X-Ray Determination of a Crystal System

Extract

The Debye Scherrer method (1917) of determining a crystal system by observation of X-ray interferences on randomly oriented crystal particles amounts in the mathematical problem to deriving quadratic equations for three variables from unknown integer multiples of these variables. In my opinion it is not only physically, but also mathematically reasonable to treat this problem from a geometrical point of view. Let L,M, and N be three non-parallel vectors. Vectors P can be derived by multiplication with the integers n₁, n₂ and n₃, so that

P = n₁L + n₂ M + n₃ N.