Defects in the crystal structure of metals

The previous post  has assumed a uniform and error-free structure of the metals.
However, such ideal crystals do not exist in reality or can only be achieved
approximately on a very small scale under extreme expense (for example in so-
called whiskers).

Figure: Ideal crystal microstructure

Real metals do not have a perfect lattice structure but show so-
called crystallographic defects. At these defects, the real lattice deviates from the
idealized perfect structure.
Figure: Real crystal microstructure with crystallographic defects

The figure above shows examples of different crystallographic defects, which can
be subdivided depending on their impact on the surrounding structure. The
following sections discuss these types of impurities more closely:

 0-dimensional crystallographic defects (punctiform defects)

 1-dimensional crystallographic defects (linear defects)

 2-dimensional crystallographic defects (area-shaped defects)

 3-dimensional crystallographic defects (volume-shaped defects)

Point defects:Point defects are also referred to as 0-dimensional defects and disturb
the lattice only within a very limited (punctiform) region. The following sections
discuss these types of point defects:

 vacancies

 Substitutional atoms

 Interstitial atoms

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
 Figure: Crystallographic point defects
  Vacancies
The vacancies are sites in the structure that are not occupied by an atom and thus
remain vacant. The vacancy density usually increases exponentially with
increasing temperature. The reason for this is the increased lattice vibration, which
“tears” some atoms from their regular sites. If the atoms migrate by self-diffusion
to the metal surface, they leave a vacancy defect in the material. However, this also
means that vacancies in a metal can not be avoided in principle, since they are in
a thermodynamic equilibrium. These types of vacancies are also called thermal
vacancies.

At 1 quadrillion (1015) atoms comes at room temperature about one vacancy.

Immediately below the melting temperature already one vacancy comes at 10,000
atoms (104).

Vacancies can also be “trapped” in the material by rapid cooling from the hot state.
However, these are not in thermodynamic equilibrium and partially heal over time
due to diffusion processes (athermal vacancies).

Substitutional atom

However, there are not only vacancies interfering with a lattice structure. In
addition, a metal is not free of foreign atoms. In the lattice structure, these foreign
atoms can displace the actual metal atoms and thus occupy their lattice sites. Since
the actual metal atom has been substituted by the foreign atom, it is also called
a substitutional atom.

Interstitial atoms
A further possibility of the arrangement of foreign atoms consists in the storage on
an interstitial space, e.g. in the cube center of a face centered cubic unit cell (also
referred to as octahedral site). Atoms that are not on regular sites but have
interposed there between, are referred to as interstitial atoms.

Foreign atoms can migrate (diffuse) particularly well through the material due to
lattice vibrations if there are many vacancies. There is plenty of room to get from
one vacancy to another. Therefore, vacancies play an important role in diffusion
processes of foreign atoms!

Line defects

Line defects are also called 1-dimensional crystallographic defects. They disturb
the crystalline structure within a larger area compared to point defects. This only
includes the so-called edge dislocations and the screw dislocations:

 edge dislocations

 screw dislocations

Figure: Edge dislocation

A edge dislocation is a lattice plane that ends in the metal structure without further
connection. It can be thought of as an inserted atomic plane in the already existing
structure. The “edge” of this inserted atomic plane is also referred to as
a dislocation line or dislocation core and often symbolized in drawings with a “T”.
Along these dislocation lines, the lattice structure is heavily distorted and has
stresses. The dislocation line either forms a closed ring or exits the surface of the
crystal (grain) or terminates at other defects.

In contrast to a edge dislocation, a screw dislocation winds an atomic plane along

the dislocation line through the crystal like the thread of a screw. In a crystal
always combinations of both types of dislocation occur.

Dislocations occur during solidification of melts or due to stresses in the metal. But
they are also introduced by plastic deformation (work hardening or strain
hardening). Dislocations play a central role in deformation processes, since they
are largely responsible for the good ductility of the metals.

The dislocation density in a crystal is given as the total length of all dislocation
lines per volume. Dislocation lines with a total length of about 1 km are found per
square millimeter in a metal. Cold working increases the dislocation length per
square millimeter to around 1 million kilometers! From a dislocation density of
about 100 million kilometers per square millimeter, however, the material is so
damaged that it is destroyed in principle.

Planar defects
Compared to linear crystallographic defects, planar defects disturb the lattice
structure in a spatially larger area. The following defects fall into this
categorization of the so-called 2-dimensional defects:

 high angle grain boundaries

 low angle grain boundaries

 phase boundaries

 stacking fault

Grain boundary

Grain boundaries delimit areas in a crystal within the lattice structure shows a

uniform spatial orientation. These boundaries are structureless regions of thickness
on the order of only 2 to 4 atomic distances. The uniformly aligned areas
themselves are referred to as grains or as crystallites. The unit cells are identical
for each grain, they only have a different spatial orientation (rotated, mirrored,
etc.).

Figure: Grain boundary

The grain structure is formed during the solidification of the molten metal, since a
melt usually does not solidify starting from a single point but at many points at the
same time (exception: single crystals or monocrystals!). At each of these
solidification points (so-called nuclei), the lattice structure is formed with its own
orientation. The growing grains collide after complete solidification of the melt
and thus form the grain boundaries.
Small angle grain boundary

A deviation of the crystal orientation can also arise if several dislocations are
superimposed. Since these errors change the lattice orientation by only a few
degrees (<15 °), one also speaks of a low angle grain boundary. Due to the better
delimitation, the grain boundaries described above are often referred to as high
angle grain boundaries.

Figure: Low angle grain boundary

Twin grain boundary

A special type of grain boundary is the so-called twin boundary. In this case, the
opposing lattice structures are just ordered in mirror image. Such a twin grain
boundary has a high symmetry and thus low energy.

Twin boundaries are often seen under the microscope as straight lines, while
“normal” grain boundaries are characterized by more curvy lines. Twin grain
boundaries are very often formed in metals like brass, copper and austenite (γ-Fe).

While grain boundaries generally form incoherent interfaces, twin grain boundaries
show a fully coherent interface (for the concept of coherence, see the next section).

Phase boundary

The so-called phase boundary forms another type of planar crystallographic

defects.
A phase may be an accumulation of alloying elements in the host lattice of the
metal. Thus a phase boundary spatially delimits two different chemical structures.
Depending on how the structures of the different phases merge, a distinction is
made between a coherent, partially coherent or incoherent phase boundary.

Figure: Phase boundary

With a coherent phase boundary, the two structures merge into one another
without any gaps. This is true if the two phases have a consistent structure and
similar chemical properties.

However, if the phases differ somewhat in their properties, the lattice structures no
longer completely merge into one another. Therefore dislocations must be present
at regular intervals. One then speaks of a partially coherent phase boundary..

By contrast, with an incoherent phase boundary, neither the lattice structures nor

the chemical properties of the two phases match. The structure is similar to a high
angle grain boundary, but consists of two distinct phases. The phase boundaries are
not distorted to the extent that is the case with high angle grain boundaries.

Stacking fault

Another planar defect is the so-called stacking fault. It is a locally different

stacking sequence of otherwise periodically arranged planes. For example, the
stacking sequence of the closest packed planes in the face-centered cubic lattice
with normally ABCABC may locally have the sequence ABACAB. Such stacking
faults can arise when a dislocation is split into two smaller dislocations.

Figure: Stacking fault

Bulk defects

Bulk defects are also referred to as 3-dimensional defects and interfere with the
lattice structure to a greater extent than the planar defects do:

 precipitations

 pores

 inclusions
The so-called precipitations are an accumulation of chemical compounds (phases)
in the metal. In addition to precipitations, pores or other inclusions are among the
3-dimensional defects.
Shahin Kerimli

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