## What is a Phase diagram?

A phase diagram is a representation that shows the different metallurgical changes that occur when a mixture of more than one component system is gradually cooled, usually from the liquid phase to the solid phase. The phase diagram is also known as an equilibrium diagram. The diagram shows the phase transition or phase changes during the cooling process. In metallurgy or material science, a phase is characterized by boundaries across which there exist discontinuities in the physical properties of the system.

A pure substance can exist in different phases, namely, solid, liquid, and gas (vapor phase). Similar characteristics can be observed for the solid phase, characterized by different crystal structures.

During the cooling process, especially when the cooling process occurs relatively slow, the phases can be assumed to be in equilibrium with each other at a given temperature. The phase transformations are governed by temperature, pressure, and composition. However, the phase diagram is usually measured in a temperature-composition domain, with the temperature at the y-axis and composition at the x-axis.

## Major features of the phase diagram

The major features of the phase diagram are:

• Triple point
• Phase boundaries
• Two-dimensional phase diagrams
• Three-dimensional phase diagrams

### Triple point

It is a point in the phase diagram that is characterized by an intersection of the equilibrium lines. A point where the three phases, solid, liquid, and gas of a substance co-exist, is also known as a metastable state. The sublimation curve, vaporization curve, and fusion curve of a substance in a thermodynamic equilibrium meet at a single point.

The triple point of water is considered as  according to the 2019 redefinition of the SI units. At this condition (triple point), it is relatively possible to change all the water to ice, liquid water, or vapor by making small changes in temperature and pressure.

The liquid-gas or liquid-vapor, solid-gas, and solid-vapor represent the minimum pressure at which the water can exist in a liquid phase. At a condition below the triple point of water, the phase transition of solid ice occurs directly to liquid-vapor (water-vapor), this process is known as sublimation. However, above the triple point of water, the substance when heated first converts to liquid water and then upon further heating, turns into the vapor phase.

### Phase boundaries

Phase boundaries can be defined as the connection line or the junction between two crystals that differs by the lattice structures. The phase boundaries are usually divided into three types, namely, coherent, semi-coherent, and incoherent phase boundaries. When the atomic configurations are the same at the boundary plane and are characterized by continuous lattice crystals the phase boundary can be termed as coherent. Semi or partial coherent phase boundaries can occur when there exists large misfits or dis-continuity characterized by dislocations. In the incoherent phase boundary, the atomic arrangement is unordered and the atomic co-ordinations at the boundary resemble the behavior of liquid.

### Two-dimensional phase diagrams

The two-dimensional phase diagrams are generally the pressure-temperature phase diagrams with the temperature at the x-axis and pressure at the y-axis. The diagram shows the temperature-pressure curves and the equilibrium lines.

### Three-dimensional phase diagrams

The three-dimensional phase diagram is characterized by three thermodynamic quantities. It is also known as a $p-v-T$ diagram. The with quantities p, v, and T at three different axes. There lies a line in the phase diagram known as the triple line where the solid, liquid, and gas phases are in equilibrium. The critical point is a point in the three-dimensional phase diagram.

## Important definitions of the phase diagram

• Sublimation: A process when the substance directly goes from the solid-vapor phase. For example, freeze-dried substances are created by the sublimation process. The other name of freeze-drying is Lyophilization.
• Deposition: A process when a system goes from gas to liquid state. It is also the reverse process of sublimation.
• Melting: A process when a substance goes from a solid to a liquid state. Every substance has its specific melting point.
• Fusion: It is a reverse of melting when a substance goes from liquid to solid phase.
• Vaporization: A process when a substance goes from liquid to vapor phase.
• Condensation: A process when a substance goes from vapor to liquid phase. It is the reverse of vaporization.
• Critical point: It is a point in a temperature-pressure phase diagram where the liquid state and the gaseous state of a substance co-exists. Beyond the critical point, the substance acts as a single-phase known as the supercritical fluid.
• Solidus: The solidus line is a line on a phase diagram, below which a substance acts as solid. It is the locus of temperature below which it is only characterized by solid. The solid is characterized by large intermolecular forces.
• Liquidus: It is a line in the phase diagram above which is characterized by only liquid. Intermolecular forces are relatively less in the liquid phase compared to the solid phase but more than gaseous phase.

## Solid solutions

An alloy is generally a mixture of two or more materials, out of which, at least one of the components must be a metal. The material having the largest composition is termed as a solvent and the remaining inclusions are termed as solute. This type of mixture is known as a solid-solid solution. There are two types of solid solutions, interstitial type, and substitutional type. When the size of the atoms is very small such that they can occupy interstitial spaces, the solid solution is known as an interstitial solid solution. When the atoms occupy the regular matrix positions, such type of solid solution is known as a substitutional solid solution.

## Phase rule

The phase rule is coined by Gibbs, which is a rule related to variables in a thermodynamic system. The rule is applied to determine the degree of freedom of the components present in a system.

The phase rule is given by the expression,

$F=C-P+2$

where,

$F$ = Degree of freedom

$C$= number of components in the system

$P$ = Number of phases

For a one-component and one-phase system, the number of degrees of freedom associated with the system is two. For a one-component and two-phase system, the number of degrees of freedom is one, while for a one-component and three phases, the number of degrees of freedom is zero.

In the case of a multicomponent system, the number of phases may be less than the counted value, if the components are in a chemical equilibrium (Chemical equilibrium is a state where the reactants have zero chemical potential to initiate a chemical change).

## Context and Applications

The topic finds its application in the areas of materials science and metallurgical science, which are taught in the following curriculum

• Masters in Science (Chemistry)
• Bachelors in Science (Chemistry)
• Bachelors in Technology (Metallurgy)

## Practice Problems

1. Which of the following summarizes the triple point?
1. A point where the phases have different properties.
2. A point where the three phases co-exist in equilibrium.
3. A point is present in two-dimensional phase diagrams.
4. A point is present in three-dimensional phase diagrams.

Correct option- b

Explanation: A triple is a point in the phase diagram where the three phases, solid, liquid, and gas co-exist in equilibrium.

2. Which of the following characterizes the triple point in a three-dimensional phase diagram?

1. A triple point is a surface or area in the phase diagram.
2. A triple point is a line in the phase diagram.
3. A triple point co-exists with the critical point.
4. A triple point is a point in the phase diagram.

Correct option- d

Explanation: In a three-dimensional phase diagram, the triple point is always a point.

3. For a system having distinct phases and components, the degree of freedom can be determined by which of the following rule?

1. Gibbs phase rule
2. The lever rule
3. Hume-Rothery rule
4. None of these

Correct option- a

Explanation: Gibbs phase rule provides the relationship between the number of components in a system, the number of phases, and the degree of freedom.

4. Under what conditions, a fluid can be termed as supercritical?

1. Any fluid below the critical point.
2. Any fluid above the critical point.
3. Any fluid falling below the triple point.
4. None of these.

Correct option- b

Explanation: Substances that exist above the critical point are termed supercritical fluid.

5. Which of the following options represents correctly about the solidus line?

1. All the substances exist in the solid phase below the solidus line.
2. All the substances exist in the liquid phase above the solidus line.
3. All the substances exist in the vapor phase below the solidus line.
4. Both a and b are correct.

Correct option- d

Explanation: The solidus line lies just below the liquid phase characterized by the liquidus line present at the top. Below the solidus line, the substance exists in the solid phase.

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### Types of Phase Diagrams and Their Applications in Metallurgy

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