Calculation of crystal truncation rod structure factors for arbitrary rational surface terminations

The technique of crystal truncation rod (CTR) diffraction is widely used for studying the structure of crystalline surfaces and interfaces. The theory and experimental details of the technique are well established; however, published methods for structure-factor calculations are typically based on a simple surface cell geometry. A method is presented for determining a surface coordinate system which results in a reciprocal lattice that is simply defined in terms of the surface termination. Based on this surface coordinate system, a general formalism for the calculation of CTR structure factors is re-derived, which may be easily applied to any surface that can be represented as a rational plane of a bulk crystal system.