Norm minimized Scattering Data from Intensity Spectra

We apply the $l_1$ minimizing technique of compressive sensing (CS) to non-linear quadratic observations. For the example of coherent X-ray scattering we provide the formulae for a Kalman filter approach to quadratic CS and show how to reconstruct the scattering data from their spatial intensity distribution.Comment: 26 pages, 10 figures, reordered section

Glass transition in Ultrathin Polymer Films : A Thermal Expansion Study

Glass transition process gets affected in ultrathin films having thickness comparable to the size of the molecules. We observe systematic broadening of glass transition temperature (Tg) as the thickness of the polymer film reduces below the radius of gyration but the change in the average Tg was found to be very small. Existence of reversible negative and positive thermal expansion below and above Tg increased the sensitivity of our thickness measurements performed using energy dispersive x-ray reflectivity. A simple model of Tg variation as a function of depth expected from sliding motion could explain the results. We observe clear glass transition even for 4 nm polystyrene film that was predicted to be absent from ellipsometry measurements of thicker films.Comment: 11 pages, 5 figure

Surface morphology and magnetic anisotropy in (Ga,Mn)As

Atomic Force Microscopy and Grazing incidence X-ray diffraction measurements have revealed the presence of ripples aligned along the $[1\bar{1}0]$ direction on the surface of (Ga,Mn)As layers grown on GaAs(001) substrates and buffer layers, with periodicity of about 50 nm in all samples that have been studied. These samples show the strong symmetry breaking uniaxial magnetic anisotropy normally observed in such materials. We observe a clear correlation between the amplitude of the surface ripples and the strength of the uniaxial magnetic anisotropy component suggesting that these ripples might be the source of such anisotropy.Comment: 3 pages, 4 figures, 1 table. Replaced with published versio

Crystal truncation rods in kinematical and dynamical x-ray diffraction theories

Crystal truncation rods calculated in the kinematical approximation are shown to quantitatively agree with the sum of the diffracted waves obtained in the two-beam dynamical calculations for different reflections along the rod. The choice and the number of these reflections are specified. The agreement extends down to at least $\sim 10^{-7}$ of the peak intensity. For lower intensities, the accuracy of dynamical calculations is limited by truncation of the electron density at a mathematically planar surface, arising from the Fourier series expansion of the crystal polarizability