(IUCr) Filtering

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A crystal monochromator set to reflect a chosen wavelength $\lambda$ in the direction $2\theta_m$ from a set of lattice planes (hkl) according to Bragg law does not reflect neutrons of only this $\lambda$ wavelength, but also its higher harmonics $\lambda/2, \lambda/3, \dots, \lambda/n$ giving rise to a 2nd, 3rd, $\dots$ and nth-order contamination in the monochromatized beam. To minimize this disturbance, neutron diffraction patterns are usually recorded with neutron wavelengths of about $\lambda = 1$ Å where the contribution of the higher order contaminations is negligible. On the other hand there are cases when the use of longer wavelengths is advisable, such as the investigation of complex powder patterns with many overlapping peaks. In this case the longer wavelength has the advantage that it stretches out the diffraction pattern to higher $2\theta$ -angles, thus increasing the angular separation of the adjacent peaks and improving the resolution. The practical difficulty in using longer wavelengths is that above 1 Å the intensity of the higher order contaminations (especially $\lambda/2$ )gets more pronounced. At sufficiently high wavelengths the intensity of the second-order contamination may even exceed that of the fundamental monochromatic wavelength. In such cases these higher order contaminations must be eliminated by an appropriate neutron filter. If the monochromator is a germanium single crystal and only reflections from lattice planes with three odd indices are used, the second order reflections are eliminated automatically (see Section 2). Hence in this case only the third-order contamination must be filtered out from the monochromated beam.

There are numerous neutron filters described in the literature, such as polycrystalline filters, mechanical velocity selector, resonance filter and single crystal filters. The most practical and efficient of these appear to be the polycrystalline filters, and among the single crystal filters a special crystal of graphite (so-called pyrolytic graphite). They are easy to use and have high transmission for the fundamental wavelength.

Pyrolytic graphite is a crystalline form of graphite with pronounced preferred orientation. The hexagonal c-axis is highly aligned so as to have a single crystal structure in that direction but the a-axis has a random orientation in the basal plane. If a parallel beam of neutrons passes through such a crystal parallel to the c-axis, the shorter wavelengths get scattered through Bragg reflections from the lattice planes while the longer wavelengths remain unaffected since they cannot satisfy the Bragg equation. Thus the pyrolytic graphite is transparent to longer wavelengths and opaque to shorter ones.

Figure 3 shows the total neutron scattering cross section as a function of the incident neutron energy for a collimated neutron beam having a Maxwellian energy distribution incident parallel to the c-axis of a pyrolytic graphite crystal. The figures above the peak positions are the indices of the reflecting planes (hkl) responsible for the scattering of neutrons of a particular energy (wavelength).

**Figure 3:** Total cross section per atom (in barns) *vs.* energy for pyrolytic graphite crystal aligned with the c-axis parallel to the incident white neutron beam. After Loopstra, 1966.
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It can be seen that below and above the 004 peak there are ranges of energies with very low scattering cross section, suggesting that pyrolytic graphite is transparent to neutrons having energies in those ranges while eliminating their higher order contaminations through scattering. Most of the investigators using pyrolytic graphite as a neutron filter were concerned with the elimination of the second-order contamination, because it was found that a sufficient size of crystal for eliminating $\lambda/2$ was always sufficient for the higher order contamination as well.

Loopstra (1966) suggested the use of a wavelength of $\lambda = 2.6$ Å for neutron powder diffractometry which has its second and third order contaminations at E = 48.4meV and 108.9 meV respectively. It can be seen from Fig. 3 that the total neutron scattering cross sections corresponding to these two energies are high suggesting that they will be filtered out. On the other hand, the total scattering cross section for the fundamental wavelength ( $\lambda = 2.6$ Å corresponding to E = 12.1 meV) is very low.

Bergsma and Van Dijk (1967) measured the total neutron scattering cross section of pyrolytic graphite at room temperature and at liquid nitrogen temperature and showed that a 4 cm thick crystal of this type was an excellent filter for the elimination of higher order contamination from a neutron beam with its primary energy in the ranges of 4-5 meV and 11-14 meV (corresponding to $\lambda = 4.52-4.04$ Å and $\lambda =2.73-2.42$ Å respectively). They also found that the transmission of the primary neutron beam with an energy of E = 13.5 meV ( $\lambda = 2.46$ Å) through a 3.8 cm thick pyrolytic graphite can be increased from 67% at room temperature to 74% by cooling it down to liquid nitrogen temperature (because cooling the crystal reduces the contribution of the thermal diffuse scattering to the total neutron scattering cross section hence increases the transmission). The second-order transmission did not change by cooling the pyrolytic graphite.

Shirane and Minkiewicz (1970) showed that the efficiency of a filter of a given thickness increases as the mosaic spread of the pyrolytic graphite decreases. The transmission ratios of the primary ( $\lambda$ ) and secondary ( $\lambda/2$ ) components for the 2 $^{\prime\prime}$ thick pyrolytic graphite filter with different mosaic spreads are given in Table 1.

Heller and Saad (1975) showed that by turning the pyrolytic graphite slightly out of position while keeping its orientation axis parallel to the incident neutron beam, the energy range for filtering can be increased and by using a graphite filter with a small mosaic spread, the loss of neutron intensity of the fundamental wavelength can be reduced for required reduction of the higher order contamination.

**Table 1:** Observed transmission ratios of 2 $^{\prime\prime}$ thick pyrolytic graphite filters for the primary neutron wavelengths of $\lambda=2.44$ Å or $\lambda = 2.34$ Å. After Shirane and Minkiewicz, 1970.
		Mosaic spread
wavelength	6.5 $^\circ$	3.5 $^\circ$	1.0 $^\circ$
$\lambda$	${1\over 2}$	${3\over 4}$	${5\over 6}$
${\lambda\over 2}$	${1\over 20}$	${1\over 1500}$	${1\over 15,000}$

Frikkee (1975) investigated the neutron transmission through a pyrolytic graphite filter as a function of the filter orientation with respect to the beam and showed that tuned pyrolytic graphite filters are useful for neutron beams having fundamental wavelength between 2.23 and 3.96 Å while cooled polycrystalline Be filters would be more efficient for wavelengths greater than 3.96 Å.

4. Filtering