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Thermal Equilibrium DiagramThermal Equilibrium DiagramAlso known as Phase Diagram or Constitutional Diagram.Very important in the study of the alloy.Definition:-The Diagram which records the type of phase in material and change in phase is called Equilibrium Diagram.Equilibrium condition means a very slow process taking infinitely long time for any changes to occurs. E.g. very slow heating or cooling process.

Thermal Equilibrium DiagramFor equilibrium three controllable variable are:- Temperature, Pressure and Composition.At atmospheric value pressure assume to be constant. So phase diagram changes due to variation in temperature & composition.

Due to this phase diagram are called Thermal Equilibrium Diagram.

Importance and ObjectiveShows the phases which exists in equilibrium in any combination of temperature and compositions.

Shows the relationship between the composition , temperature and structure of an alloy in series.

Study of phase separation, solidification of metal and alloys , purification of material. structural changes due to heat treatment, casting etc

Marks Liquidus and Solidus lines..

LimitationsEquilibrium condition means a very slow process taking infinitely long time for any changes to occurs. E.g. very slow heating or cooling process.

In actual practice as under welding and casting conditions equilibrium conditions are not obtained.

This limits the use of equilibrium diagram. Sometimes it is used to some extent in predicting the phase relations, compositional changes and structure in the system not at equilibrium.

ClassificationUnary (one Component) phase diagram plotted as pressure on the vertical axis and temperature on the horizontal axis.

Binary (two Component) phase diagram here pressure is constant and temperature on the vertical axis and compositions on the horizontal axis.

Ternary (three Component) phase diagram and so on.

Terms used in phase diagramPhase:-Any structure which is physically distinct microscopically may be considered as a phase.(uniform chemical compositions).

System:-Substance or group of substance isolated from its surrounding in such a way that it completely unaffected by surrounding. composed of gases, liquids, solids or their mixtures.

Terms used in phase diagramComponents:-It may be elements, compounds or solutions.A system having one component called as Unary system.A system having two component called as Binary system. there can be Ternary or Quaternary system too.Equilibrium:-Minimum free energy of a system under specified combination of pressure , Temperature, Composition and total volume is called Equilibrium state.

Terms used in phase diagramDegree of freedom:-It is the number of external and internal variables of the system that may be changed independently without causing appearance or disappearance of a phase.Structural Constituents:-The phases in alloys are not uniformly distributed throughout the structure. The association of phases in distinct fashions may be refers to as a structural constituents of alloy.CuAl2, FeAl3 and MnAl3 are constituents in aluminium alloys.Pearlite, Martensite, Sorbite are micro constituents in steel.

Gibbs Phase RuleGibbs' phase rule describes the degrees of freedom (F) in a closed system at equilibrium, in terms of the number of separate phases (P) and the number of chemical components (C) in the system.F + P = C + 2Where 2 represent two external variables, pressure & temperature.For metal and alloy we take pressure 1 atm.So, F = C P + 1F>0 and P B At B solidification start at c solidification is complete.Between B and C the system contain both solid + liquid phase.Between C and D solid phase appearNow, Degree of freedomAt AB, F = 1At BC, F = 0At CD, F =1

ABCDCooling curve for Binary solid solution.Liquid metal cools from A -> B At B solidification start, At c solidification is complete.The temperature range between B and C is known as Freezing Zone.This freezing zone is due to change in the composition of solid and liquid phases.Between C and D solid phase appearDegree of freedomAt AB, F = 2At BC, F = 1At CD, F =2

ABCDCooling curve for Binary Eutectic System:-Here line AB is same as in both above cases.But in line BC the metal which is excess start crystallize.At point C now the two liquid metal solidify so here 3 phases created. Line DE is pure solid line.Thus, a binary eutectic system solidifies in two different modes as a combination of pure metal and binary alloy with solid solution formation systems. Now, Degree of freedomAt AB, F = 2At BC, F = 1At CD, F =0At DE, F=1

TemperatureABEDCPhase Diagram Binary phase diagrams classified as under:-Components completely soluble in the liquid state and Completely soluble in the solid state (Type I)Insoluble in the solid state: the eutectic reaction (Type II)Partly soluble in the solid state: the eutectic reaction (Type III)Formation of a congruent-melting intermediate phase (Type IV) The peritectic reaction (Type V)

Transformations in the solid state Allotropic changeOrder-disorderThe eutectoid reactionThe peritectoid reaction

Two Metals Completely Soluble in the Liquid and Solid States (Type I) Since the two metals are completely soluble in the solid state, the only type of solid phase formed will be a substitutional solid solution. The two metals will generally have the same type of crystal structure and differ in atomic radii by less than 8 percent.

Construction of Phase Diagram The result of running a series of cooling curves for various combinations or alloys between metals A and B, varying in composition from 100 percent A & 0 percent B to 0 percent A & 100 percent B is shown in the diagram in the figure given below.Two Metals Completely Soluble in the Liquid and Solid States (Type I)

Two Metals Completely Soluble in the Liquid and Solid States (Type I) The cooling curves for the pure metals A and B show only a horizontal line because the beginning and end of solidification take place at a constant temperature.However, since intermediate compositions form a solid solution, these cooling curves shows two breaks or change in slope.

It is now possible to construct actual phase diagram by plotting temperature vs. composition. The appropriate points are taken from the series of cooling curves and plotted on the new diagram as shown by the diagram at RHS in the above figure. Two Metals Completely Soluble in the Liquid and Solid States (Type I) left axis represents the pure metal A, TA is plotted along this line. Similarly, TB is plotted. intermediate compositions are % of A and B, A vertical line representing the alloy80A-20B is drawn, and T1 and T2 from cooling curveare plotted along this line.

The same procedure is used for the other compositions.

Two Metals Completely Soluble in the Liquid and Solid States (Type I)The phase diagram consists of two points, two lines, and three areas.Two points:- TA and TB represent the freezing points of the two pure metals.Two lines:-The upper line, obtained by connecting the points showing the beginning of solidification, is called the liquidus; and the lower line, determined by connecting the points showing the end of solidification, is called the solidus line.Three area:-The area above the liquidus line is a single-phase region, and any alloy in that region will consist of a homogeneous liquid solution. Similarly, the area below the solidus line is a single-phase region, and any alloy in this region will consist of a homogeneous solid solution.Between the liquidus and solidus lines there exists a two-phase region. Any alloy in this region will consist of a mixture of a liquid solution and a solid solution.Chemical Composition of Phases To determine the actual chemical composition of the phases of an alloy, draw a horizontal temperature line, called a tie line, to the boundaries of the field as shown in the figure given below.

The points of intersection are dropped to the base line, and the composition is read directly.80A-20B at the temperature T. The alloy is in a two-phase region.the phase is a solid solution of of composition 90A-10B. In the other phase the liquid solution of composition 74A-26B.

Relative Amounts of Each Phase (The Lever Rule) The vertical line will divide the horizontal line into two parts. The point where the vertical line intersects the horizontal line may be considered as the fulcrum of a lever system. This is known as the Lever Rule. In the above figure, Liquid (percent) = (mn / mo) x 100 Solid (percent) = (no / mo) x 100

By inserting the numerical values, we get

Liquid (percent) = (10 / 16) x 100 = 62.5 Solid (percent) = (6 / 16) x 100 = 37.5

right side of the tie line gives phase.left side of the tie line gives liquid phase.

Equilibrium Cooling of a Solid Solution Alloy Phase changes that occur at various stages during equilibrium cooling of a solid solutions.

T0 is a homogeneous single-phase liquid solution and remains so until temperature T1 is reached. Since T1 is on the liquidus line, freezing/solidification now begins. The first nuclei of solid solution to form, 1, composed of 95A-5B.

Since the solid solution in forming takes material very rich in A from the liquid, the liquid must get richer in B.

In view of this, just after the solidification, the composition of the liquid is approximated as 69A-31B.

When the lower temp. T2 is reached, the liquid composition is at L2.

The only solid solution in equilibrium with L2 and therefore the only solid solution forming at T2 is 2. Equilibrium Cooling of a Solid Solution Alloy

Equilibrium Cooling of a Solid Solution Alloy It can be seen from the diagram that 2 is composed of 10B. Hence, as the temperature is decreased, not only does the liquid composition become reach in B but also the solid solution. At T2, crystals of 2 are formed surrounding the 1 composition cores (primary dendrites 1) and also separate dendrites of 2 as shown in the figure given below.

Non equilibrium Cooling of a Solid Solution Alloy In actual practice it is extremely difficult to cool under equilibrium conditions. Since diffusion in the solid state takes place at very slow rate,

Since the diffusion is too slow with crystal growth, not enough time will be allowed to achieve uniformity in the solid, and the average composition will be between 1 and 2 say 2.

Non equilibrium solidus line 1 to 5 shown dotted in the figure.

solidification should be completed at T4 but ,Application of Lever Rule at T4 gives,

L4 (percent) = (4T4 / 4L4) x 100 25 percent

Non equilibrium Cooling of a Solid Solution Alloy

Non equilibrium Cooling of a Solid Solution Alloy Solidification will therefore continue until T5 is reached.

At this temperature the composition of the solid solution 5 coincides with the alloy composition, and solidification is complete.

The last liquid to solidify, L5, is richer in B than the last liquid to solidify under equilibrium conditions.

The final solid consists of a cored structure with a higher-melting central portion surrounded by the lower-melting, last-to-solidify shell. Thus as crystal grows, there will be a difference in chemical composition from the center to the outside of the grain. Homogenization To solve the coring problem,Industrially preferred method is of homogenization of the cored structure by diffusion.

At room temperature, for most metals, the diffusion rate is very slow, but if the alloy is reheated to a temperature below the solidus line, diffusion will be more rapid and homogenization will occur in a relatively short time.

However, extreme care must be exercised in this treatment not to cross the solidus line; otherwise liquidation of grain boundaries will occur, damaging the shape in the solid state. Two Metals Completely Soluble in the Liquid State and Completely Insoluble in the Solid State (Type II) Technically, no two metals are completely insoluble in each other.

However, in some cases the solubility is so restricted that for practical purpose they may be considered insoluble.

The series of cooling curves for the pure metals and various alloys are shown in the figure given below.

Two Metals Completely Soluble in the Liquid State and Completely Insoluble in the Solid State (Type II) The cooling curves for the pure metals A and B show a single horizontal line at their freezing points.

As B is added to A & As A is added to B, the temperature for the beginning of solidification is lowered.

since each metal lowers the freezing point of the other, the line connecting the points showing the beginning of solidification, the liquidus line, must show a minimum. alloys is also lowered. Two Metals Completely Soluble in the Liquid State and Completely Insoluble in the Solid State (Type II) This is shown by the upper dotted line in the above figure, showing a minimum at point E, known as the eutectic point, for a composition of 40A-60B.

the end of solidification occurs at a fixed temperature. The lower horizontal line at TE, shown dotted in the above figure, is known as eutectic temperature.

In one alloy, the eutectic composition 40A-60B, complete solidification occurs at a single temperature, the eutectic temperature.

The actual phase diagram of temperature vs. composition, as shown in the figure given below.

Two Metals Completely Soluble in the Liquid State and Completely Insoluble in the Solid State (Type II) The phase diagram consists of four areas.The area above the liquidus line is a single-phase homogeneous liquid solution, since the two metals are soluble in the liquid state .The remaining three areas are two-phase areas.

Every two-phase area on a phase diagram must be bounded along ahorizontal line by single phases.

To determine the phases that exist in the two-phase areaTo determine the phases that exist in the two-phase areaTo determine the phases that exist in the two-phase area MFE in the above diagram, a horizontal tie line OL is drawn. This line intersects the liquidus at L, which means that liquid is one of the phases existing in the two-phase area and intersects the left axis at point O. The left axis represents a single phase, the pure metal A, which below melting point is solid. Therefore, the two phases are liquid and solid A The two phases that exist in area NEG are liquid and solid B (labelled as Liquid + Solid B).Eutectic Composition:-It is common practice to consider alloys to the left of the eutectic composition as hypoeutectic alloys and those to the right as hypereutectic alloys.

The way solidification takes place and resulting microstructures at various stages can be studied by following the slow cooling of different alloys.

The process is explained by study of slow cooling of Alloy 1 (eutectic composition), Alloy 2 (hypoeutectic alloys) and Alloy 3 (hypereutectic alloys) in the figure given below.

Alloy 1 (Eutectic Composition) Alloy 1 is the eutectic composition 40A-60B.As it is cooled from temperature T0, it remains a uniform liquid solution until it reaches point E, on the horizontal eutectic temperature line.

this is the intersection of the liquidus and solidus lines, he liquid must now start to solidify, and the temperature cannot drop until the alloy is completely solid.

The liquid will solidify into a mixture of two phases.

Eutectic Reaction:-The change of this liquid of composition E into two solids at constant temperature is known as the eutectic reaction and may be written as

Since solidification of eutectic alloy occurs at constant temperature, its cooling curve would be the same as that for a pure metal.

The eutectic solidification however is not congruent as there is a difference in composition between the liquid and the individual solid phases.

Alloy 2 (Hypoeutectic Alloys) Alloy 2, a hypoeutectic alloy composed of 80A-20B, remains a uniform liquid solution as shown at (1) until the liquidus line temperature T1 is reached. At this point the liquid L1, is saturated in A, and as the temperature is dropped slightly, the excess A must solidify as shown at (2).The liquid by depositing crystals of pure A must become richer in B. It can be seen that at temperature T2, solid is pure A and liquid composition L2 is 70A-30B. The amount of A and L2 can be calculated using the Lever Rule as under.A (percent) = (x2L2 / T2L2) x 100 = (10 / 30) x 100 = 33 %L2 (percent) = (T2x2 / T2L2) x 100 = (20 / 30) x 100 = 67 %Alloy 2 (Hypoeutectic Alloys) The microstructure would appear as shown at (3). As the solidification continues, the amount of pure solid A increases gradually by continued precipitation from the liquid.When the alloy reaches xE, the eutectic line, the liquid is at point E.

Phase Liquid Solid A Chemical Composition 40A-60B 100A Relative amount (TExE / TEE) x 100 = 33 %(xEE / TEE) x 100 = 67 %

Alloy 3 (Hypereutectic Alloys) Alloy 3, a hypereutectic alloy composed of 10A-90B, undergoes the same cooling process as alloy 2.

The area below the solidus line and to the left of the eutectic composition is labelled Solid A + Eutectic mixture That to the right, Solid B + Eutectic mixture.

Microstructures different than lamellar type are also possible when eutectic reaction takes place. The different types of microstructures are as shown in the figure given below.

Two Metals Completely Soluble in the Liquid State but only Partly Soluble in the Solid State (Type III)

Alloy 1:-

Alloy 1 composed of 95A-5B, when slowly cooled, will follow a process exactly the same as any alloy in Type I.

at T1, it will begin to solidify by forming crystals of solid solution extremely rich in A.

The process continues, with the liquid getting richer in B and gradually moving down along the liquidus line. The solid solution, also getting richer in B, is moving down along the solidus line.

When the solidus line is finally crossed at T4the entire solid will be a homogeneous solid solution

Alloy 2:-Alloy 2, 30A-70B is the eutectic composition and remains liquid until the eutectic temperature is reached at point E. Since this is also the solidus line, the liquid now undergoes the eutectic reaction, at constant temperature, forming a very fine mixture of two solids.The two solids that make up eutectic mixture are given by the extremities of the eutectic-temperature line, of composition F and of composition G. AT, TE percent) = (EG / FG) x 100 = (20 / 70) x 100 = 28.6 percent (percent) = (EF / FG) x 100 = (50 / 70) x 100 = 71.4 percent AT, HKJ (percent) = (KJ / HJ) x 100 = (25 / 85) x 100 = 29.4 percent (percent) = (HK / HJ) x 100 = (60 / 85) x 100 = 70.6 percent

Alloy 3:-

Alloy 3:-Alloy 3, 60A-40B, remains liquid until the liquidus line is reached at T3. The liquid starts to solidify crystals of primary solid solution very rich in A.

As the temperature decreases the liquid becomes richer and richer in B, gradually moving down and to the right along the liquidus line until it reaches point E. Just above the eutectic temperature TE, there exist two phases as under. Phase Liquid Primary Chemical Composition 30A-70B 80A-20B Relative Amounts 40 percent 60 percent Alloy 4:-

Alloy 4:-Alloy 4, 85A-15B, initially follows the same process as described for Alloy I. Solidification starts at T2 and is complete at T5,the resultant solid being a homogeneous single phase, the solid solution (85A-15 B).At M, the solution is unsaturated. The solvus line FH shows the decrease in solubility of B in A with decreasing temperature. at point N The solution is saturated in B. Below this temperature, under slow cooling, the excess B comes out of solution. At room temperature, the alloy will consist mostly of with a small amount of excess , primarily along the grain boundaries.

(percent) = (HP / HJ) x 100 = (5 / 85) x 100 = 5.88 percentCongruent-melting Intermediate Phase (Type IV) When one phase changes into another phase isothermally (at constant temperature) and without any change in chemical composition, it is said to be congruent phase change or congruent transformation.

All pure metals solidify congruently.

Compounds are called intermediate phases because they are single phases that occur between the terminal phases on a phase diagram. Congruent-melting Intermediate Phase (Type IV)

In, the intermediate alloy phase is shown as a vertical line.

Since it is a compound, it is indicated as AmBn, where m and n number of atoms in the compound.

If the compound shows no solubility for either pure metal and the pure metals show some solubility for each other, the equilibrium diagram will look as shown in the figure given below.Congruent-melting Intermediate Phase (Type IV)

The Peritectic Reaction (Type V) In the peritectic reaction a liquid and a solid react isothermally to form a new solid on cooling. The reaction is expressed in general as under.

The new solid formed is usually an intermediate phase as shown in the figure given below, but in some cases it may be a terminal solid solution.

The Peritectic Reaction (Type V)

The Peritectic Reaction (Type V) It can be seen in the above figure that the compound AmBn, 70A-30B, when heated to the peritectic temperature, point G, decomposes into two phases, liquid and solid A. Therefore, it can be said that it is an incongruent melting intermediate alloy.

It can be seen that the peritectic reaction is just the reverse of the eutectic reaction, where a single phase formed two new phases on cooling.

The liquidus line is TADETB and the solidus line is TATPGJTETB. The peritectic reaction line is TPD. Notice that only part of this line, the length TPG, coincides with the solidus line.

The Eutectoid Reaction similar to eutectic reaction but does not involve the liquid.

In this case, a solid phase transforms on cooling into two new solid phases.

The Eutectoid Reaction

The Peritectoid Reaction This is a fairly common reaction in the solid state.

The new solid phase is usually an intermediate alloy, but it may also be a solid solution.