PSI - Issue 74

Pavol Mikula et al. / Procedia Structural Integrity 74 (2025) 56–61 Pavol Mikula / Structural Integrity Procedia 00 ( 2025) 000–000

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4

BPC monochromator

BPC monochromator

Rocking BPC analyzer

BPC analyzer (fixed position)

θ M

α 0

θ M

α 0

L MS

L MS

L SA

Cd slit

L SA

α 1

slit

θ Α

α 1

θ Α

L AD

R M

α 2

R M

α 2

2θ S

2θ S

Polyc rystalline sample

R A

R A

Point detector

Point detector

Polyc rystalline sample

Fig. 3. Three-axis diffractometer setting employing Si(111) BPC monochromator and Ge(311) BPC analyzer as used in the studies ( R M , R A - radii of curvature, θ M , θ S , θ A - Bragg angles) for vertical and horizontal positions of the sample of the cylindrical form.

Fig. 3 (for small widths of the samples), a maximum resolution of this setting can be achieved for minimal 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 θ M ) ≠ 1 and L SA /( R A ·sin θ A ) ≠ 1, a general formula for minimizing the dispersion between all elements (not dependent on α 1 and α 2 ) was derived by Vrána et al. (1994) as 2 tan θ S = tan θ M /(1 - L MS /( R M ·sin θ M )) + tan θ A /(1 - L SA /( R A ·sin θ A )). (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. The feasibility tests were carried out on the 3-axis neutron diffractometer operatin g at the neutron wavelength of 0.162 nm and installed at the Řež research reactor. 5. High resolution experimental results As examples of an excellent resolution of the 3-axis setting, Fig. 4 shows the diffraction analyzer rocking curves for a well annealed α -Fe(110) non-deformed pins of the diameter of 4.9 mm situated at the sample position in vertical and horizontal sample position, see Mikula et al. (2020). From the inspection of Fig. 3 when using a simple formula ∆θ A ≈ - ∆ (2 θ S ) valid for large values of R A ( ∆θ S = -( ∆ d S / d 0,S )· tan θ S , d 0,S is the strain free lattice spacing), the differences of the lattice spacings for elastic strains ε = ( ∆ d S / d 0,S ) can be simply determined by using the Bragg condition.

20000

FWHM = (0.130 ± 0.002) deg

FWHM = (0.101±0.003) deg

10000

8000

15000

10 mm slit R A =9 m

(a) No slit

6000

10000

(b)

4000

5000 Intensity / relative

2000 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

∆θ A / deg

∆θ A / deg

Fig. 4. Analyzer rocking curves for the non-deformed α -Fe(110) samples of φ = 5 mm situated at the sample position in vertical – (a) and horizontal position - (b).

Then, Fig. 5 shows the analyzer rocking curves of the Ti-Gr 2 samples having the hexagonal HCP structure: the initial standard one, deformed ones by the C-E method and 3 plastically deformed ones by the C-E method always in combination with the RS method. For the analysis, the diffracted beam from the Ti-Gr 2 lattice planes (101) was used. It can be seen from Fig. 5a, the initial sample provides us the diffraction profile which can be considered as a profile of the standard sample having the minimum FWHM instrumental value. On the other hand, the applied deformation procedures, namely, the ones including the RS method have a considerable influence on FWHM s. However, from Figs. 5c-5e we cannot distinguish the plastic deformation amount related to the individual C-E and RS methods. Therefore, we also used standard sample and the one after application of the 1 x C-E method. When comparing the