A substance which is composed of two or more chemical elements such that metallic atoms predominate in composition and the metallic bond predominates is called an alloy. The element present in largest proportion is called the “base metal” and all other elements present are known as “alloying elements”.

Alloying elements can drastically change, (improve) physical, chemical, mechanical and electrical properties of the base metal. The solidification of metal alloys is clearly demonstrated by means of equilibrium diagrams which are convenient graphic representations of changes in state due to variations in temperature and concentration.

“Equilibrium diagrams”, also called “constitutional and phase diagrams”, enable the phase content of the alloy to be determined at any temperature and composition. They enable the phase transformations to be followed in heating and cooling the alloy under equilibrium conditions, i.e., when all processes in the given system are reversible. This means that changes occurring in a system as a result of processes proceeding in one direction are fully compensated by changes due to the reversal of the process in the system.

An Equilibrium Diagram (Importance and Objectives):


I. Shows at a glance the phases which exist in equilibrium for any combination of temperature and alloy composition;

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

III. Provides with the knowledge of phase composition and phase stability as a function of temperature, pressure and composition;

IV. Permits to study and control processes as- Phase separation, Solidification of metals and alloys, Purifications of materials. The growth and doping single crystals, and structural changes produced by heat treatment, casting etc.


Equilibrium/phase diagrams are classified as:

1. Unary (or One-Component) Phase Diagram:

It is plotted as pressure on vertical axis and temperature on the horizontal axis.

2. Binary (or Two-Component) Phase Diagram:


It finds extensive uses.

3. Ternary (or Three-Component) Phase Diagram:

“Equilibrium diagrams are plotted with the concentration as the abscissa and the temperature as the ordinate”.



A system is a substance (or group of substances) so isolated from its surroundings that it is unaffected by these and is subjected to changes in overall composition, temperature, pressure or total volume only to the extent followed by the investigator. A system may be composed of gases, liquids, solids or any combination of them and may involve metals and non-metals, either separately or in any combination.

An alloy system is a combination of two or more elements forming the alloys which are considered within a specified range of temperature, pressure and concentration.

A system is classified according to the number of components that constitute the system.



A component is a unit of the composition variable of the system. A system having one component is called a Unary system and the systems having two, three and four components are known as Binary, Ternary and Quaternary systems respectively.


A phase is a physically and chemically homogeneous portion of a system, separated from the other portions by a surface, the interface. For instance, a homogeneous liquid solution is a single-phase system; a mixture of crystals of two types, differing in composition and structure separated by an interface, or the coexistence of the liquid alloy and its crystals comprise two- phase systems.

Structural Constituents:

The phases in alloys are not necessarily uniformly distributed throughout the structure. There are certain ways in which these phases may be associated to form the structure. The association of phases in a recognizably distinct fashion may be referred to as a structural constituent of the alloy.

It is customary to call those parts of the micro-structure that have a clearly indentifiable appearance under the microscope the constituents of the structure. An “eutectic” is a structural constituent of the alloy. Pearlite, Martensite and Sorbite are microconstituents in steel.

Gibb’s Phase Rule:

All changes which takes place in a system consisting of several phases, in accordance with external conditions (temperature and pressure), conform to the so-called phase rule. The phase rule establishes the relationship between the number of degrees of freedom, the number of components, and the number of phases.

It is expressed mathematically as follows:

F = C + n-P … (2.1)

Where, F = Number of degrees of freedom in the system (the number of variable factors),

C = Number of components in the system,

P = Number of phases in equilibrium, and

n = Number of external factors (for example, temperature and pressure).

The number of degrees of freedom is the quantity of independent external or internal variable factors (temperature, pressure, and concentration) which may be altered without causing the disappearance of a phase or the formation of a new phase in the system.

In studying chemical equilibrium, temperature and pressure are regarded as external factors determining the state of the system. The effects of pressure may be neglected in applying the phase rule to metal systems leaving only one variable external factor-temperature.

The equation will then be:

F = C+1-P … (2.2)

All internal and external factors (concentration and temperature, respectively) have definite values in a system that is in equilibrium.

Since the degrees of freedom cannot be less than zero then

C-P + 1 > 0

P ≤ C+ 1 … (2.3)

i.e., the number of phases in a system cannot exceed the number of components plus one. Therefore, no more than three phases may be in equilibrium in a binary system, no more than four in a ternary system, etc.

I. In cases when the maximum possible number of phases is in equilibrium, the number of degrees of freedom equals zero (F = 0). This is called non-variant equilibrium.

II. A system in non-variant equilibrium may exist only under entirely definite conditions; at a constant temperature and at a definite composition of all phases involved.

A pure metal at the solidification temperature, for example – is a one component system consisting of two phases of indentical composition,

F = 1+1-2 = 0

This means it is a non-variant system. In this case, the temperature cannot be selected or changed arbitrarily. There is only one temperature at which the system is in equilibrium. This is the melting (or solidifying) point for the given metal. If the number of phases is less than the maximum possible number by one, the number of degree of freedom will also increase by one (F = 1). Such a system is said to be monovariant.

An alloy of two metals, for example, is a two component two phase system, in the general case, at the beginning of solidification. Therefore, F = 1 in this case. A system with F = 2 is bivariant. Therefore, the system may be in equilibrium at different temperatures and concentrations.

It may be noted that:

1. The phase rule applies to dynamic and reversible processes, where a system is heterogeneous and in equilibrium and where the only external variables are pressure, temperature and concentration.

2. The phase rule becomes particularly useful when dealing with multicomponent systems to determine whether the microstructures are in equilibrium or not.

3. The phase rule may be used to formulate certain rules of geometry which apply to phase diagrams and are useful in the preparation of phase diagrams.

Classification of Equilibrium Diagrams:

Equilibrium diagrams may be classified according to the relation of the components in the liquid and solid states as follows:

1. Components completely soluble in the liquid state:

(i) And also completely soluble in the solid state,

(ii) But partly soluble in the solid state (Eutectic reaction),

(iii) But insoluble in the solid state (Eutectic Reaction),

(iv) Peritectic reaction

2. Components partially soluble in the liquid state:

(i) But completely soluble in the solid state,

(ii) And partly soluble in the solid state.

3. Components completely insoluble in the liquid state and completely insoluble in the solid state.

Solid Solution (Isomorplwiis System) – Two Metals (or components) Completely Soluble in the Liquid and Solid States:

The main conditions for complete/unlimited solubility in the solid state (as discussed under solid solution) are:

(i) Two components should have the same type of crystal.

(ii) Sizes of the atoms should be very similar (the difference in size for iron, nickel, or cobalt base alloys must not exceed 8 per cent). A difference in size over 15 per cent prevents the formation of solid solutions due to the extreme distortion of the solvent crystal lattice.

Fig. 2.8 shows the equilibrium diagram for a system of components that are completely mutually soluble in both the liquid and solid states. The upper line (called liquidus) corresponds to the temperatures at which the alloys begin to solidify.

The lower line (called solidus) indicates the completion of solidification. In the temperature interval between the liquidus and solidus the alloys are in semi-solid state, i.e. they consist of crystals of a solid solution of metals A and B and the liquid alloy.

Let us now consider solidification of an alloy containing 60% B (Fig. 2.8). Freezing starts at temperature t1, where the first crystal of the solid solution of metals A and B separate from the liquid alloy. Below temperature t1, the ‘solid solution’, in equilibrium in the liquid phase, is determined by the point of intersection of a horizontal line, passing through the given temperature, with the solidus.

The concentration of the liquid phase is determined by the intersection of the same temperature line with the liquids. For example, at a temperature of t2, points p and q represent the concentrations of the solid and liquid phases, respectively. At temperature t3, they are represented by points p ‘and q’. Thus, in solidification, the composition of the liquid phase continuously varies along the liquidus while that of solid phase varies along the solidus.

For example, the ratio by weight between the liquid and solid phases at a temperature t2 may calculated by using lever rule as follows:

An alloy containing 60% B completely solidifies at temperature t4.

Equilibrium diagram for copper-nickel alloys which are example of complete mutual solubility in both the liquid and solid phases is shown in Fig. 2.9.

Alloys forming homogeneous solid solutions are widely used as engineering materials.

Equilibrium Diagram of an Alloy Subject to ‘Peritectic Transformation’:

Fig. 2.13 shows equilibrium diagram of alloys whose components have complete mutual solubility in liquid state and limited solubility in the solid state (alloys with a peritectic transformation). This diagram differs from the proceeding type (Fig. 2.12) in that the crystals of beta solid solution, precipitated at the beginning of solidification, react with the liquid alloy of a definite composition to form new crystals of alpha solid solution. This transformation or reaction occurs at a constant temperature and is called peritectic transformation.

In the equilibrium diagram:

I. Line abc is the liquidus and adec is the solidus.

II. Point d represents the maximum solubility of metal B in metal A at temperature tp.

III. Point e is the same for metal A and metal B.

IV. Points k and f represent maximum solubility at normal temperatures. Thus, lines dk and ef show the variation in solubility in the alpha and beta solid solutions upon cooling.

Let us consider the solidification of alloys 1, 2 and 3 which contain 40% B and 60% A, 61% B and 39% A, and 80% B and 20% A, respectively, in order to explain diagram better.

The solidification of ‘Alloy 3’ containing 80% B alloy begins at temperature t1 when crystals of beta solid solution precipitate from the liquid alloy. At temperature tp the liquid phase has the composition conforming to point b and the crystals of solid solution are enriched by metal A to the maximum concentration shown by the point e.

Here the alloy completely solidifies according to a peritectic transformation that consists in an interaction between the liquid alloy of composition B with the fully saturated β crystals (point e). The structure of the solid alloy will be a peritectic mixture of two solid solutions (α + β) whose compositions will vary along the lines dk and ef at a further fall in temperature.

The solidification of ‘Alloy 2’ containing 61% B begins at temperature t2 and finishes at the peritectic temperature tp. The alloy completely solidifies at a constant temperature.

The solidification of ‘Alloy 1’ containing 40% B begins at temperature t3 and crystals of beta solid solution precipitate from the liquid phase. In this alloy the liquid phase is in excess after the pertiectic transformation. The alloy completely soldifies at temperature t4 and consists only of crystals of alpha solid solution.

Ternary Equilibrium Diagram:

The properties of a pure metal are improved by addition of alloying elements. Simple binary alloys possess 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.

Thus, manganese added to steel containing sulphur confers upon it better forging properties by combining with sulphur to form manganese sulphide (MnS), which gets ejected from steel. Such additions of manganese to steel are very difficult to illustrate the alloy diagram method. However, if only three components are present, an alloy diagram may be plotted by means of triangular co­ordinates as shown in Fig. 2.14.

Each of the components of a ternary alloy is represented by one of the corners of an equilateral triangle. The sides of the triangle represent an alloy system of three binary alloy diagrams AB, AC and BC. The individual metals in the alloy are A, B and C.

All the possible combinations of the three components are then formed from the lengths of perpendicular from any given point O. From the diagram it will be seen that O represents 40% of A, 40% of B and 20% of C. To construct a diagram with the angle as the base, temperatures are plotted at right angles to the plane of the triangle. The development of the diagram ultimately results in a solid metal, each side of model representing one of the three binary systems.

As to binary diagrams, the phase rule, the composition vertical rule and the lever rule are equally applicable to ternary diagrams.

Summary of Common Type of Phase Transformations in Metallurgical Equilibrium Diagrams:

Zone Refining:

I. “Zone refining” is a technique to remove impurities and to obtain a pure material viz. pure semiconductors, particularly Silicon and Germanium for transistor fabrications.

II. It uses the principle of phase separation; and is based on the fact that the first solid frozen out is purer than the average composition while the liquid becomes enriched in the solute which is deposited at the other end of the rod (semiconductor).

Let us consider that pure crystal are to be obtained for a given alloy A-B of overall composition Co. Refer to Fig. 2.24.

III. The alloy is melted to a liquid solution and then cooled. On reaching point Z, the solidification of A (semiconducting material) begins whose composition will be given by Cs. If the remaining liquid is thrown away, the remainder will be rich in A.

IV. Now, if it is again melted and again cooled the solidification of A will begin at Z2, which will give solid composition of A as C’s purer than Cs.

V. Again the remaining liquid is thrown and process is repeated; by doing so we can get very pure crystal of A.

Since the remaining liquid is being thrown away every time, the purified material will be very small.

Segregation Factor (k):

It is the tendency to segregate the solute atoms during the solidification in binary system and is given by:

For zone refining factor, k ≤ 1. Liquid has greater concentration of solute atoms.

During zone refining the impurity (solute atoms) redistribute themselves. The solid rejects solute atom at the liquidus resulting in an increase of concentration of the solute in the liquid.

Zone Refining Process:

I. In zone refining process, the material to be purified is in the form of a long rod. At any time, only a small length of this rod is melted with the aid of an induction coil or an electron beam.

II. The coil or beam is moved slowly from one end to the other end of the rod, continuously solidifying the melting zone and remelting the fresh material ahead. Surface tension forces are usually strong enough to hold the molten zone in place without the need for a container, which may contaminate the melt.

III. If the zone is passed across many times, each time in the same direction, the material at the starting end becomes much purer than the rest of the rod.

In a typical case, ten passes of the molten zone can reduce the impurity level to as low as 10-6 times the initial value.