## Solid state formula (XII)

``Relation between ‘a’ and ‘r

Primitive unit cell: r= a/2

Body centered cubic unit cell (bcc): r = √ 3(a/4)

Face centered cubic unit cell (fcc): r= a/ (2√ 2)

``Distance between two neighboring atom

Primitive unit cell: distance (2r) =a

Body centered cubic unit cell (bcc): distance (2r) = 0.866a

Face centered cubic unit cell (fcc): distance (2r) = 0.707a

``Packing efficiency = 4/3 π r^3 (z/a^3)

``Density of unit cell = density of crystal (ρ) = (z.M) / (N a^3)

``Number of unit cell in w gram of any substance = 1/z. (w.N / M)

``Dimension of voids in a close packed arrangement:

``Dimension of octahedral void : r = 0.414 R [r= radius of octahedral void, R= radius of the particle]

``Dimension of octahedral void : r = 0.225 R [r= radius of tetrahedral void, R= radius of the particle]

``Number of tetrahedral voids in ccp/fcc close packing = 2Z (Z= number of particles in a unit cell)

``Number of octahedral voids in ccp/fcc close packing = Z (Z= number of particles in a unit cell)

``Distance between two tetrahedral voids along a body diagonal = ( 3a)/2

``Shortest distance between two tetrahedral voids =a/2

``Shortest distance between two octahedral voids = a/ 2

``Distance between tetrahedral and octahedral void = V3.a/4

``Pyknometric density = (X ray density - pyknometric density) / X ray density

``Bragg’s equation: nλ = 2d sinӨ

[ λ= wavelength of X ray, d = spacing of the crystal layers, Ө = the angle between incident ray and the plane, n= an integer]