Calculate the packing factor of CaTiO3. It has a perovskite structure. Data: ionic radii Co²+ = 0.106 nm, Ti4+ = 0.064 nm, O² = 0.132 nm; lattice constant is a = 2(rTi4+ + ro2-). Ca2+ 02- T14+ Consider the ions as rigid spheres. 1. 0.581 or 58.1% 2. -0.581 or -58.1 % 3. 0.254 or 25.4%

A compound of titanium and oxygen contains 28.31% oxygen by mass.(a) If the compound’s empirical formula is TixO, calculate x to four significant figures.(b) The nonstoichiometric compounds TixO can be described as having a Ti2+-O2- lattice in which certain Ti2+ ions are missing or are replaced by Ti3+ ions. Calculate the fraction of Ti2+ sites in the nonstoichiometric compound that are vacant and the fraction that are occupied by Ti3+ ions.

An alloy structure (element: Co, Y, Si) adopts the cubic crystal structure with lattice constant a = 5.19 Å. Please determine (1) the bond length between Co-Y, Co-Si, Y-Si. (2) the density of the alloy. (Hint: atomic weight for Co: 58.9 g/mol; Y: 88.9 g/mol; Si: 28 g/mol; Avogadro constant: NA = 6.022 ×10²³ mol-1).

Given edge lengths and face angles, predict the shape ofeach of the following crystals.a. a = 3 nm, b = 3 nm, c = 3 nm; α = 90°, β° = 90,γ = 90°b. a = 4 nm, b = 3 nm, c = 5 nm; α = 90°, β° = 100,γ = 90°c. a = 3 nm, b = 3 nm, c =5nm; α = 90°, β° = 90 ,γ = 90°d. a = 3 nm, b = 3 nm, c = 5 nm; α = 90°, β° = 90,γ = 120°

2. The equilibrium fraction of lattice sites that are vacant in silver (Ag) at 700°C is 2 x 10-6. Calculate the number of vacancies (per meter cubed) at 700°C. Assume a density of 10.35 g/cm3 and an atomic weight of 107.87 g/mol for Ag.

A hypothetical metal has a tetragonal unit cell for which the lattice parameters (in nm) are a=b=0.550, c=0.673 and all angles are 90 degrees. If there are 5 atoms per unit cell and the atomic packing factor is 0.63, determine the atomic radius in nm. Use 3.14 for pi. Give your answer to 3 decimal places. I got 0.197 the first time and it was incorrect.

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)…

A hypothetical metal with an atomic radius of 0.171 nm has an orthorhombic unit cell for which the a, b, and c lattice parameters are 0.479, and 0.725, and 0.978 nm, respectively. It has an atomic weight of 126.91 g/mol and a theoretical density of 4.92 g/cm3. Determine the APF of the metal. Use NA = 6.022 x 1023

4- The unit cell of 52Cr²4 metal is BCC, if the density of Cr= 7.19 Mg/m³; determine the lattice constant of Cr unit cell?

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