Special interaction between quasiperiodic grain boundaries and lattice dislocations in crystalline solids

A theoretical model is suggested which describes phason imperfections (specific excitations) in a quasiperiodic grain boundary in a polycrystalline solid as dilatation flexes. In the framework of the model, an elastic stress field of the quasiperiodic grain boundary is calculated as a stress field created by an ensemble of dilatation flexes (phason imperfections) located in the boundary. It is shown that there is a special elastic interaction between crystal lattice defects and quasiperiodic grain boundaries comprising phason imperfections. The strengthening effect in plastically deformed polycrystalline solids is quantitatively described which is related to the special elastic interaction between lattice dislocations and quasiperiodic grain boundaries. Received: 29 October 1996 / Revised: 22 August 1997 / Accepted: 13 November 1997     

Scaling in colloidal crystallization

Summary The process of colloidal crystallization has already been separately investigated by light scattering mearurements of the crystalline order (Bragg peaks) and of long-ranged density fluctuations (small-angle scattering). We present the firstsimultaneous small- and large-angle light scattering experiment. Our measurements have been performed on hard-sphere colloids of different particle densities. We show results for the temporal evolution of crystallization and find two distinct regimes: homogeneous nucleation and diffusion- or reaction-limited growth at early times, followed by ripening of the Lifshitz-Slyozov or Lifshitz-Allen-Cahn type. To our preliminary experience, we can already state that the results are always consistent in both partial experiments. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994. With deep regret we have to announce that Prof. Klaus Sch?tzel, who inspired and guided the work presented here, has died in October 1994.     

Grain growth and phason-strain field in quasicrystalline Al-Li-Cu

We report on grain growth and related structure change in single phased Al-Li-Cu quasicrystals. The icosahedral phase grains have been investigated using scanning ion microscopy and transmission electron microscopy. Regular boundaries between large grains have been observed both before and after high temperature annealing. The electron diffraction study shows that the grain growth is accompanied by a reduction of the phason-strains. The orientation relation between grains sets the 2-fold icosahedral axes parallel, and the coincidence of the planes depends on the phason strain-field. The effect of phason-strain field on these boundaries is discussed. It is proposed that the phason strain elimination can play a role in the grain growth. Received 1 February 1999 and Received in final form 12 May 1999     

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     

On the problem of the relation between phason elasticity and phason dynamics in quasicrystals

It has recently been claimed that the dynamics of long-wavelength phason fluctuations has been observed in i-AlPdMn quasicrystals [S. Francoual et al. Phys. Rev. Lett. 91, 225501 (2003); A. Létoublon et al. 54, 753 (2001)]. We will show that the data reported call for a more detailed development of the elasticity theory of Jarić and Nelsson [M.V. Jarić and D.R. Nelsson, Phys. Rev. B 37, 4458 (1988)] in order to determine the nature of small phonon-like atomic displacements with a symmetry that follows the phason elastic constants. We also show that a simple model with a single diffusing tile is sufficient to produce a signal that (1) is situated at a “satellite position” at a distance q from each Bragg peak; that (2) has an intensity that scales with the intensity of the corresponding Bragg peak; (3) falls off as 1/q²; and (4) has a time decay constant that is proportional to 1/Dq². It is thus superfluous to call for a picture of “phason waves” in order to explain such data, especially as such “waves” violate many physical principles.     

Random cluster models for icosahedral phase alloys

We present results on computer generated random cluster models for icosahedral phase alloys. By the application of physically motivated constraints on the local atomic cluster configurations, the model achieves long range translational order comparable to, or greater than, that found in simple icosahedral alloys such asi-AlMnSi andi-AlLiCu. The parallel and perpendicular space structures are explored in some detail including a comparison with experimental powder diffraction patterns and an examination of the phason fluctuations. The latter are shown to decrease markedly with increased constraint on the local environment, but the remaining phason strain would seem finally not to vanish with increasing model size. Our model is compared with other cluster models for quasicrystalline materials and is shown to possess a density and connectivity very close to those of Elser's (best) model and those predicted by Henley for a canonical tiling. The relation of this model to recently discovered icosahedral phase alloys with resolution limited diffraction peak widths, which are essentially free of phason strain, is also discussed.     

Magnetic field correlations in random flow with strong steady shear

We analyze the magnetic kinematic dynamo in a conducting fluid where a stationary shear flow is accompanied by relatively weak random velocity fluctuations. The diffusionless and diffusion regimes are described. The growth rates of the magnetic field moments are related to the statistical characteristics of the flow describing divergence of the Lagrangian trajectories. The magnetic field correlation functions are examined, and their growth rates and scaling behavior are established. General assertions are illustrated by the explicit solution of a model where the velocity field is short-correlated in time.     

A theoretical analysis of epitaxial growth of CuInS2 by chemical vapour deposition

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.     

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     

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.     

Isotropic and anisotropic physical properties of quasicrystals

Since quasicrystals have positional and orientational long-range order, they are essentially anisotropic. However, the researches show that some physical properties of quasicrystals are isotropic. On the other hand, quasicrystals have additional phason degrees of freedom which can influence on their physical behaviours. To reveal the quasicrystal anisotropy, we investigate the quasicrystal elasticity and other physical properties, such as thermal expansion, piezoelectric and piezoresistance, for which one must consider the contributions of the phason field. The results indicate that: for the elastic properties, within linear phonon domain all quasicrystals are isotropic, and within nonlinear phonon domain the planar quasicrystals are still isotropic but the icosahedral quasicrystals are anisotropic. Moreover, the nonlinear elastic properties due to the coupling between phonons and phasons may reveal the anisotropic structure of QCs. For the other physical properties all quasicrystals behave like isotropic media except for piezoresistance properties of icosahedral quasicrystals due to the phason field.     

Numerical entropy and phason elastic constants of plane random tilings with any 2D-fold symmetry

We perform Transition matrix Monte Carlo simulations to evaluate the entropy of rhombus tilings with fixed polygonal boundaries and 2D-fold rotational symmetry. We estimate the large-size limit of this entropy for D=4 to 10. We confirm analytic predictions of [N. Destainville et al., J. Stat. Phys. 120, 799 (2005) and M. Widom et al., J. Stat. Phys. 120, 837 (2005)], in particular that the large size and large D limits commute, and that entropy becomes insensible to size, phason strain and boundary conditions at large D. We are able to infer finite D and finite size scalings of entropy. We also show that phason elastic constants can be estimated for any D by measuring the relevant perpendicular space fluctuations.     

Intermediate stages of a transformation between a quasicrystal and an approximant including nanodomain structures in the Al-Ni-Co system

Transition states between decagonal quasicrystal and periodic approximants are studied in the Al-Ni-Co system at a measured composition of Al_71.3Ni_11.3Co _17.4 by high-resolution transmission electron microscopy and electron diffraction. The nanodomain structures appearing after annealing at 1270 K show periodic fluctuations coherently embedded in domains with the coarse order of a one-dimensional quasicrystal. Further annealing at lower temperatures changes the features of nanodomain structures and results in an increase in more periodic structures. These can be strongly disordered and full of defects but tiling analysis and electron diffraction patterns show that they correspond to locked phason strain values of two closely related periodic approximants. We conclude that the periodic approximants do not result from a continuous increase in phason strain but from the growth of seeds with a locked phason strain.     

Dynamics of phason fluctuations in the i-AlPdMn quasicrystal

We report on the study of the dynamics of long wavelength phason fluctuations in the i-AlPdMn icosahedral phase using coherent x-ray scattering. When measured with a coherent x-ray beam, the diffuse intensity due to phasons presents strong fluctuations or speckles pattern. From room temperature to 500 degrees C the speckle pattern is time independent. At 650 degrees C the time correlation of the speckle pattern exhibits an exponential time decay, from which a characteristic time tau is extracted. We find that tau is proportional to the square of the phason wavelength, which demonstrates that phasons are collective diffusive modes in quasicrystals, in agreement with theoretical predictions.     

Polymer-mediated interactions of fluid membranes in a lyotropic lamellar phase: a small angle X-ray and neutron scattering study

Small angle X-ray and neutron scattering data on an effective three-component lamellar phase composed of water, a non adsorbing water-soluble polymer (polyvynilpyrolidone), fluid membranes, made from a mixture of a cationic surfactant (cetylpiridiumchloride) and a cosurfactant (hexanol), are presented for various membrane as well as polymer concentrations. The data are fitted with a recently proposed model which takes into account the geometry and the fluctuations of these periodic structures. This allows a quantitative study of the polymer contribution to the smectic compression modulus of the lamellar phase. Four different regimes of polymer confinement are expected. The associated variations in are compared to a recent theoretical model, which predicts the polymer-mediated contribution to the smectic compression modulus. Received 20 January 1998     

Phase diagram of randomly polymerized membrane

Using a replica formalism, a generalization of a recent mean field model corresponding to the observed wrinkling transition in randomly polymerized membranes is presented. In this model we study the effects of global fluctuations of the surface normals to the flat membrane, which can be introduced by a random local field. In absence of these global fluctuations, we show that, the model exhibits both continuous and discontinuous transitions between flat and wrinkled phases, contrary to what has been predicted by Bensimon et al. and Attal et al. Phase diagrams both in replica symmetry and in breaking of replica symmetry in sense of Almeida and Thouless are given. We have also investigated the effects of global fluctuations on the replica symmetry phase diagram. We show that, the wrinkled phase is favored and the flat phase is unstable. For large global fluctuations, the transition between wrinkled and flat phases becomes first order. Received: 3 December 1997 / Revised: 31 March 1998 / Accepted: 3 August 1998     

Quantum correlations close to a square pattern forming instability

We analyze the quantum fluctuations of the degenerate optical parametric oscillator close to an instability for the formation of a square pattern. While strong correlations between the fluctuations of the signal modes emitted at the critical wave number and with opposite wave vector are present both below and above threshold, no features signaling the square character of the pattern forming above threshold have been identified below threshold in the spatio-temporal second-order coherence. We also explore in which regimes a reduced few mode model gives meaningful results. Received 17 September 2002 / Received in final form 11 November 2002 Published online 26 February 2003     

Elastohydrodynamic problems in quasicrystal elasticity theory and wave propagation

Elastohydrodynamic problems of decagonal quasicrystals are analysed where the phonon field obeys wave equation and the phason field obeys diffusive wave equation. Basic equations are solved in the quasiperiodic plane and periodic plane, respectively. Final governing equations of dynamic behaviours of decagonal quasicrystals are obtained. A general solution is derived in terms of introduced three auxiliary functions, where two individually satisfy a fourth-order partial differential equation and one satisfies a second-order hyperbolic diffusion equation. Using the derived governing equations, elastic waves propagating in the quasiperiodic plane and a plane containing the period axis are analysed. Secular equations are obtained. It is found that differing from conventional crystals, at least four branches of elastic waves exist when the phonon–phason coupling is present. Moreover, acoustic waves have attenuation during wave propagation. Phason fluctuations exhibit exponential decaying behaviour due to kinematic viscosity and damping. The phase speeds are isotropic in the quasiperiodic plane and anisotropic in a plane with the periodic axis. The section of the slowness surfaces is plotted.     

Stability of Crystal Growth Face and Dissolution Face in Crystallization from Solution under Microgravity

The stability of the shapes of crystal growth face and dissolution face in a two-dimensional mathematical model of crystal growth from solution under microgravity is studied.It is proved that the stable shapes of crystal growth face and dissolution face do exist,which are suitably shaped curves with their upper parts inclined backward properly.The stable shapes of crystal growth faces and dissolution faces are calculated for various values of parameters,Ra,Pr and Sc.It is shown that the stronger the convection relative to the diffusion in solution is,the more backward the upper parts of the stable crystal growth face and dissolution face are inclined.The orientation and the shape of dissolution face hardly affect the stable shape of crystal growth face and vice versa.