Metastable and transient states of chemical ordering in Fe-V nanocrystalline alloys

Chemical ordering of the disordered alloys Fe0.78V0.22, Fe0.53V0.47, Fe0.39V0.61, and Fe0.37V0.63 was performed by annealing at temperatures from 723 to 973 K. The initial state of chemical disorder was produced by high-energy ball milling, and the evolution of order was measured by neutron diffractometry and by 57Fe Mössbauer spectrometry. The hyperfine magnetic field distributions obtained from the Mössbauer spectra provided quantitative measurements of the number of antisite Fe atoms in the partially ordered alloys. The long-range order parameters in steady state after long annealing times were used as states of metastable equilibrium for a generally successful comparison with the metastable Fe-V phase diagram calculated by Sanchez et al. [Phys. Rev. B 54, 8958 (1996)]. For the metastable equilibrium state of order in Fe0.53V0.47 at low temperatures, the order parameters were smaller than expected. This corresponded to an abundance of antisite atoms, which were not removed effectively by annealing at the lower temperatures

In an Ising model with spin-exchange dynamics damage always spreads

We investigate the spreading of damage in Ising models with Kawasaki spin-exchange dynamics which conserves the magnetization. We first modify a recent master equation approach to account for dynamic rules involving more than a single site. We then derive an effective-field theory for damage spreading in Ising models with Kawasaki spin-exchange dynamics and solve it for a two-dimensional model on a honeycomb lattice. In contrast to the cases of Glauber or heat-bath dynamics, we find that the damage always spreads and never heals. In the long-time limit the average Hamming distance approaches that of two uncorrelated systems. These results are verified by Monte-Carlo simulations.Comment: 5 pages REVTeX, 4 EPS figures, final version as publishe

Study of Alpha-Sigma Phase Transformation in Mechanically Alloyed Fe-Cr-Sn Alloys

The solubility of tin is significantly extended by mechanical alloying in near equiatomic Fe-Cr alloys. The influences of Sn concentration and of grain size on the kinetics of formation of the sigma-phase have been studied using different techniques. The sigma-phase formation is much faster for as-milled alloys than it is for conventional alloys. The sigma-phase formation rate decreases with the increase of Sn concentration in alloys with nanometer-sized grains as it does in coarse-grained alloys. The mechanisms which are responsible for the slowing-down of the alpha-sigma transformation are different in both kinds of alloys

Spectral fluctuations of tridiagonal random matrices from the beta-Hermite ensemble

A time series delta(n), the fluctuation of the nth unfolded eigenvalue was recently characterized for the classical Gaussian ensembles of NxN random matrices (GOE, GUE, GSE). It is investigated here for the beta-Hermite ensemble as a function of beta (zero or positive) by Monte Carlo simulations. The fluctuation of delta(n) and the autocorrelation function vary logarithmically with n for any beta>0 (1<<n<<N). The simple logarithmic behavior reported for the higher-order moments of delta(n) for the GOE (beta=1) and the GUE (beta=2) is valid for any positive beta and is accounted for by Gaussian distributions whose variances depend linearly on ln(n). The 1/f noise previously demonstrated for delta(n) series of the three Gaussian ensembles, is characterized by wavelet analysis both as a function of beta and of N. When beta decreases from 1 to 0, for a given and large enough N, the evolution from a 1/f noise at beta=1 to a 1/f^2 noise at beta=0 is heterogeneous with a ~1/f^2 noise at the finest scales and a ~1/f noise at the coarsest ones. The range of scales in which a ~1/f^2 noise predominates grows progressively when beta decreases. Asymptotically, a 1/f^2 noise is found for beta=0 while a 1/f noise is the rule for beta positive.Comment: 35 pages, 10 figures, corresponding author: G. Le Cae

On random flights with non-uniformly distributed directions

This paper deals with a new class of random flights $\underline{\bf X}_d(t),t>0,$ defined in the real space $\mathbb{R}^d, d\geq 2,$ characterized by non-uniform probability distributions on the multidimensional sphere. These random motions differ from similar models appeared in literature which take directions according to the uniform law. The family of angular probability distributions introduced in this paper depends on a parameter $\nu\geq 0$ which gives the level of drift of the motion. Furthermore, we assume that the number of changes of direction performed by the random flight is fixed. The time lengths between two consecutive changes of orientation have joint probability distribution given by a Dirichlet density function. The analysis of $\underline{\bf X}_d(t),t>0,$ is not an easy task, because it involves the calculation of integrals which are not always solvable. Therefore, we analyze the random flight $\underline{\bf X}_m^d(t),t>0,$ obtained as projection onto the lower spaces $\mathbb{R}^m,m<d,$ of the original random motion in $\mathbb{R}^d$. Then we get the probability distribution of $\underline{\bf X}_m^d(t),t>0.$ Although, in its general framework, the analysis of $\underline{\bf X}_d(t),t>0,$ is very complicated, for some values of $\nu$, we can provide some results on the process. Indeed, for $\nu=1$, we obtain the characteristic function of the random flight moving in $\mathbb{R}^d$. Furthermore, by inverting the characteristic function, we are able to give the analytic form (up to some constants) of the probability distribution of $\underline{\bf X}_d(t),t>0.$Comment: 28 pages, 3 figure

Differences between regular and random order of updates in damage spreading simulations

We investigate the spreading of damage in the three-dimensional Ising model by means of large-scale Monte-Carlo simulations. Within the Glauber dynamics we use different rules for the order in which the sites are updated. We find that the stationary damage values and the spreading temperature are different for different update order. In particular, random update order leads to larger damage and a lower spreading temperature than regular order. Consequently, damage spreading in the Ising model is non-universal not only with respect to different update algorithms (e.g. Glauber vs. heat-bath dynamics) as already known, but even with respect to the order of sites.Comment: final version as published, 4 pages REVTeX, 2 eps figures include

Chaotic behavior and damage spreading in the Glauber Ising model - a master equation approach

We investigate the sensitivity of the time evolution of a kinetic Ising model with Glauber dynamics against the initial conditions. To do so we apply the "damage spreading" method, i.e., we study the simultaneous evolution of two identical systems subjected to the same thermal noise. We derive a master equation for the joint probability distribution of the two systems. We then solve this master equation within an effective-field approximation which goes beyond the usual mean-field approximation by retaining the fluctuations though in a quite simplistic manner. The resulting effective-field theory is applied to different physical situations. It is used to analyze the fixed points of the master equation and their stability and to identify regular and chaotic phases of the Glauber Ising model. We also discuss the relation of our results to directed percolation.Comment: 9 pages RevTeX, 4 EPS figure

A ^(119)Sn Mössbauer Spectrometry Study of Li-SnO Anode Materials for Li-Ion Cells

Anodes of SnO were charged reversibly with Li to capacities greater than 600 mAh/g, The anode materials were characterized by 119Sn Mössbauer spectrometry at 11 and 300 K, and by X-ray diffractometry at 300 K. Trends in the valence of Sn were as expected when the Sn oxides are reduced in the presence of Li. At low Li capacities the SnO is reduced to small particles of β-Sn, and with increasing Li capacity an alloy of Li_(22)Sn_5 is formed. Although the Li_(22)Sn_5 develops over a range of Li concentrations in the anode material, the Li_(22)Sn_5 that forms at low Li insertions is not typical of bulk Li_(22)Sn_5 in either its structural or electrochemical properties. The recoil-free fraction of the Sn oxide (and perhaps the metallic Sn) in the anode materials showed an anomalously large temperature dependence. This is indicative of nanoparticles or a severely defective structure. We monitored the changes in the Li-SnO and Li-Sn materials during atmospheric exposure over times up to 2 months. This oxidation process of Sn was very much the reverse of the Sn reduction during the Li insertion, although it occurred over a much longer time scale. We also report the temperature dependencies of recoil-free fractions for standard samples of β-Sn, SnO_2, and the alloy Li_(22)Sn_5