Chemistry Reference
In-Depth Information
Figure1.31.
Material constant
C
m
defined by Equation 1.58a and calculated for different pure
elements with atomic number
Z
. The maxima at
Z
=
14, 28, 45, and 77 reflect a small volume of the
respective atoms while the minima at
Z
=
11, 19, 37, 55, and 85 occur for relatively large atoms
(alkali metals). The quantity is important for the calculation of the refractive index and the critical
angle of total reflection. Data from
http://xdb.lbl.gov
; reproduced with permission from Center for
X-Ray Optics and Advanced Light Source, Lawrence Berkeley National Laboratory.
The small quantity of
δ
is due to the small amplitude of the electrons'
oscillations. Because of the high photon frequencies corresponding to the
short wavelengths of X-rays, only small amplitudes can occur.
The quantity
β
is even smaller than
δ
. Table 1.8 lists values of
δ
and
β
for
some compounds and pure elements, calculated for Mo-K
α
radiation. For
compounds, solutions, or mixtures,
δ
and
β
have to be calculated according to
the additive law already applied in Equation 1.41:
X
δ
total
c
i
δ
i
(1.60)
X
β
total
c
i
β
i
(1.61)
Again, the
c
i
terms are the different mass fractions of the individual elements
i
with respective values
δ
i
and
β
i
.
1.5.2DiffractionandBragg'sLaw
The phenomenon of a so-called diffraction occurs when a wave hits an obstacle.
A parallel wave front hitting a small obstacle or opening deviates from its
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