Structural analysis of diamond mosaic crystals for neutron monochromators using synchrotron radiation

Diamond & Related Materials 37 (2013) 41–49

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Structural analysis of diamond mosaic crystals for neutron monochromators using synchrotron radiation M. Fischer a, A.K. Freund b, c, S. Gsell a, M. Schreck a,⁎, P. Courtois c, C. Stehl a, G. Borchert d, A. Ofner d, M. Skoulatos e, f, K.H. Andersen g a

Universität Augsburg, Institut für Physik, D-86135 Augsburg, Germany Via Cordis, F-33400 Talence, France Institut Laue–Langevin, F-38042 Grenoble, France d Forschungs-Neutronenquelle Heinz Maier-Leibnitz (FRM II), Technische Universität München, D-85747 Garching, Germany e Helmholtz Centre Berlin for Materials and Energy, D-14109 Berlin, Germany f Laboratory for Neutron Scattering, Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland g European Spallation Source, S-22363 Lund, Sweden b c

a r t i c l e

i n f o

Article history: Received 13 March 2013 Received in revised form 19 April 2013 Accepted 21 April 2013 Available online 9 May 2013 Keywords: Diamond single crystal Heteroepitaxy Neutron monochromator Mosaic spread

a b s t r a c t The beams extracted from thermal neutron sources such as nuclear reactors are monochromatised by Bragg diffraction using imperfect single crystals with an angular mosaic spread of typically 0.2–0.8°. For neutron wavelengths below 1.5 Å, the highest reflectivity of all crystalline materials is expected for diamond. Nowadays diamond single crystals with an appropriate mosaic spread exceeding a thickness of 1 mm can be grown by heteroepitaxy on an Ir/yttria-stabilised zirconia bilayer deposited on a Si(001) single crystal. To explain the observed neutron reflectivity being below the theoretically expected value, we have studied the spatial distribution of the mosaic structure of two crystals by high resolution X-ray diffraction using a laboratory X-ray source and synchrotron radiation. The first sample (A) showed a uniform mosaic spread of 0.18° ± 0.02° across the 1 cm wide sample. The peak shift of the X-ray rocking curves of 0.08° indicated a weak curvature of the crystal lattice. The measured absolute neutron peak reflectivity of 34% corresponded to 90% of the value predicted by theory. The peak width of the neutron rocking curve for the second sample (B) was twice as big, but here the peak reflectivity of 13% corresponded to only half of the theoretical value. This unfavourable behaviour could be assigned to a substantial spatial variation of the mosaic spread deduced from the synchrotron X-ray studies. X-ray diffraction with high spatial resolution indicated a mosaic block size below 50 μm for sample A. This was consistent with chemical etching experiments on the surface of a comparable sample which showed both randomly distributed dislocations and others that are arranged in boundaries of several 10 μm large domains. © 2013 Elsevier B.V. All rights reserved.

1. Introduction Due to the combination of many favourable parameters, diamond represents an outstanding material with a broad range of applications (e.g. electronics, cutting tools, electrochemistry). Recent theoretical calculations by Freund [1] have predicted that diamond should also be a “potential gem for neutron instrumentation”. Thanks to the high scattering power and the low attenuation, an increase of the neutron flux by up to a factor 4 for hot and thermal neutrons is expected when compared to commonly used monochromator materials like Ge, Si and Cu. Because neutron scattering experiments are very often flux limited the ideal monochromator is not a perfect single crystal but a mosaic crystal with a suitable mosaic spread in the range of 0.2–0.8°, ⁎ Corresponding author. Tel.: +49 821 598 3401; fax: +49 821 598 3425. E-mail address: [email protected] (M. Schreck). 0925-9635/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.diamond.2013.04.012

comparable to the neutron beam divergence. Then intensity and resolution are optimised. The so-called ideal mosaic crystal is defined as a uniform composite of perfect, slightly misaligned crystallites called mosaic blocks whose size should not exceed the so-called primary extinction length that is of the order of a few tens of μm for hot and thermal neutrons, depending on wavelength. If the mosaic blocks are bigger, the process of primary extinction can reduce the reflectivity and eventually the neutron flux available at the experiment. Thus, in addition to the mosaic spread and the uniformity of its angular and spatial distribution, the microstructure of the crystal, i.e. the bulk defect structure and the associated size distribution of the mosaic blocks, determines the performance of a crystal as neutron monochromator. Nowadays diamond single crystals with a suitable mosaic spread of several tenths of a degree and a lateral size of up to 2 × 2 cm 2 for individual monochromator elements can be synthesized by heteroepitaxy on single crystal iridium films. In first pioneering experiments, the neutron peak reflectivity reached between 66% and

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75% of the values predicted by theory [2]. Recently, some crystals attained up to 90% of the theoretical value which represents an excellent performance. However, many crystals produced till now have not reached this high efficiency. This reduction must be assigned to a discrepancy between the real defect structure and the mosaic block model of the ideally imperfect crystal [3]. The understanding of the reasons for this observation is very important for the successful development of efficient concepts to grow diamond crystals with optimum neutron reflection properties. As a consequence, a comprehensive analysis of the defect structure of diamond mosaic crystals was required. First, to determine the mosaic spread and its lateral distribution close to the surface, we used a standard laboratory X-ray diffraction setup with CuKα radiation, i.e. a wavelength of 1.54 Å, and parallel beam geometry. Then, intense synchrotron radiation of 1 Å wavelength made it feasible to map out the mosaic structure inside the whole bulk of 1-mm-thick crystals. In particular, a special CCD area detector (FReLoN = Fast Read out Low Noise) developed at the ESRF permits to measure several million rocking curves in parallel and thus to visualise the spatial distribution of the mosaic spread, peak position and also reflectivity. For the depth resolved analysis of the mosaic spread and the mosaic block size with high spatial resolution a small scattering volume can be defined by slits limiting the size of the primary and diffracted beams down to a few microns. Finally, with selective chemical etching in a microwave plasma it was possible to reveal details of the dislocation arrangement that constitutes the mosaic block boundaries. The aim was to correlate the observed spatial distribution of the mosaic structure with the absolute neutron reflectivity of the two samples (named A and B) under study. 2. Experimental For the growth of the freestanding heteroepitaxial diamond samples the recently developed multilayer stack Ir/YSZ/Si(001) with an off-axis angle of 4° was used as substrate (YSZ = yttria stabilised zirconia) [4,5]. Diamond nucleation via bias enhanced nucleation (BEN) was performed in a microwave plasma chemical vapour deposition (MWPCVD) setup. The process parameters for BEN were a temperature of 700–800 °C, a gas pressure of 40 mbar and 2000 W microwave power with 5–10% CH4 in H2. A negative bias voltage of about 300 V was applied to the substrate. After a short growth step at low pressure (40 mbar, 2000 W, 1% CH4 in H2, 100 ppm N2) the conditions were changed to 180–200 mbar, 3500 W microwave power, 10% CH4 and 10,000 ppm N2 in H2. After 3 h the nitrogen content in the gas phase was lowered to 400–1000 ppm. The temperature of sample B as estimated by pyrometry was 30–50 °C higher than that of sample A. The final thickness of both diamond plates was about 1 mm and the lateral size 12 × 12 mm 2. After growth the silicon substrate was etched away using a mixture of HF and HNO3. The edges of the freestanding diamond crystals were approximately parallel to the 〈100〉 directions for sample A and parallel to the 〈110〉 directions for sample B. The off-axis angle of 4° was towards [100] for both samples. The characterization of the samples comprised both, three different types of diffraction experiments using X-ray and neutron diffractometry. The X-ray diffraction geometries and the size of the probed volumes are sketched in Fig. 1(a), (b) and (c). Configuration 1 shown in Fig. 1(a) used CuKα radiation and a parallel beam formed by a graded parabolic multilayer X-ray mirror at a laboratory diffractometer (Seifert XRD 3003 PTS-HR). On the detector side an additional X-ray mirror was installed in order to separate the contributions from micro-strain and mosaic spread. The size of the beam was limited by slits to 1 mm parallel and 2 mm perpendicular to the diffraction plane. The samples were mounted on an x–y-translation stage and rocking curves (ω-scans) of the 004-reflection with 2θB = 119.48° (θB = Bragg angle) were recorded at different positions. The distribution

Fig. 1. Configurations 1, 2 and 3 of the X-ray diffraction experiments using beams from (a) a laboratory X-ray tube with a copper anode, (b) a synchrotron X-ray source combined with an area detector (FReLoN camera) to record spatially resolved rocking curves and (c) local probing of the samples by defining a small diffracting volume using slits.

of the full-width-at-half-maximum (FWHM) of the rocking curves along two perpendicular lines through the centre of each sample was determined. The curvature of the diamond plates was calculated from the peak shift Δω of the angular positions along the sample. For all subsequent measurements the direction of smallest curvature was oriented parallel to the diffraction plane. The experimental configurations 2 and 3 shown in Fig. 1(b) and (c) required intense synchrotron radiation. The experiments were performed on the optics beam line BM05 of the European Synchrotron Radiation Facility (ESRF) in Grenoble. A wavelength of 1 Å was selected by a vertically diffracting Si 111 dislocation-free double-crystal monochromator in non-dispersive configuration out of the white beam produced by a bending magnet source. The diamond sample diffracted the monochromatic beam in the horizontal plane. The horizontal divergence was 116 μrad or 0.0067°, i.e. very small compared to the widths of the measured rocking curves. Due to the high spectral resolution and the small beam divergence instrumental broadening of the rocking curves could be neglected. In configuration 2, a high-resolution large-area FReLoN camera with 2048 × 2048 pixels of 10 μm lateral size [6] was mounted at a distance of 0.6 m from the diamond crystal. The camera was positioned at twice the Bragg angle 2θB = 68.2° of the 004-reflection. A primary beam size of 10 × 8 mm 2 giving rise to a footprint at the

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sample position of 17.8 × 8 mm 2 was used to illuminate the maximum possible area of the crystals. The profile of the 004-reflection was scanned stepwise, the intensity being received by the FReLoN camera. In this way four million rocking curves could be recorded simultaneously. The shaded area shown in Fig. 1(b) corresponds to the effective scattering volume that contributed to the signal of a single pixel. The estimated width w was 30 μm. Using the software package VISROCK the rocking curve parameters FWHM and peak position for each pixel were calculated and displayed as contour maps [7,8]. The results obtained with the laboratory X-ray diffractometer from θ - 2θ scans with an analyser had shown that the contribution of lattice tilts exceeded by far the effect of d-spacing variations (strains). As a consequence the FWHM measured in the present configuration could be directly interpreted in terms of the angular mosaic spread. In configuration 3 rocking curves of the 004-reflection were taken with high spatial resolution by defining a very small diffraction volume. The area detector was replaced by a highly sensitive scintillation detector positioned at 2θB = 68.2°. Fig. 1(c) shows the diffraction geometry. A horizontal slit 1 (width w1) in the diffraction plane and a vertical slit 2 (width w2) limited the size of the primary beam. With the additional horizontal slit 3 (width w3) in front of the detector the probed volume was reduced to a minimum volume of about 4.7·10 3 μm 3, similarly to earlier experiments [9]. By positioning the sample in the y and z directions different spots were analysed. The diffracting volume can be seen as a monoclinic cell with edges a = w1 / sin2θB = 1.1·w1, b = w2 and c = w3 / sin2θB = 1.1·w3, see the inset in Fig. 1(c). The probed volume had a size of V = w1·w2·w3 / sin2θB. For each measurement the slit sizes are specified using the notation w1 / w2 / w3. Characterization of the samples by neutrons was performed at the instrument T13C of the Institut Laue–Langevin (ILL) in Grenoble [9]. This double-crystal diffractometer is located at the exit of a thermal neutron guide tube. A high quality, nearly dislocation-free germanium single crystal served as monochromator. The 335-reflection was used to select a wavelength of 1 Å. The second order intensity of this reflection is negligible and the neutron guide cuts off neutrons with wavelengths below 1 Å. The beam size was 2 × 2 mm 2. The count rate was below 10 4 s −1 so that no dead time correction was needed. The absolute peak reflectivity and the rocking curve width of the diamond 004-reflection were determined at the Bragg angle θB = 34.1°. The d-spacings of diamond 004 (0.8917 Å) and germanium 335 (0.9302 Å) and thus the corresponding Bragg angles were similar. As a consequence, the double crystal setup was considered as non-dispersive and the instrument broadening could be neglected. Then the measured rocking curves were given by a convolution of the diffraction pattern of the monochromator with that of the sample. Thanks to the very small width of the Ge monochromator rocking curve of only a few arcsec, the measured double crystal rocking curve (ω-scan) represented the angular reflectivity distribution of the diamond mosaic crystal under study. The detector was always wide open to accept the full beam reflected by the sample. The reflectivity was obtained on an absolute scale as the ratio between reflected and incident beam intensities. 3. Results The present study focused on two diamond crystals, A and B, each with a thickness of 1 mm. Fig. 2(a) shows the rocking curves of the 004-reflection taken at 11 different positions at a lateral distance of 1 mm along [100] of sample A using CuKα radiation. In Fig. 2(b) the FWHM and the peak position of the scans are plotted. The average value for the FWHM is 0.18° ± 0.02°. The low standard deviation indicates a uniform mosaic spread along this direction. The profiles show a non-monotonous shift of the peak position covering a total range of 0.08° which represents a significant fraction (44%) of the

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FWHM. A linear shift compatible with a uniform curvature and thus a constant radius all across the sample is not observed. Similar measurements on sample B are summarised in Fig. 2(d) and (e). With an average value of 0.85° ± 0.09° the width of the rocking curves is nearly five times bigger. The peak shift is again not monotonous and the peak position varies within 0.14°. The shape of both crystals is rather close to the letter S: the change of the slope indicates that they are locally curved first in one and then in the opposite sense. The results of neutron studies are given next. The rocking curves of the 004-reflection are shown in Fig. 2(c) and (f) for samples A and B, respectively. The 0.22° wide profile of sample A is slightly broader than the FWHM measured by CuKα radiation reported above. The high peak reflectivity of 34% measured for this merely 1-mm-thick crystal corresponds to 90% of the value predicted by theory for an ideal mosaic diamond crystal with the corresponding mosaic spread [1]. The results for sample B look quite different, see Fig. 2(f). The peak exhibits a pronounced shoulder on one side. Its width of 0.38° is now by more than a factor of 2 smaller than the FWHM measured by CuKα radiation. The peak reflectivity of 13% is quite low and reaches only half of the theoretical value calculated for a mosaic spread of 0.38°. The diffraction data acquired in the laboratory with CuKα radiation cannot explain this discrepancy and the microstructure of the two crystals was further investigated with synchrotron X-rays of a wavelength λ = 1 Å. This allowed us to probe the whole crystal volume thanks to the lower absorption and the possibility to sample smaller volumes due to the high photon flux available at a synchrotron source. Fig. 3(a) shows a map of the FWHM for sample A obtained from the FReLoN data. There is only a small variation over the sampled area of about 11 × 11 mm 2. The average width is 0.16° ± 0.02°. At the lower edge the width increases slightly. The measured values and the distribution show a reasonable fit with the data set acquired with the laboratory X-ray setup, see Fig. 2(b). The map in Fig. 3(b) displays the peak position. The offset at the horizontal line in the middle of the image is an artefact that stems from the fact that the whole data had to be taken in two sets. This technical limitation had no influence on the evaluation of the FWHM data shown in Fig. 3(a). We interpret the inclined line in the upper left part of the crystal in terms of a buried crack that produces a change of crystal orientation. Due to the specific shape of the scattering volume, see Fig. 1(b), its lateral position cannot be deduced from a single CCD image. The lateral variation in peak position across sample A on the order of 0.1° agrees quite well with the CuKα data (see Fig. 2(b)). The maps of rocking curve width and peak position for sample B are given in Fig. 4(a) and (b), respectively. Since the edges of sample B were cut along 〈110〉, the crystal was rotated in the diffraction plane by 45°. The mosaic spread of sample B showed a considerable variation ranging from 0.2° in the lower corner up to as much as 1.5° in the upper corner. For the sake of a better visibility of the fine structure, the colour scale in Fig. 4(a) has been limited to 0.4°. Near the centre of the image a defect can be clearly observed. The peak position in the map of Fig. 4(b) varies by ~ 0.18° with more inclined regions towards the sample edges. The FReLoN camera maps reveal a very important non-uniformity of the sample defect structure. For a direct comparison with the CuKα data displayed in Fig. 2(d) and (e) one has to discuss the values along the diagonal of sample B (the horizontal line in Fig. 4). The variations of the peak position in Figs. 2(e) and 4(b) were quite similar. In contrast, the peak width of 0.85° ± 0.09° of the rocking curves recorded with CuKα radiation was more than twice as big as the data points in the FReLoN maps, see Fig. 4(a). Considering the difference in shape and especially the depth of the probed volume for the two configurations, the present results reveal pronounced variations of the mosaic spread with depth in sample B. The results obtained in configuration 3 (Fig. 1(c)) clarify this point. Limited by the primary and secondary slits a volume of 1.9·10 6 μm3

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Fig. 2. Line scan of X-ray rocking curves of diamond 004-reflection (2θB = 119.48°) along the [100] direction of samples A (a) and B (d) using CuKα radiation. The direction of lowest curvature was in the diffraction plane and the lateral distance between two measurements was 1 mm. (b) and (e): variation of the FWHM and peak position with lateral position. (c) and (f): neutron rocking curves of the 004-reflection at λ = 1 Å and 2θB = 68.2° for samples A and B, respectively.

was probed and the step width was 50 μm. Fig. 5(a) shows the 004-rocking curves starting from the back side of crystal A. In Fig. 5(b) the intensity of the peak maximum (ω = 33.24°) and the integrated intensity below the rocking curves are displayed vs. the z-coordinate. The effective width of the probed volume is about 110 μm. The growth surface is defined as the position where half of the probed volume is situated inside the crystal. The intensity does not drop to zero before a vertical scan range of 1 mm is reached. This proves that the whole crystal volume is analysed by the X-rays. The decrease in intensity from the top to the back of the sample is determined by both absorption and secondary extinction processes. The FWHMs of the rocking curves are shown in Fig. 5(c). Starting with 0.31° near the nucleation side the value drops to ca. 0.15° within 300 μm and stays nearly constant for the remaining thickness. The absolute values match well with the mean mosaic spread determined by the FReLoN camera. The peak positions of the rocking curves vary by only ~0.02° across the thickness which indicates that the preferential orientation of the crystal lattice stays constant during the growth of 1-mm-thick crystals. Concerning mosaic spread and peak position, crystal A is quite uniform along the growth direction. So far no asymmetries or splitting of the rocking curves indicate the presence of individual mosaic blocks inside the probed volume

of 1.9·10 6 μm 3. To analyse the mosaic structure in more detail we reduced the scattering volume by two orders of magnitude to 1.9·10 4 μm 3. Four different spots 300 μm below the growth surface at a lateral distance of 45 μm were investigated. The scans in Fig. 6(a) reveal a splitting of the rocking curve into several components. The rocking curve taken at spot 1 is schematically fitted by one smaller and three major peaks with a mutual shift of about 0.05°. At spot 2 some maxima disappear and new ones show up. This happens also for spots 3 and 4, suggesting the presence of several individual blocks within the probed volume. To resolve the microstructure with an even higher spatial resolution the probed volume at spot 2 was further decreased by a factor of 4 down to 4.7·103 μm 3 and the step size was reduced to 0.01°. The positions and heights of the peaks composing the rocking curve in Fig. 6(b) are nearly identical to those contained in the profile measured with lower spatial resolution (see Fig. 6(a)). This profile was then fitted by 5 Gaussian peaks. They will be discussed in more detail in Section 4. The rocking curves recorded for sample B taken at different z-positions are plotted in Fig. 5. A strong broadening of the profiles associated with a drop in intensity towards the growth surface is observed. In Fig. 5(e) the integrated intensity is plotted vs. the z-coordinate. Surprisingly, the maximum is situated about 400 μm

Fig. 3. Sample A: 004-rocking curve FWHM (a) and peak position (b) contour maps recorded with the FReLoN camera at λ = 1 Å and 2θB = 68.2°. The ω-step width was 0.01° and the direction of smallest curvature (x-direction) was parallel to the diffraction plane that contained the [100] direction.

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Fig. 4. Sample B: FWHM of the rocking curves (a) and peak position (b) contour maps recorded with the FReLoN camera at λ = 1 Å and 2θB = 68.2°. The ω-step width was 0.05° and the direction of smallest curvature (x-direction) was parallel to the diffraction plane which contains the [100] direction.

below the surface. Similar to sample A, the mosaic spread first decreases over the first 0.4 mm down to 0.18°, see Fig. 5(f). However, the further evolution is now completely different. The mosaic spread of sample B strongly increases up to a value of 1.2° at the surface. Simultaneously, the lattice planes tilt by as much as 0.35° as deduced from the peak shift. The broadening of the mosaic spread toward the surface is also clearly monitored by rocking curves with a still improved spatial resolution of 9.5·10 3 μm 3 at different depths as shown in Fig. 7. For a z-position of 0.35 mm the curve in Fig. 7(a) is still quite symmetric but several components appear that are hidden below the envelope of the profile. Towards the surface the distribution broadens and the intensity drops continuously, see Fig. 7(b)–(d). The big error bars in the graphs calculated from the pure statistical error result from the low count rates. They limit a more quantitative evaluation and an unambiguous identification of individual mosaic blocks.

4. Discussion and additional studies According to the results for the mosaicity between 0.2° and 0.8° obtained with laboratory X-ray diffractometry both diamond crystals grown by heteroepitaxy would be suitable as neutron monochromators. However, the samples show a completely different performance as to neutron reflectivity. For crystal A the peak reflectivity of 34% corresponds to 90% of the theoretical prediction for a width of 0.22°, whereas crystal B reached only 50% of the theoretical value for a mosaic spread of 0.38° in average.

As a first effect that may contribute to this different behaviour we consider primary extinction. In the theoretical calculations [2] the ideal mosaic model was assumed including secondary and excluding primary extinction. The latter occurs for high crystal quality where the mosaic block size exceeds the primary extinction length that is a few tens of μm in the present case, depending on neutron wavelength. With increasing mosaic spread the defect density increases, too, and thus the block size decreases. Consequently, for crystal B primary extinction should be smaller than for crystal A which totally disagrees with the experimental results. Therefore, primary extinction can be ruled out as a reason for low reflectivity. This is consistent with the results of the determination of what can be considered as block size using high resolution synchrotron X-ray diffractometry. Indeed, the observation of individual peaks distributed over an angular range of 0.2°, see Fig. 6(b), when probing crystal A with a slit configuration of 36 μm/10 μm/12 μm suggests that the mosaic block size must be smaller than about 20 μm. For crystal B the block size should be still smaller, see Fig. 7. Then deviations from uniformity of the mosaic spread both laterally and in-depth have to be considered to be at the origin of low reflectivity, both on the spatial and the angular scale. This was studied in the three X-ray diffraction configurations, but only synchrotron X-rays could probe the whole sample thickness with very high local resolution. The three measurement configurations showed crystal A to be quite uniform both laterally and along the growth direction. Taking into account the difference of the volume probed, the absolute values were in reasonable agreement. The peak position map taken by the FReLoN camera

Fig. 5. Depth-resolved rocking curves at λ = 1 Å and 2θB = 68.2° in the centre of sample A (a) and B (d); (b) and (e): intensity at constant ω = 33.24° and integrated intensity as a function of z-position for both samples; (c) and (f): variation of the FWHM and peak position with depth.

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Fig. 7. Results for sample B. (a)–(d): Rocking curves at λ = 1 Å and 2θB = 68.2° for 4 different depths z = 0.35, 0.7, 0.85 and 0.95 mm using a slit configuration of 18 μm/20 μm/24 μm. The error bars represent the pure statistical error (square root of absolute counts).

Fig. 6. (a): Rocking curves at λ = 1 Å and 2θB = 68.2° of sample A measured at 4 different lateral positions 300 μm below the surface using a slit configuration of 36 μm/20 μm/24 μm. The scans were fitted with 4 to 5 individual peaks (red) using a ω-increment of 0.02° similar to the experimental data. The black curve is the sum of the components. The error bars represent the purely statistical error (square root of absolute counts). (b): rocking curve at spot 2 with a slit configuration of 36 μm/10 μm/12 μm. The ω-increment was reduced to 0.01°. The scan is decomposed into 5 Gaussian distributions (red) with widths of 0.02° and 0.04°. The black curve represents the respective sum.

permitted the detection of an extended internal defect, probably a crack or a small-angle grain boundary. However, non-uniformity was observed on the angular scale where the lateral variation of the peak position across the sample was half the mosaic spread measured with a relatively small beam compared to the sample dimension. In fact, the total intensity diffracted by a curved crystal with a small local mosaic spread is smaller than the integrated intensity of a flat crystal with a bigger uniform mosaic spread. Excluding primary extinction effects, this can be understood simply by secondary extinction. The neutrons penetrate into the crystal until they reach the secondary extinction depth that is smaller for smaller mosaic spread. Thus for crystals with bigger mosaic spread, the neutrons penetrate deeper and a bigger volume is activated that leads to an increase of integrated intensity. This argumentation is valid only when focusing effects due to lattice curvature are not present. In the present case, a dispersion of the peak position in the observed range of 0.08° for crystal A leads to a beam divergence of

0.16° which disperses the neutron beam by 5.6 mm at a distance of 2 m, which is a typical distance between monochromator and sample. This is in addition to the dispersion of beam intensity due to the mosaic spread itself. Usually the sample size on a neutron diffractometer such as the instrument D9 at the ILL is about 2 to 3 mm. Then part of the beam that would hit the sample if the monochromator were flat, will miss it. Of course, due to mosaicity part of the beam falls onto the sample, but with some loss of reflectivity, because the mosaic distribution is not rectangular but rather of Gaussian shape. Therefore, for the future application, the variation of the peak position across the monochromator should be small compared to the mosaic spread. In the present study, however, the beam was only 2 mm wide and the detector was wide open so that a reflectivity smaller than the expected one cannot be explained by angular non-uniformity, at least for crystal A. The mosaic spread data taken by the FReLoN camera for crystal B revealed a significant lateral non-uniformity. The rocking curve width varied between 0.25° at the lower and 1.2° at the upper corner as seen in Fig. 4(a). The FWHM of the rocking curves was 0.3° ± 0.1° in the central region where the neutron reflectivity profiles were taken (see Fig. 2(f)). The small variation of the mosaic spread inside the measured spot cannot explain the inferior neutron reflectivity of crystal B. The rocking curve widths of 0.85° ± 0.09° measured along the sample diagonal using CuKα radiation, see Fig. 2(d), are more than twice as big as the values deduced from the CCD maps. This discrepancy is due to the weak penetration depth of the laboratory X-rays and a pronounced variation of the mosaic spread along the growth direction as shown by the synchrotron X-ray data. The FWHM of the rocking curves of crystal A decreased from 0.31° to 0.15° within the first 300 μm from the back side and then remained nearly constant up to the surface, see Fig. 5(c). In a former work [10] the development of tilt and twist in heteroepitaxial diamond films on

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iridium had been studied in the thickness range between 0.6 and 34 μm. For the tilt a reduction from about 1° to 0.17° has been reported. Taking into account the significantly lower depth resolution in the present experiments, the data in Fig. 5(c) agree with the earlier study. Apparently, the decrease of the mosaic spread stopped after several 100 μm and then remained constant. This kind of behaviour is favourable for the synthesis of diamond neutron monochromator crystals. The 10% lack of neutron reflectivity can be assigned to small deviations from perfect uniformity. As already pointed out, the absolute value obtained represents a very substantial improvement compared to traditional monochromators. For these materials, obtaining 85–90% of the theoretical value is considered to be an excellent performance. In contrast to crystal A, the evolution of the mosaic spread of sample B along the growth direction is similar within the first 500 μm, but then the width increases significantly to values of up to 1.2° at the surface as seen in Fig. 5(f). At the same time the peak shift also increases at the same rate. The large non-uniformity both in depth as well as laterally is without any doubt a major source for the low neutron reflectivity observed. Finally, to gain information on the mosaicity distribution and composition the results from the high resolution measurements on sample A are very interesting. For a slit configuration of 36 μm/20 μm/24 μm the rocking curves split into 4 to 5 individual components as can be seen in Fig. 6(a). The coherently diffracting crystal domains or crystallites that can be associated with the mosaic blocks of the mosaic model in the probed volume are mutually tilted by typically ~0.05°. In the measurement sequence the sample was laterally shifted by 45 μm each time between four spots. In most cases a completely new peak pattern appeared. Occasionally, one peak remained unchanged (spot 1 → spot 2). In terms of block size, this observation suggests that the lateral dimension is predominantly below 45 μm, in the order of 20 μm, see Fig. 8(a). For a second measurement at spot 2 the slit size was further reduced and the number of steps was doubled (step width 0.01°). The profile in Fig. 6(b) has the same total width (~ 0.3°) and the peaks appear at the same position as in Fig. 6(a) spot 2. The curve was fitted by Gaussians with different widths ranging between 0.02° and 0.04°. The asymmetric structure on the left side suggested 3 Gaussians with lower widths though this choice is not absolutely stringent. The width of the two isolated peaks is bigger than the resolution limit of the setup so that the FWHM can be interpreted in terms of structural features of the sample. Using Scherrer's formula, peak widths of 0.02° or 0.04° would imply vertical domain sizes between 86 nm and 173 nm, values that are two orders of magnitude smaller than the height of the probed volume. As a consequence, the broadening has to be attributed to fluctuations of both the lattice orientation and the lattice parameter inside bigger blocks. This means that there could be a second kind of “mosaic structure” on a much smaller scale. In order to reveal a potential domain pattern, a sample with a comparable growth history and mosaic spread was studied by applying the etch pit technique. This sample was first thinned down to 800 μm, approximately the effective z-position of the high resolution diffraction experiments on sample A (Fig. 6). Preferential etching in a CO2/H2 MW plasma was then applied for 15 min producing etch-pits at the spots where threading dislocations emerge at the surface. Fig. 9 shows that a part of the dislocations is dispersed randomly whereas a significant fraction is clustered in linear bands showing up as dark lines in Fig. 9(b). The typical distance between these bands is several 10 μm. They are apparently the residues of similar structures seen in plain view transmission electron micrographs of heteroepitaxial diamond films after 34 μm growth [11]. The bands do not form a fully interconnected network typical for a fully polygonised mosaic crystal. Nevertheless, a regular array of dislocations with identical (or similar) Burgers vector and a distance as shown in the SEM images can easily

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Fig. 8. (a): Schematic image of a block structure that would be compatible with the diffraction data from sample A, see Fig. 6(b). (b): Schematic representation of the reduced probing volume yielding the diffraction profile shown in Fig. 6(b).

accommodate angular inclinations between neighbouring crystal regions in the order of several hundredths of a degree. Assuming a symmetrical tilt boundary and a tilt of 0.02° between two such domains, one can calculate an average spacing between dislocations of 720 nm (b = 1/2 a [110]) [12] where a is the lattice constant of diamond and b is the value of the Burgers vector. It is interesting to see in Fig. 9(c) that also on a smaller scale of a few μm part of the etch pits are arranged along short lines forming a cell structure, but there are also closely packed areas. The spacing between the etch pits averaged over the whole pattern is bigger than the average distance between the dislocations in the cell walls, but the ratio between both is not as big as on the ten times bigger scale. This observation supports the assumption that a mosaic block type structure exists on two scales, similar to the results of an X-ray diffraction study of highly oriented pyrolytic graphite (HOPG) [8]. In any case, from a certain density onwards, dislocations always tend to form walls, because they interact with each other. The combination of etch pit results with high resolution X-ray diffractometry is capable to explain the appearance of individual Bragg peaks separated by the angles actually observed. The peak width seems to originate from both lattice strains and tilts of the randomly distributed dislocations. However, the present diffraction experiment does not allow the separation of these two components. In contrast, Raman spectroscopy is only sensitive to stress. Mappings of the same sample yielded a peak width averaged over a 20 × 20 μm 2 area of 2.66 cm − 1, in comparison to 1.57 cm − 1 for a high quality single crystal. The line shape for the high quality single crystal is Lorentzian. The shape of the averaged peak deduced from the map is best described by a Voigt profile which can be fitted by the convolution of the 1.57 cm − 1 wide Lorentzian type line and a Gaussian profile with a width of 1.67 cm − 1 stemming from the non-uniform broadening due to stress fluctuations. An accurate quantitative interpretation of the width of rocking curve and the Raman line in terms of microstress would require the knowledge of shape and orientation of the stress tensor. However, the emergence of stress from varying arrangements of dislocations

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The difference between the two cases is a consequence of the different dependencies of both methods on stress tensor and scattering geometry. The present consideration allows an only qualitative conclusion that both, lattice strains and tilts, contributed to the width of the single domain rocking curve peaks obtained by high resolution X-ray diffractometry. 5. Summary

Fig. 9. SEM images of a sample similar to sample A to visualise the mosaic block structure after etching in a hydrogen/oxygen plasma. (a): Original SEM image; (b): etch-pit positions deduced from (a) marked in black to obtain a better contrast; and (c): higher resolution image to identify clearly the etch pits. The edges of the images are aligned along the diamond [100] and [010] axes, respectively.

excludes the existence of simple well-defined stress states. We therefore restrict the discussion to two ideal stress states and compare qualitatively the values that the two methods would deliver for the corresponding diffraction and scattering geometries, respectively. In case of a hydrostatic stress state, 0.04° width of the synchrotron X-ray rocking curve would require a microstress of 1.8 GPa, neglecting instrument broadening. The hydrostatic stress coefficient for the Raman line broadening yields 0.5 GPa. For the second extreme case of uniaxial stress in z-direction, XRD yields 1.1 GPa while Raman gives 1.07 GPa.

Diamond crystals with a mosaic spread between 0.2° and 0.8° and a thickness of several mm would be an ideal monochromator material for the monochromatisation of thermal and hot neutrons with a wavelength around 1 Å and below. The present study describes the characterisation of two diamond crystals with different mosaic spreads in the desired range. Both samples were grown by MWPCVD on an Ir/YSZ/Si(001) substrate with a thickness of about 1 mm. We have analysed the spatial distribution of the mosaic structure by synchrotron radiation and correlated it to neutron reflectivity data. Crystal A showed a homogeneous mosaic spread of 0.18° ± 0.02° along the growth direction of the crystal. With 0.08° the lateral peak shift of the X-ray rocking curves indicated an S-shaped curvature of the crystal lattice across the sample. An absolute neutron reflectivity of 34% corresponding to 90% of the value predicted by theory means that this 1-mm-thick crystal would already outperform germanium with a comparable mosaic spread and optimal thickness. For sample B, the peak width of the neutron rocking curve was twice as big and the corresponding peak reflectivity of 13% corresponds to only half of the theoretical value. Whereas primary extinction could be neglected, this unfavourable behaviour could be explained by a significant spatial variation of the mosaic spread determined by synchrotron X-ray studies. Diffractometry with high spatial resolution indicated mosaic block sizes around 20 μm for sample A. The etch pit technique applied to a comparable sample showed dislocations that are individually dispersed and others that are arranged in boundaries of several 10 μm large blocks. The latter generate the tilt angle between neighbouring blocks. In agreement with results of additional etch pit studies a mosaic-like pattern appears to exist on two scales, several tens of μm and several μm. It seems that the broadening of rocking curve peaks from the individual blocks is caused by both lattice strains and tilts. Concerning the suitability for neutron monochromator applications the two diamond mosaic crystals show a completely different behaviour: whereas the peak width for both is within the desired range, the peak reflectivity of crystal A is close enough to the theoretical predictions so that its implementation in a monochromator would make sense. The application of type B crystals as neutron monochromators would not improve on existing crystal monochromators. It should also be mentioned that a non-uniform curvature of the lattice planes would deteriorate the monochromator efficiency. If curvature is unavoidable, it should be rather uniform so that the beam would be focused on the sample by all elements constituting the final monochromator. The results of this study will be correlated to crystal growth conditions in order to optimise the production of platelets for a first prototype. Currently sets of 1 to 1.5 mm thick and 15 × 15 mm2 wide crystals with a mosaic structure similar to that of sample A are stacked one on top of the other to achieve a total thickness of about 5 mm and an effective rocking curve width around 0.3°. Aligning and assembling are performed at the ILL by applying high energy X-ray diffraction. Sixteen stacks will constitute the first diamond prototype monochromator to be installed at the ILL reactor in spring 2013. Prime novelty statement In the present work mm-thick heteroepitaxial diamond crystals with a mosaic spread optimised for the application as the ultimate

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monochromator material for the monochromatisation of hot and thermal neutrons have been studied by synchrotron radiation. Crystals which reach up to 90% of the theoretical predictions have been synthesized and the structural reasons for the poor performance of lower quality crystals have been clarified.

Acknowledgements We thank Dr. Tamzin Lafford (ESRF) for her kind and very efficient assistance during the experiments on beamline BM05 and Mr. Erwin Hetzler (ILL) for his help on the neutron diffractometer T13C. The authors from Augsburg gratefully acknowledge the financial support by the Neutron Centres ILL (Grenoble, France), FRM2 (Munich, Germany), HZB (Berlin, Germany), and the BMBF within contract 05K09WA1. C.S. acknowledges the support by the EC FP7 Grant #283286 HadronPhysics3.

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