What do you mean by Binary Phase Diagrams?

A diagram representing different phases or phase transformations of a system with different curves, which are at equilibrium, is termed the phase diagram. Each curve in the diagram represents a specific property or characteristic of the system. It is also sometimes termed a constitutional diagram. These diagrams represent the relationship among the temperature, pressure, compositions, and quantities of phases. The dynamics or the dynamic behavior of the system cannot be determined from the diagram when a phase takes a transition to another phase. The diagrams are used to overview the primary metallurgical changes that occur within a mixture when undergoing cooling. When the cooling process is sufficiently slow, all the phases can be assumed to be in equilibrium with each other. The word 'phases' in the phase diagram are the boundary discontinuities present in the system. For a pure substance, the phases represent liquid, solid, and gas, whereas, for a solid, the phases are characterized by different lattice arrangements constituting a lattice structure.

Phase diagrams are meant to represent mixtures such as alloy, which is a mixture of two or more substances, out of which at least one should be metal. The substance having more composition is termed as a solvent, and the remaining substances or other substances are termed as the solute. This kind of solution is known as a solid solution. Based on the solid solubility, various phase diagrams exists.

Phase diagrams are classified according to the number of phases present in the component system. They are unary phase diagrams and binary phase diagrams.

When a system is composed of two components, the obtained equilibrium diagram is a binary diagram and the corresponding system is termed a binary system. These diagrams are characterized by the temperature and compositions, while the pressure remains constant. When speaking about two components, they may be either metal such as Cu and Ni, and a compound, such as Fe and Fe3C, or two compounds, such as Al2O3 and Si2O3.

Phase diagrams are classified by the extent of solid solubilities, such as

  • Completely soluble in both the phases, that is, solid and liquid
  • Completely soluble in liquid phase with limited solubility in solid phase

Hume-Rothery conditions

For the solid solubility of an element in metal to persist, the component system must satisfy Hume-Rothery conditions. These set of rules are:

  1. There should be equality of each crystal structure in the solid solution.
  2. Atomic sizes of the two components must not differ by 15%.
  3. The elements should not form compounds with each other.
  4. The valency of the elements must be the same.

The Hume-Rothery conditions are restricted to solid solutions that form either substitutional or interstitial solutions.

Terminologies of a binary phase diagram

Some of the useful terminologies associated with the phase diagrams are,

Liquidus: Liquidus is a line on a phase diagram above which the substance is completely liquid. The corresponding temperature is known as the liquidus temperature.

Solidus: Solidus is a line on the phase diagram below which the substance is completely solid. The corresponding temperature is known as the solidus temperature.

Solvus: It is defined as a curve on a phase diagram that shows the limits of solubility of one solid phase in another. It is a function of temperature.

Intermetallic compounds: Intermetallic compounds are a class of substances that have definite proportions of two or more metals. They are characterized by the difference in their lattice structures from their constituents. In other words, intermetallic compounds form an ordered solid-state compound between their constituent metallic elements. Intermetallic compounds are naturally brittle at room temperature, having high melting points.

Critical point: It's a point on the phase diagram where the liquid and vapor curves co-exist in equilibrium. At the critical point, the densities of the two fluids (liquid and vapor) are equalized, eliminating any phase boundaries between them.

Tie line: At any point in the phase diagram, the number of phases and their corresponding composition can be computed using a method called the lever rule or the tie line method.

In the area of chemistry, the lever rule is used to determine the mole fraction of each phase in the phase diagram

In an alloy having two compounds X and Y, having phases σ and μ, the mass fraction is given by,



ϖYμ = Mass fraction of Y in μ phase

ϖYσ = Mass fraction of Y in σ phase

ϖY = Mass fraction of Y in the alloy


A diagram of a tie line represented by green color
CC0 1.0 | Image Credits: https://commons.wikimedia.org | Dr. Bader Imre

Miscibility gap: A miscibility gap is simply a region in the two-phase equilibrium diagram that shows the regions of incomplete mixability of the components.

The Eutectic binary system

The eutectic system constituents a heterogeneous mixture, whose melting and solidification temperatures are usually lower than its constituents. The temperature is so termed as the eutectic temperature, which is the lowest possible temperature of all the corresponding temperatures of the counterparts or the constituents. The corresponding point of the eutectic temperature is known as a eutectic point. The eutectic alloy having the eutectic composition usually solidifies at the end of solidification at the eutectic temperature.

An image representing the eutectic point and corresponding eutectic composition
CC BY-SA 2.5 | Image Credits: https://commons.wikimedia.org | Michbich

The Iron-Carbon phase diagram

The amount of carbon present in the form Fe3C is 6.67% of C. Taking a look at the Fe3C phase diagram, at temperature 1125C, the solubility of cementite in γ iron is 2%. This solid solution of γ iron and Fe3C is known as austenite. In the BCC (Body-centered cubic) phase, that is, α-phase and δ-phase of iron, the solubility of Fe3C is around 0.33% for α-phase and 0.1% for the δ-phase.

The transformation of austenite into ferrite and cementite can be achieved by a slow cooling process. Rapid cooling of austenite transforms it into martensite. The property of martensite is characterized by its brittleness. A solid solution of Fe3C in α-iron is termed ferrite. 


Image of Iron-carbon phase diagram
CC BY-SA 4.0 | Image Credits: https://en.wikipedia.org | AG Caesar

Context and Application

The topic finds its application in various academic curriculums and courses such as

  • Bachelor of science
  • Master of science
  • Material science and engineering
  • Metallurgical science

Practice Problems

  1. Which of the following describes a binary phase diagram?
  1. When there is a two-phase component system.
  2. When there is a single-phase component system.
  3. When there is two or more component system.
  4. None of these

Correct option- a

Explanation: A binary phase diagram is a graphical representation of a two-phase component system which are in equilibrium.

2. Which of the following is a part of the Hume-Rothery condition?

  1. Equality of crystal structures in the solid solution
  2. Atomic sizes of the elements should not differ by 15%
  3. Equality of valency of the elements
  4. All of the above

Correct option- d

Explanation: Hume-Rothery rules describe that under certain circumstances an element could dissolve in metal, forming a solid solution. Some of the rules are, equality of crystal structures, equality of valency of the elements, the elements should not form any compounds, the atomic sizes should not exceed15%.

3. Under what circumstances a martensite is formed?

  1. Rapid cooling of austenite
  2. Slow cooling of austenite
  3. Heating of austenite followed by quenching
  4. Slow cooling initially than rapidly cooling in oil

Correct option- a

Explanation: Martensite is formed when austenite is cooled rapidly.

4. Austenite is the combination of which of the following compositions?

  1. Solid solution of γ iron in Fe3C
  2. Solid solution of δ iron and Fe3C
  3. Solid solution of pearlite and martensite
  4. None of these

Correct option- a

Explanation: Austenite is a solid solution of γ iron in Fe3C.

5. If the solidification and melting temperature of a compound are lower than its corresponding constituents, then which of the following options holds true for an equilibrium system?

  1. The system is a hypo-eutectic system
  2. The system is a hyper-eutectic system
  3. The system is a eutectic system
  4. The system is a eutectoid system

Correct option- c

Explanation: For a eutectic system, the melting and the solidification temperature of the compound is lower than its corresponding constituents.

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