Two Dimensional Lattice: Real and Reciprocal

By Carlos Rivera

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This JAVA applet shows a 2-d lattice in real space and its reciprocal lattice in k-space. The structure factor is represented at each point of the reciprocal lattice by the brightness of the point.

There are two atoms per unit cell. The straight line connecting the atoms goes through the origin of the cell. The purpose of the lines in the Figure is for illustrating the construction; the lines themselves are not part of the crystal. The atoms are assumed to be point-like and the atomic form factor is unity.

The following parameters can be modified:

The length of the two primitive vectors: a₁ and a₂
The angle between the two primitive vectors: phi
The distance between the two atoms in unit the cell: 2*s=b
The angle between the line joining the two atoms in the unit cell and a₁: rho

In the real lattice the distances are given in pixels and the angles in sexagesimal degrees. The scale of the reciprocal lattice is selected arbitrarily so that the resulting plot looks good.

To see the effect of the changes press the button "Replot."

Two Dimensional Lattice: Real and Reciprocal

Important!: Your browser must be configured to run Java.

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