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. Chemical property atomelectrons An atom's electronegativity is affected by both its atomic weight and the distance that its valence electrons reside from the charged nucleus.atomic weight 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 moleculemolecule The equivalent property of a free atom is its electron affinity. electron affinity The opposite of electronegativity is electropositivity: 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.