Polonium is the only element known to crystallize in the simple cubic lattice. (a) What is the distance between nearest neighbor polo- nium atoms if the first-order diffraction of X-rays with A = 1.785 Å from the parallel faces of its unit cells appears at an angle of 20 = 30.96° from these planes? (b) What is the density of polonium in this crystal (in g cm-3)?

only (I)

Metallic copper adopts an fcc structure with density 8960 kg m-3. Draw the unit cell of copper and mark the shortest copper atom to copper atom distance. (a) How many copper atoms are there in the unit cell?(b) Use the density and mass of the unit cell to determine the lattice parameter for copper and calculate a value for the metallic radius of copper.

Calculate the density of niobium if it occupies a body-centered cubic unit cell with an atomic radius of 142.83 pm. What kind of unit cell does europium occupy if its density is 5.243 g mL−1?

Nickel has an fcc structure with a density of 8.90 g cm-3.(a) Calculate the nearest neighbor distance in crystalline nickel.(b) What is the atomic radius of nickel?(c) What is the radius of the largest atom that could fit into the interstices of a nickel lattice, approximating the atoms as spheres?

A unit cell has a=5Å, b=5Å, c-8Å, a=90°, B-90° ad y=90°. What will be the Bravais lattice for this unit cell? Mention the following for each of the given crystallographic cubic planes. (a) Intercepts in the x, y and z coordinates (b) Reciprocals (c) Final index of the crystal plane 1/2

(b) Many structures of ionic compounds have been described in terms of close packing of a large anion, X, with a cation, A, occupying tetrahedral or octahedral holes. (1) In a cubic close packed lattice, how many octahedral holes are there per lattice ion? (ii) What is the formula of a compound based upon a cubic close packed lattice in which of the octahedral holes are filled? (ii) State the coordination numbers and geometries of A and X In the crystal lattice in part (b)(ii) above.

3

Calculate the ratio of the maximum radius of an interstitial atom at the center of each face of a bcc unit cell to the radius of the host atom.

(a) Magnesium (Mg) has a hexagonal close-packed (HCP) crystal structure with the lattice parameter of a = 0.321 nm and c= 0.521 nm and the atomic radius is 0.173 nm. (i) What is the number of atoms per unit cell in HCP structure? (ii) Determine the atomic packing factor of the Mg unit cell. (iii) Is Mg containing an ideal atomic packing factor? You may justify your answer by evaluating the HCP c/a ratio. Subsequently, will slip be harder in Mg compared to the ideal HCP structure? Justify your answer.