 6.67, and n = 10. Modifying the value of n allows us to study the onset of crystallization in the domain of stability of the body-centered cubic (bcc) phase (n = 5 and n = 6.67) and in the domain of stability of the face-centered cubic (fcc) phase (n = 10). We show that, for the three systems, polymorph selection does not take place during crystal nucleation since the structure of the critical nuclei obtained for the three systems is not well defined. However, our results demonstrate that polymorph selection takes place during the growth step since growth proceeds either into the stable bcc phase for the two smaller values of n (n = 5 and n = 6.67) or into the stable fcc phase for the larger value of n (n = 10). We also show that we did not achieve complete control of polymorphism for n = 10. The growth step gives rise to either slowly growing crystallites composed of two blocks of different structures (the stable fcc form and the metastable bcc form) or rapidly growing crystallites of the metastable bcc form.     

Electronic structure of francium

This article presents the first calculations of the electronic structure of francium for the bcc, fcc, and hcp structures, using the linearized augmented plane wave (LAPW) method. Both the local density approximation (LDA) and generalized gradient approximation (GGA) were used to calculate the electronic structure and total energy of francium (Fr). The GGA and LDA both found the total energy of the hcp structure to be slightly below that of the fcc and bcc structures, respectively. This is in agreement with similar results for the other alkali metals where the bcc structure is found not to be the ground state in contradiction to experiment. The equilibrium lattice constant, bulk modulus, and superconductivity parameters were calculated. Calculations of the enthalpy of the system suggest a structural transition from hcp to bcc under a pressure of 0.57 GPa. Using the McMillan‐Gaspari‐Gyorffy theories, we found that under further pressures, in the range of 3–14 GPa, Fr could be a superconductor with critical temperature up to 7 K. This is consistent with the other alkali metals and originates from an increase of the d‐like density of states at the Fermi level, which makes the alkali metals behave like transition metals. © 2013 Wiley Periodicals, Inc.     

Bond-orientational analysis of hard-disk and hard-sphere structures

We report the bond-orientational analysis results for the thermodynamic, random, and homogeneously sheared inelastic structures of hard-disks and hard-spheres. The thermodynamic structures show a sharp rise in the order across the freezing transition. The random structures show the absence of crystallization. The homogeneously sheared structures get ordered at a packing fraction higher than the thermodynamic freezing packing fraction, due to the suppression of crystal nucleation. On shear ordering, strings of close-packed hard-disks in two dimensions and close-packed layers of hard-spheres in three dimensions, oriented along the velocity direction, slide past each other. Such a flow creates a considerable amount of fourfold order in two dimensions and body-centered-tetragonal (bct) structure in three dimensions. These transitions are the flow analogs of the martensitic transformations occurring in metals due to the stresses induced by a rapid quench. In hard-disk structures, using the bond-orientational analysis we show the presence of fourfold order. In sheared inelastic hard-sphere structures, even though the global bond-orientational analysis shows that the system is highly ordered, a third-order rotational invariant analysis shows that only about 40% of the spheres have face-centered-cubic (fcc) order, even in the dense and near-elastic limits, clearly indicating the coexistence of multiple crystalline orders. When layers of close-packed spheres slide past each other, in addition to the bct structure, the hexagonal-close-packed (hcp) structure is formed due to the random stacking faults. Using the Honeycutt-Andersen pair analysis and an analysis based on the 14-faceted polyhedra having six quadrilateral and eight hexagonal faces, we show the presence of bct and hcp signatures in shear ordered inelastic hard-spheres. Thus, our analysis shows that the dense sheared inelastic hard-spheres have a mixture of fcc, bct, and hcp structures.     

Structural stability analysis of Wigner crystal with Gaussian and Yukawa‐type positive background

Calculations of the ground‐state energies of Wigner crystals having simple cubic (sc), body‐centered cubic (bcc), face‐centered cubic (fcc), diamond, and perovskite structures and (hence) the analysis of relative stability of Wigner crystals of various different structures are reported. The positive background is represented by a periodic array of Gaussians and Yukawa‐type distribution. The effects on stability of the perturbation due to the underlying lattice have been demonstrated. Among the structures, the bcc lattice still remains the most stable known arrangement and the Yukawa‐type background leads to a lower ground state energy value compared to a Gaussian type. The calculations are done for the range of the density parameter r_s corresponding to low densities for the above two cases. The range of low‐density region favorable for Wigner crystallization is found to be above r_s=20. The role of correlation energy is suitably taken into account. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Thermodynamic and structural properties of repulsive hard-core Yukawa fluid: integral equation theory, perturbation theory and Monte Carlo simulations

The thermodynamic and structural properties of purely repulsive hard-core Yukawa particles in the fluid state are determined through Monte Carlo simulation and modeled using perturbation theory and integral equation theory in the mean spherical approximation (MSA). Systems of particles with Yukawa screening lengths of 1.8, 3.0, and 5.0 are examined with results compared to variations of MSA and perturbation theory. Thermodynamic properties were predicted well by both theories in the fluid region up to the fluid-solid phase boundary. Further, we found that a simplified exponential version of the MSA is the most accurate at predicting radial distribution function at contact. Radial distribution function of repulsive hard-core Yukawa particles are also reported. The results show that methods based on MSA and perturbation theory that are typically applied to the attractive hard-core Yukawa potential can also be extended to the purely repulsive hard-core Yukawa potential.     

Clusters as crystal fragments of silicon bulk

Silicon clusters of 13 to 43 atoms were studied with the semi-empirical method SINDO1. Crystalline structures of face-centered cubic (fcc), hexagonal close packed (hcp) and diamond type and noncrystalline structures of icosahedral type were compared. Noncrystalline structures are most stable for clusters up to 13 atoms. Clusters with 19 and more atoms of the fcc structure are preferable to the less dense diamond structure. With more than 35 Si atoms, the diamond structure is favored over the hcp structure. The binding energy of fcc and hcp structures decreases and that of the diamond structure increases with increasing cluster size. A similar trend is observed for the HOMO-LUMO energy gap which is taken as a measure of the band gap.     

Effect of polydispersity on the relative stability of hard-sphere crystals

By extending the nonequilibrium potential refinement algorithm and lattice switch method to the semigrand ensemble, the semigrand potentials of the fcc and hcp structures of polydisperse hard-sphere crystals are calculated with the bias sampling scheme. The result shows that the fcc structure is more stable than the hcp structure for polydisperse hard-sphere crystals below the terminal polydispersity.     

Controlled‐Atmosphere Flame Fusion Single‐Crystal Growth of Non‐Noble fcc,hcp, and bcc Metals Using Copper,Cobalt, and Iron

The growth of noble‐metal single crystals via the flame fusion method was developed in the 1980s. Since then, there have been no major advancements to the technique until the recent development of the controlled‐atmosphere flame fusion (CAFF) method to grow non‐noble Ni single crystals. Herein, we demonstrate the generality of this method with the first preparation of fcc Cu as well as the first hcp and bcc single crystals of Co and Fe, respectively. The high quality of the single crystals was verified using scanning electron microscopy and Laue X‐ray backscattering. Based on Wulff constructions, the equilibrium shapes of the single‐crystal particles were studied, confirming the symmetry of the fcc, hcp, and bcc single‐crystal lattices. The low cost of the CAFF method makes all kinds of high‐quality non‐noble single crystals independent of their lattice accessible for use in electrocatalysis, electrochemistry, surface science, and materials science.     

NiFe Alloy Nanoparticles with hcp Crystal Structure Stimulate Superior Oxygen Evolution Reaction Electrocatalytic Activity

Tuning the crystal phase of metal alloy nanomaterials has been proved a significant way to alter their catalytic properties based on crystal structure and electronic property. Herein, we successfully developed a simple strategy to controllably synthesize a rare crystal structure of hexagonal close‐packed (hcp) NiFe nanoparticle (NP) encapsulated in a N‐doped carbon (NC) shell (hcp‐NiFe@NC). Then, we systemically investigated the oxygen evolution reaction (OER) performance of the samples under alkaline conditions, in which the hcp‐NiFe@NC exhibits superior OER activity compared to the conventional face‐centered cubic (fcc) NiFe encapsulated in a N‐doped carbon shell (fcc‐NiFe@NC). At the current densities of 10 and 100 mA cm^?2, the hcp‐NiFe@NC with Fe/Ni ratio of ≈5.4 % only needs ultralow overpotentials of 226 mV and 263 mV versus reversible hydrogen electrode in 1.0 m KOH electrolyte, respectively, which were extremely lower than those of fcc‐NiFe@NC and most of other reported NiFe‐based electrocatalysts. We proposed that hcp‐NiFe possesses favorable electronic property to expedite the reaction on the NC surface, resulting higher catalytic activity for OER. This research provides a new insight to design more efficient electrocatalysts by considering the crystal phase correlated electronic property.     

Solid phase thermodynamic perturbation theory: test and application to multiple solid phases

A simple procedure for the determination of hard sphere (HS) solid phase radial distribution function (rdf) is proposed, which, thanks to its physical foundation, allows for extension to other crystal structures besides the fcc structure. The validity of the procedure is confirmed by comparing (1) the predicted HS solid phase rdf's with corresponding simulation data and (2) the predicted non-HS solid phase Helmholtz free energy by the present solid phase first-order thermodynamic perturbation theory (TPT) whose numerical implementation depends on the HS solid phase rdf's as input, with the corresponding predictions also by the first-order TPT but the required HS solid phase rdf is given by an "exact" empirical simulation-fitted formula. The present solid phase first-order TPT predicts isostructural fcc-fcc transition of a hard core attractive Yukawa fluid, in very satisfactory agreement with the corresponding simulation data and is far more accurate than a recent thermodynamically consistent density functional perturbation theory. The present solid phase first-order TPT is employed to investigate multiple solid phases. It is found that a short-ranged potential, even if it is continuous and differentiable or is superimposed over a long-ranged potential, is sufficient to induce the multiple solid phases. When the potential range is short enough, not only isostructural fcc-fcc transition but also isostructural bcc-bcc transition, simple cubic (sc)-sc transition, or even fcc-bcc, fcc-sc, and bcc-sc transitions can be induced. Even triple point involving three solid phases becomes possible. The multiple solid phases can be stable or metastable depending on the potential parameters.     

Molecular simulation of the crystallization of aluminum from the supercooled liquid

We report hybrid Monte Carlo molecular simulation results on the crystallization of aluminum from the supercooled liquid. We simulate the entire crystallization process at P=1 atm and at temperatures 20% and 15% below the melting temperature. We demonstrate that crystallization takes place according to the same mechanism for the two degrees of supercooling considered in this work. We show that both nucleation and growth proceed into a random mixing of the hexagonal close packed structure and of the face centered cubic (fcc) phase, with a predominance of the stable fcc form. The concentration of icosahedral (Ih)-like atoms in the supercooled liquid is found to remain constant throughout nucleation and growth, showing that Ih-like atoms do not play an active role in the crystallization process. We also find that the crystallization mechanism of aluminum differs from that observed for simple fluids. While nucleation of simple fluids first proceeds into the metastable body centered cubic (bcc) phase, the fraction of bcc-like atoms in aluminum crystallites always remains very low.     

Structure of hard sphere packings near Bernal density

The structural features of packings of similar hard spheres in the vicinity of Bernal density corresponding to space occupancy ∼0.64 have been studied. This is maximum density for disordered packings, which give way to crystallization at higher densities. The structure was analyzed using Delaunay simplices. Aggregates of simplices approximating a regular tetrahedron (polytetrahedra) in form have been studied. They have a high local density and various morphologies, but are incompatible with translation symmetry. Percolation analysis of these clusters was carried out. The “critical” nature of structural transformations at Bernal density is related with the appearance of percolation through tetrahedra. The closest disordered packings really have no significant nucleating seeds of crystal structures, as shown by a sensitive seed detection procedure. Their appearance and fast growth are observed after passing through Bernal density. The total fraction of the crystal phase increases monotonically with the density; the fcc and hcp structures appear in different proportions in the packings.     

Efficient calculation of temperature dependence of solid-phase free energies by overlap sampling coupled with harmonically targeted perturbation

We examine a method for computing the change in free energy with temperature of a crystalline solid. In the method, the free-energy difference between nearby temperatures is calculated via overlap-sampling free-energy perturbation with Bennett's optimization. Coupled to this is a harmonically targeted perturbation that displaces the atoms in a manner consistent with the temperature change, such that for a harmonic system, the free-energy difference would be recovered with no error. A series of such perturbations can be assembled to bridge larger gaps in temperature. We test this harmonically targeted temperature perturbation (HTTP) method through the application to the inverse-power soft potential, u(r)=ε(σ/r)(n), over a range of temperatures up to the melting condition. Three exponent values (n=12, 9, and 6) for the potential are studied with different crystal structures, specifically face-centered cubic (fcc), body-centered cubic (bcc), and hexagonal close packing. Absolute free energies (classical only) for each system are obtained by implementing the series to near-zero temperature, where the harmonic model becomes very accurate. The HTTP method is shown to provide very precise results, with errors in the free energy smaller than two parts in 10(5). An analysis of the thermodynamic stability of the various structures in the infinite-system limit confirms previous findings. In particular, for n=12 and 9, the fcc structure is stable for all temperatures up to melting, and for n=6, the bcc crystal becomes stable relative to fcc for temperatures above kT/ε=0.802±0.001. The effects of vacancies and other defects are not considered in the analysis.