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Notes by Category University Engineering

Mechanics & Stress Analysis*
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Non-Ferrous Alloys & Strengthening

In this notes sheet...

  1. Definitions

  2. Types of Alloying

  3. Complete Solid Solutions

  4. Partial Solid Solutions

  5. Solid Solution Hardening

  6. Precipitation Hardening


Alloys are metals mixed with other materials.These could be metal or non-metal. They are commonly used instead of pure metals, as pure metals generally have low strength and high ductility – generally in engineering, we want the opposite.

There are a number of key definitions:

  • A component is one of the elements mixed in the alloy

  • A phase is a region within a material with uniform chemical and physical properties

  • The solvent is the main component of the allow: the element/compound in highest concentration

  • The solutes are the elements/compounds that are mixed in with the solvent: they are in lower concentration

  • A solid solution is a homogeneous single-phase mixture of solute in solvent

  • The composition of a component is the percentage mass of that component in an alloy or phase

  • The constitution is the overall sum of phases

Types of Alloying

There are a number of different types of alloys, with different methods used to make them.


This is when solute atoms replace some solvent atoms.

For this to work, the Hume-Rothery rules must apply. According to these, the solute and solvent atoms should:

  • be similar in size (diameters within ~15%)

  • have the same general crystal structure

  • have the same number of valence electrons

  • have similar electronegativity

If these rules do not apply, there will be too much lattice distortion and an alternative crystal structure will form.

Interstitial Addition

This is when smaller solute atoms fit between larger solvent atoms.

In order for this to occur, the diameter of the solute atoms must be smaller than about 0.6 the diameter of the solvent atoms.

Generally, the elements that are small enough to fit in the interstitial sites of solvent structures are:

  • Boron, B

  • Carbon, C

  • Chlorine, Cl

  • Hydrogen, H

  • Nitrogen, N

  • Oxygen, O

  • Phosphorus, P

  • Sulphur, S

When all the interstitial spaces are filled, the alloy is said to have reached its limit of solubility.

Solid Solutions

This is when solvent and solute atoms mix to form a single, homogenous structure.

Complete solid solubility occurs when two metals with similar atomic diameter are melted together. As they cool slowly, the solute atoms diffuse throughout the solvent creating a uniform single phase.

Some compounds mixtures exhibit partial (limited) solid solubility. This means that they can only form a single phase up to a certain composition. Beyond this, no solute can dissolve in the solvent, and so settles in a separate phase.

  • Sugar in water is a common example: initially, all the sugar dissolves. Keep adding more, however, and it will settle on the bottom – the limit of solubility has been reached.

Complete Solid Solutions

Equilibrium phase diagrams represent the different phases present at different compositions of alloys. They are different for complete solid solutions and ferrous and non-ferrous partial solid solutions.

The cooling process that forms solid solutions is, obviously, a function of temperature. We can plot this with respect to time for different compositions of the alloy on cooling curves:

For pure substances, there is no change in temperature as the change in state occurs. In the solidification process (freezing), this is due to the latent heat of fusion: during phase-change, there is no change in kinetic energy in the particles, only the potential energy changes.

However, for a solid solution the solidification process occurs over a range of temperatures. Between these two temperatures, there is a two-phase region where some of the compound with the higher melting point starts to precipitate in the still-liquid compound with the lower melting point.

The extent of this two-phase region depends on the composition of the alloy, and is shown on an equilibrium phase diagram:

Linear Interpolation (Lever Rule)

Linear interpolation can be used to find the ratio of liquid to solid in the two-phase region, at a given composition and temperature: