Photoelasticity of sodium silicate glass from first principles

Based on density-functional perturbation theory we have computed the photoelastic tensor of a model of sodium silicate glass of composition (Na$_2$O)$_{0.25}$(SiO$_2$)$_{0.75}$ (NS3). The model (containig 84 atoms) is obtained by quenching from the melt in combined classical and Car-Parrinello molecular dynamics simulations. The calculated photoelastic coefficients are in good agreement with experimental data. In particular, the calculation reproduces quantitatively the decrease of the photoelastic response induced by the insertion of Na, as measured experimentally. The extension to NS3 of a phenomenological model developed in a previous work for pure a-SiO$_2$ indicates that the modulation upon strain of other structural parameters besides the SiOSi angles must be invoked to explain the change in the photoelstic response induced by Na

Crystal structure of LaTiO_3.41 under pressure

The crystal structure of the layered, perovskite-related LaTiO_3.41 (La_5Ti_5O_{17+\delta}) has been studied by synchrotron powder x-ray diffraction under hydrostatic pressure up to 27 GPa (T = 295 K). The ambient-pressure phase was found to remain stable up to 18 GPa. A sluggish, but reversible phase transition occurs in the range 18--24 GPa. The structural changes of the low-pressure phase are characterized by a pronounced anisotropy in the axis compressibilities, which are at a ratio of approximately 1:2:3 for the a, b, and c axes. Possible effects of pressure on the electronic properties of LaTiO_3.41 are discussed.Comment: 5 pages, 6 figure

Structural, elastic and thermal properties of cementite (Fe3_3C) calculated using Modified Embedded Atom Method

Structural, elastic and thermal properties of cementite (Fe$_3$C) were studied using a Modified Embedded Atom Method (MEAM) potential for iron-carbon (Fe-C) alloys. Previously developed Fe and C single element potentials were used to develop an Fe-C alloy MEAM potential, using a statistically-based optimization scheme to reproduce structural and elastic properties of cementite, the interstitial energies of C in bcc Fe as well as heat of formation of Fe-C alloys in L$_{12}$ and B$_1$ structures. The stability of cementite was investigated by molecular dynamics simulations at high temperatures. The nine single crystal elastic constants for cementite were obtained by computing total energies for strained cells. Polycrystalline elastic moduli for cementite were calculated from the single crystal elastic constants of cementite. The formation energies of (001), (010), and (100) surfaces of cementite were also calculated. The melting temperature and the variation of specific heat and volume with respect to temperature were investigated by performing a two-phase (solid/liquid) molecular dynamics simulation of cementite. The predictions of the potential are in good agreement with first-principles calculations and experiments.Comment: 12 pages, 9 figure

Quorum of observables for universal quantum estimation

Any method for estimating the ensemble average of arbitrary operator (observables or not, including the density matrix) relates the quantity of interest to a complete set of observables, i.e. a quorum}. This corresponds to an expansion on an irreducible set of operators in the Liouville space. We give two general characterizations of these sets. All the known unbiased reconstruction techniques, i.e. ``quantum tomographies'', can be described in this framework. New operatorial resolutions are given that can be used to implement novel reconstruction schemes.Comment: Latex, no figure

Compositional disorder and its influence on the structural, electronic and magnetic properties of MgC(Ni_{1-x}Co_{x})_{3} alloys using first-principles

First-principles, density-functional based electronic structure calculations are carried out for MgC(Ni_{1-x}Co_{x})_{3} alloys over the concentration range 0\leq x\leq1, using Korringa-Kohn-Rostoker coherent-potential approximation (KKR CPA) method in the atomic sphere approximation (ASA). The self-consistent calculations are used to study the changes as a function of x in the equation of state parameters, total and partial densities of states, magnetic moment and the on-site exchange interaction parameter. To study the magnetic properties as well as its volume dependence, fixed-spin moment calculations in conjunction with the phenomenological Landau theory are employed. The salient features that emerge from these calculations are (i) a concentration independent variation in the lattice parameter and bulk modulus at x~0.75 with an anomaly in the variation of the pressure derivative of bulk modulus, (ii) the fixed-spin moment based corrections to the overestimated magnetic ground state for 0.0\leq x\leq0.3 alloys, making the results consistent with the experiments, and (iii) the possibility of multiple magnetic states at x~0.75, which, however, requires further improvements in the calculations

Eutactic quantum codes

We consider sets of quantum observables corresponding to eutactic stars. Eutactic stars are systems of vectors which are the lower dimensional ``shadow'' image, the orthogonal view, of higher dimensional orthonormal bases. Although these vector systems are not comeasurable, they represent redundant coordinate bases with remarkable properties. One application is quantum secret sharing.Comment: 6 page

Structural stability of Fe5Si3 and Ni2Si studied by high-pressure x-ray diffraction and ab initio total-energy calculations

We performed high-pressure angle dispersive x-ray diffraction measurements on Fe5Si3 and Ni2Si up to 75 GPa. Both materials were synthesized in bulk quantities via a solid-state reaction. In the pressure range covered by the experiments, no evidence of the occurrence of phase transitions was observed. On top of that, Fe5Si3 was found to compress isotropically, whereas an anisotropic compression was observed in Ni2Si. The linear incompressibility of Ni2Si along the c-axis is similar in magnitude to the linear incompressibility of diamond. This fact is related to the higher valence-electron charge density of Ni2Si along the c-axis. The observed anisotropic compression of Ni2Si is also related to the layered structure of Ni2Si where hexagonal layers of Ni2+ cations alternate with graphite-like layers formed by (NiSi)2- entities. The experimental results are supported by ab initio total-energy calculations carried out using density functional theory and the pseudopotential method. For Fe5Si3, the calculations also predicted a phase transition at 283 GPa from the hexagonal P63/mcm phase to the cubic structure adopted by Fe and Si in the garnet Fe5Si3O12. The room-temperature equations of state for Fe5Si3 and Ni2Si are also reported and a possible correlation between the bulk modulus of iron silicides and the coordination number of their minority element is discussed. Finally, we report novel descriptions of these structures, in particular of the predicted high-pressure phase of Fe5Si3 (the cation subarray in the garnet Fe5Si3O12), which can be derived from spinel Fe2SiO4 (Fe6Si3O12).Comment: 44 pages, 13 figures, 3 Table

Ab initio study of the vibrational properties of crystalline TeO2: The alpha, beta, and gamma phases

Based on density functional perturbation theory, we have studied the vibrational properties of three crystalline phases of tellurium dioxide: paratellurite alpha-TeO2, tellurite beta-TeO2, and the new phase gamma-TeO2, recently identified experimentally. Calculated Raman and IR spectra are in good agreement with available experimental data. The vibrational spectra of alpha- and beta-TeO2 can be interpreted in terms of vibrations of TeO2 molecular units

A first-principles comparison of the electronic properties of MgC_{y}Ni_{3} and ZnC_{y}Ni_{3} alloys

First-principles, density-functional-based electronic structure calculations are employed to study the changes in the electronic properties of ZnC_{y}Ni_{3} and MgC_{y}Ni_{3} using the Korringa-Kohn-Rostoker coherent-potential approximation method in the atomic sphere approximation (KKR-ASA CPA). As a function of decreasing C at%, we find a steady decrease in the lattice constant and bulk modulus in either alloys. However, the pressure derivative of the bulk modulus displays an opposite trend. Following the Debye model, which relates the pressure derivative of the bulk modulus with the average phonon frequency of the crystal, it can thus be argued that ZnCNi_{3} and its disordered alloys posses a different phonon spectra in comparison to its MgCNi_{3} counterparts. This is further justified by the marked similarity we find in the electronic structure properties such as the variation in the density of states and the Hopfield parameters calculated for these alloys. The effects on the equation of state parameters and the density of states at the Fermi energy, for partial replacement of Mg by Zn are also discussed.Comment: 19 pages, 15 figure

Generalized Euler Angle Paramterization for SU(N)

In a previous paper (math-ph/0202002) an Euler angle parameterization for SU(4) was given. Here we present the derivation of a generalized Euler angle parameterization for SU(N). The formula for the calculation of the Haar measure for SU(N) as well as its relation to Marinov's volume formula for SU(N) will also be derived. As an example of this parameterization's usefulness, the density matrix parameterization and invariant volume element for a qubit/qutrit, three qubit and two three-state systems, also known as two qutrit systems, will also be given.Comment: 36 pages, no figures; added qubit/qutrit work, corrected minor definition problems and clarified Haar measure derivation. To be published in J. Phys. A: Math. and Ge