Concept explainers
(a) Calculate the equilibrium concentration of vacancies per cubic meter in pure copper at 850°C. Assume that the energy of formation of a vacancy in pure copper is 1.0 eV. (b) What is the vacancy fraction at 800°C?
(a)
The equilibrium concentration of vacancies per cubic meter in pure copper.
Answer to Problem 11AAP
The equilibrium concentration of vacancies per cubic meter in pure copper is
Explanation of Solution
Express the equilibrium concentration of vacancies per cubic meter in pure copper.
Here, number of vacancies per cubic meter of metal is
Express total number of atom sites per cubic meter of metal.
Here, Avogadro’s number is
Conclusion:
Write the value of Avogadro’s number, atomic mass and density of copper.
Write the value of Boltzmann’s constant.
Substitute
Substitute
Hence, the equilibrium concentration of vacancies per cubic meter in pure copper is
(b)
The vacancy fraction at 800°C.
Answer to Problem 11AAP
The vacancy fraction at 800°C is
Explanation of Solution
Express the vacancy fraction at 800°C.
Conclusion:
Substitute
Hence, the vacancy fraction at 800°C is
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Chapter 5 Solutions
Foundations of Materials Science and Engineering
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