A Large-Aperture X-Ray Monochromator with Stepped Surface

Transcription

1 Instruments and Experimental Techniques, Vol. 45, No. 6, 00, pp Translated from Pribory i Tekhnika Eksperimenta, No. 6, 00, pp Original Russian Text Copyright 00 by Latush, Mazuritsky, Soldatov, Marcelli. GENERAL EXPERIMENTAL TECHNIQUES A Large-Aperture X-Ray Monochromator with Stepped Surface E. M. Latush*, M. I. Mazuritsky*, A. V. Soldatov*, and A. Marcelli** *Rostov State University, ul. orge 5, Rostov-on-Don, Russia **Laboratori Nazionali de Frascati, Istituto Nazionale di Fisica Nucleare, Frascati, Italy Received February 13, 00; in final form, May 13, 00 Abstract An X-ray monochromator consisting of four bent cylindrical quartz crystals is described. In comparison with a single-crystal monochromator, this device offers a 3.3-fold increase signal intensity and a slightly (1.5 times) worse resolution. Electron probe microanalyzers generate characteristic X-ray radiation in a small volume of the sample. In this case, the area of the radiating surface is ~1 µm. For distances of the order of 0.5 m, this X-ray source can be considered as a point source. Application of the X-ray spectral microanalysis requires both a high intensity and good spectral resolution. These parameters are the most important characteristics of a spectrometer. Existing monochromatic crystals and X-ray optics schemes can improve one of these characteristics at the expense of degrading the another characteristic [1, ]. In this work, we present the results of the experimental validation of a new large-aperture stepped monochromator using four bent cylindrical quartz (10-11) crystals. The monochromator is designed for a Camebax-micro X-ray microanalyzer. The fundamental characteristic of any spectrometer is its spectral resolution ρ = λ/λ. Its value is determined by the range of the Bragg angles θ (the angle between the incident ray and the corresponding atomic plane of the crystal) as where λ is the radiation wavelength and θ is the Bragg angle. The better the resolution, the greater the amount of information that can be extracted from X-ray spectra; i.e., the experiment can discover closely spaced lines (details of the fine structure) of the X-ray spectrum. The resolution θ depends on the degree of mosaicity (imperfection) of the used crystal monochromator, the X-ray spectral decomposition method, and the size of the reflecting Bragg surface of the crystal. It is well known that an efficient tool for obtaining the X-ray spectra of point sources (whose dimensions are far less than the distance to the crystal monochromator) are cylindrically or spherically bent crystals (fabricated according to the Johann method, Johansson method, etc.). In this case, the aperture of the crystal is determined by the solid angle Ω at which the reflecting surface can be viewed from the position of the radiation source. The aperture is another fundamental characterρ = λ/λ = θcotθ, (1) istic of the spectrometer. Larger aperture increases the spectrometer brightness. However, it decreases the spectral resolution. In practice, a compromise between these most important parameters (the required resolution and the spectrum intensity satisfactory for particular experimental conditions) is sought. The diffractor aperture is determined by the area of the crystal reflecting surface. The working surface is located inside the diffraction (Bragg) reflection region. The diffraction zone or the diffraction reflection region is the ensemble of points on the crystal surface for which, in a given range of wavelengths λ λ λ' λ + λ, the grazing angle θ' lies within the limits θ θ θ' θ + θ. In practice, the crystal is chosen so that its intrinsic mosaicity θ c is less than θ. Obviously, the wider the diffraction zone, the greater θ and, consequently, the larger the diffractor aperture. A direct image of the diffraction zone, representing the locus of rays incident on the crystal at a certain angle, cannot be obtained; however, a numerical computer modeling is possible. In [3], images of diffraction zones calculated by the Monte Carlo method for different bends (cylindrical, spherical, toroidal, etc.) of the crystal are presented. It is shown that different types of curvature substantially change the shape of the Bragg zone. Figure 1 depicts diffraction zones on the surface of the planar, cylindrical, and spherically bent crystals which were calculated by the numerical computer modeling. Axes X and are the crystal dimensions normalized to the radius of the focal circle. The monochromatic radiation is reflected from the surface bounded by the diffraction zones shown in Fig. 1. The effective aperture of the crystal monochromator is proportional to its reflecting area. Figure 1 shows variations in the shapes of diffraction zones caused by changes in the parameter ρ. Outer contours of all diffraction zones bound the reflecting surface with ρ = 10 3 and the dark figure inside this area is the diffraction reflection zone with ρ = Similar data are presented in [4, 5]. The special stepped shape of the reflecting surface of the X-ray monochromator (Fig. ) allows us to obtain high-intensity X-ray spectra without a loss of the /0/ $ åaik Nauka /Interperiodica

2 80 LATUSH et al (a) (b) X X (c) (d) X X Fig. 1. Diffraction zones on the surface of the monochromatic crystal: (a) planar crystal; (b) Johann s cylindrical bend; (c) spherical bend; and (d) Johansson s cylindrical bend. spectral resolution. A mathematical description of this stepped shape of the reflecting surface is given in [6, 7]. Each step of the previously fabricated holder is a part of the cylindrical (or spherical) surface of the fixed radius with an attached bent crystal. Illuminating simultaneously several cylindrically (or spherically) bent crystals mounted on the same holder, we increase the monochromator brightness. Axes of symmetry of all crystals pass through the point O perpendicularly to the plane of the focal circle (Fig. 3). The radius of curvature of the central step (marked with zero index) in the plane of the focal circle is set equal to the doubled radius of the focal circle containing the source, the top of the central crystal, and the detector. The radii of curvature of the following steps decrease with the distance from the center. In polar coordinates centered at the point O, the middle point of each step lying on the focal circle is determined by the angle α i and radius R i as i R i = cosα i, = N, ( N 1),, 0, N 1, N ). () The section of the step by the plane of the focal circle is a circular arc of radius R i = OA i, where A i is the middle point of the ith step and α i = A 0 OA i. Evidently, the Bragg condition is satisfied exactly at the center of each step; i.e., the outgoing ray from the point S forms the Bragg angle θ with the tangent line drawn at the point A i. The deviation of the angle of incidence of the X-ray radiation occurring at other points of the crystal equals θ i ; i.e., it is caused by the finite value of angle ϕ i = A i OB i. Parameters θ i and ϕ i (the angular half-width of the ith step measured with respect to the point O) are related by the formula [7] θ i ( ϕ i tanα i )/( tanθ + tanα i ). (3) The spectral resolution of the whole monochromator is determined by the largest θ i. The total aperture of the monochromator is the sum of apertures of all steps. In the model of the stepped monochromator, when ϕ = const, the total aperture of the monochro-

3 A LARGE-APERTURE X-RAY MONOCHROMATOR 81 P(X, Y, ) A 0 B 0 A 1 A D 1 1 B 1 C1 S Y O' B A O' D A B C O X Fig.. X-ray optics layout for the spectral decomposition of radiation with the use of a stepped diffractor. S is the position of the X-ray source, D is the position of the detector, and P(X, Y, ) is an arbitrary point at the crystal monochromator surface. D S O D mator with (N + 1) steps is determined by the equation Ω ω ( N + 1) i = N i = N i = N i = N cosα i ) (4) where H is the height of the diffractor along the -axis and ω = B N OB N is the angular dimension of the stepped monochromator in the plane XOY. After changing to N (ρ 0) and α 0, we obtain the following definite integral: Ω (5) Three mathematical models of different stepped X-ray monochromators are detailed in [7]. The test results for the first prototype fabricated from mica crystals are given in [8]. In this paper, we present experimental test results for an operating stepped monochromator based on quartz crystals. A general view of the stepped monochromator with cylindrically bent quartz (10-11) crystals (d = Å) is shown in Fig. 4. The 0.17-mm-thick crystals were glued to the surface of a metal holder. The holder was fabricated using the results of the computer modeling carried out in accordance with the mathematical model ( ϕ = const) described elsewhere [7]. The radius of the spectrometer focal circle is 160 mm, and the height of the diffractor is 14 mm. The monochromator is asym- α i cosα α, i ) ω/ ω/ α i cosθ dα cosθ sinθ 1 + cos( θ sin( θ+ ln cos( θ+ ω/ ω/. Fig. 3. Model of the stepped diffractor in the plane of the focal circle. Fig. 4. General view of the pseudocylindrical stepped diffractor fabricated for Camebax-micro microanalyzer. metric and contains four cylindrically bent crystals forming four steps with a total width of 7 mm. In Fig. 4, the second step on the left is the central step of the diffractor. The experimental validation was performed in the spectrometric channel of the Camebax-micro X-ray spectrum analyzer (France). The experiments were carried out at the Physics Research Institute of the Rostov State University using radiation of the Mo and Sn L α emission lines (Fig. 5). The range of Bragg angles was determined by the positions of the Sn L β line (θ = ) and the Mo L α line (θ = ). Experimental values of parameter ρ corresponding to Mo and Sn L α lines of the radiation diffracted by the central crystal

4 8 LATUSH et al. Rel. intensity 100 (a) (b) Mo L α Sn L α Mo L β Sn L β E, kev Fig. 5. Emission spectra of (a) Mo and (b) Sn obtained with the help of the stepped diffractor using quartz (10-11) crystals. Curves 1 and are the spectra obtained from four and one (central) crystal, respectively. were 10 3 and 10 3, respectively. Corresponding spectra are shown in Fig. 5 (dashed lines). For the whole monochromator containing four cylindrically bent crystals, the sparameter ρ was for the Mo line and for the Sn line. These spectra are depicted by solid lines. A certain deterioration of the spectral resolution of the four-crystal monochromator in comparison with that of the single crystal device is caused by either the holder fabrication errors or the quality of the gluing of the quartz crystals to the stepped metal surface. The intensity of the spectrum maxima increased 3.3 times, which approximately corresponds to our theoretical estimates (to the ratio of the monochromator aperture to the aperture of the central step). The analysis revealed that the basic cause of the increased ρ in the stepped monochromator is the misalignment of the axes of symmetry of cylindrically bent quartz crystals. This means, for example, that, in the plane of the focal circle (see Fig. 3), one or several arcs B i A i D i have centers shifted from the point O by distances x and y along the OX and OY axes, respectively. The formulas relating the allowable error of the relative shifts x to y of cylinders' axes and the spectral resolution have the following form: x = ρrcos α i tanθ; y = ρrsinα i cosα i tanθ, (6) where R is the radius of curvature of the crystal attached to the central step. In our case, the relative shifts of the second step (α = 0.06 rad and R = 30 mm) are x = 0.6 mm and y = 0.04 mm. Bent quartz crystals were pressed against the surface of the metal holder and glued with an epoxy adhesive. Evidently, this technology cannot result in such a great (0.6 mm) shift along the OX axis. Hence, we may deduce that, in this case, the main source of this error is technological inaccuracies arising in the course of fabrication of the base: the stepped cylindrical surface of the metal holder. Replacing the cylindrically bent quartz monocrystal with the stepped monochromator containing four crystals resulted in a 3.3-fold gain in the intensity with the retained value of parameter ρ, which confirms the efficiency of this approach. ACKNOWLEDGMENTS This work was a part of the joint cooperation project carried out by the Rostov State University (Russia) and

5 A LARGE-APERTURE X-RAY MONOCHROMATOR 83 Frascati Laboratory (LNF, INFN, Italy; project MUST). It was also supported by the Ministry of Education of Russian Federation, grant REFERENCES 1. Bonnelle, C. and Mande, C., Advances in X-Ray Spectroscopy, Oxford: Pergamon, Reed, S.J.B., Electron Microprobe Analysis, Cambridge: Cambridge Univ. Press, 1997, p Mazuritskii, M.I., Soldatov, A.V., Latush, E.M., and Lyashenko, V.L., Pis ma h. Tekh. Fiz., 1999, vol. 5, no. 19, p Wittry, D.B. and Sun, D.B., J. Appl. Phys., 1990, vol. 67, no. 4, p Fraenkel, B.S., Bitter, M., von Goeler, S., et al., J. X-Ray Sci. Technol., 1997, vol. 7, p Marcelli, A., Soldatov, A.V., and Mazuritsky, M.I., UE Patent no , 1997 (Jpn. Patent no /97, 1997; US Patent no. 09/06348, 1998). 7. Mazuritskii, M.I., Latush, E.M., Soldatov, A.V., et al., Pis ma h. Tekh. Fiz., 000, vol. 6, no. 1, p Mazuritskii, M.I., Soldatov, A.V., Lyashenko, V.L., et al., Pis ma h. Tekh. Fiz., 001, vol. 7, no. 1, p..