Phase Diagram

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CL 404 : Material Science

9. Phase Diagrams

Terminology� Component:

� Chemically recognizable species (Fe and C in carbon steel)

� Phase:

� a portion of a system that has uniform physical and chemical characteristics.

� Phases are separated from each other by definite phase boundaries

� A phase may contain one or more component

� Not necessary that there be a difference in both physical and chemical characteristics. Ex: water and ice are identical in chemical makeup but considered as a separate phases

� Polymorphism (FCC, BCC structures) : Each of these structure is considered to be a separate phase

� System

� Specific body of a material under consideration (or)

� Series of possible alloys consisting of same components without regard to alloy composition (iron-carbon system)

� Homogenous (Single Phase) /heterogeneous system (two or more phases)

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Terminology

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Solvent: Major componentSolute: Minor component

Solubility Limit: At specific temp, there is a maximum conc. of solute atoms that may dissolve in the given solvent to form a solid solution. This is true for many alloy atoms. This is similar to dissolution of sugar in water. (Refer Figure). The solubility limit changes with temp.

Microstructure� The properties of an alloy depends on microstructure which is

specified by

� Number of phases

� Their proportions

� Their arrangement in space

� Microstructure depends on variables such as

� Alloying elements present

� Their concentration

� Heat treatment of an alloy

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Note: Development of an microstructure of an alloy is related to the characteristics of phase diagrams. That’s why we are interested in understanding the phase diagrams

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Equilibrium and metastable

� Equilibrium: Free energy is minimum at specified combination of T, P and composition.

� The characteristics of the system do not change with time

� Sufficient time is required to achieve equilibrium.

� Metastable: A state along the path to the equilibrium may appear to be stable

� Phase equilibrium

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Free energy

Equilibrium

Metastable state

coordinate

One component (Unary Phase

diagram)

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Composition – held constant

Phase diagram for pure substanceP, T are variables

At any point on the phase boundary, two phases on either side are in equilibrium

Point ”O” – triple point/invariant point. Here three phases are in equilibrium.

Triple point (T = 273.16 K ; P =6.04 x 10-3 atm)

These phase diagrams for many substances have been determined experimentally.

For substances such as carbon, multiple solid phases exist (allotropes) and so we have other triple points

Binary Phase Diagram

� Temperature, composition are variable parameters

� Pressure – constant

� Binary phase diagram helps us to understand and predict microstructure(having eqm /non eqm characteristics)

� Microstructure develop from phase transformation

� Appearance/disappearance of phase

� Transition from one phase to other phase7

Binary Isomorphous systems

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Isomorphous system: Complete solid solubility of the two components (both in the liquid and solid phases)

Three different phase regionsSolid (α), Liquid (L) and

solid+Liquid (α+L)

Liquidus line (Separates Liquid from Liquid + Solid)Solidus line (Separates Solid from Liquid + Solid)

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Binary Isomorphous systems

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For Cu and Ni system,

α -PhaseSubstitutional solid solution (FCC crystal structure)

At temp. below 1080ºC, Cu and Ni soluble in each other in the solidstate for all composition. This is mainly due to both Cu and Ni have

same FCC structure and identical atomic radii and electronegativity.

Metallic alloys, solid solutions are represented by Greek letters(α,β,γ…)

One component system: Melting occurs at a well defined temp.Multi-component system: Melting occurs over the range of temp.

Interpretation of Phase diagram

� Phases Present

� Determination of phase compositions

� The relative fraction of the phases

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No. of Phases Present

� Very simple

� Locate the temp. – composition point on the diagram and note the phase (s) with which the corresponding phase is labeled.

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Finding composition in 2-phase

region� Locate composition and temp. in diagram

� In two phase region, draw the tie line or isotherm at that temp

� Note intersection with phase boundaries and read the compositions at the intersections. The liquid and solid phases have these compositions.

For single phase region, read the composition is straight forward

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Amount (Relative Fraction) of

phases� Using Lever rule

� Locate composition and temp. in diagram

� In two phase region draw the tie line or isotherm

� Fraction of a phase is determined by taking the length of the tie line to the phase boundary for the other phase, and dividing by the total length of the tie line

WL = S/(R+S)

WL = (Cα –Co)/(Cα-CL)

� The lever rule is a mechanical analogy to the mass balance calculation. The tie line in the two phase region is analogous to a lever balanced on a fulcrum. 13

Derivation of Lever rule� Only two phases are present, the sum of their mass fraction must be equal to

1.0

WL + Wα = WT (1.0)

� Mass of one of the components (either Cu or Ni) that is present in the phase = Mass of that component in that alloy

WLCL + Wα Cα = WTCo

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Volume fraction

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� Phase amount in volume fraction is more preferred than mass fraction� Volume fraction can be determined by examining the microstructure� Properties of a multiphase alloy may be estimated on the basis of vol. fraction.

� Converting mass fraction into volume fraction

Problem

� A Cu-Ni alloy of composition 70 wt% Ni –30 wt% Cu is slowly heated from a temperature of 1300°C� At what temp does the first liquid phase form?

� What is the composition of this liquid phase?

� At what temp does complete melting of the alloy occur?

� What is the composition of the last solid remaining prior to complete melting?

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Problem

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Development of microstructure in

isomorphous alloys

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Equilibrium cooling (Slow cooling). We are providing sufficient time for the system to attain eqm.

a. 1300ºC: complete liquid with 35% Ni -65% Cu

b. ~1260ºC: First solid begin to form (α – 46% Ni)

c. ~1250ºC: α – 43%Ni and L-

32% Nid. ~1220ºC: Last liquid to

solidifye. Complete solid phase (35%

Cu)


isomorphous alloys

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Non-Equilibrium cooling (Fast cooling)

Compositional readjustment for change in temperature occur via diffusion (time dependent phenomenon)

But solidification involves fast cooling rates.

Diffusion in solid state is very low. So the new layers that solidify on top of the existing grains have the equilibrium composition at that temperature. This leads to formation of layered (cored) grains


isomorphous alloys� Tie-line method to determine the composition of the solid phase is

invalid

� The tie line method works for the liquid phase, where diffusion is fast

� Solidus line is shifted to the right (higher Ni contents), solidification is complete at lower T, the outer part of the grains are richer in low-melting component (Cu)

� Upon heating grain boundaries will melt first. This can lead to premature mechanical failure

� The distribution of the two elements within the grains is non-uniform

� Concentration gradients are established across the grains. The centre of each grain, which is the first part to freeze is rich in high melting element (Ni) whereas the concentration of the low melting element increases with position from this region to the grain boundary.

� This is termed as cored structure. 20

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Binary Eutectic systems

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Eutectic reaction: Transistion b/w liquid and mixture of two solid phases, α + β at eutectic concentration CE

For Ag-Cu system


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Eutectic isotherm


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Three single phase regions

α - solid solution of Ag in Cu matrixβ - solid solution of Cu in Ag matrixL – Liquid

Three two phase regions (α+L, β+L, α+ β)

Solvus line separates one solid solution from a mixture of solid solutions. Solvus line shows limit of solubility

Eutectic/invariant point: Liquid and two solid phases co-exist in eqm at the eutectic composition CE and the eutectic temp TE


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The melting point of the eutectic alloy is lower than that of the components (eutectic =easy to melt in Greek)

Three phases are in eqm along the eutectic isotherm

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Pb-Sn system (Using for soldering applications)

Development of Microstructure (Pb-

Sn system)

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We are considering different composition. But the cooling rate is slow (eqm) in all the cases

Case I: Pb rich alloy (0 -2 % Sn)

This is same as isomorphous

system (Cu-Ni) system

L Lα α→ + →

Development of Microstructure

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Case II: Room temp solubility limit to maximum solid solubility at eutectic temp

Beta phase nucleates as the alpha solid solubility is exceeded upon crossing the solvus line

L Lα α α β→ + → → +


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Case III: Eutectic composition

No changes above the eutectic temperature

At TE, the liquid transforms to the αand β phases as per

the following eutectic reaction

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`It is obvious from the eutectic reaction that composition of both the solid phases is different from that of liquid phase.

This implies that there must necessarily be a redistribution of the components.

The redistribution is accomplished by atomic diffusion.

It is an eqm cooling. Hence, sufficient time is there for the diffusion to occur. Diffusion occurs at the eutectic and liquid interface. The direction of diffusion of two components is shown in the figure (See next slide).

Pb is diffusing toward alpha layer(Pb rich phase) and Sn is diffusing toward beta layer (Sn rich phase).


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The alternating layers are formed here. Because only for this configuration, atomic diffusion of lead and tin need only occur over relatively short distances.

This structure is characteristic of the eutectic reaction.

This structure is called eutectic structure . Also called as lamellar structure.

Since, Pb is diffusing away from this region, it becomes Sn rich phase (β phase)


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Case 4: All compositions

other that eutectic when cooled across eutectic isotherm

J. Liquid (C4 % Sn)

On cooling at point K, primary α is formed (same

as case II)

On further cooling to point L, the composition of the primary alpha is changed. The composition of both alpha and L could be determined by draw a isotherm(Tie-line) at that temp

Alpha comp. L comp.


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Alpha comp. L comp. = Eutectic comp

Just above the eutectic isotherm, we have primary α and liquid which have the eutectic comp.

On further cooling to point m, the liquid (what we are left with) having eutectic comp. is

converted in to lamellar structure as per the eutectic reaction.Lamellar structure now consists

of α and β layers. This alpha is

called eutectic α.

Now a terminology “ Microconstituent” is introduced here. It is element

of an microstructure having an identifiable and characteristic structure. Here we have two microconstituents – Primary

alpha and lamellar structure

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Calculate relative amounts of

microconstituents

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Eutectic microconstituent forms from liquid having eutectic comp. (61.9 % Sn)

Consider eutectic as a separate phase and apply the lever rule to find the relative fraction of primary alpha and eutectic structure

We= P/(P+Q) [Eutectic]Wα’ = Q/(P+Q) [Primary α]

Calculate Total amounts of Phases

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Fraction of α phase could be

determined by applying lever rule across the entire α + β phase field.

Wα= (Q+R) /(P+Q+R) [αphase]Wβ = P/(P+Q+R) [β Phase]

Terminal vs. Intermediate solid

solutions

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Terminal: Solid solutions exist over the composition ranges near the concentration extremities of the phase diagram (αand β phases in Cu-Ag system)

Intermediate: it may be found at other than two extremes (Cu-Zn)

Intermediate phases/compounds

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Intermetallic compounds that have precise chemical compositions can exist in some systems

Intermetallic compound could be treated like any other phase except they are not appear as a wide region but as a vertical line in the phase diagram.

This diagram can be thought as two joined eutectic diagrams[Mg-Mg2Pb and Mg2Pb-Pb].In this case, Mg2Pb can be considered as a component

convert wt% to at% of Mg2Pb19 wt % Mg-81 wt% Pb = 66.6 at% Mg – 33.3 wt% Pb

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Other Invariant reactions

� Suffix “ic” : involves one liquid phase

� Suffix :”oid” : Involves only solid phases

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Cooling

Cooling

Cooling

Cooling

Eutectic

L

Eutectoid

Peritectic

L

Peritectoid

α β

γ α β

α β

α β γ

→ +

→ +

+ →

+ →

Congruent vs. Incongruent

TransformationCongruent Incongruent

No compositional Changes At least one phase will experience a change in composition

Ex: allotropic transformations, melting of pure component

Eutectic, eutectoid transformation, melting of alloy (isomorphous)

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Problem

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Specify temp and comp. points at which all eutectics, eutectoids, peritectics and congruent phase transformation

occur. Also, for each, write the reaction upon cooling.

Gibbs Phase Rule

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Construction of phase diagram and principles governing the conditions for phase equilibria described by law of thermodynamics

Phase rule:

P+F = C+NP= No. of phases that will coexist within a system at eqm.

F= No. of degrees of freedom or externally controlled variables (P, T, comp.)(No. of variables that can be changed independently w/o altering the no. of phases that coexist at eqm.C= No. of components in the system. Components are normally elements or stable compounds. Materials at the two extremities of the horizontal compositional axis

N- No. of non-compositional variables (T and P)

F= C-P+2 (for one component system)F=C-P+ (binary system. N is reduced to 1 as the pressure is constant

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Gibbs Phase Rule

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Cu-Ag systemF=C-P+1

Single phase region (α, β)

F=2-1+1 =2. Only two parameters are required to completely describe the system

Two phase region

F= 2-2+1 = 1. Either temp. or comp. of one of the two phases is to be specified to completely define the system

Iron-Iron Carbide diagram

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Iron-Iron Carbide diagram� We are considering only till 6.70 wt% of C as all the commercial

steels available in the market having carbon content less than 6.70 wt%. Here carbon form is graphite

� Alpha ferrite� Having BCC structure

� 0 K to 910 °C

� C is located at interstitial positions (0,0,1/2) center of edges (space available = 0.19 A°)

� Size of carbon is 0.71 A°

� Due to this size difference, the solubility is very limited (0.02 wt% at 725 °C)

� Gamma _ austenite� Having FCC structure

� 910 °C - 1410 °C

� In alloy form 725 °C - 1493 °C

� C is located at (0,0,1/2) / (1/2 ½ ½) center of diagonal.

� Void sixe -0.52 A °

� Solubility is 0.1 at 1493 °C

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Iron-Iron Carbide diagram� Delta ferrite

� BCC

� 1410 °C -1535 °C

� Solubility 0.1 at 1493 °C

� Cementite� Fe3C

� Complex orthorhombic crystal structure

� 6.67 wt% C – 25 at% C

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Various invariant reactions

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Peritectic: At 1493 °C upon cooling

δ (0.1 wt% C, BCC) + L (0.5%) = γ (0.18%, FCC)

Eutectic : At 1150 °C upon cooling

L (4.3%) = γ (1.7%, FCC) + Fe3C (complex orthorhombic, 6.67%

C)

Eutectoid : At 725 °C

Note: Of this, Eutectoid is very important as most of the phases comes into picture at this phase field. Most of the commercial steel are manufactured based on this region of phase diagram

Microstructure Development

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Case I: eutectoid composition

Lamellar structure (alternating alpha and Fe3C layers) is called Pearlite


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Hypoeutectoid alloys: Comp. of an alloy less than eutectoid

Here proeutectoid alpha is formed at the grain boundaries in order to

reduce the higher free energy associated with it


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Case III: Hypereutectoid Alloys

Here proeutectoid Fe3C is formed at grain boundaries

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Amount of phase

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Similar to Eutectic system (Refer Slides 33 and 34)

Phase Diagram

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Transcript of Phase Diagram