Physics 4340: Introduction to
Solid State Physics
Lecture 30:
More X-ray diffraction
Think about the summation:
e
iK R
R
For some arbitrary K, and for a large number
of unit cells (going towards infinitely large)
this sum is likely to yield:
A)
B)
C)
D)
E)
Infinity (infinite number of terms)
Zero (equal pos. and neg. contribs)
Always goes to 1
Number atoms in unit cell
Something else
Think about the summation:
e
iK R
R
For some special K, this sum has a simple
limiting result. What are some special K?
A)
B)
C)
D)
I like K = 0
I like K = 2p
I like K = 2p/R
I like something else for special K.
What is the sum in that limit?
Only 14 distinct
styles of lattice
in 3-d.
(Bravis and
Frankenheim)
http://hyperphysics.phy-astr.gsu.edu/hbase/solids/bravais.html
Only 5 distinct
styles of lattice
in 2-d.
http://staff.chess.cornell.edu/~smilgies/xrd/IntroductionSurfaces.html
http://www.atpm.com/8.08/periodic-table.shtml
Wigner-Seitz unit cell examples
BCC lattice
FCC lattice
http://what-when-how.com/electronic-properties-of-materials/
energy-bands-in-crystals-fundamentals-of-electron-theory-part-2/
Only 14 distinct
styles of lattice
in 3-d.
Applies equally
to the Recip.
Lattice, which
are the F.T. of
direct lattice.
http://hyperphysics.phy-astr.gsu.edu/hbase/solids/bravais.html