1 (354)

Prévia do material em texto

12 Modern Materials Solutions to Exercises (a) In the CsCl structure, the anion and cation have about the same radius; in the NaCl structure, the anion is somewhat larger than the cation; in the ZnS structure the anion is much larger than the cation. In the three compounds given, Cs+ (r = 1.81 Å) and I- (r = 2.06 Å) have the most similar radii; CsI will adopt the CsCl-type structure. The radii of Na+ (r = 1.16 Å) and I- (r = 2.06 Å) are somewhat different; Nal will adopt the NaCl-type structure. The radii of Cu+ (r = 0.74 Å) and I- (r = 2.06 Å) are very different; Cul has the ZnS-type structure. (b) As cation size decreases, coordination number of the anion decreases. In CsI, I- has a coordination number of eight; in Nal, I- has a coordination number of six; in Cul, I- has a coordination number of four. 12.58 (a) In CaF₂ the ionic radii are very similar, Ca²⁺ (r = 1.14 Å) and F⁻ (r = 1.19 Å). In ZnF₂ the cation radius is smaller and the ionic radii are more different, (r = 0.88 Å) and F⁻ (r = 1.19 Å). Cations in both structures in the exercise are shown with equal radii, so direct inspections does not answer the question. We can, however, refer to the trend that, for compounds with the same cation/anion ratio, as cation size decreases, coordination number of the anion decreases. The anion coordination number (CN) for the rutile structure is 3 and for the fluorite structure is 4. The compound with the smaller cation, will adopt the rutile structure and the compound with the larger cation, CaF₂, will adopt the fluorite structure. (Detailed analysis of coordination numbers follows.) (b) Rutile (top) structure, cation (blue) coordination number (CN) = 6, anion (green) CN = 3. [The blue cation in the interior or the cell is coordinated to the six (green) anions associated with the same cell; either of the green interior anions is associated with the triangle of blue cations located inside and at the two nearest corners of the cell.] Fluorite (bottom) structure, cation (blue) CN = 8, anion (green) CN = 4. [A blue cation at one of the face centers is coordinated to the four nearest green anions inside the cell and to four identical anions in an adjacent cell that also contains the cation. Any of the green interior anions is coordinated to a tetrahedron of blue cations located at one corner and the three nearest face centers.] 12.59 Analyze. Given three magnesium compounds in which the coordination number (CN) of is six, determine the coordination number of the anion. Plan. Use Equation 12.1 with the cation/anion ratio of each compound and the coordination number to calculate the anion coordination number in each compound. Solve. (a) MgS: 1 cation, 1 anion, cation CN = 6 # of cations per formula unit = anion coordination number # of anions per formula unit cation coordination number anion CN = cation CN # of cations per formula unit = 6x1 1 = 6 # of anions per formula unit 348