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Derive the relation for c/a ration. Also find out atomic packing factor of HCP
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Solved in 3 steps with 3 images
- Find the planer density (Po) in (atom/mm) of (100) in a face centered cubic unit cell with lattice constant of 3.5 A, and determined the atomic radius1. Show that the atomic packing factor for HCP is 0.742. Calculate the Packing Factor of the Sodium Chloride structure to know the degree of occupancy of the ions that make it up.
- The Atomic packing factor of BCC...Derive the dimension ratio c/a for regular HCP crystal. Note: Do not use the atomic packing factor.Fe has both bcc and fcc structures with difference lattice constants: the bcc lattice constant a = 2.8664 Angstrom; and the fcc lattice constant = 3.6468 Angstrom. If we treat Fe atoms as touching hard spheres, (1) Derive associated atomic radius of Fe atoms in the bcc structure (2) Derive associated atomic radius of Fe atoms in the fcc structure (3) Calculate the volume fraction of Fe atoms in the bcc structure (4) Calculate the volume fraction of Fe atoms in the fcc structure (5) Calculate the edge lengths of octahedral and tetrahedral interstitials in bcc Fe (6) Calculate the edge lengths of octahedral and tetrahedral interstitials in fcc Fe (7) The fcc Fe has a denser packed structure yet solubility of carbon (atomic radius 0.7 Angstrom, only can occupy the interstitial sites of Fe) is much higher than that in the bcc Fe. Why is it so?
- What is the process ofcalculating the Packing Efficiency of a Unit Cell?What is packing fraction ?Barium titanate (BaTiO3) is an ionic solid with a density of 6.02 g/cm3. Its structure is described by orthogonal basis vectors (i.e. at 90 degrees to each other) with lattice parameters of a = b = 0.3992 nm and c = 0.4036 nm.a) What crystal system does barium titanate belong to, based on the above information?Explain your answer. b) Find the number of Ba, O, and Ti atoms per cubic centimeter in barium titanate (i.e.provide a value for each element). c) Sketch and label the (111) plane of BaTiO3 with its atoms and dimensions.
- Compute the atomic packing factor for the rock salt crystal structure in which rC/rA = 0.414.Draw the direction indices [1 0 1] within a cubic unit cell.a) Gold (Au) has an atomic radius 0.137 nm and a density of 19.32 g/cm'. (Atomic weight of 196.97 g/mol) Determine whether it has an FCC or BCC crystal structure. Compute the packing fraction/ atomic packing factor (APF), assuming the atoms to be hard spheres. (i) (ii) b) Fig. Q4 (b) shows the unit cell of Nickel (II) oxide (NiO) with ionic radii of ry 0.069 nm and ro = 0.140 nm. Calculate the density of NiO. (Avogadro's Constant = 6.022 x 1025 mol) %3D %3D nickel (II) oxide Ni
