Problem 1. Structure factor of bcc lattice. The bec basis referred to the cubic cell has identical atoms at x, = y, = z, =0 and at x, y2 22 = 1/2. Find the structure factor S.
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- Problem 1. Structure factor of bee lattice. The bec basis referred to the cubic cell has identical atoms at x, = y, = z, = 0 and at x, = y, = z2 1/2. Find the structure factor S. Find the zeros of S.Problem 2. Structure-Property Relations: Tensor and Matrix Operations in Describing Materials Properties For a BaTiO; crystal at room temperature, its x1 [100], x2 [010], and x3 [001] directions constitute a set of orthogonal right-handed axes. To transform this set of axes system to a new right-handed axes system with direction x1'= [011], x2'= [0 ī1]. (2.a) find the transfomation matrix (a) - the set of direction cosines relating the new axes to the old. [30 (2.b) If the dielectric property in the original system is given as le, /ɛ]=|0 30 0 0 0 50 find out the dielectric constant ɛ11' along the direction x1'/[011]. (2.c) Provide a sketch of the directional dependence of its dielectric property (i.e., e' as a function of e and 4) for 0s 0 < 180 degrees. A two-dimensional drawing is fine when proper labels are given.Which of the structures have a major peak above 3000 cm¹? (Select all that apply). ob
- 2.5 a) Calculate the five lowest "free electron" bands along the A-axis in the Brillouin zone for the simple cubic lattice (analogous to Fig. 2.35). Calculate the associated eigenfunctions. b) For bands which are degenerate along the 4-axis (or at r or at X), construct linear combinations of the wave functions in such a way that the new func- 464 Problems to Chapters 1-9 tions are either invariant to the group operations, or reduce to sets of functions which transform into one another. Such sets form the basis func- tions for the irreducible representations of the group of the k-vector.Answer Q32, 33, 29Which of the structures have a major peak above 3000 cm1? (Select all that apply). none of these
- Which of the structures have a major peak between 1700 and 3000 cm¹? (Select all that apply). none of these CIWhich of the structures have a major peak between 1700 and 3000 cm¹? (Select all that apply). H none of theseProblem 1 3.1 Use the method of Section 3.1 to estimate the surface energy of (11. 200; and (220; surface planes in an fee erystal. Express your answer in J/surface atom and in J/m.
- Which of the structures have a major peak above 3000 cm'? (Select all that apply). ملی ہو □ OHe. Notice that the face atom and the corner atoms along the diagonal all touch. Solve for the length of the diagonal in terms of "r" the radius of one atom. Answer: f. Since question 3d and 3e express the length of the diagonal when the side is "a" set them equal and solve for "a", the side of length of a face- centered unit cube. Answer: g. Find the total volume of the atoms in the face-centered unit cell expressed in terms of r. Use commor equations to find the volume of atoms in the unit cell. To do this, take the volume of a sphere in terms of "r" and multiply it by the total number of atoms represented in the unit cell. Answer:Can you pls help me with number 4