C. T. Chan

Material research with tight-binding molecular dynamics

Abstract Tight-binding molecular dynamics has recently emerged as a useful method for studying the structural, dynamical and electronic properties of realistic systems. In this article, we briefly review some recent achievements of the tight-binding molecular dynamics method and discuss some opportunities for future development.

A first-principles study of compression twins in h.c.p. zirconium

Abstract Using fully self-consistent ab-initio techniques, we have determined values for{1122} and {1011} compression twin-boundary energies in h.c.p. zirconium. Experimentally, c-axis compression produces {1122} twins at temperatures below about 800 K; it has been suggested that this is due to the low energy of this type of twin. We find that the {1011} boundary has a much lower energy than the {1122} boundary, by a factor of four. Thus the ease of {1122} formation at low temperatures must be due to the other causes, such as a low barrier to twin nucleation.

Photonic Band Gap Structures: Studies of the Transmission Coefficient

Recently, there has been growing interest in the development of Photonic Band Gap (PBG) materials [1–21]. These are periodic dielectric materials exhibiting frequency regions where electromagnetic (EM) waves cannot propagate. The reason for the interest on PBG materials arises from the possible applications of these materials in several scientific and technical areas such as filters, optical switches, cavities, design of more efficient lasers, etc. [1, 2]. Most of the research effort has been concentrated in the development of two-dimensional (2D) and three-dimensional (3D) PBG materials consisting of positive and frequency independent dielectrics [1–18] because, in this case, one can neglect the possible problems related to the absorption [15, 19]. However, there is more recent work on PBG materials constructed from metals [20, 21] which suggests that these metallic structures may be very useful in the low frequency regions. In these regions, the metals become almost perfect reflectors.

Photonic Band Gaps in Periodic Dielectric Structures: Relation to the Single-Scatterer Mie Resonances

A lot of theoretical and experimental work is being done in the area of propagation of classical waves in periodic and disordered structures. The interest in this subject has grown, particularly in the last several years, due to a variety of fundamental and practical reasons. The possibility of the observation[1] of Anderson localization of EM waves in disordered dielectric structures and frequency gaps in periodic structures, in analogy to the electron waves, is of fundamental interest. The very large number of potential practical applications[2] of such photonic band gaps, such as the enhanced performance of semiconductor lasers, has also spurred interest in this topic. Studies have been done using scalar waves[3–7], EM waves[8–10] and elastic waves[11]. The existence of band gaps and localized states have been reported in a variety of cases, particularly in periodic and disordered arrays of spherical scatterers. However, the relative importance of the roles of two differrent mechanisms, single scatterer resonances and macroscopic Bragg-like resonances, in the formation of gaps and localized states is still being debated. The resolution of this question is of interest for the following reason. Most theoretical treatments of the problem involve a lot of complicated calculations. In the plane wave expansion method[7–8] that we have used, a large number of plane waves have to be used to ensure accuracy necessitating the diagonalization of large matrices and the expending of a lot of computational effort.

A Tight-Binding Model Beyond Two-Center Approximation

We present a tight-binding model which goes beyond the traditional two-center approximation and allows the hopping parameters and the repulsive energy to be dependent on the bonding environment. We show that this model works well for metallic as well as covalent systems.

Photonic Gaps for Electromagnetic Waves in Periodic Dielectric Structures: Discovery of the Diamond Structure

Electron waves traveling in the periodic potential of a crystal are arranged into energy bands separated by gaps in which propagating states are prohibited.1 It is interesting to see if analogous band gaps exist when electromagnetic (EM) waves propagate in a periodic dielectric structure (e.g., a periodic lattice of dielectric spheres of dielectric constant ea embedded in a uniform dielectric background eb). If such a band gap or frequency gap exists, EM waves with frequencies inside the gap cannot propagate in any direction inside the material. These frequency gaps are referred to as “photonic band gaps.”

First principles calculations for analysis of martensitic transformations

The change in crystal energy is calculated for atomic displacements corresponding to phonons, elastic shears, and lattice transformations. Anomalies in the phonon dispersion curves of NiAl and NiTi are analyzed and recent calculations for TiPd alloys are presented.

PHOTONIC GAPS IN PERIODIC DIELECTRIC STRUCTURES

Using a plane wave expansion method, we solved the Maxwell’s equations for the propagation of electromagnetic waves inside periodic dielectric materials, and found the existence of photonic band gaps in several classes of periodic dielectric structures.

Tight-Binding Molecular Dynamics Study of C60 and Other Carbon Clusters

The structure and dynamics of C60 buckyball and carbon clusters C n (n=2–90) have been studied with molecular dynamics simulations using a tight-binding potential model. The studies show that it is possible to nucleate a ‘buckyball-like’ cluster by cooling and compressing carbon atoms from the gas phase. The studies also show that there is a transition from one-dimensional linear and cyclic structures to two-dimensional cage structures as the number of carbon atoms reaches n=20. Magic numbers for fullerene formation energy are observed at n=50,60,70 and 84.

Transmission and reflection properties of periodic dispersive materials

The transfer matrix method has been used for the calculation of transmission and reflection properties of periodic and/or disordered dispersive photonic band gap (PBG) materials. We have studied the transmission properties of: (1) PBG materials constructed of low resistive Si wafers forming the newly proposed layer-by-layer structure and exhibiting PBG at around 100 GHz; (2) a two-dimensional square lattice consisting of metallic wires; (3) materials having structural gaps close to a polariton gap.