Steps and facets at the surface of soft crystals

We consider the shape of crystals which are soft in the sense that their elastic modulus μ is small compared to their surface tension γ, more precisely μa < γ where a is the lattice spacing. We show that their surface steps penetrate inside the crystal as edge dislocations. As a consequence, these steps are broad with a small energy which we calculate. We also calculate the elastic interaction between steps a distance d apart, which is a 1/d ² repulsion. We finally calculate the roughening temperatures of successive facets in order to compare with the remarkable shapes of lyotropic crystals recently observed by Pieranski et al. [#!Pieranski!#,#!EPJ!#]. Good agreement is found. Received 25 June 2001     

Structure and elastic properties of a nematic liquid crystal: A theoretical treatment and molecular dynamics simulation

The Frank elasticity constants which describe splay (K ₁), twist (K ₂), and bend (K ₃) distortion modes are investigated for 4-n-pentyl-4'-cyanobiphenyl (5CB) in the nematic liquid crystal. The calculations rest on statistical-mechanical approaches where the absolute values of K _i (i=1,2,3) are dependent on the direct correlation function (DCF) of the corresponding nematic state. The DCF was determined using the pair correlation function by solving the Ornstein-Zernike equation. The pair correlation function, in turn, was obtained from molecular dynamics (MD) trajectory. Three different approaches for calculations of the elasticity constants were employed based on different level of approximation about the orientational order and molecular correlations. The best agreement with experimental values of elasticity constants was obtained in a model where the full orientational distribution function was used. In addition we have investigated the approximation about spherical distribution of the intermolecular vectors in the nematic phase, often used in derivation of various mean-field theories and employed here for the construction of the DCF. We found that this assumption is not strictly valid, in particular a strong deviation from the isotropic distribution is observed for short intermolecular distances. Received 22 March 2000 and Received in final form 9 June 2000     

Correlation between growth of high-index faces, relative growth rates and crystallographic structure of crystal

According to contemporary crystal growth theories, crystals are bound by low-index faces which are the most slowly growing. However, high-index faces are observed in crystal habits more and more often. In this paper the growth of high-index faces is analysed from a crystallographic perspective. It is shown that the crystallographic structure of a given crystal, expressed by the trigonometric function of appropriate interfacial angles, influences to great degree the crystallisation process and the morphology of crystals, in particular the behaviour of high-index faces. Additionally, it is concluded that at particular crystallographic structure of a crystal, a given high-index face may exist in the habit and develop its size, although it grows much faster than the neighbouring faces. Received 31 July 2001     

Ehrlich-Schwoebel barrier controlled slope selection in epitaxial growth

We examine the step dynamics in a 1+1-dimensional model of epitaxial growth based on the BCF-theory. The model takes analytically into account the diffusion of adatoms, an incorporation mechanism and an Ehrlich-Schwoebel barrier at step edges. We find that the formation of mounds with a stable slope is closely related to the presence of an incorporation mechanism. We confirm this finding using a solid-on-solid model in 2+1 dimensions. In the case of an infinite step edge barrier we are able to calculate the saturation profile analytically. Without incorporation but with inclusion of desorption and detachment we find a critical flux for instable growth but no slope selection. In particular, we show that the temperature dependence of the selected slope is solely determined by the Ehrlich-Schwoebel barrier which opens a new possibility in order to measure this fundamental barrier in experiments. Received 11 May 1999 and Received in final form 6 November 1999     

Growth of entropy stabilized quasicrystals

A simplified version of the model by Elser and Joseph for the process of growth of an entropically stabilized, two-dimensional quasicrystal with no dynamics in the bulk, is proposed. The phason fluctuations are modeled by a scalar field on a periodic lattice. The choice of the master equation for the growth is restricted by the requirement that its detailed balance solution describes the equilibrium fluctuations of the field with a quadratic Hamiltonian. The model is parametrized by the chemical potential bias and the microscopic surface tension coefficient . The phase diagram of the system on the plane (, ) shows several distinct regimes of growth, separated by relatively narrow transition zones. Within the regions corresponding to these regimes, the phason fluctuations do not depend on and . Analytic expressions for the spectra of phason fluctuations are obtained and confirmed by numerical simulation. Received 30 June 2000     

Homogeneous nucleation and growth in iron-platinum vapour investigated by molecular dynamics simulation

Homogeneous nucleation and growth from binary metal vapour is investigated by molecular dynamics simulation. It is focused here mainly on the iron-platinum system with a mole fraction of 0.5. The simulations are started in the highly supersaturated vapour phase. Argon is added as carrier gas removing the heat of condensation from the forming clusters. The embedded atom method is employed for modelling of the force field of iron and platinum. The simulation runs are evaluated with respect to the nucleation rate, monomer temperature, monomer amount, and with respect to the size of the largest cluster in the system including possible pure metal clusters. It turns out that depending on the composition of the complete system pure platinum clusters with sizes up to 10 to 15 atoms are formed in addition to binary clusters. Due to the high temperature of these clusters iron atoms less likely condense at the beginning of the particle formation simulation. This leads to temporary difference in the temperatures of the platinum and the iron subsystems, which eventually approach each other when only binary clusters are present. In summary, the results obtained from the cluster statistics show that pure platinum nucleation and growth can take place to some extent within the binary system.     

Growth kinetics of self-assembled monolayers of thiophene and terthiophene on Au(111): An infrared spectroscopic study

The growth kinetics of self-assembled monolayers (SAMs) of thiophene compounds on Au(111) surfaces was revealed by Fourier-transform infrared reflection absorption spectroscopy (FT-IR-RAS). Thiophene and terthiophene form well-ordered SAMs on Au(111) surfaces by immersing gold substrates into their ethanol solutions for ca. 15 h. Gibbs free energies for the adsorption processes of thiophene and terthiophene were found to be identical. However, the growth and molecular orientation of SAMs are different between two thiophene compounds. Terthiophene in SAMs orients parallel to the surface. The SAM growth of terthiophene obeys a time-dependent Langmuir scheme. On the other hand, the thiophene SAM undergoes a two-step growth process with unique molecular orientations. In the primary phase, thiophene assumes a parallel orientation on the Au(111) surface. In the second phase, thiophene is oriented close to the normal of the surface. The different growth process between thiophene and terthiophene is attributable to the topology of sulfur positions in the molecules. Received 23 May 2001 and Received in final form 11 February 2002     

Competition between kinetic and surface tension anisotropy in dendritic growth

The combined effect of an anisotropic surface tension and interface kinetics in dendritic crystal growth is studied numerically by a fully dynamical front-tracking method in two dimensions. It is shown how kinetic effects can be incorporated into the algorithm without causing numerical instabilities. The results are compared to the theory of E.A. Brener and V.I. Mel'nikov (Adv. Phys. 40, 53 (1991)). A particularly interesting case arises when the directions of minimum surface tension and minimum kinetic effect are different. In this case, when the deviation from local equilibrium is increased, the predicted transition from dendrites growing into the direction of the minimum surface stiffness to the direction of minimum kinetic effect is confirmed. Dendrites near this transition show strong oscillations and correlated side-branching. The transition where the oscillating dendrites change direction shows hysteresis. Received 30 September 1999 and Received in final form 23 February 2000     

Noise-assisted mound coarsening in epitaxial growth

Two types of mechanisms are proposed for mound coarsening during unstable epitaxial growth: stochastic, due to deposition noise, and deterministic, due to mass currents driven by surface energy differences. Both yield the relation H=(RWL)² between the typical mound height W, mound size L, and the film thickness H. An analysis of simulations and experimental data shows that the parameter R saturates to a value which discriminates sharply between stochastic () and deterministic () coarsening. We derive a scaling relation between the coarsening exponent 1/z and the mound-height exponent which, for a saturated mound slope, yields . Received: 11 November 1997 / Revised in final form: 28 November 1997 / Accepted: 28 November 1997     

Phase-field study of free growth in a channel: from thermal to chemical solidification

The thermal and the chemical phase-field models for free growth in a two-dimensional channel are both studied in their one-sided version for which diffusion only occurs in the liquid. We compare the steady state fingers obtained in our phase-field simulations with the results of boundary integral techniques available in the literature. The excellent agreement found between both methods provides a valuable benchmark of the one-sided thin-interface phase model which makes use of an antitrapping current. Coexistence of several steady states predicted by the Green’s function calculations is also recovered. The dynamical stability of two competing modes (symmetric and asymmetric finger) is studied and the extension of their respective basins of attraction is evaluated. General implications of our results for a large class of isotropic systems are discussed.     

Anchoring transitions with polar and non-polar nematic liquid crystals on incompletely oxidized silane substrates

The active oxygen gas arising from a plasma reactor is used to realize progressive chemical modifications onto silane coatings that could be particularly interesting as alignment layers for liquid crystal display applications. Depending on the oxygen density grafted onto the substrate, these alignment layers provide different zenithal anchoring angles, or pretilt angles, with anchoring transitions, for polar and non-polar nematic liquid crystals as 5CB and MBBA, respectively. The anchoring transitions are found to be smoother with the polar nematics. Such a behavior is discussed in terms of the differential wetting model by adding a cosine term to the interaction energy between the nematic and the substrate. A local justification is proposed for this symmetry breaking term. Received: 18 May 1998     

Equilibrium shape and size of supported heteroepitaxial nanoislands

We study the equilibrium shape, shape transitions and optimal size of strained heteroepitaxial nanoislands with a two-dimensional atomistic model using simply adjustable interatomic pair potentials. We map out the global phase diagram as a function of substrate-adsorbate misfit and interaction. This phase diagram reveals all the phases corresponding to different well-known growth modes. In particular, for large enough misfits and attractive substrate there is a Stranski-Krastanow regime, where nano-sized islands grow on top of wetting films. We analyze the various terms contributing to the total island energy in detail, and show how the competition between them leads to the optimal shape and size of the islands. Finally, we also develop an analytic interpolation formula for the various contributions to the total energy of strained nanoislands.     

Improvement of absolute band gaps in 2D photonic crystals by anisotropy in dielectricity

Two-dimensional (2D) photonic band gaps (PBG) structure fabricated from anisotropic dielectric is studied by solving Maxwell's equations with use of plane-wave expansion method. Numerical simulations show that absolute photonic band gaps can be substantially improved in two dimensional square and triangular lattices of cylinders by introducing anisotropy in material dielectricity. Owing to different refractive indices for electromagnetic waves with E- and H-polarization, the quasi-independent adjustment of band gaps for the E- and H-polarization modes can be implemented by uniaxial crystals with their extraordinary axis parallel to the cylinders. Large absolute band gaps can be created for uniaxial cylinders in air with a positive anisotropy. In the case of air holes in background uniaxial dielectric with even a weak negative anisotropy, the absolute band gap can be increased 2-3 times. Large absolute band gap can also be obtained in other complex configurations of uniaxial and biaxial materials and this enables a full exploitation of potential utilization for anisotropic materials available in nature. Such a mechanism of band gap adjustment should open up a new scope for designing band gaps in 2D PBG structures. Received 26 January 1999     

Branched crystal morphology of linear polyethylene crystallized in a two-dimensional diffusion-controlled growth field

The branched crystal morphology of linear polyethylene formed at various temperatures from thin films has been studied by atomic-force microscopy (AFM), transmission electron microscopy (TEM), electron diffraction (ED) pattern and polymer decoration technique. Two types of branched patterns, i.e. dendrite and seaweed patterns, have been visualized. The fractal dimension d _f = 1.65 of both dendrite and some of seaweed patterns was obtained by using the box-counting method, although most of the seaweed patterns are compact. Selected-area ED patterns indicate that the fold stems tilt about 34.5^° around the b-axis and polymer decoration patterns show that the chain folding direction and regularity in two (200) regions are quite different from each other. Because of chain tilting, branched crystals show three striking features: 1) the lamella-like branches show two (200) regions with different thickness; 2) the crystals usually bend towards the thin region; 3) the thick region grows faster by developing branches, thus branches usually occur outside the thick region. The branched patterns show a characteristic width w, which gives a linear relationship with the crystallization temperature on a semilogarithmic plot. Received 15 March 2002 and Received in final form 29 April 2002     

A discrete nonlinear mass transfer equation with applications in solid-state sintering of ceramic materials

The evolution of grain structures in materials is a complex and multiscale process that determines the material's final properties [1]. Understanding the dynamics of grain growth is a key factor for controlling this process. We propose a phenomenological approach, based on a nonlinear, discrete mass transfer equation for the evolution of an arbitrary initial grain size distribution. Transition rates for mass transfer across grains are assumed to follow the Arrhenius law, but the activation energy depends on the degree of amorphization of each grain. We argue that the magnitude of the activation energy controls the final (sintered) grain size distribution, and we verify this prediction by numerical simulation of mass transfer in a one-dimensional grain aggregate.     

Phase transitions in simple models of rod-like and disc-like micelles

The interplay of interactions between micelles, and the aggregation of these micelles into large, highly anisotropic micelles, is studied. Simple, hard-body, models of rod-like and disc-like micelles are used, which allows us to apply fundamental measure theory to determine the free energy. Then we study the phase transition from the fluid phase to a liquid crystalline phase. We find that aggregation induces a strongly first order transition from a fluid phase of small micelles to a close packed liquid crystalline phase of infinitely large micelles. Received: 3 December 1997     

Elastic theory of defects in toroidal crystals

We report a comprehensive analysis of the ground-state properties of axisymmetric toroidal crystals based on the elastic theory of defects on curved substrates. The ground state is analyzed as a function of the aspect ratio of the torus, which provides a non-local measure of the underlying Gaussian curvature, and the ratio of the defect core energy to the Young modulus. Several structural features are discussed, including a spectacular example of curvature-driven amorphization in the limit of the aspect ratio approaching one. The outcome of the elastic theory is then compared with the results of a numerical study of a system of point-like particles constrained on the surface of a torus and interacting via a short-range potential. Electronic supplementary material  Supplementary material in the form of a pdf file available from the journal web page at and are accessible for authorised users.