Strain and Precision Lattice Parameter Measurements by the X-Ray Divergent Beam Method. I

An X-ray method is described which permits a precise determination of the interplanar spacings in a crystal. The method is capable of disclosing small differences in interplanar spacings even between various sets of (hkl) planes of the same form and, therefore, serves as a basis for a stress-strain analysis. An error analysis of this method shows that the minimum measurable strains in the lattice, expressed as Δd/d, are a function of the diffraction angle θ. For θ varying from 35° to 65°, the minimum measurable strains vary from 0.03% to 0.009%. A precision determination of the lattice parameter of a zone-refined tungsten crystal yielded a0=3.16566±0.00002 Å. Limitations and possible applications of the method to problems in physical metallurgy and solid state physics are presented.