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.     

Comparative study of microstructural evolution during melting and crystallization

Molecular dynamics simulations, with the interaction between atoms described by a modified analytic embedded atom method, have been performed to obtain the atomic-scale details of isothermal melting in nanocrystalline Ag and crystallization from supercooled liquid. The radial distribution function and common neighbor analysis provide a visible scenario of structural evolution in the process of phase transition. The results indicate that melting at a fixed temperature in nanocrystalline materials is a continuous process, which originates from the grain boundary network. With the melting developing, the characteristic bond pairs (555), (433), and (544), existing in liquid or liquidlike phase, increase approximately linearly till completely melted. The crystallization from supercooled liquid is characterized by three characteristic stages: nucleation, rapid growth of nucleus, and slow structural relaxation. The homogeneous nucleation occurs at a larger supercooling temperature, which has an important effect on the process of crystallization and the subsequent crystalline texture. The kinetics of transition from liquid to solid is well described by the Johnson-Mehl-Avrami equation.     

Two liquid phases of water in the deeply supercooled region and their roles in crystallization and formation of LiCl solution

The properties of supercooled liquid water and the mechanism of crystallization in it were investigated using time-of-flight secondary ion mass spectrometry and reflection absorption infrared spectroscopy. The self-diffusion of the water molecules commences at 136 K, and then the liquid-liquid phase transition occurs at 160-165 K. The latter is evidenced not only by the occurrence of fluidity but also by the formation of a LiCl solution. The infrared absorption band also changes drastically above 160 K due to crystallization of water (on the Au film) and the formation of LiCl solution (on the LiCl film). The immediate crystallization and dissolution of LiCl are thought to be characteristic of normal water that is created in a deeply supercooled region, indicating that viscous liquid water (T > 136 K) is transformed into supercooled liquid water at around 160 K. The crystallization kinetics is different between these two phases because the former (latter) involves nuclear growth (spontaneous nucleation). Without nuclei, crystallization is quenched below 160 K in the present experiment. It is suggested that the viscous liquid phase coexists at the surface or grain boundaries of metastable ice Ic.     

Free energy landscapes for homogeneous nucleation of ice for a monatomic water model

We simulate the homogeneous nucleation of ice from supercooled liquid water at 220 K in the isobaric-isothermal ensemble using the MW monatomic water potential. Monte Carlo simulations using umbrella sampling are performed in order to determine the nucleation free energy barrier. We find the Gibbs energy profile to be relatively consistent with that predicted by classical nucleation theory; the free energy barrier to nucleation was determined to be ~18 k(B)T and the critical nucleus comprised ~85 ice particles. Growth from the supercooled liquid gives clusters that are predominantly cubic, whilst starting with a pre-formed subcritical nucleus of cubic or hexagonal ice results in the growth of predominantly that phase of ice only.     

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.     

Crystallization at the glass transition in supercooled thin films of methanol

The stability of an amorphous material depends on how fast and by what mechanism crystallization occurs. Based on crystallization rate measurements through optical reflectivity changes in supercooled methanol thin films, it is observed for the first time that there is a definitive and detectable change of the crystallization mechanism at the glass transition temperature T(g). For methanol glasses below T(g)=103.4 K, crystallization occurs as an interface controlled, one-dimension process at frozen-in embryo sites, while in the deep supercooled liquid phase above T(g) crystallization is diffusion controlled in two dimensions with a constant nucleation rate and an activation energy of 107.8(+/-4.7) kJ/mol.     

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.     

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.     

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.     

Fluctuation‐assisted crystallization of an iPP/PEOc polymer alloy prepared on a single multicatalyst reactor granule

The new fluctuation‐assisted mechanism for nucleation and crystallization in the isotactic polypropylene/poly(ethylene‐co‐octene) alloy has been studied. We found that the liquid–liquid phase separation (LLPS) had a dominant influence on the crystallization kinetics through the nucleation process. After LLPS, the nucleation of crystallization mainly occurred at the interface of the phase‐separated domains. It is because that the concentration fluctuations of the LLPS induced the motion of polymer chains and possibly some segmental alignment and/or orientation in the concentration gradient regions through interdiffusion, which could assist the formation of nuclei for crystallization. In other words, the usual nucleation energy barrier could be overcome (or at least partially) by the concentration fluctuation growth of LLPS in the unstable regions. This could be viewed as a new kind of heterogeneous nucleation and could be an addition to the regular nucleation and growth mechanism for crystallization. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 166–172, 2009     

热致型液晶聚合物的等温和非等温晶化动力学

利用等温和非等温方法详细研究了芳香族聚酯──热致型聚合物对，对’－联苯二甲酸二辛酯的结晶相和液晶相形成机理，并计算了相变过程中的表面自由能与温度系数，研究结果表明：从介晶相开始的结晶过程是二维异相成核、三维线性增长的，而从各向同性液相开始的液晶相形成过程则是二维异相成核二维线性增长的．对两个晶化过程的表面自由能的研究表明，该聚合物液晶相形成过程的相转变表面自由能比结晶过程小得多，预示了它将具有更大的晶化速率．研究还发现，该聚合物的液晶相形成过程具有比结晶过程大得多的温度敏感性．     

Atomic‐Level Mechanisms of Nucleation of Pure Liquid Metals during Rapid Cooling

To obtain a material with the desired performance, the atomic‐level mechanisms of nucleation from the liquid to solid phase must be understood. Although this transition has been investigated experimentally and theoretically, its atomic‐level mechanisms remain debatable. In this work, the nucleation mechanisms of pure Fe under rapid cooling conditions are investigated. The local atomic packing stability and liquid‐to‐solid transition‐energy pathways of Fe are studied using molecular dynamics simulations and first‐principle calculations. The results are expressed as functions of cluster size in units of amorphous clusters (ACs) and body‐centered cubic crystalline clusters (BCC‐CCs). We found the prototypes of ACs in supercooled liquids and successfully divided these ACs to three categories according to their transition‐energy pathways. The information obtained in this study could contribute to our current understanding of the crystallization of metallic melts during rapid cooling.     

Molecular dynamics simulation of the homogeneous crystallization of liquid rubidium

The homogeneous crystallization of liquid rubidium models containing 500, 998, and 1968 particles in the basic cube was studied by the molecular dynamics method. The liquid crystallized over the temperature range 70–182.5 K predominantly with the formation of a body centered cubic (BCC) structure. The mechanism of crystallization was different from that accepted in classic nucleation theory. Crystallization developed as an increase in the number of atoms with Voronoi polyhedra of the 0-6-0-8 and 0-4-4-6 types, the formation of bound groups (clusters) from these atoms, and growth of these groups as in the coagulation of an impurity from a supersaturated solution. At the initial stage, bound groups had a very loose structure and included a fairly large number of atoms with polyhedra of other types. The linear dimension of the largest group rapidly approached the basic cube size. The atoms with the 0-6-0-8 and 0-4-4-6 Voronoi polyhedra played a leading role in crystallization and activated the transition of bound group atoms with other coordination types into a BCC coordination. The probability of formation of a bound group of a given size was found to be independent of the volume of the liquid model. Cluster size fluctuations especially strong over the temperature range 180–185 K played an important role in the formation of 0608 clusters of a threshold (“critical”) size.     

纳米粒子相变的分子动力学研究：Cu453的性质、结构与结晶成核

Molecular dynamics （MD） computer simulations have been carried out to study the structures, properties and crystal nucleation of nanoparticles with 453 Cu atoms. Structure information was analyzed from the MD simulations, while properties of nanoparticles of Cu453, such as melting point, freezing temperature, heat capacity and mo- lar volumes, have been estimated. The face center cubic （FCC） phase and icosahedron （Ih） phase were observed during the quenching process, and nucleation rates of crystallization to FCC crystal of Cu453 at temperatures of 650, 700, 750, and 800 K were analyzed. Both classical nucleation theory （CNT） and diffuse interface theory （DIT） were used to interpret our observed nucleation rates. The free energy and diffuse interface thickness between the liquid and the FCC crystal phases were estimated by the CNT and DIT respectively, and the results show that the DIT does not work properly to the system.     

Crystal nucleation in binary hard sphere mixtures: a Monte Carlo simulation study

We present calculations of the nucleation barrier during crystallization in binary hard sphere mixtures under moderate degrees of supercooling using Monte Carlo simulations in the isothermal-isobaric semigrand ensemble in conjunction with an umbrella sampling technique. We study both additive and negatively nonadditive binary hard sphere systems. The solid-fluid phase diagrams of such systems show a rich variety of behavior, ranging from simple spindle shapes to the appearance of azeotropes and eutectics to the appearance of substitutionally ordered solid phase compounds. We investigate the effect of these types of phase behavior upon the nucleation barrier and the structure of the critical nucleus. We find that the underlying phase diagram has a significant effect on the mechanism of crystal nucleation. Our calculations indicate that fractionation of the species upon crystallization increases the difficulty of crystallization of fluid mixtures and in the absence of fractionation (azeotropic conditions) the nucleation barrier is comparable to pure fluids. We also calculate the barrier to nucleation of a substitutionally ordered compound solid. In such systems, which also show solid-solid phase separation, we find that the phase that nucleates is the one whose equilibrium composition is closer to the composition of the fluid phase.     

Formation of crystal nuclei near critical supersaturation in small volumes

This work deals with the nucleation of crystals in confined systems in response to the recent high interest in research on crystallization in emulsion and microemulsion droplets. In these confined systems, crystallization often occurs at high supercooling; thus, nucleation determines the overall crystallization process. A decrease in the volume of the confined mother phase leads to the higher supercooling needed for the phase transition. We have numerically solved kinetic equations in order to determine the conditions under which the first crystal nuclei are formed by homogeneous and heterogeneous nucleation from supercooled melt and supersaturated solution, depending on the volume of the mother phase. Supersaturation (or supercooling) increases with decreasing volume of the mother phase. The nucleation barrier depends linearly on the logarithm of volume of the mother phase in all cases under consideration, as follows from the numerical solution of kinetic equations.     

Investigation of the Mechanism of Colloidal Silicalite‐1 Crystallization by Using DLS,SAXS, and 29Si NMR Spectroscopy

Colloidal silicalite‐1 zeolite was crystallized from a concentrated clear sol prepared from tetraethylorthosilicate (TEOS) and aqueous tetrapropylammonium hydroxide (TPAOH) solution at 95 °C. The silicate speciation was monitored by using dynamic light scattering (DLS), synchrotron small‐angle X‐ray scattering (SAXS), and quantitative liquid‐state ²⁹Si NMR spectroscopy. The silicon atoms were present in dissolved oligomers, two discrete nanoparticle populations approximately 2 and 6 nm in size, and crystals. On the basis of new insight into the evolution of the different nanoparticle populations and of the silicate connectivity in the nanoparticles, a refined crystallization mechanism was derived. Upon combining the reagents, different types of nanoparticles (ca. 2 nm) are formed. A fraction of these nanoparticles with the least condensed silicate structure does not participate in the crystallization process. After completion of the crystallization, they represent the residual silicon atoms. Nanoparticles with a more condensed silicate network grow until approximately 6 nm and evolve into building blocks for nucleation and growth of the silicalite‐1 crystals. The silicate network connectivity of nanoparticles suitable for nucleation and growth increasingly resembles that of the final zeolite. This new insight into the two classes of nanoparticles will be useful to tune the syntheses of silicalite‐1 for maximum yield.     

Spinodal patterns indicating unstable regime of polymer crystallization

It has been considered that crystallization of polymer from melt proceeds via the coexistence of molten matrix and growing crystals that have once overcome a nucleation barrier to a critical size. The nucleation process has often been explained analogously with so-called nucleation and growth (NG) behavior of the phase separation of a binary mixture in metastable conditions, although the crystallization in one-component polymer is not a real component separation but a phase transition. Among the mechanisms of polymer crystallization, the topic is whether a liquid–liquid transition between states of different densities within one-component polymers takes place before the aforementioned nucleation process. The liquid–liquid transition between states, which is probably driven by chain orientation, is also categorized into NG and the controversial spinodal decomposition (SD) type processes depending on the quenching depth. This article provides the optical microscopic observations that favor the occurrence of the SD-like process when a one-component polymer melt is very rapidly quenched below a stability limit, including a drastic morphological change from a spherulitic to a spinodal pattern at the critical (or spinodal) temperature. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1817–1822, 2004     

Molecular dynamics studies of the kinetics of phase changes in clusters III: structures, properties, and crystal nucleation of iron nanoparticle Fe331

Molecular dynamics (MD) computer simulations have been carried out to study the structures, properties, and crystal nucleation of iron nanoparticles with 331 Fe atoms or with diameter around 2 nm. Structure information for the nanoparticles was analyzed from the MD simulations. Three crystalline phases and one amorphous phase were obtained by cooling the nanoparticles from their molten droplets at different cooling rates or with different lengths of cooling time periods. Molten droplets froze into three different solid phases and a solid-solid transition from a disordered body-centered cubic (BCC) phase to an ordered BCC phase were observed during the slow cooling and the quenching processes. Properties of nanoparticle Fe₃₃₁, such as melting point, freezing temperature, heat capacity, heat of fusion, heat of crystallization, molar volume, thermal expansion coefficient, and diffusion coefficient, have been estimated. Nucleation rates of crystallization to two solid phases for Fe₃₃₁ at temperatures of 750, 800, and 850 K are presented. Both classical nucleation theory and diffuse interface theory are used to interpret our observed nucleation results. The interfacial free energy and the diffuse interface thickness between the liquid phase and two different solid phases are estimated from these nucleation theories.     

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.