Binary Phase Diagrams

• Two-component systems have binary phase diagrams. Apart from temperature

and pressure, we have one composition variable for each of the phases in
equilibrium.
• We then need a three-dimensional diagram to plot the variations in pressure,
temperature and composition. In order to simplify the representation of the
phase relationships on paper, binary phase diagrams are usually drawn at
atmospheric pressure, showing variations in temperature and composition only.
• Pressure changes often produce no significant effect on the equilibrium and,
therefore, it is customary to ignore the pressure variable and the vapour phase.
• In such cases, one of the variables has been arbitrarily omitted and the phase
rule for the condensed phase is written in modified form
• F= C-P+1
 Isomorphous System
• The simplest binary phase diagram is obtained for a system exhibiting
complete liquid solubility as well as solid solubility (Isomorphous System).
• The two components dissolve in each other in all proportions both in the
liquid and the solid states.
• Clearly, the two components must have the same crystal structure besides
satisfying the other Hume Rothery’s conditions for extensive solid solubility.
• Ex: Cu–Ni, Ag–Au, Ge–Si and Al2O3–Cr2O3
• Two phases on the phase diagram, the liquid and the solid phases.
• Single-phase regions are separated by a two-phase region (L + S), where both liquid and solid co-exist.
• As we move from a single-phase region (1), we cross into a two-phase region (2), and then again into a
single-phase region (1)(1-2-1 rule).
• The phase boundary between the liquid and the two-phase region is called the liquidus. The boundary
between the solid and the two-phase region is called the solidus.
• When only one phase is present, the composition axis gives the composition of
that phase directly.
• When two phases are present, the compositions of the phases are not the same.
• They should be read according to the following convention:
• At the temperature of interest T, a horizontal line called the tie-line is drawn as
shown in Fig. 7.2. The points of intersection of the tie-line with the liquidus and
the solidus give, respectively, the liquid and the solid compositions, cl and cs, which
are in equilibrium with each other.
• Thus, in Fig. 7.2, at 2180°C, for an overall composition co = 73% Cr2O3 (27% Al2O3),
• We have The liquid composition cl = 57% Cr2O3 (43% Al2O3), and
• The solid composition cs = 82% Cr2O3 (18% Al2O3).
• The phase rule can be applied to this phase diagram, using the modified
form For the single-phase region (liquid or solid), F = 2 – 1 + 1 = 2. So,
both temperature and the composition of the phase can be
independently varied (within limits).
• In the two-phase region, F = 2 – 2 + 1 = 1.
Here, we have three variables:
(i) Temperature
(ii) Composition of the liquid phase
(iii) Composition of the solid phase
• As F = 1, only one of these three is independent. If we arbitrarily choose
the temperature, the compositions of the two phases are automatically
fixed and are given by the ends of the tie-line drawn at that temperature.
• If we specify the composition of one of the phases arbitrarily, the
temperature and the composition of the other phase are automatically
fixed. There is no three-phase equilibrium in systems exhibiting complete
solid solubility.
Free energy Vs Composition Phase Diagrams
 Systems with a Miscibility Gap
• A miscibility gap is a region in a phase diagram for a mixture of
components where the mixture exists as two or more phases – any
region of composition of mixtures where the constituents are not
completely miscible.
• A system in which the liquid phase is approximately ideal, but for the
solid phase ΔHmix > 0, i.e. the A and B atoms ‘dislike’ each other.
Free energy Vs Composition Phase Diagrams
 Eutectic phase diagram
• Many pairs of elements and compounds are unlikely to satisfy the
conditions for complete solid solubility.
• For instance, the size difference between two atoms or ions can be
appreciably more than 15%.
• Similarly, the other conditions for extensive solubility may not be satisfied.
• The solid solubility is therefore limited in a number of binary systems. But
it is never zero.
• A very small quantity of any component will always dissolve in another
component as this increases the configurational entropy and lowers the
free energy of the crystal.
• When solid solubility is limited and the melting points of the components
are not vastly different, a eutectic phase diagram usually results. As an
example,the Pb–Sn phase diagram is shown in Fig. 7.3.
• As there is complete liquid solubility, the liquid phase extends over all compositions
above the melting temperatures of the components.
• The solid phase at the left end is the lead-rich which dissolves only a limited amount
of tin.
• This solubility decreases with decreasing temperature. This limit of the solid
solubility is indicated by the phase boundary between α and α+ β called solvus.
• The solid solution phase at the right end is the tin-rich β, with only a very small
quantity of lead dissolved in it.
 phase boundaries on this diagram are as follows

• The three two-phase regions are separated by a horizontal line corresponding to the temperature Te called the eutectic
temperature.
• Below the eutectic temperature, the material is fully solid for all compositions. The composition which remains fully liquid
up to the eutectic temperature during cooling is called the eutectic composition. At the eutectic temperature, the
following eutectic reaction takes place:
• cooling → L α+β← heating
• Summary of Pb-Sn eutectic diagram:
• eutectic temperature Te = 183°C, composition of liquid ce = 62% Sn (38% Pb),
• composition of α, cαe = 18% Sn (82% Pb), and composition of β, cβe = 97% Sn (3% Pb).
• At the eutectic temperature Te, three phases are in equilibrium. F = 2 – 3 + 1 = 0. The eutectic temperature Te and the
compositions of the three phases, ce, cαe and cβe are all fixed and none of them can be varied arbitrarily.
• On slightly increasing the temperature above Te, either one or both of α and β phases would disappear. On slight decrease
of temperature below Te, the liquid phase would transform as per reaction to a mixture of α and β.
• To denote the zero degree of freedom, the eutectic reaction is called an invariant reaction. The eutectic temperature is
known as an invariant temperature.
• A similar invariant reaction occurring entirely in the solid state, where the
liquid phase is replaced by a third solid phase γ, is called a eutectoid
reaction:
• cooling →γ α+β← heating
• The corresponding invariant temperature is called the eutectoid
temperature.
Free energy Vs Composition Phase Diagrams