a. Discuss the difference between a lattice, basis and crystal structure. Feel free to use diagrams to aid your answer. (L2 - 5 points) b. Consider the cubic crystal system. Justify how the line [hk] is perpendicular to the (hk) plane. (L2-5 points) c. Niobium (Nb) has the body-centered cubic (BCC) crystal with a lattice parameter a = 0.3294 nm. Find the planar concentrations as the number of atoms per nm of the (100), (110), and (111) planes and indicate which plane has the most concentration of atoms per unit area? (L2 - 10 points) 2/3 d. Sometimes the number of atoms per unit area nwfice on the surface of a crystal is estimated by using the relation "surface=ulk where nuk is the concentration of atoms in the bulk. Compare nrface values with the planar concentrations that you calculated in (c) above and discuss the difference. (L2-5 points) [Note: The BCC (111) plane does not cut through the center atom and the (111) plane has one- sixth of an atom at each corner.]