Solid Solution Strengthening

A materials strength can be improve by adding different soluble elements to the parent matrix (i.e., alloying), which impede the movement of dislocations in the crystal.

The fact that the alloys are stronger than the pure metal is because of the addtion of solute atoms. Solute atoms can form either a substitution solid solution or interstitial solid solution in a sovent/parent metal and act as atomic-sized obstacles to the motion of dislocation. Hence, solid solutions offers more strength than pure metals.

In general, the size of solute atom can be larger or smaller than the parent atom. Large solute atom creates a compresive stress field around it, small solute atom create a tensile stress field around it and an interstitial atom create a compressive stress field. This can be easily visualize be thinking about the force felt by the bonds to maintain same bond length.

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Interaction between solute atom and dislocation :

On addition of solute atom, the solute atom sits near the dislotion to redure strain-energy. Solute-dislocation interaction locks dislocation and couse immobilization or pinning of the dislocation. For example large solute will sit near the tension side of edge dilocation and similarly, smaller atom will sit near the compressive side of edge dislocation, which enentually balances the both stress field created by dislocation as well as solute atom. Which results in lowering the strain energy.

Now, when external stress is applied then solute atom restrict the motion of dislocation and hence material strength increases.

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Humes-Rohtery rules for substitutional solid solution :

Humes-Rohtery shows the factors which control the tendency for the fomation of substitutional solid solution are -

1. Relative size factor :
   When the atomic size of two atoms differ by less then 15 percent then the size factor is favourable for substitutional solid solution. and if their atomic radii differ by less than 8% then it shows ultimate solid solution.
2. Crystal structure factor :
   Solid solution is favoured when both the elements have same crystal structure.
3. Relative valancy :
   An element with higher valancy dissolves to a greater extend in a lower valance element than vice versa. For example, zinc (valancy = 2) is much more soluble in copper than the opposite because excess electron is good than electron deficiency. \[ \frac{e}{a} \textrm{ Ratio} = \textrm{ Summation of valence electrons of all atoms over the number of atoms} \]
4. Chemical affinity factor :
   Greater the affinity difference between two elements, more restricted will be the solubility as both the atom will tend to form ionic bond. \[ \text{% ionic} \propto \text{ electronegativity difference} \]

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Solid-solution vs Compound

#	Solid-Solution	Compound
1	SS have no fixed composition. The concentration is a variable	Compound have fixed solute concentration
2	Can't be expressed by formula	Compounds have a chemical formula
3	Solid solution melt or solidify over a range of temperature	Compound melt or solidify at a constant temperature like a pure element
4	Crystal structure of SS is same as the parent element	Crystal structure can be differ from either of the components.
5	Not chemically bonded	In compound atoms are chemically bonded to each other.
6	Example : Ferrite, Austenite, Brass	Fe3C, NaCl