Development of Microstructure
Cu-Zn Phase Diagram
Stability of Hume-Rothery Phases in Cu-Zn
Isothermal Transformation Diagram
Transformation Rate diagram
A phase diagram is a type of chart used to show conditions at
which thermodynamic distinct phases can occur at equilibrium.
It conveniently and concisely displays the control of phase
structure of a particular system.
The three controllable parameters that will affect phase structure
are temperature, pressure, and composition.
• To show phases are present at different compositions and
temperatures under slow cooling (equilibrium) conditions.
• To indicate equilibrium solid solubility of one element/compound in
• To indicate temperature at which an alloy starts to solidify and the
range of solidification.
• To indicate the temperature at which different phases start to melt.
• Amount of each phase in a two-phase mixture can be obtained.
• Phase diagrams are classified based on the number of
components in the system
Single component systems have unary diagrams.
Two-component systems have binary diagrams and so on..
A thermodynamic law which governs the
conditions for phase equilibrium.
Useful in interpreting Phase Diagrams.
P is the number of phases present
F is termed the number of degrees of freedom
C in represents the number of components in the
N is the number of non compositional
variables, which do not depend on the
composition of system.
A common phase diagram in which
pressure is held constant whereas
temperature and composition are kept
They represent the relationships
between temperatures and
compositions of phases at the
equilibrium, which influence the
microstructure of the alloy.
Many microstructures develop from
phase transformations either it be
transition of one phase into another or
appearance or disappearance of the
phase which do occur on altering the
A common example for a binary
isomorphous alloy is Cu-Ni system.
A study of this diagram would enable us
to predict the transformations and
equilibrium or nonequilibrium
In practical situations diffusion is not as slow to allow
the readjustments in diffusion while maintaining the
How it differs from equilibrium cooling?
Diffusion slow in α phase
Composition changes with radial composition
and a greater proportion of liquid present
Shift of solidus line to higher Ni contents to
average composition of α
Slower the cooling rate and more rapid the
diffusion process smaller the displacement
Solidification complete at 1478 F instead of 1493
F with 35% average Ni content
Segregation occurs where the concentration
gradients are established across grains
Formation of core-structure with center rich in
high melting element whereas increase in
concentration of low melting element on going
towards grain boundary
Melting below the equilibrium melting
temperature of alloy may happen
Loss in mechanical integrity due to thin liquid
film that separates the grains.
Intermediate Phases :
● Pure iron on heating undergoes two changes in the crystal structure before
● At room temperature it exists in α-ferrite upto 1674 F, which has a
BCC crystal structure.
● At 1185 F it get polymorphically transformed into FCC γ-austenite and
it persists till 2541 F when it reverts back to BCC δ-ferrite.
● At 6.7% carbon concentration Cementite(Fe3C) is formed.
● Iron melts at 2800 F.
Intermediate Reactions :
● Eutectic :
>The above is the governing eqn.
> The phase changes from a to b.
> The pearlite structure forms due
to the difference b/w parent &
> This is called Pearlite because
of its look of a pearl.
Diffusion through minimal distance by
C-atoms leads to layered structure.
Composition left to the
eutectoid, between 0.022 and 0.76 wt%
C, is called hypoeutectoid alloy.
At c, the microstructure consists entirely
of γ-austenite grains.
On cooling, at d, small α particles form
along γ-grain boundaries.
The composition becomes richer in
carbon and α particles grow larger on
cooling till 727.C.
Once the temperature is lowered below
727.C all the γ-phase gets transformed
α-phase is present as a continuous
matrix phase surrounding the isolated
Composition right to the
eutectoid, between 0.76 and 2.14 wt% C, is
called hyper eutectoid alloy.
At g, the microstructure consists entirely of
On cooling, at h, small cementite particles
starts forming along γ-grain boundaries.
Cementite composition remains constant as
the temperature changes until 727.C.
On lowering the temperature below 727.C
all the γ-phase gets transformed into
The resulting microstructure consists of
pearlite and proeutectoid cementite as
Cu-Zn system displays a sequence of phases along
the alloy composition called Hume-Rothery phases.
The criterion for the stability of these phases as per
Hume-Rothery concept is a contact of the Brillouin
zone (BZ) plane with the Fermi surface (FS) where FS
is considered to be a sphere within the nearly
free electron approximation.
Interaction between the BZ boundary & FS opens a
pseudo-gap and reduces the electronic energy,
leading to the lowering of the overall structure
The relative stability of the α,β, and γ-structures is
possibly connected with the relative contribution of
the Hume-Rothery effect.
The close-packed α and β-structures begin to
transform to new high-pressure phases, and the
vacant γ-structure is shown to be stable up to at
least 50 GPa.
The γ-phase shows an anomalous behaviour of some
physical properties, such as resistivity, magnetic
susceptibility, Hall effect, magnetoresistance and
thermoelectric power, which was accounted for by
the band-structure effect associated
with the BZ–FS interaction.
All these observations supports the idea of
the enhancement of the Hume-Rothery
mechanism on compression.
The influence of other alloying elements
on Fe-Fe3C system
Depending on the particular alloying
element and its concentration the positions
of phase boundaries and the shapes of the
phase fields do alter.
One of the important changes is the shift in
position of the eutectoid with respect to
temperature and to carbon concentration.
Steels are normally alloyed for other
reasons,however—usually either to
improve their corrosion resistance or to
render them amenable to heat treatment.
Iron-Iron carbide eutectoid reaction:
Temperature plays an important role in the rate of
the austenite-to-pearlite transformation . The
temperature dependence for an iron–carbon alloy
of eutectoid composition is indicated in Figure.
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 a specimen composed of
100% austenite to the temperature indicated; that
temperature was maintained constant
throughout the course of the reaction.
A more convenient way of representing both
the time and temperature dependence of this
transformation is in the bottom portion of
The dashed curve corresponds to 50% of
In interpreting this diagram, note first that
the eutectoid temperature (1341F)is
indicated by a horizontal line; at
temperatures above the eutectoid.
The austenite-to-pearlite transformation will
occur only if an alloy is super cooled to
below the eutectoid; as indicated by the
curves, the time necessary for the
transformation to begin and then end
depends on temperature.
The transformation rate increases with decreasing temperature such that at
( 1000 F) only about 3 s is required for the reaction to go to 50% completion.
In previous graph Very rapid cooling of 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.
The transformation of austenite to pearlite begins at the
intersection, point C (after approximately 3.5 s), and has reached
completion by about 15 s, corresponding to point D. Figure 10.14 also
shows schematic microstructures at various times during the
progression of the reaction.
The thickness ratio of the ferrite and cementite layers in pearlite is
approximately 8 to 1. However, the absolute layer thickness depends
on the temperature at which the isothermal transformation is allowed
to occur. At temperatures just below the eutectoid, relatively thick
layers of both the -ferrite and Fe3C phases are produced; this
microstructure is called coarse pearlite (shown in next slide) and the
region at which it forms is indicated to the right of the completion
curve on Figure 10.14
The thin-layered structure produced
in the vicinity 540C of is termed fine
pearlite; is the dependence of
mechanical properties on lamellar
thickness. Photomicrographs of
coarse and fine pearlite for a
eutectoid composition are shown in
For iron–carbon alloys of other
compositions, a proeutectoid phase
(either ferrite or cementite) will
coexist with pearlite, Thus
additional curves corresponding to a
proeutectoid transformation also
must be included on the isothermal
transformation diagram. A portion
of one such diagram for a 1.13 wt%
Materials Science and Engineering-William
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Stability of Hume-Rothery phases in Cu–Zn
alloys at pressures up to 50 GPa by V F
Degtyareva1, O Degtyareva