5. In a close-packed array containing N spheres, there are N octahedral holes and 2N tetrahedral holes. Use this information to answer the following: a) The structure of solid Al203 consists of an hcp array of oxide ions with the Al3+ ions in octahedral holes. What fraction of the octahedral holes contains Al3+ ions? b) The mineral spinel has the formula MgAl2O4. The structure is based on a ccp array of oxide ions with the Mg²+ ions in tetrahedral holes and the Al3+ ions in octahedral holes. What fraction of each type of hole is occupied by the respective ion?

Do both unit cells shown below represent the same compound? Titanium Calcium Охygen

5)

The unit cell of strontium titanate SrTiO3 is depicted on the left in the figure below showing the crystal structure as confirmed by X-ray diffraction experiments. The lattice constant is a - 3.9 × 10-¹0 m. A typical X-ray powder diffraction spectrum is displayed on the right. The wave length of the X-ray beam (Cu-Ka radiation) is λ = 1.54 × 10-¹⁰ m. Unit cell of SrTiO3; Sr atoms are shown in blue, Ti in black and the oxygen atoms are in red. Normalized intensity (a.u.) (001) 20 (011) 30 (III) 40 (200) (210) 50 (211) (220) (300) 60 20 (degrees) 70 (310) (311) >(222) (320) 80 90 (17) 100 X ray powder diffraction data for SrTiO3; the plot shows an overlay for two different SrTiO3 samples. [L. da Silva et al, J. Nanomat., doi:10.1155/2012/890397] a) Identify the Bravais lattice of SrTiO 3and specify the basis for the primitive unit cell shown in the figure. b) Explain how the Miller indices (hkl) describe a family of lattice planes. State a set of possible reciprocal lattice vectors. c)…