Stationary states of crystal growth in three dimensions

A new Markov process describing crystal growth in three dimensions is introduced. States of the process are configurations of the crystal surface, which has a terrace-edge-kink structure. The states are continuous along edges but discrete across edges, in accordance with the very different rates for the two types of captures of particles. Stationary distributions, describing steady crystal growth, are found in general. To our knowledge, these are the first examples of stationary distributions for layered crystal growth in three dimensions. The steady growth rate and other quantities are obtained explicitly for two interacting edges. For many interacting edges, growth behavior is determined (a) in various asymptotic regimes including thermodynamic limits, (b) via simulations, and (c) using series (cluster) expansions in the slope of the surface, the first three coefficients being computed. The theoretical growth rates show a marked dependence on surface dimensions. This may contribute to the size dependence and dispersion in the observed growth rate of small crystals.     

Steady needle growth with 3-D anisotropic surface tension

The effect of the anisotropic interfacial energy on dendritic growth has been an important subject, and has preoccupied many researchers in the field of materials science and condensed matter physics. The present paper is dedicated to the study of the effect of full 3-D anisotropic surface tension on the steady state solution of dendritic growth. We obtain the analytical form of the first order approximation solution in the regular asymptotic expansion around the Ivantsov’s needle growth solution, which extends the steady needle growth solution of the system with isotropic surface tension obtained by Xu and Yu (J. J. Xu and D. S. Yu, J. Cryst. Growth, 1998, 187: 314; J. J. Xu, Interfacial Wave Theory of Pattern Formation: Selection of Dendrite Growth and Viscous Fingering in a Hele-Shaw Flow, Berlin: Springer-Verlag, 1997).The solution is expanded in the general Laguerre series in any finite region around the needle-tip, and it is also expanded in a power series in the far field behind the tip. Both solutions are then numerically matched in the intermediate region. Based on this global valid solution, the dependence of Peclet number Pe and the interface’s morphology on the anisotropy parameter of surface tension as well as other physical parameters involved are determined. On the basis of this global valid solution, we explore the effect of the anisotropy parameter on the Peclet number of growth, as well as the morphology of the interface.     

Steady needle growth with 3-D anisotropic surface tension

The effect of the anisotropic interfacial energy on dendritic growth has been an important subject, and has preoccupied many researchers in the field of materials science and condensed matter physics. The present paper is dedicated to the study of the effect of full 3-D anisotropic surface tension on the steady state solution of dendritic growth. We obtain the analytical form of the first order approximation solution in the regular asymptotic expansion around the Ivantsov’s needle growth solution, which extends the steady needle growth solution of the system with isotropic surface tension obtained by Xu and Yu (J. J. Xu and D. S. Yu, J. Cryst. Growth, 1998, 187: 314; J. J. Xu, Interfacial Wave Theory of Pattern Formation: Selection of Dendrite Growth and Viscous Fingering in a Hele-Shaw Flow, Berlin: Springer-Verlag, 1997). The solution is expanded in the general Laguerre series in any finite region around the needle-tip, and it is also expanded in a power series in the far field behind the tip. Both solutions are then numerically matched in the intermediate region. Based on this global valid solution, the dependence of Peclet number Pe and the interface’s morphology on the anisotropy parameter of surface tension as well as other physical parameters involved are determined. On the basis of this global valid solution, we explore the effect of the anisotropy parameter on the Peclet number of growth, as well as the morphology of the interface.      

Eddy diffusivity in convective hydromagnetic systems

An eigenvalue equation, for linear instability modes involving large scales in a convective hydromagnetic system, is derived in the framework of multiscale analysis. We consider a horizontal layer with electrically conducting boundaries, kept at fixed temperatures and with free surface boundary conditions for the velocity field; periodicity in horizontal directions is assumed. The steady states must be stable to short (fast) scale perturbations and possess symmetry about the vertical axis, allowing instabilities involving large (slow) scales to develop. We expand the modes and their growth rates in power series in the scale separation parameter and obtain a hierarchy of equations, which are solved numerically. Second order solvability condition yields a closed equation for the leading terms of the asymptotic expansions and respective growth rate, whose origin is in the (combined) eddy diffusivity phenomenon. For about 10% of randomly generated steady convective hydromagnetic regimes, negative eddy diffusivity is found.     

Phase-field modeling of faceted growth in solidification of alloys

A regularization of the surface tension anisotropic function used in vapor-liquid-solid nanowire growth was introduced into the quantitative phase-field model to simulate the faceted growth in solidification of alloys. Predicted results show that the value of δ can only affect the region near the tip, and the convergence with respect to δ can be achieved with the decrease of δ near the tip. It can be found that the steady growth velocity is not a monotonic function of the cusp amplitude, and the maximum value is approximately at ε=0.8 when the supersaturation is fixed. Moreover, the growth velocity is an increasing function of supersaturation with the morphological transition from facet to dendrite.     

Exact steady states to a nonlinear surface growth model

We report on exact stationary solutions to a nonlinear evolution equation describing the collective step meander on a vicinal surface subject to the Bales-Zangwill growth instability [O. Pierre-Louis et al., Phys. Rev. Lett. 80, 4221 (1998)]. Firstly, attention is focused on periodic solutions (steady states) which admit vertical points (or diverging local slopes). Such solutions, which are determined by a theoretical analysis, reveal that the nonlinear evolution equation may admit a non stationary solution with spike singularities or/and caps (dead-core solution) at maxima or/and minima. In a second part, steady states are, mathematically, generalized to a family of evolution equations. Finally, the effect of smoothening by step-edge diffusion is also revisited.     

When does coarsening occur in the dynamics of one-dimensional fronts?

Dynamics of a one-dimensional growing front with an unstable straight profile are analyzed. We argue that a coarsening process occurs if and only if the period lambda of the steady-state solution is an increasing function of its amplitude A. This statement is rigorously proved for two important classes of conserved and nonconserved models by investigating the phase diffusion equation of the steady pattern. We further provide clear numerical evidence for the growth equation of a stepped crystal surface.     

Photoluminescence properties of a single tapered CuO nanowire

Photoluminescence spectroscopy has been employed in order to explore the optical emission properties of a single CuO nanowire, grown on a copper grid in static air by simple thermal oxidation method. As the diameter of the single tapered CuO nanowire decreases, the green emission of the nanowire gradually shifts towards the higher energy side. A steady blue shift of 20 nm of the photoluminescence (PL) peak has been attributed to nanosize effect. Higher surface to volume ratio and enhanced surface defects along the growth direction of the nanowire might be responsible for the observed PL behavior. In addition, crystallization process along the length of the nanowire during growth to form pure CuO structure from the precursor state may also have some role in observed shift in the PL peak.     

Growth and decrescence of two-dimensional crystals: A Markov rate process

A Markov rate process whose transitions are captures and escapes of single atoms from the edge of a two-dimensional crystal is introduced. The stochastic equilibrium states of this process describe steady crystal growth, crystal-fluid equilibrium, and steady crystal decrescence. Exact and asymptotic growth rates are found. This extends recent results which dealt only with capture events. One application is to the growth of lamellar crystals from polymers.     

介质材料二次电子发射特性对微波击穿的影响

以介质填充的平行板放电结构为例,本文主要研究了介质填充后微波低气压放电和微放电的物理过程.为了探究介质材料特性对微波低气压放电和微放电阈值的影响,本文采用自主研发的二次电子发射特性测量装置,测量了7种常见介质材料的二次电子发射系数和二次电子能谱.依据二次电子发射过程中介质表面正带电的稳定条件,计算了介质材料稳态表面电位与二次电子发射系数以及能谱参数的关系.在放电结构中引入与表面电位相应的等效直流电场后,依据电子扩散模型和微放电中电子谐振条件,分别探讨了介质表面稳态表面电位的大小对微波低气压放电和微放电阈值的影响.结果表明,介质材料的二次电子发射系数以及能谱参数越大,介质材料的稳态表面电位也越大,对应的微波低气压放电和微放电阈值也越大.所得结论对于填充介质的选择有一定的理论指导价值.