Crystal Structure (2008)
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Transcript of Crystal Structure (2008)
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Crystal structure
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Learning ObjectiveStudents should be able to:• Differentiate between crystalline, noncrystalline,
single crystal and polycrsytal.
• Derive the relationship between unit cell edge length and atomic radius for face centered and body centered cubic
• Compute density and atomic packing factors for crystal
• Specify the miller indices for crystallography plane and direction
• 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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• Formation crystal structure depends– Chemistry of fluid– Condition under which is being solidified– Ambient pressure
• Crystallization-Process forming crystalline structure.
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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
Si Oxygen
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 with direction: 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.
E (diagonal) = 273 GPa
E (edge) = 125 GPa
200 m
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 one can construct.
• Lattice parameters- spacing between unit cells in 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 14 Bravais lattice
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Crystal system
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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
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• Face Centered Cubic (FCC)
n= 4
coordination no = 12
22ra
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• Hexagonal Close Packed Structure
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 FCC crystal structure
Vc
nVs
APF
cellunit of vol.
sphere x vol.ofatom of no.
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Theoretical density
ex; If a hypothetical metal crystalline with BCC crystal structure. Calculate its density. Given A= 26.98 amu/atom, atomic diameter 0.286nm
AcNV
nA
so'no.avogadr x cell)/unit cell(cmunit of vol.
(g/mol) weight atomic x atom of no. 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 : iron
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Allotropy: Carbon
Graphite Diamond
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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 square bracket
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Lets do another example…
Axis x y z
Head (H)
1 ½ 0
Tail (T) 0 1 1
Projection (H-T)
1 -½ -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 PlaneThe 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 ( )