When the accuracy of a lattice parameter determination is carried beyond about 0.01 % it becomes of special importance to consider the equivalence of λ and θ in solving the Bragg equation for d. A reference angle on the observed diffractometer profile must be identified with the corresponding wavelength, of the incident X-ray spectral distribution. Exact identity is not possible because the diffractometer profiles are broadened, distorted asymmetrically, and displaced from their correct positions by amounts dependent on the shape of the incident spectral lines, the angular separation of the Kα1,2
doublet lines, and the specimen, instrumental, and geometrical aberrations innerent in the experimental method. The aberration functions vary with the experimental conditions and are Bragg-angle-dependent, thereby introducing systematic errors which are not eliminated by extrapolation procedures.
Most of the published diffractometer measurements of lattice parameters have used as the reflection angle, 28, of the diffractometer profile the peak P(2θ) or the midpoint of chords at various heights above background M1/2(2θ), M2/3(2θ), etc., of the Kα1
line. The relationship between these various angular measures of the line profile is not constant; P(2θ) may be equai to, greater than, or less than M1/2(2θ), depending on the asymmetry of the line profile. The X-ray wavelengths currently used in diffractometry refer to the peak P(λ) of the spectral distribution. The use of P(λ) with different angular measures of the diffractometer profiles results in a range of d's from which different values of the lattice parameters are calculated. The selection of arbitrary methods of defining 2θ does not take into account the significant aspects of the diffraction process, nor does it facilitate the correction of the data for systematic errors inherent in the experimental measurements.