**1.** ZnS crystallizes with the space group, with *a= *3.8227(1) Å and *c =* 6.2607 Å

**a)**Draw projections of the unit cell along the [001] and [110] directions.

**b)** Show (1 2 10) and (0003) planes on the projections.

**c)** Calculate the 2*θ* angles at which diffraction from the (1 2 10) plane will occur for no monochromated CuKα radiation.

**2.** A phase diagram of the Gd-Bi binary system is presented below. You need to grow crystals of GdBi2 from the self-flux. How would you do it? What composition and temperatures would you use and why?

**3.** The crystals of MoO2 can be grown by chemical vapor transport with I2. The growth direction is from 900º C to 700º C. Explain the growth direction in terms of the thermodynamic parameters, *K*, *ΔH*, *ΔS*.

**4.** Derive the ground term for Dy³+ and calculate its effective magnetic moment in units of μB. Assume that a compound containing Dy³+ can be fully magnetized with a strong magnet. What magnetic moment per Dy³+ in units of μB can you achieve? Explain your answer.

**5.** Using the Drude theory of metals, derive the velocity of conduction electrons in *n*-doped Si at 20º C (electron concentration is 10²º cm-³).

Calculate the average velocity of conduction electrons in the same Si according to the free electron model, assuming that EF = 1.12e*V*. By comparing the two velocities, would you predict the two theories to give relatively similar values for electrical conductivity?

**Note:** Within the free electron model, the average energy of electrons is

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