Rule of Solid Solubility

• Positive deviation of the enthalpy of mixing and consequently limited solid solubility may be predicted from known atomic properties.

Hume-Rothery- empirical rules to predict solid solubility

• For solid solubility exist b/t two elements, the following settlements are always true:

• Atomic Size: the atomic radii of the two elements must be with in 15 % of each other.

• Crystal Structure: the type of crystal structure must be same.

• Chemical Valence: The valence of the two elements must differ by no more than one.

• Electro negativity: It must be nearly equal if not, a compound may be formed as a result of the difference in affinity for electrons.

Atomic Size

• Extensive substitutional solid solution occurs only

• If the relative difference between the atomic diameters (radii) of the two species is less than 15%.

• If the difference > 15%, the solubility is limited.• Comparing the atomic radii of solids that form

solid solutions,

Crystal Structure Rule

• For appreciable solid solubility, the crystal structures of the elements must be identical.

• Although the crystal structure remains un changed

• However, the dimension of the unit crystal cell changes progressively with addition of solutes.

Valency Rule

• A metal will dissolve a metal of higher valency to a greater extent than one of lower valency.

• Or a solute of higher valency is more likely to dissolve in a solvent of lower valency.

• The solute and solvent atoms should typically have the same valence in order to achieve maximum solubility

• E.g copper dissolve up to 38.3 atomic percent Zinc

• But zinc dissolve only 2.8 atomic percent copper

Electronegativity

• Chemical property that describes the ability of an atom to attract electrons (or electron density) towards itself.

• An atom's electronegativity is affected by both its atomic weight and the distance that its valence electrons reside from the charged nucleus.

• The higher the associated electronegativity number, the more an element or compound attracts electrons towards it.

Electronegativity,

• It is not strictly an atomic property, • But rather a property of an atom in a molecule• The equivalent property of a free atom is its

electron affinity. • The opposite of electronegativity is

electropositivity: • A measure of an element's ability to donate

electrons.

Electro negativity

• Electro negativity: It must be nearly equal • If not, a compound may be formed as a result

of the difference in affinity for electrons• If electron affinity is the same for each

component, • No compound will be formed and the one

phase region will be retained

The Electro negativity

Electronegativity difference close to 0 gives maximum solubility.

• The more electropositive one element and the more electronegative the other,

• The greater is the likelihood that they will form an intermetallic compound instead of a substitutional solid solution.

• Ordered intermetallic compounds are formed if the components have very different electronegativity.

•

• The compounds limits the amount of solid solution that can occur between the elements.

• The actual extent of solid solubility depends on the stability of the intermediate phase

• The more stable the compound the less is the extent of the primary phase field.

• E.g Mg2Pb in alloy of Mg with Pb

• The principle of the fourth rule is that • The single solution becomes unstable with

regards to the compound, whose free energy near its ideal composition will be lowest.

• The phase regions (compound plus solid solution) then appear and the phase diagram no longer contains the broad region of complete solubility.

• The first three rules are based on the increase in enthalpy due to distortion of the crystal lattice,

• Disruption of crystal structure, in crude sense unsaturated bonds.

• There distortion leads to appreciable positive deviation and therefore limited mutual solid solubility.