3. Show that the angle between a lines (bonds) joining a site of a dia its four nearest neighbors is cos-¹0 Note, a diamond lattice is a FCC la atom basis.

1. Many substances crystallize in a cubic structure. The unit cell for such crystals is a cube having an edge with a length equal to do. -Face diagonal a. What is the length, in terms of do, of the face diagonal, which runs diagonally across one face of the cube? (Hint: Use the Pythagorean theorem.) b. What is the length, again in terms of do. of the cube diagonal, which runs from one corner, through the center of the cube, to the opposite corner? (Hint: Make a right triangle having a face diagonal and an edge of the cube as its sides, with the hypotenuse equal to the cube diagonal, then use the Pythagorean theorem again.) 2. In an FCC structure, the centers of the atoms are found on the corners of the cubic unit cell and at the center of each face. The unit cell has an edge whose length is the distance from the center of one corner atom to the center of another corner atom on the same edge. The atoms on the diagonal of any face are touching. One of the faces of the unit cell is shown…

ii) Sketch the Face Centered Cubic (FCC) unit cell. Compare the calculation of Effective Number of atoms in Face Centered Cubic (FCC) structure and Body Centered Cubic (BCC) structure with example materials.

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

Tungsten (W) has the BCC crystal structure. The atomic radius is R = 0.137 nm and the atomic mass is M = 183.95 g/mole. %3D What is the density of Tungsten in g/cm³? Given: Avogadro's Number NA = 0.6023 × 1024 (atoms/mole) Select one: O a. 5.30 O b. 6.28 Oc. 2.534 Od. 6.77 Oe. 19.28

Sketch the planar cross section for the following planes in the FCC structure (label the edge lengths in terms of a and R) and calculate the planar densities for the three planes (do so in terms of both atoms/nm2 AND the dimensionless quantity): a. (001)b. (011)c. (111)

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?

You are given the density of a metal as 2.07 g/cm³. You are advised the crystallographic structure is fcc, and the atomic mass is 25.5 g/mol. What is the atomic radius of the metal? a. 0.15 nm b. 0.12 nm c. 0.11 nm d. 0.18 nm

3 Copper Unit Cell Uniqueness Here's a weird way to describe the structure of copper: Cu falls into the tetragonal crystal system with a = 0.256 nm, c = 0.362 nm = a√√2, and atoms located at 000 and. Its density is 8.94 g/cc at room temperature. (a) Draw a few adjacent units cells of the structure as described in this "weird" way. You should be able to see that there is a much more convenient way to describe the structure. What is it? (The point I wish to make is that there are many different unit cells that can be used to describe any given crystal, so we usually choose the one that is easiest to visualize.) (b) Calculate the radius of a copper atom using the above information. (c) Calculate the lattice parameter of the "better" unit cell of Cu.

Answer only 1