
What the picture illustrates is a simple, but
farreaching truth: 





Plastic
deformation proceeds  atomic step by atomic step  by the
generation and movement of dislocations 






The whole art of forging consists simply of
manipulating the density of dislocations,
and, more important, their ability of
moving through the lattice. 


After a dislocation has passed through a crystal
and left it, the lattice is complely
restored, and no traces of the dislocation is left in the lattice. Parts of the
crystal are now shifted in the plane of the movement of the dislocation (left
picture). This has an interesting consquence: Without
dislocations, there can be no elastic stresses whatsoever in a single
crystal! (discarding the small and very localized stress fields
around point defects). 

We already know enough by now, to
deduce some elementary properties of dislocations which must be generally valid. 


1. A dislocation is
onedimensional defect because the
lattice is only disturbed along the
dislocation line (apart from small
elastic deformations which we do not count as defects farther away from the
core). The dislocation line thus can be described at any point by a
line vector
t(x,y,z). 


2. In the dislocation core the bonds between atoms are
not in an equilibrium configuration, i.e.
at their minimum enthalpy value; they are heavily distorted. The dislocation
thus must possess energy (per unit of
length) and entropy. 


3. Dislocations move under the influence of external forces which
cause internal stress in a crystal. The area swept by the movement defines a
plane, the glide plane, which always (by
definition) contains the dislocation line vector. 


4. The movement of a dislocation moves the whole crystal on one side of the glide
plane relative to the other side. 


5. (Edge) dislocations could (in principle)
be generated by the agglomeration of point
defects: selfinterstitial on the extra halfplane, or vacancies on
the missing halfplane. 

Now we add a new
property. The fundamental quantity defining an arbitrary dislocation is its
Burgers
vector
b. Its
atomistic definition follows from a Burgers
circuit around the dislocation in the real crystal, which is
illustrated below 










Left picture:
Make a closed circuit that encloses the dislocation from
lattice point to
lattice point (later from atom to atom). You obtain a closed chain of the base
vectors which define the lattice. 


Right picture:
Make exactly the same chain of base vectors in a perfect reference lattice.
It will not close. 


The special vector needed for closing
the circuit in the reference crystal is by
definition the Burgers vector
b. 

It follows that the Burgers vector of a (perfect) dislocation is of
necessity a lattice vector. (We will see
later that there are exceptions, hence the qualifier "perfect"). 

But beware! As always with conventions, you
may pick the sign of the Burgers vector at
will. 


In the version given here (which is the usual
definition), the closed circuit is around the dislocation, the Burgers vector
then appears in the reference crystal. 


You could, of course, use a closed circuit in the
reference crystal and define the Burgers vector around the dislocation. You
also have to define if you go clockwise or counter clockwise around your
circle. You will always get the same vector, but the sign will be different!
And the sign is very important for calculations! So whatever you do, stay consistent!. In the picture above we went
clockwise in both cases. 

Now we go on and learn a new thing:
There is a second basic type of
dislocation, called screw dislocation.
Its atomistic representation is somewhat more difficult to draw  but a Burgers
circuit is still possible: 









You notice that here we chose to go clockwise  for no particularly good reason 

If you imagine a walk along the
nonclosed Burges circuit, which you keep continuing round and round, it
becomes obvious how a screw
dislocation got its name. 


It also should be clear by now how Burgers
circuits are done. 


But now we will turn to a more formal description
of dislocations that will include all possible
cases, not just the extreme cases of pure edge or screw
dislocations. 




