1. Chapter 3: Crystal & Amorphous structure in materials Part 1
DMT125 Materials Science
Chapter 3: Crystal & Amorphous structure in materials
Part 1
26 November 2013
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2. Contents Space lattice & unit cells Crystal systems & bravais lattices
Principal metallic crystal structures
BCC
FCC
HCP
Atom positions & directions in cubic unit cells
Miller indices
Comparisons of FCC, HCP & BCC crystal structures
Volume, planar & linear density unit cell calculations
Amorphous materials
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3. Space lattice & unit cells
Solids maybe categorized into:
Crystalline solids
Amorphous solids
Crystalline solids due to orderly structure of their atoms, molecules or ions, possess well-defined shapes
Metals are crystalline, composed of well-defined crystals or grains
Amorphous solids have poor or no long-range order & do not solidify with symmetry & regularity of crystalline solids
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4. Space lattice & unit cells
Crystalline solid
Long range order (LRO) - Atoms or ions of a solid are arranged in a pattern that repeats itself in 3D, they form a solid
Example
Metals
Alloys
Some ceramics
Short range order (SRO) – Atoms & ions are not arranged in a long-range, periodic & repeatable manner
1 oxygen atom is covalently bonded to 2 hydrogen atoms
Amorphous – materials with only short-range order
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5. Space lattice & unit cells
Atomic arrangements in crystalline solids can be described by referring the atoms to the points of intersection of a network of lines in 3D
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6. Space lattice & unit cells
In an ideal crystal, the grouping of lattice points about any given point are identical with the grouping about any other lattice point in the crystal lattice
Unit cell - Each space lattice can thus be described by specifying the atom positions in a repeating pattern
Motif – a group of atoms organized in a certain arrangement relative to each other & associated with lattice points
Lattice constants
axial length a, b & c
Interaxial angles alpha, beta & gamma
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7. Crystal systems & bravais lattices
There are 4 basic types of unit cells:
Simple
Body centered
Face-centered
Base-centered
In cubic system, there 3 types of unit cells
Simple cubic
Body-centered cubic
Face-centered cubic
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8. Principal metallic crystal structures
Most elemental metals (~90%) crystallize upon solidification into 3 densely packed crystal structures
Body-centered cubic (BCC)
Face-centered cubic (FCC)
Hexagonal close-packed (HCP)
Most metals crystallize in these dense-packed structures because energy is released as atoms come closer together & bond more tightly with each other
Thus resulting in lower & more stable energy arrangements
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9. Principal metallic crystal structures
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10. Principal metallic crystal structures: BCC
Each cells has equivalent of 2 atoms/ unit cell
Relationship between length of the cube side a & atomic radius R
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11. Principal metallic crystal structures: BCC
Atomic packing factor (APF)
Many metals such as iron. Chromium, tungsten, molybdenum & vanadium have BCC crystal at room temperature
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12. Principal metallic crystal structures: BCC
Example 1
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13. Principal metallic crystal structures: FCC
Atoms in FCC crystal structure are packed as close together as possible
APF = 0.74
Each cells has equivalent of 4 atoms/ unit cell
Relationship between length of the cube side a & atomic radius R
Many metals such as aluminium, copper, lead, nickel & iron at elevated temperatures crystallize with FCC crystal structure
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14. Principal metallic crystal structures: FCC
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15. Principal metallic crystal structures: HCP
APF = 0.74
Atoms structures packed as tightly as possible
Each cells has equivalent of 6 atoms/ unit cell
Ratio c/a
Ration of the height c of the hexagonal prism of HCP crystal structure to its basal side a
Metals like cadmium & zinc have ratio higher than ideality
Atoms in the structures are slightly elongated along the c axis
Metals like magnesium, cobalt, zirconium, titanium & beryllium have ratio less than ideality
Atoms in the structures are slightly compressed in the direction along c axis
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16. Principal metallic crystal structures: HCP
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17. Atom positions & directions in cubic unit cells
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18. Atom positions & directions in cubic unit cells
Crystallographically equivalent
Atom spacing along each direction is the same
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19. Principal metallic crystal structures: HCP
APF = 0.74
Atoms structures packed as tightly as possible
Each cells has equivalent of 6 atoms/ unit cell
Ratio c/a
Ration of the height c of the hexagonal prism of HCP crystal structure to its basal side a
Metals like cadmium & zinc have ratio higher than ideality
Atoms in the structures are slightly elongated along the c axis
Metals like magnesium, cobalt, zirconium, titanium & beryllium have ratio less than ideality
Atoms in the structures are slightly compressed in the direction along c axis
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20. Principal metallic crystal structures: HCP
Example 2
Draw the following direction vectors in cubic unit cells:
a) [100] & [110]
b) [112] c) d)
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21. 26 November 2013
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22. Miller indices
Reciprocals of the fractional intercepts (with fractions cleared) that the plane makes with the crystallographic x, y & z axes of the 3 nonparallel edges of the cubic unit cell
Procedure
1) choose a plane that does not pass through the origin at (0,0,0)
2) determine the intercepts of the plane in terms of the crystallographic x, y & z axes for a unit cube. These intercepts maybe fractions
3) form the reciprocals of these intercepts
4) clear fractions & determine the smallest set of whole numbers that are in the same ration as the intercepts
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23. Miller indices
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24. Miller indices: Example 3
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25. Miller indices Interplanar spacing
Dhkl, where h, k & l are the Miller indices of the planes
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26. Miller indices Example 4
Copper has an FCC crystal structure & a unit cell with a lattice constant of nm. What is its interplanar spacing d220?
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27. Miller indices
Solution
= nm
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28. End of Part 1 Copyright © Mr.Mohd. Azarulsani b. Md. Azidin
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