Alloys: Phase Diagrams
• Most engineering metallic materials are not pure metals of
one kind, but alloys that contain atoms of more than one
metal or of a metal and a nonmetal. In an alloy, the
combination of atoms of the basic metal A, the solvent, and
of the added metal B, the solute, may be a solid solution or
it may be a compound, and in a metal the grains
representing different solid solutions or compounds may be
mixed together.
• Solid solutions are of two kinds:
– In a substitutional solution, the atoms of the solute replace some
atoms of the solvent in its crystal cells. Such a solution is formed
under the following conditions:
• The atoms of the two metals do not differ in diameter by more
than 15%.
• Their space lattices are similar.
• They are close to another in the electromotoric series.
– An interstitial solid solution is formed if the atoms of the solute
occupy positions in between the atoms of the solvent in its cell.
Obviously this is only possible if the solute atoms are much
smaller than those of the solvent. Even then the solubility is
limited. The most common example is that of steel, where the C
atoms are located in the Fe cells.
– Solid solubility increases with temperature as it does with liquid
solutions. Correspondingly, solute atoms precipitate on cooling
(by diffusion) out of the atoms of the solvent.
– Substitutional solid solutions in which there is a long-range order
of the two metallic atoms and the composition is well defined in
simple ratios of atom fractions are considered as intermetallic
compounds. They have a sharp melting point and other
characteristics of distinct chemical species. Very often, such
compounds have higher melting points than either of the elements,
and they care hard and brittle.
– The lever rule can be used to determine the weight proportions of
the two components at 1300°C as follows:
%liquid (46 Ni) 
% solid (63 Ni) 
ed
62  52
100 
100  66.67%
ec
62  47
d c
100  33.33%
ec
• Eutectic alloy equilibrium diagrams
– Just as a limited amount of salt can be dissolved in water, there are
many instances where a limited amount of the alloying ingredient
can be absorbed by the solid mixture.
– The elements of a binary alloy may be completely soluble in the
liquid state but only partially soluble in the solid state.
– When the alloying ingredient is present in amounts above the
maximum solubility percentage, the alloying ingredient
precipitates out. In aqueous solutions, the precipitate falls to the
bottom of the container.
– In metallic alloys, the precipitate remains suspended as pure
crystals dispersed throughout the primary metal.
– In chemistry, a mixture is different from a solution. Salt in water
forms a solution. Sugar crystals mixed with salt crystals form a
mixture. A mixture of two solid ingredients with no solubility is
known as a eutectic alloy. Since the two ingredients do not mix,
reducing the temperature below the eutectic line results in crystals
of both pure ingredients forming.
– In another basic type of a phase diagram, the two components A
and B are fully mutually soluble in the liquid phase but completely
insoluble in the solid state.
– The melting temperatures of the alloys decrease from both ends,
and there is a particular composition called the eutectic which has
the lowest melting temperature.
• The Fe-C Phase Diagram
– The phase diagrams of actual alloys differ from the idealized forms
because there is always some partial solid solubility available.
– C < 0.1% low carbon steels
• cans, automobiles body panels, sheet metal parts (UTS =
350MPa, e = 35%)
– C ~ 0.2% structural beams
• UTS = 420MPa, e = 30%
– C ~ 0.3% - o.45% medium carbon steel
• machine parts
– C ~ 0.7% railroad rails
• UTS = 800MPa, e = 10%
• Grain size
– fine grained steel is stronger and tougher than steel with coarse
grains.
– g is soft and ductile
• perlite => a + Fe3C
• a => FCC
• Fe3C => an orthorhombic structure
– C < 0.8% => hypoeutectic
– C > 0.8% => hypereutectic
0.8  0.25
 71wt%
0.8  0.025
eutectoid (0.8% C)  29 wt% (perlite)
α (0.025%) 
1.2 - 0.8
Fe3C (6.67% C) 
 6.8%
6.67 - 0.8
γ(0.8% C)  93.2% (perlite)
• Recovery, recrystallization, and grain growth
– the strain hardened metal is stronger and harder but it is less ductile
– recovery and recrystallization may revert these properties back to
the precold-worked state
– Recovery:
• Some of the stored internal strain energy is relieved, as a result
of enhanced atomic diffusion at the elevated temperature.
– recrystallization:
• Can be used with all metals to relieve stresses induced during
cold working. It involves heating the material in a furnace to a
specific temperature (recrystallization temperature) and
holding it there for a long time.
• Induces the formation and growth of strain-free grains within
the grains already formed.
• The resulting microstructure is essentially the microstructure
that existed before any cold working and is softer and more
ductile than the cold-worked microstructure.
• Recrystallization
– Even after recovery is complete, the grains are still in a relatively
high strain energy state. Recrystallization is the formation of a
new set of strain free and equiaxed grains that have low dislocation
densities and are characteristic of precold-worked condition. The
driving force to produce this new grain structure is the difference
in internal energy between the strained and unstrained material.
The new grains form as very small nuclei and grow until the
completely replace the parent material, processes that involve
short-range diffusion.
– The recrystallization process is more sensitive to temperature than
it is to exposure time. Recrystallization will occur naturally over a
wide range of temperatures; however, the reaction rates increase at
higher temperatures.
• Grain growth
– After recrystallization is complete, the strain-free grains will
continue to grow if the metal specimen is left at the elevated
temperature - a phenomenon called grain growth. Grain growth
does not need to be preceded by recovery and recrystallization; it
may occur in all polycrystalline materials, metals, and ceramics.
– An energy is associated with grain boundaries, as explained in
Section 4.5. As grains increase in size, the total boundary area
decreases, yielding an attendant reduction in the total energy; this
is the driving force for grain growth.
– Grain growth occurs by the migration of grain boundaries.
Obviously, not all grains can enlarge, but some grow at the
expense of others that shrink. Thus, the average grain size
increases with time, and at any particular instant there will exist a
range of grain sizes. Boundary motion is just the short range
diffusion of atoms from one side of the boundary to the other. The
directions of boundary movement and atomic motion are opposite
to each other, as shown in Figure 9.6.
• Cold working versus hot working
– As a material is worked and the dislocations move, plastic strain
builds up. If the strain occurs at a high enough temperature (above
recrystallization temp.), there will be sufficient thermal energy to
anneal out the lattice distortions.
– Forming operations above the recrystallization temperature are
known as hot working, since annealing occurs simultaneously with
the plastic forming. The material remains ductile.
– If the plastic forming takes place at a low temperature, there will
be insufficient thermal energy to anneal out the dislocations. The
material will become progressively stronger, harder, and more
brittle until it eventually fails. This is known as cold working.
• Microstructural and property changes in iron-carbon alloys
– Some of the basic kinetic principles of solid state transformations
are now extended and applied specifically to iron - carbon alloys in
terms of the relationships between heat treatment, the development
of microstructure, and mechanical properties. This system has
been chosen because it is familiar and because a wide variety of
microstructures and mechanical properties are possible for ironcarbon (or steel) alloys.
– Isothermal transformation diagrams
• consider again the iron-iron carbide eutectoid reaction,
γ(0.77 wt% C)  α(0.022 wt% C)  Fe3C(6.70 wt% C)
• which is fundamental to the development of microstructure in
steel alloys. Upon cooling, austenite, having an intermediate
carbon concentration, transforms to a ferrite phase, having a
much lower carbon content, and also to cementite, which a
much higher concentration. For carbon atoms to selectively
segregate in the cementite phase, diffusion is necessary.
– Temperature plays an important role in the rate of the austenite-topearlite transformation. The temperature dependence for an ironcaarbon alloy of eutectoid composition is indicated in Figure 9.9,
which plots S-shaped curves of the percentage transformation
versus the logarithm of time at three different temperatures. For
each curve, data were collected after rapidly cooling off a
specimen composed of 100% austenite to the temperature
indicated; that temperature was maintained constant throughout
the course of the reaction.
• Steel Hardening Processes:
– Hard steel resists plastic deformation. Steel is hard if it has a
homogeneous, austenitic structure with coarse grains. Some steels
(with little carbon) are difficult to harden.
– The basic hardening processes consist of heating to approximately
50 degrees C above the A3 critical line, allowing austenite to form,
and then quenching rapidly. Hardened steel consists primarily of
martensite and bainite.
– Martensite is a supersaturated solution of carbon in alpha iron.
– Bainite is not hard as martensite, but it does have good impact
strength and fairly high hardness.
– Neither martensite nor bainite are equilibrium substances - they are
not found on the iron-carbon equilibrium diagram but are formed
during the quenching operation.
– The allotropy of iron combined with the large difference in C
solubility in beta and alpha irons is thus the basis of hardening of
steel. The process is accomplished by first hearing the steel into an
austenitic range, holding it there long enough to obtain austenite
grains with uniform composition and then quenching the part for
fast cooling. If the cooling rate is not fast enough, the martensite
will not form fully or not at all. This is best illustrated by means of
a diagram constructed from observations of isothermal
transformations. Such a diagram is called a time-temperature
transformation (TTT) diagram. This diagram, for an eutectoid
carbon steel, is shown in Fig. 2.16. It is obtained by carrying out
experiments like the one indicated by the line A - E. The
austenitized material is first quenched into a salt bath of
temperature T, line A-B. Then it is held at this temperature for a
certain time, say, until point C, and then quenched to room
temperature. Next time it is held at T until point D, next time until
E, and so on. The microstructures so obtained are studied.
– A more convenient way of representing both the time and
temperature dependence of this transformation is in the bottom
portion of Figure 9.10. Here, the vertical and horizontal axes are,
respectively, temperature and the logarithm of time. Two solid
curves are plotted; one represents the time required at each
temperature for the initiation or start of the transformation; the
other is for the transformation conclusion. The dashed curve
corresponds to 50% of transformation completion. These curves
were generated from a series of plots of the percentage
transformation versus the logarithm of time taken over a range of
temperatures. The S-shaped curve in the upper portion of Figure
9.10, illustrates how the data transfer is made.
– An actual isothermal heat treatment curve (ABCD) is
superimposed on the isothermal transformation diagram for a
eutectoid iron-carbon alloy in Figure 9.11. Very rapid cooling
austenite to a temperature is indicated by the near vertical line AB,
and the isothermal treatment at this temperature is represented by
the horizontal segment BCD. Of course, time increases from left
to right along this line. The transformation of austenite to pearlite
begins at the intersection, point C (after approximately 3.5 sec),
and has reached completion by about 15 sec, corresponding to
point D. Figure 9.11 also shows schematic microstructures at
various times during the progression of the reaction.
– The hardness obtainable in quenched steels depends on the amount
of carbon. Steels with less than 0.3% cannot be successfully
hardened. For steels with 0.3% to 0.6% carbon, the maximum
obtainable hardness increases from about 48 Rc to about 66 Rc.
– The steel quenched through the martensite transformation is very
hard and brittle and, because of the brittleness, it cannot in most
instances be used in this state. It is, therefore, subjected to another
heat-treatment process called tempering. This is done by heating
the part to some temperature below 723C, holding it at this
temperature for a certain period of time, and quenching it again.
During tempering the martensitic tetragonal, highly distorted
structure reverts to regular BCC and allows the carbon atoms to
migrate and form some very fine iron carbide crystals. Hardness
decreases but ductility improves.
– The changes in hardness and ductility depend on the temperature
and time of tempering. The temperature has a much larger effect
than time. Therefore, in practical terms the temperature is given
assuming that the time will be of the order of one half to several
hours. There are several typical temperature ranges of tempering:
• 100-200C Upon reaching 200C the martensite is fully
decomposed. Structural changes are obtained on a very fine
scale and cannot be detected under a microscope. Hardness
almost does not change at all; some ductility is obtained. This
is called fine-tempered martensite.
• 200-300C Structure is still tempered martensite, but hardness
decreases to 55-58 Rc. However, in this range, due to
precipitation of oxides and nitrides a decrease of toughness
may occur. This is called blue brittleness because it occurs at
temperatures that leave a blue oxide of film on the steel.
• 360-723C The higher the temperature in this range, the coarser
the cementite particles. At or above 650C these particles can
easily be resolved under an optical microscope. Because of
their spherical shape, the structure is called spheroidite. The
decrease of hardness and increase of ductility are almost
linearly proportional to tempering temperature. The range of
hardness extends from about 60 Rc for martensite down to
about 20 Rc for shperoidite.