Faceting at the silicon (100) crystal-melt interface: Theory and experiment

Quantitativeness of phase-field simulations for directional solidification of faceted silicon monograins in thin samples

We report the results of a two-dimensional reference model for the formation of facets on the left and right side of a silicon monograin that is solidified by pulling a thin sample in a constant temperature gradient. Anisotropy functions of both the surface energy and the kinetic attachment coefficient are adapted from a recent model for free growth of silicon micrometer-sized grains [Boukellal et al., J. Cryst. Growth 522, 37 (2019)0022-024810.1016/j.jcrysgro.2019.06.005.]. More precise estimates of the physical parameters entering these functions are obtained by reanalyzing available experimental results. We show that the reference model leads to a differential equation for the shape of the solid-liquid interface. The numerical solutions of this equation give a reference law Λ(V_{f}) relating the facet length Λ to the facet normal velocity V_{f}. In parallel, phase-field simulations of the reference model are performed for two growth orientations, [001] and [011]. Facet lengths Λ obtained from simulations at different facet velocities are first extrapolated to the limit of vanishing interface width. This extrapolation is made possible by constructing a master curve common to the whole range of V_{f} values considered. The extrapolated Λ values are then compared with the ones predicted by the Λ(V_{f}) reference law. Both sets give comparable values, with an accuracy of a few percent, which confirms that the phase-field model can give quantitative results for faceted solidification of silicon.

Physical origins of temperature continuity at an interface between a crystal and its melt

We justify and discuss the physical origins for the assumption of temperature continuity at crystal/melt interfaces by performing atomistic simulations. We additionally answer why the crystal/melt interfaces differ from the typical solid/liquid interfaces, which usually exhibit dissimilarities and a resulting temperature drop. We present results for pure silver modeled using the embedded-atom method and Lennard-Jones potential function and contrast the results with each other. We find that the temperature continuity at an interface between a crystal and its melt originates from the perfect vibrational coupling, which is caused by the interfacial structural diffusivity. This study provides fundamental insights into the heat transfer for cases of extremely large heat flux and thermal gradients occurring during rapid melting and solidification. The findings additionally determine the role of rough surfaces in manipulating the thermal conductance in nanodevices.

Direct calculation of the solid-liquid Gibbs free energy difference in a single equilibrium simulation

Computing phase diagrams of model systems is an essential part of computational condensed matter physics. In this paper, we discuss in detail the interface pinning (IP) method for calculation of the Gibbs free energy difference between a solid and a liquid. This is done in a single equilibrium simulation by applying a harmonic field that biases the system towards two-phase configurations. The Gibbs free energy difference between the phases is determined from the average force that the applied field exerts on the system. As a test system, we study the Lennard-Jones model. It is shown that the coexistence line can be computed efficiently to a high precision when the IP method is combined with the Newton-Raphson method for finding roots. Statistical and systematic errors are investigated. Advantages and drawbacks of the IP method are discussed. The high pressure part of the temperature-density coexistence region is outlined by isomorphs.

High-frequency mechanical stirring initiates anisotropic growth of seeds requisite for synthesis of asymmetric metallic nanoparticles like silver nanorods

High-speed stirring at elevated temperatures is shown to be effective in the symmetry-breaking process needed for the growth of the hard-to-synthesize silver nanorods from the polyol reduction of silver ions. This process competes with the facile formation of more symmetrical, spherical and cubic, nanoparticles. Once the seed is formed, further growth proceeds predominantly along the long axis, with a consequent increase of the particles' aspect ratio (that of the nanorod). When stirring is stopped shortly after seed formation, nanorods with a broad distribution of aspect ratios are obtained, while when the high-frequency stirring continues the distribution narrows significantly. The width of the nanorods can only be increased if the initial concentration of Ag(+) ions increases. Reducing the stirring speeds during seed formation lowers the yield of nanorods. Molecular dynamics simulations reveal that the formation of a nanometer-scale thin boundary region between a solid facet of the nanoparticle and the liquid around it, and the accommodation processes of metal (Ag) atoms transported through this boundary region from the liquid to the solid growth interface, are frustrated by sufficiently fast shear flow caused by high-frequency stirring. This arrests growth on seed facets parallel to the flow, leading, together with the preferential binding of the capping polymer to the (100) facet, to the observed growth in the (110) direction, resulting in silver nanorods capped at the ends by (111) facets and exposing (100) facets on the side walls.

A molecular dynamics study of the role of relative melting temperatures in reactive Ni/Al nanolaminates

Molecular dynamics (MD) simulations using a recently developed first-principles-based embedded-atom-method (EAM) potential are used to simulate the exothermic alloying reactions of a Ni/Al bilayer initially equilibrated at 1200 K. Simulations are performed in the isobaric-isoenthalpic (NPH) ensemble, which provides insight into the influence of pressure on atomic mixing and the subsequent alloying reaction. For pressures lower than 8 GPa, the mechanism of mixing is the same: as mixing and reaction occur at the interface, the heat generated first melts the Al layer, and subsequent mixing leads to further heat generation after which the Ni layer melts, leading to additional mixing until the alloying reactions are completed. However, for simulations at pressures higher than 8 GPa, the reaction does not occur within the time interval of the simulation. The results will be compared with our previous simulations of a Ni/Al bilayer using a different interatomic potential, which predicts substantially different pressure-dependent melting behavior of the pure components. This comparative study suggests that pressure-dependent melting behavior of components of reactive materials can be used to influence reaction rates and mechanisms.

On the phase diagram of water with density functional theory potentials: The melting temperature of ice I(h) with the Perdew-Burke-Ernzerhof and Becke-Lee-Yang-Parr functionals

The melting temperature (T(m)) of ice I(h) was determined from constant enthalpy and pressure (NPH) Born-Oppenheimer molecular dynamics simulations to be 417+/-3 K for the Perdew-Burke-Ernzerhof and 411+/-4 K for the Becke-Lee-Yang-Parr density functionals using a coexisting ice (I(h))-liquid phase at constant pressures of P=2500 and 10,000 bar and a density rho=1 g/cm(3), respectively. This suggests that ambient condition simulations at rho=1 g/cm(3) will rather describe a supercooled state that is overstructured when compared to liquid water.

Atomistic simulation study of the structure and dynamics of a faceted crystal-melt interface

A detailed analysis of the structure and dynamics of the crystal-melt interface region in silicon, modeled with the Stillinger-Weber potential, is performed via molecular dynamics simulations. The focus is on the faceted (111) crystal-melt interface, but properties of the rough (100) interface are also determined. We find an intrinsic 10-90 interface width of 0.681+/-0.001 nm for the coarse-grained density profile at the (111) interface and a 0.570+/-0.005 nm width at the (100) interface. Coarse-grained profiles of a suitably defined local order parameter are found to show a smaller width anisotropy between (111) and (100) interfaces while the order profiles exhibit a 0.20-0.25 nm shift in position toward the crystal phase relative to the corresponding density profiles. The structural analysis of the layer of melt adjacent to the (111) facet of the crystal finds ordered clusters with average lifetimes of 16 ps , as determined from autocorrelations of time-dependent layer structure factors, and cluster radii of gyration from 0.2 nm for the smallest cells to as large as 1.5 nm .

Kinetic coefficient of steps at the Si(111) crystal-melt interface from molecular dynamics simulations

Nonequilibrium molecular dynamics simulations are applied to the investigation of step-flow kinetics at crystal-melt interfaces of silicon, modeled with the Stillinger-Weber potential [Phys. Rev. B 31, 5262 (1985)]. Step kinetic coefficients are calculated from crystallization rates of interfaces that are vicinals of the faceted (111) orientation. These vicinal interfaces contain periodic arrays of bilayer steps, and they are observed to crystallize in a step-flow growth mode at undercoolings lower than 40 K. Kinetic coefficients for both [110] and [121] oriented steps are determined for several values of the average step separation, in the range of 7.7-62.4 A. The values of the step kinetic coefficients are shown to be highly isotropic, and are found to increase with increasing step separation until they saturate at step separations larger than approximately 50 A. The largest step kinetic coefficients are found to be in the range of 0.7-0.8 m(sK), values that are more than five times larger than the kinetic coefficient for the rough (100) crystal-melt interface in the same system. The dependence of step mobility on step separation and the relatively large value of the step kinetic coefficient are discussed in terms of available theoretical models for crystal growth kinetics from the melt.

Crystal-melt interface stresses: atomistic simulation calculations for a Lennard-Jones binary alloy, Stillinger-Weber Si, and embedded atom method Ni

Molecular-dynamics and Monte Carlo simulations have been used to compute the crystal-melt interface stress (f) in a model Lennard-Jones (LJ) binary alloy system, as well as for elemental Si and Ni modeled by many-body Stillinger-Weber and embedded-atom-method (EAM) potentials, respectively. For the LJ alloys the interface stress in the (100) orientation was found to be negative and the f vs composition behavior exhibits a slight negative deviation from linearity. For Stillinger-Weber Si, a positive interface stress was found for both (100) and (111) interfaces: f{100}=(380+/-30)mJ/m{2} and f{111}=(300+/-10)mJ/m{2}. The Si (100) and (111) interface stresses are roughly 80 and 65% of the value of the interfacial free energy (gamma) , respectively. In EAM Ni we obtained f{100}=(22+/-74)mJ/m{2}, which is an order of magnitude lower than gamma. A qualitative explanation for the trends in f is discussed.

Crystal-liquid phase relations in silicon at negative pressure

The stable and metastable melting relations for silicon in the diamond and Si136 clathrate-II structures at positive and negative pressures are calculated by molecular dynamics computer simulation. The simulated liquid and crystalline clathrates undergo cavitation at approximately -3 and -12 GPa. Between these limits a stretched crystal would transform directly to gas in response to a mechanical instability. Most importantly, the clathrate-II crystal becomes thermodynamically stable over the diamond at negative pressure below -1 GPa at the melting point. Si136 should then crystallize from a slightly stretched liquid, which would have the same volume as a diamond-structure crystal.