Practical X-Ray Spectrometry

The X-ray region is normally considered to be that part of the electromagnetic spectrum lying between 0.1-100 Å, being bounded by the γ-ray region to the short wavelength side and the vacuum ultra-violet region to the long wavelength side. The actual boundary between the X-ray and vacuum ultra-violet region is not clearly defined and for many years the 50–500 Å mid-region has not been exploited by practical spectroscopists to any great degree. Over the last few years however this wavelength range has been examined both from the short wavelength end by the X-ray spectroscopist and from the long wavelength end by workers in the fields of plasma and astrophysics. It is now common practice to refer to this particular region as the soft X-ray and vacuum ultra-violet region.

The basic function of the spectrometer is to provide a means of isolating a selected wavelength from the polychromatic beam of characteristic radiation excited in the sample, in order that individual intensity measurements can be made. Although this is normally achieved by making use of the specific diffracting property of large single crystals, this is not by any means the only way of selecting a specific wavelength range and other methods which have been employed include the use of diffraction gratings,¹⁾ balanced filters^2-3) and energy resolution in the form of pulse height selection. The usual wavelength range of the conventional X-ray spectrometer is between 0.2 to 15 Å and over this region the single crystal is certainly the most efficient and versatile means of dispersion, particularly in combination with pulse height selection for the removal of harmonic overlap (See Chapter 4). However, the recent successful attempts to extend the operating range of the X-ray spectrometer into the soft X-ray and vacuum ultra-violet region have provided greater incentive for a more detailed study of the use of gratings in this region as well as the exclusive use of pulse height selection. Since measurements in the soft X-ray region invariably require some modification to the commercially available spectrometer, usually by way of modification to the source of primary radiation and the detector, it is the intention to first consider dispersion in the conventional wavelength range and then to discuss the soft X-ray region as a separate topic.

The basic problem of X-ray detection is that of converting the X-rays into a form of energy which can be measured and integrated over a finite period of time. There are numerous ways of doing this and each method depends upon the ability of X-rays to ionise matter. The fundamental difference between the various classes of detector is the subsequent fate of the electrons which are produced by the ionisation process.

Pulse height selection affords a method of isolating a moderately narrow range of wavelengths from a spectrum by virtue of energy separation as opposed to wavelength separation as, for example, in crystal dispersion. By use of a proportional counter each incident wavelength is converted into a voltage pulse or rather a pulse distribution, of characteristic pulse amplitude and the function of the pulse height selector is to allow only a specific and chosen range of pulse amplitudes to pass to the scaling circuits. The idealised principle of such a system is illustrated in Fig. 4.1.

The net intensity of emitted characteristic X-radiation from an element in a matrix is related to the concentration of that element. Fig. 5.1 illustrates the theoretical correlation between the peak intensity R _P of an element with its concentration C. The true background response R _b is given by the intercept of the curve on the ordinate. The slope m of the curve, sometimes called

the calibration factor, is equal to \(\frac{{{{R}_{p}}-{{R}_{b}}}}{C}\) and the concentration is given by

The basis of quantitative X-ray fluorescence spectrometry is to follow the identification of a certain element in a mixture of elements (the matrix) with a measurement of the intensity of one of its characteristic lines, then to use this intensity to estimate the concentration of that element. By use of a range of standard materials a calibration curve can be constructed in which the peak response of a suitable characteristic line is correlated with the concentration of the element. Fig. 6.1 illustrates a typical case where the peak counting rates (R _b ) from a range of elements (1–5) are plotted against the concentration of a certain element i. By fitting the calibration curve parameters into the equation for a straight line it will be seen that the slope of the curve “m” is equal to counts per second per percent and this can be used as a calibration factor for the element in that specific matrix. Once m has been established from standards the net peak minus background response can be divided by m to give the concentration of the element in an unknown but similar matrix. If such a curve were constructed in practice, by an experienced operator using a series of completely homogeneous standards it would be found that, on repeating each measurement a number of times, a certain degree of spread in the count data would occur. This spread is due to certain random errors associated with each reading and would define the precision of the measurement.

The preceding chapters have discussed the various random and systematic errors which can arise during an analysis either from the equipment or from the sample to be analysed and it is the purpose of this section to discuss the methods which are available for reducing these errors to an acceptable value. The first problem is however, to define an acceptable value. Instrumental techniques are invariably adopted for one reason only, this being the inherent speed of the instrumental method compared to classical wet techniques. Since practically all analytical instruments are nothing more than rapid, versatile and frequently very expensive comparison devices, recourse has nearly always to be made to the use of chemically analysed or synthesised standards. Basically no data obtainable by an instrumental technique can be more accurate than that of the standards with which they were compared, although the random errors of the chemical analysis can be reduced by graphical or mathematical interpolation. A calibration graph is thus inherently more precise than its individual points. It is frequently impracticable to start with basic measurements of weight, volume etc. and one must invariably accept either the chemically or synthesised standard as the ultimate limit to the accuracy obtainable, or settle for very precise trend information which may or may not be of comparable accuracy.

Since X-ray spectrometry is essentially a comparative method of analysis, it is vital that all standards and unknowns be presented to the spectrometer in a reproducible and identical manner. Any method of sample preparation must give specimens which are reproducible and which, for a certain calibration range, have similar physical properties including mass absorption coefficient, density and particle size. In addition the sample preparation method must be rapid and cheap and must not introduce extra significant systematic errors, for example, the introduction of trace elements from contaminants in a diluent.

Since X-ray fluorescence spectrometry is essentially a method which counts atoms, the question naturally arises as to what is the minimum number of atoms which are required in order to give a measurable signal above background. Analyses based on the measurement of a small number of atoms fit conveniently into two categories, the first where the number of analysed atoms is small in comparison with the total number of atoms making up the sample i.e. in the analysis of low concentrations and second, where the number of atoms is small because the total sample weight is small i.e. in the analysis of limited quantites of material. These two cases must be considered separately since, as will be seen later, they have little in common.