Phase Diagrams Slides, Slides of Physics

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Phase Diagrams

Module-

1) Equilibrium phase diagrams, Particle

strengthening by precipitation and precipitation

reactions

2) Kinetics of nucleation and growth

3) The iron-carbon system, phase transformations

4) Transformation rate effects and TTT diagrams,

Microstructure and property changes in iron-

carbon system

Contents

Mixtures – Solutions – Phases (contd…)

 When two phases are present in a system, it is not necessary that there be a difference in both physical and chemical properties; a disparity in one or the other set of properties is sufficient.

 A solution (liquid or solid) is phase with more than one component; a mixture is a material with more than one phase.

 Solute (minor component of two in a solution) does not change the structural pattern of the solvent, and the composition of any solution can be varied.

 In mixtures, there are different phases, each with its own atomic arrangement. It is possible to have a mixture of two different solutions!

Gibbs phase rule

 In a system under a set of conditions, number of phases ( P ) exist can be related to the number of components ( C ) and degrees of freedom ( F ) by Gibbs phase rule.

 Degrees of freedom refers to the number of independent variables (e.g.: pressure, temperature) that can be varied individually to effect changes in a system.

 Thermodynamically derived Gibbs phase rule :

 In practical conditions for metallurgical and materials systems, pressure can be treated as a constant (1 atm.). Thus Condensed Gibbs phase rule is written as:

P F C 2

P F C 1

Phase diagram – Useful information

 Important information, useful in materials development and selection, obtainable from a phase diagram:

• It shows phases present at different compositions and temperatures under slow cooling (equilibrium) conditions.
• It indicates equilibrium solid solubility of one element/compound in another.
• It suggests temperature at which an alloy starts to solidify and the range of solidification.
• It signals the temperature at which different phases start to melt.
• Amount of each phase in a two-phase mixture can be obtained.

Unary phase diagram

 If a system consists of just one component (e.g.: water), equilibrium of phases exist is depicted by unary phase diagram. The component may exist in different forms, thus variables here are – temperature and pressure.

Hume-Ruthery conditions

 Extent of solid solubility in a two element system can be predicted based on Hume-Ruthery conditions.  If the system obeys these conditions, then complete solid solubility can be expected.  Hume-Ruthery conditions:

• Crystal structure of each element of solid solution must be the same.
• Size of atoms of each two elements must not differ by more than 15%.
• Elements should not form compounds with each other i.e. there should be no appreciable difference in the electro- negativities of the two elements.
• Elements should have the same valence.

Isomorphous binary system

 An isomorphous system – phase diagram and corresponding microstructural changes.

Tie line – Lever rule (contd….)

 Procedure to find equilibrium relative amounts of phases ( lever rule ):

• A tie-line is constructed across the two phase region at the temperature of the alloy to intersect the region boundaries.
• The relative amount of a phase is computed by taking the length of tie line from overall composition to the phase boundary for the other phase, and dividing by the total tie- line length. In previous figure, relative amount of liquid and solid phases is given respectively by:

UV

cV

CL

UV

Uc

CS CL CS 1

Eutectic binary system

 Many of the binary systems with limited solubility are of eutectic type – eutectic alloy of eutectic composition solidifies at the end of solidification at eutectic temperature. E.g.: Cu-Ag, Pb-Sn

Eutectic system – Cooling curve – Microstructure

(contd….)

Eutectic system – Cooling curve – Microstructure

(contd….)

Invariant reactions

 Observed triple point in unary phase diagram for water?  How about eutectic point in binary phase diagram?

 These points are specific in the sense that they occur only at that particular conditions of concentration, temperature, pressure etc.

 Try changing any of the variable, it does not exist i.e. phases are not equilibrium any more!

 Hence they are known as invariant points, and represents invariant reactions.

 In binary systems, we will come across many number of invariant reactions!

Invariant reactions (contd….)