|
LomerCotrell and stair-rod dislocations |
|
|
Lets look at the reaction between two perfect dislocations on
different glide planes which are split into Shockley partials, e.g. with the
(perfect) Burgers vectors
b1 = a/2[1,1,0] on the (111) plane
b2 = a/2[101] on the (1,1,1) plane
|
|
|
If you have not yet produced your personal Thompson tetrahedra - now is the time
you need it! |
|
|
The two Shockley partials meeting first will always react to
form a dislocation with the Burgers vector ( |
|
|
|
|
|
|
|
|
|
|
|
uUe your Thompson tetrahedron to verify this! |
|
This is a new type of Burgers vector. A dislocation with this
Burges vector is called a Lomer-Cotrell
dislocation. |
|
|
A Lomer-Cotrell dislocation now borders two stacking faults on two different {111}
planes, it is utterly immobile. |
|
|
The total
structure resulting from the reaction - a Lomer-Cotrell dislocation at the
tip of two stacking fault ribbons bordered on the other side by Shockley
partials - is called a stair-rod
dislocation because it is reminiscent of the "stair-rod" that
keeps the carpet ribbons in place that are coming down a stair. What it looks
like is shown in the link. |
|
It is clear that this is a reaction
that must and will occur during plastic deformation. Since it makes
dislocations completely immobile, it acts as a hardening mechanism; it makes plastic
deformation more difficult. |
|
Another speciality in
fcc-crystals, which would never occur to you by hard thinking alone, are
stacking fault tetrahedra. |
|
|
Stacking fault tetrahedra are special forms of point defect
agglomerates. Lets see what the are and how they form by again looking at low
energy configurations: |
|
Frank partials bonding a vacancy disc
have a rather high energy (b = a/3 [111], b2
= a2/3) compared to a Shockley partial
(b2 = a2/6) or Lomer-Cotrell
dislocation (b2 = a2/18), which also can
bound stacking faults. Is there a possibility to change the dislocation
type? |
|
|
There is! Imagine the primary stacking fault to be triangular.
Let the Frank partial dissociate into a Lomer-Cotrell dislocation and a
Shockley partial which can move on one of the other {111}-planes
intersecting the edge of the triangular primary stacking faults. (If you do not
have a Thompson tetrahedra by now, it serves you right!) |
|
|
Let the Shockley partials move; wherever they meet they form
another Lomer-Cotrell dislocation. If you keep them on other triangular areas,
they will finally meet at one point - you have a
tetrahedron formed by stacking
faults and bound by Lomer-Cotrell dislocations; the whole process is shown
in the link. |
|
|
If this seems somewhat outlandish, look at the
electron microscopy pictures
in the link! |
|
Next, lets look at slightly more
complicated fcc-crystals: the
diamond structure
typical not only for diamond, but especially for Si, Ge,
GaAs, GaP, InP, ... Now we have two atoms in the base of the crystal, which makes
things a bit more complicated. |
|
|
First of all, the extra lattice plane defining an edge
dislocation may now come in two
modifications called "glide"- and "shuffle" set, because the
inserted half-plane may end in two distinct atomic positions as shown below.
The properties of dislocations in semiconductors - not only their mobility but
especially their possible states in the bandgap - must depend on the
configuration chosen. |
|
|
|
|
|
|
|
|
|
|
|
Which configuration is the one chosen by the crystal? It is
still not really clear and a matter of current research. |
|
|
|
|
The basic geometry in bcc
lattices is more complicated, because it is not a close-packed lattice. |
|
|
The smallest possible perfect Burgers vector is |
|
|
|
|
|
|
|
|
|
|
|
Glide planes are usually the most densely packed planes, but
in contrast to the fcc lattice, where the {111} planes are by far
most densely packed, we have
several planes with very
similar packing density in bcc crystals, namely {111},
{112} and {123}. |
|
|
This offers many possibilities for glide systems, i.e. the combinations of possible
Burgers vectors and glide planes. Segments of dislocations, if trapped on one
plane may simply change the plane (after re-aligning the line vector in the
planes). |
|
|
Stacking faults (and split dislocations) are not observed
because the stacking fault energies are too large. |
|
|
But the core of the dislocations, especially for screw
dislocations, can now be extended and rather complicated. Screw dislocations in
<111> directions, e.g., have a core with a threefold symmetry.
This leads to a basic asymmetry between the forward and backward movement of a
dislocation: |
|
|
|
|
|
|
|
Imagine an oscillating force acting on a
bcc metal - Fe for that matter. The screw dislocation will follow
the stress and oscillate between two bowed out positions. As long as the
maximum stresses are small compared to the critical stress needed to induce
large scale movement, the process should be completely reversible. |
|
However, due to the asymmetry between forwards
and backwards movement, there is a certain probability that once in a while the
screw dislocation switches glide planes. It then may move for a large distance,
inducing some deformation, In due time, things change irreversibly leading to a
sudden failure called "fatigue". |
|
This is only one mechanism for fatigue and only serves to
demonstrate the basic concept of long-time changes in materials under load due
to details in the dislocation structure of materials. |
|
|
|
|
|
More about dislocations in bcc lattices in
the link |
© H. Föll