2. Magnetite or Fe3O4 consists of Feo and Fe203 mixed at the unit cell level wit

Question

2. Magnetite or Fe3O4 consists of Feo and Fe203 mixed at the unit cell level with one Fe and two Fe ions for every 4 o2 ions per unit cell. The unit cell has a cubic 3+ basis with an edge length of0.839 nm. If the density of this material is 5.24 g/cm a. Determine the number of units of Fe304 per unit cell b. Using the data on ionic radii in Table 12.3, determine the ionic packing factor. The ionic packing factor is defined the same way it was for the atomic packing factor was defined for metallic crystals

Explanation / Answer

a) Number of units of Fe3O4 per unit cell = 8 * (2/4) + 8* (1/2) = 8 units
b) Ionic packing factor for Fe3O4 = [4 ( 4r3 / 3) + 4 (4R3 / 3) ] / (2r + 2R)3
radius of Fe+2 , r = 0.077 nm ; radius of Fe+3 , R = 0.069 nm
     [4 ( 4r3 / 3) + 4 (4R3 / 3) ] / (2r + 2R)3 = [4*(4*0.0773 / 3) + 4*(4*0.0693 / 3)] / (2*0.077 + 2*0.069)3
Ionic packing factor = 0.5283

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