X-ray characteristic lines

Measurements of the characteristic X-ray line spectra of a number of elements were first reported by H. G. J. Moseley in 1913. He found that the square root of the frequency of the various X-ray lines exhibited a linear relationship with the atomic number of the element emitting the lines. This fundamental Moseley law shows that each element has a characteristic X-ray spectrum and that the wavelengths vary in a regular fiishion form one element to another. The wavelengths decrease as the atomic numbers of the elements increase. In addition to the spectra of pure elements, Moseley obtained the spectrum of brass, which showed strong Cu and weak Zn X-ray lines this was the first XRF analysis. The use of XRF for routine spectrochemical analysis of materials was not carried out, however, until the introduction of modern X-ray equipment in the late 1940s. 

Table 2.2 lists the energies and line-widths of the characteristic X-ray lines from a few possible candidate materials. In practice Mg Ka and A1 Ka are the two used universally because of their line energy and width and their simple use as anode material. 

It has always been difficult to do quantitative work with the characteristic x-ray lines of elements below titanium in atomic number. These spectra are not easy to obtain at high intensity (8.4), and the long wavelength of the lines makes attenuation by absorption a serious problem (Table 2-1). The use of helium in the optical path has been very helpful. The design of special proportional counters, called gas-flow proportional counters,20 has made further progress possible, and it is now possible to use aluminum Ka (wavelength near 8 A) as an analytical line (8.10). 

This technique can be applied to samples prepared for study by scanning electron microscopy (SEM). When subject to impact by electrons, atoms emit characteristic X-ray line spectra, which are almost completely independent of the physical or chemical state of the specimen (Reed, 1973). To analyse samples, they are prepared as required for SEM, that is they are mounted on an appropriate holder, sputter coated to provide an electrically conductive surface, generally using gold, and then examined under high vacuum. The electron beam is focussed to impinge upon a selected spot on the surface of the specimen and the resulting X-ray spectrum is analysed. 

Both characteristic X-ray line and continuous spectra were used to evaluate the performances of the resists. To determine exposure parameters (i.e. sensitivity and contrast) irradiations were carried gut in this study using the aluminum Kot- 2 emission line at 8.3t A generated by means of a modified Vacuum Generators Limited model EG-2 electron beam evaporation gun. The resist samples were exposed through a mask (A) consisting of a range of aluminum foils of different thicknesses supported on an absorbing nickel frame in order to vary the X-ray flux. 

As we have seen in Chapter 1, we need something near a plane wave in order to see the finest details of the specimen stracture. A single-axis diffractometer utilises a beam that is very far from a plane wave. Thus, single-crystal rocking curves are broadened due to the beam divergence, and the spectral width of the characteristic X-ray lines. 

Luo et al. [83] used an ANN to perform multivariate calibration in the XRF analysis of geological materials and compared its predictive performance with cross-validated PLS. The ANN model yielded the highest accuracy when a nonlinear relationship between the characteristic X-ray line intensity and the concentration existed. As expected, they also found that the prediction accuracy outside the range of the training set was bad. 

X-ray fluorescence spectrometry (XRF) is a non-destructive method of elemental analysis. XRF is based on the principle that each element emits its own characteristic X-ray line spectrum. When an X-ray beam impinges on a target element, orbital electrons are ejected. The resulting vacancies or holes in the inner shells are filled by outer shell electrons. During this process, energy is released in the form of secondary X-rays known as fluorescence. The energy of the emitted X-ray photon is dependent upon the distribution of electrons in the excited atom. Since every element has a unique electron distribution, every element produces... 

FIGURE 18 Average crystallite size measurement by X-ray line broadening. The width of characteristic X-ray lines decreases markedly as cerium dioxide powder is sintered. The crystallites grow from an initial size of 50 to 400 A after heating in air for several hours. 

E is the energy of characteristic X-ray line and Fisa constant called the Fano factor, which has a value of 0.12 for Si(Li). electronic noise factor, plays an important role in the resolution. Reduction of the electronic noise will improve the resolution of the EDS detector. Thus, the Si(Li) diode and the preamplifier are mounted in a cylindrical column (the cryostat) so that they can operate at the temperature of liquid nitrogen (-196°C) in order to reduce the electrical noise and increase the signal-to-noise ratio. 

There are three main matrix effects in XRF primary absorption, secondary absorption and secondary fluorescence. Primary absorption refers to the radiation that is absorbed on the beam s path to reach the atoms to be excited. Secondary absorption refers to absorption of fluorescent radiation from atoms that occur along its path inside the specimen to the detector. Secondary fluorescence refers to the fluorescent radiation from the atoms which are excited by the fluorescent radiation of atoms with a higher atomic number in the same specimen. This phenomenon is possible when energy of the primary fluorescent radiation from heavier atoms is sufficient to excite secondary fluorescence from lighter atoms in the specimen. The absorption effects reduce the intensity of characteristic X-ray lines in spectrum, while secondary fluorescence increases the intensity of lighter elements. The matrix factors of EDS analysis in an electron microscope (EM) are described later in Section 6.8. 

The characteristic x-ray lines were discovered by W. H. Bragg and systematized by H. G. Moseley. The latter found that the wavelength of any particular line decreased as the atomic number of the emitter increased. In particular, he found a linear relation (Moseley s law) between the square root of the line frequency v and the atomic number Z ... 

It is important to note that for all but the lightest elements, the wavelengths of characteristic X-ray lines are independent of the physical and chemical state of the element because the transitions responsible for these lines involve electrons that take no part in bonding, Thus, the position of the Ku lines for molybdenum is the same regardless of whether the target is the pure metal, its sullide. or its oxide... 

Because of the limited penetration of characteristic x-ray lines from the source, most samples can be assumed to be infinitely thick that is, the intensity of the measured x-ray fluorescence line will not increase if the sample thickness is increased. For infinitely thick samples, the intensity of fluorescence from element x is related to concentration by the relationship... 

The best way of obtaining such a source is to make use of the characteristic x-rays from an x-ray anode. However, it is a well known fact that characteristic x-ray lines have a finite width or energy spread. Such widths decrease with decreasing atomic number. It should be noted also that K x-ray lines are preferable as excitation... 

Henry Moseley, a young graduate student working at Cambridge, UK, in 1913, discovered the relationship between wavelength for characteristic X-ray lines and atomic number. After recording the X-ray spectra from numerous elements in the periodic table, he deduced the mathematical relationship between the atomic number of the element and the wavelength of the K line. A similar relationship was found between the atomic number and the Kp line, the L line, and so on. The relationships were formulated in Moseley s Law, which states that... 

The discussions above show that each component of the energy spectrum as a poissonian distribution, and the sum of any number of components also has a poissonian distribution. This also means that the i-th component can be considered to be defined by a channel at energy Ei in the multichannel analyzer memory. If the ni counts in each of s adjacent channels are summed to arrive at the total counts within a peak associated with a particular characteristic x-ray line, then the number of counts in the peak can be reported as... 

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