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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dispersion of the whole system which means that the orientation of the momentum  k domains related to the monochromator and analyzer are matched to that of the sample. By treating it in momentum space, for L MS /( R M ·sin  M ) ≠ 1 and L SA /( R A ·sin  A ) ≠ 1, a general form ula for minimizing the dispersion between all elements (not dependent on  1 and  2 ) was derived by Vrána et al. (1994) as (1) The optimizing of the parameters of the setting according to the condition (1) then results in a maximum peak intensity and a minimum FWHM of the analyzer rocking curve which is called as focusing in scattering. However, in some cases, it is difficult to fulfil it, namely, due to possible limitations given by L MS , L SA , R M , and R A . The experimental tests were carried out on the 3- axis neutron diffractometer installed at the Řež research reactor LVR-15. Si(111)-monochromator and Si(311)-analyzer single crystals which had the dimensions of 200x40x4 mm 3 and 20x40x1.3 mm 3 (length x width x thickness), respectively. The monochromator Si(111) providing the neutron wavelength of 0.162 nm had a fixed curvature with a radius R M of about 12 m. The radius of curvature of the analyzer was changeable in the range from 3.6 m to 36 m and the best resolution with the minimum FWHM of the analyzer rocking curve was in our case obtained for R A = 9 m. 3. Experimental results As examples of an excellent resolution of the 3-axis setting, Fig. 2 shows the diffraction analyzer rocking curves for a well annealed  -Fe(110) standard pins of the diameter of 2 mm and 8 mm and for a steel plate of 2 × 7 × 15 mm 3 2 tan  S = tan  M /(1 - L MS /( R M ·sin  M )) + tan  A /(1 - L SA /( R A ·sin  A )).

20000

FWHM = (0.070 ± 0.002) deg

FWHM = (0.084 ± 0.002) deg

5000

FWHM = (0.132 ± 0.002) deg

3000

5 mm Cd slit R A =9 m (c)

4000

No slit R A =9 m (b)

15000

No slit R A =9 m (a)

3000

2000

10000

2000

5000 Intensity / relative

1000

1000 Intensity / relative

Intensity / relative

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0

 A / deg

 A / deg

 A / deg

Fig. 2. α -Fe(110) diffraction profiles documenting the instrument resolution when using a well annealed 2 mm and 8 mm standard samples – (a) and (b), respectively and a steel plate of the dimensions of 2 × 7 × 15 mm 3 – (c).

(thickness x width x length) dimensions in which case a 5 mm Cd slit limiting the incident beam was used. All samples were put on the second axis in the vertical position. Recently, it has been found that the setting provides a sufficiently high resolution, though slightly relaxed, when wider slits (e.g. up to 20 mm) or wider samples are used. It could be used e.g. for measurements of peak shifts ∆ θ S on samples of large dimensions when the resolution is comparable to the one of conventional strain/stress scanners, see Hutchings and Krawitz (1992), Mikula et al. (1997), Seong et al. (2011). Fig. 3 then documents the effect of plastic deformation on the FWHM of the analyzer rocking curve for maraging steel plate (2 × 8 × 15 mm 3 ) of a 3D-printing material (as printed). Then, Fig. 4 shows the rocking curves related to two samples (also in the form of plates of 2 × 7 × 17 mm 3 ) of Inconel 718 used for additive manufacturing, namely, the wrought one – (a) and the SLM (selective laser melting)

FWHM = (0.314 ± 0.004) deg

8000

5 mm Cd slit R A =9 m

6000

4000

2000 Intensity / relative

0

-0.4 -0.2 0.0

0.2

0.4

 A / deg

Fig. 3. Analyzer rocking curves for the plastically deformed α -Fe(110) maraging steel sample set in the vertical position.