Why the name Reciprocal lattice ?

[mkbh_10]

Why the name Reciprocal lattice ?? Is it because the dimensions get bigger & we are able to understand the structure on a macro level & removing the infinities that occur in h, k, l plane system ??

 

[kanato]

Look at the units, they are reciprocal of length. The reciprocal lattice vectors are defined by $$a_i \cdot g_j = 2\pi \delta_{i,j}$$ so g has to have units that are the inverse of a, and the g vectors for a lattice.

 

[charng]

The term "reciprocal lattice" refers to a mathematical concept in crystallography that is closely related to the concept of a crystal lattice. The reciprocal lattice is a mathematical construct that helps us understand the periodicity and symmetry of a crystal structure, and it is defined as the set of all points in reciprocal space that are equivalent to the original crystal lattice points.

The term "reciprocal" in this context refers to the fact that the reciprocal lattice is the Fourier transform of the crystal lattice. Just as a crystal lattice is a three-dimensional representation of the structure of a crystal, the reciprocal lattice is a three-dimensional representation of the diffraction pattern produced by the crystal. This reciprocal relationship is what gives the lattice its name.

Furthermore, the reciprocal lattice is essential in X-ray crystallography, as it allows us to determine the structure of a crystal by analyzing the diffraction pattern produced when X-rays are scattered off the crystal. The reciprocal lattice helps us to understand the relationship between the positions of atoms in a crystal and the diffraction pattern observed, making it a crucial tool in the study of crystal structures.

Therefore, the name "reciprocal lattice" is based on its fundamental mathematical relationship with the crystal lattice and its important role in understanding the structure of crystals. It is not related to the size or scale of the lattice, but rather to its reciprocal relationship with the crystal lattice and its use in crystallography.