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Register a new userMinimal phase-field crystal modeling of vapor-liquid-solid coexistence and transitions
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A phase-field crystal model based on the density-field approach incorporating high-order interparticle direct correlations is developed to study vapor-liquid-solid coexistence and transitions within a single continuum description. Conditions for the realization of the phase coexistence and transition sequence are systematically analyzed and shown to be satisfied by a broad range of model parameters, demonstrating the high flexibility and applicability of the model. Both temperature-density and temperature-pressure phase diagrams are identified, while structural evolution and coexistence among the three phases are examined through dynamical simulations. The model is also able to produce some temperature and pressure related material properties, including effects of thermal expansion and pressure on equilibrium lattice spacing, and temperature dependence of saturation vapor pressure. This model can be used as an effective approach for investigating a variety of material growth and deposition processes based on vapor-solid, liquid-solid, and vapor-liquid-solid growth.
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We propose a two-dimensional phase-field-crystal model for the (2$times$1)-(1$times$1) phase transitions of Si(001) and Ge(001) surfaces. The dimerization in the 2$times$1 phase is described with a phase-field-crystal variable which is determined by solving an evolution equation derived from the free energy. Simulated periodic arrays of dimerization variable is consistent with scanning-tunnelling-microscopy images of the two dimerized surfaces. Calculated temperature dependence of the dimerization parameter indicates that normal dimers and broken ones coexist between the temperatures describing the charactristic temperature width of the phase-transition, $T_L$ and $T_H$, and a first-order phase transition takes place at a temperature between them. The dimerization over the whole temperature is determined. These results are in agreement with experiment. This phase-field-crystal approach is applicable to phase-transitions of other reconstructed surface phases, especially semiconductor $ntimes$1 reconstructed surface phases.
Chemical vapor deposition (CVD) of two-dimensional (2D) materials such as monolayer MoS2 typically involves the conversion of vapor-phase precursors to a solid product in a process that may be described as a vapor-solid-solid (VSS) mode. Here, we report the first demonstration of vapor-liquid-solid (VLS) growth of monolayer MoS2 yielding highly crystalline ribbon-shaped structures with a width of a few tens of nanometers to a few micrometers. The VLS growth mode is triggered by the reaction between molybdenum oxide and sodium chloride, which results in the formation of molten Na-Mo-O droplets. These droplets mediate the growth of MoS2 ribbons in the crawling mode when saturated with sulfur on a crystalline substrate. Our growth yields straight and kinked ribbons with a locally well-defined orientation, reflecting the regular horizontal motion of the liquid droplets during growth. Using atomic-resolution scanning transmission electron microscopy (STEM) and second harmonic generation (SHG) microscopy, we show that the ribbons are homoepitaxially on monolayer MoS2 surface with predominantly 2H- or 3R-type stacking. These findings pave the way to novel devices with structures of mixed dimensionalities.
In this paper the relationship between the density functional theory of freezing and phase field modeling is examined. More specifically a connection is made between the correlation functions that enter density functional theory and the free energy functionals used in phase field crystal modeling and standard models of binary alloys (i.e., regular solution model). To demonstrate the properties of the phase field crystal formalism a simple model of binary alloy crystallization is derived and shown to simultaneously model solidification, phase segregation, grain growth, elastic and plastic deformations in anisotropic systems with multiple crystal orientations on diffusive time scales.
Kinetics of separation between the low and high density phases in a single component Lennard-Jones model has been studied via molecular dynamics simulations, at a very low temperature, in the space dimension $d=2$. For densities close to the vapor (low density) branch of the coexistence curve, disconnected clusters of the high density phase exhibit ballistic motion, the kinetic energy distribution of the clusters being closely Maxwellian. Starting from nearly circular shapes, at the time of nucleation, these clusters grow via sticky collisions, gaining filament-like nonequilibrium structure at late times, with a very low fractal dimensionality. The origin of the latter is shown to lie in the low mobility of the constituent particles, in the corresponding cluster reference frame, due to the (quasi-long-range) crystalline order. Standard self-similarity in the domain pattern, typically observed in kinetics of phase transitions, is found to be absent in this growth process. This invalidates the common method, that provides a growth law same as in immiscible solid mixtures, of quantifying growth. An appropriate alternative approach, involving the fractality in the structure, quantifies the growth of the characteristic length to be a power-law with time, the exponent being surprisingly high. The observed growth law has been derived via a nonequilibrium kinetic theory.
Vapor transportation is the core process in growing transition-metal dichalcogenides (TMDCs) by chemical vapor deposition (CVD). One inevitable problem is the spatial inhomogeneity of the vapors. The non-stoichiometric supply of transition-metal precursors and chalcogen leads to poor control in products location, morphology, crystallinity, uniformity and batch to batch reproducibility. While vapor-liquid-solid (VLS) growth involves molten precursors at the growth temperatures higher than their melting points. The liquid sodium molybdate can precipitate solid MoS2 monolayers when saturated with sulfur vapor. Taking advantage of the VLS growth, we achieved three kinds of important achievements: (a) 4-inch-wafer-scale uniform growth of MoS2 flakes on SiO2/Si substrates, (b) 2-inch-wafer-scale growth of continuous MoS2 film with a grain size exceeding 100 um on sapphire substrates, and (c) pattern (site-controlled) growth of MoS2 flakes and film. We clarified that the VLS growth thus pave the new way for the high-efficient, scalable synthesis of two-dimensional TMDC monolayers.
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