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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
Short Answer: No, it is not expected for Frenkel defects for anions to exist in relatively large concentrations in ionic ceramics. This is because the larger size of anions makes it energetically unfavorable for them to move into interstitial sites, which would lead to significant lattice stress and distortion. Even at elevated temperatures, the concentration of Frenkel defects involving anions will remain relatively low due to these unfavorable energetic conditions.

Step by step solution

01

Introduction to Frenkel Defects

Frenkel defects are a type of point defect found in ionic crystals. They occur when an ion, usually a cation, is displaced from its crystal lattice site and into an interstitial site nearby. This creates a pair of defects: a vacancy and a cation interstitial. These defects can affect the physical properties and behavior of ceramic materials.
02

Comparison of Cations and Anions

In ionic ceramics, there are two types of ions: cations and anions. Cations are positively charged ions, usually smaller in size, while anions are negatively charged ions and generally larger in size. The size difference between cations and anions is important when considering the possibility of Frenkel defects.
03

Formation of Frenkel Defects in Anions

As discussed earlier, Frenkel defects typically involve a relatively smaller ion moving into an interstitial site. For anions to form Frenkel defects, they would need to occupy the interstitial sites in the crystal lattice. However, due to their larger size, it is energetically unfavorable for anions to leave their original lattice site and move into the interstitial sites, as doing so would significantly increase the lattice stress and distortion.
04

Influence of Concentration on Frenkel Defects of Anions

The presence of Frenkel defects is typically associated with an increase in the overall entropy of the system, which can be favorable at higher temperatures. It means that the concentration of Frenkel defects can potentially increase with temperature. However, due to the unfavorable energetic conditions for anions to form Frenkel defects, their concentration will generally remain relatively low, even at elevated temperatures.
05

Conclusion

Based on the above exploration, we would not expect Frenkel defects for anions to exist in ionic ceramics in relatively large concentrations. This is because the formation of such defects for larger anions is energetically unfavorable due to the significant lattice stress and distortion that would result from the movement of anions into the interstitial sites.

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Most popular questions from this chapter

(a) Suppose that \(\mathrm{CaO}\) is added as an impurity to \(\mathrm{Li}_{2} \mathrm{O}\). If the \(\mathrm{Ca}^{2+}\) substitutes for \(\mathrm{Li}^{+}\), what kind of vacancies would you expect to form? How many of these vacancies are created for every \(\mathrm{Ca}^{2+}\) added? (b) Suppose that \(\mathrm{CaO}\) is added as an impurity to \(\mathrm{CaCl}_{2}\). If the \(\mathrm{O}^{2-}\) substitutes for \(\mathrm{Cl}^{-}\) what kind of vacancies would you expect to form? How many of these vacancies are created for every \(\mathrm{O}^{2-}\) added?

Using the data given below that relate to the formation of Schottky defects in some oxide ceramic (having the chemical formula \(\mathrm{MO}\) ), determine the following: (a) The energy for defect formation (in eV), (b) the equilibrium number of Schottky defects per cubic meter at \(1000^{\circ} \mathrm{C},\) and (c) the identity of the oxide (i.e., what is the metal M?) $$\begin{array}{rcc} \hline \boldsymbol{T}\left(^{\circ} \boldsymbol{C}\right) & \boldsymbol{\rho}\left(\boldsymbol{g} / \mathrm{cm}^{3}\right) & \boldsymbol{N}_{\boldsymbol{s}}\left(\boldsymbol{m}^{-3}\right) \\ \hline 750 & 3.50 & 5.7 \times 10^{9} \\ 1000 & 3.45 & ? \\ 1500 & 3.40 & 5.8 \times 10^{17} \\ \hline \end{array}$$

The unit cell for \(\mathrm{Fe}_{3} \mathrm{O}_{4}\left(\mathrm{FeO}-\mathrm{Fe}_{2} \mathrm{O}_{3}\right)\) has cubic symmetry with a unit cell edge length of \(0.839 \mathrm{nm} .\) If the density of this material is \(5.24 \mathrm{g} / \mathrm{cm}^{3},\) compute its atomic packing factor. For this computation, you will need to use ionic radii listed in Table 12.3.

When kaolinite clay \(\left[\mathrm{Al}_{2}\left(\mathrm{Si}_{2} \mathrm{O}_{5}\right)(\mathrm{OH})_{4}\right]\) is heated to a sufficiently high temperature, chemical water is driven off. (a) Under these circumstances, what is the composition of the remaining product (in weight percent \(\mathrm{Al}_{2} \mathrm{O}_{3}\) )? (b) What are the liquidus and solidus temperatures of this material?

Compute the atomic packing factor for the rock salt crystal structure in which \(r_{\mathrm{C}} / r_{\mathrm{A}}=0.414\).
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