problems "Essential Solid State Physics Notes", Study notes of Solid State Physics

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Solid State Physics Assignment 2 Deadline: March 4, 23:59 1. [20 points] X-ray diffraction of [B@@GPOnl (ATES COISANE of the conventional unit cell is/28GI65) (Pm) is done using X-rays with a FUNCGHZATOMUNS (OnerizstyorleRpeAk in the diffraction pattern is at 2 = 823°. What are the possible Miller indices for this peak? 2. [20 points] Samples of a monatomic cubic crystal is analyzed with Debye-Scherrer camera. It is known that the sample a The approximate positions of the first four /@iffirac) incident beam Figure 1: Illustration of Problem 1. Schematic view of the Debye-Scherrer camera. Diffraction peaks are recorded on the film strip. (Tdentify the crystal Struchires Of the Sample) [ Hint: Be careful when identifying the Bragg angle.] 3. [20 points] A {eq metal shows first ring in the powder photo- graph at #2228" BeTOSEEVER | The ENCIGHEE of the X-ray is IN5amAG 4. [20 points] Calculate the geometrical structure factor for diamond erystal, Based on your result, determine whether{{(@3), (23), (@Wy planes can manifest themselves in the X-ray diffrac- tion pattern. The Miller indices refer to the primitive cell. (Can Gach Of these planes appear in the) diffraction pattern for sphalerite? 5. [20 points] Consider a linear ionic crystal, i.e. a 1D chain of 2N ions of alternative charge +q with a repulsive potential energy A/R” (A, n are positive constants, R is the distance between nearest neighbors). Derive the crystal energy for the equilibrium separation between the ions.