# crystal systems

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Crystal types and details about crystal systemTRANSCRIPT

- 1. 1 CRYSTAL SYSTEMCRYSTAL SYSTEM1

2. CrystalTranslational VectorCrystal StructureCrystal LatticeUnit cellLattice ConstantSymmetry OperationPacking FactorMiller IndicesInter-planar Spacing CRYSTAL SYSTEM2 3. A crystal is a solid in which atoms are arranged in some regular repetition pattern in alldirections.CRYSTAL SYSTEM3CrystalCrystals (at a given temperature, pressure, and volume) between moleculesand atoms than liquids. Its to break the bonds. 4. CrystallineAmorphous.Polycrystallne*Crystal TypesSingle PyriteCrystalAmorphousCRYSTAL SYSTEM 4SolidPolycrystallinePyrite form(Grain) 5. * Difference between crystalline & non-crystallineCrystalline Non-crystalline5 CRYSTAL SYSTEMCRYSTAL SYSTEM5 6. CRYSTAL SYSTEM6Translational Lattice VectorsA lattice translation operation is definedby the displacement of a crystal by acrystal translation vector.Rn = n1 a + n2 bThis is translational symmetry.The vectors a, b are known as latticevectors and (n1, n2) is a pair of integerswhose values depend on the lattice point.PPoint D(n1, n2) = (0,2) 7. *A CRYSTAL STRUCTURE is a periodic arrangement of atomsin the crystal that can be described by a LATTICELattice: A 3D translationally periodic arrangement of points in space.Basis: A group of atoms associated with each lattice point to represent crystalstructure.7 CRYSTAL SYSTEM 8. CRYSTAL SYSTEM8Crystal LatticeBravais Lattice (BL) All atoms are of the same kind All lattice points are equivalentNon-Bravais Lattice (non-BL)Atoms can be of different kind Some lattice points are notequivalentA combination of two or more BLBravais LatticeNon-Bravais Lattice 9. The smallest component of the crystal which when stackedtogether with pure translational repetition reproduces thewhole crystal.9CRYSTAL SYSTEMSabSSSSSSSSSSSSSS 10. Primitive (P) unit cells contain only a single lattice point. Internal (I) unit cell contains an atom in the body center. Face (F) unit cell contains atoms in the all faces of the planes composing the cell.CRYSTAL SYSTEM 10 11. CRYSTAL SYSTEM11Crystal Structure 11 12. The numbers a,b,c specifying the size of a unit cell (in fact,conventional unit cell) are called its lattice constantFor cubic lattice, the lattice constant,Where,=density of the latticen= number of particlesM= molecular weight of the crystalNA =Avogadro number12a=(nM/NA)1/3 13. Symmetry OperationsSymmetry Operation: A symmetry operations is one which leaves thecrystal unchanged such as translation, rotation, reflection or inversion.5-fold symmetry:N-fold axes with n=5 or n>6 does not occur in crystalsAdjacent spaces must be completely filled (no gaps, no overlaps).13 CRYSTAL SYSTEM 14. *Atomic Packing Factor*Atomic Packing Factor (APF) is defined as the volume ofatoms in the unit cell divided by the volume of the unit cell.CRYSTAL SYSTEM 14 15. Close-packed directions are cube edges. Coordination = 6(nearest neighbors)a = 2r,r = a/2Atomic Radius, r=0.5aa 16. Volume of atoms in unit cell*Volume of unit cell*assume hard spheresatomsunit cellAPF =43volume1 p (0.5a) 3a3atomvolumeunit cellAPF =aR=0.5aclose-packed directionsNumber of lattice point 8 x 1/8 =1 atom/unit cell APF = 0.52, That means the percentage of packing is 52% 17. Atoms touch each other along cube diagonals. Coordination # = 8Ex: Cr, Fe , Molybdenum2 atoms/unit cell: 1 center + 8 corners x 1/8Atomic Radius ,r =a x (3)1/2/4 18. aClose-packed directions:length = 4R =atomsunit cell atomAPF =432 p ( 3a/4)3volumea3volumeunit cell3 aaR2 a3 a APF for a body-centered cubic structure = 0.68 19. Atoms touch each other along face diagonals. Coordination = 12Ex: Al, Cu, Ni,Ag4 atoms/unit cell: 6 face x 1/2 + 8 corners x 1/8Atomic Radius ,r = a x (2)1/2/4 20. Close-packed directions:length = 4R = 2 aNumber of lattice point :6 x 1/2 + 8 x 1/8= 4 atoms/unit cellatomsunit cell atomAPF =434 p ( 2a/4)3volumea3volumeunit cell2 aa APF for a face-centered cubic structure = 0.74 21. Miller Indices Miller Indices is a group of smallest integers which represent a directionor a plane.To determine Miller indices of a plane, take the following steps:1) Determine the intercepts of the plane along each of the threecrystallographic directions2) Take the reciprocals of the intercepts3) If fractions result, multiply each by the denominator of the smallestfraction. 22. CRYSTAL SYSTEM(233)22 23. For orthorhombic, tetragonal and cubicunit cells (the axes are all mutuallyperpendicular), the inter-planarspacing is given by: For cube a = b = c than23 CRYSTAL SYSTEMh, k, l = Miller indicesa, b, c = unit cell dimensionsa2 2 2 h k ldhkl 24. REFERENCESCRYSTAL SYSTEM 24 25. CRYSTAL SYSTEM25

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