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- 4. A silicon sample has, at 300 K, o = 10-6 S/cm, Ny = Nc %3D = 1 x 1019 cm-3, %3D 1000 cm2/s, and u, = 600 cm2/s. Find the energy gap of the material at 300 K and the conductivity at 500 %3D K. Assume that Ny, N, H, and u, are independent of V' temperature.8. What is the difference in packing efficiency between the hcp structure and the ccp structure? 9. For a two dimensional lattice with, a1= a a2= a/2 D- T1/3 (a) what is the area of a primitive cell? (b) show that the lattice is a rectangular lattice? (c) draw the Wigner-Seitz cell of this lattice and show that the area of the Wigner-Seitz cell is the same as in (a).Please ans me
- A gas-phase ¹H¹27I molecule, with a bond length of 160.92 pm, rotates in three-dimensional space. a. Calculate the zero point energy associated with this rotation. b. What is the smallest quantum of energy that can be absorbed by this molecule in a rotational excitation?55. Which of the following images depicts the (001) plane of the FCC crystal structure? A' B' D' E' d. a. A B C f. C. E FAt 23° K, the crystal structure transforms from BCC to HCP keeping density same. The 0 cubic face in BCC is a = 3.42 A and in HCP is == 1.53. The lattice constant in HCP a structure is, 0 (a) 2.64 A 0 (b) 3.16 A 0 (c) 2.16 A 0 (d) 2.42 A
- 15. Soft modes and lattice transformations. Sketch a monatomic linear lattice of lattice constant a. (a) Add to each of six atoms a vector to indicate the direction of the displacement at a given time caused by a longitudinal phonon with wavevector at the zone boundary. (b) Sketch the crystal structure that results if this zone boundary phonon becomes unstable (w → 0) as the crystal is cooled through Tc. (c) Sketch on one graph the essential aspects of the longitudinal phonon dispersion relation for the monatomic lattice at T well above Tc and at T = Tc. Add to the graph the same information for phonons in the new structure at T well below Tc.Iron has a Body- Centered Cubic (BCC) structure with atomic radius 0.123 Å. Find the lattice constant. Select one: A. 2.314 Å B. 0 C. 0.2840 Å O D. 4.587 ÅProblems 1. Tetrahedral angles. The angles between the tetrahedral bonds of diamond are the same as the angles between the body diagonals of a cube, as in Fig. 10. Use elemen- tary vector analysis to find the value of the angle.
- 1. Write down all the possible Burgers vectors of perfect dislocations in an FCC metal. 2. For an a/2[1 dislocation line moving on a (11-1) plane in an FCC crystal, what are the line directions (in Miller indices) if the dislocation is of (i) pure screw and (ii) pure edge character? For an a/2[1 dislocation line moving on a (11-1) plane in an FCC crystal, what are the line directions (in Miller indices) if the dislocation is of (i) pure screw and (ii) pure edge character?4. Consider a simple cubic system with lattice constant a = 5 Å. Determine the atom density (atoms/cm²) for the (100), (110), and (111) planes.19. Construct the reciprocal lattice for a two-dimensional lattice in which a = 1.25 Å, b= 2.50 Å, and y = 120°. 20. A unit cell has the dimensions a= 4 Å, b= 6 Å, e = 8 A, a = ß = 90°, y = 120°. Determine: a) a", b*, and e* for the reciprocal cell. b) The volume of the real and reciprocal unit cells. c) The spacing between the (210) planes. d) The Bragg angle 0 for reflection from the ahove nlanes