Question

How are the spacings, symmetry, spot intensities, and systematic absences found in a diffraction pattern related to the unit cell of which it is derived? Be sure to define the reciprocal lattice effect and systematic absences.

Answer 1

Spacing: if the radius of each sphere is assumed as 1 cm then the volume of the space occupied in the unit cell can be found.

%space occupied by sphere =Vsphere/Vcellx100 this is also called as packing fraction

Empty space = 100-space occupied by sphere

Symmetry: in general, any given atom can be transferred to one or more atoms of the same type and with similar surroundings within the unit cell by symmetry operation. For all atoms in unit cell assign the coordinates along with symmetry operation.

Symmetric absence: any symmetry elements with a translational components including cell centring vectors will produce systematic absence from a diffraction pattern, peaks whose intensity is zero.

Systematic absence: the absence of any diffraction intensity at specific sets of reciprocal lattice points.

Reciprocal lattice represents the fourier transformation of another lattice. Reciprocal lattice is usually a periodic spatial function in real space and is also known as direct lattice.