Using combinatorial molecular beam epitaxy (COMBE), we have deposited a one-dimensional (1D) combinatorial library of La<sub>2-x</sub>Sr<sub>x</sub>CuO<sub>4</sub> (LSCO) single-crystal thin films with different Sr content above the optimum doping level. A study of this LSCO library allows a detailed evaluation of the COMBE method. We have also developed and tested a custom-made multiple-probe transport measurement set-up that allowed us to measure the <i>R(T)</i> curves from more than 2,000 different samples (pixels in the 1D combinatorial library of LSCO) within one week. We also studied in detail the dependence of the crystal structure (specifically, the <i>c</i>-axis lattice constant) on the Sr content and on the type of epitaxial strain (compressive or tensile). For the films grown on LSAO substrates, we found that the <i>c</i>-axis lattice constant of LSCO films <i>decreased</i> as the Sr content was increased. This we attribute to the reduction in epitaxial strain that occurs because of Sr-doping-induced decrease of in-plane lattice constant of LSCO. Next, we have detected a small deviation of the beam profile from the linear dependence, noticeable for the deposition area larger that 1". If an array of substrates is used whereby some substrates are separated by more than 1" and if the stoichiometry is optimized at or close to the center of the array, in the films positioned at the outer edges of the array this effect causes slight off-stoichiometry and generation of secondary-phase defects.
It has recently been shown that x-ray diffraction from the doped holes in cuprates can be enhanced by 3-4 orders of magnitude by exploiting resonance effects in the oxygen K shell. This new type of anomalous scattering is direct way of probing ground state inhomogeneity in the mobile carrier liquid of high temperature superconductors. Here we describe a model which quantifies the relationship between experimental count rates and the structure factor for doped holes in this technique. We describe first efforts to detect inhomogeneity in thin films of La<sub>2</sub>CuO<sub>4+δ</sub> and report some peculiar observations. We attempt to offer some explanation.