For the SiLi detector, the FWHM at energy E is given by FWHME¼ ðFWHM20þ 21:1FEÞ0:5, where FWHM0 is the resolution at energy 0 and F is the Fano factor, which is a measure of the statisti
Trang 1of the Mn Ka peak This measure is chosen because
readily available 55Fe is a source of this X-ray line
For the Si(Li) detector, the FWHM at energy E is
given by FWHME¼ ðFWHM20þ 21:1FEÞ0:5, where
FWHM0 is the resolution at energy 0 and F is the
Fano factor, which is a measure of the statistical
fluctuations in the ionization and charge collection
processes.Table 3lists the performance of a range of
X-ray spectrometers
Other energy-dispersive spectrometer technology
Ger-manium detectors have properties similar to those of
Si(Li) detectors and are preferred for use at higher
energies They are found on AEM, PIXE, and
syn-chrotron X-ray fluorescence (SXRF) instruments The
silicon drift detector (SDD) is based on
charge-coupled semiconductor technology and can provide
energy resolution similar to that of the monolithic
Si-crystal EDS, but at a count rate of 500 kHz
Further-more, an energy resolution of 140 eV can be achieved
at only 13C The detector area can be made as
large as 400 mm2 so that low currents can be used
for high count rates It is possible to count at more
than 1 MHz, but the resolution degrades as the count
rate increases This makes the detector unsuitable for
quantitative analysis but ideal for mapping of mineral
grains
X-Ray bolometry has been developed using
thin-film Ag microcalorimeters, transition edge sensors,
and superconducting quantum interference devices
Such detectors have energy resolutions down to 2 eV
and count rates of only 1 kHz In theory, arrays of
these millimetre-sized devices could be constructed
giving a high overall count rate The operating
tem-perature is 70–100 mK and it is possible to achieve
this using multistage Peltier cooling and an adiabatic
demagnetization refrigerator
Matrix Corrections
X-Ray intensities are measured in units of counts per second per nanoampere of beam current The weight percent concentration of an element in a sample, Csamp, is related to the characteristic X-ray intensity, Isamp, by the equation Csamp¼ Cstd(Isamp/
Istd)([MATRIX]samp/[MATRIX]std), where [MATRIX] denotes the effect of the chemical composition of the matrix on the X-ray intensity and ‘std’ refers to a standard of known composition
There are four approaches to matrix corrections:
1 Empirical methods assume that each element lin-early influences the X-ray intensity of each other element A table of coefficients, analysed element against matrix element, is drawn up using extra-polations from measurements of binary alloys and solid solution series These are known as alpha coefficients
2 The ZAF corrections separately compute the effects of atomic number (Z), absorption (A), and secondary fluorescence (F): ZAF ¼ R/S f(w)(1 þ g), where R is the back-scattering fraction and S is the X-ray generation factor due to stopping power; both of these are functions of atomic number The function of the mass attenuation coefficient, f(w), corrects for the absorption of the X-rays as they pass through the sample towards the detector The additional contribution when a matrix X-ray fluoresces an analysed element (Em>Ec,a) is represented by g
3 The f(rz) methods: f is defined as the ratio of the X-ray intensity from a thin layer, dz, of sample at a mass depth (rz) to the X-ray intensity of a similar layer isolated in space The f(rz) procedures inte-grate this X-ray intensity ratio function, corrected for multicomponent systems, from the surface to a
Table 3 X ray spectrometer devices
Crystal/device a Dispersion method b Resolution FWHM (eV) c
Max practical c ount rate (kHZ) Energy range (keV) Collection area (mm 2 )
a LiF, Lithium fluoride; PET, pentaerythritol; TAP, thallium acid phthalate; WSix, tungsten silicides; Ge, germanium; SDD, silicon drift detector.
b WDS, Wavelength dispersive spectrometry; EDS, energy dispersive spectrometry.
c FWHM, Full width half maximum.
112 ANALYTICAL METHODS/Mineral Analysis