The document discusses the two principal forms of solids: crystalline and non-crystalline (amorphous) materials, detailing their structural differences, properties, and examples. It explains concepts such as space lattice, unit cells, and various crystal structures including body-centered cubic (bcc), face-centered cubic (fcc), and hexagonal close-packed (hcp). Additionally, it covers atomic packing factors and theoretical density calculations based on crystal structures.

1. crystalline and non-crystalline materials
• Solids exist in nature in two principal forms: crystalline and non-crystalline
(amorphous)
Crystalline material:
• Ordered arrangement (long range periodicity) of their ions, atoms or molecules
• Repeating periodic array over large atomic distances
• Crystals exhibit sharp melting point
• Any single crystal- a single grain – no grain boundaries
• Most crystalline solids – more grains – polycrystalline
• Whiskers – single crystals - dia/thickness to length ratio- very high
Crystalline
Single crystal
Whiskers

2. Crystalline materials
• Anisotropy
Material properties - directional dependent in single crystals
• Isotropic nature
Material properties - directional independent of polycrystalline materials
During solidification Atomic arrangement at grain boundary

3. Noncrystalline (amorphous) materials
• No ordered arrangement (long range periodicity)
• Also called as supercooled liquids
• Example: ordinary glass, glycerine and most of the polymers
• Can be produced by preventing crystallization by high cooling rate (106 K/s)
• Gradually softens (gel like) on heating
• Atoms in crystals- closely packed – high density than amorphous
Non-crystalline

4. Space lattice
• Lattice points and space lattice
• Infinite array of points arranged in 3D
• Unit cell-the smallest unit –forms space lattice

5. The Bravais lattices
• A 3D space lattice can be generated by three vectors a, b and c
• 14 ways of arranging points in 3D - therefore 14 Bravais lattices
• They belong to 7 crystal systems.

7. 14 ways of arranging points in 3D - therefore 14 Bravais lattices

8. BCC
• 8 atoms at the corners, I atom at the centre
• Centre and corner atoms touch one another along cube diagonal
• a=unit cell length, R = radius of the atom
a=4R/√3
• Ex: Cr, W, iron..etc
• 1 atom from center +1/8 atom at each corners
• Total, 2 atoms are associated with one BCC unit cell
• The coordination number-nearest neighbours-8
a
a

9. Atomic packing factor (APF):
= Volume of atoms in a unit cell/total unit cell volume
= Vs/Vc
BCC unit cell - APF=0.68
Vs = average number of atoms (n) X volume of one atom (Va)
Simple Cubic structure – APC= 0.52
Va = (4/3) * π r3
APF = (nVa)/Vc

10. Simple Cubic structure

12. FCC
• 8 atoms at each corner, 6 atoms at the centers of all the cube faces
• a and R related with a=2√2R
• Corner atoms touches the face atoms
• Each corner atom shares among 8 unit cells
• Face centered atoms belong to 2 unit cells
• 1/8th of corner atoms and ½ of the face centered atoms – total 4 atoms
associated with FCC
• The coordination number -12
• Ex: copper, aluminium, silver, gold etc
• Metals show high APF – electron cloud

13. Atomic packing factor-0.74

14. • We can calculate theoretical density, if the crystal structure is
known
Density ρ = n A/Vc NA
n = number of atoms associated with each unit cell
A = atomic weight
Vc =Volume of the unit cell
NA= Avagadro’s number (6.023 X 1023 atoms/mole)

16. HCP
• Another common crystal structure
• The top and bottom faces-6 at the regular hexagons and
surround a single atom at the centre
• Midplane – 3 atoms
• 1/6th of top and bottom 12 corner atoms
½ of each of the two centre face atoms
• 3 midplane interior atoms
• Total number of atoms associated : 6
• The coordinate number :12
• Atomic packing factor (APF): 0.74
• Ex: Mg, Ca, Ti..etc

17. APF = 0.74

18. Summary
• Stability-metastability
• Atomic bonds
• Crystalline and non-crystalline materials
• Space lattice, unitcell
• Different crystal structures
• BCC, FCC and hcp structures