Question

Side-centered cubic (scc) cell Top view 1) (5 points) Walter White who lives in Simeranya (a utopic city in Anarres) prepares blue crystals, named as myth, which adopt a side-centered cubic (scc) cell, where atoms occupy the center of sides of a cubic cell. (The myth molecule is assumed to have a perfect spherical shape.) a) Find out how many atoms are present in each unit cell. b) Calculate the atomic packing factor (APF) of scc unit cell. c) Given the density of the material as 6.184 g/cm and a molar mass of 132 g/mol, determine the radius (in nm) of myth molecule. d) Find the linear density (in nm) of the following vectors in scc; (111), (110), and (100). (You can choose the origin as one of the corners of scc cell.) e) Determine the number of holes with coordination numbers 6, 8, and 12 per unit cell. 2) (5 points) Jesse Pinkman, Walter White's business associate, prepares blue myth crystals. After the synthesis, he uses powder XRD method to check if he prepared the right material. He decides that he has a contamination in the sample since he observes one extra peak that does not match to those of myth. a) Given the XRD data below, assign the Miller indices of all the peaks that belong to myth crystalline material (1= 0.15418 nm, n= 1 for Bragg's Law). (Diffraction angles are 18.72, 26.6, 28.64, 32.68, 42.64, 54.62°) b) Find the peak that belongs to impurity. Give the diffraction angle. c) Calculate the planar densities (in atoms/nm) of the following the crystallographic planes; (222), (100), and (220). Units: NA= 6.02x10atoms/mol

Answer 1

In this at the volume enit cell given unit cell all atoms ane present edge of the cell . So the effective contribution of each atom to the is I present in the present in the Total number of atom unit cell is 12 So the effective number of atom unit cell is £ x 12 2 3 volume of each atom Is Where as is the radius of Suppose 'a is the length of the unit cell . Then (2072 + @ I atom A Tr3 each an n o al 2872 or a 2 212 g volume of the unit cell The is a 3 z (272) 73 2 16 12 23

APF 2 Volume occupied by the total number of atoms. - Volume of the unit cell px / 1672 x5 3 2 2 - AT T Vevo HER 20555 Mass of each atom 2 132 61023X1023 8 huone & unit cell - density i volume of unit cel - Mass of unit cell a3 a 3x 132 6.184 x 6.023 x 1023 ar, opo y32 3X132 6.184 x 6.0 23x10 23 x 16 V2 2 4.6987 x 10-25 or 8 27.77 X 109 cm The radius of the molecule is 7.778109