Material science-Specification of composition

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SUMMARY

The discussion centers on calculating the weight percentage of germanium (Ge) required to form a substitutional solid solution with silicon (Si) to achieve a specific atom density of 2.43x10^21 Ge atoms per cubic centimeter. The initial calculation yielded 72% Ge, but the correct value is 11.7%. The formula used for concentration, C1=(m1/(m1+m2))*100%, was applied incorrectly. The problem originates from "Materials Science and Engineering: An Introduction" by William D. Callister, specifically in Chapter 5, question #4.22.

PREREQUISITES
  • Understanding of substitutional solid solutions in materials science
  • Familiarity with atomic density calculations
  • Knowledge of mass and weight percentage formulas
  • Basic concepts of material properties, specifically for Ge and Si
NEXT STEPS
  • Review atomic density calculations in materials science
  • Study the principles of solid solution formation
  • Examine Chapter 5 of "Materials Science and Engineering: An Introduction" by William D. Callister
  • Practice problems related to weight percentage and concentration calculations
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Students and professionals in materials science, particularly those focusing on alloy composition and solid solution behavior, as well as educators teaching materials engineering concepts.

mugzieee
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Im given this problem:
Ge forms a substitutional solid solution with Si. find the weight% of Ge, that must be added to Si to yield an alloy that contains 2.43x10^21 Ge atoms per cubic centimetr. The densities of pure Ge and Si are 5.32 and 2.33 g/cm^3, respectively.

then I have a formula that says C1=(m1/m1+m2)*100% where C1 is the concentration in weight % of material 1 and m1 is the mass of material 1, and m2 is the mass of material 2. I use this formula, and i get 72% for Ge, but the correct answer is 11.7%. does anyone know what i am doing wrong?
 
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Is this problem from Materials Science and Engineering Intro by William D CallisteR?

If it is then it's question # 4.22. Anyway try doing #4.20 first, or just simply use the equation that's given in # 4.20.
 
it is that book, but it is in chapter 5, not chapter 4.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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