Instabilities and Bifurcations of Nonlinear Impurity Modes

We study the structure and stability of nonlinear impurity modes in the discrete nonlinear Schr{\"o}dinger equation with a single on-site nonlinear impurity emphasizing the effects of interplay between discreteness, nonlinearity and disorder. We show how the interaction of a nonlinear localized mode (a discrete soliton or discrete breather) with a repulsive impurity generates a family of stationary states near the impurity site, as well as examine both theoretical and numerical criteria for the transition between different localized states via a cascade of bifurcations.Comment: 8 pages, 8 figures, Phys. Rev. E in pres

Fast mechanical synthesis, structure evolution, and thermal stability of nanostructured CoCrFeNiCu high entropy alloy

International audienceA powder of equiatomic CoCrFeNiCu high entropy alloy (HEA) was prepared by shortterm (120 min) high energy ball milling (HEBM). Our structural and chemical analysis showed that microsized particles of fcc CoCrFeNiCu with a grain size of 8 nm were obtained after 120 min of HEBM at 694/1388 rpm. The structural/phase evolution of CoCrFeNiCu HEA powder and its thermal stability were explored by high-temperature XRD at 600 °C, 800 °C and 1000 °C, by DSC up to 1500 °C, through the consolidation by SPS at 800 °C and 1000 °C, and characterized using XRD, SEM and EDX analyses. In-situ HT XRD analysis during 5.5 h of annealing showed the involvement of transient phases: the bcc phase that appeared in 1 h of annealing at 600 °C and disappeared at higher temperatures; and the fcc 1 phase (Cu-rich) arising in 2 h of annealing at 800 °C and disappearing at 1000 °C in 3 h of annealing. SPS consolidation at 1000 °C and annealing at 1000 °C for 5.5 h were found to result in the formation of singlephase fcc 2 CoCrFeNiCu alloy with a lean amount of Cu. The melting points for Cu-rich and Cudepleted HEAs were found as 1118 °C and 1288 °C (Calphad calculations) and 1115 °C and 1365 °C (DSC measurements), respectively. SPS consolidation at 1000 °C under a pressure of 50 MPa yielded the single-phase fcc CoCrFeNiCu 0.5 alloy that turned thermodynamically more favorable than the equiatomic one. Thus, we can suppose thereupon, that the equiatomic fcc phase that appears after 120 min of HEBM is metastable because of the excess of Cu atoms. During annealing in the temperature range 800-1000 °C, the Cu-rich fcc 1 phase precipitates from the initial single-phase alloy, while the "mother phase" transforms into the more stable Cudepleted fcc 2 phase. The chemical compositions of Cu-depleted and Cu-rich phases for the SPSconsolidated HEA CoCrFeNiCu alloy (at 800 °C) were determined from TEM-EDX analyses. Optimal combination of short-term HEBM and SPS consolidation can be recommended as a facile route to fabrication of single-phase fcc equiatomic CoCrFeNiCu HEA powders and bulk materials with good structural/elemental homogeneity