Anisotropy analysis of the surface stress and surface energy in Cu surfaces with the modified embedded atom method

Taking Cu as an example, the surface stress and surface energy in three low index surfaces and two families of representative surfaces and belong to [0 0 1]- and -rotating axis respectively, have been calculated using MEAM. For the three low index surfaces, the decrease in the surface energy is small after relaxation, while the surface stresses in the surface planes τ_xx and τ_yy show opposite changes (decreasing and increasing) for inward and outward relaxations. The resulting relaxation direction is related to the normal stress τ_zz before relaxation. For the surfaces of the and families, with the increasing angle α (between the and (1 0 0) planes, and between and (0 0 1) planes, respectively), the surface stress and surface energy go through an oscillatory change. The surface stress and surface energy are symmetric about the planes (1 0 0), (1 1 0) and (0 1 0) at α=0^°, 45^° and 90^°, and about the planes (0 0 1) and (1 1 0) at α=0^° and 90^° respectively, due to crystal symmetry.     

The q-gamma and (q,q)-polygamma functions of Tsallis statistics

An axiomatic definition is given for the q-gamma function of Tsallis (non-extensive) statistical physics, the continuous analogue of the q-factorial of Suyari [H. Suyari, Physica A 368 (1) (2006) 63], and the q-analogue of the gamma function of Euler and Gauss. A working definition in closed form, based on the Hurwitz and Riemann zeta functions (including their analytic continuations), is shown to satisfy this definition. Several relations involving the q-gamma and other functions are obtained. The (q,q)-polygamma functions , defined by successive derivatives of , where ln_qa=(1−q)⁻¹(a^1−q−1),a>0 is the q-logarithmic function, are also reported. The new functions are used to calculate the inferred probabilities and multipliers for Tsallis systems with finite numbers of particles N?∞.     

Scaling and memory effect in volatility return interval of the Chinese stock market

We investigate the probability distribution of the volatility return intervals τ for the Chinese stock market. We rescale both the probability distribution P_q(τ) and the volatility return intervals τ as to obtain a uniform scaling curve for different threshold value q. The scaling curve can be well fitted by the stretched exponential function , which suggests memory exists in τ. To demonstrate the memory effect, we investigate the conditional probability distribution P_q(τ|τ₀), the mean conditional interval 〈τ|τ₀〉 and the cumulative probability distribution of the cluster size of τ. The results show clear clustering effect. We further investigate the persistence probability distribution P_±(t) and find that P₋(t) decays by a power law with the exponent far different from the value 0.5 for the random walk, which further confirms long memory exists in τ. The scaling and long memory effect of τ for the Chinese stock market are similar to those obtained from the United States and the Japanese financial markets.     

Modelling of phase transitions and reaction at CO adsorption on oxygen precovered Pd(1 1 1)

Using the interaction parameters up to the third neighbors and activated form of O and CO diffusion and their reaction, the model has been proposed for Monte-Carlo simulations describing the catalytic O + CO → CO₂ reaction and occurring phase transitions on Pd(1 1 1) surface. Upon adsorption of CO the pre-adsorbed oxygen transforms from p(2 × 2)_O phase into and phases in the limit of room and moderate temperatures, respectively. We demonstrate that the kinetic effects determine both the occurrence of the p(2 × 1)_O and disappearance of the phases at moderate and low temperatures, respectively. Using reaction rate as a fit parameter, we show that at room temperature the start of the reaction can be synchronized with the occurrence of phase.     

Crystal field effect and geometric frustration in Er2Ti2O7 —an XY antiferromagnetic pyrochlore

Magnetic susceptibility of powder Er₂Ti₂O₇ (ErT) is measured between 300 K and 80 K. shows a Curie-Weiss (CW) type behaviour with   ErTiO_3.5 and . A crystal field (CF) analysis of our experimental data, g-values (g_∥=0.27 and g_⊥=7.8) and the positions of two CF levels (reported earlier from an inelastic neutron scattering study) provide CF parameters and CF levels of the ground ⁴I_15/2 and excited multiplets of ErT. The theoretical follows a CW-type behaviour, with . Single-ion magnetic anisotropy (χ_⊥−χ_∥) is 9500×10⁻⁶ emu/mol ErTiO_3.5 at 300 K, which increases by ∼54 times at 10 K and ErT resembles an XY planar system. It can be inferred from CF analysis that the earlier observed change of from −13 K to −22 K below 50 K is not due to the CF effect. Nuclear hyperfine (HF) levels of ¹⁶⁷ErT and ¹⁶⁶ErT are calculated and the theoretical curve of vs. T (K) for T<T_N matches the observed results. Mössbauer lines expected for ¹⁶⁶ErT are also predicted.     

Reverse Monte Carlo simulations and Raman scattering of an amorphous GeSe4 alloy produced by mechanical alloying

The short and intermediate range order of an amorphous GeSe₄ alloy produced by Mechanical Alloying were studied by Reverse Monte Carlo simulations of its X-ray total structure factor and Raman scattering. The simulations were used to compute the , and partial distribution functions and the , and partial structure factors. We calculated the coordination numbers and interatomic distances for the first and second neighbors. The data obtained indicate that the structure of the alloy has important differences when compared to alloys prepared by other techniques. There are a high number of Se-Se pairs in the first shell, and some of the tetrahedral units formed seemed to be connected by Se-Se bridges.