research papers Neutron transmission through pyrolytic graphite monochromators

Transcription

1 Journal of Applied Crystallography ISSN Received 4 October 2000 Accepted 1 February 2001 Neutron transmission through pyrolytic graphite monochromators D. F. R Mildner,* M. Arif and S. A. Werner National Institute of Standards and Technology, Gaithersburg, MD 20899, USA. Correspondence e- mail: david.mildner@nist.gov # 2001 International Union of Crystallography Printed in Great Britain ± all rights reserved Thermal neutron transmission measurements have been made as a function of wavelength on a pyrolytic graphite monochromator crystal that has been set to diffract a horizontal beam at different take-off angles. The major dips in the transmission caused by the various re ections have been identi ed. These results can be used for the design of a beamline on which more than one instrument is placed. The transmission data show that it is best for the monochromator with the greatest (horizontal) take-off angle to be placed upstream, with monochromators with decreasing take-off angles progressively further downstream. The order of instruments for which the wavelength is greater than 0.43 nm is unimportant. 1. Introduction It is often necessary to know the beam characteristics for each instrument when more than one instrument is placed on the same neutron beamline, whether at a pulsed source or a reactor. In particular, the spectrum transmitted through the monochromator of the upstream instrument is required for an adequate description of the capabilities of the downstream instrument. This means that the upstream monochromator crystal should have high transmission except, of course, at the wavelength corresponding to the particular Bragg angle setting of the crystal. In this situation, pyrolytic graphite is a desirable monochromator because of its low absorption cross section, which is three orders of magnitude lower than that of copper or germanium. Highly oriented pyrolytic graphite is highly attractive as a monochromator (Riste & Otnes, 1969) because it has high re ectivity and may be described as an ideally imperfect non-absorbing crystal. It is also a good lter (Bergsma & Van Dijk, 1967; Shirane & Minkiewicz, 1970; Shapiro & Chesser, 1972) for thermal neutrons because of its aligned hexagonal axis, but random orientation in the basal plane, which allows it to be a tunable lter (Frikkee, 1975; Vorderwisch et al., 1999). Consequently, pyrolytic graphite should be a good monochromator for a beamline with multiple instruments. 2. Experimental conditions We have performed neutron transmission measurements through a ZYA grade (0.4 mosaic) pyrolytic graphite monochromator crystal set to diffract thermal neutrons at different wavelengths. The measurements were performed on the C3 beamline, used for the time-of- ight small-angle neutron diffractometer SAND (Thiyagarajan, Urban et al., 1998) at the Intense Pulsed Neutron Source at Argonne National Laboratory. (The source operates at 30 Hz with 450 MeV protons in 0.3 ms wide pulses impinging on a depleted uranium target with a time-averaged current of 15 ma.) The high-energy neutrons produced by spallation are slowed down in a grooved 24 K solid methane moderator designed to maximize the cold neutron ux while preserving the narrow pulse width at all cold neutron wavelengths. Graphite and beryllium re ectors decoupled by a 0.5 mm layer of cadmium surround the moderator. A cryogenically cooled (77 K) MgO lter (Thiyagarajan, Crawford & Mildner, 1998) of cross section 60 mm by 60 mm and length 100 mm is used to reduce the fast neutron ux by over two orders of magnitude, while transmitting over 70% of the cold neutrons. This limits the shortest useful wavelength to about 0.1 nm, while frame overlap (30 Hz source frequency and 9 m source± detector distance of the SAND instrument) restricts the longest wavelength to 1.4 nm. The depleted-uranium target produces delayed neutrons (fraction ) that result in a time-independent background that degrades the quality of the results, particularly at the longest wavelengths for which there are few neutrons in the pulsed beam. However, a drum chopper of diameter 185 mm and with a B 4 C shell of thickness 10 mm, operating at 15 Hz, suppresses the delayed neutron background, and can almost entirely eliminate the background at the longer wavelengths. A pair of crossed Soller collimators convergent to a point on the detector provides collimation of 3.4 mrad. Various B 4 C apertures of various sizes placed in the beam determine the sample size to be 15 mm in diameter. Fig. 1 shows a schematic diagram of the experimental arrangement. The pyrolytic graphite monochromator crystal, 50 mm high, 75 mm wide and 1.85 mm thick, was placed in the sample position and oriented at an angle relative to the incident beam. The data were recorded as a function of time-of- ight using two at (`pancake'), low-ef ciency BF 3 ionization 258 Mildner et al. Pyrolytic graphite monochromators J. Appl. Cryst. (2001). 34, 258±262

2 Figure 1 A schematic diagram of the experimental arrangement for the neutron transmission measurements of the graphite monochromator. chambers, M1 and M2, placed before the collimation and after the sample, at distances of 5.65 and 8.65 m, respectively, from the moderator. The location of the detectors gives a crude wavelength scale. Each detector was masked with a B 4 C `crispy mix'. Differences in intensity in the beam monitor are caused by time-averaged variation (<1% about the mean) in the proton beam current, but not by variation in moderator characteristics that would in uence the thermal spectrum. Hence differences in neutron spectra are negligible and data in the rst detector before the sample are used to normalize any differences in beam currents delivered in the various runs. Fig. 2 shows the wavelength spectrum of the incident beam measured by the rst detector, with a mean wavelength of 0.54 nm. Small dips in the spectrum are attributed to the single-crystal MgO lter. area detector of the diffractometer, which for these measurements were set to a time resolution of 2%, or / = 2%. This reduces the statistical variation in the data at the longer wavelengths for which the ux distribution weighted by the detector cross section decreases as approximately 4. The data collected with the transmitted-beam monitor are used for determining the transmission T(), the attenuation () and the total cross section () of the crystal as a function of wavelength. If the neutron count rates for a given, with the crystal of thickness t in and out of the beam, are I t () andi 0 (), respectively, then I t ˆI 0 T ˆI 0 exp t eff Š ˆ I 0 exp N t eff Š; where () =N(), N = mm 3 is the atom number density for graphite, and the effective thickness of the crystal is given by t eff = tcosec. The transmission T() for a given run is obtained from the ratio of the counts with and without the crystal, modi ed by the background B; that is, T ˆ I t BŠ sample = I 0 BŠ empty : 2 Since this is a ratio measurement, differences in detector ef ciency as a function of can be ignored. Fig. 3 shows the results of the various transmission runs through the graphite monochromator, set to diffract a beam at 1 3. Results Data were collected with the graphite monochromator crystal set at nominal angles of 90, 45, 32 and 22 to the incident beam, so that the 002 re ection corresponded to diffraction in the horizontal plane at wavelengths,, of , , and nm, respectively. In addition, a background run was performed with the crystal removed. Each data set was collected for 3 h. The operating program of the instrument bins the data for each monitor detector into variable time channels commensurate with those for the position-sensitive Figure 2 The wavelength spectrum of the incident beam measured by the rst detector. (The wavelength dependence of the detector has not been removed.) Figure 3 The transmission results for the graphite monochromator set to diffract the beam at angles of 90,45,32 and 22. J. Appl. Cryst. (2001). 34, 258±262 Mildner et al. Pyrolytic graphite monochromators 259

3 Table 1 Wavelengths (nm) of the principal identi ed dips in the transmission data of Fig. 3. hkl PG90 PG45 PG32 PG ± ± the four different angles. Table 1 shows the wavelengths corresponding to the principal dips in the transmission data caused by Bragg scattering for each crystal setting. Each data set shows dips corresponding to the diffraction from the 002 and 004 re ections and, in the case of =90, higher order re ections as well. In addition, there are non-00l re ections that can diffract in a non-horizontal plane and cause broader dips at the shorter wavelengths; these dips are identi ed in Appendix A. The positions of these dips give the wavelength calibration of the data, ˆ 2dl 1 sin ; where d is the interplanar spacing of the crystal. The non-00l re ections are not useful for calibration purposes because the turbostratic nature of the hexagonal layers causes broad asymmetric transmission dips. Fig. 4 shows the calibration of Figure 4 The calibration of the 90 transmission run from the 00l transmission dips. 3 the 90 transmission run, with = (3) nm and = 85.4 (4). (The uncertainties, given within parentheses, are the standard deviations obtained from the least-squares linear t.) This seemingly poor calibration is caused by a paucity of points, the relaxed time resolution of the data and lack of knowledge of the precise setting of the monochromator. The diffracted beam was not measured directly because the purpose of our measurements was to illustrate the transmission through a pyrolytic graphite monochromator crystal. The calibration of the other runs is presented in Table 2, though errors cannot be assessed when there are only two 00l transmission dips. 4. Analysis Table 3 shows the average transmission at the longer wavelengths (>0.5 nm) for the different transmission runs, neglecting the 002 re ection dips. The data do not show any drop in transmission as a function of wavelength. This is not surprising. The absorption cross section for carbon [ a = (7) barns at = nm] is so small that even at = 1.4 nm, a t = (11) for =90, and T = In addition, the incoherent scattering is negligible. Consequently the transmission measurements are most sensitive to any impurities. Fig. 5 shows a plot of logt versus the effective thickness t eff = tcosec of crystal through which the beam passes. The results for the 32 run are inconsistent with the rest of the data (see also Fig. 3); we have no adequate explanation for this. A t to the other three data points gives an attenuation coef cient ave = (9) mm 1, averaged over the incident spectrum. This compares with a theoretical value of mm 1 at = 0.54 nm. However, this corresponds to an average transmission loss of only 1% in the measurement from the expected values. We note that at the shorter wavelengths, in the region where the non-00l re ections are available, the transmission is reduced considerably. This is caused by the multiplicity of re ections with broad dips that contribute to the scattering cross section at shorter wavelengths, and is most prominent at the smaller values. (It is not caused by the increased effective thickness, which would affect the entire wavelength range; in any case, the incoherent scattering from carbon is negligible.) For the smaller settings, the 10l re ections with their broad asymmetric dips in transmission occur at wavelengths longer than the 002 re ection, whereas the opposite is true for the larger (see Fig. 6). The cross over occurs when the wavelengths for the 101 and 002 re ections are, by equation (7) (see Appendix A), equal. This is given by tan = 4(3 1/2 )(a 0 /c 0 ) [4 3(a 0 /c 0 ) 2 ] 1,or = 35.2, equivalent to a horizontally diffracted beam at = nm. This de nes the onset of the considerably reduced transmission for shorter wavelengths. This has importance when more than one monochromating crystal is placed on the same beamline. The monochromator with the greatest take-off angle (and with the longest diffracted wavelength) should be placed rst, while that with smallest take-off angle (and with the shortest diffracted wavelength) should be placed last. This is fortunate because it 260 Mildner et al. Pyrolytic graphite monochromators J. Appl. Cryst. (2001). 34, 258±262

4 Table 2 Calibration, =2dl 1 sin +, of the measurements from the 00l transmission dips. Nominal orientation angle ( ) Calibration orientation angle ( ) Calibration (nm) (4) (3) (2) (9) ± ± Table 3 Average transmission for wavelengths greater than 0.5 nm. Orientation angle ( ) Transmission at long t eff (mm) = tcosec (22) (44) (25) (27) allows for a more convenient placing of spectrometers, particularly when instruments can be located on only one side of the beamline. On the other hand, the greatest wavelength diffracted from a 10l re ection occurs at nm from the 100 re ection at = 0. Hence, a monochromator set to give a beam of wavelength greater than 0.43 nm ( ' 40 )maybe placed after those with lower settings, because as shown in Fig. 3, the transmission is not greatly reduced in this region as it is below 0.4 nm. APPENDIX A Graphite has a hexagonal lattice with vectors a 0 and c 0 of magnitude a 0 = nm and c 0 = nm. The reciprocallattice vectors have lengths given by b 1 = b 2 =2/a 0 (2/3 1/2 )= nm 1, and b 3 =2/c 0 = nm 1. The generalized reciprocal-lattice vector corresponding to the crystal plane with Miller indices (hkl) is given by s hkl =2[ (h + k)/a 0,(h k)/3 1/2 a 0, l/c 0 ], in Cartesian components, with a magnitude given by s hkl 2 = b 1 2 (h 2 + hk + k 2 )+ b 3 2 l 2. The Bragg dips occur when 2ks = s hkl 2, where the incident wavevector is given by k =(2/)k 0 =(2/)(x + y + z), and where, and are the direction cosines of k 0, the unit vector in the direction of the neutron beam, with respect to the principal axes of the graphite crystal. We obtain the wavelength hkl for the hkl re ection, hkl ˆ dhklf 2=a 2 0 h k h k =3 1=2 2=c 0 lšg; 4 corresponding to the planar spacing d hkl ˆ 4=3a 2 0 h 2 hk k 2 l 2 =c 2 0Š 1=2 : 5 The Bragg angle hkl 0 corresponding to this re ection is given by sin hkl 0 ˆ d hkl h k =a 0 h k =3 1=2 a 0 l=c 0 Š: 6 The monochromating crystal is aligned relative to the beam such that the (00l) graphite planes make an angle to the beam direction k 0, whereas the alignment within the planes is random with azimuthal angle '. Let = cos cos', = cos sin' and = sin. Then hkl ˆ dhklf 2=a 2 0 cos cos ' h k cos sin ' h k =3 1=2 Š 2=c 0 sin lg 7 and sin hkl 0 ˆ d hkl cos cos ' h k =a 0 cos sin ' h k =3 1=2 a 0 sin l=c 0 Š: 8 Consider the set of re ections hkl =00l. The wavelength 00l =2c 0 sin/l and 0 00l =. This gives rise to sharp dips in the transmission that move to shorter wavelengths as the angle is decreased. This is illustrated in Fig. 6. On the other hand, the Figure 5 Values of t determined from the average transmission at long wavelengths with cosec, which is proportional to the effective thickness of crystal through which the beam passes. Figure 6 The location in orientation angle ±wavelength (±) space of the sharp transmission dips caused by the 002 and 004 re ections. Also shown are the 100 re ection and the ranges of the broad dips caused by the 10l re ections for l = 1 and 2. J. Appl. Cryst. (2001). 34, 258±262 Mildner et al. Pyrolytic graphite monochromators 261

5 Table 4 Calculated wavelengths (nm) for various re ections hkl and for different crystal settings. hkl =90 =45 =32 = ± ± hkl re ections give broad dips because there is random orientation in the basal plane. Table 4 gives the values of the wavelengths corresponding to the maximum value of these re ections for the graphite crystal placed to diffract at the different orientation angles. For cos 6ˆ 0, the maximum wavelength of the 10l re ections occurs when (cos' + sin'/3 1/2 ) is a maximum, i.e. 2/3 1/2 when ' =30. Fig. 6 shows the broad range of wavelengths that correspond to the transmission dips of the 10l re ections. We acknowledge the experimental assistance of P. Thiyagarajan, D. G. Wozniak and K. Littrell. This work has bene- ted from the use of the Intense Pulsed Neutron Source at the Argonne National Laboratory; this facility is funded by the US Department of Energy, BES-Materials Science, under contract W Eng-38. SAW acknowledges support from the National Science Foundation, Physics Division, grant No References Bergsma, J. & Van Dijk, C. (1967). Nucl. Instrum. Methods, 51, 121± 124. Frikkee, E. (1975). Nucl. Instrum. Methods, 125, 307±312. Riste, T. & Otnes, K. (1969). Nucl. Instrum. Methods, 75, 197±202. Thiyagarajan, P., Crawford, R. K. & Mildner, D. F. R. (1998). J. Appl. Cryst. 31, 841±844. Thiyagarajan, P., Urban, V., Littrell, K., Ku, C., Wozniak, D. G., Belch, H., Vitt, R., Toeller, J., Leach, D., Haumann, J. R., Ostrowski, G. E., Donlevy, L. I., Hammonds, J., Carpenter, J. M. & Crawford, R. K. (1998). The Performance of the Small-Angle Diffractometer, SAND at IPNS, inicans XIV±The Fourteenth Meeting of the International Collaboration on Advanced Neutron Sources, June 14±19, 1998, Starved Rock Lodge, Utica, Illinois, edited by J. M. Carpenter & C. Tobin, Vol. 2, pp. 864±878. Spring eld, VA: National Technical Information Service. Shapiro, S. M. & Chesser, N. J. (1972). Nucl. Instrum. Methods, 101, 183±186. Shirane, G. & Minkiewicz, V. J. (1970). Nucl. Instrum. Methods, 89, 109±110. Vorderwisch, P., Stuhr, U. & Hautecler, S. J. (1999). J. Neutron Res. 7, 119± Mildner et al. Pyrolytic graphite monochromators J. Appl. Cryst. (2001). 34, 258±262