Phase Transformation Lecture equilibrium, Phase Diagram

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Materials Engineering MM-501 Phase Transformation in Solids

MM-501 Phase Transformation in Solids

Fall Semester-2015

Engr. Muhammad Ali SiddiquiLecturer, Metallurgical Engineering Department, NED UETBE: Mehran UET, 2007ME: NED UET, 2011

Lecture No: 021. Equilibrium2. One-component systemsEnthalpy and entropy dependence on P and TGibbs free energy dependence on P and TEffect of pressure on the equilibrium phase diagram for pure iron3. Phase Diagrams (Binary System)Type I, II and III Phase Diagrams, 2

Study of phase transformation concerned with how one or more phases in an alloy (or in a system) change into new phase or mixture of phases.The reason why a transformation occur.? because the initial state of the alloy is unstable relative to the final slate. A phase can be defined as a portion of a system whose properties and composition are homogeneous but physically distinct from other parts of the system. The Transformations that occur at constant temperature and pressure ,the stability of a system is determined by its Gibbs free energy (G). 3Equilibrium

The Gibbs free energy, G of a system is defined by the equation.

G = H - TS WhereH is the enthalpy, is the measure of the heat content of the system.T the absolute temperature, and S the entropy of the system, is the measure of the randomness of the system.4

Enthalpy is a measure of the heat content of the system and is given H = E + PVWhere E, the internal energy of the system, P the pressure, and V the volume.E = internal energy arises from the total kinetic and potential energies of the atoms within the system. Kinetic energy can arise from atomic vibration in solids or liquids and from translational and rotational energies for the atoms and molecules within a liquid or gas; whereas potential energy arises from the interactions, or bonds, between the atoms within the system.5

H = E + PV For referenceIf a transformation or reaction occurs the heat that is absorbed or evolved will depend on the change in the internal energy of the system.However it will also depend on changes in the volume of the system and the term PV takes this into account, so that at constant pressure the heat absorbed or evolved is given by the change in H. 6

When dealing with condensed phases (solids and liquids) the PV term is usually very small in comparison to E, that is H = E + PV. This is the very first approximation.A system is said to be in equilibrium when it is in the most stable state, i.e. shows no desire to change. An important consequence of the laws of classical thermodynamics is that at constant temperature and pressure a closed system will be in stable equilibrium if it has the lowest possible value of the Gibbs free energy, or in mathematical terms dG = 0 and graphically is shown as :



Fig: A schematic variation of Gibbs free energy with the arrangement of atoms. Configuration 'A' has the lowest free energy and is therefore the arrangement when the system is at stable equilibrium. Configuration 'B' is a metastable equilibrium.Arrangment of Atoms


Equilibrium States: dG = 0 dG = 0 dG 0


One-component systems

11Cp = Specific heat, quantity of heat (in joules) required to raise the temperature of the substance by one degree KelvinThe specific heat of most substances is easily measured and easily available. In general it varies with temperature as shown.


a. Variation of Specific Heat with Temperatureb. Variation of enthalpy (H) with absolute Temperature of a pure substancec. Variation of entropy (S) with absolute Temperature of a pure substance

Finally the variation of G with temperature shown in next Fig.

which is obtained by combining Fig. b and c & using Equation G = H-TS. 13


G decreases with increasing T at a rate given by - S.

Fig. Variation of Gibbs free energy with temperature.

The relative positions of the free energy curves of solid and liquid phases are illustrated in Fig. 15

Variation of enthalpy (H) and free energy (G) with temperature for the solid and liquid phases of a pure metal. L is the latent heat of melting, T m the equilibrium melting temperature.




Fig. Effect of pressure on the equilibrium phase diagram for pure ironPressure, Kbar

Type-I Two Metals Completely Soluble in liquid and solid state

Figure: Determination o f a phase diagram by thermal analysis.

A) Cooling curves of six alloys of various compositions are determined experimentally. Temperature is shown on the vertical axis as a function of time on the horizontal axis. B) The fusion temperature and the liquidus and solidus temperatures are then plotted ,IS a function of composition to form the phase diagram.

Determination of Phase Composition

If an alloy consists of more than one phase, the amount of each phase present can be found by applying the lever rule to the phase diagram.The lever rule can be explained by considering a simple balance. The composition of the alloy is represented by the fulcrum, and the compositions of the two phases by the ends of a bar. The proportions of the phases present are determined by the weights needed to balance the system.

So,fraction of phase C1 = (C2- C) / (C2- C1)and,fraction of phase C2=(C - C1) / (C2- C1).

Lever Rule: Determine the Phase Amount

Type-II- Two Metals Completely Soluble in Liquid State and Completely insoluble in the solid state. (Eutectic phase diagram)Eutectic phase diagramdescribes behavior of the alloys,twocomponents of whicharecompletelysolubleinliquidstateandentirely insolubleinsolidstate.

This diagram hastwoliquidus curves, starting from the freezing points of thetwometalsandintersectingina minimum point eutectic point.

Type-III- Two Metals Completely Soluble in Liquid State but Partly soluble in the solid state