The Precision Determination of Lattice Constants by the Powder and Rotating Crystal Methods and Applications

Abstract

A method that makes possible the attainment of a very high degree of precision in the determination of lattice constants (in some cases more than 1:200,000, even with crystals of lower symmetry) is described. The method and its applications, which has been in steady development since 1934 (in Riga, University of Latvia), tries to eliminate the errors of the Debye-Scherrer-Hull and rotating crystal methods by a careful experimental technique, based on: (1) Very exactly built cameras of a reasonable diameter (64 mm); (2) Elimination of all well-known errors of the powder and rotating crystal methods (e.g., elimination of film shrinkage errors by a new method of putting the film into the camera); (3) Locating the camera in a specially constructed thermostat so that the temperature some hours before and during exposure is kept constant. The films obtained in this way are very clear, especially in the important back-reflection region, with distinct lines (or spots) that can be measured exactly. As no standard substances are necessary and the absorption corrections are negligible (using very thin samples), the method must be regarded absolute. Of course, the sample (crystal) must be prepared, mounted, and centered under the microscope, a procedure that is not difficult. Applications: lattice constants and expansion coefficients (even within the range of 10°C); quantitative solubility determinations; appearance of new phases and transition points; the determination of the exact value of Avogadro's number; molecular and atomic weight determinations (if the exact density values are known); statement of imperfections in crystals.