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PHYS 353 Solid State Physics Study Guide for Part 1: Crystal Structure and Diffraction, Assignments of Solid State Physics

Christian Brothers University (CBU)Solid State Physics

A study guide for the first part of a university course on solid state physics, focusing on crystal structure and diffraction. It includes an outline of the topics covered, study questions, and collected homework assignments. The guide covers the concepts of basis, lattice, crystal directions and planes, fourier series, diffraction, and crystal binding. Students are expected to understand the differences between various lattice types, crystal structures, and symmetry operations, as well as the principles of bragg's law and the reciprocal lattice.

Typology: Assignments

Pre 2010

Uploaded on 08/13/2009

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PHYS 353 SOLID STATE PHYSICS STUDY GUIDE FOR PART 1
Crystal Structure
Chapters: 1,2,3
OUTLINE:
A. Basis
B. Lattice
1. lattice vectors
2. symmetries
3. primitive lattice cell
4. rotations, reflections, inversions
5. Bravais lattices
C. Crystal directions and planes
1. Miller indices
2. body centered
3. face centered
4. NaCl, CsCl, diamond
5. bonding
D. Fourier Series
E. Diffraction
1. review
2. Bragg's Law
3. reciprocal lattice
4. Brillouin zones
5. amplitude factor, structure factor, atomic form factor
6. temperature dependence
F. Crystal Binding
1. ionic
2. covalent
3. metal
4. VandeWaal forces
STUDY QUESTIONS: (for 1st test - not for collected homework assignment)
1. Distinguish between basis, lattice, and crystal structure.
2. For a 2-D lattice, draw the 5 types of lattices and give the special symmetry operations that
distinguish each from the rest.
3. Distinguish the NaCl from the CsCl structure. Give the basis and lattice type of each. Also
distinguish the hcp from the fcc lattice.
4. What is the Bragg Law for diffraction? How can it be explained by the wave theory?
pf3

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PHYS 353 SOLID STATE PHYSICS STUDY GUIDE FOR PART 1

Crystal Structure Chapters: 1,2, OUTLINE: A. Basis B. Lattice

  1. lattice vectors
  2. symmetries
  3. primitive lattice cell
  4. rotations, reflections, inversions
  5. Bravais lattices C. Crystal directions and planes
  6. Miller indices
  7. body centered
  8. face centered
  9. NaCl, CsCl, diamond
  10. bonding D. Fourier Series E. Diffraction
  11. review
  12. Bragg's Law
  13. reciprocal lattice
  14. Brillouin zones
  15. amplitude factor, structure factor, atomic form factor
  16. temperature dependence F. Crystal Binding
  17. ionic
  18. covalent
  19. metal
  20. VandeWaal forces STUDY QUESTIONS: (for 1st test - not for collected homework assignment)
  21. Distinguish between basis, lattice, and crystal structure.
  22. For a 2-D lattice, draw the 5 types of lattices and give the special symmetry operations that distinguish each from the rest.
  23. Distinguish the NaCl from the CsCl structure. Give the basis and lattice type of each. Also distinguish the hcp from the fcc lattice.
  24. What is the Bragg Law for diffraction? How can it be explained by the wave theory?

PHYS 353 Solid State Study Guide for Part 1 page 2

  1. Define the reciprocal lattice vector ( G ). Expand n( r ) in a Fourier series and then show that n( r + T ) = n( r ) where T is a lattice translation vector, r is any position in the lattice, and n is the electron density.
  2. Define the Brillouin zones.
  3. Define the scattering amplitude and relate the structure factor to it. Relate the form factor to the structure factor. COLLECTED HOMEWORK ASSIGNMENTS:
  4. Draw five different types of 2-D lattices, identify each type, and tell what distinguishes each type from the others.
  5. In an sc lattice: a) where do the atoms touch? b) what is the side length, s, in terms of the radius of the atoms, r? c) what is the hole size in terms of the side length? d) what is the hole size in terms of the radius of the atoms?
  6. Answer the questions posed in problem 2 for an fcc lattice.
  7. Answer the questions posed in problem 2 for a bcc lattice.
  8. Based on your answers to problems 2, 3 and 4, and based on the sizes of Na, Cs, and Cl given in the notes, which lattice type would you expect for NaCl and which for CsCl - and WHY?
  9. What is the packing fraction for: a) an sc type lattice? b) an fcc lattice? c) a bcc lattice?
  10. Draw four planes in an sc lattice, give the designation (Miller indices) of each, draw a line perpendicular to each plane, and specify each line, i.e., give the [hkl] of each line.
  11. Demonstrate by means of a drawing that shows areas above and below the axis for three cases (i.e., chose different values for n and m values for each case) that: sin( )cos(m )d 0 2 0

^ 

n   

  1. (a) Define some function of position over a finite length interval, a, and assume f(x) = f(x+a). [Choose any function other than the saw-toothed wave which is used as an example in these notes.] b) Find its Fourier Series (up to a reasonable number of terms). (c) Graph the function and then graph the Fourier Series on top of it to show how close the two are. [Use a computer graphing package or do it by hand on graph paper.] [NOTE: Fourier series in math books are often given in terms of q: f() = f(+2); but in our case we are dealing with x, not with ; in our case we replace  by kx where k=2/a. Be sure to a. Be sure to give definite values to k and a, and be sure to include units also!]