Question

(BIOPHYSICS)

In three paragraphs describe what “reciprocal space” is

Answer 1

Reciprocal space is also called Fourier space, k- space, or momentum space in contrast to real space or direct space.However, the distance between the lattice points is equal to the inverse of corresponding inter-planar d-spacing in direct lattice. Here, the word lattice indicates a set of mathematical points in direct space which satisfy translational symmetry.The vector that connects two points in reciprocal space is called as the reciprocal lattice vector ‘G’The reciprocal lattice can be constructed for each direct crystal lattice. The indices of points in reciprocal lattice represent the Miller indices of planes in direct crystal lattice.

Since electrons are treated as waves in quantum mechanics, with a wave vector k=2πλk=2πλ. Here, the wave vector kk has similar dimensions as the reciprocal lattice vector GG. Thus, the electrons present in crystals can be treated mathematically as waves ((Bloch waves) in reciprocal space.The regions in reciprocal space where the Bloch waves can travel are called as allowed energy regions. In contrast, where they can’t travel are called as forbidden energy regions. These regions are formed due to the interaction of Bloch waves with the periodic potential of the crystal under investigation.

The Bloch waves some times interact with the heat carriers (phonons) in crystals to yield finite conductivity. Reciprocal lattice is commonly used to study electron-phonon interactions in periodic crystals.X-ray, electron and neutron diffraction phenomenons can be explained well in reciprocal space. The Ewald sphere construction in reciprocal space is simply a pictorial representation of Bragg’s law.