To U-process to occur the decaying phonon to have a wave vector "'q "'1 that is roughly half of the diameter of the Brillouin zone, because otherwise quasimomentum would not be conserved.
42.
"' Figure 2 . : " "'k "-vectors exceeding the first Brillouin zone ( red ) do not carry more information than their counterparts ( black ) in the first Brillouin zone.
43.
"' Figure 2 . : " "'k "-vectors exceeding the first Brillouin zone ( red ) do not carry more information than their counterparts ( black ) in the first Brillouin zone.
44.
This results in a very complicated set intersecting of curves when the dispersion relations are calculated because there is a large number of possible angles between evaluation trajectories, first and higher order Brillouin zone boundaries and dispersion parabola intersection cones.
45.
The first Brillouin zone is the locus of points in reciprocal space that are closer to the origin of the reciprocal lattice than they are to any other reciprocal lattice points ( see the derivation of the Wigner-Seitz cell ).
46.
A related concept is that of the "'irreducible Brillouin zone "', which is the first Brillouin zone reduced by all of the symmetries in the point group of the lattice ( point group of the crystal ).
47.
A related concept is that of the "'irreducible Brillouin zone "', which is the first Brillouin zone reduced by all of the symmetries in the point group of the lattice ( point group of the crystal ).
48.
For instance, in CuPt type B ordering, the L point of the Brillouin zone fold back to the ?-point, and the folded band repels the original conduction band minimum and bring down the bottom of conduction band.
49.
There are also second, third, " etc . ", Brillouin zones, corresponding to a sequence of disjoint regions ( all with the same volume ) at increasing distances from the origin, but these are used less frequently.
50.
As long as the sum of " k " 1 and " k " 2 stay inside the first Brillouin zone ( gray squares ) " k " 3 is the sum of the former two conserving phonon momentum.
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