材料科学专业英语 (1)

1/ 21/ 2 1
a
a
a3
a 2r
[0001] direction
a2
c = 1.633 a
a1
1/ 21/ 2 1
c
1.633a
a1, a2, a3 are close packed directions
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- Planar density and close packed plane
2a
2a a
If the radius of atom is r:
a 2 2r
[100] direction:
1/ 21/ 2 1
a
a
[110] is close packed direction
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Example 2: BCC structure
(110) plane
[111] is close packed direction
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• Atomic bonds - Metallic bonding
The valence electrons are freely shared by all the atoms in the structure.
- Ionic bonding Atom give up one or more electrons – positive charge (Cation) Atom accept one or more electrons – negative charge (Anion) Coulombic attraction force – source of ionic bonding
• Only those electrons which occupy the outermost shell will involve in chemical reaction; called valence electrons • The outer shell need to be fully filled for being stable
a2
1 ac
1 1.633a2
(0001) is close packed plane
- Packing density
Volume occupied by atoms/unit cell volume
- FCC/HCP structure (they are the same)
4 4 r3 4 4 r3
Bragg’s equation
(110) plane
2 2a2
(100) plane
1 a2
(110) Has higher planar density than (100)
Example 3: HCP structure
(0001) Basal plane
c a3 a1
3 1 3 1 6 2
4
3 a2
3a 2
2
(1010) Prism plane
[111] direction:
1/ 211/ 2 2
3a
3a
If the radius of atom is r:
a 4 r 3
[110] direction:
1/ 21/ 2 1
2a
2a
[100] direction:
1/ 21/ 2 1
a
a
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Example 3: simple cubic structure (100) plane
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- Position
The position of an atom is described with reference to the axes of the unit cell and the unit dimensions of the cell
E.g. FCC structure
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In cubic structure, if atom C is shifted to the position circled by the dash line, fcc stacking may be converted to the hcp stacking.
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• Lattice - Lattice: means a three-dimensional array of points coinciding with atom positions (or sphere centers). - Unit cell: the smallest group of atoms that shows the geometry of the structure.
3 a3
3 0.74 (2 2r)3
- BCC structure
2 4 r3 2 4 r3
3 a3
3 0.68 ( 4 r)3
3
- Simple cubic structure
4 r3 4 r3 3 3 0.52 a3 (2r)3
- Plane spacing:
The distance between two parallel planes
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- HCP structure – Miller indices
- Planes (hkil) i= - (h+k)
Basal plane :(0001) Prism plane: (1010)
(0110); (1100)
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Determination of Miller Indices for a Plane Within a Hexagonal Unit Cell
y (010)
Equivalent plane { }
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- HCP structure – Miller indices
- Direction [uvtw] t= - (u+v)
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Conversion from 3-index system to 4-index system
[010] in 3-index system becomes [1120] in 4-index system.
Correction
“Principle quantum number” should be corrected as “Principal quantum number”.
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Atomic Structure
• Atomic structures - Atom consists of nucleus (positive charged) and Electrons (negative charged)
[110]
y
Equivalent direction < hkl>
x
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Planes: (hkl) z
x
(110) (111)
• Find intercepts with x, y, z • Get reciprocals • Multiple the reciprocals to get minimum integers
Therefore the (hkil) indices are (1101 ).
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- Linear density (LD) and close packed direction
Example 1: FCC structure
(001) plane
[110] direction:
1/ 211/ 2 2 2
Direction, [hkl] z
[112] [111]
• Draw a vector from original point along the direction to be defined • Project it on three axes • multiple three number to get minimum integers
- Covalent bonding Two or more atoms share electrons such that each achieves stability. covalent bonding is directional
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Chapter 2: Crystal Structures • Crystalline structure: regular, long range order
] c2
Байду номын сангаас
Exercise
➢ determine the miller indices of the plane shown in the hexagonal unit cell
➢Assuming a=c, calculate the distance between two parallel plans
• Parameters of the unit cell: axial lengths (a, b, and c) angles between axes(α,β, and γ)
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- 7 possible unit cell geometries distinguish from each other by length of unit cell edges and the angles between the edges
• Amorphous (glass) structure: no long range order
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• Crystalline structure - Close-Packed Structures
Close-Packed
Non-Close-Packed
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• Crystalline structure - Close-Packed Structures
Example 1: FCC structure
(001) plane
2 a2
(111) plane
3 1 3 1 6 2
4
3 a2
3a 2
2
(011) plane
(111) is close packed plane
4 1 2 1 4 2
2
2a2
2a2
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Example 2: BCC structure
electron Nucleus
H (1): C (6): O (8): Si (14):
1s1 1s22s22p2 1s22s22p4 1s22s22p63s23p2
• Pauli exclusion principle: only two electrons can occupy the same orbital
[100] direction:
1/ 21/ 2 1
a
a
a 2r
[110] direction:
1/ 21/ 2 1
2a
2a
[100] is close packed direction
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Example 4: HCP structure
c
(0001) Basal plane
a1, a2, a3 directions: (2110)
Position a Position b
Layer A Layer B
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Close-packed cubic structure-FCC
First Layer A Second Layer B Third Layer C
ABCABC
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Close-packed hexagonal structure-HCP First Layer A Second Layer B Third Layer A ABAB
- Different crystal has different equation
- Cubic:
1 d2
h2 k2 l2 a2
<100> : d = a
<110> : d a / 2 <111> : d a / 3
- Hexagonal:
1 4 h2 hk k 2 l2
d2
[ 3
a2
b c
d
e
f
a
a: 0,0,0
b: 0,0,1
c: 0,1,1
d: 1,1,1
e: 1 ,0, 1
22
f:
1 ,1, 1 22
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- Crystallographic Directions and Planes (Miller indices)
Define direction and planes in unit cell