crystal structure (2008) (chapter 1)
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Crystal structure
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Learning Objective
Students should be able to:
Differentiate between crystalline, noncrystalline, single crystaland polycrsytal.
Derive the relationship between unit cell edge length andatomic radius for face centered and body centered cubic
Compute density and atomic packing factors for crystal
Specify the miller indices for crystallography plane anddirection
Relate the crystal structure with material properties
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Fundamental Concept
a crystal structure is a unique arrangement
of atoms in a crystal.
Composed of a unit cell
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Crystal Structure
Crystal structure
Crystalline MaterialNoncrsytalline material
(Amorphous)
Single Crystal polycrystal
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Crystalline Material
Crystalline material-atoms, molecules or ion
packed in a regularly ordered, repeating pattern,
extending in 3 spatial dimension.
Single crystal-the periodicity of the pattern
extends throughout a certain piece of material.
Polycrystalline material-comprised of many
single crystal or grain
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atoms pack in periodic, 3D arrays typical of:
Crystalline materials...
-metals
-many ceramics
-some polymers
atoms have no periodic packing
occurs for:
Noncrystalline materials...
-complex structures-rapid cooling
crystalline SiO2
noncrystalline SiO2"Amorphous" = Noncrystalline
Adapted from Fig. 3.18(a),
Callister 6e.
MATERIALS AND PACKING
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Polycrystalline material
grains
Crystalline Amorphous
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Single Crystals
-Properties vary withdirection: anisotropic.
-Example: the modulus
of elasticity (E) in BCC iron:
Polycrystals
-Properties may/may not
vary with direction.
-If grains are randomly
oriented: isotropic.(Epoly iron= 210 GPa)
-If grains are textured,
anisotropic.
200 mm
SINGLE VS POLYCRYSTALS
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Unit cell- smallest structural unit or building
block that can describe the crystal structure.Repetition of the unit cell generates the entire
crystal.
Primitive unit cell- smallest possible unit cell onecan construct.
Lattice parameters-spacing between unit cellsin various direction.
Unit cell
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Unit Cells?
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Concept test
which one is
unit cell
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Crystal system
Point group of lattice
7 unique crystal system Cubic
Hexagonal Tetragonal
Rhombohedral
Orthorhombic
Monoclinic
Triclinic
By adding additional lattice point to 7 basic shapes form 14Bravais lattice
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Metallic crystal structure
Most found crystal structure in common metal Body centered cubic (BCC)
Face centered Cubic (FCC)
Hexagonal close-packed (HCP)
Simple cubic (SC) one lattice point at each of the eight corners
a= lattice parameter
a=2r
n= no. of atom per unit cell
n= 1
coordination no : no of
adjacent atom that touch
atom at lattice point= 6
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Body Centered Cubic (BCC)
3
4ra
n = 2
coordination no: 8
http://www.uncp.edu/home/mcclurem/lattice/vrml/bcc1.wrl -
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Face Centered Cubic (FCC)
n= 4
coordination no = 12
22ra
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Hexagonal Close PackedStructure
c/a =1.633
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Atomic Packing Factor (APF)
Efficiency of atomic arrangement in a unit cell.
Exercise: calculate APF for SC,BCC and FCCcrystal structure
Vc
nVs
APF
cellunitofvol.
spherex vol.ofatomofno.
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Theoretical density
ex; If a hypothetical metal crystalline with BCC
crystal structure. Calculate its density. GivenA= 26.98 amu/atom, atomic diameter0.286nm
AcNV
nA
so'no.avogadrxcell)/unitcell(cmunitofvol.
(g/mol)weightatomicxatomofno.3
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Polymorphism allotropic
transformation
the ability of a solid material to exist in more
than one form or crystal structure.
Example: Carbon and iron
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Allotropy: Carbon
Graphite Diamond
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Allotropy : iron
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Crystallography Direction and Plane
(by using miller indices)
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Crystallography direction
Line between two
point or a vector
Axis x y z
Head (H) 0 1 1
Tail (T) 0 0 1
Projection
(H-T)
0 1 0
Enclosed [ O 1 O]
Enclosed in squarebracket
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Lets do another example
Axis x y z
Head (H) 1 0
Tail (T) 0 1 1
Projection
(H-T)
1 - -1
Reduction
(x 2)
2 -1 -2
Enclosed [ 2 ]1 2
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Try it by yourself!!
(0,0,0)
Axis x y z
Head (H)
Tail (T)
Projection
(H-T)
Reduction(x )
Enclosed [ ]
You have to come to the class to get more examples.
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Crystallography Plane
The procedure:
1. If the plane passes through the selected origin
Another parallel plane must be constructed OR
Establish new origin
2. Determine either the plane is intersects or parallels with three axes.
3. Get the reciprocals.
4. If necessary, reduce the number.
5. Enclosed with parentheses , ( )
Remember the integer in enclosure is not separated by commas
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Example:
Axis x y z
Intercepts 1
reciprocals 0 1 0
Reduction(if necessary)
- - -
Enclosed ( 0 1 0 )
Reciprocal: 1/(value)
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Example 2:
Axis x y z
Intercepts 1 1
reciprocals 1 1 0
Reduction(if necessary)
- - -
Enclosed ( 1 1 0 )
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Try it by yourself!!
(0,0,0)
You have to come to the class to get more examples
Axis x y z
Intercepts
reciprocals
Reduction(if necessary)
Enclosed ( )
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