Instruments at pulsed neutron sources

In Section 3.1 it was noted that only three pulsed neutron sources (ISIS, LANSCE and IBR-2) currently operate at the nominal parameters, and a further two (SNS and J-PARC) are in the startup phase. The most advanced of the stress diffractometers constructed at these sources are ENGIN-X (ISIS) and VULCAN (SNS), the so-called third generation neutron strain scanners. Their configuration is an exemplary embodiment of the trends in the development of this experimental technique.

FIG. 47. Fibre-optical lens for neutron focusing [115, 116].

FIG. 48. Diagram of a Kirkpatrick–Baez mirror [117].

The main objectives set during the construction of these instruments were:

to reduce the gauge volume to ~1 mm³; to reduce data acquisition time during 3-D scanning to less than 1 h; to improve the spatial resolution, at least along one direction in the sample, to about 0.1 mm; to extend the accessible d_hkl range in order to simultaneously register 10 diffraction peaks or even more; and finally to combine other procedures and techniques with neutron diffraction which are useful or necessary for better characterization of the samples.

A diagram of the ENGIN-X stress diffractometer [119] at ISIS, which was described in Section 3.9^, is shown in Fig. 50. The instrument features a relatively large flight path from the source to the sample position (50 m) providing good Δd/d resolution; two detectors placed at scattering angles 2θ₀ = ±90°, which facilitates strain measurement in two perpendicular directions simultaneously,

FIG. 49. Left: Schematic of a nested Wolter optics. Right: HERO nested X ray optics illustrating the concept of nested mirrors for large gains [118].

and radial collimators in front of the detectors, which are used to accurately define the gauge volume.

Placing detectors at ±90° provides the most favourable shape for the gauge volume, and in addition, allows for large angular coverage in the vertical plane, as the divergence perpendicular to the diffraction plane does not affect the resolution. Thus, the convergence of scattering angles at ENGIN-X is ±14°

FIG. 48. Diagram of a Kirkpatrick–Baez mirror [117].

The main objectives set during the construction of these instruments were:

to reduce the gauge volume to ~1 mm³; to reduce data acquisition time during 3-D scanning to less than 1 h; to improve the spatial resolution, at least along one direction in the sample, to about 0.1 mm; to extend the accessible d_hkl range in order to simultaneously register 10 diffraction peaks or even more; and finally to combine other procedures and techniques with neutron diffraction which are useful or necessary for better characterization of the samples.

A diagram of the ENGIN-X stress diffractometer [119] at ISIS, which was described in Section 3.9^, is shown in Fig. 50. The instrument features a relatively large flight path from the source to the sample position (50 m) providing good Δd/d resolution; two detectors placed at scattering angles 2θ₀ = ±90°, which facilitates strain measurement in two perpendicular directions simultaneously,

FIG. 49. Left: Schematic of a nested Wolter optics. Right: HERO nested X ray optics illustrating the concept of nested mirrors for large gains [118].

FIG. 50. Diagram of a TOF neutron strain scanner. The elastic strain is measured along the directions of the momentum transfer vectors q₁ and q₂. The gauge volume is given by the intersection of incident and diffracted beams defined by slits and collimators. Figure and descriptions are from Ref. [120].

in the horizontal and ±21° in the vertical plane. For the selection of the gauge volume size, a set of radial collimators with the same angle of divergence is used (Fig. 51). The current set of collimators allows gauge volume selection from 0.5–4 mm in the horizontal plane.

FIG. 51. Design of two radial collimators with the same divergence but different spatial resolutions. Figure and descriptions are from Ref. [119].

The design of the VULCAN stress diffractometer [121] at the SNS pulsed source differs in some details only: a little shorter flight path (43.5 m), a larger scattering angle range in the horizontal plane (2θ = 60–150°). Vulcan has a larger flux of neutrons from the source as the average power (~1 MW) at SNS is approximately 5 times higher than the power at ISIS, and an advanced neutron guide system [120], which includes focusing sections of logarithmic form (Fig. 52), also leads to improved spatial resolution, reduced measurement time and an expanded range of applications. In particular, VULCAN is widely used for in situ measurements [122]; a large range of scattering angles and the presence of a small angle scattering detector allow good control of the microstructure changes during the experiment. An additional feature is a large degree of flexibility for intensity resolution optimization, which is provided by an interchangeable focusing section (3 m) of the neutron guide system.

The available wavelength range on both diffractometers ranges from 0.5–6 × 10⁻¹ nm. This allows the recording of d_hkl between 0.4 and 4 × 10⁻¹ nm, i.e. ~20 individual peaks of α-Fe are visible simultaneously, supporting a detailed analysis of microstresses and anisotropic effects.

FIG. 52. Diagram of the VULCAN diffractometer at the SNS. Figure and descriptions are from Ref. [120].

7.2.1. Trends in analysis of experimental data measured on a TOF stress diffractometer

One of the main features of TOF stress diffractometers is the ability to measure a large number of diffraction peaks simultaneously and, consequently, the possibility of using the Rietveld method for characterization of the crystalline state. In the simplest implementation, this method enables the averaging of the lattice parameters in the crystal lattice over the gauge volume. In addition, one of the possibilities of this method is the analysis of anisotropy effects that influence the position and width of the diffraction peaks, as well as the effects of texture on the intensity of the peaks. Another important task is a separation of different factors that determine the diffraction line broadening. An effective solution of both these tasks has been found, but has not yet been widely implemented.

An overview of new approaches to the analysis of the diffraction peak shape, which increase the reliability of the extraction of strain contribution to anisotropic broadening, can be found in Ref. [101]. In particular, anisotropic broadening of the diffraction lines caused by a spatially varying scalar variable, such as variations in the composition of the bulk material, has recently been

analysed [123]. The method was adapted for all crystal systems, embedded in a program for Rietveld refinement and tested on a model object with a hexagonal lattice (ε-FeN_0.433). Analysis of the diffraction data based on the proposed model by fitting individual lines and by using the Rietveld profile refinement gave a comparable result.

It is interesting to note that the measurement of a large number of peaks at a TOF stress diffractometer facilitates (at least in principle) the determination of a stress free lattice parameter by using the algorithm proposed in Ref. [124], which is based on the elastic anisotropy of the material. The most consistent account of the elastic properties of textured material is provided by the Material Analysis Using Diffraction (MAUD) software package [93]. In the literature there are already good examples of joint quantitative analysis of both the texture and the residual stress tensor (see, e.g., Refs [125, 126]).

7.2.2. Neutron diffraction and other modes of neutron scattering at pulsed sources

At TOF stress diffractometers the study of internal stresses can be easily coupled with additional capabilities such as small angle neutron scattering (SANS) neutron radiography and tomography (neutron imaging) or both.

SANS allows the determination of the geometrical characteristics of large scale inhomogeneities, which have a coherent scattering length different from that of the matrix. SANS is actively used, for example, to analyse the precipitation of nanoclusters in ODS steels [127]. For the simultaneous analysis of internal stresses and microstructural characteristics with the VULCAN stress diffractometer, a special detector is placed at small scattering angles for data acquisition of momentum transfers in the range from 0.01 to 0.2 × 10⁻¹ nm⁻¹. Through this, the identification of irregularities in the material with sizes from several to several tens of nm is possible. The combined analysis of diffraction and SANS data is particularly useful for in situ studies of processes in materials under the influence of external factors such as temperature, loading, etc.

In recent years the neutron imaging technique has been considerably developed, which is primarily due to advances in 2-D detectors which have provided the required spatial resolution (better than 0.1 mm). Like diffraction, neutron imaging is a non-destructive method for the analysis of the internal structure of complex objects and any changes to the structure with time. The combination of diffraction analysis of internal stresses with neutron imaging opens new possibilities for the in-depth characterization of materials. It is especially promising for pulsed neutron sources, where energy selective transmission imaging can easily be implemented. In the first experiments, effective contrast enhancement and contrast variation of neutron imaging

exploiting Bragg edge effects have been demonstrated (see, e.g., Fig. 53 from Ref. [128]). Good wavelength resolution at TOF stress diffractometers offers the possibility of obtaining 3-D information on the distribution of internal stresses that, in principle, allows the reconstruction of tomographic images of the stresses [129].

FIG. 53. Radiographic images of an iron and copper cylinder. Left: The direct image obtained for a wavelength above 4×10^-1 nm shows no significant contrast between Fe and Cu. The white rings are guides to the eye to mark the phase boundaries. Centre: Ratio of two images taken for λ above a Bragg edge of copper. Right: Ratio of two images taken for λ above a Bragg edge of ferrite.