MCEN 5024. Fall 2003.
Phase equilibrium diagrams.
Overview
Phase diagrams assist in the interpretation of microstructure of metals.
Traditional sectioning, mounting, polishing and etching techniques are often used
to determine the microstructure including around regions of failure (e.g. welds,
inclusions, fracture sites) which can then be subsequently related to the physical
(typically mechanical) properties. This forms the basis of structure – property
relationships.
Thus, phase equilibrium diagrams ‘define the region of stability’ of the phases that
can occur in an alloy system under the conditions of constant pressure.
Equilibrium diagrams are presented in the form of temperature versus composition
and represent the interrelationship between phases, temperature and composition
only under equilibrium conditions.
A metal quenched from a higher temperature to a lower temperature may contain
phases that are non-equilibrium phases i.e. may normally only exist at higher
temperatures, not at the lower temperature.
Given sufficient time at this lower temperature, a non-equilibrium phase may
convert via diffusion to its equilibrium state at this lower temperature.
When we are considering the effects of time and temperature on microstructure
then we need to use time – temperature transformation (TTT) continuous cooling
transformation (CCT) diagrams.
Isomorphous alloy systems.
The simplest phase diagram to consider is the isomorphous system which is a
two-component, so called binary, alloy system.
Only one type of crystal structure is observed. A classic example is that of copper –
nickel shown below:
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These two elements combine to form a single liquid and a single solid phase. With
reference to the above diagram, we define two lines: the liquidus and the solidus.
Above the liquidus line the region of stability for the liquid phase.
The region below the solidus line is the region of stability for the solid phase. The
region between the liquidus and the solidus is where both liquid and solid phases
co-exist.
In the case of the copper-nickel system, this is a substitutional alloy in that there is
a direct substitution of one type of atom for another so that solute atoms come into
the lattice to take up positions typically occupied by solvent atoms.
The atomic diameter of copper is 2.551 Å and that of nickel is 2.487 Å. The
difference is negligible (2%) and hence only leads to a slight distortion of the lattice
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thus they are truly soluble and whatever the composition, they form a FCC
structure. Solid-solubility of one metal in another only occurs if the diameters of the
metals differ by less than 15% (Hume Rothery rule).
This is directly related to the strains put on the solvent lattice by the solute atoms. If
we replace nickel with silver (also FCC), which is similar chemically to copper, we
find that the solubility of silver in copper or copper in silver is less than one percent.
The atomic diameter of silver is 2.884 Å, which is about 13% larger than that of the
copper atom.
Other considerations for the formation of an alloy relate to their electro-potential. A
more electronegative element will combine with an electropositive element
ionically through sharing of valence electrons. This is not considered an alloy in the
sense discussed here.
On the other hand, two elements lying close to one another in the periodic table
tend to act in a similar manner chemically leads to metallic rather than ionic
bonding. This will however only occur if both metals have the same valence and
crystallize in the same lattice form.
An alternative to the formation of a substitutional alloy is that instead of displacing
a solvent atom, the solute atom resides in the interstices between the atoms. This
is termed an interstitial alloy.
Interstitial solid solutions only occur if the solute atom has an apparent diameter
smaller than 0.59 that of the solvent. The four most important interstitial solute
atoms are carbon, nitrogen, oxygen and hydrogen.
Interstitial solute atoms dissolve much more readily in transition metals (Fe, Vn, W,
Ti, Cr, Th, Zr, Mn, U, Ni, Mo) than in other metals primarily due to their incomplete
valence electron configuration.
Interstitial atoms can diffuse easily through the lattice, hopping from one interstitial
position to another and therefore can have a large impact on the properties of the
solvent than might be expected at first sight.
One of the major interstitial alloys is that of carbon in iron where the iron – carbon
phase diagram represents one of the most important classes of alloys known.
These two elements form a eutectic system.
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The copper nickel phase diagram represents an alloy system in which the free
energy–composition curves for a given temperature intersect at only one
composition.
Other systems exhibit equivalent curves but intersect at two compositions forming
a minima or maxima at a given composition / temperature.
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In this case, both the liquidus and solidus curves are tangential to each other and
to an isothermal line at the point of intersection.
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Such points are termed incongruent points whereby the freezing of the alloy at
such a point is equivalent to that of the freezing of a pure metal.
The resulting solid however is not a pure component but a solid solution of the two
metals. There are a number of alloys that show minima in the liquidus / solidus
curves. An example is the gold-nickel system:
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MCEN 5024. Fall 2003.
Eutectic systems.
In eutectic systems (e.g. copper – silver), there is a composition at which the alloy
freezes at a lower temperature than all of the other compositions. Thus, under slow
(pseudo – equilibrium) cooling conditions, this composition would freeze at a single
temperature, however, instead of forming a single phase as above, it forms two
different solid phases. Hence, at the eutectic temperature (an invariant point), the
liquid freezes to form two solid phases. The eutectic point in the copper – silver
system occurs at 28.1% copper and 779.4oC.
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If we compare this to the gold – nickel system, we see obvious similarities between
the two. We note however that in the case of the gold – nickel system, the alloy
with composition at the minima first solidifies as a single solid homogenous
solution, which then upon further cooling breaks down into two solid phases as it
passes through the miscibility gap.
(Note: this is related to the relative sizes of the gold and nickel atoms such that a
lower lattice strain is achieved when the gold and nickel atoms arrange themselves
in alternating layers when compared to isolated clusters of gold and nickel atoms.
A still greater decrease in the strain energy is achieved if segregation occurs such
that two distinct crystal phases occur, one gold rich and the other nickel rich).
Again, going back to the copper – silver phase diagram, we not that there is no
miscibility gap such that the liquid is able to transform directly into a two-phase
mixture.
In order for a system to exhibit a miscibility gap, there must be a tendency for the
atoms of the same kind to segregate in the solid state. A miscibility gap as shown
by the gold – nickel system can only occur if the component metals are very similar
chemically and crystallize in the same lattice form since the two components need
to be capable of dissolving in each other at high temperatures. In a eutectic
system, the two components do not need to have the same crystal structure nor do
they have to be chemically similar.
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The peritectic transformation.
Besides the eutectic reaction, another three-phase reaction between a liquid and a
solid to form a new and different phase occurs at the peritectic point.
As an example we can study the iron – nickel phase diagram. In this system, the
atomic diameters are almost identical (Fe, 2.476, Ni, 2.486) and both are from
group VIII of the periodic table and hence chemically similar. Both crystallize in the
FCC form, Ni is FCC at all temperatures but the stable form of Fe is BCC above
1390oC and below 910oC.
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