EXCITATION AND NATURE OF X-RAYS; X-RAY SPECTRA
13
1.5. THE CONTINUOUS SPECTRUM
1.5.1. Nature
The continuous spectrum, also referred to as the general spectrum,
white spectrum, continuum, and Bremsstrahlung, is characterized by four
features: a continuous range of wavelengths (analogous to white light)
having an abrupt short~wavelength limit Amin, rising to a maximum intensity
AImax , and falling off gradually at longer wavelengths. The AImax occurs
at '" I.5A min and, for practical purposes, may be regarded as the effective
wavelength of the continuum, that is, a single wavelength having substantially the same absorption in a given absorber as the continuum.
The continuum also has two less prominent features (G13). A second
intensity maximum, very poorly defined compared with AI max , occurs at a
wavelength greater than AImax and different for each target element-for
example, 1.5, 0.9, and 0.8 A for tungsten, copper, and chromium, respectively. The phenomenon is of unknown origin, and is independent of applied
potential. The other feature is an abrupt intensity discontinuity occurring
at the wavelength of the absorption edge of the target element, the intensity
increasing by a factor of 2-5 on the long-wavelength side of the discontinuity.
The phenomenon results from the abrupt change in absorption of the target
for continuous radiation excited below the surface and emerging through
the overlying target layer. The magnitude of the discontinuity increases as
the path length of the x-rays in emerging from the target increases, that is,
as the angle between the incident electrons and target approaches 90° and
as the angle between the emergent x-rays and target decreases.
The continuum may be recorded by directing the primary beam into
the x-ray spectrometer. This may be done by turning the x-ray tube about
its axis or, more conveniently, by placing a piece of paraffin or polyethylene
in the specimen chamber and scattering some of the primary radiation into
the spectrometer.
1.5.2. Generation
The electrons incident upon an x-ray tube target may interact with the
target in any of several ways:
I. They may backscatter from the target toward the general direction
from which they arrived. The fraction so scattered increases with the atomic
number of the target-about half are scattered by the heaviest elements,
very few by the lightest.
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CHAPTER 1
2. They may scatter within the target surface, interacting with the
outermost electrons in the target atoms or with the plasma-the electr.on
"gas" that permeates metals. Many of these valence and plasma electrons
are ejected from the target as low-energy «50-eV) secondary electrons.
Each such interaction extracts 10--100 eV from the incident electron. Most
of the incident electrons that do not backscatter undergo this process.
3. They may undergo Rutherford scatter in the high Coulombic field
near the nuclei of the target atoms. Most such interactions are elastic, that
is, do not result in loss of energy.
4. They may interact with the inner electrons in the target atoms. The
probability of such interactions is small compared with that for process 2
above. This is the process that gives rise to the characteristic line spectrum
of the target element and is the subject of Section 1.6.
5. They may undergo inelastic Rutherford scatter in passing near target
atoms without collision, giving up some or all of their energy (speed) as
x-ray photons. At the potentials involved in practical x-ray spectrometry
«100 kV), only 0.5-1% of the electrons bombarding the target undergo
this process. This is the process that gives rise to the continuum and is the
subject of this section.
The effect of acceleration potential and target atomic number on the
extent of electron scatter within the target surface is discussed in Section 21.7
and shown in Figure 21.14.
The continuous spectrum, then, arises from the relatively few electrons
that undergo stepwise inelastic nuclear scatter and deceleration in the target.
The continuous spectrum arises when high-speed electrons undergo
stepwise deceleration in matter (hence the German term Bremsstrahlung,
which means, literally, "braking radiation"). p-ray, internal-conversion,
photo, Compton-recoil, and Auger electrons all produce continuous x-rays,
but x-ray tubes are the principal source. X-ray tubes are discussed later;
let it suffice here to say that electrons from a hot tungsten filament are
accelerated by a positive potential of up to 100 kV to a metal target, where
they undergo deceleration with consequent generation of continuous xradiation. Deceleration of other high-speed particles, such as protons,
deuterons, tritons, a-particles, and heavier ions, does not generate observable continuum (Section 1.8). However, a very low-intensity continuum
may be generated by electrons ejected from target atoms by ion collision.
The continuum cannot be generated by secondary excitation, that is,
by irradiation of matter with high-energy x-rays, because photons do not
undergo stepwise loss of energy. However, continuum may appear in
EXCITATION AND NATURE OF X-RAYS; X-RAY SPECTRA
15
secondary x-ray beams due to scatter of incident continuum from the
specimen and to generation by photo, recoil, and Auger electrons resulting
from interaction of the incident x-rays with the specimen.
1.5.3. Short-Wavelength Limit
Consider an electron moving from filament to target in an x-ray tube
operating at (peak) potential V. The shortest wavelength Amin that this
electron can possibly generate is emitted if the electron decelerates to zero
velocity in a single step, giving up all its energy as one x-ray photon. The
energy Ee gained by the electron between filament and target is
Ee= eV
(1.21 )
where e is the electronic charge in electrostatic units, and V is potential in
volts. The energy of the x-ray photon Ez is [see Equation (1.16)]
Ez = he/Acm
If the electron gives all its energy to the photon,
(1.22)
and
he/AcID = eV
(1.23)
giving
Acm
= he/eV
(1.24)
Substituting the same values and conversion factors as were used in Equation (1.17), one gets
(1.25)
.1.= l2,396/V
where A is in angstroms, V in (practical) volts.
Equation (1.25) is the Duane-Hunt law (D28). It permits the calculation of the Duane-Hunt limit or short-wavelength limit Amin (angstroms)
for an x-ray tube operating at any specified potential V (volts), and of the
minimum potential at which an x-ray tube must be operated to produce a
specified wavelength. However, if this wavelength is to be generated at high
intensity, the x-ray tube must be operated at a potential several times that
indicated by the equation (Section 1.5.5). When Equation (1.25) is applied
to an x-ray tube operating from a full-wave supply, V is peak potential.
The analogy of Equations (1.25) and (1.18) is evident. Many workers use
the symbol .1.0 or AswL (for short-wavelength limit) instead of Amin.