PHYS01200804001 Sohrab Abbas - Homi Bhabha National Institute

for a positive value of b c i.e. for V O and V H > 0. Over this small region, the spheres LR and LL of
radius k O drawn about the origin O and reciprocal lattice point H respectively, appear as planes
intersecting the bisector LQ of OH at the point L in the plane of incidence. The spheres QR and
QQ of radius K, centred at O and H respectively, are the asymptotes to the hyperbolic dispersion
surface comprising branches labelled and β, denoting the branch closer to the point L. The
dispersion surface has a remarkable property viz. that for any allowed ψ, the energy flow averaged
over the planar spacing d and represented by the current density vector
J
ψ
K
m
2 2
0 O H
K (17)
H
is directed along the normal [132] to the dispersion surface at the corresponding tie point.
Fig.3 Reciprocal space representation of the Bragg diffraction in a single crystal.
18