Post on 07-Apr-2015
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Crystallographic PositionsBody Centered Cubic Structure
(BCC)
Face Centered Cubic Structure
(FCC)
Where Are The Atoms Located ?x
y
z
x
y
z
Crystallographic Positions
x
y
z
100
011001
½ ½ ½
Crystallographic DirectionsBody Centered Cubic Structure
(BCC)
Face Centered Cubic Structure
(FCC)
y
z
x
y
z
In Which Direction Are The Atoms Touching?x
Crystallographic Directions, [u v w]
x
y
z
[101]
[010]
[111]
Crystallographic Directions, [u v w]
x
y
z
[010]
[121]
Crystallographic Directions, [u v w]
x
y
z
[101]
[011]
Family of Crystallographic Directions, <u v w>
x
y
z
[101]or
[101]
<110>
]110[],101[],110[],011[]101[],110[],011[],101[]011[],011[],101[],110[
[110]or
[110]
Crystallographic DirectionsBody Centered Cubic Structure
(BCC)
Face Centered Cubic Structure
(FCC)
y
z
x
y
z
In Which Direction Are The Atoms Touching?[111] for BCC and [110] for FCC
x
Crystallographic Directions: Linear Density (LD)BCC: Atoms Touch Along the
[111] Direction
y
z
x
[111]
[100]
[110]
4ra3 o =
[111] DirectionClosest Packed Direction
1a3
4rLDo==
[110] Direction
612.0 3
42
2a2
2rLDo
=
==rr
[100] Direction
866.0 3
42
a2rLD
o
=
==rr
Crystallographic Directions: Linear Density (LD)FCC: Atoms Touch Along the
[110] Direction 4ra2 o =
[111] Direction
1a3
4rLDo==
[110] Direction: Closest Packed Dir.
[100] Direction
707.0 2
42
a2rLD
o
=
==rr
y
z
x
[111]
[100][110]
408.0
243
2a3
2rLDo
=
==rr
Crystallographic PlanesBody Centered Cubic Structure
(BCC)
Face Centered Cubic Structure
(FCC)
y
z
x
y
z
In Which Plane Are The Atoms Closest Packed?x
Crystallographic Planes: Miller Indices (hkl)
x
y
z
x
y
z
Given a Geometric Plane
If Necessary, Move the Origin so that All Intercepts are Found within the Unit Cell
Determined the Intercepts
Take Reciprocal
Change to Smallest Integer
(hkl)
Crystallographic Planes: Miller Indices (hkl)
x
y
z
x
y
z
(111)
(121) x
y
z
x
y
z
(010)
(020)
Crystallographic Planes: Miller Indices (hkl)
x
y
z
x
y
z
(210)
x
y
z
x
y
z
(021)
x’
z’
x’
y’
Crystallographic Planes: Miller Indices (hkl)
x
y
z
x
y
z
Given a Miller Indices (hkl)
If Necessary, Move the Origin. Move in the Positive Direction for a Negative Indices
Take Reciprocal
Indicate the Intercepts
Connect the Dots
(121)
Crystallographic Planes: Miller Indices (hkl)
x
y
z
x
y
z
Given a Miller Indices (hkl)
If Necessary, Move the Origin. Move in the Positive Direction for a Negative Indices
Take Reciprocal
Indicate the Intercepts
Connect the Dots
(211)z’
y’
Family of Crystallographic Planes
x
y
z{111}
)111(),111(),111(),111()111(),111(),111(),111(
(111)
{111}
x
y
z
Series of Crystallographic Planes
x
y
z
(121)
(010)
Crystallographic PlanesBody Centered Cubic Structure
(BCC)
Face Centered Cubic Structure
(FCC)
y
z
x
y
z
In Which Plane Are The Atoms Closest Packed?{111} for BCC and {100} for FCC
x
Crystallographic Planes: Planar Density (PD)
BCC
y
z
x
BCC: Atoms Touch Along the <111> Directionsand Are Closest Packed in {110} Planes
4ra3 o =
0.589 3
4rπr
aπrPD 2
2
2o
2
=
==(100) Plane
(110) Plane
0.834 3
4r2
r2πa2r2πPD 2
2
2o
2
=
⋅=
⋅=
Closest Packed PD
Crystallographic Planes: Planar Density (PD)FCC: Atoms Touch Along the <110> Directions
and Are Closest Packed in {111} Planes
4ra2 o =
0.785 2
4rr2π
ar2πPD 2
2
2o
2
=
⋅=
⋅=
(100) Plane
(110) Plane
0.555 2
4r2
r2πa2r2πPD 2
2
2o
2
=
⋅=
⋅=
x
y
z
Crystallographic Planes: Planar Density (PD)FCC: Atoms Touch Along the <110> Directions
and Are Closest Packed in {111} Planes
4ra2 o =
901.0
232
21
6rπ3
2rπ3
PD
22
=
⋅
⋅+⋅⋅=
oo aa
(111) Plane
Closest Packed PDx
y
z