Lecture notes
Packing of Atoms
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- University Of Leeds (UoL)
Full lecture notes of packing of atoms in metals
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Range of scalePacking Of Atoms In Metals
scale cm)
10-3
a structural feature a
•
Macro structure 103 →
engineering structure
•
Microstructure 10-3 → 10-8 Size and shape of
grains ; phases and boundaries between
a
Nanostructure 10
-
•
crystal and glass structure
' °
to
_
atoms and ions
Microstructure and nanostructure can be controlled to alter properties of the material .
crystal structure : smallest scale of controllable structural feature
-
.
In crystal , the atoms arranged in regular , repeating 3D patterns and the crystal is solid
•
a are ,
.
Most metals @ room temp 1 of 3 crystal structures
•
pure occur in .
Think of the atoms in a crystal structure as hard spheres -
for pure metals , only one size of hard sphere needs
to be considered .
In order to build up a 3D
packing pattern (crystal) we start by :
1) packing atoms ZD in atomic planes
2) Stack planes on top of one another to make crystals .
Close
packing of spheres
-
° '
A
single layer of spheres is closest A second layer of spheres is placed in the
-
5 2
packed with a
hexagonal indentations left by the first layer .
Space is
4 3
co ordination of each sphere trapped between the layers which is not filled
-
.
•
2 different types of holes ( so -
called interstitial sites) ;
by the spheres .
tetrahedral (1- ± ) holes with 4
. . . . .
Octahedral 6) holes with 6
•
•
nearest sphere neighbours .
⑧
nearest sphere neighbours
r =
0.225
F- 0.414
radius ratio , r =
radius of largest sphere that would fit in the hole
radius of atom
when a 3rd layer of spheres is placed in the indentations of the second layer there are 2 Choices ;
1)
A
the 3rd layer lies in
% the 3rd layer lies in the
indentations in line alternative indentations
B
directly c
with the 1ˢᵗ layer B
A
.
leaving it
staggered with
respect to both previous layers .
ABA
Hexagonal close
packing CHCP) ABC cubic close
packing (CCD)
-
-
, Definitions
Packing Of Atoms In Metals
lattice point :
one of a set of theoretical points that are distributed in a periodic fashion in 3D space .
Unit cell : basic structural unit that is repeated in a crystalline structure
Lattice constant : length of unit cell
edge and /or
angle between
crystallographic axes .
Examples ;
3)
The third important crystal structure for metals is body -
centred cubic (Bcc) .
Close packed directions the structure but no close packed planes BCC
in
packing
-
-
.
is less dense than Fcc and HCD Structure of below 911°C
.
tungsten , chromium and iron .
approx 6hm
.
crystal structures d- Fe BCC a =
0.287hm
20×20×20
,
15×15×15
1×1×1 2×2×2 3×3×3 8×8×8
^
9 atoms 35 atoms 91 atoms 1241 atoms
7471 atoms v ooo
17261 atoms
How many atoms metals ? Metalto specimen preparation
are in the crystals in real
graphic
Reflected light microscopy :
steel with 0.01% carbon I. Small specimen with flat side is cut out of the metal
2. Specimen embedded in resin (used samples are 30mm
:::::::
diameter and 13mm thick)
the microstructure
3. Specimen polished to a mirror finish -
would not be
.
Useful for observation under the microscope .
↑ \ 4. Surface is etched ( for steels usually with a 2%
grain of
grain boundary
solution of nitric acid in alcohol )
iron
5. Any crystal (grain) boundaries present are visible
's
There are 10 G- thousand million million) atoms in because they appear as shallow steps on the surface
each
grain (crystal) of the specimen .
surface before etching
÷
- - - - -
- - - - - -
surface after etching
1
The relative sizes of the unit cell and grain for
crystal) of the iron can perhaps be appreciated by
thinking about the
following if : we could send an
atom sized ship through a 20 mm crystal from 1 grain boundary to the next , how
long would it
-
-
take if it passed 1 unit cell
every second ?
BCC iron has lattice parameter a =
0.287hm
=
0.287×10-9m .
Ship passes 1 unit cell , or 0.287×10 -9m every second
,
.
,
Grain boundaries 20µm apart .
(20×10 -6m)
i. time taken = 20×10-6 m = 69686s =
19.4 hours
=
0.287×10 -9ms -
'
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