Microabsorption of X-ray intensity in randomly packed powder specimens

The microabsorption of X-rays diffracted from planar granular powder specimens is caused by bulk porosity and surface roughness of the material. Methods of stochastic geometry are used to describe the geometrical characteristics of powder by volume fraction, mean chord length of powder particles, and density-density correlation function (covariance). Towards the surface of the specimen, the volume fraction of powder particles decays continuously from the bulk value to zero. Within the framework of the kinematic theory, analytical expressions are derived for both bulk and surface contributions to the microabsorption of symmetrically diffracted X-rays in randomly packed powder specimens with particles of irregular shape. Previous theoretical estimates and empirical formulae are discussed as limiting cases of the present more general results.