Prospects for application of X-ray anomalous transmission effect to monochromatization of broadband spectrum

1 Introduction

For X-ray structure investigations in synchrotron radiation (SR) beams, monochromatization of X-ray broadband spectrum using double-crystal schemes is often used. These schemes allow keeping the beam direction while re-setting to another wavelength; they also provide a high peak reflectivity and a good energy resolution [1]. Usually, for photon energies E = 4–30 keV, the Bragg–Bragg scheme based on silicon crystals with diffractions from (111)–(111) or (220)–(220) crystallographic planes is used [2]. However, such a scheme is found to be unacceptable for photons with higher energies because of both larger device sizes and loss of energy resolution at low diffraction angles [3]. Therefore, for photon energies in the range of E = 20–100 keV, the Bragg–Laue scheme is used [4]; moreover, the Laue-crystal is elastically bent to increase the transmission bandwidth [5]. The bending curvature is limited by the crystal mechanical properties. Thus, the focusing is effective only at long distances (∼10–30 m) between the source and the monochromator, thus, it cannot be applied to new sources with smaller sizes. For monochromatization of high energy photons, diffractions with high Miller indices are used [6]. That provides increasing the diffraction angles, but the peak reflectivity decreases sufficiently.

An alternative to the diffraction monochromatization is the Bormann monochromatization [7]. A highly structurally perfect crystal selects two monochromatic beams from the incident broadband spectrum: one of them, transmitted, T_i, propagates along the incident beam direction, and another one, diffracted, R_i, propagates along the Laue diffraction direction at the angle 2θ_i = 2 arcsin(λ_i/2d). The Bormann effect has been used for precision investigations of fluorescence, Compton scattering [8], polarization [9], and coherent control of pulsed X-ray beam [10].

An important advantage of the Bormann scheme is maintaining the direction of the transmitted monochromatized beam under retuning for another wavelength. This allows applying the scheme to produce monochromatic photon beams in beam lines of broadband radiation sources. However, the Bormann scheme has not been used for this purpose because of low transformation efficiency and a high background signal from the primary beam. Indeed, in the direction of the transmitted beam, there propagates the whole broadband spectrum attenuated by exp(−μt), where μ is the linear coefficient of photo absorption and t is the crystal thickness. According to [7] the scattering in the μt range from 5 to 10 is intermediate between that predicted by approximations for thin and thick crystals. So, we’ll call this range intermediate. When μt ≥ 10, the broadband beam is attenuated more than by four orders of magnitude, while the peak transmission coefficient for germanium being ≈ 4% [11]. This allows one to hope for the selection of a monochromatic beam with a contrast >10³ from the broadband spectrum. Such a contrast is quite sufficient for the structure X-ray investigations. Thus, it is expected that in the intermediate thickness range it is possible to select contrasting monochromatic bands of sufficiently high intensity from the broadband spectrum using the Bormann effect. The purpose of this study is the experimental determination of quantitative characteristics of the spectrum formed from the broadband spectrum by the Bormann diffraction in the range of intermediate μt values.

2 Samples and experiment technique

The objects under investigation were (001) germanium plates with the thickness 1.0 mm and dislocation density ρ <10² cm^–2, and also the plates of the dislocation-free silicon (001) with thicknesses 0.36, 0.46, 0.59, and 0.67 mm. The plate surfaces were subjected to the optical and chemical polishing to remove the disturbed surface layer. Structural perfection was controlled by measuring the (004) diffractions using a double-crystal spectrometer in (n, −n) scheme. The selected samples gave rocking curve widths less than 12–15” under diffraction of the Cu-K_α1 radiation.

The source of incident radiation was an X-ray tube BSV-27 with a copper target. The transmitted and diffracted beams integral intensities were measured by recording Cu-K_α (220) diffraction rocking curves from a Bormann crystal “by transmission” according to the scheme shown in Fig. 1. The scan step was 0.0025°, accumulation time –10 s. The transmission band of the secondary monochromator based on the high-oriented graphite crystal, HOPG, was set to ΔE E = 6.9·10^–3 at the Cu-K_α line (E = 8.047 keV). The angular divergence of the incident beam was varied in the range from 0.008 to 0.040 degrees that corresponded to the characteristic range of the broadening geometric factor for diffraction curves in XRD.

Measurements of the broadband spectrum transmitted through the Bormann crystal and the monochromatized bands cut out by this crystal were carried out with a SDD-detector X-100 (Amptek, USA). The detector replaced the secondary monochromator during measurements. The spectrum accumulation time was 300 s with the detector integral counting rate not more than 10⁴ counts/s.

3 Results and discussion

Integral intensity of the Cu-K_α1,2 transmitted Bormann beam monochromatized by the germanium (220) diffraction was T_i = 0.24·10^-6 rad in our scheme at μt = 36.9. The obtained value is close to the data [11], where Cu-K_α1,2 measurements by a standard method for (220) Ge gave T_i = 0.45·10^-6 rad at μt = 32.1 and T_i  = 0.241·10^–6 rad at μt = 44.3. This allows comparing our quantitative results at various μt.

Let’s consider variations of the integral intensity and the contrast of the transmitted Bormann beam in the intermediate μt range (Fig. 2). According to Fig. 2 in the range μt = 5–10, as μt increases, the Bormann beam integral intensity drops by a factor of 3, while the peak/background (P/B) ratio increases more than by two orders of magnitude. In this connection, the optimization of the Bormann monochromator by μt is of interest.

Let’s evaluate the peak transmission coefficient which can be obtained by this method of monochromatization. According to the literature data [11], the peak transmission coefficient for (220) germanium is 4% at μt = 10–12. This value is larger than for a double-crystal Bragg monochromator using large Miller indices. It is convenient to determine the energy resolution of an instrument by the half-widths of Cu-K_α1 and Cu-K_α2 peaks in the rocking curve of the crystal using the Bormann monochromatization (Fig. 3). At the angle distance of 0.065° between the peaks the half-width of each peak is 0.025° corresponding to ΔE/E = 1.03·10^–3.

An adjustment of energy resolution may be done by simply varying the incident beam divergence with slit collimation. Indeed, Δ E / E = ctg θ · Δ θ ,(1) where Δθ= (Δθ²_gm + ω²)^1/2, ω is the half-width of the rocking curve, Δθ_gm = (Δθ²_div + Δθ²_con)^1/2 is the geometry factor determined by the angle divergence Δθ_div and convergence Δθ_con of the incident beam.

In Fig. 3, two (220) Si rocking curves obtained “by transmission” for the doublet Cu-K_α1,_α2 at Δθ_gm = 2.34·10^-2 deg and 3.5·10^-2 deg are shown. Because of a small half-width value ω ≤ 15² of the rocking curve, its contribution to Δθ is insignificant, so, the experimental values Δθ= 2.6·10^-2 deg and 3.4·10^-2 deg (Fig. 3) are close to those calculated from the beam line geometry. These correspond to ΔE/E = 1.03·10^-3 and 1.35·10^–3, respectively. The coincidence of the calculated and the experimental Δθ values confirms the possibility of adjusting the energy resolution of the beam line by simply changing the slit width in front of the monochromator.

Figure 4 visually illustrates the work of the Bormann crystal as a monochromator for a broadband spectrum. A known example of such a spectrum is the spectrum of an X-ray tube bremsstrahlung radiation (Fig. 4, curve A). After transmitting through the crystal-monochromator, both the broadband spectrum and characteristic spectrum lines K_α and K_β of the target material maintain practically unchanged when the resonance tuning of the crystal is varied. Therefore, only one of the obtained distributions is shown in Fig. 4 (curve B). In the background, the peaks of monochromatized radiation are revealed, their positions corresponding to different crystal tunings.

The same crystal under resonance tunings for various wavelengths has different μt values. As it is seen from the Fig. 4, the contrast of the monochromatized radiation peaks sharply increases both with decreasing energy E of photons emitted by the monochromator and with related increasing value μt of the Bormann crystal. So, at μt = 8.48, 11.06, and 12.51 (peaks 7, 8, and 9) the P/B ratio is 67.7, 159, and more than 220, respectively. The remaining part of the continuous spectrum propagates strictly straightforward and transmits through the crystal as through an ordinary filter. This would create a broadband background in the diffraction pattern, which has to be removed additionally. For removing the background, the effect of displacement of the transmitted Bormann peak relative to primary one can be used.

It is known [7] that under the Bormann effect, the separation of wave fields within the crystal takes place. Estimation of the distance between the field parts on the exit surface of a Si crystal with thickness 0.67 mm for the diffraction (220) in Cu-K_α1 radiation according to the theory [7] gives ≈ 240μm. The experimentally observed displacement of the curve 3 (Fig. 5) relative to the primary beam is 196μm. For the germanium crystal of 1.0 mm thickness, the experimental displacement is 240μm. This displacement is sufficient for cutting the direct beam by a knife slit mounted behind the crystal for removing the broadband background.

Note, that under monochromatization of the broadband beam by the (220) diffraction from Ge crystal with μt = 36.9 (Fig. 5, curve 4), there was observed a substantial narrowing of the transmitted beam at least by a factor 2.5. This result is caused by compression of the wave field within a “thick” crystal with μt >10, which according to the theory [7] may improve the energy resolution by an order of magnitude and more. However, the energy resolution improvement with increasing μt is accompanied by substantial dropping the peak reflectivity, for example, down to ∼ 0.1% at μt = 30. Therefore, the monochromatization with a “thick” crystal is reasonable only in special cases.

In the scheme under consideration, with μt = 5–10, one can not count on additional focusing the radiation due to the Bormann effect. This means that as the wavelength decreases with ctgθ in Equation (1) the energy resolution will worsen. So, for λ= 0.31 Å (E = 40 keV) at Δθ_gm = 2.34 10^-2 deg for Si (220) we get ΔE/E = 5 10^-3, which results in an additional broadening of the diffractions in the diffraction pattern of the High-Energy X-Ray Diffraction (HEXD).

Let’s calculate the diffraction broadening value at Bragg angle θ: Δ θ = Δ E / E tg θ = ctg θ M Δ θ gm 2 + ω 2 tg θ ,(2) where θ and θ_M are diffraction angles of the sample and the monochromator, respectively.

For small diffraction angles 2θ <20 deg, which are used for HEXD, ctg θ_M· tg θ ≤2. Thus, the contribution of non-monochromaticity into the broadening does not exceed more than twice the divergence of the primary beam. Certainly, under analyzing the diffraction curve profile shape, it is necessary to take into account the non-monochromaticity ΔE/E ≈ 5 10^–3 as, for example, in the Kα₁α₂ doublet of an X-ray tube where ΔE/E ≈ 3 10^–3.

A disadvantage of the Bormann monochromatization is low stability of perfect crystals in powerful fluxes of primary radiation. Therefore, under fluxes of more than 10¹³–10¹⁴ photons/s, one has either to take steps for forced cooling or to mount an additional device in front of the Bormann crystal, for example, a Bragg monochromator for reducing the thermal load.

It seems rather perspective to apply Bormann monochromatization to some new sources of X-ray radiation, for example, a laser-electron generator (LEXG) [12, 13]. This new source provides a beam of ∼ 10¹² photons/s with an angle divergence ∼ 15 mrad, a small half-width of the energy spectral band ΔE/E≤3–10%, a central-symmetric angle distribution of photons over energies, and a relatively sharp high energy edge of the energy distribution. With such beam features, not only its monochromatization, but also its monitoring is necessary, because the beam may vary noticeably due to small instabilities in the LEXG performance.

The Bormann monochromatization provides a unique opportunity for monitoring of the transmitted monochromatized beam by diagnostics of the diffracted beam (Fig. 1, pos. 6) in the real time regime. Indeed, these beams correspond to the same resonance tuning of the crystal, i.e. they have the same wavelength. Additionally, the intensity ratio of the transmitted to the diffracted beam for each λ is constant and close to unity. From Fig. 6 it is seen that both the coordinates of gravity center and the axis sizes of the figure change considerably as the X-ray photon energy is varied [12, 13]. This figure corresponds to the 2d-shape of the diffraction curve and can be registered by a CCD matrix placed in the diffracted beam. Analysis of the 2d-images will allow tracking, with interval ≈ 5 s, variations of the average photon energy of the LEXG beam with sensitivity not worse than ΔE /E = 5·10^-4 and correcting the sample diffraction pattern in the real time regime.

The Bormann effect is expedient to use for obtaining monochromatized photon beams with energy more than 30 keV for HEXD. In the intermediate thickness range when μt = 8–10, the peak transmission coefficient for Ge (220) diffraction is ≈ 4–5%, and the contrast of the monochromatic band selected by the Bormann beam from the broadband spectrum is more than 250. For E = 30–50 keV, the energy resolution ΔE /E which can be obtained with (220) diffractions of germanium and silicon is at the level 3–6. 10^–3, and is conveniently regulated by tuning the collimation of the primary beam. Substantial improvements of the energy resolution can be achieved by increasing the crystal thickness up to μt = 30 due to compression of the wave field inside the crystal, although in this case the peak transmission coefficient drops down to 0.1%.

Due to the presence of two identical beams – one transmitted and one diffracted by Laue – there is a unique opportunity for monitoring the intensity of the transmitted monochromatized beam and the spot shape of the diffracted beam. Such a monitoring is especially promising for new sources of X-ray radiation [13–15] and allows not only a high-sensitivity control of the source stability but also correcting the diffraction pattern of the sample in the real time regime.