Extracting information from X-ray diffraction patterns containing Laue oscillations

Abstract

The presence of Laue oscillations in a film grown on a solid surface is broadly taken as indicating a high quality, crystallographically aligned film of the targeted compound. In this paper we briefly review the origins of both Laue oscillations and Kiessig fringes and show how they can be used together to determine if extra thickness exists above or below the coherently diffracting domains. The differences between experimental and “ideal” films are discussed and the effect of structural features (roughness, different thickness coherently diffracting domains and thickness in addition to the coherently diffracting domains) are illustrated with experimental and simulated data for metal and mixed-metal chalcogenide films of titanium, bismuth, vanadium/iron, and bismuth/molybdenum. Examples are given showing how quantitative information can be extracted from experimental diffraction patterns.

Ultrasmooth Epitaxial Pt Thin Films Grown by Pulsed Laser Deposition

“…The sample deposited at 300 °C in Ar + O 2 possesses the highest crystal quality, showing oscillations in a more extended range. The out-of-plane domain size ( L ⊥ ), determined from Scherrer’s equation, is close to the thickness determined by XRR ( t ), confirming no additional thickness above or below the coherently diffracting domains . The conductivities of the samples deposited at 300 °C are among the highest in this study (>6 × 10 6 S/m).…”

Expanding the Composition Range of Transition Metal Dichalcogenide Alloys, Fex(FeyV1–ySe2)

“…Compositions from XRF data, thickness measurements from XRR data, analysis of Laue oscillations in specular XRD patterns, analysis of cross-sectional STEM-EDS data, and Rietveld refinements of diffraction patterns were used to quantify the amounts of substitution, intercalation, and potential impurity phases . The specular XRD patterns for samples 2 – 4 and 6 – 8 each contain Laue oscillations on either side of the 001 Bragg reflection (Figure ), from which the average number of coherently diffracting dichalcogenide unit cells in each sample can be determined . Patterns with Laue oscillations that extend to greater ranges of 2θ values around the Bragg peak, such as that for sample 2 , indicate that the majority of the crystalline domain thicknesses in the sample are narrowly distributed around the average.…”

“…h i b i t e d .side of the 001 Bragg reflection (Figure7), from which the average number of coherently diffracting dichalcogenide unit cells in each sample can be determined 40. Patterns with Laue oscillations that extend to greater ranges of 2θ values around the Bragg peak, such as that for sample 2, indicate that the majority of the crystalline domain thicknesses in the sample are narrowly distributed around the average.…”

Method to Determine the Distribution of Substituted or Intercalated Ions in Transition-Metal Dichalcogenides: FexVSe2 and Fe1–xVxSe2

“…Laue oscillations are clearly visible on either side of the 001 peak (Figure b). Laue oscillations arise from the incomplete destructive interference from a finite number of coherently diffracting unit cells and can be used to calculate the number of unit cells in a coherently diffracting domain (CDD) . The Laue oscillations in Figure b correspond to 44 unit cells in the CDD.…”

“…Laue oscillations arise from the incomplete destructive interference from a finite number of coherently diffracting unit cells and can be used to calculate the number of unit cells in a coherently diffracting domain (CDD). 43 The Laue oscillations in Figure 1b Å]. The Kiessig fringes, which are also apparent in Figure 1b at low angles, were used to calculate the total film thickness of 271.0(2) Å using a modified form of Bragg's law to account for refraction.…”