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Answer:
Element Atomic Radius (nm) Crystal Structure Electronegativity Valence
Cu 0.1278 FCC 1.9 +2
C 0.071
H 0.046
O 0.060
Ag 0.1445 FCC 1.9 +1
Al 0.1431 FCC 1.5 +3
Co 0.1253 HCP 1.8 +2
Cr 0.1249 BCC 1.6 +3
Fe 0.1241 BCC 1.8 +2
Ni 0.1246 FCC 1.8 +2
Pd 0.1376 FCC 2.2 +2
Pt 0.1387 FCC 2.2 +2
Zn 0.1332 HCP 1.6 +2
The answers to the question are
(a) Copper will form substitutional solid solution with complete solubility with
Ni due to their very similar size, equal valency and similar electronegativities as well as Pd, and Pt but less likely with aluminium due to size and valency difference
(b) Copper will form substitutional solid solution of incomplete solubility with Ag, Al, Co, Cr, Fe, Zn
(c) Copper will form interstitial solid solution with
C, H, O due to the large difference between the size of copper atomic radius and the smaller atomic radii of C, H and O
Explanation:
Substitutional solid solution rules
the following are the Hume-Rothery rules for substitutional solid solutions:
1. Less than 15%difference between the atomic radius of the solute and solvent:
2. Similarity in the crystal structures of solute and solvent;
3. The valency of the solvent and solute must be similar before they can be said to be completely soluble in each other.
A lower valency metal is more likely to dissolve in one higher valency.
4. The electronegativities of the solute and solvent should be similar a wide variation in electronegativity will lead to the formation of intermetallic compounds rather than a solid solutions.
One must identify which of the elements listed form all three potential solid solution types if combined with Copper. There are four criteria for complementarity.
- The discrepancy in ionic radius between copper and the other metal must be less than 15%, which is equal to [tex](\Delta R\%)[/tex].
- crystallinity that is of the same.
- Electronegativities that are similar to each other.
- Similar or almost identical valencies.
These criteria are tabulated is defined in the attached file for each element.
- [tex]Ni, Pd, and \ Pt[/tex] Â satisfy all of the conditions and thus produce the fully soluble formation of solid solutions. [tex]Co \ and\ Fe[/tex] exhibit allotropic transitions to an FCC crystalline structure at high temperatures, resulting in solid solubility at these temperature changes.
- Incompletely soluble formation of the solid formula[tex]Ag, Al, Co, Cr, Fe,\ and\ Zn[/tex] exist. Every one of these metals has [tex]BCC\ or \ HCP[/tex] crystal structures, and/or the difference in atomic radii between them and Cu is bigger than [tex]\pm 15\%[/tex], and/or they have a valence apart from 2+.
- The formation of a solid solution is produced by the elements [tex]C, H, and \ O[/tex]. These elements have much smaller atomic radii than [tex]Cu[/tex].
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