1. Callister problem 4.6- Purpose: to learn the factors that control the solid s
ID: 1080732 • Letter: 1
Question
1. Callister problem 4.6- Purpose: to learn the factors that control the solid solubility and to understand the effects of changing each factor. (Hume solid solubility) Rothery rules for 4.6 Atomic radius, crystal structure, electronegativity, and the most common valence are given in the following table for several elements; for those that are nonmetals, only atomic radii are indicated Element Atomic Radius (nm) 0.1246 0.071 0.046 0.060 0.1445 0.1431 0.1253 0.1249 0.1241 0.1387 0.1332 Crystal Structure Electro-negativity Valence FCC HCP BCC BCC FCC HCP Al Fe Pt Which of these elements would you expect to form the following with nickel: (a) a substitutional solid solution having complete solubility (b) a substitutional solid solution of incomplete solubility (c) an interstitial solid solution Red brass has a warm reddish tint with many applications including musical instruments like the sax. It is 85 wt% Cu-15 wt% Zn. i) What is the atomic % Zn ? The Zn also helps strengthen the brass. ii) Suggest a reason why the Zn addition increases alloy strength Sterling silver is an alloy composed of 92.5 wt% Ag & 7.5 wt% Cu? i) What is the composition in terms of at %. ") Why do you think that Cu was added to pure Ag to make the alloy? 2a. 2b.Explanation / Answer
Hume-Rothery rules are a set of rules that describe the fundamental conditions required for an element to dissolve in a metal to form solid solutions or alloys.
For the combination to form a solid solution, if the metal to be dissolved from now termed as the solute should have the following qualities with respect to the metal in which is it dissolved (the solvent).
- The atomic radii difference between the two metals should be less than or equal to 15% as given by the formula Difference = [(radius of solute - radius of solvent)/(radius of solvent)]x100
- Solute and solvent should have same valency states. A metal of greater valency wil be a good solute in a metal of lower valency.
- Solute and solvent electronegativity difference should be low. If it is large they will form compounds rather than stay as solid solutions.
- The crystal structure of both solute and solvent should be the same.
a) Thus, the metals given which will form solid solutions of complete solubility in Ni are Ag, Al and Pt though the solubility of Ag in Ni will not be so appreciable as their radii difference is 15.9% but otherwise all three have similar crystal structure, not large electronegativity difference and similar or greater valencies (except Ag).
b) From the previous conclusions, it can be observed that the metal Ag might form an incomplete solid solution with Ni while the other metals will not form proper solid solutions as their crystal structures themselves are radically unsuitable to form alloys with Ni.
Hume-Rothery rules also dictate the similarities between solute and solvent required for the former to form a interstitial solid solution in the latter. They are as follows.
- The solute atomic radii should not be more than 59% of that of the solvent.
- They should possess similar electronegativity lest they form compounds.
- They should possess similar valency with increasing difference decreasing solubility.
c) Thus the elements that possess radii less than 59% of that of Ni are C, H and O. Among these, the electronegativity of O is too great compared to that of Ni and so nickel oxides are expected rather than interstitial solutions and the valency of carbon is greater than that of Ni but the variable valency of Ni to +4, same as carbons will overcome this factor. Therefore, with Ni, H and C will form proper interstitial solutions.
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