Experimental Method to Determine theAbsolute Efficiency Curve of a WavelengthDispersive SpectrometerJorge Trincavelli,1,2,* Silvina Limandri,1,2Alejo Carreras,2,3and Rita Bonetto2,41Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba, Ciudad Universitaria, 5000, Córdoba,Argentina2Consejo Nacional de Investigaciones Científicas y Técnicas de la República Argentina, Ciudad Universitaria, 5000, Córdoba,Argentina3Instituto de Investigaciones en Tecnología Química, Universidad Nacional de San Luis, CC 290, 5700, San Luis, Argentina4Centro de Investigación y Desarrollo en Ciencias Aplicadas Dr. Jorge Ronco, Calle 47 No257; Facultad de Ciencias Exactas yFacultad de Ingeniería de la UNLP, 1900 La Plata, ArgentinaAbstract: A method for the experimental determination of the absolute efficiency of wavelength dispersivespectrometers was developed, based on the comparison of spectra measured with a wavelength dispersivesystem and w ith an energy dispersive spectrometer. The aim of studying this parameter arises because itsknowledge is necessary to perform standardless analysis. A simple analytical expression was obtained for theefficiency curve for three crystals ~TAP, PET, and LiF! of the spectrometer used, within an energy range from0.77 to 10.83 keV. Although this expression is particular for the system used in this work, the method may beextended to other spectrometers and crystals for electron probe microanalysis and X-ray fluorescence.Key words: detection efficiency, wavelength dispersive X-ray spectrometer, electron probe microanalysis,standardless microanalysisINTRODUCTIONThe detection efficiency « of an X-ray spectrometer is ameasurement of the probability of detecting an emittedphoton; it depends on the photon energy and on certaincharacteristics of the spectrometer. A detailed knowledge ofthis dependence may not be necessary for some analyticalroutine applications involving standards, since the efficiencyis the same for sample and standard, and they cancel out.Nevertheless, a full description of the efficiency is crucial forquantitative standardless analysis as stated by Fournier et al.~1999! and Goldstein et al. ~1994! and for the determinationof atomic parameters; see, for example, Merlet et al. ~2006!,Merlet and Llovet ~2006!, Bonetto et al. ~2004!, and Trinca-vellietal.~2002!. In the particular case of a wavelengthdispersive spectrometer ~WDS!, to have reliable informa-tion of the efficiency becomes a must, due to the greatvariations of this parameter with photon energy, whichcould produce large errors.In wavelength dispersive systems, the spectrum is ac-quired by varying the position of an analyzing crystal,which diffracts the X-rays coming from the sample accord-ing to Bragg’s law. The geometrical ar rangement containsthe X-r ay source ~that is to say, the sample!, the crystal, andthe detector on the perimeter of a circle of radius r, knownas the Rowland circle. The crystal planes are bent to radius2r and the crystal surfaces can be ground to radius r~Johansson geometry! or not ~Johann geometry!. The X-raysdiffracted by the crystal are usually collected by gas-filledproportional counters.For these kind of spectrometers, the efficiency «WDSisdifficult to predict and depends on the quantum efficiencyof the proportional counter, on geometrical factors, and onthe reflectivity of the analyzing crystal. Three semiempiricalmethods to determine «WDSwere reported. One of theminvolves the measurement of characteristic line intensitiesfor different pure elements: the ratio between measuredintensities and the ones predicted by an analytical modelserves as estimation for «WDS~Wernisch, 1985!. In thesecond one, a spectrum is measured for a single-elementsample without characteristic lines in the region of interestand compared with an analytical prediction for bremsstrah-lung ~Smith & Reed, 1981!. The third method, explained byMerlet et al. ~2006! and Merlet and Llovet ~2006!, is similarto the previous one, but the bremsstrahlung emission wasobtained by Monte Carlo simulation.The disadvantage of these methods is that they need agood description of the spectrum, which cannot be givenReceived February 22, 2008; accepted March 25, 2008*Corresponding author. E-mail: [email protected]. Microanal. 14, 306–314, 2008doi:10.1017/S1431927608080379MicroscopyANDMicroanalysis© MICROSCOPY SOCIETY OF AMERICA 2008with the required degree of accuracy; in addition, they arerestricted to electron excitation beams. The third methodinvolves the prediction of bremsstrahlung from thin targetsinstead of thick targets; thus, it is more precise than theother two, although the uncertainties obtained can reach10% for energies around 1 keV.A different strategy was developed in this work, basedon the comparison of two experimental spectr a: one ofthem measured with an energy dispersive spectrometer~EDS! and the other with the wavelength dispersive spec-trometer whose efficiency is to be determined.EXPERIMENTALMeasurements were performed with a scanning electronmicroscope LEO 1450VP at the Laboratorio de MicroscopíaElectrónica y Microanálisis ~LABMEM! of the UniversidadNacional de San Luis, operated in the high vacuum mode,i.e., with a chamber pressure of 0.5 Pa. This equipment isfurnished with an energy dispersive spectrometer EDAXGenesis 2000 with a resolution of 129 eV for the Mn-Kaline ~5.893 keV! and with a wavelength dispersive spectrom-eter INCAWAVE 700.The energy dispersive detector is a Si~Li! SUTW Sap-phire with ultrathin polymer window and aluminum ohmiccontact. The crystal front area is 10 mm2, with a circularcollimator with an aperture of ~7.7 6 0.2! mm2. The dis-tance of this collimator from the source is 6.9 cm. Theultrathin window is a Moxtek AP3.3 containing a 380 mmthick silicon support structure with 77% open area. Thewindow itself is composed of: polymer—300 nm thick,density 1.4 g/cm3~69% C, 3% H, 21% O, and 7% N massconc entrations!; aluminum—30 nm thick, density 2.7 g/cm3;and boron hydride—20 nm thick, density 2.0 g/cm3~92% Band 8% H mass concentrations!. The dead layer thicknesswas estimated to be about ~72 6 17! nm by means of themethod suggested previously by Bonetto et al. ~2001!.The arrangement of the WDS system is Johansson typefor the crystals used in this work: TAP, PET, and LiF. Someof their characteristics are specified in Table 1. The photonsdiffracted by the analyzing crystal are collected by twoproportional