Quantitative structural and elastic characterization of superlattices

I present a general procedure for quantitative structural refinement of superlattice structures. To analyze a wide range of superlattices, a general kinematical diffraction model which includes random fluctuations is derived. This model requires only the average structure factor of a single layer of each constituent and is shown to be equivalent to earlier, less general models. By implementing a non-linear fitting algorithm which fits the entire x-ray diffraction spectrum, refined parameters that describe the average superlattice structure, and deviations from this average are obtained.

The results of structural refinement are compared to structural results obtained independently by other measurements. The roughness introduced artificially during growth of Mo/Ni and Nb/Cu superlattices is accurately reproduced by the refinement. The lattice parameters obtained from this refinement procedure are in good agreement with the independent EXAFS and XPD studies on Ag/Mn and transmission x-ray diffraction on Nb/Cu. The relative thicknesses of the layers can be accurately determined, as proven for Cu/Ni in comparison with chemical analysis, for W/Ni compared to the calibrated sputtering rate, and for Mo/Ni compared to the low angle spectrum. The refinement procedure is then extended to study crystalline/amorphous Pb/Ge and high T$\sb{\rm C}$ thin films and superlattices. In high T$\sb{\rm C}$ superlattices, the roughness of the layers, interdiffusion, and lattice strains are quantitatively determined.

The results of the structural characterization are applied to the study of elastic properties of Nb/Cu and Fe/Cu superlattices. The elastic properties for Nb/Cu show the biaxial modulus increases by $\approx$18%, the shear modulus decreases by $\approx$35%, and the flexural modulus does not change with decreasing modulation wavelength. The Fe/Cu superlattices exhibit a structural phase transition as a function of layer thickness in which bcc $\alpha$-Fe transforms into fcc $\gamma$-Fe. The $\alpha$-Fe/Cu superlattices exhibit a $\approx$25% decrease in the shear modulus. This anomalous softening in the shear modulus disappears on formation of $\gamma$-Fe. The elastic anomalies are correlated to structural changes and compared to recent theoretical models.