PHYS01200804001 Sohrab Abbas - Homi Bhabha National Institute

The depth Z is measured from the incidence surface along n i and
2
sin B S sin B S
,
k
O
H
(35)
is called the extinction distance. In the symmetric Laue case, S 2cos B / kO H
and is e.g., 64
μm for the {220} Si reflection with 2Å neutrons.
In the general Laue case, the component of along n i vanishes as can be seen by taking a dot
product of in Eq. (33) with n i . Thus is normal to n i , lies in the plane of incidence and
2
varies sinusoidally in magnitude with Z. At depths which are integral multiples of / 1 y , the
net current vector
J
m
k O
(1 O
/ 2)
(36)
m
is identical to that for the incident wave modified by the average refractive index. At depths
2
z (m 1/ 2) / 1 y on the other hand,
(1 O
/ 2)
2
2
J
b ,
m1/2
y k
O
k
(37)
H
m(1 y )
which is predominantly in the diffracted wave direction for fractional values of y. At the centre of
diffraction (y = 0),
J k H
b (1
m 1/2 O
/ 2) / m
, propagates totally along the diffracted direction,
the factor b in the numerator compensating the changed cross section of the diffracted beam. This
periodic variation with depth of the energy flow direction (Eqs.(33-34)) is termed ‘Pendellösung’,
due to its analogy with the energy transfer between two weakly coupled pendulums.
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