Procedure

This experiment is about finding the reciprocal vectors for a given lattice. In theory, a lattice is infinite, but for the sake of simplicity we have finite lattice. The experiment contains 4 lattices which are simple cubic, body centered cubic, face centered cubic and hexagonal closed packing lattice.

Finding reciprocal vectors

The first step involves finding primitive vectors for a given lattice. Once that is done, the relations mentioned earlier can be used to find the reciprocal vectors.

The steps to the experiment are given below

• The interface will contain a canvas in which the different finite lattices in question are shown.
• The interface contains a dropdown to select lattice, a button to select atoms (which is a toggle switch) and a button to check the choice made.
• Usually, a lattice point is chosen to be the origin of these reciprocal vectors and the vectors are drawn out from there. But in this experiment, such a concept does not exist.
• It is expected that atoms are selected sequentially as head and tail of primitive vectors of the lattice and that all atoms are unique. It is expected that different atoms which have similar surroundings to the so called origin lattice point is chosen and then a corresponding lattice point is chosen which together creates one primitve vector.
• Even though the vectors obtained do not have a common origin, they are brought to a common origin during evaluation of the selection, retaining the validity of the selection if the magnitudes and directions of the vectors obtained are correct.
• It is required that not only the direction of the vectors chosen are right but also their magnitudes. Once the atoms are picked in the above mentioned order, the validness of the selection can be tested.

Note

Some lattices have been showed with an atom radius that is smaller than the mathematically proven one to help with the visibility of the lattice points to the user.