Accurate d-spacings from zero-order Laue zone patterns

Experimental d-spacing values are criteria towards the identification of crystallites by electron diffraction. Conclusive identifications often rely on accurate d-spacings. It is shown here that accurate orthogonal components (in mm) for the primitive unit vectors of a zero-level diffraction pattern can be obtained through least-squares processing of (x,y) coordinates for all spots on the film. Valid vectors from the origin spot to any spot in the plane of the film are integer linear combinations of the two selected unit vectors. Accurate lengths and standard deviations for such vectors therefore can be calculated from the least-squares results. Corresponding d-spacings can then be calculated from the vector lengths on the film and the camera constant. In order to obtain d-spacing values that are not only precise, but also accurate, an accurate value of the camera constant should be used. This requires calibration of the experimental setup with reference materials in the same experimental conditions, with careful control of the sample height. For the same quality of measurements, the improvement in the accuracy of the d-spacings obtained with the proposed method is approximately proportional to the square root of the number of measurements taken. Practically, typical improvement in accuracy is about threefold, and accuracies of a fraction of a percent in d-spacings are achievable in this way. The above approach has been programmed as an option in the NRCBED program.