Phase Diagram:Two Component System

MTE/III SEMESTER/MSE/MTE 2101 1

CHAPTER 2 (CONTD.)

Binary Phase System1. Description of Binary Phase Diagram2. Construction of Binary Phase Diagram3. Interpretation of Binary Phase Diagram

i. Modified Gibb’s Phase Ruleii. Tie-Lineiii. Lever Rule

4. Problems based on Binary Phase Diagram


BINARY PHASE DIAGRAMS (ISOMORPHOUS PHASE DIAGRAM)

This is a two component system. In this phase diagram, temperature and

composition are variable parameters, and pressure is held constant normally 1 atm.

Temperature is taken on Y-axis and various compositions of the two components on X-axis.

Ni-Cu, Au-Ag, Cr-Mo are examples of binary phase diagram.

Fig: Binary Phase Diagram

Liquidus

SolidusA

B


Description of Binary Phase Diagram For all combinations of temperature and

composition above liquidus curve (AB), the mixture is in the liquid state.

Liquidus temperature as the temperature above which a material is completely liquid.

The solidus temperature is the temperature below which the alloy is 100% solid.

For all combinations of temperature and composition below solidus curve (BA), the mixture is in the solid state.

Point A and B represent the melting temperatures of individual alloy.

The temperature difference between the liquidus and the solidus is the freezing range of the alloy.

Liquidus

SolidusA

B

Fig: Binary Phase Diagram


Construction of Binary Phase Diagram Phase diagrams for a binary alloy system can be obtained

from the cooling curves of the system at various compositions of the two components.

Let us consider two metals A and B. Curve A and B represent the cooling curve of pure metal A

and B. Curve U,V,W,X represent cooling curves of alloy of A and B

at different compositions.NOTE: Phase diagram show the relationship of phases at equilibrium conditions. This means the phases present at particular temperature and composition don't change with time.

UV

W

X

Fig: Cooling curves of metal A and B, alloy mixture of A and B


These temperature points are re-plotted (projected from the cooling curves) on a temperature versus composition diagram by taking temperature on the Y axis and composition of the alloys on X axis.


Interpretation of Binary Phase Diagram – Using Phase Rule, Tie-Line and Lever Rule For a binary system of known composition and temperature that is at equilibrium, at least

three kinds of information are available: (1) the phases that are present, (2) the compositions of these phases, and (3) the percentages or fractions of the phases.

For determining the degrees of freedom in a binary phase diagram, Modified Gibb’s Phase Rule ( P+F = C+1) is used. (Pressure is assumed to be 1 atm)

To determine the phase composition present at any point, Tie Line is used. To determine the amount of each phase present at any point, Lever Rule is used.


Pic Courtesy: Material Science and Metallurgy, K.R.Phaneesh


Modified Gibb’s Phase Rule: Points A and B represent the melting temperatures of A and B. The degrees of freedom, F =

0 at these points because number of phases, P=2, Number of components, C=1. These points are called as “Invariant Points”.Region 1: Single phase homogeneous region. Number of Components, C =2 (i.e. Liq.A and Liq.B) Number of Phases, P = 1 (i.e. Liquid Phase)

Applying Modified Gibb’s Phase Rule(P+F = C+1): Number of Degrees of Freedom, F = 2


Region 2: Mixture of solid and liquid phase. Number of Components, C = 2. (i.e. Liq + α) Number of Phases, P = 2. (i.e. Liquid and Solid)Applying Modified Gibb’s Phase Rule(P+F = C+1): Number of Degrees of Freedom, F = 1

Region 3: Single phase solid region. Similar to region 1.


Let us consider an alloy consisting of 60% A and 40% B. At point L, the mixture is a single phase homogeneous liquid at T₁°C. At point N, the mixture is fully in solid state at T₃°C. At point M, where solidification is in progress, there is a two phase mixture of solid and

liquid, both of metals A and B. Two questions arise: 1. What are solid and liquid composition?

2. What are the amounts of solid and liquid phase?


Phase Composition (Tie - Line): At point M, a horizontal “tie line” or “constant temperature line” is drawn which

intersects the liquidus and solidus curves at ‘O’ and ‘P’ respectively. Perpendicular lines from ‘O’ and ‘P’ to the X-axis gives the liquid and solid phase

composition. Liquid is 80% A and 20% B; Solid is 10% A and 90% B. Line OMP is called as “TIE – LINE”.

Note: At T₂° C, the solid and liquid phase composition of an alloy combinations between ‘O’ and ‘P’ are same.


Amount of each phase present (Lever Rule): Lever Rule states that,” The relative amount of each phase is directly proportional

to the length of opposite lever arm”. The tie-line OMP has two arms OM and MP which intersects the liquidus and solidus curves. According to Lever Rule, the length MP touching the solidus proportional to the amount of

liquid phase present at M and the length OM touching the liquidus is proportional to the amount of solid phase present at M.

Therefore,Amount of liquid phase at M = × 100 = × 100 = 71.42% .Amount of solid phase at M = × 100 = × 100 = 28.58% .


PROBLEMS BASED ON BINARY PHASE SYSTEM

Q1.) Determine the degrees of freedom in a Cu-40% Ni alloy at (a) 1300°C, (b) 1250°C, and (c) 1200°C.

Reference: Example 10.6; The Science and Engineering of Materials, Donald Askeland and Pradeep Phule


Q2.) Determine the composition of each phase in a Cu-40% Ni alloy at 1300°C, 1270°C, 1250°C, and 1200°C.



Q3.) Calculate the amounts of and L at 1250°C in the Cu-40% Ni alloy shown in Figure.


Phase Diagram:Two Component System

Engineering

Transcript of Phase Diagram:Two Component System