Solid State
Seven crystal systems, Nearest neighbours and Point defects
Several crystal systems:
Sl.No | Crystal Systems | Bravais lattices | Maximum symmetry elements | Parameters of unit cell |
Examples | |
Intercepts | Crystal Angle | |||||
1. | Cubic (Regular) | Primitive F.C.C; B.C.C - 3 | Nine plane of symmetry thirteen axes of symmetry | a = b = c | α = β = γ = 90° | NaCl, Zinc blende Cu, KCl, CaF_{2}, ZnS, Cu_{2}O, Diamond, Alums, Pb, Ag, Au, Mg |
2. | Tetragonal | Primitive body centre - 2 | Five plane of symmetry Five axes of symmetry |
a = b ≠ c | α = β = γ = 90° | White Sn, SnO_{2}, CaSO_{4}, TiO_{2}, ZrSiO_{4}, PbWO_{4}, KH_{2}PO_{4} |
3. | Orthorhombic | Primitive F.C.C, B.C.C, E.C.C - 4 | Three plane of symmetry Three axes of symmetry |
a ≠ b ≠ c | α = β = γ = 90° | KNO_{3}, K_{2}SO_{4}, BaSO_{4}, PbCO_{3}, Mg_{2}SiO_{4}, Rhombic sulphur |
4. | Hexagonal | Primitive - 1 | Seven plane of symmetry Seven axes of symmetry |
a = b ≠ c | α = β = 90°, γ = 120° | Graphite, ZnO, CdS, Wurtzite, HgS, Ice, PbI_{2}, Beryl, Mg, Zn, Cd |
5. | Trigonal {Rhombohedral} | Primitive - 1 | Seven plane of symmetry Seven axes of symmetry |
a = b = c | α = β = γ ≠ 90° | CaCO_{3} (calcite) HgS, quartz Mn |
6. | Monoclinic | Primitive B.C.C - 2 | One plane of symmetry One axis of symmetry |
a ≠ b ≠ c | α = γ = 90°, β ≠ 90° | Na_{2}SO_{4}.10H_{2}O, CaSO_{4}. 2H_{2}O, Monoclinic sulphur |
7. | Triclinic | Primitive - 1, Total = 14 | No plane of symmetry No axis of symmetry |
a ≠ b ≠ c | α ≠ β ≠ γ ≠ 90° | K_{2}Cr_{2}O_{7}, H_{3}BO_{3}, CuSO_{4}.5H_{2}O |
- Tricks for several crystal system:
Remember 1^{st} letters C T O H T M T
Remember number of bravais lattices 3 2 4 1 1 2 1
Observe inequality of intercept upto "O" then for remaining it reverse for H, T, last M & T all are unequal.
First 3 crystal angles are equal to 90°.
H γ = 120°,
Trigonal Rhombohedral means Rhombus so α = β = γ ≠ 90°
M γ ≠ 90°
Triclinic either intercept & crystal angle all are not equal. - Point defect: Missing of a point from lattice site during formation of crystal lattice is known as point defect.
- Classification of point defect:
- Stoichiometric defect:
- Vacancy: When constituent particles missing, then vacancy defects occurs.
- Frenkel defect: Ionic compound with low coordination number (4) can show this Eg: AgBr, ZnS
- Schottky: Ionic compound with high coordination number (6 or 8) can show this eg: NaCl.
- Trick: All alkali & alkaline earth metal halides compounds shows schottky defect.
- Due to Frenkel defect density of compound will not change.
- Due to schottky defect density of compound decreases.
- Non-stoichiometric defects:
(1) Metal excess defect: This is due to anion vacancies or due to the presence of extra cations at interstitial site.
Eg: ZnO in hot condition shows this
(2) Metal deficiency defect: This defect is due to absence of positive ion from lattice site or extra interstitial negative ion.
Eg: Ni_{0.98}O_{1.0}; Fe_{0.93}O_{1.0} - Nearest neighbours:
- The closest distance between centres of two atoms in a crystal lattice is called nearest neighbour.
- Trick to find closest distance
(1) always we need to find 2r value. - Closest distance in simple cubic is a = 2r ⇒ 2r = a
- Closest distance (nearest neighbour) in B.C.C. since atoms touch along body diagonal
\therefore 4r = \sqrt{3} \ a
Nearest neighbour distance is (2r) = \frac{\sqrt{3}}{2} \ a - Nearest neighbour in F.C.C
since atoms touch along face diagonal
4r = \sqrt{2} \ a\Rightarrow 2r = \frac{a}{\sqrt{2}}
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1. Cationic vacancies produced = [number of cations of higher valence × difference in valence of the host cation and cation of higher valence]