Theoretical stability,thin film synthesis and transport properties of the Mon +1GaCn MAX phase

The phase stability of Mo_{n +1}GaC_n has been investigated using ab‐initio calculations. The results indicate stability for the Mo₂GaC phase only, with a formation enthalpy of –0.4 meV per atom. Subsequent thin film synthesis of Mo₂GaC was performed through magnetron sputtering from elemental targets onto Al₂O₃ [0001], 6H‐SiC [0001] and MgO [111] substrates within the temperature range of 500 °C and 750 °C. High structural quality films were obtained for synthesis on MgO [111] substrates at 590 ºC. Evaluation of transport properties showed a superconducting behavior with a critical temperature of approximately 7 K, reducing upon the application of an external magnetic field. The results point towards the first superconducting MAX phase in thin film form. (© 2015 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

Efficient computation of Lyapunov functions for nonlinear systems by integrating numerical solutions

Nonlinear Dynamics - A strict Lyapunov function for an equilibrium of a dynamical system asserts its asymptotic stability and gives a lower bound on its basin of attraction. For nonlinear systems,...     

The ferric/ferrous ratio in basalt melts at different oxygen pressures

Samples of two types of natural basalt were equilibrated over a range of oxygen pressures at four different temperatures, and then quenched to room temperature. Except at the lowest temperature, where magnetic crystals formed under the most oxidizing conditions, totally amorphous samples were obtained. The Mössbauer spectra of 45 samples of the quenched basaltic melts were measured at room temperature. The relationship obtained between the oxidation state and oxygen fugacity differs to some extent from those relations previously described in the literature, in not yielding a linear relationship between log(farric/ferrous) and log(fo₂). This might indicate a more involved redox process than that described by a simple reaction between oxides and/or the influence of the cation composition in the process of glass formation. An investigation was made of the kinetics of the redox process. For the experimental setup used, redox equilibrium would be reached within three hours. Finally, three naturally quenched basalt glasses were analyzed for comparison; two showed lower oxidation states than previously found in Icelandic rocks.     

Phase stability of Crn+ 1GaCn MAX phases from first principles and Cr2GaC thin‐film synthesis using magnetron sputtering from elemental targets

Ab‐initio calculations have been used to investigate the phase stability and magnetic state of Cr_{n+ 1}GaC_n MAX phase. Cr₂GaC (n = 1) was predicted to be stable, with a ground state corresponding to an antiferromagnetic spin configuration. Thin‐film synthesis by magnetron sputtering from elemental targets, including liquid Ga, shows the formation of Cr₂GaC, previously only attained from bulk synthesis methods. The films were deposited at 650 °C on MgO(111) substrates. X‐ray diffraction and high‐resolution transmission electron microscopy show epitaxial growth of (000?) MAX phase. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stopping Rules for the Stochastic Nested Partitions Method

We have recently developed a global optimization methodology for solving combinatorial problems with either deterministic or stochastic performance functions. This method, the Nested Partitions (NP) method has been shown to generate a Markov chain and with probability one to converge to a global optimum. In this paper, we study the rate of convergence of the method through the use of Markov Chain Monte Carlo (MCMC) methods, and use this to derive stopping rules that can be applied during simulation-based optimization. A numerical example serves to illustrate the feasibility of our approach.