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We report a detailed study of the synthesis, composition, magnetic structure, and transport properties of a quasi-one-dimensional antiferromagnet FeBi4S7 that contains chains of edge-sharing FeS6 octahedra. High-resolution powder X-ray diffraction (PXRD) analysis, aided by variation of synthetic conditions, suggests that the true formula of the material is Fe1.2Bi3.8S7, due to the minor substitution of Fe into Bi sites. This finding is in agreement with crystal structure refinement from neutron powder diffraction data as well as with the small band gap of 0.23 eV determined from electrical transport measurements. Analysis of the neutron diffraction pattern collected below the antiferromagnetic ordering temperature of 64 K revealed ferromagnetic coupling between the Fe moments in the chains of FeS6 octahedra. The overall ordering, however, is antiferromagnetic due to the antiparallel arrangement of moments on neighboring chains. The collinear spin arrangement is described by a k-vector (1, 0, 1/2), which indicates doubling of the unit cell in the c direction and the loss of the C-centering translation as compared to the nuclear cell. The ferromagnetic nature of the sulfidebridged chains of Fe2+ ions in FeBi4S7, in contrast to the antiferromagnetic coupling between Fe moments in compounds with similar structural fragments, can be justified by the analysis of metric parameters that characterize the Fe−S bonding in these materials. 

Critical particle size can be determined with known surface energy. The surface enthalpy of yttrium titanate pyrochlores was determined to be 4.07 ± 0.32 J m⁻² by calorimetry, and the lower limit of critical particle size for this is around 5.0 nm.

 

In this paper, we consider the linear convection-diffusion equation in one dimension with periodic boundary conditions, and analyze the stability of fully discrete methods that are defined with local discontinuous Galerkin (LDG) methods in space and several implicit-explicit (IMEX) Runge-Kutta methods in time. By using the forward temporal differences and backward temporal differences, respectively, we establish two general frameworks of the energy-method based stability analysis. From here, the fully discrete schemes being considered are shown to have monotonicity stability, i.e. the$L^2$norm of the numerical solution does not increase in time, under the time step condition$\tau \le \mathcal {F}(h/c, d/c^2)$, with the convection coefficient$c$, the diffusion coefficient$d$, and the mesh size$h$. The function$\mathcal {F}$depends on the specific IMEX temporal method, the polynomial degree$k$of the discrete space, and the mesh regularity parameter. Moreover, the time step condition becomes$\tau \lesssim h/c$in the convection-dominated regime and it becomes$\tau \lesssim d/c^2$in the diffusion-dominated regime. The result is improved for a first order IMEX-LDG method. To complement the theoretical analysis, numerical experiments are further carried out, leading to slightly stricter time step conditions that can be used by practitioners. Uniform stability with respect to the strength of the convection and diffusion effects can especially be relevant to guide the choice of time step sizes in practice, e.g. when the convection-diffusion equations are convection-dominated in some sub-regions.

 

The phase transitions in MnNiGe compounds were explored by manipulating the heat treatment conditions and through hydrostatic pressure application. As the quenching temperature increased, both the first-order martensitic structural transition temperatures and magnetic transition temperatures decreased relative to those in the slowly-cooled samples. When the samples were quenched from 1200 ^∘C, the first-order martensitic structural transition temperature lowered by more than 200 K. The structural transitions also shifted to lower temperature with the application of hydrostatic pressure during measurement. Temperature-dependent x-ray diffraction results reveal that the changes of the cell parameters resulting from the structural transitions are nearly identical for all samples regardless of the extensive variation in their structural transition temperatures. In addition, neutron scattering measurements confirm the magnetic structure transition between simple and cycloidal spiral magnetic structures.