Physics for Geologists, Second edition

Electromagnetic radiation 67
(negative electrode). This is roughly how they are produced today for medical
and dental purposes. The X stands for unknown. X-rays are emitted from an
excited atom, varying in intensity and wavelength from element to element.
They are produced in a vacuum tube by accelerating electrons in a high-
voltage field from the cathode to collision with the anode, where the X-rays
are generated. Like y-rays, they are not deflected by a magnetic field, so they
are not charged particles.
X-rays have frequencies between about 100 x 10'' Hz and about 100 x
1018 Hz (wavelengths between about and about 10-l2 m shorter
than ultra-violet and so of a higher frequency). Like other electromagnetic
radiation, they show wave characteristics of interference, diffraction and
polarization. They show particle characteristics in their scattering, and in
the fluorescence they excite in some materials (a property used in analysis,
as we shall see). They have varying penetrative power, and affect photo-
graphic emulsions. When X-rays pass through material, the material itself
becomes a source of X-rays and electrons. The secondary X-rays consist of
scattered and fluorescent rays, the scattered rays being of about the same
energy as the primary rays, the fluorescence being weaker, as you would
expect. X-rays can be polarized by a block of carbon.
Light can be diffracted by passing it through a finely-ruled grating. In
1912, Max Laue, a German physicist, thought of measuring the wavelength
of X-rays by passing them through crystals and measuring the diffraction -
replacing the grating by the lattice of the crystal. Soon X-rays were to be
used to analyse the atomic lattice structure of crystals, and X-rays and
crystallography have been closely related ever since.
X-rays also originate in space (as do infrared and radio waves), and such
sources seem to lie close to the galactic plane (through the Milky Way) with
few exceptions. Very few of these sources are identifiable with visible objects.
The Sun is one.
X-ray diffraction (XRD)
X-rays, being electromagnetic radiation, can be diffracted like light. The
grating equation, Equation 4.5, ny = d sin cp applies; but since h, is of the
order of 1 nm, d has to be smaller than is possible (or practicable) in a man-
ufactured grating - say, 1 km. Fortunately crystals commonly have the right
spacing between the layers of atoms: sodium chloride, calcite, gypsum, for
example.
If the X-ray beam is inclined to the crystal (Figure 6.1) at an angle 0, there
will be a scattering from successive layers of atoms. Because the 'reinforcing'
parallel path lengths differ by 2d sin 0, we have the Bragg Equation,
nh, = 2d sin 8, (6.1)
where 0 is the angle of incidence, d is the distance between layers of crystal
atoms, and n is an integer. Different angles diffract different wavelengths.
Copyright 2002 by Richard E. Chapman