Hume-Rothery rules

Hume-Rothery rules

Hume-Rothery rules

The Hume-Rothery rules are a set of basic rules describing the conditions under which an element could dissolve in a metal, forming a solid solution. There are two sets of rules, one which refers to substitutional solid solutions, and another which refers to interstitial solid solutions.


=Substitutional Solid Solution RuleFor substitutional solid solutions, the Hume-Rothery rules are::1. The atomic radii of the solute and solvent atoms must differ by no more than 15%:

:: % mbox{ difference} = left ( frac{(r_{solute} - r_{solvent})}{r_{solvent ight ) * 100 le 15%

:2. The crystal structures of solute and solvent must match.

:3. Maximum solubility occurs when the solvent and solute have the same valency. Metals with lower valency will tend to dissolve metals with higher valency.

:4. The solute and solvent should have similar electronegativity. If the electronegativity difference is too great, the metals will tend to form intermetallic compounds instead of solid solutions.


= Interstitial Solid Solution Rules =

For interstitial solid solutions, the Hume-Rothery rules are:

:1. Solute atoms must be smaller than the pores in the solvent lattice.

:2. The solute and solvent should have similar electronegativity. [ cite encyclopedia | title = Hume-Rothery Rules | encyclopedia = Van Nostrand's Scientific Encyclopedia | publisher = John Wiley & Sons, Inc. | date = 2002 ]

References

*cite web | last = Bhadeshia | first = H. K. D. H. | title = Solid Solutions: The Hume-Rothery Rules | url=http://www.msm.cam.ac.uk/phase-trans/2004/titanium/hume.rothery.html | accessdate = 2007-11-24


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