Depositing spacing layers on magnetic film with liquid phase epitaxy

Liquid phase epitaxy spacing layer is compatible with systems which are hard-bubble proofed by use of second magnetic garnet film as capping layer. Composite is superior in that: circuit fabrication time is reduced; adherence is superior; visibility is better; and, good match of thermal expansion coefficients is provided

Similar Sublattices and Coincidence Rotations of the Root Lattice A4 and its Dual

A natural way to describe the Penrose tiling employs the projection method on the basis of the root lattice A4 or its dual. Properties of these lattices are thus related to properties of the Penrose tiling. Moreover, the root lattice A4 appears in various other contexts such as sphere packings, efficient coding schemes and lattice quantizers. Here, the lattice A4 is considered within the icosian ring, whose rich arithmetic structure leads to parametrisations of the similar sublattices and the coincidence rotations of A4 and its dual lattice. These parametrisations, both in terms of a single icosian, imply an index formula for the corresponding sublattices. The results are encapsulated in Dirichlet series generating functions. For every index, they provide the number of distinct similar sublattices as well as the number of coincidence rotations of A4 and its dual.Comment: 8 pages, paper presented at ICQ10 (Zurich, Switzerland

Investigation of the growth of garnet films by liquid phase epitaxy

Liquid phase expitaxy was investigated to determine its applicability to fabricating magnetic rare earth garnet films for spacecraft data recording systems. Two mixed garnet systems were investigated in detail: (1) Gd-Y and (2) Eu-Yb-Y. All films were deposited on Gd3Ga5012 substrates. The uniaxial anisotropy of the Gd-Y garnets is primarily stress-induced. These garnets are characterized by high-domain wall mobility, low coercivity and modest anisotropy. Characteristic length was found to be relatively sensitive to temperature. The Eu-Yb-Y garnets exhibit acceptable mobilities, good temperature stability and reasonable quality factors. The uniaxial anisotropy of these garnets is primarily growth-induced. The system is well suited for compositional "tailoring" to optimize specific desirable properties. Liquid phase epitaxy can be used to deposit Gd3Ga5012 spacing layers on magnetic garnet films and this arrangement possesses certain advantages over more conventional magnetic filmspacing layer combinations. However, it cannot be used if the magnetic film is to be ion implanted

The rings of n-dimensional polytopes

Points of an orbit of a finite Coxeter group G, generated by n reflections starting from a single seed point, are considered as vertices of a polytope (G-polytope) centered at the origin of a real n-dimensional Euclidean space. A general efficient method is recalled for the geometric description of G- polytopes, their faces of all dimensions and their adjacencies. Products and symmetrized powers of G-polytopes are introduced and their decomposition into the sums of G-polytopes is described. Several invariants of G-polytopes are found, namely the analogs of Dynkin indices of degrees 2 and 4, anomaly numbers and congruence classes of the polytopes. The definitions apply to crystallographic and non-crystallographic Coxeter groups. Examples and applications are shown.Comment: 24 page

The application of amino acid racemization in the acid soluble fraction of enamel to the estimation of the age of human teeth

Estimation of age-at-death for skeletonised forensic remains is one of the most significant problems in forensic anthropology. The majority of existing morphological and histological techniques are highly inaccurate, and show a bias towards underestimating the age of older individuals. One technique which has been successful in forensic age estimation is amino acid racemization in dentine. However, this method cannot be used on remains where the post-mortem interval is greater than 20 years. An alternative approach is to measure amino acid racemization in dental enamel, which is believed to be more resistant to change post-mortem. The extent of amino acid racemization in the acid soluble fraction of the enamel proteins was determined for modem known age teeth. A strong correlation was observed between the age of the tooth and the extent of racemization. No systematic bias in the direction of age estimation errors was detected. For the majority of teeth analyzed, the presence of dental caries did not affect the results obtained. In a minority of cases, carious teeth showed a higher level of racemization than would be expected given the age of the individual. These results indicate that amino acid racemization in enamel has the potential to be used in age estimation of skeletal remains. (C) 2007 Elsevier Ireland Ltd. All rights reserved

Icosahedral multi-component model sets

A quasiperiodic packing Q of interpenetrating copies of C, most of them only partially occupied, can be defined in terms of the strip projection method for any icosahedral cluster C. We show that in the case when the coordinates of the vectors of C belong to the quadratic field Q[\sqrt{5}] the dimension of the superspace can be reduced, namely, Q can be re-defined as a multi-component model set by using a 6-dimensional superspace.Comment: 7 pages, LaTeX2e in IOP styl

Four types of special functions of G_2 and their discretization

Properties of four infinite families of special functions of two real variables, based on the compact simple Lie group G2, are compared and described. Two of the four families (called here C- and S-functions) are well known, whereas the other two (S^L- and S^S-functions) are not found elsewhere in the literature. It is shown explicitly that all four families have similar properties. In particular, they are orthogonal when integrated over a finite region F of the Euclidean space, and they are discretely orthogonal when their values, sampled at the lattice points F_M \subset F, are added up with a weight function appropriate for each family. Products of ten types among the four families of functions, namely CC, CS, SS, SS^L, CS^S, SS^L, SS^S, S^SS^S, S^LS^S and S^LS^L, are completely decomposable into the finite sum of the functions. Uncommon arithmetic properties of the functions are pointed out and questions about numerous other properties are brought forward.Comment: 18 pages, 4 figures, 4 table

From solid solution to cluster formation of Fe and Cr in α\alpha-Zr

To understand the mechanisms by which Fe and Cr additions increase the corrosion rate of irradiated Zr alloys, a combination of experimental (atom probe tomography, x-ray diffraction and thermoelectric power measurements) and modelling (density functional theory) techniques are employed to investigate the non-equilibrium solubility and clustering of Fe and Cr in binary Zr alloys. Cr occupies both interstitial and substitutional sites in the {\alpha}-Zr lattice, Fe favours interstitial sites, and a low-symmetry site that was not previously modelled is found to be the most favourable for Fe. Lattice expansion as a function of alloying concentration (in the dilute regime) is strongly anisotropic for Fe additions, expanding the $c$-axis while contracting the $a$-axis. Defect clusters are observed at higher solution concentrations, which induce a smaller amount of lattice strain compared to the dilute defects. In the presence of a Zr vacancy, all two-atom clusters are more soluble than individual point defects and as many as four Fe or three Cr atoms could be accommodated in a single Zr vacancy. The Zr vacancy is critical for the increased solubility of defect clusters, the implications for irradiation induced microstructure changes in Zr alloys are discussed.Comment: 15 pages including figure, 9 figures, 2 tables. Submitted for publication in Acta Mater, Journal of Nuclear Materials (2015