Critical state soil mechanics: Difference between revisions

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The '''Hume-Rothery rules''', named after [[William Hume-Rothery]], 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 defect|interstitial]] solid solutions.


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==Substitutional Solid Solution Rules==
For substitutional solid solutions, the Hume-Rothery rules are:


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:1. The [[Atomic radius|atomic radii]] of the solute and [[solvent]] atoms must differ by no more than 15%:


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::<math> % \mbox{ difference} = \left ( \frac{r_{solute} - r_{solvent}}{r_{solvent}} \right ) \times 100 \le 15%.</math>
 
:2. The [[crystal structure]]s of solute and solvent must match.
 
:3. Complete [[solubility]] occurs when the solvent and solute have the same [[Valence (chemistry)|valency]].<ref>'''Foundations of Materials Science and Engineering''', 4th ed., W. Smith and J. Hashemi, pp.139-140 (2006).</ref>  A metal will dissolve a metal of higher valency to a greater extent than one of lower valency.
 
:4. The solute and solvent should have similar [[electronegativity]].  If the electronegativity difference is too great, the metals will tend to form [[Intermetallics|intermetallic compounds]] instead of solid solutions.
 
==Interstitial Solid Solution Rules==
 
For [[Interstitial defect|interstitial]] solid solutions, the Hume-Rothery rules are:
 
:1. Solute atoms must be smaller than the interstitial sites in the solvent lattice.
 
:2. The solute and solvent should have similar [[electronegativity]].<ref>{{cite encyclopedia | title = Hume-Rothery Rules  | encyclopedia = Van Nostrand's Scientific Encyclopedia | publisher = John Wiley & Sons, Inc | year = 2002 }}</ref>
 
==Notes==
{{reflist}}
 
==References==
*{{cite web | last = Bhadeshia | first = H. K. D. H. | authorlink=Harry Bhadeshia |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}}
 
==Further reading==
 
*{{Cite book |last=Mizutani |first=Uichiro  |title=Hume-Rothery Rules for Structurally Complex Alloy Phases  |publisher=Taylor & Francis |date=2010 |isbn=978-1-4200-9058-1}}
 
{{DEFAULTSORT:Hume-Rothery Rules}}
[[Category:Materials science]]
[[Category:Rules]]

Latest revision as of 20:35, 8 September 2013

The Hume-Rothery rules, named after William Hume-Rothery, 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 Rules

For 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%:
2. The crystal structures of solute and solvent must match.
3. Complete solubility occurs when the solvent and solute have the same valency.[1] A metal will dissolve a metal of higher valency to a greater extent than one of lower 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 interstitial sites in the solvent lattice.
2. The solute and solvent should have similar electronegativity.[2]

Notes

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References

Further reading

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  1. ↑ Foundations of Materials Science and Engineering, 4th ed., W. Smith and J. Hashemi, pp.139-140 (2006).
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