Material Science & Engineering : Ferrous & Non-Ferrous Metals and Alloys

By Akhil Gupta|Updated : April 22nd, 2021


Any restriction to the movement of the dislocations are said to increase the strength of the material. Different ways to hinder dislocation motion / Strengthening mechanisms are as follows



Any restriction to the movement of the dislocations are said to increase the strength of the material. Different ways to hinder dislocation motion / Strengthening mechanisms are as follows:

  Solid solution strengthening:

(i). Impure foreign atoms in a single-phase material produces lattice strains which can anchor the dislocations.

(ii). Effectiveness of this strengthening depends on two factors: size difference and volume fraction of solute.

Conditions for unlimited solubility:

Hume-Rothary rule: Two materials will combine and form alloys only when the conditions of Hume and Rothary are satisfied. Before these conditions can be applied, crystal structure of both the materials should be same. The conditions are:

  1. Difference in atomic radius of both the materials should be less than 15 %.
  2. Crystal Structure: The materials must have the same crystal structure; otherwise,

there is some point at which a transition occurs from one phase to a second phase

with a different structure.

  1. Valency of both the materials should be same.
  2. Electronegativity and electron affinity of both the materials should be comparative.

Alloying the element either produces interstitial or substitutional impurity.

Interstitial solid solution:

(i). Solute atoms are much smaller than the solvent atoms, so they occupy interstitial position in solved lattice.

Example: Carbon, nitrogen, hydrogen and boron are the element which commonly form interstitial solid solutions.

Substitutional solid solution: Solute atoms size roughly similar to solvent atoms. Due to similar size solute atoms occupy vacant site in solvent atoms.

Interstitial void is always smaller than the impurity, so it creates compressive strain within the material. If the atomic radius of substitutional impurity is smaller it produces tension strain field and if substitutional impurity size is bigger it produces compressive strain field. These strain field create barrier in the movement of dislocation, that is why strength increases. Larger the strain field created by impurity atom, more will be increase in strength.

Solute atoms interact with dislocations in many ways:

(i). Elastic interaction

(ii). Modulus interaction

(iii). Stacking-fault interaction

(iv). Electrical interaction

(v). Short-range order interaction

(vi). Long-range order interaction

The yield strength, tensile strength, and hardness of the alloy are greater than those of the pure metals. This is one reason why we most often use alloys rather than pure metals.


  • A phase is a physically distinct, chemically homogeneous, and mechanically separable region in a system in equilibrium.
  • If more than one phase is present in a given system, each phase will have its own distinct properties and a boundary separating it.
  • Gases are always single phase. Liquids can be single phase (salt solution) or two phases (oil and water). Solids can be Multiphase or single phase (Pure metal).

4.1.   Gibb’s phase rule

F +P = C + 2

where, F = No. of degrees of freedom.

P = No of phases present.

C = No. a component

2 is for temperature and pressure.

When pressure is held constant

F+ P=C+1 , 1 is only for temperature.


For pure metal at solidification

C=1, P=2

F=0 , which states that temperature can not be varied without disturbing equilibrium of system.

Note: At triple point, degree of freedom is zero.

4.2.   Phase equilibrium

It is related to consistency in the physical and chemical characteristics of the phase with respect to time. It does not specify the time length required for attaining equilibrium conditions.

Metastable state

In case of solid systems, the equilibrium state is never completely achieved because the rate of approach to equilibrium is extremely slow, such a system is said to be in a non-equilibrium or metastable state.

4.3.   Solid solution

(i). When a particular crystal structure of the solvent is maintained during alloying, the alloy is called a solid solution.

(ii). Solute is the minor element that is added to the solvent, and solvent is the major element of solution.

(iii). The amount of solute that may be dissolved by the solvent is generally a function of temperature (with pressure constant) and usually increase with temperature.

There are two types of solid solutions:

4.3.1 substitutional solid solution

If the size of the solute atom is similar to that of the solvent atom, the solute atoms can replace solvent atoms to form a substitutional solid solution.

Example: Brass, in which zinc (solute atom) is introduced into the lattice of copper (Solvent).

Two conditions are generally required to from complete substitutional solid solution.

(i) Two elements must have similar crystal structure.

(ii) The difference in their atomic radii should be less than 15%.


If the size of the solute atom is much smaller than that of the solvent atom the solute atom can occupy an interstitial position forming interstitial solid solution.

Since the space of the lattice structure are restricted in size, only atoms with atomic radii less than 1 angstrom are generally form interstitial solid solution. These are hydrogen (0.46), boron (0.97), Carton (0.77). Nitrogen (0.71) and Oxygen (0.60).

More solute atoms may be dissolved interstitially until the solution become saturated at that temperature.

Interstitial solid solutions normally have limited solubility and generally are of a little importance.

Carbon dissolves in iron interstitially. The maximum solubility of Carbon in gamma-iron (F.C.C.) is 2% at 1150°F while maximum solubility of carbon in alpha-iron (B.C.C.) is only 0.025% at 727°C.

Two necessary conditions for forming interstitial solid solution are:

(i) The solvent atom must have more than one valence.

(ii) The atomic radius of solute atom must be less than 59% of the atomic radii of solvent atom.

Example: Steel, where carbon atoms are present in interstitial positions between iron atoms with maximum percentage of 2. Atomic radius of carbon is 0.071 nm which is less than 59% of 0.125 nm radius of iron atom.


Phase diagram is a plot on temperature-composition space showing the stability of various phases.

  • A phase diagram is also called an equilibrium or constitutional diagram. It shows the relationship between temperature, the compositions and the quantities of phases present in an alloy system under equilibrium conditions.
  • When temperature is altered many microstructures develop due to phase transformation. It may involve transition from one phase to another phase. Thus, these diagrams are helpful in predicting phase transformation and the resulting microstructures.

5.1.   Type of phase diagram

5.1.1. Unary phase diagram (single component)

It is used mainly for carbon and pure metal. There is very limited practical utilities of such diagram plotted between temperature and Pressure axis.

Example: Water, graphite, metallic carbon, diamond.

5.1.2 Binary phase diagram (two components)

Type I: the materials which are completely soluble in liquid as well as solid state (binary isomorphous systems)

(i). Since, the most metals are completely soluble in solid slate, the only type of solid phase formed will be a substitutional solid state.

(ii). The two metals will generally have the same type of crystal structure and differ in atomic radii by less than 8%. The corresponding such diagram shown below:

Cu -Ni is one of the examples of these types of phase diagram. Cu-Ni mixes with each other completely in liquid as well solid state without any limitation.

Melting point of copper (Cu) = 1083°C

Melting point nickel (Ni) = 1452°C.

The cooling curve for the pure copper is given below.

Cooling curve with 100 % copper

The cooling curve for the pure nickel is given below.

Cooling curve with 100 % nickel

The cooling curve for the mixture of copper and nickel is shown below. It can be noted that now there is no fixed melting point like it was for pure copper or nickel, rather the solidification takes over a range of temperature.


The temperature composition graph is drawn using cooling curves.

 Phase diagram

This phase diagram consists of two points, two lines and three areas. The two points of the diagram indicates the melting point of the two pure metal.

(i). The upper line, obtained by connecting the points showing the beginning of solidification is called liquidous line, and the lower line, determined by connecting the points showing the end of solidification is called the solidus line.

(ii). Area above the liquidus line is single phase region and any alloy in that region will consist of homogeneous liquid solution. Similarly, lower region is homogeneous in nature.

(iii). In between the solidus and liquidus line there exist a two-phase region. It is the mixture of both solid and liquid, it is mushy in type.

(iv). Upon cooling a sample of Cu-Ni with Cu% Ni from p to s, following transformation are observed.

Cu—Ag eutectic Phase

(i). Eutectic means in Latin word Eu means nice & tactic means melting. Here number of phase equal to 3.

(ii). As per Gibb’s law:

F + P = C + 1

At eutectic point

F = 0, So by Gibb’s law

O + P = 2 + 1; P = 3.

So, three phase α, β, L will be there at eutectic point.

Phase diagram of Cu-Ag

α phase: It is rich in copper and Ag is present as solute and has FCC structure.

β phase: It is rich in Ag and Cu is present as solute and again has FCC structure.

(α + β) phase constitutes of pure copper and pure silver.

Below line CEG (779°C), there is only partial solubility of Ag in Cu (a phase) and Cu in Ag (phase). Maximum solubility of Ag in Cu occurs at 779°C and is 8%. Likewise, maximum solubility of Cu is 8.8% in Ag again at 779°C.

Solvus line demarcates between a and (α + β) phases and β and (α + β) phases.

Various type of phase diagram reaction

Iron-Carbon phase diagram

(i). The Fe-Fe3C is defined by five individual phases and four invariant reactions. Five phases are: α-ferrite (BCC) Fe-C solid solution, γ-austenite (FCC) Fe-C solid solution, δ-ferrite(BCC) Fe-C solid solution, Fe3C (iron carbide) or cementite - an inter-metallic compound and liquid Fe-C solution. Four invariant reactions are eutectic, Eutectoid, monotectic and peritectic.

(ii). As shown in fig.18 by left axes, pure iron upon heating exhibits two allotropic changes. One involves α -ferrite of BCC crystal structure transforming to FCC austenite, γ-iron, at 910C. At 1400°C, austenite changes to BCC phase known as δ-ferrite, which finally melts at 1536°C.

(iii). Carbon present in solid iron as interstitial impurity, and forms solid solution with ferrites/austenite as depicted by three single fields represented by α, γ and δ. Carbon dissolves least in α -ferrite in which maximum amount of carbon soluble is 0.02% at 723°C.

(iv). This limited solubility gives the shape and size of interstitial position in BCC (α-ferrite However, carbon present greatly influences the mechanical properties of α-ferrite. α-ferrite can be used as magnetic material below 768°C. Solubility of carbon in γ-iron reaches its maximum, 2.11%, at a temperature of 1147°C.

(v). Higher solubility of carbon in austenite a property FCC structure and corresponding interstitial sites. Phase transformations involving austenite plays very significant role in heat treatment of different steels. Austenite itself is non-magnetic. Carbon solubility in δ-ferrite is maximum (00.1%) at 1495°C.

(vi). As this ferrite exists only at elevated temperature, it is of no commercial.

(vii). Out of these four solid phases, cementite is hardest and brittle that is used in different forms to increase the strength of steels. α-ferrite, on the other hand is softest and act as matrix of a composite material.

(viii). Based on %C dissolved in it, a Fe-C solution is classified as: commercial pure irons with less than 0.008%C: steels having %C between 0.008-2.11., while coat irons have Carbon in the range of 2 11%-6.67%.

 Iron-carbon phase diagram

(ix). Thus, commercial pure iron is composed of exclusively α-ferrite at room temperature.

(x). The presence of Si promotes the formation of graphite instead of cementite.

(xi). Fe-C system constitutes four invariant reactions:

(a). Peritectic reaction at 1495°C and 0.16%C.

δ-ferrite + L ↔ γ-iron (austenite)

(b). Monotectic reaction 1495°C and 0.51%C.

L ↔ L+ γ-iron (austenite)

(c). Eutectic reaction at 1147°C and 4.3%C.

L ↔ γ-iron + Fe3C (cementite) [

The mixture of γ-iron + Fe3C (cementite) is called the ledeburite.

(d). Eutectoid reaction at 723°C and 0.8%C.

γ-iron L ↔ α-ferrite + Fe3C (cementite) [pearlite]

(xii). Product phase of eutectic reaction is called ledeburite, while product from eutectoid reaction is called pearlite. During cooling to room temperature, ledeburite transforms into pearlite and cementite.

(xiii). Pearlite is in reality not a single phase, but a micro-constituent having alternate thin layers of α-fertile (~88%) and Fe3C cementite (~12%). Steels with less than 0.8%C (mild steels up to 0.3%C, medium carbon steels with C between 0.3%-0.8% i.e. hypo-eutectoid Fe-C alloys) i.e. consists pro-eutectoid α-ferrite in addition to pearlite, while steels with carbon higher than 0.8% (high-carbon steels i.e. hyper-eutectoid Fe-C alloys) consists of pearlite and pro-eutectoid cementite.

(xiv). Phase transformations involving austenite i.e. processes those involve eutectoid reaction are of great importance in heat treatment of steels.

(xv). Additions of alloying elements to Fe-C system bring changes (alternations to positions of phase boundaries and shapes of fields) depends on that particular element and its concentration.

(xvi). Fe-C alloys with more than 2.11%C are called cast irons. Phase transformations in cast irons involve formation of pro-eutectic phase on crossing the liquidus. During the further cooling. liquid of eutectic composition decomposes into mixture of austenite and cementite, known as ledeburite. On further cooling through eutectoid temperature austenite Converted to pearlite.

(xvii). The different structures for the various phases of steel are indicated in the figure. As can be noticed, the structure of ferrite is thick and rounded whereas that of cementite tends to be thin and needle-like. Ferrite is soft and cementite is very hard.

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Akhil GuptaAkhil GuptaMember since Oct 2019
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Piyush Singh

Piyush SinghMay 11, 2021

Is these materials sufficient for ese pre?

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