112 ANALYTICAL METHODS/Mineral Analysis Table X ray spectrometer devices Crystal/devicea Dispersion method b Resolution FWHM (eV)c Max practical c ount rate (kHZ) Energy range (keV) Collection area (mm2) LiF PET TAP WSix Si(Li) Ge SDD Bolometer WDS WDS WDS WDS EDS EDS EDS EDS 4 100 90 110 50 50 50 40 20 20 500 1.5 0.8 0.2 (0.3) 1 0.2 300 300 300 300 10 10 100 0.5 10 200 190 250 10 12 2.2 0.9 20 40 20 1200 1200 1200 1200 30 30 400 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 of 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 FWHME ¼ FWHM20 ỵ 21:1FEị0:5, where FWHM0 is the resolution at energy and F is the Fano factor, which is a measure of the statistical fluctuations in the ionization and charge collection processes Table lists the performance of a range of X-ray spectrometers Other energy-dispersive spectrometer technology Germanium 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 synchrotron X-ray fluorescence (SXRF) instruments The silicon drift detector (SDD) is based on chargecoupled semiconductor technology and can provide energy resolution similar to that of the monolithic Sicrystal EDS, but at a count rate of 500 kHz Furthermore, an energy resolution of 140 eV can be achieved at only À13 C 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 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 thinfilm Ag microcalorimeters, transition edge sensors, and superconducting quantum interference devices Such detectors have energy resolutions down to eV and count rates of only kHz In theory, arrays of these millimetre-sized devices could be constructed giving a high overall count rate The operating temperature 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 Csamp ¼ 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: Empirical methods assume that each element linearly influences the X-ray intensity of each other element A table of coefficients, analysed element against matrix element, is drawn up using extrapolations from measurements of binary alloys and solid solution series These are known as alpha coefficients The ZAF corrections separately compute the effects of atomic number (Z), absorption (A), and secondary fluorescence (F): ZAF ẳ R/S f(w)(1 ỵ 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 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 integrate this X-ray intensity ratio function, corrected for multicomponent systems, from the surface to a