共查询到20条相似文献,搜索用时 21 毫秒
1.
A phase-field model that takes into account the bending energy of fluid vesicles is presented. The Canham-Helfrich model is
derived in the sharp-interface limit. A dynamic equation for the phase-field has been solved numerically to find stationary
shapes of vesicles with different topologies and the dynamic evolution towards them. The results are in agreement with those
found by minimization of the Canham-Helfrich free energy. This fact shows that our phase-field model could be applied to more
complex problems of instabilities. 相似文献
2.
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. 相似文献
3.
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 相似文献
4.
Faceting transitions in crystal growth and heteroepitaxial growth in the anisotropic phase-field crystal model
下载免费PDF全文
![点击此处可从《中国物理 B》网站下载免费的PDF全文](/ch/ext_images/free.gif)
We modify the anisotropic phase-field crystal model(APFC),and present a semi-implicit spectral method to numerically solve the dynamic equation of the APFC model.The process results in the acceleration of computations by orders of magnitude relative to the conventional explicit finite-difference scheme,thereby,allowing us to work on a large system and for a long time.The faceting transitions introduced by the increasing anisotropy in crystal growth are then discussed.In particular,we investigate the morphological evolution in heteroepitaxial growth of our model.A new formation mechanism of misfit dislocations caused by vacancy trapping is found.The regular array of misfit dislocations produces a small-angle grain boundary under the right conditions,and it could significantly change the growth orientation of epitaxial layers. 相似文献
5.
Massa MV Dalnoki-Veress K Forrest JA 《The European physical journal. E, Soft matter》2003,11(2):191-198
We present a detailed study of the kinetics of
crystallization for thin films of poly(ethylene oxide) (PEO).
Measurements of the growth rate have been carried out using
optical-microscopy techniques on films of monodisperse PEO.
Films with thicknesses from 13 nm to ~2 m were crystallized
isothermally at temperatures ~20°C below the melting point. A
remarkable non-monotonic
slowing-down of the crystal growth is observed for films with
thickness less than ~400 nm. The changes in the growth rate from
bulk-like values is significant and corresponds to a factor of
40 decrease for the thinnest films studied. The morphologies of
isothermally crystallized samples are studied using atomic-force
microscopy. We find that a morphology, similar to
diffusion-controlled growth (dendritic growth and densely
branched growth), is observed for films with
h < 150 nm. In addition,
changes in the morphology occur for thicknesses consistent with
changes in the growth rate as a function of film thickness. 相似文献
6.
Summary A theoretical analysis has been carried out to investigate the kinetics involved in the CVD growth of CuInS2. A stagnant-layer model is assumed for the numerical, simulation. Computational results for the growth rate as a function
of the substrate temperature, mean, gas velocity and partial pressures in the reaction tube are obtained. This analysis indicates
that the substrate temperature plays a dominant role in the growth rate, which is consistent with our experimental data.
Paper presented at the ?V International Conference on Ternary and Multinary Compounds?, held in Cagliari, September 14–16,
1982. 相似文献
7.
S. Schinzer S. Köhler G. Reents 《The European Physical Journal B - Condensed Matter and Complex Systems》2000,15(1):161-168
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 相似文献
8.
J. Kundin C. Yürüdü J. Ulrich H. Emmerich 《The European Physical Journal B - Condensed Matter and Complex Systems》2009,70(3):403-412
In this paper work we present a phase-field/Monte-Carlo hybrid algorithm for the simulation of solutal growth of organic crystals.
The algorithm is subsequently used for an investigation of diffusion effects on the growth mechanisms. This method combines
a two-scale phase-field model of the liquid phase epitaxial growth and a Monte-Carlo algorithm of the 2D nucleation and thus
is faster than previous purely Monte Carlo simulations of crystal growth. The inclusion of supersaturation and diffusion in
the method allows the study of crystal growth under various growth conditions. Parameters used in the hybrid algorithm are
bound to the energetic parameters of crystal faces, which can be estimated from a detailed study of the actual crystal structure
based on a connected nets analysis, which allows the prediction of the shape and morphology of real crystals. The study of
the diffusion effect is carried out based on an example of a hydroquinone crystal, which grows from the water solution at
various supersaturations. The dependencies of the growth rate and the nucleation rate on the supersaturation indicate the
change of the growth mechanism from spiral growth to 2D nucleation. The difference in the growth rate for various faces is
in agreement with the crystal morphologies derived from the attachment energy method and observed experimentally. The main
result of the simulation is the evaluation of engineering limits for choosing appropriate external process conditions. 相似文献
9.
Jolanta Prywer 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,25(1):61-68
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 相似文献
10.
11.
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 相似文献
12.
13.
M. Dubé C. Daneault V. Vuorinen M. Alava M. Rost 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,56(1):15-26
We investigate the structure and dynamics of the interface between
two immiscible liquids in a three-dimensional disordered porous
medium. We apply a phase-field model that includes explicitly
disorder and discuss both spontaneous and forced imbibition.
The structure of the interface is dominated by a length scale
ξ× which arises from liquid conservation. We further show
that disorder in the capillary and permeability act on different
length scales and give rise to different scalings and
structures of the interface properties. We conclude with a
range of applications. 相似文献
14.
Zhi-Yuan Li Ben-Yuan Gu Guo-Zhen Yang 《The European Physical Journal B - Condensed Matter and Complex Systems》1999,11(1):65-73
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 相似文献
15.
P. Nozières F. Pistolesi S. Balibar 《The European Physical Journal B - Condensed Matter and Complex Systems》2001,24(3):387-394
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 相似文献
16.
Spatschek R Hartmann M Brener E Müller-Krumbhaar H Kassner K 《Physical review letters》2006,96(1):015502
We present a continuum theory which predicts the steady state propagation of cracks. The theory overcomes the usual problem of a finite time cusp singularity of the Grinfeld instability by the inclusion of elastodynamic effects which restore selection of the steady state tip radius and velocity. We developed a phase-field model for elastically induced phase transitions; in the limit of small or vanishing elastic coefficients in the new phase, fracture can be studied. The simulations confirm analytical predictions for fast crack propagation. 相似文献
17.
18.
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 相似文献
19.
J. Kundin H. Emmerich 《The European Physical Journal B - Condensed Matter and Complex Systems》2008,63(1):25-36
A hybrid algorithm that combines a phase-field model and a lattice gas model evolving according to a kinetic Monte-Carlo (KMC)
simulation scheme is used to investigate the dynamics of vicinal surface growth during vapor phase epitaxy. The algorithm
is computationally far more efficient than pure KMC schemes, and this gain in efficiency does not correspond to a loss in
information on the kinetics of individual atoms. We present numerical studies on the temperature dependence of macroscopic
properties of the growing surface, evaluating the relevant stochastic processes (attachment, detachment, diffusion and island
dynamics) as a function of their rates. We show that the temperature at which step flow is replaced by island nucleation depends
on incoming flux, diffusion parameters and interstep distance. Moreover, we validate these finding by comparison to experiments
and by analytical investigations. 相似文献
20.
Melting points in mixtures of a crystallizable polymer
with a low-molar-mass diluent depend on both, the diluent
fraction and the crystal thickness. A differentiation of the two
factors can be achieved by temperature-dependent SAXS
experiments. A corresponding study, complemented by DSC,
dilatometry, microscopy and AFM-imaging, was carried out for
mixtures of a poly(ethylene-co-octene) with
n-C16H34,
c-C16H32
and methyl-anthracene, respectively. All diluents lead for a
constant crystal thickness to melting point depressions in
agreement with Raoult's law. On the other hand, the effect of
the diluents on the thickness of the crystals formed at a fixed
crystallization temperature varies. While in the presence of the
two alkanes thicker crystals form, no effect arises for the
methyl-anthracene—as was previously found for the
octene-co-units. We consider these observations as a further
support for our view that polymer crystallization follows a
multi-stage route which includes a passage through an
intermediate mesomorphic phase. Under such conditions crystal
thicknesses would only be affected if the diluent is still
present in the mesomorphic phase and stay invariant if the
diluent molecules are already rejected when this intermediate
phase forms. 相似文献