Equipment for the definition of the

In neutron diffraction stress measurements, it is important that the signal is obtained from a defined volume in space that contains part of the specimen material. This is achieved by placing beam defining apertures for the incident and diffracted beams, either in the form of slits, or in the form of radial collimators.

The simplified sketch in Fig. 7 illustrates how a sampling volume is defined through apertures (in this case, slits) placed in the incident and diffracted beams.

The intersection of the thus defined incident and diffracted beams is called the sampling volume or the gauge volume. The signal recorded on the detector in neutron strain and stress measurements originates from this volume.

Beam defining equipment, i.e. slits or radial collimators, is manufactured from materials with a very high absorption cross-section for thermal neutrons.

There are four elements with isotopes with such a high cross-section: gadolinium,

FIG. 7. Simplified representation of the definition of the sampling volume within a specimen through the intersection of the incident and diffracted neutron beams. The beam defining apertures are indicated as slits, but radial collimators can also be used for bean definition.

cadmium, boron and lithium [26]. For collimators, in most cases, materials containing gadolinium are applied because the high absorption of gadolinium allows the use of thin layers, thus reducing ‘dead’ area. For slits, cadmium is often used, with which a thickness of 1–2 mm is usually sufficient. Also, cadmium can be cut, bent and formed easily. An obvious disadvantage is the high toxicity of cadmium, and, where this constitutes a problem, alternative materials such as boron nitride or boron carbide can be used to manufacture slits.

The ISO technical specification [3] for the method for stress determination by neutron diffraction introduces three definitions for the sampling volume.

These refer to the nominal gauge volume, the instrumental gauge volume and the sampled gauge volume.

The sampling volume depicted in Fig. 7 corresponds to the nominal gauge volume. This definition is based on the simplifying assumption of non-diverging parallel beams with sharp edges defined by the beam apertures, and the size of the nominal gauge volume is given by the openings provided through the 3.3.4.2. Monochromatization — wavelength determination

Figure 6 in Section 3.1.5 illustrates the beam intensity distribution in a typical neutron beam emanating from a thermal moderator at a steady state source. With a neutron beam containing this spectrum of neutron energies impinging onto the specimen, it would not be possible to obtain distinguishable diffraction peaks. For this reason, the following techniques are applied:

— At most steady state source based instruments the neutron beam is monochromatized by means of single crystal or highly orientated polycrystal monochromators. This leads to a neutron beam with a narrow band of neutron wavelengths being directed to the specimen (see Fig. 3 in Section 3.1.5) and the response of one chosen set of lattice planes (hkl) is studied in the experiment.

— At pulsed sources, the flight time of neutrons between the source and the neutron detector is measured in addition to the location where the neutron is registered on the detector. This measurement of neutron travel time (TOF) can either be facilitated through the use of narrow neutron pulses (narrow both in terms of their length in time and their velocity spread) or through the installation of rotating choppers in the incident beam in order to establish a starting point in time and space for the travel of the neutrons.

Through this TOF technique, which is also described in other sections, measurements with a white neutron beam are possible and multipeak diffraction spectra are obtained, as opposed to the monochromatic instruments where measurements are mostly based on a single diffraction peak.

3.3.5. Equipment for the definition of the sampled gauge volume

In neutron diffraction stress measurements, it is important that the signal is obtained from a defined volume in space that contains part of the specimen material. This is achieved by placing beam defining apertures for the incident and diffracted beams, either in the form of slits, or in the form of radial collimators.

The simplified sketch in Fig. 7 illustrates how a sampling volume is defined through apertures (in this case, slits) placed in the incident and diffracted beams.

The intersection of the thus defined incident and diffracted beams is called the sampling volume or the gauge volume. The signal recorded on the detector in neutron strain and stress measurements originates from this volume.

Beam defining equipment, i.e. slits or radial collimators, is manufactured from materials with a very high absorption cross-section for thermal neutrons.

There are four elements with isotopes with such a high cross-section: gadolinium,

FIG. 7. Simplified representation of the definition of the sampling volume within a specimen through the intersection of the incident and diffracted neutron beams. The beam defining apertures are indicated as slits, but radial collimators can also be used for bean definition.

apertures installed and the diffraction angle. In most cases, experimenters refer to this nominal gauge volume when specifying the sampling volume size for a given experiment.

In reality, a neutron beam will be characterized by a flux distribution across the beam and an angular divergence of the beam. This results in the sampling volume being different from the nominal gauge volume. Normally, there is a gradually decreasing neutron intensity around the edges, and because of the beam divergence, the volumetric extent of the sampling volume is usually larger than the nominal gauge volume would indicate. This ‘real’ sampling volume is defined as the instrumental gauge volume. The term sampled gauge volume refers to a situation where the instrumental gauge volume is not completely filled by the material under investigation. This special case is not discussed here.

The discussion of the different sampling volume definitions should help the reader to understand two important differences between the use of slits and radial collimators as beam defining equipment.

Figure 8 illustrates the definition of a sampling volume through slits.

Figure 8(a) shows the idealized situation where non-diverging beams define the nominal gauge volume, whereas Fig. 8(b) shows exactly the same situation, but with diverging neutron beams. It can be seen that the spatial extent of the instrumental gauge volume in Fig. 8(b) is larger than that of the nominal gauge volume. The consequence of this is that the beam defining apertures, i.e. the front opening of the slits, have to be placed as close as possible to the location of the sampling volume. Otherwise, with a larger distance the instrumental gauge volume becomes larger because of the beam divergence and the spatial resolution of the measurement is compromised.

The use of radial collimators is shown in Fig. 9. Radial collimators for both the incident and the diffracted neutron beam are positioned such that the gauge volume is located at the focal distance that corresponds to their geometries. The effect of beam divergence is limited because the sampling volume is located at the narrowest point of the diverging beams. At the same time, radial collimators can be positioned at a much greater distance from the sampling volume than slits, so more space is available for specimen translation or rotation. This can be important when measurements are performed on large specimens or on specimens with an irregular shape. Additional effects associated with the use of radial collimators in neutron strain measurements have been analysed by Pirling [27].

At most monochromatic instruments, slits are used nowadays for the sampling volume definition. Nevertheless, radial collimators are becoming more popular and are used on a regular basis at the stress measurement facilities at ILL (SALSA), HZB (E3) and FRM II (STRESS-SPEC). For TOF instruments, it is normal practice that radial collimators are used in front of the detector systems.

FIG. 8. Illustration of ‘nominal’ and ‘instrumental’ gauge volumes as generated by slits in the incoming and diffracted neutron beams: (a) nominal gauge volume, based on the assumption of non-diverging incoming and diffracted neutron beams; (b) instrumental gauge volume, reflecting the more realistic situation of diverging neutron beams.

FIG. 9. Illustration of sampling volume as generated by radial collimators in the incident and diffracted neutron beams.