What is the reciprocal lattice to a fcc lattice?
The reciprocal lattice to an FCC lattice is the body-centered cubic (BCC) lattice. Consider an FCC compound unit cell.
How do you do reciprocal lattice?
- To get the reciprocal lattice in 3D, we need 3 basis vectors.
- These are defined using the basis vectors of the crystal as below, where V is the volume of the unit cell.
- The magnitude of the reciprocal lattice basis vector is (1/corresponding interplanar spacing).
What is the use of reciprocal lattice?
The reciprocal lattice to the direct space x-lattice obtained by Fourier transform into the k-space , is a basis for construction of the theory of condensed matter physics. It enables to formulate Bloch theory of electrons and of other quasiparticles by diagonalization the lattice Hamiltonians in k-space.
What is the dimension of a reciprocal lattice vector?
The reciprocal lattice of the simple cubic lattice is itself a simple cubic lattice with the length of each side being 2π/a.
What is the reciprocal lattice of a primitive vector?
Then the reciprocal lattice primitive vector is: 2D lattice: If the direct lattice is in the x-y plane and the primitive vectors are: and area of primitive cell is: Then the reciprocal lattice primitive vectors are:
How do you find the reciprocal lattice?
Now we define the reciprocal lattice as the set of wave vectors →k k → for which the corresponding plane waves Ψk(→r) Ψ k ( r →) have the periodicity of the Bravais lattice →R R → . Thus we are looking for all waves Ψk(r) Ψ k ( r) that remain unchanged when being shifted by any reciprocal lattice vector →R R →.
What is a reciprocal lattice plane?
(A lattice plane is a plane crossing lattice points.) The direction of the reciprocal lattice vector corresponds to the normal to the real space planes. The magnitude of the reciprocal lattice vector is given in reciprocal length and is equal to the reciprocal of the interplanar spacing of the real space planes.
What is reciprocal lattice vector in X-ray diffraction?
In neutron and X-ray diffraction, due to the Laue conditions, the momentum difference between incoming and diffracted X-rays of a crystal is a reciprocal lattice vector. The diffraction pattern of a crystal can be used to determine the reciprocal vectors of the lattice. Using this process, one can infer the atomic arrangement of a crystal.