Which of these elements would you expect to form the following with copper? (a)

Question

Which of these elements would you expect to form the following with copper?

(a) A substitutional solid solution having com- plete solubility

(b) A substitutional solid solution of incomplete solubility

(c) An interstitial solid solution

*please be thorough in your reasoning and if you write this out by hand please make sure its readable. thank you*

Impurities in Solids 5.11 Atomic radius, crystal structure, electronegativ- ity, and the most common valence are given in the following table for several elements; for those that are nonmetals, only atomic radii are indicated. Atomic RadiusCrystalElectro- Element (nm)Structure negativity Valence Cu FCC 1.9 0.1278 0.071 0.046 0.060 0.1445 0.1431 0.1253 0.1249 0.1241 0.1246 0.1376 0.1387 0.1332 FCC FCC HCP BCC BCC FCC FCC FCC HCP 1.9 1.5 1.8 1.6 1.8 1.8 2.2 2.2 1.6 Ag Al Co Cr +2 +2 Pd Pt +2 +2

Explanation / Answer

The requirements for complete substitutional solubility are, the difference in atomic radii between Cu and the other element (deltaR%) must be less than +/-15%, the crystal structures must be the same, the electronegativities must be similar, and the valence should be the same, or nearly the same. Keeping these point in mind we are going to calculate deltaR% for each,

deltaR% = [(atomic radius of element - atomic radius of Cu)/atomic radius of Cu] x 100

and,

delta(Electronegativity) or delta(E) = electronegativity of element - electronegativity of Cu

So we have for all the elements,

element     deltaR(%)    crystal type     delta(E)     Valence

    Cu               -                  FCC               -                 +2

    C               -44                                             

    H               -64                                                 

    O               -53

    Ag             +13              FCC               0                 +1

    Al              +12               FCC              -0.4               +3

    Al               -2               HCP              -0.1               +2

    Al               -2               BCC              -0.3               +3

    Al               -3               BCC              -0.1               +2

    Al               -3               FCC              -0.1               +2

    Al               +8               FCC              -0.3               +2

    Al               +9               FCC              -0.3               +2

    Al               +4               HCP              -0.3               +2

a) So looking at the above table we can say that Ni, Pt and Pd satisfies the conditions necessary to form substitutional solid solution having complete solubility.

b) Ag, Al, Co, Cr, Fe and Zn would form substitutional solid solution of incomplete solubility. They all have atomic radii which are very different than Cu (greater then 15%), or different crystal structure (BCC or HCP) or differ in their valence.

c) C, H, and O would form interstitial solid solutions. These all have atomic radii much smaller then radii of Cu.

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