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Chapter 12: Problem 28

Would you expect Frenkel defects for anions to exist in ionic ceramics in relatively large concentrations? Why or why not?

Short Answer

Expert verified
Explain your answer. Answer: No, Frenkel defects for anions are unlikely to exist in ionic ceramics in relatively large concentrations. This is because anions are generally larger in size and less mobile than cations, making them less likely to form Frenkel defects in the lattice structures of ionic ceramics.

Step by step solution

01

Understand Frenkel defects in ionic ceramics

Frenkel defects are a type of point defect in ionic ceramics, where an ion from its correct lattice site is missing and becomes an interstitial ion, residing in the interstitial space of the lattice. This defect leaves behind a vacancy in the lattice site without any overall loss of ions. It usually occurs in ionic compounds with a significant difference in the size of the cations and anions.
02

Analyze the presence of Frenkel defects in anions

To determine if Frenkel defects for anions are likely to exist in ionic ceramics in relatively large concentrations, we need to understand the factors that influence the formation of these defects. In general, Frenkel defects are more common for cations in ionic ceramics due to their relatively smaller size. The smaller size of cations makes them more mobile in the lattice structure, and thus, more likely to form Frenkel defects. On the other hand, anions are usually larger in size and less mobile, making them less likely to form Frenkel defects.
03

Conclusion and explanation

Based on the factors influencing the formation of Frenkel defects, we would not expect Frenkel defects for anions to exist in ionic ceramics in relatively large concentrations. This is primarily due to the larger size and less mobile nature of anions in the lattice structures of ionic ceramics, making it less likely for these defects to form.

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Most popular questions from this chapter

The unit cell for \(\mathrm{Cr}_{2} \mathrm{O}_{3}\) has hexagonal symmetry with lattice parameters \(a=0.4961 \mathrm{~nm}\) and \(c=1.360 \mathrm{~nm}\). If the density of this material is \(5.22 \mathrm{~g} / \mathrm{cm}^{3}\), calculate its atomic packing factor. For this computation assume ionic radii of \(0.062 \mathrm{~nm}\) and \(0.140 \mathrm{~nm}\), respectively, for \(\mathrm{Cr}^{3+}\) and \(\mathrm{O}^{2-}\).

Using the Molecule Definition Utility found in both "Metallic Crystal Structures and Crystallography" and "Ceramic Crystal Structures" modules of \(V M S E\), located on the book's web site [www.wiley.com/ college/callister (Student Companion Site)], generate (and print out) a three-dimensional unit cell for titanium dioxide, \(\mathrm{TiO}_{2}\), given the following: (1) The unit cell is tetragonal with \(a=0.459 \mathrm{~nm}\) and \(c=0.296 \mathrm{~nm},(2)\) oxygen atoms are located at the following point coordinates: \(\begin{array}{llllll}0.356 & 0.356 & 0 & 0.856 & 0.144 & \frac{1}{2} \\\ 0.664 & 0.664 & 0 & 0.144 & 0.856 & \frac{1}{2}\end{array}\) and (3) Ti atoms are located at the following point coordinates: \(\begin{array}{llllll}0 & 0 & 0 & & 1 & 0 & 1 \\ 1 & 0 & 0 & & 0 & 1 & 1 \\\ 0 & 1 & 0 & & 1 & 1 & 1 \\ 0 & 0 & 1 & & \frac{1}{2} & \frac{1}{2} & \frac{1}{2} \\ 1 & 1 & 0 & & & & \end{array}\)

Compute the atomic packing factor for cesium chloride using the ionic radii in Table \(12.3\) and assuming that the ions touch along the cube diagonals.

Determine the angle between covalent bonds in an \(\mathrm{SiO}_{4}^{4-}\) tetrahedron.

Compute the atomic packing factor for the diamond cubic crystal structure (Figure 12.15). Assume that bonding atoms touch one another, that the angle between adjacent bonds is \(109.5^{\circ}\), and that each atom internal to the unit cell is positioned \(a / 4\) of the distance away from the two nearest cell faces ( \(a\) is the unit cell edge length).
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