The document discusses different types of crystal structures that describe how atoms are arranged in crystalline solids. It notes that there are 7 crystal systems and 14 standard unit cells that can describe all possible lattice networks. It then focuses on metallic crystal structures, stating that 90% of elemental metals crystallize into one of three structures: body-centered cubic (BCC), face-centered cubic (FCC), or hexagonal close-packed (HCP). Tables with lattice parameters are provided for various metals for each crystal structure type.

2. Crystal Structure
BCC
FCC
HCP

3. rhombohedral a = b = c simple rhombohedral
α = β = γ ≠ 90 o
Crystal system
only 7 different types of unit cells
14 standard (Bravais) unit cells could
describe all possible lattice networks
crystal axial lengths &
system interaxial angles space lattice
cubic a = b = c simple cubic
α = β = γ = 90 o body-centered cubic
face-centered cubic
tetragonal a = b ≠ c simple tetragonal
α = β = γ = 90 o body-centered tetragonal
orthorhombic a ≠ b ≠ c simple orthorhombic
α = β = γ = 90 o body-centered orthorhombic
base-centered orthorhombic
face-centered orthorhombic
monoclinic a ≠ b ≠ c simple monoclinic
α = γ = 90 o ≠ β base-centered monoclinic
triclinic a ≠ b ≠ c simple triclinic
α ≠ β ≠ γ ≠ 90
hexagonal a = b ≠ c simple hexagonal
α = β = 90 o
γ = 120 o

7. Metallic crystal structures
90% elemental metals crystallize into three
crystal 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

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

9. FCC

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

11. HCP
coordination number = 12
total 2 atoms per unit cell
APF = 0.74
the closest packing possible of spherical
atoms
c/a ratio for ideal HCP structure is 1.633

14. THANK YOU