Process for purification of solids

A process for purifying solids, especially silicon, by melting and subsequent resolidification, is described. Silicon used in solar cell manufacturing is processed more efficiently and cost effectively

The Projective Line Over the Finite Quotient Ring GF(2)[xx]/<x3−x>< x^{3} - x> and Quantum Entanglement I. Theoretical Background

The paper deals with the projective line over the finite factor ring $R\_{\clubsuit} \equiv$ GF(2)[$x$]/$$. The line is endowed with 18 points, spanning the neighbourhoods of three pairwise distant points. As $R\_{\clubsuit}$ is not a local ring, the neighbour (or parallel) relation is not an equivalence relation so that the sets of neighbour points to two distant points overlap. There are nine neighbour points to any point of the line, forming three disjoint families under the reduction modulo either of two maximal ideals of the ring. Two of the families contain four points each and they swap their roles when switching from one ideal to the other; the points of the one family merge with (the image of) the point in question, while the points of the other family go in pairs into the remaining two points of the associated ordinary projective line of order two. The single point of the remaining family is sent to the reference point under both the mappings and its existence stems from a non-trivial character of the Jacobson radical, ${\cal J}\_{\clubsuit}$, of the ring. The factor ring $\widetilde{R}\_{\clubsuit} \equiv R\_{\clubsuit}/ {\cal J}\_{\clubsuit}$ is isomorphic to GF(2) $\otimes$ GF(2). The projective line over $\widetilde{R}\_{\clubsuit}$ features nine points, each of them being surrounded by four neighbour and the same number of distant points, and any two distant points share two neighbours. These remarkable ring geometries are surmised to be of relevance for modelling entangled qubit states, to be discussed in detail in Part II of the paper.Comment: 8 pages, 2 figure

Size effects in the magnetic behaviour of TbAl_2 milled alloys

The study of the magnetic properties depending upon mechanical milling of the ferromagnetic polycrystalline TbAl_2 material is reported. The Rietveld analysis of the X-ray diffraction data reveals a decrease of the grain size down to 14 nm and -0.15 % of variation of the lattice parameter, after 300 hours of milling time. Irreversibility in the zero field cooled - field cooled (ZFC-FC) DC-susceptibility and clear peaks in the AC susceptibility between 5 and 300 K show that the long-range ferromagnetic structure is inhibited in favour of a disordered spin arrangement below 45 K. This glassy behaviour is also deduced from the variation of the irreversibility transition with the field (H^{2/3}) and frequency. The magnetization process of the bulk TbAl_2 is governed by domain wall thermal activation processes. By contrast, in the milled samples, cluster-glass properties arise as a result of cooperative interactions due to the substitutional disorder. The interactions are also influenced by the nanograin structure of the milled alloys, showing a variation of coercivity with the grain size, below the crossover between the multi- and single-domain behaviours.Comment: 23 pages, 11 figures, to appear in J. Phys.: Condens. Ma

Structure peculiarities of cementite and their influence on the magnetic characteristics

The iron carbide $Fe_3C$ is studied by the first-principle density functional theory. It is shown that the crystal structure with the carbon disposition in a prismatic environment has the lowest total energy and the highest energy of magnetic anisotropy as compared to the structure with carbon in an octahedron environment. This fact explains the behavior of the coercive force upon annealing of the plastically deformed samples. The appearance of carbon atoms in the octahedron environment can be revealed by Mossbauer experiment.Comment: 10 pages, 3 figures, 3 tables. submitted to Phys.Rev.

Harmonic Generation from Relativistic Plasma Surfaces in Ultra-Steep Plasma Density Gradients

Harmonic generation in the limit of ultra-steep density gradients is studied experimentally. Observations demonstrate that while the efficient generation of high order harmonics from relativistic surfaces requires steep plasma density scale-lengths ($L_p/\lambda < 1$) the absolute efficiency of the harmonics declines for the steepest plasma density scale-length $L_p \to 0$, thus demonstrating that near-steplike density gradients can be achieved for interactions using high-contrast high-intensity laser pulses. Absolute photon yields are obtained using a calibrated detection system. The efficiency of harmonics reflected from the laser driven plasma surface via the Relativistic Oscillating Mirror (ROM) was estimated to be in the range of 10^{-4} - 10^{-6} of the laser pulse energy for photon energies ranging from 20-40 eV, with the best results being obtained for an intermediate density scale-length

Projective Ring Line Encompassing Two-Qubits

The projective line over the (non-commutative) ring of two-by-two matrices with coefficients in GF(2) is found to fully accommodate the algebra of 15 operators - generalized Pauli matrices - characterizing two-qubit systems. The relevant sub-configuration consists of 15 points each of which is either simultaneously distant or simultaneously neighbor to (any) two given distant points of the line. The operators can be identified with the points in such a one-to-one manner that their commutation relations are exactly reproduced by the underlying geometry of the points, with the ring geometrical notions of neighbor/distant answering, respectively, to the operational ones of commuting/non-commuting. This remarkable configuration can be viewed in two principally different ways accounting, respectively, for the basic 9+6 and 10+5 factorizations of the algebra of the observables. First, as a disjoint union of the projective line over GF(2) x GF(2) (the "Mermin" part) and two lines over GF(4) passing through the two selected points, the latter omitted. Second, as the generalized quadrangle of order two, with its ovoids and/or spreads standing for (maximum) sets of five mutually non-commuting operators and/or groups of five maximally commuting subsets of three operators each. These findings open up rather unexpected vistas for an algebraic geometrical modelling of finite-dimensional quantum systems and give their numerous applications a wholly new perspective.Comment: 8 pages, three tables; Version 2 - a few typos and one discrepancy corrected; Version 3: substantial extension of the paper - two-qubits are generalized quadrangles of order two; Version 4: self-dual picture completed; Version 5: intriguing triality found -- three kinds of geometric hyperplanes within GQ and three distinguished subsets of Pauli operator

Reduction of the Yb valence in YbAl3 nanoparticles

Measurements of specific heat, dc magnetic susceptibility, and Yb LII and LIII x-ray absorption near-edge structure XANES and extended x-ray absorption fine structure EXAFS on YbAl3 milled alloys are reported. X-ray diffraction patterns are consistent with a reduction in particle size down to 10 nm and an increase in the lattice strain up to 0.4% for 120 h of milling time. A decrease in the mean valence from 2.86 for the unmilled alloy to 2.70 for 120 h milled YbAl3 is obtained from the analysis of XANES spectra. From the analysis of spectra in the EXAFS region, an increase in the mean-square disorder of neighbor distance with milling time is detected in good agreement with the results of x-ray diffraction. Size effects strongly influence the magnetic and thermal properties. The value for the maximum of the magnetic susceptibility decreases around 30% for 120 h milled alloy and an excess specific heat, with a peak around 40 K in the milled samples, is derived. These changes in the physical properties along the milled YbAl3 alloys are associated with the reduction in particle size. Such a reduction leads to the existence of a large number of Yb2+ atoms at the surface with respect to the bulk affecting the overall electronic state

De la faille alpine à la fosse de Puysegur (Nouvelle-Zélande) : résultats de la campagne de cartographie multifaisceaux GEODYNZ-SUD, Leg 2

Le Leg 2 de la campagne GEODYNZ-SUD, menée au SW de la Nouvelle-Zélande, a permis de reconnaître les structures qui accompagnent du Nord au Sud le passage de la faille alpine à la subduction oblique sous la marge du Fiodland, puis à celle naissante, intra-océanique sous la ride de Macquarie. Au Nord et au-dessus de la plaque australienne subductée vers l'Est, un faisceau longitudinal de décrochements converge vers le système transpressif de la faille alpine en découpant la marge continentale. Au Sud, la déformation décrochante est strictement localisée au sommet de la ride de Macquarie. (Résumé d'auteur