Exam review
al_awa
361_04_planesdirections_c.pptToday we test the clickers again
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We now venture into the world of
Metals
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Metallic xl Structures
Face-Centered Cubic (FCC)
Body-Centered Cubic (BCC)
Hexagonal Close-Packed (HCP)
f02_03_pg42
FCC
Atoms at 8 corners & 6 faces
Equivalent of
? whole atoms.
Atomic Packing Factor
(APF)= .74
Fig. 3.1
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f02_03_pg42.jpg
FCC Cubic structure
STM of Platinum
Dept. Kings.edu/chemlab, Property of IBM
A scanning tunneling microscope (STM) is an instrument for imaging surfaces at the atomic level.
What’s an STM image?
http://en.wikipedia.org/wiki/Scanning_tunneling_microscope
Tunneling=quantum mechanics term.
Works by measuring force of interaction between the probe and the surface.
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Atoms….
You are under our control!
- 1990: IBM scientist Don Eigler used an STM to move single xenon atoms on a nickel surface
- The engineers moved 35 atoms to spell out "IBM" in a 10 micrometer logo.
FCC examples
Lab-grown copper (SEM)
Etched Aluminum (SEM)
Gold
Galena (Pb ore)
0.3 mm
A scanning electron microscope (SEM) produces images by scanning a sample with a focused beam of electrons. Yields topography and composition.
What’s an SEM image?
http://en.wikipedia.org/wiki/Scanning_electron_microscope
A scanning electron microscope (SEM) is a type of electron microscope that produces images of a sample by scanning it with a focused beam of electrons. The electrons interact with electrons in the sample, producing various signals that can be detected and that contain information about the sample's surface topography and composition.
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f02_03_pg42
BCC
Atoms at 8 corners & 1 in center of cube
Equivalent of ? whole atoms
APF = .68
Fig. 3.2
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f02_03_pg42.jpg
BCC Cubic structure
STM of Aluminum (100) surface
https://wiki.fysik.dtu.dk/dacapo/Examples
BCC examples
Molybdenum
Iron
f07_03_pg54
Hexagonal
System
a1 = a2 = a3 ≠ z
- = 90º
g = 120º
Fig. 3.7
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f07_03_pg54.jpg
f03_03_pg43
HCP
Atoms at 12 corners, 3 in interior,
2 centered on basal planes
Equivalent of ? whole atoms
(APF)= .74
Fig. 3.3
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f03_03_pg43.jpg
Hexagonal structure
STM of Nickel surface structure.
Dept. Kings.edu/chemlab, Property of IBM
Zinc hand sample
Hexagonal structure
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SEM of Fine Cadmium powder
http://www.sciencephoto.com/media/8998/enlarge
SEM of ZnO nanowires
http://www.lac.tu-clausthal.de/en/arbeitsgruppen/angewandte-photonik-lac/projekte/zinc-oxide-nanowires-for-photonic-applications/
Hexagonal structure
HCP Examples
Titanium crystals
Cadmium crystal bar
Magnesium (SEM)
Atomic Packing Factors
BCC = 0.68 FCC = 0.74 HCP = 0.74
Metallic xl Structures
Body-Centered Cubic (BCC) APF = 0.68
Na, Fe, Cr, Mo, W
Face-Centered Cubic (FCC) APF = 0.74
Cu, Al, Ag, Au, Pb, Ni, Pt
Hexagonal Close-Packed (HCP) APF = 0.74
Ti, Zn, Cd, Co, Mg
Crystallographic Directions
Section 3.9
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Crystallographic direction
A vector between two points in a crystal.
Example:
y
x
z
Unit cube
And I should know this because….
Helps us communicate about crystals no matter where we are in the world…
http://lillypad.lilly.com/around-the-world.jpg
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A systematic study of symmetric tilt-boundaries in
hard-sphere f.c.c. crystals
Abstract
A new method is developed for the search of mechanically stable configurations of symmetric tilt boundaries in hard sphere f.c.c. crystals. The problem of finding out relative displacements which minimize the total volume of two crystal blocks forming a boundary, is simplified to a problem of positioning a single atom sphere relative to a block which consists of real and “image” atoms; the latter are placed in such a way to reflect the arrangement in the other crystal block. The method (the image atom method) has been applied to the analysis of symmetric coincidence boundaries with [100], [110] and [111] tilt axes with ∑-values 3–103. For the [100] (013)∑5 boundary, the procedure of the analysis is described in detail; the derived structures are compared with those by computer simulation. Numerical data are given in tabulated forms for some boundaries.
Steps for finding
Crystallographic Directions
Examples
y
y
1
2
3
4
x
z
Unit cube
x
z
y
x
z
y
x
z
Family of Directions
In the same family:
Vector 1
Vector 2
y
x
z
Unit cube
Family of Directions: <1 1 0>
y
x
z
Unit cube
1= [1 1 0]
2 = 3= [1 1 0]
4 = [1 1 0]
5 = [1 1 0]
4
3
1
2
5
p_pg44
- Structurally equivalent
- Atomic packing is equivalent
Family of Directions: <1 1 0>
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p_pg44.jpg
p_pg44
- Structurally equivalent
- Atomic packing is equivalent
Family of Directions: <1 1 0>
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p_pg44.jpg
f07_03_pg54
[a1 a2 a3 z]
Vector:
[1 0 0 1]
Hexagonal
Crystallographic directions
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f07_03_pg54.jpg
Other Directions
[ 1 1 0]
[ 1 0 2]
[ 1 1 1]
[ 2 1 1]
[ 2 1 1]
[ 0 0 1]
[ 1 0 1]
Wednesday:
Clicker Questions will include finding Crystallographic Planes and Crystallographic Directions
Solved Examples posted
on Canvas
Section 3.10
Crystallographic Planes:
Miller Indices
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Steps for finding
Crystallographic Planes
Examples
1
2
3
z
x
y
Families of Planes
(100)
(010)
(001)
{100}
{010}
{001}
Family of Planes MI: (X Y Z)
Structurally equivalent planes: {X Y Z}
Hexagonal Crystallographic planes:
The basal plane
Other Planes:
( 1 2 3)
(0 0 1)
(0 1 1)
(1 1 2)
(2 0 1)
(1 0 1)
Notation Summary
Solved Examples posted on Canvas:
Files>Assignments, Homework, Extra Credit
