Multi-stepped diffractor constructed with constant step width angle (multi-stepped monochromator)

Abstract: A diffractor for electromagnetic radiation is based on a pseudo-spherical stepped geometry designed under the constant step width conditions. The diffractor consists of a few small pseudo-spherical curved dispersive elements (oriented crystal surfaces or gratings) that are located on a focal circle. The location on the focal circle of each element is made to guarantee the same Bragg angle for the incident radiation. Thus a diffractor is an array of diffracting elements ("steps"), each one contributing to the total solid angle of the diffractor, that increase the spectral output of the device without decreasing the resolution. Scheme and parameters of different devices based on the analysis of x-rays secondary are described.

Description: The present invention relates to a diffractor for electromagnetic radiation, such as x-rays, or neutrons. More particularly, the diffractor is based on a multi-stepped geometry, wherein each dispersive step subtends a constant step width angle as seen from the source. An aim of the invention is to provide a diffractor specially dedicated to the x-rays range, based on a multi-stepped geometry directed to replace the plane or curved crystals in apparatus like x-ray microanalyzer, x-ray photoelectron, spectrometer for chemical analysis, ecc. For this purpose, the diffractor according the present invention consists of a few small spherical curved dispersive elements (oriented crystal surfaces or gratings) that are located on a focal circle. The location on the focal circle of each element is made to guarantee the same Bragg angle for the incident radiation. Thus a diffractor according to the present invention is an array of diffracting elements ("steps"), each one contributing to the total solid angle of the diffractor, that increases the spectral output of the device without decreasing the resolution. In many spectral devices characteristic radiation is generated by a small area of the sample surface. In such a case the source can be considered point like. In this case the conventional energy dispersive focusing technique is made either by cylindrical curved crystal [Advances in X-Ray Spectroscopy, Eds. C. Bonnelle, C. Mande, (Oxford, U.K., 1982)] or by doubly curved, on spherical or toroidal surfaces, crystal monochromators [US Patent 4,882,780; US Patent 4,807,268]. These diffractors focus the monochromatic radiation onto the entrance detector slit. According to the Bragg's equation, the spectral resolution Δλ/λ depends both on Θ and ΔΘ: Δλ/λ=ΔΘ/tanΘ The intensity of the monochromatic radiation is proportional to the area of the diffractor surface, that reflects x-rays under the given Bragg's angle Θ within the range ±ΔΘ. However, increasing the reflecting area, a widening of the aperture ratio of the diffractor occurs associated to a simultaneous decrease of the spectral resolution. In the last decade analytical investigations of the shape and size of the reflecting area of a crystal-monochromator surface, employing different focusing methods have been carried out [D.B. Wittry and S. Sun, J. Appl. Phys. 67, 1633 (1990); D.B. Wittry and S. Sun, J. Appl. Phys. 68, 387 (1990); D.B. Wittry and S. Sun, J. Appl. Phys. 69, 3886 (1991); D.B. Wittry and S. Sun, J. Appl. Phys. 71, 564 (1992); W.Z. Chang and D.B. Wittry, J. Appl. Phys. 74, 2999 (1993)]. Indeed, x-ray diffractors with double curved crystal provide significantly greater aperture ratio compared to that based on the cylindrical Johann or Johannson geometries. For such devices assuming an incidence angle Θ>20° and a crystal height of L<0.1R, the reflecting surface projection on the XZ plane is rectangular and the projection on the focal circle plane (XY plane) is an arc of radius R=2r, where r is the focal circle radius. The knowledge of the shape of the reflecting surface allows an estimation of the parameters of a spherical diffractor designed with a stepped surface [D.B. Wittry and S. Sun, J. Appl. Phys. 69, 3886 (1991)] and in the case of constant step height, the aperture of this diffractor is larger than a spherical curved crystal. It is an object of the present invention to provide a stepped diffractor according to claim 1, which is based on the physical condition that each single dispersive element of the diffractor subtends a constant step width angle as seen from the source. With such design the efficiency of the diffractor is maximised and it is greater than both a spherical diffractor [US Patent 4,882,780; US Patent 4,807,268] and a stepped diffractor constructed under the constant step height condition [D.B. Wittry and S. Sun, J. Appl. Phys. 67, 1633 (1990)]. A better acknowledgement of the invention will be obtained with the subsequent detailed description and with referring to the accompanying drawings. In the drawings: Figure 1 is a pictorial view of a three steps (because of the symmetry there are really five steps) diffractor; Figure 2 is a detailed view of the upper part of a single step of the diffractor (the bottom part of a step is the same according to the symmetry with respect to the focal plane; Figure 3 is the topography of the reflecting area of the radiation focused by the. diffractor surface under different Bragg angle deviation (see text); Figure 4 is the scheme of a stepped surface diffractor under the ϕ=constant condition (ϕ is the half width-angle of the i-th step) in the focusing circle plane; Figure 5 is a diagram of the gain obtained by replacing a spherical diffracting crystal as that reported in the publication: "W.A.Caliebe et al., Rev. Sci. Instrum. 67 (1996) pag..3359" with a multi stepped diffractor using Ge crystal with. different reflecting planes at the energy of Cr-K β ; and Figure 6 is the same as Fig. 5 using Si crystal with different reflecting planes. Fig.1 shows a scheme of a three step device (actually the array is formed by five elements because of the symmetry). The shadowed areas show the reflecting surface of each step of the device placed on the Rowland circle of radius R. Figure 2 shows in more details the upper part of a single diffracting element (step) of the diffractor (the bottom part of the step is omitted according to the fact that there is a symmetry with respect to the focal plane). In addition in Fig. 3 is shown the calculated topography of the radiation focused on the diffractor surface under different Bragg angle deviations. As the deviations from the Bragg angle lead out of the Bragg's conditions, such deviations result in a lower resolution. Three areas are reported in Fig. 3 that produce different spectral resolutions (the darker area corresponds to the higher resolution). The results of Fig. 3 are very important to the understanding of the gain in the spectral output of the present device when compared with a spherical bent diffracting monocrystal like those in US Patent 4,882,780 and US Patent 4,807,268. Indeed, this figure shows that only a small region (with the form of a butterfly) of the entire surface contributes to the high resolution reflection of the electromagnetic radiation. Therefore, it is necessary, in ordinary device, to limit the reflecting area of the crystal to get a high spectral resolution, clearly in contrast with the need to use a large area to increase the throughput. In the present multi stepped geometry the special geometric design allows to enhance the contribution of the central and best part of the topography (the dark butterfly) increasing the number of the diffracting elements. Thus we can obtain both high resolution condition for all the surface of the diffractor, and an increase of the total solid angle. Finally, Fig. 4 presents the scheme of the stepped surface diffractor in the focal plane with all parameters used for the calculation of the theoretical parameters of the device. In the XZ plane each step is a curved strip along z-axis of length L (crystal height). It lies on a spherical surface of radius R i where R i =OA i , O' is the centre of the focal circle and h i =B i D i is the height of the i-th step. Here ϕ is the half width-angle of the i-th step in the focal circle plane. In particular, OA 0 =R 0 =2r; where r is the focusing circle radius; A i is the point of intersection between the i-th step surface and the focal circle; OA i is the curvature radius of the i-th step; S is the focusing point; E i B i is the part of the i-th step shadowed by the (i+1)-th step. In the plane of Fig. 4 the steps are shown by the arcs 2ϕ i =2(A i B i ), where i=0, 1,..., N. In the following, the equations to calculate this diffractor scheme are discussed. The value of the Bragg angle deviation ΔΘ is calculated for given magnitudes of: λ, Δλ and Θ. The initial value ϕ 0 =γ 0 was determined by using the equation (see D.B. Wittry and S. Sun, J. Appl. Phys. 67, 1633 (1990)) 2ΔΘ = X 2 cotΘ + X 3 cot 2 Θ - XZ 2 cot 2 Θ The Eq. (2) determines the co-ordinates of the boundaries of the reflection area on the spherical crystal surface. The radius R 0 =2r establishes the curvature of the central step. One time fixed the focal circle radius r, the parameters of the remaining steps are evaluated with the following formulae: R i = R i-1 sin(γ i-1 )/sin(Δ i ) tan(α i ) = (R 0 2 - R i 2 ) / R i γ i = α i + ϕ i ϕ i = α i - Δ i where α i =A 0 OA i , Δ i =A 0 Od i-1 , γ i =A 0 OB i and ϕ i =A i OB i (i≥ 1). In the present work Δ i is evaluated by using an iterative method according to the condition ϕ =constant. The source is placed on the focal circle and the half width angle of the diffractor on the focal plane, excluding the areas where shadow effect occurs, is given by: Ω =2(Ω 0 + ΣΩ i ) where Ω 0 =A 0 SE 0 and Ω i =D i-1 SE i . Taking into account the increase of the angle width of the reflecting surface, the diffractor aperture ratio is given by the central step aperture times the factor Ω/Ω 0 . The ratio Ω/Ω sp (where Ω sp is the solid angle of a spherical monocrystal diffractor [US Patent 4,882,780; US Patent 4,807,268] and Ω is the solid angle of the multi stepped diffractor here described) is an actual estimation of the gain of this device when compared with an ideal spherical crystal device with the same focal circle and size. For a better understanding of the advantages of the diffractor according to the present invention, the performances of the present device with previous stepped diffractor constructed under the constant step height conditions [D.B. Wittry and S. Sun, J. Appl. Phys. 69, 3886 (1991)] are hereinafter evaluated. In order to compare these two designs we performed calculations with the same set of parameters of D.B. Wittry and S. Sun, J. Appl. Phys. 69, 3886 (1991), i.e., focal circle radius r=50 mm, Bragg's angle Θ=22.76°, h=0.15 mm and central step half-width A 0 B 0 =3.87 mm. For the h=constant condition when the step number increases its size decreases. As a consequence, a diffractor aperture based on the ϕ=constant condition is slightly bigger. Although the number of steps are the same in both cases, for i=7, B x increases from 15.05 mm to 38.60 mm, moreover, the solid angle of the present diffractor is about 5 times larger than a stepped diffractor under constant step height conditions. For practical applications, as already described before, a fundamental property of this device is that the increase of the aperture ratio does not determine a reduction of the resolution. Indeed, the latter combines both high aperture ratio and high resolution at the same time. This really unique condition is fulfilled for different Bragg's angles and focal circle radii. In the resolution range of 5·10 -5 <Δλ/λ<10 -4 that corresponds to the range of the more recent high resolution spectrometers [V. Stojanoff, K. Hämäläinen, D.P. Siddons, J.B. Hastings, L.E. Berman, S. Cramer, G. Smith, Rev. Sci. Instrum. 63, 1125 (1992)], that also coincide with the typical silicon rocking curve width (5") in the angular range 25°<Θ<45°, [T. Matsushita and H.-O Hashizume, in: Handbook on Synchrotron Radiation, ed. E.E. Koch (North-Holland, Amsterdam, 1983) p. 261.] the average value of the aperture for this device is in all the range greater than 0.058 sr with fluctuations of about 15%. Another example of x-ray monochromator based on the present type of diffractor is illustrated at the energy of the Ce L 2 -edge (λ=2.012 Å). With a resolution of - 9*10 -5 and a focal circle radius of R=400 mm, a device constructed with thin Si (220) crystals collects a solid angle 50 times greater than a spherically curved crystal [US Patent 4,882,780; US Patent 4,807,268]. Other kind of x-ray instruments are those used as x-ray microanalysers. The latter need a high aperture ratio but such instruments are not so demanding in resolution (Δλ/λ>10 -3 ). Actually, in these devices the diffractor surface could use plates of muscovite (mica), which typically provides high plasticity. A diffractor for a microanalyser of the CAMEBAX-micro type with 160 mm focal circle radius, in the x-ray range suitable to analyse Fe (Z=26) and Ti (Z=22), could use the muscovite crystallographic planes (311) and (201) under the Bragg's angles of 34.83° and of 32.82° respectively. With a diffractor height of L=16 mm a wide aperture (0.066 sr) associated to a moderate resolution of Δλ/λ=10 -3 is obtained for the first case, while in the second case an aperture of 0.039 sr and a resolution of Δλ/λ=7*10 -4 are calculated. The estimated gain is about 15-30 times that of the spherical diffractor of US Patent 4,882,780 and US Patent 4,807,268. A further example of experimental apparatus which could implement the embodiment shown in Fig. 1 is an ESCA spectrometer. The characteristic radiations of the x-ray photons (Al Kα or Mg Kα) of an x-ray photoelectron spectrometer, when absorbed by the sample, are known to induce the appearance of free photoelectrons. The intensity and the contrast of x-ray photoelectron spectra are remarkably magnified by intense incident quantum flux. The properties of the stepped surface permit to design new kind of spectrometers that allow to obtain high contrast spectra in micro-samples. Here we report the parameters for an x-ray monochromator at the Mg Kα energy (λ=9.89 Å). An acceptance of 0.17 sr is obtained with the following parameters: a focal circle radius of r=100 mm, a diffractor height of L=20 mm and a resolution Δλ/λ=3*10 -3 . The x-ray beams should be diffracted by a device made again by muscovite planes (001) (2d=19.93 Å) working at Θ=29.90°. The diffractor should consist of only five steps, but the intensity advantage over a conventional spherical curved crystal should be larger than 30. More recently a diffraction based device using spherical crystal elements was designed for high resolution x-ray fluorescence measurements in the Cr K β energy [W.A.Caliebe, S. Bajt and C-C. Kao, Rev. Sci. Instrum. 67(1996) 1.]. In Figures 5 and 6 we present the comparison of the device of W.A.Caliebe, S. Bajt and C-C. Kao, Rev. Sci. Instrum. 67(1996)-1 when the spherical diffracting crystal is replaced by the multi stepped diffractor of similar size according to the present invention. The gain here is very high in all the range of the resolution both with Ge (Fig. 5) and Si (Fig. 6) crystals. Moreover it is very important to underline, looking at the results of these two figures, that to get the larger gain we had only to use the Si(111) surface, no needs at all to use higher order reflections, or other crystals and orientations with different spacing. Another useful application of the present multi stepped diffractor should be the replacement of the conventional curved monocrystal in laboratory EXAFS spectrometer based on x-ray diffractometer coupled to rotating anode, like the RIGAKU one [K.Tohji, Y. Et al., Rev. Sci. Instrum. 54 (1983) pag. 1482-1487], with a proper multi stepped device. Finally; it should be noted that the device according to the invention, realised locating some. small spherically curved dispersive elements (monocrystals or gratings) on a focal circle and disposing said elements in a way to fulfil the same Bragg reflection condition for the incident radiation, allows advantageously to increase the throughput with respect to a spherical bent crystal device without affect the resolution, where usually mechanical stresses disturb the performance of these device.

Claims: A diffractor for electromagnetic radiation and neutrons, more particularly for x-ray sources, which is based on a multi-stepped geometry realised by locating on a focal circle spherically curved dispersive elements such as crystals or gratings, characterised in that each said dispersive element subtends a constant step width angle as seen from the source, each element (step) being shifted in a way to fulfil the same Bragg reflection condition for the incident radiation without affecting the spectral resolving power and in order to increase the throughput with respect to both a spherical bent crystal device and a stepped diffractor constructed under the constant step height condition. A diffractor for electromagnetic radiation according to claim 1, characterised in that the number of the diffracting elements is properly increased, thus obtaining an increase of the total throughput with respect to a spherical bent cristal device and both high resolution condition for all the surface of the diffractor, and an increase of the total solid angle. Use of a diffractor for electromagnetic radiation according to the preceding claims, in instruments that monochromatize radiation, such as x-ray microanalysis systems, x-ray photoelectron for chemical analysis (ESCA) and x-ray absorbion spectroscopy (EXAFS) apparatuses. Use of a diffractor according to the preceding claims, for the construction of a high resolution "post" monochromator such as those used in spin-dependent x-ray absorption up to the resolution in the meV range, or of a monochromator for hard x-ray and neutron radiation. A diffractor according to the preceding claims, characterized in that said stepped surfaces are concave surfaces as seen from the source.

Inventors: MARCELLI AUGUSTO, MAZURITSKY MIKHAIL, SOLDATOV ALEXANDRE, MARCELLI, AUGUSTO, MAZURITSKY, MIKHAIL, SOLDATOV, ALEXANDRE
Applicants: ISTITUTO NAZ DI FISICA NUCLEAR, ISTITUTO NAZIONALE DI FISICA NUCLEARE
Application year: 1997
Main classification: G21K1
IPC codes: G01N23, G21K1