Screened Coulomb interactions in metallic alloys: I. Universal screening in the atomic sphere approximation

We have used the locally self-consistent Green's function (LSGF) method in supercell calculations to establish the distribution of the net charges assigned to the atomic spheres of the alloy components in metallic alloys with different compositions and degrees of order. This allows us to determine the Madelung potential energy of a random alloy in the single-site mean field approximation which makes the conventional single-site density-functional- theory coherent potential approximation (SS-DFT-CPA) method practically identical to the supercell LSGF method with a single-site local interaction zone that yields an exact solution of the DFT problem. We demonstrate that the basic mechanism which governs the charge distribution is the screening of the net charges of the alloy components that makes the direct Coulomb interactions short-ranged. In the atomic sphere approximation, this screening appears to be almost independent of the alloy composition, lattice spacing, and crystal structure. A formalism which allows a consistent treatment of the screened Coulomb interactions within the single-site mean-filed approximation is outlined. We also derive the contribution of the screened Coulomb interactions to the S2 formalism and the generalized perturbation method.Comment: 28 pages, 8 figure

First-principles Calculation of the Formation Energy in MgO-CaO Solid Solutions

The electronic structure and total energy were calculated for ordered and disordered MgO-CaO solid solutions within the multiple scattering theory in real space and the local density approximation. Based on the dependence of the total energy on the unit cell volume the equilibrium lattice parameter and formation energy were determined for different solution compositions. The formation energy of the solid solutions is found to be positive that is in agreement with the experimental phase diagram, which shows a miscibility gap.Comment: 11 pages, 3 figure

Local Charge Excesses in Metallic Alloys: a Local Field Coherent Potential Approximation Theory

Electronic structure calculations performed on very large supercells have shown that the local charge excesses in metallic alloys are related through simple linear relations to the local electrostatic field resulting from distribution of charges in the whole crystal. By including local external fields in the single site Coherent Potential Approximation theory, we develop a novel theoretical scheme in which the local charge excesses for random alloys can be obtained as the responses to local external fields. Our model maintains all the computational advantages of a single site theory but allows for full charge relaxation at the impurity sites. Through applications to CuPd and CuZn alloys, we find that, as a general rule, non linear charge rearrangements occur at the impurity site as a consequence of the complex phenomena related with the electronic screening of the external potential. This nothwithstanding, we observe that linear relations hold between charge excesses and external potentials, in quantitative agreement with the mentioned supercell calculations, and well beyond the limits of linearity for any other site property.Comment: 11 pages, 1 table, 7 figure

THEORY OF FOURTH ORDER STRUCTURE AND RAMAN SCATTERING IN LIQUID 4He

On montre que l'intensité IR de la diffusion Raman de la lumière de 4He liquide est sensible en même temps à la structure à courte portée du liquide et à la partie à courte portée de l'interaction entre la lumière et deux atomes d'hélium. L'IR calculée en utilisant le modèle théorique le plus réaliste est de 40 % plus grande que la valeur donnée par l'expérience.It is shown that the Raman intensity IR form liquid 4He is sensitive to both the short-range structure of the fluid and the short-range part of the interaction of the light with two He atoms. The calculated IR for the most realistic model is 40 % larger than experiment

CALCULATED ELECTRON-PHONON COUPLING AND SUPERCONDUCTING TC OF TRANSITITION METALS : Mo AND Pd

Les paramètres λ et α2 F (ω) du couplage electron-phonon sont calculées pour Mo et Pd. La valeur obtenue λ = 0,40 est en assez bon accord avec la temperature de la transition supraconductrice du Mo. La valeur obtenue pour Pd est λ = 0,41Electron-phonon parameters λ and α2F(ω) are calculated for Mo and Pd. The value λ = 0.40 for Mo agrees well with superconducting Tc ; for Pd λ is 0.41

Hybrid Monte Carlo on Hilbert spaces

The Hybrid Monte Carlo (HMC) algorithm provides a framework for sampling from complex, high-dimensional target distributions. In contrast with standard Markov chain Monte Carlo (MCMC) algorithms, it generates nonlocal, nonsymmetric moves in the state space, alleviating random walk type behaviour for the simulated trajectories. However, similarly to algorithms based on random walk or Langevin proposals, the number of steps required to explore the target distribution typically grows with the dimension of the state space. We define a generalized HMC algorithm which overcomes this problem for target measures arising as finite-dimensional approximations of measures [pi] which have density with respect to a Gaussian measure on an infinite-dimensional Hilbert space. The key idea is to construct an MCMC method which is well defined on the Hilbert space itself. We successively address the following issues in the infinite-dimensional setting of a Hilbert space: (i) construction of a probability measure [Pi] in an enlarged phase space having the target [pi] as a marginal, together with a Hamiltonian flow that preserves [Pi]; (ii) development of a suitable geometric numerical integrator for the Hamiltonian flow; and (iii) derivation of an accept/reject rule to ensure preservation of [Pi] when using the above numerical integrator instead of the actual Hamiltonian flow. Experiments are reported that compare the new algorithm with standard HMC and with a version of the Langevin MCMC method defined on a Hilbert space.Hamiltonian dynamics Splitting technique Absolute continuity Hybrid Monte Carlo

First-principles calculation of the magnetic properties of paramagnetic fcc iron

Using the disordered local moment picture of itinerant magnetism, we present calculations of the temperature and volume dependence of the magnetic moment and spin-spin correlations for fcc Fe in the paramagnetic state. These calculations are based on the parameter-free, first principles approach of local spin density functional theory and the coherent potential approximation is used to treat the disorder associated with the random orientation of the local moments

Hybrid Monte Carlo on Hilbert spaces

The Hybrid Monte Carlo (HMC) algorithm provides a framework for sampling from complex, high-dimensional target distributions. In contrast with standard Markov chain Monte Carlo (MCMC) algorithms, it generates nonlocal, nonsymmetric moves in the state space, alleviating random walk type behaviour for the simulated trajectories. However, similarly to algorithms based on random walk or Langevin proposals, the number of steps required to explore the target distribution typically grows with the dimension of the state space. We define a generalized HMC algorithm which overcomes this problem for target measures arising as finite-dimensional approximations of measures pi which have density with respect to a Gaussian measure on an infinite-dimensional Hilbert space. The key idea is to construct an MCMC method which is well defined on the Hilbert space itself. We successively address the following issues in the infinite-dimensional setting of a Hilbert space: (i) construction of a probability measure Pi in an enlarged phase space having the target pi as a marginal, together with a Hamiltonian flow that preserves Pi; (ii) development of a suitable geometric numerical integrator for the Hamiltonian flow; and (iii) derivation of an accept/reject rule to ensure preservation of Pi when using the above numerical integrator instead of the actual Hamiltonian flow. Experiments are reported that compare the new algorithm with standard HMC and with a version of the Langevin MCMC method defined on a Hilbert space

Self-consistent electronic structure of alpha-phase Hume-Rothery electron compound alloys Cu/sub c/Zn/sub 1-c/, Cu/sub c/Ga/sub 1-c/, and Cu/sub c/Ge/sub 1-c/

We have performed charge self-consistent electronic structure calculations for the ..cap alpha..-phase Hume-Rothery electron compound alloys Cu/sub c/Zn/sub 1-c/, Cu/sub c/Ga/sub 1-c/, and Cu/sub c/Ge/sub 1-c/ having electron to atom ratios 1:1, 1:2, and 1:3 for each alloy series. The calculations are based on the self-consistent-field Korringa-Kohn-Rostoker coherent-potential approximation (KKR-CPA). We show results for the densities of states and Fermi surface of these alloys; the behavior of these quantities is quite different from that predicted on the basis of the rigid band model. We also show results for the ground state properties of the Cu/sub c/Zn/sub 1-c/ alloys that were obtained on the basis of a recent generalization of the density functional theory to random alloys. The theory provides a basis for understanding the concentration variation of the lattice parameter (Vegards' Law) of Cu/sub c/Zn/sub 1-c/ alloys at the microscopic quantum mechanical level