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Chapter 12: Problem 5

On the basis of ionic charge and ionic radii given in Table \(12.3,\) predict crystal structures for the following materials: (a) \(\mathrm{CaO},\) (b) \(\mathrm{MnS}\) (c) \(\mathrm{KBr},\) and (d) \(\mathrm{CsBr}\). Justify your selections.

Short Answer

Expert verified
Answer: The likely crystal structures and coordination numbers for each material are: (a) CaO: Rock salt structure (NaCl-type) - Octahedral coordination with a coordination number of 6. (b) MnS: Zinc blende structure (ZnS-type) - Tetrahedral coordination with a coordination number of 4. (c) KBr: Rock salt structure (NaCl-type) - Octahedral coordination with a coordination number of 6. (d) CsBr: Cesium chloride structure (CsCl-type) - Cubic coordination with a coordination number of 8.

Step by step solution

01

Find the formula of each material

To predict the crystal structure of each material, we must first write the chemical formula for CaO, MnS, KBr, and CsBr. (a) CaO: Calcium has a +2 charge, and Oxygen has a -2 charge. (b) MnS: Manganese has a +2 charge, and Sulfur has a -2 charge. (c) KBr: Potassium has a +1 charge, and Bromine has a -1 charge. (d) CsBr: Cesium has a +1 charge, and Bromine has a -1 charge.
02

Calculate ionic radii ratios

We can use the provided ionic radii in Table 12.3 to find the ratio of cation radius to anion radius (rc/ra) for each material. (a) CaO: rc (Ca虏鈦�) = 100 pm, and ra (O虏鈦�) = 140 pm, so the radius ratio (rc/ra) = 100/140 = 0.714 (b) MnS: rc (Mn虏鈦�) = 83 pm, and ra (S虏鈦�) = 184 pm, so the radius ratio (rc/ra) = 83/184 = 0.451 (c) KBr: rc (K鈦�) = 138 pm, and ra (Br鈦�) = 194 pm, so the radius ratio (rc/ra) = 138/194 = 0.711 (d) CsBr: rc (Cs鈦�) = 170 pm, and ra (Br鈦�) = 194 pm, so the radius ratio (rc/ra) = 170/194 = 0.876
03

Determine the coordination numbers and crystal structures based on the critical radius ratio

Using the critical radius ratio, we can predict the coordination numbers and the crystal structures for each material. (a) CaO: The radius ratio (0.714) suggests a coordination number of 6. Therefore, the crystal structure is likely to be an octahedral structure, like the rock salt structure (NaCl-type). (b) MnS: The radius ratio (0.451) suggests a coordination number of 4. Therefore, the crystal structure is likely to be a tetrahedral structure, like the zinc blende structure (ZnS-type). (c) KBr: The radius ratio (0.711) suggests a coordination number of 6. Therefore, the crystal structure is likely to be an octahedral structure, like the rock salt structure (NaCl-type). (d) CsBr: The radius ratio (0.876) suggests a coordination number of 8. Therefore, the crystal structure is likely to be a cubic structure, like the cesium chloride structure (CsCl-type).
04

Conclusion

To summarize, the predicted crystal structures for the given materials are: (a) CaO: Rock salt structure (NaCl-type) - Octahedral coordination (b) MnS: Zinc blende structure (ZnS-type) - Tetrahedral coordination (c) KBr: Rock salt structure (NaCl-type) - Octahedral coordination (d) CsBr: Cesium chloride structure (CsCl-type) - Cubic coordination

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Most popular questions from this chapter

(a) A three-point transverse bending test is conducted on a cylindrical specimen of aluminum oxide having a reported flexural strength of \(390 \mathrm{MPa}(56,600 \mathrm{psi})\). If the specimen radius is \(2.5 \mathrm{~mm}\) (0.10 in.) and the support point separation distance is 30 \(\mathrm{mm}\) (1.2 in.), predict whether you would expect the specimen to fracture when a load of \(620 \mathrm{~N}\left(140 \mathrm{lb}_{\mathrm{f}}\right)\) is applied. Justify your prediction. (b) Would you be \(100 \%\) certain of the prediction in part (a)? Why or why not?

The corundum crystal structure, found for \(\mathrm{Al}_{2} \mathrm{O}_{3}\), consists of an HCP arrangement of \(\mathrm{O}^{2-}\) ions; the \(\mathrm{Al}^{3+}\) ions occupy octahedral positions. (a) What fraction of the available octahedral positions are filled with \(\mathrm{Al}^{3+}\) ions? (b) Sketch two close-packed \(\mathrm{O}^{2-}\) planes stacked in an \(A B\) sequence, and note octahedral positions that will be filled with the \(\mathrm{Al}^{3+}\) ions.

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

Magnesium oxide has the rock salt crystal structure and a density of \(3.58 \mathrm{~g} / \mathrm{cm}^{3}\). (a) Determine the unit cell edge length. (b) How does this result compare with the edge length as determined from the radii in Table \(12.3\), assuming that the \(\mathrm{Mg}^{2+}\) and \(\mathrm{O}^{2-}\) ions just touch each other along the edges?

Cite one reason why ceramic materials are, in general, harder yet more brittle than metals.
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