PSI - Issue 43

Pavol Mikula et al. / Procedia Structural Integrity 43 (2023) 119–123 Author name / Structural Integrity Procedia 00 (2022) 000 – 000

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1. Introduction The conventional neutron strain/stress scanners, which are in fact powder diffractometers equipped with a position sensitive detector (PSD), evaluate some existing variations of lattice spacing within a sample. The required spatial resolution is usually of the order of millimeters and is determined by the dimensions of the gauge volume when for much smaller one, detector signal becomes too small and thus the measurement is being impractical. The strain/stress scanner is usually equipped with a bent perfect crystal (BPC) monochromator which has optimized curvature with respect to luminosity and resolution in a limited range of scattering angles 2  S , see e.g. Noyan and Cohen (1987), Hutchings and Krawitz (1992) and Stelmukh (2002). The principle of the measurements of variations of lattice spacing consists in the precise determination of the d hkl -lattice spacing of particularly oriented crystal planes of the sample. In neutron and X-ray diffraction the angular positions of the diffraction maxima are directly related to the values of the lattice spacing through the Bragg equation 2 d S · sin θ S = λ ( d S = d hkl , θ S - Bragg angle, λ – the neutron wavelength) and thus offers a unique non-destructive technique for the investigation of e.g. strain/stress fields. The lattice strain ε is defined as ε = ∆ d / d 0,S , and by differentiation of the Bragg condition we arrive at ε = ∆ d / d 0,S = -cot θ S · ∆θ S . Therefore, the change of ∆ d in the sample indicates a change in the scattering angle 2 θ S by a shift ∆ (2 θ S ) of the diffraction peak position for particular reflecting planes. The shift ∆θ S permits the determination of the average lattice macrostrain over the irradiated gauge volume. The conversion of strains to stresses is carried out by using appropriate elastic moduli, see Noyan and Cohen (1987), Hutchings and Krawitz (1992). Conventional two axis neutron scanners usually use, for strain determination, beam optics elements, namely: Focusing and optimally bent monochromator, a system of slits before and after the sample creating a gauge volume element (irradiated by the beam coming from the monochromator) and a position sensitive detector (PSD) imaging the diffraction profile coming from the irradiated gauge volume, see e.g. Mikula et a. (1996), Mikula et al. (1997), Seong et al. (2011). The resolution of the conventional scanner is thus determined mainly by the thickness and curvature of the monochromator, the widths of the slits (usually in the order of 1-3 millimeters), the divergence of the beam diffracted by the gauge volume and the spatial resolution of PSD. The combination of all these uncertainties results in an uncertainty ( FWHM of the gaussian image in PSD) of about roughly (5-8)x10 -3 rad. It appears sufficient for the measurement of  (2  hkl ) angular shifts brought about by strains, but not for measurements of changes of diffraction line profiles imaged by PSD which would permit to carry out microstrain and grain size studies of e.g. plastically deformed polycrystalline samples, see e.g. Delhez et al. (1982), Davydov et al. (2008). 2. High-resolution three axis diffraction setting Rather a long time ago ( see Vrána et al. (1994), Macek et al. (1996), Hirschi et al. (1998) ), first attempts with a high-resolution three-axis setting as schematically shown in Fig. 1, were tested. Following the schematic drawing shown in Fig. 1 (for small widths of the samples), a maximum resolution of this setting can be achieved for minimal

BPC monochroma tor

Rocking BPC analyzer

 M

 

L MS

L SA

Cd slit

 

 

R M

 

 S

Polyc rystalline samp le

R A

Point detec tor

Fig. 1. Three axis diffractometer setting employing BPC monochromator and analyzer as used in the feasibility studies ( R M , R A - radii of curvature, θ M , θ A - Bragg angles) for vertical position of a polycrystalline sample.