Effects of porosity and surface roughness on the X-ray intensity reflected from a powder specimen

The effects of specimen granularity in the reflection method of powder diffractometry are isolated by comparing the fluorescent intensity from a large number of Cu powder specimens to that from a polished bulk sample. The fluorescence radiation is excited by monochromatic Mo Kα radiation. An approximate relationship between the reduction in the fluorescence intensity and that in the Bragg scattering is presented. The average chord lengths inside particles and pores are introduced as unambiguous and relevant packing parameters and practical methods of determining them are described. In the fluorescence measurements, intensity reductions due to both the average porosity and surface roughness are observed, and the components are separated through a model calculation. The porosity reduction is independent of the scattering angle except close to normal incidence, where the effect vanishes. The magnitude of the effect is P₀ = −ΔI/I = (0.42±0.08)(1−α)/μ₁, where α is the relative density of the specimen, μ the linear absorption coefficient of the solid, and ₁ the average chord length inside the particles. The surface roughness effect is found to depend on the type of powder and on the compaction pressure; the effect practically vanishes for slightly compressed powders of regular particle shapes. Implications in regard to powder diffraction measurements are discussed and a procedure of correcting for the granularity effects is described.