2.4.2. Continuum X-Rays

Continuum radiation (also called bremsstrahlung, "braking radiation") is produced by the deceleration of incident-beam particles. In EMP analysis, incident electrons are slowed to varying degrees by the strong electromagnetic field of the atomic nuclei. Bremsstrahlung is also produced in other particle beam techniques such as PIXE. Particle deceleration results in the production of X-rays with continuum of energies from the highest possible energy (all kinetic energy transformed into a photon and the impinging particle stopped) to lowest energy (no energy transformed). The former case is termed the short-wavelength limit (swl) and may be expressed as:

The probability of producing photons at the short-wavelength limit is very low but increases as the wavelength increases. At low energy, the probability is high, but the number of emitted photons drops off again because low energy continuum radiation is absorbed within the sample. Each incident electron actually undergoes many interactions to produce the continuum. The intensity of the continuum radiation emitted by a decelerating particle is:

Thus, the intensity of the continuum produced by electron bombardment (EMP) is greater than that of comparably accelerated protons (PIXE) because although they experience similar coulombic forces (f), the mass of a proton is 1836x greater. However, protons penetrate more deeply into the sample and will consequently undergo more interactions, producing a slight increase in the intensity of the continuum.

The proportion of the total energy of the electron beam incident upon a sample that is emitted as the continuum in EMP analysis is approximately:

This fraction is very small! A sample of iron (Z = 26) bombarded by 15 keV electrons produces only 0.04% of its energy as continuum X-rays, the rest is dissipated as heat in the sample and, to a very much lesser extent, as characteristic X-rays. Continuum radiation is peculiar to particle (electrons or protons) bombardment; bombarding the sample with X-rays, as in X-ray fluorescence analysis, does not produce the continuum. As a consequence, backgrounds are substantially lower in X-ray fluorescence analysis and element detectabilities better. The X-rays used to bombard the sample in X-ray fluorescence are the continuum radiation produced from the cathode target and the low efficiency of continuum production makes it necessary to cool the X-ray tube.

The intensity of the continuum (I_c) is a function of atomic number (Z) and the energy of interest (E). It may be modeled using Kramer's equation, derived from classical theory in 1923:

Although the intensity of the continuum is proportional to atomic number and beam current, it has the same shape for all values of these. Note also that this model of the continuum has infinite intensity at E = 0. However, this does not occur because X-ray photons with very low energies are absorbed by the sample and converted into heat. As a result, the continuum is humped with intensities decreasing to zero at E = 0 and E = E_o.

Figure 2.4.2a. Continuum X-ray emission. The EDS spectrum at left was accumulated on a small carbon inclusion within meteoritic metal. It shows the typical humped shape of continuum radiation, caused by absorption of the least energetic X-rays. The small peak near channel 622 is due to fluorescence of the enclosing Fe-Ni metal.

The peak in the continuum ( l _max) is located at approximately 1.5 times l _swl. Increasing E_o shifts l _max towards l _swl, l _swl moves to shorter wavelengths, and the overall X-ray output across the continuum increases (Figure 2.4.2b). Thus, increasing the E_o does not improve the peak to background ratio. Increasing the incident current also increases the total X-ray output, but l _max and l _swl remain the same.

Figure 2.4.2b. Effect of changing X-ray tube current (mA), accelerating potential (keV), and target atomic number (Z) on the continuous spectrum.

Continuum radiation does not contain any useful information and limits the minimum detectable amount of an element. In addition, it can create problems in determining the backgrounds for characteristic energy peaks (nonlinearity). At some ranges of E, the continuum has a slight upward curvature (e.g., at Na), elsewhere a downward curvature (e.g., at Zn). If backgrounds for a spectral peak of interest are measured too far from the peak and a linear background interpolation used, the peak intensity will be incorrectly determined. However, if the backgrounds are not taken too far from the peak position and the element analyzed is a major one, a linear approximation for the continuum is adequate. It is during trace-element analysis that backgrounds are most critical and nonlinearity can become a significant problem.

Cartoon by Jason Hooten.

Copyright 1997-2003, James H. Wittke

Last update: 01/18/2006 01:47 PM.