What is it about?
Three different methods for the derivation of the general formulae of interplanar spacing in a lattice are presented, using elementary geometry, intermediate Cartesian axes, and reciprocal lattice vectors, respectively.
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Why is it important?
The very basic, simple, and essential concepts contained in older classical textbooks are very valuable as they often provide a consistent, effective, and critical basis for reviewing materials already published. Basic principles are still valuable and relevant in current research. Remarkable results are often published by today’s research community but these published materials usually have their basis on fundamental theories developed long ago even though this may not be clearly specified. At the present time, it is unfortunate that work based on clarifying basic principles, can be considered as too fundamental to be published. We hope that the discussions here can increase the popularity of working in areas of fundamental theory and its applications, and attract the attention of researchers to increase their ability to solve new problems with fundamental principles
Perspectives
In molecules the environments of two physical distinct positions can be identical if the positions are related by a specific symmetry operation since direction is unimportant in a molecule. But direction is very important in a crystal and equivalence from one direction cannot ensure equivalence in other directions. The anisotropic properties of the crystal are related to direction. In a lattice, identical environments should be ensured by translation operations, while sites only related by other symmetry operations have less equivalence. That is why Wyckoff sites and lattice nodes are different concepts in crystallography. The properties in a lattice acquired from translation are consistent with the fact that the environments of all nodes in a lattice are identical.
Yue Liu
Shenyang Normal University
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This page is a summary of: Comparison of calculations for interplanar distances in a crystal lattice, Crystallography Reviews, May 2017, Taylor & Francis,
DOI: 10.1080/0889311x.2017.1323332.
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