A method for the accurate determination of crystal truncation rod intensities by X-ray diffraction

A method is described for determining the structure factor F(Q) at a scattering vector Q along a crystal truncation rod (CTR) by measuring the total power diffracted with the crystal fixed. When a detector collects the entire diffracted beam, P_CTR/ P₀ = _pσT[λ|F(Q)|/a₀ sin θ sin χ]², where P₀ and P_CTR are the powers of the incident and diffracted beams, p is a polarization factor, σ_T is the Thompson cross section, λ is the X-ray wavelength, a₀ is the area of a two-dimensional unit cell and θ and χ are diffractometer angles. No terms due to instrumental resolution are required for measurement of the structure factor. Simple expressions are derived relating structure factors to the integrated intensity of rocking curves employing a receiving slit wide enough to accept the diffracted beam in one direction only. Measurements employing a narrow slit are useful in measuring CTR intensity at grazing incidence (i.e. small perpendicular momentum transfer) or for specular reflection (i.e. small parallel momentum transfer). For the more general case (large perpendicular and parallel momentum transfer), accurate measurements are more easily made when the detector collects the entire diffracted beam