Download DoITPoMS

Dissemination of IT for the Promotion of
Materials Science (DoITPoMS)




About DoITPoMS
Events
Mailing List
Contact Us


Micrograph Library
Teaching and Learning Packages

Community (login required)

Integrating e-Learning into Materials Education
This Workshop, scheduled for 23 June 2004 in
Liverpool, is being rescheduled for Easter 2005.
Further information
© University of Cambridge
DoITPoMS, Department of Materials Science and Metallurgy, University of Cambridge
http://www.doitpoms.ac.uk/index.html
Phase diagrams and solidification
http://www.doitpoms.ac.uk/tlplib/phase-diagrams/index.php
Solid Solutions
http://www.doitpoms.ac.uk/tlplib/solid-solutions/index.php
Exsolution in phase diagrams
A binary solid solution can show a phase diagram as follows:
liquidus
solidus
The solidus and liquidus separate the single phase regions. This is similar to the Cu-Ni phase
diagram. If the system demonstrates exsolution, then there will be a region in the solid state where
two solid phases form from the solid solution. This is common and most solid solutions
demonstrate it to some degree.
Miscibility gap
In a eutectic phase diagram, the two-phase solid region meets the solidus/liquidus.
Solid solution regions are usually denoted with Greek letters, for example  for ferritic
iron and  for austenitic iron.
Demonstration of phase separation
The transition from a single phase to two phases (and vice-versa) can be easily demonstrated
using a mixture of two suitable liquids.
A mixture of cyclohexane and aniline can exist as two separate phases or as a single phase,
depending on the temperature. The thermodynamic transition between these two states can be
understood by considering the balance between entropy and enthalpy (see Thermodynamics
section in this TLP).
Aniline and cyclohexane are immiscible over a wide range of compositions below about 35 ºC. In
this immiscible region there exists an aniline-rich and a cyclohexane-rich phase, separated by a
boundary, seen as a meniscus. When this mixture is heated, the volume of one phase increases at
the expense of the other. This can be seen as movement of the meniscus, provided the heating is
slow enough. At the transition temperature for the particular composition, there will no longer be
two discernable phases.
A significant point occurs when the distinction between the two coexisting phases reduces to zero.
Here the domains present in the mixture can switch easily between aniline-rich and cyclohexanerich. The composition variance is on such a scale as to interfere with light passing through it.
Light will scatter in proportion to the squared difference in n, the index of refraction, of the two
phases. Therefore light scatters more as the number of domain interfaces increases. Hence light is
scattered strongly by the mixture across a small temperature range around the transition
temperature.
At the critical point, the scattering is so intense that the system becomes opaque. This
phenomenon is called critical opalescence. The domains demonstrate some interesting properties,
such as fractal shapes, and there is a peak in the heat capacity. This critical transition temperature
is a maximum with respect to the composition. Thus it can be determined by interpolating
transition temperatures from known compositions.
Demonstration
A mixture of equal quantities of cyclohexane and aniline contained in a sealed vial is heated to
approximately 35 ºC (i.e. just above the critical temperature), using a water bath (or water from a
hot tap). The mixture is allowed to cool, and a laser is pointed at the vial so that it shines onto a
screen opposite, as shown in the diagram below.
When the critical temperature is reached and the mixture goes from a single phase to two phases,
the spot of light on the screen is disrupted as the phases separate. The spot ‘flickers' and then
becomes totally diffuse. It will eventually form a single spot again once the transition is
completed and the two chemicals have completely separated. The pattern of events can also be
seen in reverse as the mixture is heated.
View video showing the laser light (as seen on the screen) flickering and spreading out to become
completely opaque as the mixture cools through the transition temperature (1.2 MB) ... in separate
window ... video alone
The video has been speeded up by a factor of about 10.
View video showing the vial, which has been filmed perpendicular to the direction of the laser
light (left to right) (920 KB) ... in separate window ... video alone
Initially, the laser light is seen as a single beam passing through the mixture, but as the transition
point is reached, the beam spreads out. The single beam eventually reforms, once the transition is
complete. This video has been speeded up by a factor of about 200.
Precipitates from solid solution
The precipitation of a solid phase from a liquid matrix is governed by a balance between the
thermodynamic driving force and the energy penalty for creating new solid-liquid surface
interfaces. This determines the size and shape of the precipitates. The precipitation of a solid
phase from a solid parent phase is very similar.
There are various types of interface between solid phases:
a. Coherent - there is perfect registry of the lattices.
b. Coherent with strain - it is quite likely for there to be some strain with the interface, due
to imperfect matching. The strain energy increases with the size of the growing particle,
and there is a transition to a semi-coherent interface.
c. Semi-coherent interface - the introduction of dislocations reduces the strain energy (but
they themselves contribute to the energy of the system).
d. Incoherent - there is no matching of the interface.
Coherent
Coherent with strain
Semi-coherent
Incoherent
In general, the interfacial free energy will be minimised with better matching of the two phases.
Incoherent interfaces have high energy and are relatively mobile because of the greater freedom
of atomic motion.
The stresses present in the parent matrix as the precipitate grows strongly influences the shape of
the precipitate. By modelling the precipitate as an ellipsoid of revolution, the following graph
shows how the strain energy is related to the shape.
Growth as discs or plates is clearly preferred. A precipitate particle will likely have some
coherent and some incoherent interfaces with the matrix. The greater mobility of the incoherent
interfaces leads to faster growth in these directions. This anisotropic growth leads to plate and
disc morphologies. The bounding coherent interfaces will be parallel to crystallographic planes in
the matrix.
Solid solution precipitation/exsolution is used to strengthen many alloys. This is known as
precipitation hardening , or age hardening. It involves quenching an alloy to a supersaturated
state (where the amount of dissolved solute is greater than the equilibrium amount predicted by
the phase diagram). A heating schedule can then be applied to control the nature of the
precipitation. For example in Al-Cu, a very fine dispersion of q particles hardens the a phase.
This age-hardened alloy is used in aerospace applications.
View micrograph of a precipitation hardened sample of Al-Cu
At lower temperatures, it is preferable to have incoherent precipitates, as the greater strains
produce more resistance on dislocation motion. At higher temperatures however, the greater
mobililty of the incoherent interfaces allows larger particles to grow at the expense of smaller
ones (called coarsening), and the system becomes less effective at strengthening. So for high
temperature use, coherent particles are used, such as the g' precipitate in nickel-based superalloys
(here a phenomenon called order hardening provides the strengthening mechanism, rather than
the strain fields).
View micrograph of an order hardened sample of Nickel superalloy
Ceramics, which are typically brittle, can also benefit from solid solution precipitation. Zirconia
based compounds can be toughened by having tetragonal structure particles in the monoclinic
matrix. Propagation of cracks through the zirconia requires the transformation of these
precipitates to the monoclinic form. This requires an input of energy, provided by the stress,
hence the material is toughened.
Another use of solid solution precipitation lies in nano-materials. By precipitating from a solid
solution, the nanometre (10-9 m) scale of the microstructure can provide many beneficial effects.
For example, the presence of 5 nm diameter carbide particles in steel piano wires helps make it
the world's strongest structural material (with some ductility). Precipitation from a liquid phase is
too fast to produce such small scale particles.