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M. Velasquez

Publications and source records attributed to M. Velasquez.

2 recordsLinked to original sources

Growth of Ca$_2$MnO$_4$ Ruddlesden-Popper structured thin films using Combinatorial Substrate Epitaxy

The local epitaxial growth of pulsed laser deposited Ca$_2$MnO$_4$ films on polycrystalline spark plasma sintered Sr$_2$TiO$_4$ substrates was investigated to determine phase formation and preferred epitaxial orientation relationships ($ORs$) for isostructural Ruddlesden-Popper (RP) heteroepitaxy, further developing the high-throughput synthetic approach called Combinatorial Substrate Epitaxy (CSE). Both grazing incidence X-ray diffraction and electron backscatter diffraction (EBSD) patterns of the film and substrate were indexable as single-phase RP-structured compounds. The optimal growth temperature (between 650 $^{\circ}$C and 800 $^{\circ}$C) was found to be 750 $^{\circ}$C using the maximum value of the average image quality (IQ) of the backscattered diffraction patterns. Films grew in a grain-over-grain pattern such that each Ca$_2$MnO$_4$ grain had a single $OR$ with the Sr$_2$TiO$_4$ grain on which it grew. Three primary $ORs$ described 47 out of 49 grain pairs that covered nearly all of RP orientation space. The first $OR$, found for 20 of the 49, was the expected RP unit-cell over RP unit-cell $OR$, expressed as [100][001]$_{film}$||[100][001]$_{sub}$. The other two $ORs$ were essentially rotated from the first by 90$^{\circ}$, with one (observed for 17 of 49 pairs) being rotated about the [100] and the other (observed for 10 of 49 pairs) being rotated about the [110] (and not exactly by 90$^{\circ}$). These results indicate that only a small number of $ORs$ are needed to describe isostructural RP heteroepitaxy and further demonstrate the potential of CSE in the design and growth of a wide range of complex functional oxides.

cond-mat.mtrl-sci

On the Geometry of Conformally Stationary Lorentz Spaces

In this paper we study several aspects of the geometry of conformally stationary Lorentz manifolds, and particularly of GRW spaces, due to the presence of a closed conformal vector field. More precisely, we begin by extending to these spaces a result of J. Simons on the minimality of cones in Euclidean space, and apply it to the construction of complete, noncompact maximal submanifolds of both de Sitter and anti-de Sitter spaces. Then we state and prove very general Bernstein-type theorems for spacelike hypersurfaces in conformally stationary Lorentz manifolds, one of which not assuming the hypersurface to be of constant mean curvature. Finally, we study the strong $r$-stability of spacelike hypersurfaces of constant $r$-th mean curvature in a conformally stationary Lorentz manifold of constant sectional curvature, extending previous results in the current literature.

math.DG