Macroscopic theory of dielectric solids. I. The model of molecular optics

1977 ◽  
Vol 55 (24) ◽  
pp. 2169-2179 ◽  
Author(s):  
J. E. Sipe
Keyword(s):  
Constitutive Relations ◽  
Pair Correlation ◽  
Finite Size ◽  
Amorphous Solid ◽  
Amorphous Solids ◽  
Uniform Density ◽  
Macroscopic Theory ◽  
Standard Result ◽  
Dielectric Solids ◽  
Spatially Varying

An improved derivation is given of the macroscopic electrodynamic equations for dielectric solids of finite size composed of molecules with a given polarizability, α = α(ω), interacting only via the retarded dipole–dipole coupling. We present a derivation of the constitutive relations for both crystalline and amorphous solids, which is not based on an expansion in powers of α, and in which the radiative reaction forces are carefully taken into account. The spatially varying density and pair correlation function of an amorphous solid, defined with the help of spatial averaging procedures, are shown to satisfy an integral 'counting' relation, which puts a condition on any physically consistent model of an amorphous solid. In the absence of dissipative damping, a medium is shown to be characterized by a real, in general spatially varying, dielectric constant. For solids of uniform density, crystalline or amorphous, we obtain the standard result that inside such a medium light propagates without scattering. For amorphous solids with varying density, the theory forms the basis of the macroscopic theory of light scattering from density in-homogeneities.

Development of the Grain Size Distribution During the Crystallization of an Amorphous Solid

2011 ◽  
Vol 1308 ◽  
Author(s):  
Andreas Bill ◽  
Ralf B. Bergmann
Keyword(s):  
Grain Size ◽  
Size Distribution ◽  
Grain Size Distribution ◽  
Growth Rates ◽  
Amorphous Solid ◽  
Amorphous Solids ◽  
Nucleation And Growth ◽  
Analytic Description ◽  
Silicon Thin Films ◽  
Random Nucleation

ABSTRACTWe present an overview of the theory developed over the last few years to describe the crystallization of amorphous solids. The microstructure of the crystallizing solid is described in terms of the grain size distribution (GSD). We propose a partial differential equation that captures the physics of crystallization in random nucleation and growth processes. The analytic description is derived for isotropic and anisotropic growth rates and allows for the analysis of different stages of crystallization, from early to full crystallization. We show how the timedependence of effective nucleation and growth rates affect the final distribution. In particular, we demonstrate that for cases described by the Kolmogorov-Avrami-Mehl-Johnson (KAMJ) model applicable to a large class of crystallization processes a lognormal type distribution is obtained at full crystallization. The application of the theory to the crystallization of silicon thin films is discussed.

Dislocation Core Spreading at Interfaces between Crystalline and Amorphous Solids

2001 ◽  
Vol 673 ◽  
Author(s):  
Huajian Gao ◽  
Lin Zhang ◽  
Shefford P. Baker
Keyword(s):  
Dislocation Core ◽  
Amorphous Solid ◽  
Amorphous Solids ◽  
Equilibrium Structure ◽  
Fundamental Question ◽  
Closed Form Solutions ◽  
Transmission Electron ◽  
Dependent Behavior ◽  
Amorphous Substrate ◽  
Core Width

ABSTRACTA fundamental question addressed here is concerned with the equilibrium structure of a dislocation core at an interface between a crystalline and an amorphous solid. This is motivated by experimental observations that the contrast of dislocations at an interface between a crystalline film and an amorphous substrate disappears under transmission electron microscopy. We have developed a mathematical moedl to describe the time-dependent behavior of dislocation core spreading as a function of the adhesive strength of the interface. The equilibrium core width and the rate of core spreading are determined in closed form solutions.

scholarly journals The collective dynamics of self-propelled particles

2008 ◽  
Vol 595 ◽  
pp. 239-264 ◽  
Author(s):  
VISHWAJEET MEHANDIA ◽  
PRABHU R. NOTT
Keyword(s):  
Particle Concentration ◽  
Near Field ◽  
Continuous Process ◽  
Pair Correlation ◽  
Fluid Motion ◽  
Finite Size ◽  
Two Dimensions ◽  
Creeping Flow ◽  
Hydrodynamic Interactions ◽  
Dynamic Simulations

We propose a method for the dynamic simulation of a collection of self-propelled particles in a viscous Newtonian fluid. We restrict attention to particles whose size and velocity are small enough that the fluid motion is in the creeping flow regime. We propose a simple model for a self-propelled particle, and extended the Stokesian Dynamics method to conduct dynamic simulations of a collection of such particles. In our description, each particle is treated as a sphere with an orientation vector p, whose locomotion is driven by the action of a force dipole Sp of constant magnitude S0 at a point slightly displaced from its centre. To simplify the calculation, we place the dipole at the centre of the particle, and introduce a virtual propulsion force Fp to effect propulsion. The magnitude F0 of this force is proportional to S0. The directions of Sp and Fp are determined by p. In isolation, a self-propelled particle moves at a constant velocity u0p, with the speed u0 determined by S0. When it coexists with many such particles, its hydrodynamic interaction with the other particles alters its velocity and, more importantly, its orientation. As a result, the motion of the particle is chaotic. Our simulations are not restricted to low particle concentration, as we implement the full hydrodynamic interactions between the particles, but we restrict the motion of particles to two dimensions to reduce computation. We have studied the statistical properties of a suspension of self-propelled particles for a range of the particle concentration, quantified by the area fraction φa. We find several interesting features in the microstructure and statistics. We find that particles tend to swim in clusters wherein they are in close proximity. Consequently, incorporating the finite size of the particles and the near-field hydrodynamic interactions is of the essence. There is a continuous process of breakage and formation of the clusters. We find that the distributions of particle velocity at low and high φa are qualitatively different; it is close to the normal distribution at high φa, in agreement with experimental measurements. The motion of the particles is diffusive at long time, and the self-diffusivity decreases with increasing φa. The pair correlation function shows a large anisotropic build-up near contact, which decays rapidly with separation. There is also an anisotropic orientation correlation near contact, which decays more slowly with separation. Movies are available with the online version of the paper.

scholarly journals Commentary: Considerations in the Measurement of Glass Transition Temperatures of Pharmaceutical Amorphous Solids

2019 ◽  
Vol 21 (1) ◽  
Author(s):  
Ann Newman ◽  
George Zografi
Keyword(s):  
Glass Transition ◽  
Amorphous Solid ◽  
Amorphous Solids ◽  
Scanning Calorimetry ◽  
Modulated Differential Scanning Calorimetry ◽  
Preparation Methods ◽  
Glass Transition Temperatures ◽  
Pharmaceutical Applications ◽  
Sample Preparation Methods

AbstractAn increased interest in using amorphous solid forms in pharmaceutical applications to increase solubility, dissolution, and bioavailability has generated a need for better characterization of key properties, such as the glass transition (Tg) temperature. Although many laboratories measure and report this value, the details around these measurements are often vague or misunderstood. In this article, we attempt to highlight and compare various aspects of the two most common methods used to measure pharmaceutical Tg values, conventional and modulated differential scanning calorimetry (DSC). Issues that directly impact the Tg, such as instrumental parameters, sample preparation methods, data analysis, and “wet” vs. “dry” measurements, are discussed.

scholarly journals Exploring the jamming transition over a wide range of critical densities

2017 ◽  
Vol 3 (4) ◽  
Author(s):  
Misaki Ozawa ◽  
Ludovic Berthier ◽  
Daniele Coslovich
Keyword(s):  
Large Scale ◽  
Volume Fraction ◽  
Pair Correlation ◽  
Orientational Order ◽  
Finite Size ◽  
Important Change ◽  
Three Dimensions ◽  
Length Scales ◽  
Jamming Transition ◽  
Wide Range

We numerically study the jamming transition of frictionless polydisperse spheres in three dimensions. We use an efficient thermalisation algorithm for the equilibrium hard sphere fluid and generate amorphous jammed packings over a range of critical jamming densities that is about three times broader than in previous studies. This allows us to reexamine a wide range of structural properties characterizing the jamming transition. Both isostaticity and the critical behavior of the pair correlation function hold over the entire range of jamming densities. At intermediate length scales, we find a weak, smooth increase of bond orientational order. By contrast, distorted icosahedral structures grow rapidly with increasing the volume fraction in both fluid and jammed states. Surprisingly, at large scale we observe that denser jammed states show stronger deviations from hyperuniformity, suggesting that the enhanced amorphous ordering inherited from the equilibrium fluid competes with, rather than enhances, hyperuniformity. Finally, finite size fluctuations of the critical jamming density are considerably suppressed in the denser jammed states, indicating an important change in the topography of the potential energy landscape. By considerably stretching the amplitude of the critical “J-line”, our work disentangles physical properties at the contact scale that are associated with jamming criticality, from those occurring at larger length scales, which have a different nature.

scholarly journals Tracer Diffusion Mechanism in Amorphous Solids

2011 ◽  
Vol 2011 ◽  
pp. 1-11
Author(s):  
P. K. Hung ◽  
P. H. Kien ◽  
H. V. Hue
Keyword(s):  
Thermal Annealing ◽  
Amorphous Alloys ◽  
Reasonable Agreement ◽  
Diffusion Mechanism ◽  
Amorphous Solid ◽  
Relaxation Effect ◽  
Amorphous Solids ◽  
Tracer Diffusion ◽  
Large Bubble ◽  
Spherical Void

Tracer diffusion in amorphous solid is studied by mean of nB-bubble statistic. The nB-bubble is defined as a group of atoms around a spherical void and large bubble that represents a structural defect which could be eliminated under thermal annealing. It was found that amorphous alloys such as CoxB100−x (x=90, 81.5 and 70) and Fe80P20 suffer from a large number of vacancy bubbles which function like diffusion vehicle. The concentration of vacancy bubble weakly depends on temperature, but essentially on the relaxation degree of considered sample. The diffusion coefficient estimated for proposed mechanism via vacancy bubbles is in a reasonable agreement with experiment for actual amorphous alloys. The relaxation effect for tracer diffusion in amorphous alloys is interpreted by the elimination of vacancy bubbles under thermal annealing.

Influence of Plural Scattering on the Image Quality of Thick Amorphous Objects in Transmission Electron Microscopy

1978 ◽  
Vol 36 (3) ◽  
pp. 230-243 ◽  
Author(s):  
H. Rose
Keyword(s):  
Electron Microscopy ◽  
Three Dimensional ◽  
Finite Size ◽  
Amorphous Solid ◽  
Solid Objects ◽  
Transmission Electron ◽  
Carbon Foils ◽  
Shortrange Order ◽  
Arbitrary Objects

The ultimate goal of electron microscopy is to elucidate the three-dimensional atomic structure of arbitrary objects. Objects are generally classified with respect to their inherent structural symmetries. The extreme cases of total order and total disorder are perfect crystals and entirely amorphous objects. In the former case the atoms are arranged in a periodic order; in the latter they are distributed at random. Neither perfect crystals nor completely amorphous solid objects exist in reality. The finite size of the atoms gives rise in every solid amorphous object to a certain shortrange order that rules out complete disorder. The amorphous carbon foils commonly used as supporting films are an example of this behavior.

Using delaunay triangularization to characterize non-affine displacement fields during athermal, quasistatic deformation of amorphous solids

Soft Matter ◽  
2021 ◽  
Vol 17 (38) ◽  
pp. 8612-8623
Author(s):  
Weiwei Jin ◽  
Amit Datye ◽  
Udo D. Schwarz ◽  
Mark D. Shattuck ◽  
Corey S. O'Hern
Keyword(s):  
Displacement Field ◽  
Simple Shear ◽  
Strain Field ◽  
Local Strain ◽  
Amorphous Solid ◽  
Amorphous Solids ◽  
Displacement Fields

Representation of the local strain field using Delaunay triangularization and the associated quadrupolar, non-affine displacement field for an amorphous solid undergoing athermal, quasistatic simple shear.

Scaling Properties of two-dimensional Star-branched Polymers grown by Diffusion

2006 ◽  
Vol 947 ◽  
Author(s):  
Guillermo Ramirez-Santiago ◽  
Carlos I. Mendoza
Keyword(s):  
Correlation Function ◽  
Fractal Dimension ◽  
Pair Correlation ◽  
Finite Size ◽  
Branched Polymers ◽  
Size Analysis ◽  
Radius Of Gyration ◽  
Two Dimensional ◽  
Scaling Properties ◽  
Pure Diffusion

ABSTRACTWe present an off-lattice numerical algorithm based upon pure diffusion to construct two-dimensional star-branched polymers with one, three, six and twelve branches. We built up structures with a total of up to 30,000 monomer units. For each one of them averages over one hundred independent configurations were taken. From a finite size analysis the scaling properties of the pair correlation function as well as the radius of gyration were obtained. Our findings indicate that the fractal dimension of the structures are: df=1.21 (0.03) for a linear polymer, df==1.21(0.02), for three branches, df==1.23 (0.02) for six branches and df=1.26 (0.03) for twelve branches.

Macroscopic theory of dielectric solids. II. The theory of Brillouin scattering from rare gas crystals

1978 ◽  
Vol 56 (2) ◽  
pp. 199-215 ◽  
Author(s):  
J. E. Sipe
Keyword(s):  
Local Field ◽  
Scattering Theory ◽  
Short Range ◽  
Brillouin Scattering ◽  
Microscopic Model ◽  
Rare Gas ◽  
Dielectric Tensor ◽  
Macroscopic Theory ◽  
Effective Electric Field ◽  
Dielectric Solids

We extend the macroscopic theory of dielectric solids to include the description of the Brillouin scattering of light by deriving expressions for the dielectric constant in the absence of strains, and for the Pockels elasto-optic coefficients, from a microscopic model appropriate for the rare gas crystals. The constituent atoms are regarded as polarizable particles coupled by the dipole–dipole interaction, which we treat by introducing the usual microscopic effective electric field, and by the short-range higher multipole and Vander Waals interactions, which are included in the microscopic model by associating with each atom an effective polarizability that depends on the distance between the atom and its nearest neighbors. We define the macroscopic fields by space averaging over volume elements of linear dimensions Δ satisfying a [Formula: see text], where a is the interatomic spacing and λ the wavelength in vacuo; using a new theorem relating the microscopic effective electric field and macroscopic electric and polarization fields, we are able to derive a constitutive relation, involving the strain tensor, from our microscopic model. While the largest contribution to the Pockels coefficients appearing in this relation is due to variations in the dielectric tensor that result from deviations of the macroscopic density from its value in the absence of strains, we find that two other contributions appear because strain fields affect the dielectric tensor by changing both the local field and the values of the effective polarizabilities. If the short-range interactions are neglected, our theory leads to the same ratios of Pockels coefficients obtained from the microscopic scattering theory of Werthamer (when an error in that theory is corrected), but the values of the Pockels coefficients we obtain contain a local field correction, which the microscopic scattering theory does not take into account. The contribution of the short-range interactions to the Pockels coefficients is estimated by obtaining values of the effective polarizabilities from calculations of the polarizabilities of pairs of rare-gas atoms; we find that the contribution is non-negligible and thus demonstrate that new information on these short-range interactions can be obtained from the results of Brillouin scattering experiments.

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