CHAPTER 3 : PHASE DIAGRAMS

Introduction Phase diagrams , are also known by the names equilibrium/constitutional diagrams

, are a very important tool used in the study of alloys. A phase diagram consists of two parameters – temperature , taken on the

ordinate and the alloy composition taken on the abscissa. Role of the phase diagram :- Shows the phases in equilibrium for a given allow composition, at a glance. Shows the relationship between the composition , temperature, and alloy

structure in series. Permits to study and control processes such as Phase separation ,Solidification of

metals and alloys , Purification of materials ,The growth and doping single crystals, and the structural changes produced by heat treatment ,casting ,etc. .

Solid Solutions • A solid solution is defined as a solid

mixture containing a minor component uniformly distributed within the crystal lattice of the major component. ( as shown in the two possible cases )

• The key feature of a solid solution is that the metals retain their homogeneity and hence their solubility after their transformation to a solid crystalline state.

• An example of a solid solution would be Copper 64% and Zinc 36%

• The solid solutions comprise of atoms of almost the same atomic radius , and they tend to form a single phase and the elements are soluble in both their solid and liquid states .

Classification of Solid solutions :

Substitutional Interstitial

Disordered Ordered

• Substitutional Solid Solutions have a direct substitution of one type of atom for another so that solute atoms (Cu) enter the crystal to take positions normally occupied by solvent atoms (eg . Ni atoms).

• Disordered Substitutional Solid Solutions are those type of solid solutions in which the solute atoms are randomly distributed in the solvent lattice structure , hence disordered.

• Ordered Substitutional Solid Solutions are those in the disordered solution is cooled slowly , causing atomic re-arrangement because of the diffusion due to cooling causing uniform distribution of solute and solvent atoms.

• Interstitial Solid Solutions are those in which the solute atoms occupy the interstitial positions in the solvent crystal lattice , without any replacement of solvent atoms , on account of a very small solute atomic size relative to that of the solvent. (around a factor of 70 )

Intermediate phases • In many binary alloy systems, when the chemical affinity of metals is great, their

mutual solubility becomes limited or reduced and a so called “intermediate phase” is formed.

• The intermediate phase may have either narrow or wide ranges of homogeneity and may or may not include a composition having a simple chemical formula.

• For example the phase CuAl exists in a homogeneity ,that does not include the composition CuAl.

• Intermediate phases may range between ideal solid solutions and the ideal chemical compound.

• The intermediate phases are the phases that form in the intermediate regions of the equilibrium diagram.

• They are usually classified into two types : Intermetallic compounds of • a)fixed composition or b)variable composition.

Comparison between the types

Intermetallic compounds of fixed composition

• They obey the usual valency laws ,like ordinary chemical compounds. Eg. NaCl.

• An example could be Mg2Sn has 29.08% of Mn.

Intermetallic compounds of variable composition

• They do not obey the valence laws and are also known as electron compounds.

• Examples could be Ratio 3/2 –beta , like Cu3Al,Ratio 21/13-gamma like Cu9Al4 or ratio 7/4-Epsilon like Cu3Al

Phase rules

• The following are the rules which are to be followed while interpreting the phase diagrams :

• Prediction of Phases • From a phase diagram , specific information can be

obtained only if a temperature and a composition is specified.

• This can be done by using both temperature and composition parameters to identify the point on the phase diagram.

• Once done , depending on its location ,identify the phase present at that particular point .

• Phase composition• To find the phase composition at a particular

temperature like 500 degrees Celsius , draw a horizontal line OP , that hits the liquidus and a vertical line that hits the solidus curve from P . This would automatically indicate the phase composition for the required temperature.

Lever arm Principle• Besides indicating the number of phases and phase composition , the phase

diagram also tells the proportion of co-existing phases at a given temperature.• To determine the relative amount of the two phases , erect an ordinate at a point

say (85% Sb) on the scale which gives the total composition of the alloy. • The intersection of this vertical blue line and a given isothermal line OP (at a given

temperature) is the fulcrum of the simple lever system and OM and MP are the two lever arms as shown in the previous figure.

• This is commonly referred to as the lever rule because the amount of a given phase multiplied by its lever arm is equal to the amount of the other phase multiplied by its (or the other) lever arm.

• The isothermal line is also referred to as the Tie line since it joins the composition of the two phases in equilibrium at a specific temperature.

• When expressed mathematically it gives us the foll :• 1.The amount of solid phase • i.e. (MP/OP)*100• 2.The amount of liquid phase• i.e. (OM/OP)*100

• The phase rule, also known as the Gibbs Phase Rule, establishes the relationship between the number of degrees of freedom (F),the number of components(C) and the number of phases(P).

• It is mathematically expressed as follows :

P+F=C+2• P->Number of phases (Solid or liquid and so on) ;• F->Number of degrees of freedom (pressure ,temperature ,concentration and so

on) without altering the equilibrium• C->Number of Components n the system (For example Pb-Sn)• In metallurgical systems the pressure is regarded as remaining fixed at one atm

and hence the pressure variation is neglected.• Phase rule applies to dynamic and reversible processes, where a system is in

heterogeneous equilibrium and where the external variable are only temperature , pressure and concentration.

• It is used while dealing with multicomponent systems to determine whether the microstructures are in equilibrium or not.

Gibbs Phase rule

Energy in the intermediate phase• The formation of a new intermediate phase in a

system is associated to the change in free energy of the system.

• The free energy has two components :- 1)Chemical energy 2)Non chemical free energies.

• Let us assume that “x” be the width of the new intermediate phase formed in the system.

• If “G” is the amount of decrease in free energy/unit volume , then the total free energy decrease would be G*x , considering unit cross sectional area of the couple.

• Non chemical free energy is brought into play for the creation of the new intermediate phase , and a mechanical work is done while doing so due to volume change.

• Hence the total free energy change is the sum of the interfacial energies and the mechanical work done .

Phase diagram • A great deal of information concerning to phase

changes in many alloy systems has been accumulated and the best method of recording the data is in the form of phase diagram.

• A phase diagram shows the limits of composition and temperature within which the various constituents or phases of the alloys are stable.

• The structural changes and compositional changes of the constituents in equilibrium at a fixed temperature can be ascertained using the phase diagrams.

• If two metals of a binary solution ( such as Cu-Ni) are mixed in different proportions, melted and cooled , and a cooling curve is constructed for each composition,.

• When the temperatures at which solidification starts and completes for various compositions with respect to time would lead to the phase diagram.

Classification of Phase diagram • The classification is as follows :- • Unary (or one component) phase diagram which is plotted as pressure on the

vertical axis and temperature on the horizontal axis .• Binary (or two components) phase diagram which is plotted with temperature

taken on the vertical axis and the various concentrations taken on the horizontal axis commonly.

• Ternary (or three components) phase diagram which is plotted three dimensionally between three components and the equilibrium associated with each other and the vertical axis usually taken comprises of the temperature as the common parameter (discussed more in the successive slides).

Phase changes in alloys• Phase changes can be analyzed for the alloys in two ways :-• 1)For two metals completely soluble in liquid state and insoluble in the solid state • 2) For two metals completely soluble in liquid state and partially soluble in the

solid state

For two metals completely soluble in liquid state and insoluble in the solid state Consider the Bismuth Cadmium system as shown :

Four phase fields are seen on Fig. 5 above: • a fully molten region, • two regions in which liquid and solid coexist, • a completely solid region.

• The two liquidus lines slope downwards from the melting points of the pure materials to meet at a point known as the eutectic point (E).

• Material of the eutectic composition will undergo the transformation liquid -> solid (Bi+Cd) at the temperature 144 degrees Celsius.

• Since the formation of the two solids occurs simultaneously, this will be also reflected in the microstructure.

• The two solids are strongly mixed in this eutectic structure, sometimes as particles or ”stars” of one solid surrounded by the other, or maybe as laminations as shown in the drawing.

• Note that unlike all other alloys, eutectic compositions have no extended freezing range but they freeze at a definite temperature similarly to pure metals.

• For two metals completely soluble in liquid state and partially soluble in the solid state

• A eutectic system can occur when terminal solid solutions exist on both ends of thebinary equilibrium phase diagram. An example of a binary eutectic system is lead (Pb) -tin (Sn). • Although the atomic size difference is less than 10%, Pb has an FCC crystalstructure while Sn is an unusual metal with a non-cubic tetragonal structure. This resultsin limited solid state solubility with the maximum solubility of Sn in the FCC Pb equal to19.2 wt%Sn while only 2.5wt% of Pb is soluble in the tetragonal Sn structure. • At compositions and temperatures, which exceed these solubility limits, two solid

phaseswill exist in equilibrium. The phase is the FCC Pb with some substitutional Sn atomsand the phase is tetragonal Sn with only a few substitutional Pb atoms.• These maximum solid-state solubility both occur at 183 deg. Cel. which is referred to

as the eutectic temperature. • At this temperature, there exists a point on the phase diagram(a single combination of composition and temperature) where three phases (the two solids and a liquid) can exist simultaneously in equilibrium.

Ternary Phase diagrams • The properties of a pure metal are

improved by the addition of alloy elements.• Simple binary alloys process certain

improved properties than the pure metals.• Further improvement in qualities or

properties of a binary alloy is frequently gained by adding a third element, eg , the addition of nickel to Steel (Fe-C) improves toughness and the addition of lead to brass (Cu-Zn) improves machinability.

• A ternary equilibrium diagram presents a three component system , that is it deals with three metals say A,B and C.

• The complete equilibrium is indicated in a three dimensional figure.

• The temperature is always plotted vertically.

• We have liquidus and solidus planes in a ternary system unlike the liquidus and solidus lines in a binary system .

Cooling Curves

• A mathematical curve while plotting the temperature as a function of time as different alloys in the system are very slowly cooled.

• This method is basically used to determine the temperature at which phase change ( from solid to liquid ) occurs.

• The study is useful in :-– Studying the changes that occur during solidification of alloys, and – In determining transformations subsequent to solidification .

Cooling curve of pure metal or compound

• The liquid metal initially cools at a rate called as the cooling rate until we reach the beginning of the thermal arrest.

• During thermal arrest the phase change occurs and the metal liberates its latent heat of fusion while keeping the temperature constant to reach to the end of the thermal arrest.

• This point is referred to as the freezing point of the metal.

• On further cooling the metal tends to reach the room temperature.

• The Slopes before and after thermal arrest ,by value , depend upon the specific heats of the liquid and solid metals , respectively.

Equilibrium diagrams of Iron and Iron -Carbide diagram

• Iron is molten above 1536 deg. Celsius. It solidifies in a BCC Structure (Delta).

• On further cooling at 1400 Celsius , a phase change occurs and the atoms rearrange themselves into the Gamma from which is FCC and non magnetic.

• On further cooling at 910 Celsius, another phase change occurs from FCC non magnetic gamma iron to BCC non magnetic alpha iron.

• Finally at 768 Celsius ,the alpha iron becomes magnetic without a change in the lattice structure .

Cooling curve for Iron

Equilibrium diagram for Iron Carbide System

• The iron carbon equilibrium diagram indicates the phase changes that occur during heating and cooling and the nature and amount of the structural components that exist in any temperature. It also establishes a relation between the microstructure and properties of steel and cast irons and provides a basis for the understanding of the principles of heat treatment.

• The iron carbon equilibrium has a peritectic point , eutectic and eutectoid point.• When Delta iron + liquid when cooled below peritectic point causes it to be converted to

Austenite. (Occurs around 2720 Fahrenheit)• The liquid cools to an eutectic mixture of austenite and cementite at a temperature of 2066

Fahrenheit and the reaction is called as a eutectic reaction.• Eutectic point is at 4.3% carbon content and the eutectic mixture is not usually seen in the

microstructure, because austenite is not stable at room temperature and must undergo another reaction during cooling.

• The eutectoid reaction occurs at 1333 Fahrenheit and is represented by a horizontal line with the eutectic point at 0.83% carbon content .

Features :- 1)When steel of 0.4 % carbon (hypoeutectoid steel) is converted entirely into austenite above • The upper critical temperature line and whencooled below the line the structure of iron

changes from FCC TO BCC causing ferrite crystals to grow in size at the expense of austenite.At 1344 Fahrenheit , austenite has 0.83 % (max limit it can hold in solid solution) , the temperature drops further , and carbon precipitates as cementite at 723 degrees Celsius.

• Cementite and still separating Ferrite form alternate layers until all the remaining austenite is consumed. The lamellae structure contains 0.83% of carbon and is known as pearlite.

• Other transformations are also possible such as eutectoid steel into pearlite as well as hypereutectoid steel to cementite.

Ledeburite Structure