Example Questions: Lecture 2
The graph on the left shows the conductivity for "pristine" $\mathrm{NaCl}$.
- From the graph, estimate the:
- Energy of cation ion migration, and
- Energy of schottky defect formation.
- What do you expect the following impurities to have on the conductivity of this material?
- $\mathrm{KCl} ; \mathrm{NaBr} ; \mathrm{CaCl}_{2} ; \mathrm{AgCl} \mathrm{Na}_{2} \mathrm{O}$

Question

Example Questions: Lecture 2
The graph on the left shows the conductivity for "pristine" $\mathrm{NaCl}$.
- From the graph, estimate the:
- Energy of cation ion migration, and
- Energy of schottky defect formation.
- What do you expect the following impurities to have on the conductivity of this material?
- $\mathrm{KCl} ; \mathrm{NaBr} ; \mathrm{CaCl}_{2} ; \mathrm{AgCl} \mathrm{Na}_{2} \mathrm{O}$

Accepted Answer

∻Solution∻ ‖ 1 ⋮ **Estimate the energy of cation ion migration**: To estimate the energy of cation ion migration from the graph, locate the point where the conductivity begins to increase significantly. This point corresponds to the temperature at which cations have enough energy to migrate. Use the Arrhenius equation to relate the temperature to the activation energy. ‖ ‖ 2 ⋮ **Estimate the energy of Schottky defect formation**: Schottky defect formation energy can be estimated by finding the temperature at which the conductivity due to intrinsic defects becomes significant. This temperature corresponds to the energy required to form a Schottky defect. Use the Arrhenius equation to calculate this energy. ‖ ‖ 3 ⋮ **Effect of impurities on conductivity**: The impurities in an ionic crystal can either increase or decrease the conductivity depending on their nature and the type of defects they introduce. ‖ ∻Answer∻ ⚹ Since the graph is not provided, I cannot give specific numerical answers. However, the methodology described above can be used to estimate the energies from the graph. For the impurities, typically: - $ \mathrm{KCl} $ may increase conductivity due to similar ionic size facilitating ion migration. - $ \mathrm{NaBr} $ may slightly alter conductivity due to different anion size and potential for defect formation. - $ \mathrm{CaCl}_{2} $ may increase conductivity by introducing more charge carriers (Ca^2+ replacing Na^+). - $ \mathrm{AgCl} $ and $ \mathrm{Na}_{2} \mathrm{O} $ may decrease conductivity due to their potential to form defect complexes or alter the defect equilibrium. ⚹ ∻Key Concept∻ ⚹ Estimating energies from conductivity graphs ⚹ ∻Explanation∻ ⚹ The activation energy for ion migration and defect formation can be estimated from the temperature dependence of conductivity using the Arrhenius equation. ⚹ ∻Key Concept∻ ⚹ Effect of impurities on conductivity ⚹ ∻Explanation∻ ⚹ Impurities can act as dopants, changing the concentration and mobility of charge carriers, thus affecting the material's conductivity. ⚹◊What factors can contribute to the conductivity of NaCl when impurities like KCl, NaBr, CaCl2, AgCl, or Na2O are present?⍭ Generate me a similar question◊

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