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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.