 |
In most crystals
and under most circumstances there is no such thing as
a straight dislocation. Real dislocations contain kinks and jogs - sudden
deviations from a straight line on atomic dimensions. |
|
These defects within a defect may strongly influence the
mobility of dislocations and are thus of importance. |
|
 |
They owe their existence first of all to the fact that
dislocations always "live" in a crystals - in a periodic arrangement
of atoms. We have not used that fact so far, except in a rather abstract way
for the very definition of dislocations with the
Volterra cut. Now it is time to
appreciate the effects of the crystal on the fine structure of
dislocatons. |
|
|
Kinks (and jogs) may be produced by several mechanisms, in
particular they may be formed by the movement of the dislocation. |
|
First, let's look at kinks. For that we
first have to consider the concept of the Peierls potential of a dislocation. |
|
|
Consider the movement of an edge dislocation as shown below.
The green circles symbolize the last atom on the inserted half- plane of an
edge dislocation. In local equilibrium its distance to the atoms to the left or
right will be same for basic reasons of symmetry, cf. the perspective drawing of an edge
dislocation. |
|
|
|
|
|
|
|
|
|
|
|
If the dislocation is to move, the last atom (and the ones
above to some extent) has to press against the neighboring atom on one side and
move away from the atom on the other side. That is clearly a situation with a
higher energy which can be cast into a potential energy curve as shown in the
illustration. At some point when both lattice plans are most affected, there is
a maximum and a new minimum as soon as the dislocation has moved by one Burgers
vector. The minima and maxima of this Peierls potential are along
directions of high symmetry. |
|
|
To overcome the maximum of the Peierls potential, the stress
has to be larger than some intrinsic critical shear stress tcrit. |
|
The Peierls potential defines special
low-energy directions in which the dislocation prefers to lie. This is the
third rule for directions that dislocations
like to assume! (Try to remember the first and second rule, or use the links). |
|
|
In other words, the inserted half-plane for the
easy-to-imagine case of an edge dislocation should be clearly defined and
should be in a symmetric position between
its neighbour planes - exactly as we always have drawn it. |
|
|
A dislocation that is almost, but not quite an edge
dislocation, thus would prefer to be a pure edge dislocation over long
distances and concentrate the "non-edginess" in small parts of its
length as shown below. The same is true for screw dislocations, even so it is
not quite as easy to contemplate. |
|
|
|
|
|
|
|
|
|
|
|
The dislocation runs in the minima of the Peierls potential as
long as possible and then crosses over briskly when it has to be. The
transition from one Peierls minimum to the next one is called a kink as shown in the picture above. |
|
The kinks that come into existence in
this way are called geometric kinks. But
there is also a second kind, the thermal equilibrium
(double)-kink, i.e. a crossing over to a neighboring Peierls valley
followed by a "jump" back. |
|
|
A kink, or better a double-kink, is simply a defect in an
otherwise straight dislocation line, adding some energy and entropy. Since the
formation energy of a double
kink is not too large, they will be present in
thermal equilibrium with
concentrations following a standard Boltzmann distribution. |
|
|
To make that perfectly clear: While a dislocation by itself is
never in thermal equilibrium, i.e. will never form spontaneously by thermal
activation, this is not true for the defects it may contain. Double-kinks, seen
as defects in a dislocation line, form and disappear spontaneously, if
sufficient thermal energy is available; their number or density thus will
follow a Boltzmann distribution. |
|
|
Once a thermal double-kink has been formed, the two single
kinks may move apart; if the process is repeated, we have a new mode of dislocation movement for an otherwise
perhaps immobile dislocation. This is shown below. |
|
|
|
|
|
|
|
|
|
|
Kinks then are
steps of atomic dimension in the
dislocation line that are fully contained in the glide
plane of the dislocation |
|
|
With this general definition, we can consider kinks in all
dislocations, not just edge dislocations. |
|
Screw dislocations have a Peierls
potential, too, and thus they may contain kinks. The kink, per definition, is
then a very short a piece of dislocation with edge
character. |
|
|
This has far reaching consequences: A screw
dislocation with a kink now either has a specific
glide plane - the glide plane of the kink - or the kink is an
anchor point for the screw dislocation. |
|
|
Kinks can do more: As indicated above, at not too low
temperatures when the generation of thermal double kinks becomes possible, the
applied stress may be below the critical shear stress needed to move the
dislocation in toto (i.e. move it across the Peierls potential), but might be
large enough to separate double kinks and thus promote dislocation movement and
plastic deformation. We have one of several effects here that make crystals
"softer" at high temperatures. |
|
The best way to investigate kinks
are internal friction experiments. |
|
|
An oscillating deformation is chosen, e.g. by vibrating a thin
specimen driven by an electromagnetic field. The amplitude and thus the
internal stress and strain are easily measured. As long as the stress is not
too large, deformation proceeds by the generation and the movement of kinks.
This is a fully reversible process and the response to an external stress thus
is purely elastic even though a dislocation moved! |
|
|
However, in contrast to elasticity just coming from stretching
the bonds between the atoms, the generation and movement of double kinks takes
time and is strongly temperature dependent. Specific time constants are
involved and a peculiar frequency dependence of the elastic response will be
observed which contains information about the kinks. More about
internal friction in the
link. |
|
|
|
|
The term "Jogs" is sometimes considered to be the term for
all "breaks" or steps in a dislocation line with atomic dimensions.
Kinks then would be a subclass of jogs with the speciality of being in the
glide plane. |
|
|
However, it is customary to use the term "jogs" for
all steps that are not contained in the glide
plane. Looking just at the inserted half-plane of an edge
dislocation, jogs and kinks would look like this: |
|
|
|
|
|
|
|
|
|
|
|
But remember: Jogs and kinks can occur in any dislocation, not
just edge dislocations - they are just not as easily drawn! |
|
Jogs in edge dislocations are
obviously prime places for the emission or absorption of point defects as is
shown in the next illustration which looks at the inserted half-plane of an
edge dislocation. |
|
|
|
|
|
|
|
|
|
The movement of jogs by emission or absorption of
point defects means that the dislocation moves. This particular process of
dislocation movement is called climb of
dislocations. It is a movement that does not take place in the glide plane of the
dislocation. |
|
Generally speaking, we define: |
|
|
Conservative movement
of dislocations = movement in the glide plane =
glide (for short) = movement
without assistance of point defects. |
|
|
Non
conservative movement of dislocations = movement not in the glide plane
= climb (for short) = movement
needing the assistance of point defects. |
|
|
|
|
How do kinks and jogs come into
existence? Three mechanisms can be identified. |
|
|
1. Thermally activated
generation of double kinks as discussed above. |
|
|
2. Thermally induced generation of jogs by absorption or emission of point defects. This
mechanism is thermally induced (and not "activated") because it
responds to a super- or undersaturation of point defects. At large under- or
supersaturations, the process becomes more likely. Here we have one of the
source/sink
processes needed for point defect equilibrium. |
|
|
3. Intersection of
dislocations |
|
The last process is new and needs
some explanation. Lets look at the movement of an edge dislocation in the
following geometry: |
|
|
|
|
|
|
|
|
|
|
The intersection of the edge dislocation with the screw
dislocation produces one jog each per dislocation. (Consider the cut-and-move
procedure and you will see why). It is clear that the same thing happens for
the intersection of arbitrary mixed dislocations - a jog characterized by the
Burgers vector of the dislocation that moved across will be generated. |
|
This gives us a general relation and
explains to some extent why plastic deformation is an extremely non-linear
process: |
|
|
Movement of dislocations generates jogs. |
|
|
Jogs influence severely the movement of dislocations - so there is some feedback in the process of plastic deformation, and
feedback of any kind is the hallmark of non-linear processes. |
|
Considering jogs and kinks (together
with knots), we start to consider real
dislocations - and its getting complicated. |
|
|
And don't forget: All those great electron
microscope pictures showing all kinds of dislocations, never show the jogs and kinks! They are simply too
small. So even dislocation that look like perfect straight lines in a
TEM picture, may be full of jogs and kinks. |
|
|
|
|
There is one last property induced by
these defects in a defect: |
|
|
Jogs, kinks and their combinations may produce "debris" left behind by a moving dislocation,
because it is often "better" for dislocations to tear away from
immobile parts like jogs, leaving behind a trail of point defects which in turn
may agglomerate. |
|
|
If the jog is large extending over several lattice planes, a
whole trail of small dislocation loops may form. The
formation of a trail of
vacancies in the wake of a jogged moving screw dislocation is illustrated
in the link |
|
|
|
|
|
Some more text to come - but try the
exercise anyway! |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
© H. Föll (Defects - Script)
