Density-wave theory of dislocations in crystals

The density-wave theory of Ramakrishnan and Yussouff is extended to provide a scheme for describing dislocations and other topological defects in crystals. Quantitative calculations are presented for the order-parameter profiles, the atomic configuration, and the free energy of a screw dislocation with Burgers vector b=(a/2, a/2, a/2) in a bcc solid. These calculations are done using a simple parametrization of the direct correlation function and a gradient expansion. It is conventional to express the free energy of the dislocation in a crystal of size R as (λb2/4π)ln(αR/‖b‖), where λ is the shear elastic constant, and α is a measure of the core energy. Our results yield for Na the value α≃1.94a/(‖c1’’‖)1/2 (≃1.85) at the freezing temperature (371 K) and α≃2.48a/(‖c1’’‖)1/2 at 271 K, where c1’’ is the curvature of the first peak of the direct correlation function c(q). Detailed results for the density distribution in the dislocation, particularly the core region, are also presented. These show that the dislocation core has a columnar character. To our knowledge, this study represents the first calculation of dislocation structure, including the core, within the framework of an order-parameter theory and incorporating thermal effects.

Topological defects in crystals: A density-wave theory

A new approach for describing dislocations and other topological defects in crystals, based on the density wave theory of Ramakrishnan and Yussouff is presented. Quantitative calculations are discussed in brief for the order parameter profiles, the atomic configuration and the free energy of a screw dislocation with Burgers vector b = (a/2, a/2,a/2 ) in a bcc solid. Our results for the free energy of the dislocation in a crystal of sizeR, when expressed as (λb 2/4π) ln (αR/|b|) whereλ is the shear elastic constant, yield, for example, the valueα ⋍ 1·85 for sodium at its freezing temperature (371°K). The density distribution in the presence of the dislocation shows that the dislocation core has a columnar character. To our knowledge, this study represents the first calculation of dislocation structure, including the core, within the framework of an order parameter theory incorporating thermal effects.

Sintering of beta titanium: Role of dislocation pipe diffusion

Sintering of titanium in its high temperature beta phase was studied by isothermal dilatometry. The sintering shrinkage y did not follow the normal time exponent type of behaviour, instead being described by the equation y = Kt(m)/[1-(A+Bt)(2)], where m = 1.93 +/- 0.07, with an activation energy of 62-90 kJ mol(-1). A detailed analysis of these results, based on the 'anomalous' diffusion behaviour reported for beta titanium, is carried out. It is shown that the generation of a high density of dislocations during the alpha --> beta phase transformation, coupled with sluggish recovery at the sintering necks, enables sintering mass transport by pipe diffusion through dislocation cores from sources of matter within the particles to become dominant.

Grain Refinement at the Nanoscale Via Mechanical Twinning and Dislocation Interaction in a Nickel-Based Alloy

A nanostructured surface layer was formed on an Inconel 600 plate by subjecting it to surface mechanical attrition treatment at room temperature. Transmission electron microscopy and high-resolution transmission electron microscopy of the treated surface layer were carried out to reveal the underlying grain refinement mechanism. Experimental observations showed that the strain-induced nanocrystallization in the current sample occurred via formation of mechanical microtwins and subsequent interaction of the microtwins with dislocations in the surface layer. The development of high-density dislocation arrays inside the twin-matrix lamellae provides precursors for grain boundaries that subdivide the nanometer-thick lamellae into equiaxed, nanometer-sized grains with random orientations.

Size Effects in Micro-bending Deformation of MEMS Devices Based on the Discrete Dislocation Theory

In the present research, the discrete dislocation theory is used to analyze the size effect phenomena for the MEMS devices undergoing micro-bending load. A consistent result with the experimental one in literature is obtained. In order to check the effectiveness to use the discrete dislocation theory in predicting the size effect, both the basic version theory and the updated one are adopted simultaneously. The normalized stress-strain relations of the material are obtained for different plate thickness or for different obstacle density. The prediction results are compared with experimental results.

Effect of misfit dislocation originated from strained layer on photoluminescence properties of InxGa1-xN/GaN multiple quantum wells

In-x Ga1-xN/GaN multiple quantum well (MQW) samples with strain-layer thickness lager/less than the critical one are investigated by temperature-dependent photoluminescence and transmission electron microscopy, and double crystal x-ray diffraction. For the sample with the strained-layer thickness greater than the critical thickness, we observe a high density of threading dislocations generated at the MQW layers and extended to the cap layer. These dislocations result from relaxation of the strain layer when its thickness is beyond the critical thickness. For the sample with the strained-layer thickness greater than the critical thickness, temperature-dependent photoluminescence measurements give evidence that dislocations generated from the MQW layers due to strain relaxation are main reason of the poor photoluminescence property, and the dominating status change of the main peak with increasing temperature is attributed to the change of the radiative recombination from the areas including dislocations to the ones excluding dislocations.

Measurement of threading dislocation densities in GaN by wet chemical etching

We demonstrate a technique based on wet chemical etching that enables quick and accurate evaluation of edge- and screw/mixed-type threading dislocations (TDs) in GaN. Large and small etch pits are formed by phosphoric acid on the etched surfaces. The large etch pits are attributed to screw/mixed TDs and the small ones to edge TDs, according to their locations on the surface and Burgers vectors of TDs. Additionally, the origin of small etch pits is confirmed by a transmission electron microscopy. The difference in the size of etch pits is discussed in view of their origin and merging. Overetching at elevated temperatures or for a long time may result in merging of individual etch pits and underestimating of the density of TDs. Wet chemical etching has also been proved efficient in revealing the distribution of TDs in epitaxial lateral overgrowth GaN.

ELECTRON-STATES OF A VACANCY IN THE CORE OF THE 90-DEGREES PARTIAL DISLOCATION IN SILICON

An LCAO scheme (linear combination of atomic orbitals) taking into account ten atomic orbitals (s-, p-, and d-type) is used to calculate the electronic structure of a vacancy present in the core of the reconstructed 90 degrees partial dislocation in silicon. The levels in the band gap are extracted using Lanczos' algorithm and a continued fraction representation of the local density of states. The three-fold degenerate stale of the ideal vacancy is split into three levels with energies 0.26, 1.1, and 1.9 eV measured from the valence band edge.

Dislocation Reduction in GaN on Sapphire by Epitaxial Lateral Overgrowth

High quality GaN is grown on GaN substrate with stripe pattern by metalorganic chemical vapor deposition by means of epitaxial lateral overgrowth. AFM,wet chemical etching, and TEM experiments show that with a two-step ELOG procedure, the propagation of defects under the mask is blocked, and the coherently grown GaN above the window also experiences a drastic reduction in defect density. In addition, a grain boundary is formed at the coalescence boundary of neighboring growth fronts. The extremely low density of threading dislocations within wing regions makes ELOG GaN a potential template for the fabrication of nitride-based lasers with improved performance.

Role of surface trap states on two-dimensional electron gas density in InAlN/AlN/GaN heterostructures

In order to clarify the effect of charged dislocations and surface donor states on the transport mechanisms in polar AlInN/AlN/GaN heterostructures, we have studied the current-voltage characteristics of Schottky junctions fabricated on AlInN/AlN/GaN heterostructures. The reverse-bias leakage current behaviour has been interpreted with a Poole-Frenkel emission of electrons from trap states near the metal-semiconductor junction to dislocation induced states. The variation of the Schottky barrier height as a function of the AlN layer thickness has been measured and discussed, considering the role of the surface states in the formation of the two dimensional electron gas at AlN/GaN interface.

Determination of a misfit dislocation complex in SiGe/Si heterostructures by image deconvolution technique in HREM

The core structure of a dislocation complex in SiGe/Si system composed of a perfect 60degrees dislocation and an extended 60 dislocation has been revealed at atomic level. This is attained by applying the image deconvolution technique in combination with dynamical diffraction effect correction to an image taken with a 200 kV field-emission high-resolution electron microscope. The possible configuration of the dislocation complex is analyzed and their Burgers vectors are determined. (C) 2003 Elsevier B.V. All rights reserved.

Time-Dependent Density Functional Molecular Orbital and Excited State Calculations on Bis(porphyrinyl)butadiynes in the Monocationic, Neutral, Monoanionic, and Dianionic Oxidation States

We report a theoretical study of the multiple oxidation states (1+, 0, 1−, and 2−) of a meso,meso-linked diporphyrin, namely bis[10,15,20-triphenylporphyrinatozinc(II)-5-yl]butadiyne (4), using Time-Dependent Density Functional Theory (TDDFT). The origin of electronic transitions of singlet excited states is discussed in comparison to experimental spectra for the corresponding oxidation states of the close analogue bis{10,15,20-tris[3‘,5‘-di-tert-butylphenyl]porphyrinatozinc(II)-5-yl}butadiyne (3). The latter were measured in previous work under in situ spectroelectrochemical conditions. Excitation energies and orbital compositions of the excited states were obtained for these large delocalized aromatic radicals, which are unique examples of organic mixed-valence systems. The radical cations and anions of butadiyne-bridged diporphyrins such as 3 display characteristic electronic absorption bands in the near-IR region, which have been successfully predicted with use of these computational methods. The radicals are clearly of the “fully delocalized” or Class III type. The key spectral features of the neutral and dianionic states were also reproduced, although due to the large size of these molecules, quantitative agreement of energies with observations is not as good in the blue end of the visible region. The TDDFT calculations are largely in accord with a previous empirical model for the spectra, which was based simplistically on one-electron transitions among the eight key frontier orbitals of the C4 (1,4-butadiyne) linked diporphyrins.