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SUBJECT:CRYSTAL STRUCTUREGUIDANCE BY:-ANIL SIR

NAME:RATHOD VISHAL.ENROLLMENT NO:140950119066SEM:3

DEPARTMENT OF MECH.

ITM UNIVERSE

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Crystal Structure

BCC

FCC

HCP

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rhombohedral a = b = c simple rhombohedralα = β = γ ≠ 90 o

Crystal systemonly 7 different types of unit cells14 standard (Bravais) unit cells coulddescribe all possible lattice networkscrystal axial lengths &system interaxial angles space lattice

cubic a = b = c simple cubicα = β = γ = 90 o body-centered cubicface-centered cubic

tetragonal a = b ≠ c simple tetragonalα = β = γ = 90 o body-centered tetragonal

orthorhombic a ≠ b ≠ c simple orthorhombicα = β = γ = 90 o body-centered orthorhombicbase-centered orthorhombicface-centered orthorhombic

monoclinic a ≠ b ≠ c simple monoclinicα = γ = 90 o ≠ β base-centered monoclinic

triclinic a ≠ b ≠ c simple triclinicα ≠ β ≠ γ ≠ 90

hexagonal a = b ≠ c simple hexagonalα = β = 90 oγ = 120 o

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Metallic crystal structures90% elemental metals crystallize into threecrystal structures:• body-centered cubic (BCC)• a (nm) R (nm)• Cr 0.289 0.125• Fe 0.287 0.124• Mo 0.315 0.136• K 0.533 0.231• Na 0.429 0.186• Ta 0.330 0.143• W 0.316 0.137• V 0.304 0.132

• hexagonal close-packed (HCP)• a c (nm) R (nm)• Al 0.2973 0.5618 0.143• Zn 0.2665 0.4947 0.133• Mg 0.3209 0.5209 0.160• Co 0.2507 0.4069 0.125• Zr 0.3231 0.5148 0.160• Ti 0.2950 0.4683 0.147• Be 0.2286 0.3584 0.113

• face-centered cubic (FCC)• a (nm) R (nm)• Al 0.405 0.143• Cu 0.3615 0.128• Au 0.408 0.144• Pb 0.495 0.175• Ni 0.352 0.125• Pt 0.393 0.139• Ag 0.409 0.144

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coordination number = 8total 2 atoms per unit cell4 R√3 a = 4 R a = ——√3atomic packing factor (APF)volume of atoms in unit cellAPF = ——————————volume of unit cellAPF = 0.68

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FCC

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coordination number = 12total 4 atoms per unit cell4 R√2 a = 4 R a = ——√2APF = 0.74the closest packing possible of sphericalatoms cubic closest-packed

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HCPcoordination number = 12total 2 atoms per unit cellAPF = 0.74the closest packing possible of sphericalatomsc/a ratio for ideal HCP structure is 1.633

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