Download presentation

Presentation is loading. Please wait.

1
**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

2
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

3
**The new reciprocal basis reads**

Let’s show that the form really a set of basis vectors coordinates with respect to the reciprocal basis Note: in the lecture we introduced reciprocal basis vectors so that Application in solid state physics -we have basis vectors (not necessarily orthogonal) Metric tensor Reciprocal lattice vectors

4
**-We know from the conventional approach**

As an example let’s consider the reciprocal lattice of the bcc lattice in real space -We know from the conventional approach bcc: a1=a(½, ½,-½), a2=a(-½, ½,½) and a3=a(½,- ½,½) and -Now we use the metric tensor etc.

Similar presentations

OK

AGC DSP AGC DSP Professor A G Constantinides©1 Signal Spaces The purpose of this part of the course is to introduce the basic concepts behind generalised.

AGC DSP AGC DSP Professor A G Constantinides©1 Signal Spaces The purpose of this part of the course is to introduce the basic concepts behind generalised.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on credit default swaps aig Ppt on management by objectives Ppt on self awareness activities Ppt on touch screen controlled robot Ppt on p/e ratio Ppt on power line communications Ppt on 2nd world war deaths Ppt on group development phases Ppt on rc coupled amplifier experiment Ppt on db2 mainframes definition