Calculation of the optical conductivity for the Anderson impurity model using the slave boson technique

The optical conductivity of the Anderson impurity mode l has been calculated by emp l oying the slave boson technique and an expansion in powers of l i N, where N is the d egeneracy o f the f electron level . This method has been used to find the effective mass of the conduction electrons for temperatures above and below the Kondo tempera ture. For low temperatures, the mass enhancement is f ound to be large while a t high t emperatures, the mass enhancement is sma ll. The conductivity i s f ound to be Drude like with frequency dependent effective mass and scattering time for low independent effective mass and temperatures and scattering time f requency for high t emperatures. The behavior of both the effective mass and the conductivity is in qualitative agreement with experimental r esul t s .

Polytypism and Silicon carbide : a solid state nuclear magnetic resonance study

A survey of predominantly industrial silicon carbide has been carried out using Magic Angle Spinning nuclear magnetic resonance (MAS nmr); a solid state technique. Three silicon carbide polytypes were studied; 3C, 6H, and 15R. The 13C and 29 Si MAS nmr spectra of the bulk SiC sample was identified on the basis of silicon (carbon) site type in the d iff ere n t pol Y t Y pes • Out to 5.00 A fro mac en t r a lsi 1 i con (0 r carbon) atom four types of sites were characterized using symmetry based calculations. This method of polytype analysis was also considered, in the prelminary stages, for applications with other polytypic material; CdBr 2 , CdI 2 , and PbI 2 " In an attempt to understand the minor components of silicon carbide, such as its surface, some samples were hydrofluoric acid washed and heated to extreme temperatures. Basically, an HF removable species which absorbs at -110 ppm (Si0 2 ) in the 29 Si MAS nmr spectrum is found in silicon carbide after heating. Other unidentified peaks observed at short recycle delays in some 29 Si MAS nmr spectra are considered to be impurities that may be within the lattice. These components comprise less than 5% of the observable silicon. A Tl study was carried out for 29 Si nuclei in a 3C ii polytype sample, using the Driven Equilibrium Single-Pulse Observation of T1 (DESPOT) technique. It appears as though there are a number of nuclei that have the same chemical shift but different T1 relaxation times. The T1 values range from 30 seconds to 11 minutes. Caution has to be kept when interpreting these results because this is the first time that DESPOT has been used for solid samples and it is not likely in full working order. MAS nmr indicates that the 13C and 29 Si ~sotropic chemical shifts of silicon carbide appear to have a reciprocal type of relationship_ Single crystal nmr analysis of a 6H sample is accordance with this finding when only the resultant isotropic shift is considered. However, single crystal nmr also shows that the actual response of the silicon and carbon nuclear environment to the applied magnetic field at various angles is not at all reciprocal. Such results show that much more single crystal nmr work is required to determine the actual behavior of the local magnetic environment of the SiC nuclei.

Solid state NMR chemical shifts as an alternative to diffraction data in the determination of SIC polytypic structures

Silicon carbide, which has many polytypic modifications of a very simple and very symmetric structure, is an excellent model system for exploring, the relationship between chemical shift, long-range dipolar shielding, and crystal structure in network solids. A simple McConnell equation treatment of bond anisotropy effects in a poly type predicts chemical shifts for silicon and carbon sites which agree well with the experiment, provided that contributions from bonds up to 100 A are included in the calculation. The calculated chemical shifts depend on three factors: the layer stacking sequence, electrical centre of gravity, and the spacings between silicon and carbon layers. The assignment of peaks to lattice sites is proved possible for three polytypes (6H, 15R, and 3C). The fact that the calculated chemical shifts are very sensitive to layer spacings provides us a potential way to detennine and refine a crystal structure. In this work, the layer spacings of 6H SiC have been calculated and are within X-ray standard deviations. Under this premise, the layer spacings of 15R have been detennined. 29Si and 13C single crystal nmr studies of 6H SiC polytype indicate that all silicons and carbons are magnetically anisotropic. The relationship between a magnetic shielding tensor component and layer spacings has been derived. The comparisons between experimental and semi-empirical chemical shielding tensor components indicate that the paramagnetic shielding of silicon should be included in the single crystal chemical shift calculation.

HG 186.15-186.25-1

Coarse grained section with two different fine grained domains. Towards the left hand side the domain is dark and has no inclusions of coarse grains. The right hand side has some coarser materials.

HG 186.9-187.0 D.E. Thin Section

Coarse grained sample with grains varying from small to medium in size. They range from sub-angular to sub-rounded in shape. The sample is abundant in lineations and comet structures. Minor amounts of grain stacking are present. Inclusions of a clay rich, fine grained domain.

HG 291.40-291.55 Thin Section

Coarse grained sample with inclusions of finer grained sediment. Clasts are small to large in size and angular to sub-rounded in shape. Grain crushing is abundant in this sample, and lineations and minor grain stacks can also be seen.

HG 303.85-303.95

This is a dark grey, coarse grained sediment with inclusions of fine grained sand. Lineations and grains stacking are the most common features seen, along with grain crushing (mainly edge-to-edge). A few minor rotation structures can also be observed with comet structures.

HG 149.70-149.85

Brown sediment with clasts ranging from small to medium in size. Clast shape ranges from angular to rounded. Lineations and grain crushing are abundant throughout the sample. This sample also includes several inclusions of darker and fine grained domains. Comet structures can also be seen in some areas of the sample.

TVD #9 PB

Dark brown sediment (almost black), with a few clasts that are very well dispersed. The clasts range from small to medium in size. The clast shape ranges from sub-angular to rounded. The sample is mainly structureless. There are a few inclusions of a lighter domain. This domain contains more clasts than the darker one.

9 AUG B-2-B

This sample contains multiple domains. One domain is a fine grained greyish-brown ground mass, with some small clasts. Another domain is a dark grey, structure-less ground mass. Another domain is a light greyish-brown domain that is generally fine grained with clay inclusions.

WR-2

Dark brown sediment with clasts ranging from small to large in size. Clast shape ranges from angular to sub-rounded. The main domain mainly contains larger aggregates. There is one domain inclusion in this sample. It mainly contains small and medium sized clasts, and contains many lineations. Necking structures can be commonly seen in the main domain between larger aggregates. This sample also contains many elongated clasts and inclusions of clay material.

1544 BH17 NP 2014

Brown sediment with inclusions of a clay rich domain. Clasts range from small to medium in size and angular to sub-rounded in shape. Lineations can be commonly seen throughout the sample, along with water escape structures in the clay rich domain. Rotation structures, comet structures, and grain crushing are also present.