Physical Principles of Electron Microscopy: An Introduction to TEM ...

168 Chapter 6
a three-dimensional diffraction grating and reflects (strongly diffracts) x-ray
photons if their wavelength � satisfies the Bragg equation:
n� = 2 d sin�i (6.9)
As before, n is the order of the reflection (usually the first order is used), and
� i is the angle between the incident x-ray beam and atomic planes (with a
particular set of Miller indices) of spacing d in the crystal. By continuously
changing � i, different x-ray wavelengths are selected in turn and therefore,
with an appropriately located detector, the x-ray intensity can be measured
as a function of wavelength.
The way in which this is accomplished is shown in Fig. 6-6. A primaryelectron
beam enters a thick specimen (e.g., in an SEM) and generates xrays,
a small fraction of which travel toward the analyzing crystal. X-rays
within a narrow range of wavelength are Bragg-reflected, leave the crystal at
an angle 2�i relative to the incident x-ray beam, and arrive at the detector,
usually a gas-flow tube (Fig. 6-6). When an x-ray photon enters the detector
through a thin (e.g., beryllium or plastic) window, it is absorbed by gas
present within the tube via the photoelectric effect. This process releases an
energetic photoelectron, which ionizes other gas molecules through inelastic
scattering. All the electrons are attracted toward the central wire electrode,
connected to a +3-kV supply, causing a current pulse to flow in the powersupply
circuit. The pulses are counted, and an output signal proportional to
the count rate represents the x-ray intensity at a particular wavelength.
Because longer-wavelength x-rays would be absorbed in air, the detector
and analyzing crystal are held within the microscope vacuum. Gas (often a
mixture of argon and methane) is supplied continuously to the detector tube
to maintain an internal pressure around 1 atmosphere.
To decrease the detected wavelength, the crystal is moved toward the
specimen, along the arc of a circle (known as a Rowland circle; see Fig. 6-6)
such that the x-ray angle of incidence �i is reduced. Simultaneously, the
detector is moved toward the crystal, also along the Rowland circle, so that
the reflected beam passes through the detector window. Because the
deflection angle of an x-ray beam that undergoes Bragg scattering is 2�i, the
detector must be moved at twice the angular speed of the crystal to keep the
reflected beam at the center of the detector.
The mechanical range of rotation is limited by practical considerations; it
is not possible to cover the entire spectral range of interest (� � 0.1 to 1 nm)
with a single analyzing crystal. Many XWDS systems are therefore equipped
with several crystals of different d-spacing, such as lithium fluoride, quartz,
and organic compounds. To make the angle of incidence �i the same for xrays
arriving at different angles, the analyzing crystal is bent (by applying a