# Reciprocal lattice and the metric tensor

## Presentation on theme: "Reciprocal lattice and the metric tensor"— Presentation transcript:

Reciprocal lattice and the metric tensor
Concept of a metric and the dual space is known from the theory of relativity -line element ds measuring the distance between 2 neighboring events in space time reads metric tensor coordinate differentials -in flat space time with coordinates In 3D real space we can represent a vector by its coordinates xi according to basis vectors

Changing the basis to changes the coordinates Matrix A and B are related according to -quantities with a subscript transform like the basis vectors and are called covariant -quantities with a superscript transform like the coordinates are called countervariant Now we construct a new set of basis vectors, the countervariant basis, which is identical to the basis of the reciprocal space Consider the scalar product metric tensor where -as we know from relativity