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.     

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.     

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.     

Polymorph selection in the crystallization of hard-core Yukawa system

Colloid-colloid interactions in charge-stabilized dispersions can to some extent be represented by the hard-core Yukawa model. The crystallization process and polymorph selection of hard-core Yukawa model are studied by means of smart Monte Carlo simulations in the region of face-centered-cubic (fcc) phase. The contact value of hard-core Yukawa potential and the volume fraction of the colloids are fixed, while the Debye screening length can be varied. In the early stage of the crystallization, the precursors with relatively ordered liquid structure have been observed. Although the crystal structure of thermodynamically stable phase is fcc, the system crystallizes into a mixture of fcc and hexagonal close-packed (hcp) structures under small Debye screening length since the colloidal particles act as effective hard spheres. In the intermediate range of Debye screening length, the system crystallizes into a mixture of fcc, hcp, and body-centered-cubic (bcc). The existence of metastable hcp and bcc structures can be interpreted as a manifestation of the Ostwald’s step rule. Until the Debye screening length is large enough, the crystal structure obtained is almost a complete fcc suggesting the system eventually reaches to a thermodynamically stable state.     

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.     

Insights into the molecular mechanism underlying polymorph selection

We use molecular simulations to study polymorph selection during the crystallization of charge-stabilized colloidal suspension. By modifying the conditions of crystallization, we invert the stability of two polymorphs and induce the formation of crystallites whose structure is predominantly that of the stable polymorph. However, our simulations reveal that kinetics play a major role not only during the nucleation step but also in the growth mechanism. The growth of postcritical crystallites of the stable polymorph proceeds through a complex mechanism involving the cross-nucleation of a third metastable polymorph followed by the conversion of this third polymorph into the stable structure.     

Phase behavior of density-dependent pair potentials

Phase diagram is calculated by a recently proposed third-order thermodynamic perturbation theory (TPT) for fluid phase and a recently proposed first-order TPT for solid phases; the underlying interparticle potential consists of a hard sphere repulsion and a perturbation tail of an attractive inverse power law type or Yukawa type whose range varies with bulk densities. It is found that besides usual phase transitions associated with density-independent potentials, the density dependence of the perturbation tail evokes some additional novel phase transitions including isostructural solid-solid transition and liquid-liquid transition. Novel triple points are also exhibited which includes stable fluid (vapor or liquid)-face-centered cubic(fcc)-fcc and liquid-liquid-fcc, metastable liquid-body-centered cubic(bcc)-bcc. It also is found that the phase diagram sensitively depends on the density dependence and the concrete mathematical form of the underlying potentials. Some of the disclosed novel transitions has been observed experimentally in complex fluids and molecular liquids, while others still remain to be experimentally verified.     

Permeation hysteresis in PdCu membranes

H 2 permeation hysteresis has been observed during cycling of a 3 mum thick supported PdCu membrane with approximately 50 atom % Pd through the fcc/bcc (face-centered cubic/body-centered cubic) miscibility gap between 723 and 873 K. Structural investigations after annealing of membrane fragments under H 2 at 823 K reveal retardation of the fcc(H) --> bcc(H) transition, which is attributed to the occurrence of metastable hydrogenated fcc PdCu(H) phases. The H(2) flux at 0.1 MPa H(2) pressure difference in the well-annealed bcc single phase regime below 723 K can be described by J(H2) = (1.3 +/- 0.2) mol.m (-2).s (-1) exp[(-11.1 +/- 0.6) kJ.mol (-1)/( RT)] and that in the fcc single phase regime above 873 K by J(H2) = (7 +/- 2) mol.m (-2).s (-1) exp[(-30.3 +/- 2.5) kJ.mol (-1)/( RT)].     

Additive perturbed molecular assembly in two-dimensional crystals: differentiating kinetic and thermodynamic pathways

During attempts to produce novel two-dimensional cocrystals by coadsorbing components in a binary mixture, the formation of a metastable form was observed in analogy to the phenomenon of additive-induced polymorph formation reported in three-dimensional crystallization. Mechanistic insights into this phenomenon were gained through the use of scanning tunneling microscopy and several adsorbate/additive combinations. One additive plays a critical role in forming a disordered assembly through a process that is primarily kinetic whereas another additive thermodynamically stabilized an intermediate form, resulting in interrupting a phase transformation to a more stable form. These additive effects elucidate one of the potential pathways to kinetically isolate a metastable polymorph formed during cocrystallization in three-dimensional crystallization.     

Direct calculation of the crystal-melt interfacial free energy via molecular dynamics computer simulation

We review our recent work on the direct calculation of the interfacial free energy, gamma, of the crystal-melt interface via molecular dynamics computer simulation for a number of model systems. The value of gamma as a function of crystal orientation is determined using a thermodynamic integration technique employing moving cleaving walls [Phys. Rev. Lett. 2000, 85, 4751]. The calculation is sufficiently precise to resolve the small anisotropy in gamma, which is crucial in determining the kinetics and morphology of dendritic growth. We report values of gamma for the hard-sphere and Lennard-Jones systems, as well as recent results on the series of inverse-power potentials. For the inverse sixth-, seventh-, and eighth-power systems, we determine gamma for both fcc and bcc crystal structures. For these systems, the bcc-melt gamma is lower than that for fcc crystals by about 25%, consistent with recent experiments and computer simulations on fcc-forming systems that show preferential formation of bcc nuclei in the initial stages of crystallization. In addition, we show that our results give a molecular interpretation of Turnbull's rule, which is the empirical relationship between gamma and the enthalpy of fusion.     

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.     

Bcc and Fcc transition metals and alloys: a central role for the Jahn-Teller effect in explaining their ideal and distorted structures

Transition metal elements, alloys, and intermetallic compounds often adopt the body centered cubic (bcc) and face centered cubic (fcc) structures. By comparing quantitative density functional with qualitative tight-binding calculations, we analyze the electronic factors which make the bcc and fcc structures energetically favorable. To do so, we develop a tight-binding function, DeltaE(star), a function that measures the energetic effects of transferring electrons within wave vector stars. This function allows one to connect distortions in solids to the Jahn-Teller effect in molecules and to provide an orbital perspective on structure determining deformations in alloys. We illustrate its use by considering first a two-dimensional square net. We then turn to three-dimensional fcc and bcc structures, and distortions of these. Using DeltaE(star), we rationalize the differences in energy of these structures. We are able to deduce which orbitals are responsible for instabilities in seven to nine valence electron per atom (e(-)/a) bcc systems and five and six e(-)/a fcc structures. Finally we demonstrate that these results account for the bcc and fcc type structures found in both the elements and binary intermetallic compounds of group 4 through 9 transition metal atoms. The outline of a theory of metal structure deformations based on loss of point group operation rather than translational symmetry is presented.     

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.     

Polymorphs of 1,1-bis(4-hydroxyphenyl)cyclohexane and multiple Z' crystal structures by melt and sublimation crystallization

Close packing conflict in a metastable polymorph of the pure title host (Z' = 2, melt crystal m) is resolved in the stable form (Z' = 1, sublimed crystal s) as O-H...O hydrogen bond changes to O-H...pi interaction. Melt crystallization and sublimation show a greater percentage of high Z' structures in CSD statistics.     

On the mechanism of crystalline polymorph selection by polymer heteronuclei

The phase-selective crystallization of acetaminophen (ACM) using insoluble polymers as heteronuclei was investigated in a combined experimental and computational effort to elucidate the mechanism of polymer-induced heteronucleation (PIHn). ACM heteronucleates from supersaturated aqueous solution in its most thermodynamically stable monoclinic form on poly(n-butyl methacrylate), whereas the metastable orthorhombic form is observed on poly(methyl methacrylate). When ACM crystals were grown through vapor deposition, only the monoclinic polymorph was observed on each polymer. Each crystallization condition leads to a unique powder X-ray diffraction pattern with the major preferred orientation corresponding to the crystallographic faces in which these crystal phases nucleate from surfaces of the polymers. The molecular recognition events leading to these outcomes are elucidated with the aid of computed polymer-crystal binding energies using docking simulations. This investigation illuminates the mechanism by which phase selection occurs during the crystallization of ACM using polymers as heteronuclei, paving the way for the improvement of methods for polymorph selection and discovery based on heterogeneous nucleation promoters.     

Crystal structure of thermosensitive gel spheres of poly(N-isopropylacrylamide) in the deionized aqueous suspension as studied by the static light-scattering measurements

Static light-scattering measurements of deionized suspensions of the thermosensitive gels of poly(N-isopropylacrylamide) with various degrees of cross-linking and sizes were made at 20 and 40 °C. Sharp scattering peaks are observed in the scattering curve, and they were attributed to the face-centered cubic (fcc) and/or body-centered cubic lattices (bcc) in the distribution of gel spheres. The fcc and bcc crystal structures formed in the stable and unstable conditions, respectively, i.e., the former formed more favorably at high sphere concentrations and/or low temperatures. The closest intersphere distances were much longer than the hydrodynamic diameters of the gel spheres especially at low sphere concentrations. These experimental results emphasize the important role of the extended electrical double layers in the crystallization of gel spheres, though the contribution of the double layers in gel systems is weak compared with that in the typical colloidal spheres.     

Comparing the structural stability of PbS nanocrystals assembled in fcc and bcc superlattice allotropes

We investigated the structural stability of colloidal PbS nanocrystals (NCs) self-assembled into superlattice (SL) allotropes of either face-centered cubic (fcc) or body-centered cubic (bcc) symmetry. Small-angle X-ray scattering analysis showed that the NC packing density is higher in the bcc than in the fcc SL; this is a manifestation of the cuboctahedral shape of the NC building block. Using the high-pressure rock-salt/orthorhombic phase transition as a stability indicator, we discovered that the transition pressure for NCs in a bcc SL occurs at 8.5 GPa, which is 1.5 GPa higher than the transition pressure (7.0 GPa) observed for a fcc SL. The higher structural stability in the bcc SL is attributed primarily to the effective absorption of loading force in specific SL symmetry and to a lesser extent to the surface energy of the NCs. The experimental results provide new insights into the fundamental relationship between the symmetry of the self-assembled SL and the structural stability of the constituent NCs.     

Cross-nucleation between ROY polymorphs

Cross-nucleation between polymorphs is a newly discovered phenomenon important for understanding and controlling crystal polymorphism. It contradicts Ostwald's law of stages and other theories of crystallization in polymorphic systems. We studied the phenomenon in the spontaneous and seeded melt crystallization of 5-methyl-2-[(2-nitrophenyl)amino]-3-thiophenecarbonitrile (ROY), currently the most polymorphic system of known structures. We observed extensive and sometimes selective cross-nucleation between ROY polymorphs. Certain polymorphs could not nucleate without the aid of others. The new polymorph was found to be more or less thermodynamically stable than the initial one but to always grow faster than or as fast as the initial one. The temperature and surface characteristics of the seed crystals affected the occurrence of cross-nucleation. Our results show that the pathway of crystallization in polymorphic systems is not determined solely by the initial nucleation, but also by cross-nucleation between polymorphs and the different growth rates of polymorphs. This study identified a new metastable polymorph of ROY, the 10th of the family.     

多体展开势能函数在碳族元素原子簇研究中的应用III. 锗原子族的结构和相对稳定性

基于从晶体锗确立的多体展开势能函数, 本文通过坐标完全优化, 发现小的锗原子簇分子(Ge~2~Ge~14)倾向于形成密堆积结构, 表面原子分布以蝶形四元环(D~2d)为主; 常见立方晶体“微观晶体碎片”的分层优化结果表明, 在Ge~15~Ge~100范围内, 多数壳层的原子到分子中心的距离均受到压缩, 且以畸变的简单立方、面心立方及体心立方较为稳定; 在这些畸变密堆积结构中, 表面原子向内压缩最为严重, 使整个分子趋于球形化。较为开放的金刚石类层状原子族只有当所含原子数达数百以上时才可能相对更为稳定。     

Polymorph formation studied by 3D nucleation simulations. Application to a yellow isoxazolone dye, paracetamol, and L-glutamic acid

Knowledge of the nucleation and growth behavior of polymorphs is vital in a variety of industrial applications. With the aid of the growth probability method the nucleus size is obtained as a function of the driving force for crystallization by simulating the growth probability of clusters of various sizes. From these values the cluster interfacial energy can be computed, allowing for the determination of the nucleation rate. The simulations show that nucleation of the metastable form of a yellow isoxazolone dye dominates at higher driving forces while below a certain driving force the stable form nucleates. Two other compounds show dominant nucleation of their stable form, even at extreme driving forces. This is in accordance with experimental findings for all these compounds. The growth probability method is therefore a promising indicator for polymorph nucleation behavior.