Introduction to Crystal Structure.pdf

Materials Science and Engineering

1. Dr. Jayanta Kr. Mahato
Associate Professor
Mechanical Engineering Dept.
ShobhitDeemed to-be University

2. Outline of the Lecture
• Lattice
• Basis
• Crystal Structure
–Poly Crystal
–Single Crystal
• Unit Cell
• Cubic Crystal System
–Simple Cubic(SC) ,
–Face Centered Cubic (FCC) ,
–Body Centered Cubic (BCC)
-The seven crystal system
-Hexagonal close pack unit cell (HCP)
Dr. Jayanta Kr. Mahato, Assoc. Prof., Mechanical Engineering

3. Crystal structure = Lattice + Basis
Lattice:-
"An infinite periodic array of points in a space"
The arrangement of points defines the lattice symmetry
A lattice may be one, two or three dimensional (3D)
Basis (Motif):-
A group of one or more atoms , located in a particular way
with respect to each other and associated with each point ,
is known as the Motif or Basis.
Lattice Basis (Motif)

4. Crystal structure = Lattice + Basis
Dr. Jayanta Kr. Mahato, Assoc. Prof., Mechanical Engineering

5. Crystal structure = Lattice + Basis
Whenanatomoridenticalgroupof
atomsisattachedtoeverylattice
point,weobtainacrystalstructure.
Dr. Jayanta Kr. Mahato, Assoc. Prof., Mechanical Engineering

6. Crystals: Classification
Crystals
Single Crystal Poly Crystal
•Singlecrystal:Inthis
typeofcrystalperiodicityis
maintainedthroughoutthe
body.
•Polycrystal:Inthistype
ofcrystalperiodicityisnot
maintainedthroughoutthe
body.
Poly CrystalSingle Crystal

7. Lattice Point
Unit Cell
UnitCell:Atomsorgroupofatomsforminga
buildingblockofthesmallestacceptablesizeofthe
wholevolumeofacrystalisdefinedasaunitcell.
Atom
Pointtoberemember:Latticepointsarelocatedat
thecorneroftheunitcellandinsomecases,at
eitherfacesorthecentreoftheunitcell.

8. Types of Cubic Cells
Types of Cubic Cells
Simple Cubic Body Centered Cubic Face Centered Cubic
Simple Cubic Body Centered Cubic Face Centered Cubic
Dr. Jayanta Kr. Mahato, Assoc. Prof., Mechanical Engineering

9. Body Centered Cubic (BCC) Crystal Structure
Dr. Jayanta Kr. Mahato, Assoc. Prof., Mechanical Engineering

10. Face Centered Cubic (FCC) Crystal Structure
Dr. Jayanta Kr. Mahato, Assoc. Prof., Mechanical Engineering

11. Hexagonal Close-Packed (HCP) Crystal Structure
Dr. Jayanta Kr. Mahato, Assoc. Prof., Mechanical Engineering

12. Total Atomic Numbers per Simple CubicUnit Cell
Totalnumber of
atomsperSimple
Cubicunitcellis
8*(1/8) = 1 atom
Eachcorner atom
sharedby8unitcells

13. Total Atomic Numbers per BCCUnit Cell
Totalnumber of
atomsperBCCunit
cellis
8*(1/8) + 1 = 2 atom
Eachcorner atom
sharedby8unitcells
Dr. Jayanta Kr. Mahato, Assoc. Prof., Mechanical Engineering

14. Total Atomic Numbers per FCCUnit Cell
TotalnumberofatomsperFCCunitcellis
8*(1/8) + 6*(1/2) = 4 atoms
Eachcorner atom
sharedby8unitcells
Each face atom
sharedby2unitcells
Dr. Jayanta Kr. Mahato, Assoc. Prof., Mechanical Engineering

15. Total Atomic Numbers per HCPUnit Cell
TotalnumberofatomsperHCPunitcellis
6*(1/6)*2 + 2*(1/2) + 3 = 6 atoms
Eachcorner atom
shared by three
primitiveunitcells
3inter
whole
atom
Eachface atom
sharedby2unitcells
Dr. Jayanta Kr. Mahato, Assoc. Prof., Mechanical Engineering

16. 7 Unique Arrangements of Unit Cell
Dr. Jayanta Kr. Mahato, Assoc. Prof., Mechanical Engineering

17. Properties of Unit Cell: Properties of Materials
1. No of Atoms Per Unit Cell
2. Coordination Number
3. Lattice Constant
4. Atomic Radius
5. Atomic Packing Fraction (APF)
No of Atoms Per Unit Cell
Effective no of atoms per unit cell
Factors Responsible for Properties of Unit Cell:
Properties of Materials
Dr. Jayanta Kr. Mahato, Assoc. Prof., Mechanical Engineering

18. Mechanical Properties of Materials: In General
Increasing Strength
Dr. Jayanta Kr. Mahato, Assoc. Prof., Mechanical Engineering

19. Coordination Number
Coordinationnumber(N):Thehighestnumberofnearest
neighboratomsorionssurroundinganatomorion.
Simple Cubic
N = 6
BCC
N = 8
FCC
N = 12
HCP
N = 12
Dr. Jayanta Kr. Mahato, Assoc. Prof., Mechanical Engineering

20. Atomic packing factor (APF)
Atomicpackingfactor(APF):APFisthesumofthe
spherevolumesofallatomswithinaunitcell(assuming
theatomichard-spheremodel)dividedbytheunitcell
volume
Dr. Jayanta Kr. Mahato, Assoc. Prof., Mechanical Engineering

21. Atomic Packing Factor for FCC
Dr. Jayanta Kr. Mahato, Asst. Prof., Mechanical Engineering

22. Home Work
CalculatetheAtomicPacking
Factor(APF)forSimpleCubic
andBCCStructure.
Dr. Jayanta Kr. Mahato, Assoc. Prof., Mechanical Engineering

23. Aboutthecrystalstructure.
TypesofCrystalStructure
AbouttheUnitCell.
CubicCrystalSystem
–SimpleCubic(SC),
–BodyCenteredCubic(BCC)
–FaceCenteredCubic(FCC)
-Hexagonalclosepackunitcell(HCP)
CoordinationNumber
AtomicPakingFactor(APF)
Thesevencrystalsystem
Summary
Fromthislecturewehavelearnedabout:
Dr. Jayanta Kr. Mahato, Assoc. Prof., Mechanical Engineering