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]