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 die crystal fixed. When a detector collects the entire diffracted beam, P(CTR)/P0 = psigma(T)[lambda\F(Q)\/a0 sin theta sin chi]2, where P0 and P(CTR) are the powers of the incident and diffracted beams, p is a polarization factor, sigma(T) is the Thompson cross section, lambda is the X-ray wavelength, a0 is the area of a two-dimensional unit cell and theta and chi 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.