ubic (b) face-centred cubic (c) close-packed hexagon

4. Platinum (atomic radius = 1.38 Å) crystallizes in a cubic closely packed structure. Calculate the edge length of the face- centered cubic unit cell and the density of platinum.

Platinum (Pt) has the FCC crystal structure, an atomic radius of 0.1387 nm, and an atomic weight of 195.08 g/mol. What is its theoretical density? g/cm³

→Compare (100) and (111) surfaces in FCC. Which one should have a lower surface energy?

a. For a FCC crystal, list all the planes in the {1 2 1} family. b. Would you expect a family in a face-centered orthorhombic (FCO) crystal to have more or fewer planes than the same family in a FCC crystal? Explain your answer.

A Lanthanum (atomic mass 138.91 g/mol) sample has a lattice parameter 3.77Å. Assume it contains 514 vacancies per 200 unit cells. Calculate (a) the number of vacancies per cm³, (b) density of the sample and (c) compare the number of vacancies per unit cell between the sample given and a perfect Lanthanum sample. Assume T=400C.*

Question 2. HfO2 has the CaF2 crystal structure. Calculate the density of HfO2 in kg/m³ if the ionic radii are Hf* = 0.083 nm and O²- = 0.132 nm.

3. Under what conditions, will the body centered tetragonal lattice become (a) a bcc structure? (b) an fcc structure?

1. It is often convenient to represent a fcc lattice as simple cubic, with a cubic primitive cell of side a and a four-point basis. (a) Show that the structural factor is then either 4 or 0 at all points of the simple cubic reciprocal lattice. (b) Show that when points with zero structural factor are removed, the remaining points of the reciprocal lattice makes up a bcc cubic lattice with conventional cell of side 4л/a. Why is this expected?

Molybdenum, a BCC metal has an atomic radius of 0.136 nm. (a) Calculate the d-spacing for the (211) plane.