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Fundamentally, the Hume-Rothery rules are restricted to binary systems that form either substitutional or interstitial solid solutions. However, this approach limits assessing advanced alloys which are commonly multicomponent systems. Free energy diagrams (or
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235:) are based on geometrical restraints. Likewise are the advancements being done to the Hume-Rothery rules. Where they are being considered as critical contact criterion describable with
403:"Introduction the properties and behavior of metals (And alloys) depend on their: Structure Processing history and Composition Engr PPT video online download"
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Valency factor: two elements should have the same valence. The greater the difference in valence between solute and solvent atoms, the lower the solubility.
153:{\displaystyle \%{\text{ difference}}=\left({\frac {r_{\text{solute}}-r_{\text{solvent}}}{r_{\text{solvent}}}}\right)\times 100\%\leq 15\%.}
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Goodman, D. A.; Bennett, L. H.; Watson, R. E. (January 1983). "Valency effects and relative solubilities in transition metal alloys".
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containing TM elements there is a difficulty in interpretation of the Hume-Rothery electron concentration rule as the e/a values for
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have been quite controversial for a long time and no satisfied solutions have yet emerged.
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Solute atoms should have a smaller radius than 59% of the radius of solvent atoms.
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Wang, Zhijun; Huang, Yunhao; Liu, C. T.; Li, Junjie; Wang, Jincheng (4 Apr 2019),
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For substitutional solid solutions, the Hume-Rothery rules are as follows:
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486:"The Physics of the Hume-Rothery Electron Concentration Rule"
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Callister, William D.; Rethwisch, David G. (January 2018).
433:"Atomic packing and size effect on the Hume-Rothery rule"
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324:, 4th ed., W. Smith and J. Hashemi, pp.139-140 (2006).
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389:"The Structure of Metals - PPT video online download"
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484:Mizutani, Uichiro; Sato, Hirokazu (January 2017).
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175:occurs when the solvent and solute have the same
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222:Solid solution rules for multicomponent systems
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16:Rules for elements dissolving in a solid metal
203:solid solutions, the Hume-Rothery Rules are:
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182:The solute and solvent should have similar
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363:"Solid Solutions: The Hume-Rothery Rules"
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62:atoms must differ by no more than 15%:
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418:Van Nostrand's Scientific Encyclopedia
168:of solute and solvent must be similar.
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367:PT (Phase Transformations) Group Home
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301:(10th ed.). Wiley. p. 992.
420:. John Wiley & Sons, Inc. 2002.
46:Substitutional solid solution rules
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195:Interstitial solid solution rules
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188:intermetallic compounds
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416:"Hume-Rothery Rules".
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30:could dissolve in a
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58:of the solute and
20:Hume-Rothery rules
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536:. Retrieved
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342:(1): 91–96.
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270:Gibbs energy
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201:interstitial
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40:interstitial
34:, forming a
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443:: 139–144,
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538:2007-11-24
281:References
173:solubility
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373:16 August
171:Complete
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139:≤
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490:Crystals
254:See also
260:CALPHAD
177:valency
119:solvent
108:solvent
60:solvent
28:element
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244:alloys
95:solute
585:Rules
453:S2CID
32:metal
552:ISBN
508:ISSN
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303:ISBN
242:For
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164:The
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