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1) For each of the following crystal structures, sketch the first Brillouin zone. Label the
reflecting planes. Recall the rules for Bragg diffraction listed in square brackets (a
table of allowed reflections is given in Appendix C of ReedHill and Abbaschian). For
each, calculate the fraction of states in the first zone that are filled when the Fermi
surface (assume spherical) contacts the first Brillouin Zone.
a)
simple cubic [all reflections allowed]
b)
bcc [allowed reflections from planes where the sum
h
+
k
+
l
is even]
c)
fcc [allowed reflection from planes where
h
,
k
, and
l
are either all odd or all even]
NOTE: For assistance understanding BZ’s go to
http://phycomp.technion.ac.il/~nika/brillouin_zones.html
http://www.tf.unikiel.de/matwis/amat/semi_en/kap_2/backbone/r2_1_5.html
(The latter includes a nice description of how 3D band structures are represented in 2D)
2) For each of the following alloys, state the factor (electrochemical, size, or electron
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This note was uploaded on 12/05/2011 for the course MSE 4100 taught by Professor Hennig during the Fall '11 term at Cornell University (Engineering School).
 Fall '11
 Hennig

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