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The
smelting and
forging of metals marks the
beginning of civilization - the art of
working metals was for thousands of years the major "high tech"
industry of our ancestors. |
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Trial and error over this period of time lead to
an astonishing degree of perfection, as can be seen all around us and in many
museums. In the state museum of Schleswig-Holstein in Schleswig, you may admire the
damascene
blades of our Viking ancestors. |
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Two kinds of iron or steel were welded together
and forged into a sword in an extremely complicated way; the process took
several weeks of an expert smith's time. All this toil was necessary if you
wanted a sword with better properties than those of the ingredients. The
damascene technology, shrouded in mystery, was needed because the vikings
didn't know a thing about defects in crystals - exactly like the Romans, Greek,
Japanese (india) Indians, and everbody else in those times. |
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You might enjoy finding and browsing through
several modules to this
topic which are provided "on the side" in this Hyperscript. |
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Exactly why
metals could be plastically deformed, and why the plastic deformation properties could be
changed to a very large degree by forging (and magic?) without changing the
chemical composition, was a mystery for thousands of years. |
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No explanation was offered before 1934,
when Taylor, Orowan and
Polyani discovered
(or invented?)
independently the dislocation. |
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A few years before (1929), U. Dehlinger (who, around
1969 tried to teach me basic mechanics) almost got there, he postulated
so-called "Verhakungen" as
lattice defects which were supposed to mediate plastic deformation - and they
were almost, but not quite, the real thing. |
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It is a shame up to the present day that the
discovery of the basic scientific principles governing metallurgy, still the
most important technology of
mankind, did not merit a Nobel prize - but
after the war everything that happened in science before or during the war was
eclipsed by the atomic bomb and the euphoria of a radiantly beautiful nuclear
future. The link pays
tribute to some of the men who were instrumental in solving one of the
oldest scientific puzzles of mankind. |
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Dislocations can be perceived easily in some
(mostly two-dimensional) structural pictures on an atomic scale. They are
usually introduced and thought of as extra lattice planes inserted in the
crystal that do not extend through all of the crystal, but end in the
dislocation line. |
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This is shown in the schematic three-dimensional view of an edge
dislocations in a cubic primitive lattice. This beautiful picture (from Read?)
shows the inserted half-plane very clearly; it serves as the quintessential
illustration of what an edge dislocation looks like. |
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Look at the picture and try to grasp the concept.
But don't forget |
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1. There is no
such crystal in nature: All real lattices are more complicated -
either not cubic primitive or with more than one atom in the base. |
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2. The exact
structure of the dislocation will be more complicated. Edge dislocations are just an extreme form of the
possible dislocation structures, and in most real crystals would be split into
"partial" dislocations and look much more complicated. |
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We therefore must introduce a more general and
necessarily more abstract definition of what constitutes a dislocation. Before
we do that, however, we will continue to look at some properties of (edge)
dislocations in the simplified atomistic view, so we can appreciate some
elementary properties. |
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First, we look at a simplified but principally
correct rendering of the connection between
dislocation
movement and plastic
deformation - the elementary process of metal working which contains
all the ingredients for a complete solution of all the riddles and magic of the
smith´s art. |
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Generation of an edge dislocation
by a shear stress |
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Movement of the dislocation
through the crystal |
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Shift of the upper half of the crystal
after the dislocation emerged |
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This sequence can be seen animated in the link |
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This calls for a little exercise |
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What the picture illustrates is a simple, but
far-reaching truth: |
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Plastic
deformation proceeds - atomic step by atomic step - by the
generation and movement of dislocations |
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The whole art of forging consists simply of
manipulating the density of dislocations,
and, more important, their ability of
moving through the lattice. |
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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). |
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We already know enough by now, to
deduce some elementary properties of dislocations which must be generally valid. |
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1. A dislocation is
one-dimensional 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). |
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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. |
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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. |
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4. The movement of a dislocation moves the whole crystal on one side of the glide
plane relative to the other side. |
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5. (Edge) dislocations could (in principle)
be generated by the agglomeration of point
defects: self-interstitial on the extra half-plane, or vacancies on
the missing half-plane. |
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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 |
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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. |
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Right picture:
Make exactly the same chain of base vectors in a perfect reference lattice.
It will not close. |
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The special vector needed for closing
the circuit in the reference crystal is by
definition the Burgers vector
b. |
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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"). |
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But beware! As always with conventions, you
may pick the sign of the Burgers vector at
will. |
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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. |
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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 clock-wise or counter clock-wise 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
clock-wise in both cases. |
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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: |
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You notice that here we chose to go clock-wise - for no particularly good reason |
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If you imagine a walk along the
non-closed Burges circuit, which you keep continuing round and round, it
becomes obvious how a screw
dislocation got its name. |
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It also should be clear by now how Burgers
circuits are done. |
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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. |
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© H. Föll