Class 20 – Polycrystalline
Materials
Reading
• Chapter 1 in Engler and Randle
• Chapter
Ch t 2 in
i Rohrer,
R h
pp. 69-80
69 80
Prof. M.L. Weaver
Polycrystallography
•Polycrystals composed of many small single crystals (called grains) with different orientations
joined at interfaces called grain boundaries.
grain
ga
grain
boundary
Grains tend to be
randomly orientated
Contact
C
t t atomic
t i force
f
microscope (AFM) image
of thermally etched Al2O3
polycrystal.
p
y y
•Microstructures have both geometric and crystallographic characteristics that influence
f
their
properties.
•Among geometric are the distribution of grain sizes & aspect ratios.
•Among crystallographic are the orientation of the crystallites with respect to external sample
reference
f
frame
f
(macroscopic
(
i surface
f
off the
h sample),
l ) and
d the
h orientation
i
i off the
h crystallites
lli
with
ih
respect to one another (the misorientation).
32
Polycrystallography (continued)
•The orientation of the grains with respect to external sample surface is typically shown on special
stereographic projection known as a pole figure.
Fig. (001) pole figure
Fig
shows the positions of
poles of each Al2O3
polycrystalline grain.
Grains
G
i tend
t d to
t be
b
randomly orientated
•The grains numerical label is used to designate the location of its pole.
•The center of the circle represents the surface normal [001] ┴ (001).
•This information can be constructed from XRD pole figure (shown above right), SEM/EBSD
( l t
(electron
backscatter
b k
tt diffraction-next
diff ti
t slide),
lid ) or TEM/SAED (selected
( l t d area electron
l t
diff
diffraction).
ti )
33
Recall Stereographic projections
(Case
(
studyy of how structure determines properties)
p p
)
Microcrystalline Fe one nanoindent
sample
l ttaken
k with
ith UNT’
UNT’s
Environmental-SEM (Quanta)
with electron backscatter
diffraction (EBSD) detector
•Hardness and Elastic Modulus
vary from grain to grain which
exhibit different crystallographic
orientation
Figure above. Pole figure for all
Berkovich nanoindentations
(technique to measure hardness
and elastic modulus). Black spots
on the stereographic triangle
represent various indentations. 34
Preferred Orientation (Texture)
•Eq. (3) from last class becomes invalid when you have (a) preferred orientation (texture), i.e. the
crystals making up the specimen are not randomly orientated in space.
•Preferred orientation of crystal grains cause large disagreements between calculated and
observed
b
d iintensities.
ii
•The reason for this is that each peak in the pattern is caused by diffraction from a different subset
of the particles in the material.
•If the particles are distributed in a truly random fashion, then the number of particles in each
orientation
i t ti should
h ld b
be id
identical.
ti l
•However, if the particles have a shape anisotropy, this might not be true.
•Assume particles are hexagonal platelets (below Figure). In a packed powder sample, plate-like
particles
ti l are mostt lik
likely
l tto lilie with
ith th
their
i b
basall plane,
l
(0001)
(0001), parallel
ll l tto th
the reference
f
plane.
l
•Thus the (0001) diffraction peak will originate from a greater number of particles than other peaks,
such as the (1010).
•As a result of this preferred orientation, the (000l)-type reflections will be intensified relative to
(hki0) t
(hki0)-type
reflections.
fl ti
•In general anything that changes the assumed random distribution of particles will affect the
distribution of relative intensities.
Figure shows texture in a powder diffraction sample. Highly
•Also, a few large particles, in an otherwise anisotropic particles are likely to have similar alignments.
fi powder
fine
d pressed
d sample,
l can affect
ff t the
th
distribution of intensities (Figure):
•Materials produced by sintering,casting,or
35
deformation frequently causes some texture.
Preferred Orientation (Texture)
(continued)
•Deformation texturing is due to the tendency of the grains in a polycrystalline material to rotate
during plastic deformation.
•Each grain undergoes slip and rotation in a complex way that is determined by the imposed forces
and by the slip and rotation of adjoining grains, the result is a preferred nonrandom orientation.
•It can occur in metals, ceramics, rocks and in both natural and artificial polymeric fibers and
sheets.
•Macroscopic properties of materials are influenced by texture due to anisotropy
36
Preferred Orientation (Texture)
(continued)
•Pole figures usually give a statistical
distribution of poles from a very large
number of grains
grains.
•Example on right is for Al alloy (6111)
sheet (cubic texture) that has been rolled
and recrystallized causing the <100> axes
to be preferentially aligned along rolling,
normal and transverse directions.
Grains tend to be
preferentially
orientated or
textured along
<100> axes.
Recall the simplified stereographic
(001) projection for cubic crystal.
[[001]]
[010]
[100]
RD=rolling direction
TD=transverse direction
XRD pole
fi
figure
maps for
6111 Al
alloy.
y
3 poles with respect to sample normal.
Pole figures can be prepared for any
set of planes
37
Thin Film Growth often results in
Preferred Orientation (Texture)
•Sputtered (physical vapor deposition) ZnO thin film is HCP (Zincite) of Wurtzite crystal structure.
•Columnar growth normal to Si substrate with high (0002) texture.
X ray diffraction (XRD):
X-ray
2000
(002)
1800
Cross-sectional bright field TEM:
Intennsity
1600
1400
1200
1 bilayer 200ºC
1 bilayer 250ºC
1 bilayer 350ºC
1 layer ZnO 200ºC
1000
800
(100)
600
400
((101))
200
0
30
35
40
2
(0002) Pole figure
from XRD:
showing strong out of
plane fibrous (0002)
texture (z-axis
perpendicular to the
substrate).
ZnO
Si substrate
38
Preferred Orientation (Texture)
(continued)
Randomly
oriented
PE chains
Semi-oriented
PE chains after
1200%
deformation
Highly oriented
PE chains after
3600%
deformation
39