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Interfacial roughness in superlattices is currently a topic of significant interest as a result of its impact on device applications and its influence on thin-film phenomena. In this work we examine the effects of interfacial roughness on x-ray diffraction from superlattices. By means of a Taylor expansion of the amplitude reflection coefBcient of the multilayer, we present general expressions for the specular, diffuse, and total diffracted intensity from a rough multilayer and examine how these quantities are influenced by roughness distributions and correlations among the interfaces. We present analytical solutions for exemplary structures including superlattices with no roughness, correlated roughness, uncorrelated roughness, and partially correlated roughness. We also present a model for cumulative roughening in multilayers and characterize its diffraction signature. We show how specific configurations of interfacial roughness give rise to a variety of additional features in diffraction spectra beyond the customary pseudo-Debye-Wailer attenuation. Specifically, we illustrate how roughness distributions induce broadening of the diffraction features, and how modulations in the diffuse scattering result directly from interfacial roughness correlations. We also show that partial correlation of interfacial roughness constitutes a second important source of peak broadening.

Small- and large-angle x-ray scattering from epitaxial Fe(001) on an MgO(001) surface has been measured as a function of film thickness, using grazing incidence x-ray scattering. Small-angle scattering shows that for Fe thicknesses less than 15 monolayers, the Fe is islanded with Fe[110]∥MgO[100]. For deposition at 360 °C, the Fe lattice parameter increases toward the MgO surface net spacing with increasing thickness in the 1–10 monolayer coverage regime, and then relaxes back toward the bulk Fe lattice parameter at greater thicknesses. Agglomeration of the islands results in changes in the Fe lattice parameter and in the high-angle peak widths. Prior to agglomeration, the measured in-plane lattice parameter versus thickness is described by a pairwise site interaction between the island and the substrate interface nets. Strain relaxation subsequent to agglomeration is described by continuum elasticity theory.

Due to the large positive heat of mixing associated with the Cu-Cr binary system, solid solutions exist only as nonequilibrium states. In this study, a series of metastable Cu-Cr alloys ranging in composition from 14.1 to 75.4% copper was fabricated by sputter deposition. Symmetric, asymmetric, and grazing incidence x-ray diffraction geometries were used to trace the phase transition from bcc to fee crystal structures with increasing Cu fraction. It is shown that the transition takes place not by a two-phase region suggested by equilibrium thermodynamics, but rather through gradual disordering of the bcc lattice as copper atoms are substitutionally accommodated. At a critical saturation near 71% Cu, the bcc structure becomes unstable relative to the fee and a phase transition occurs. The free energies of the kinetically constrained Cu-Cr system are modeled and the results are found to agree well with observed behavior.

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