Clarifications of concepts concerning interplanar spacing in crystals with reference to recent publications

Abstract

Large number of papers are published each year on most areas of science, the majority being dependent on previously derived theories. It sometimes seems obvious that the authors have accepted the conventionally accepted theories that are the basis for their work without fully understanding all the details. We have reviewed several recent papers in the field of crystallography and found that several fundamental concepts have been applied in a manner that needs to be clarified. There are important principles imbedded in the conventional definition of Miller indices. Failure in understanding the advantages inherent within this definition has led in some recent publications to an improper redefinition of Miller indices and confusion between the concepts of lattice node and Wyckoff site and between symmetry equivalence and environment equivalence of points in lattice. Related problems involve the misleading claims that the node density among parallel lattice planes with the same Miller indices can be different, and also that lattice interplanar spacing can be different between adjacent parallel lattice planes. In this work, these problems have been clarified. A new method to calculate the relative lattice node density between planes with different Miller indices in a lattice has been developed. It illustrates that in a lattice, the node density of all the other planes with different Miller indices has already been determined if the node density of a particular plane with specified Miller indices is known. Related experimental results have also been discussed. The work shows that it is sometimes problematic for researchers to interpret experimental data via well-known theories without a full understanding of the basic science involved.