1 Sketch schematically a σ and π bond between two p orbitals.
2 What are the relationships between a, b, and c and α , β, and ϓ for cubic, orthorhombic, and monoclinic crystal systems?
3 Why are x-rays (as opposed to other EM wavelength ranges) used to measure interplanar spacing of crystals?
4 How can diffraction with neutrons (as opposed to x-rays) provide additional information regarding crystal structures?
5 Consider a grain boundary that is tilted with respect to its neighbor along one axis only. What is the relationship between the spacing of dislocations that form along this interface and the tilt angle, and why does this regular spacing only happen for relatively small tilting angles?
6 Starting with the defect reaction, derive an expression for the concentration of Schottky defects in a ZrO2 crystal as a function of temperature.
7 Define dislocation slip and climb. Explain the role that both vacancies and interstitials can have in the climb process.
8 At temperatures above 0 K all materials have point defects, using an argument based on Gibbs free energy explain why this is the case.
9 Why do we say, in general terms, that relative to a bulk crystal, grain boundaries exhibit higher surface energy?
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