mm231 for students

Interpretation of Phase Diagrams

A binary phase diagram can be used to determine three important types of information:

(1) The phases, that are present

(2) The composition of the phases

(3) The percentages or fractions of the phases.

The phases that are present can be determined by locating the temperature-composition point on the diagram and noting the phase(s) present in the corresponding phase field. 30wt%Ni-70wt%Cu at 1315 C (2400 F) Point lies totally within the liquid field, the alloy would be a liquid. The same alloy at 1095 C (2000 F), designated point c within the solid solution, , field, only the single phase would be present. At alloy at 1190 C (2170 F) (point b) would consist of a two-phase mixture of Solid solution, , and liquid, L.

Prediction of Phases

Prediction of Chemical Compositions of Phases

1. A tie line is constructed across the two-phase

region at the temperature of the alloy.

2. The intersections of the tie line and the phase boundaries on either side are noted. 3. Perpendiculars are dropped from these intersections to the horizontal composition axis, from which the composition of each of the respective phases is read.

To compute the equilibrium concentrations/Chemical Composition of the two phases, the following procedure is used:

Prediction of Chemical Compositions of Phases

Locate the point on the phase diagram. If only one phase is present, the composition of the phase is the overall composition of the alloy. At Point (A), at corresponding T, only Liquid is present , so composition will be 30wt%Ni-70wt%Cu. At Point (C) only the phase is present, so the composition is 30wt%Ni-70wt%Cu.

Prediction of Chemical Compositions of Phases At Point (B) considering the 30wt%Ni-70wt%Cu alloy at 1190 C (2170 F) with the two-

phase, + L, field.

The perpendicular line from the liquidus boundary

to the composition axis is 20wt%Ni-80wt%Cu,

which is the composition, CL, of the liquid phase.

The composition of the solid-solution phase, C,

is read from the perpendicular line from the

solidus line down to the composition axis, in

this case 35wt%Ni-65wt%Cu.

Prediction of Amounts of Phases

The single and two-phase situations must be

treated separately.

In the single phase region: Since only one phase is

present, the alloy is composed entirely of that

phase; i.e. the phase fraction is 1.0 or 100%.

At 60 wt% Ni40 wt% Cu alloy at 1100oC(point A),

Only is present alloy is completely or 100%

The relative amounts (fraction/%) computed with phase diagrams.

Prediction of Amounts of Phases

If the composition and temperature position is located within a two-phase region, things are more complex. The tie line must be utilized in conjunction with a procedure that is often called the lever rule (or the inverse lever rule)

Steps to determine Phase Amount using Lever Rule

1. The tie line is constructed across the two-phase region at the temperature of the alloy.

2. The overall alloy composition is located on the tie line.

3. The fraction of one phase is computed by taking the length of tie line from the overall

alloy composition to the phase boundary for the other phase, and dividing by the total

tie line length.

4. The fraction of the other phase is determined in the same manner.

5. If phase percentages are desired, each phase fraction is multiplied by 100.

.

LEVER RULE

When the composition axis is scaled in weight percent, the phase fractions computed using

the lever rule are mass fractionsthe mass (or weight) of a specific phase divided by the

total alloy mass (or weight). The mass of each phase is computed from the product of each

phase fraction and the total alloy mass.

In the employment of the lever rule, tie line segment lengths may be determined either by

direct measurement from the phase diagram using a linear scale, preferably graduated in

millimeters, or by subtracting compositions as taken from the composition axis.

Derivation of Lever Rule

Example:

At point B (35 wt% Ni, 1250C) on figure below, what are the mass fraction liquid and the mass

fraction solid?

Mark the point at mentioned composition and temperature

Draw a tie Line

Drop the perpendicular line from the intersection of Tie line with liquidus line and solidus line.

Problem 2 Calculate the amount of each phase present in 1 kg of a

(i) 40wt.% Ni at a) 1500oC b)1250oC

(ii) 50 wt.% Ni- 50 wt.% Cu alloy

at

a) 1400C,

b) 1300C

c) 1200C.

(iii) 80 wt.% Cu at a) 1175oC b) 1100oC

LEVER RULE FOR EUTECTIC

Two Scenarios

Alloy Represented by A

A

Problem1

For a 40 % Sn-60 wt % Pb alloy at 150oC, for below diagram (a) What Phase(s) is (are) present? (b) What is (are) the composition (s) of the phases

10%Sn,90%Pb 98%Sn,2%Pb

Problem2

(a) At what temperature does the first liquid phase

form?

(b) What is the composition of this liquid phase?

(c) At what temperature does complete melting of the

alloy occur?

(d) What is the composition of the last solid remaining

prior to complete melting?

A leadtin alloy of composition 30 wt% Sn70 wt% Pb is slowly heated from a temperature of (

150oC).

Problem3

A 65 wt% Ni35 wt% Cu alloy is heated to a temperature within the liquid-phase region. If

the composition of the phase is 70 wt% Ni, determine:

(a) The temperature of the alloy

(b) The composition of the liquid phase

(c) The mass fractions of both phases

Problem 4

A 40 wt% Pb60 wt% Mg alloy is heated to a temperature within the + liquid-phase region. If the

mass fraction of each phase is 0.5, then estimate:

(a) The temperature of the alloy

(b) The compositions of the two

phases

For alloys of two hypothetical metals A and B, there exist an , A-rich phase and a , B-

rich phase. From the mass fractions of both phases for two different alloys provided in

the table below, (which are at the same temperature),determine the composition of the

phase boundary (or solubility limit) for both and phases at this temperature.

Alloy Composition Fraction Phase Fraction Phase

70 wt% A30 wt% B 0.78 0.22

35 wt% A65 wt% B 0.36 0.64

PROBLEM 5

A magnesiumlead alloy of mass 7.5 kg consists of a solid a phase that has a composition just slightly below the solubility limit at 300oC. (a) What mass of lead is in the alloy? (b) If the alloy is heated to (400oC ), how much more lead may be dissolved in the phase without exceeding the solubility limit of this phase?

PROBLEM 6

Eutectic Reaction

Liquid Two Solids

L + Eutectic Point

L

L+ L+

+

EQUILIBRIUM PHASE TRANSFORMATIONS

Eutectic

Point

Eutectoid Reaction


Solid Two Solids

+

+

+ +

Eutectoid

Point

Peritectic Reaction


Liquid +Solid Solid

L +

L +

+ +

Peritectic

Point

Peritectoid Reaction


Solid+ Solid Solid

+

+

+ +

Monotectic Reaction


Liquid Liquid+ Solid

L1 L2+

L1

L1+ L1+ L2

L2+

mm231 for students

Documents