Second Chapter

PHASE DIAGRAM

Phase diagram

• a phase diagram is a type of graph used to show the equilibrium conditions between the thermodynamically-distinct phases.

• Phase Diagrams, which indicate the phases present at a given temperature and composition, have often proved a difficult concept to understand.

• These are known as equilibrium diagrams. Temperature is plotted on or ordinate (y-axis) and composition (in binary phase diagram or pressure (unitary phase diagram) on abscissa (x-axis) in the phase diagram.

• The compositions is expressed in % weight. Phase diagram are always drawn equilibrium state because the system always tries to be stable.

Classification of phase diagrams

• Unary phase diagram (single components system).

• Binary phase diagram (two components system).

• Tertiary phase diagram (three components System).

• Quarter phase diagrams (four components systems).

Fig T-P phase diagram for iron. I am not sure that I believe that there is a critical point for liquid and γ-Fe.

The diagram indicated different phases as a function of temperature and pressures. Crystal form of iron such as BCC (alpha,α), FCC (Gamma, γ) and HCC (Delta, δ) are obtain as increasing the temperatures. The BCC form converted to HCP form near a pressure of about 125 atm. Above the eutectic point temperature, i.e., 9100C BCC converted to FCC. at a peritectic point temperature, i.e., 14950C liquid + HCP converted to FCP.Temp range for BCC = upto 9100C.FCC = 920-14100CHCC = 1410-15390C.

Unary phase diagram (single components system).

Binary phase diagram (two components system).Such diagram of results of two components systems. In addition pressure and temperature, a third variable, composition is also involved now. It therefore three dimensional diagram to depict phases. However for the simplicity of plotting phase diagrams on paper; the temperature is always taken on ordinate and composition on abscissa for a specified pressure.The binary diagram of two components are A and B. Percentage weight components. Percentage weight composions of A raies from 0 to 100 from left to right while that of B varies from between 0 to 100 from right to left on horizental axis named as composition or C axis. There are two phase regions, viz the solid and liquid. The solid phase region lies middle of the straight line called as tie-line. The liquid phase region lies above the solid phase lines.

A phase diagram for a binary system displaying a eutectic point. The eutectic point is the point at which the liquid phase L borders directly on the solid phase α + β.

Classification of binary phase diagram

• Eutectic Phase diagram• Eutectoid phase diagram• Paritactic phase diagram• Peritectoid phase diagram

Eutectic Phase diagram• An eutectic phase diagram

is obtained when the melting point of the two components of the phase diagram are neither very close nor much different .

• The eutectic system involves the transformation of a liquid phase into two other solid phases on cooling and vice versa, and expressed as

• L (liquid phase) → α+β (solid Phase)

Some uses of Eutectic phase diagram• Some uses include:• eutectic alloys for soldering, composed of tin (Sn), lead (Pb) and sometimes

silver (Ag) or gold (Au). • casting alloys, such as aluminum-silicon and cast iron (at the composition

for an austenite-cementite eutectic in the iron-carbon system). • brazing, where diffusion can remove alloying elements from the joint, so that

eutectic melting is only possible early in the brazing process. • temperature response, i.e. Wood's metal and Field's metal for fire sprinklers. • non-toxic mercury replacements, such as galinstan. • experimental metallic glasses, with extremely high strength and corrosion

resistance. • eutectic alloys of sodium and potassium (NaK) that are liquid at room

temperature and used as coolant in experimental fast neutron nuclear reactors.

Eutectoid Phase diagram• In eutectoid system, a

solid phase replaces the liquid phase of eutectic system.

• The eutectoid system involves the transformation of a solid phase into two other solid phases on cooling and vice versa, and expressed as

• γ (solid phase) → α+β (solid Phase).

• In the Fe-C system, there is a eutectoid point at approximately 0.8wt% C, 723°C.

The compositions of the two new phases are given by the ends of the tie-line

through the eutectoid point. The general

eutectoid reaction is therefore:

Solid γ –> solid α + solid βor using the names given

to these phases:Austenite –> ferrite +

cementite (Fe3C)

EutectoidWhen the solution above the transformation point is solid, rather than liquid, an analogous eutectoid transformation can occur. For instance, in the iron-carbon system, the austenite phase can undergo a eutectoid transformation to produce ferrite and cementite (iron carbide), often in lamellar structures such as pearlite and bainite. This eutectoid point occurs at 727°C (1340.6 ºF) and about 0.83% carbon[5]; alloys of nearly this composition are called high-carbon steel, while those which have less carbon are termed mild steel. The process analogous to glass formation in this system is the martensitic transformation.

Iron-carbon phase diagram, showing the euctectoid transformation between austenite (γ) and pearlite.

Paritactic phase diagram• Peritectic transformations are also

similar to eutectic reactions. Here, a liquid and solid phase of fixed proportions react at a fixed temperature to yield a single solid phase.

• L + β phase → α Phase

• Since the solid product forms at the interface between the two reactants, it can form a diffusion barrier and generally causes such reactions to proceed much more slowly than eutectic or eutectoid transformations. Because of this, when a peritectic composition solidifies it does not show the lamellar structure that you find with eutectic freezing.

• Such a transformation exists in the iron-carbon system, as seen near the upper-left corner of the figure. It resembles an inverted eutectic, with the δ phase combining with the liquid to produce pure austenite at 1495 °C and 0.17 mass percent carbon

• Peritectic• Peritectic transformations are also similar to eutectic

reactions. • Here, a liquid and solid phase of fixed proportions react

at a fixed temperature to yield a single solid phase. Since the solid product forms at the interface between the two reactants, it can form a diffusion barrier and generally causes such reactions to proceed much more slowly than eutectic or eutectoid transformations. Because of this, when a peritectic composition solidifies it does not show the lamellar structure that you find with eutectic freezing.

• Such a transformation exists in the iron-carbon system, as seen near the upper-left corner of the figure. It resembles an inverted eutectic, with the δ phase combining with the liquid to produce pure austenite at 1495 °C and 0.17 mass percent carbon.

Peritectoid phase diagram

• Peritectoid phase diagrams involve transformation of two solid phases into a different solid phase on cooling and vise versa. Contrary peritectic reaction where sodid liquid phase L + β changed to another solid phase α; here solid phase changed to another solid phase. It is given by

• γ + β phase → α solid Phase

Gibbs' phase rule

• Gibbs' phase rule, stated by Josiah Willard Gibbs in the 1870s, is the fundamental rule on which phase diagrams are based.F = 2 − π + C

• where π is the number of phases present in equilibrium (Types of solid, liquid, gas phases etc). F is the number of degrees of freedom or independent variables taken from temperature, pressure and composition of the phases present. C is the number of chemical components required to describe the system

• Condensed phase rule

• In many solids with high melting temperature; the vapour pressure of the solids and even that of the liquid is negligible in comparison with atmospheric pressure.F = 1 − π + N

Figure 1 shows the equilibrium diagram for combinations of carbon in a solid solution of iron. The diagram shows iron and carbons combined to form Fe-Fe3C at the 6.67%C end of the diagram. The left side of the diagram is pure iron combined with carbon, resulting in steel alloys. Three significant regions can be made relative to the steel portion of the diagram. They are the eutectoid E, the hypoeutectoid A, and the hypereutectoid B. The right side of the pure iron line is carbon in combination with various forms of iron called alpha iron (ferrite), gamma iron (austenite), and delta iron. The black dots mark clickable sections of the diagram. Fig 1: Fe-Fe3C Phase Diagram

Iron-Iron Carbide Phase Diagram

Continue...• Allotropic changes take place when there is a change in crystal

lattice structure. From 2802º-2552ºF the delta iron has a body-centered cubic lattice structure.

• At 2552ºF, the lattice changes from a body-centered cubic to a face-centered cubic lattice type.

• At 1400ºF, the curve shows a plateau but this does not signify an allotropic change. It is called the Curie temperature, where the metal changes its magnetic properties.

• Two very important phase changes take place at 0.83%C and at 4.3% C. At 0.83%C, the transformation is eutectoid, called pearlite.

• gamma (austenite) --> alpha + Fe3C (cementite) • At 4.3% C and 2066ºF, the transformation is eutectic, called

ledeburite.

• L(liquid) --> gamma (austenite) + Fe3C (cementite)

Home assignments• Equilibrium Calculations

1. Given the Fe-Fe3C phase diagram, Fig. 1, calculate the phases present at the eutectoid composition line at:

a. T = 3000ºF b. T = 2200ºF c. T = 1333ºF d. T = 410ºF 2. Calculate the phases in the cast-iron portion of the diagram at the

eutectic composition of 4.3% C in combination with 95.7% ferrite at: a. T = 3000ºF b. T = 1670ºF c. T = 1333ºF 3. A eutectoid steel (about 0.8%C) is heated to 800ºC (1472ºF) and cooled

slowly through the eutectoid temperature. Calculate the number of grams of carbide that form per 100g of steel.

4. Determine the amount of pearlite in a 99.5% Fe-0.5%C alloy that is cooled slowly from 870ºC given a basis of 100g of alloy.

Lever Rule• To determine compositions of

phases and the relative proportions of phases to each other in Binary diagrams the LEVER RULE is used.

• Using the lever rule one can determine quantitatively the relative composition of a mixture in a two-phase region in a phase diagram. The distances l from the mixture point along a horizontal tie line to both phase boundaries give the composition:

• Nα lα = nβ lβ• nα represents the amount of

phase α and nβ represents the amount of phase β.

1. Point "I" lies above the liquidus within the liquid field.

What is the composition, in terms of the two end member components, A and B, of the liquid represented by this point?

To determine the composition of "I" you must complete the following steps:

1. Draw a line through "I" perpendicular to the AB join, i.e., the base of the diagram. This line represents a line of constant composition and is referred to as an isopleths.2. The liquid at "I" consists of a mixture of A and B, the proportions of which can be determined simply by measuring the length of three lines, AI', BI' and AB and then ratio these lengths. %A = I'B/AB *100%B = I'A/AB *100This gives us the bulk composition of the liquid at this point. If the composition point for the moves then we get a new bulk composition for

that point represented by the new liquid

Home Assignment