• # How do we define reciprocal lattice in Solid State Physics

Does Physics confuse you? Learnt the definition and other aspects of the reciprocal lattice from this page.

In Solid State physics, we use the term reciprocal lattice for an easier approach to the X-ray diffraction by lattices. I am confused about the definition of the reciprocal lattice. I need an explanation in an easier way. Bragg defined this term as the solution to the complexities of calculations with direct lattice, how does the approach to reciprocal lattice simplify the calculations?

• The technique for finding the crystal structures were limited to the X-ray diffraction from the sample crystals or powdered matter. This is an indirect technique and can give some information on the crystal structure. The methodology adopted is based on the Bragg spots and miller indices. The measurements are made of the angular positions and the intensities. This method gives some indirect assessment of the crystal structure but unfortunately these Bragg peaks, positions and intensity do not image the direct crystal lattice and the atomic arrangements for us.

Subsequently the scientists had thought of some other means to overcome this problem. They have devised a transform or method to convert the angular dispositions in Bragg positions to a lattice mode. This helps in mapping the atomic layers on this lattice where intensities can also be attributed to each point. As this is not the actual lattice but a via media to reach the more information about the actual structure this was named as reciprocal lattice. So, in essence reciprocal lattice is a way ahead to analyse the crystal structure in more details.

If you want to study these things in details consisting of the mathematics involved and other associated academic things then I would suggest you to read the book 'Kittel's Introduction to Solid State Physics' by Charles Kittel.

Knowledge is power.

• To understand the mechanism of Reciprocal Lattice, we need to consider the following points as enlisted below -
1) Reciprocal Lattice is a mathematical derivation explaining the concept of a Fourier - space where the distance between the lattice points is equal to the inverse of the corresponding inter planar d - spacing in the direct lattice.
Lattice is nothing but a set of Mathematical Points in the direct space satisfying the translational symmetry.
2) The vector connecting two points in the reciprocal space is called as the reciprocal lattice vector G.
3) The reciprocal lattice can be constructed for each crystal lattice. The indices of points in the set of reciprocal lattice would indicate the Miller Indices of planes in the direct crystal lattice.
4) X- Ray, Electron and the Neutron diffraction phenomenon can be explained conveniently in terms of reciprocal spacing.
5) Since electrons are considered to be waves in the Quantum Mechanics having wave vector K = 2 pie/ lambda where K is having the same dimension as that of lattice G.
6) The Bloch waves at times interact with the phonons in the crystal to yield finite conductivity. Reciprocal Lattice finds its place while studying the electron - phonons interaction in the periodic crystal.