Revision Notes on Solid State
Classification of solids:
Crystalline and Amorphous solids:
Based on binding forces:
Bragg Equation:
nλ = 2dsinθ,
Where
• d= distance between the planes
• n = order of refraction
• θ= angel of refraction
• λ = wavelength
Crystal Systems:
• Total number of crystal systems: 7
• Total number of Bravais Lattices: 14
Number of atoms in unit cells.
Primitive cubic unit cell:
• Number of atoms at corners = 8×1/8 =1
• Number of atoms in faces = 0
• Number of atoms at body-centre: = 0
• Total number of atoms = 1
Body-centred cubic unit cell:
• Number of atoms at corners = 8×1/8 =1
• Number of atoms in faces = 0
• Number of atoms at body-centre: =1
• Total number of atoms = 2
Face-centred cubic or cubic-close packed unit cell:
• Number of atoms at corners = 8×1/8 =1
• Number of atoms in faces = 6×1/2 = 3
• Number of atoms at body-centre: = 0
• Total number of atoms = 4
Packing Efficiency
Packing Efficiency = (Volume occupied by all the atoms present in unit cell / Total volume of unit cell)×100
Octahedral and Tetrahedral Voids:
Number of octahedral voids = Number of effective atoms present in unit cell
Number of tetrahedral voids = 2×Number of effective atoms present in unit cell
So, Number of tetrahedral voids = 2× Number of octahedral voids.
Defects in crystal:
Stoichiometric Defects
1. Schottky Defects
• Some of the lattice points in a crystal are unoccupied.
• Appears in ionic compounds in which anions and cations are of nearly same size.
• Decreases the density of lattice
• Examples: NaCl and KCl
2. Frenkel Defects
• Ion dislocate from its position and occupies an interstitial position between the lattice points
• Appears in crystals in which the negative ions are much larger than the positive ion.
• Does not affect density of the crystal.
• Examples: AgBr, ZnS
Non-Stoichiometric Defects
1. Metal Excess defect:
• Metal excess defect occurs due to
• anionic vacancies or
• presence of extra cation.
• F-Centres: hole produced due to absence of anion which is occupied by an electron.
2. Metal deficiency defect:
• Metal deficiency defect occurs
• Due to variable valency of metals
• When one of the positive ions is missing from its lattice site and the extra negative charge is balanced by some nearby metal ion acquiring two charges instead of one
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