Phase stability, ordering tendencies, and magnetism in single-phase fcc Au-Fe nanoalloys

Bulk Au-Fe alloys separate into Au-based fcc and Fe-based bcc phases, but L1$_0$ and L1$_2$ orderings were reported in single-phase Au-Fe nanoparticles. Motivated by these observations, we study the structural and ordering energetics in this alloy by combining density functional theory (DFT) calculations with effective Hamiltonian techniques: a cluster expansion with structural filters, and the configuration-dependent lattice deformation model. The phase separation tendency in Au-Fe persists even if the fcc-bcc decomposition is suppressed. The relative stability of disordered bcc and fcc phases observed in nanoparticles is reproduced, but the fully ordered L1$_0$ AuFe, L1$_2$ Au$_3$Fe, and L1$_2$ AuFe$_3$ structures are unstable in DFT. However, a tendency to form concentration waves at the corresponding [001] ordering vector is revealed in nearly-random alloys in a certain range of concentrations. This incipient ordering requires enrichment by Fe relative to the equiatomic composition, which may occur in the core of a nanoparticle due to the segregation of Au to the surface. Effects of magnetism on the chemical ordering are also discussed.Comment: 23 pages, 11 figure

Projective resolution of irreducible modules over tiled order

We indicate the method for computing the kernels of projective resolution of irreducible module over tiled order. On the base of this method we construct projective resolution of irreducible module and calculate the global dimension of tiled order. The evident view of kernels of projective resolution allows to check easily the regularity of tiled order

Tiled orders of width 3

We consider projective cover over tiled order and calculate the kernel of epimorphism from direct sum of submodules of distributive module to their sum

Large Broadening of the Superconducting Transition by Fluctuations in a 3D Metal at High Magnetic Fields: The MgB2_{2} case

It is shown that the transition to the low temperature superconducting state in a 3D metal at high magnetic field is smeared dramatically by thermal fluctuation of the superconducting order parameter. The resulting superconducting-to-normal crossover occurs in a vortex liquid state which is extended well below the mean-field $H_{c2}$. Application to MgB$_{2}$ yields good quantitative agreement with recently reported data of dHvA oscillation in the superconducting state