Monte Carlo analysis of the oxygen knock-on effects induced by synchrotron x-ray radiation in the $\mathrm{B}{\mathrm{i}}_{2}\mathrm{S}{\mathrm{r}}_{2}\mathrm{CaC}{\mathrm{u}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ superconductor

Monte Carlo analysis of the oxygen knock-on effects induced by synchrotron x-ray radiation in the $B i_{2} S r_{2} CaC u_{2} O_{8 + δ}$ superconductor

Daniele Torsello, Lorenzo Mino, Valentina Bonino, Angelo Agostino, Lorenza Operti, Elisa Borfecchia, Ettore Vittone, Carlo Lamberti, and Marco Truccato

Phys. Rev. Materials 2, 014801 – Published 5 January 2018

Abstract

We investigate the microscopic mechanism responsible for the change of macroscopic electrical properties of the $B i_{2} S r_{2} CaC u_{2} O_{8 + δ}$ high-temperature superconductor induced by intense synchrotron hard x-ray beams. The possible effects of secondary electrons on the oxygen content via the knock-on interaction are studied by Monte Carlo simulations. The change in the oxygen content expected from the knock-on model is computed convoluting the fluence of photogenerated electrons in the material with the Seitz-Koehler cross section. This approach has been adopted to analyze several experimental irradiation sessions with increasing x-ray fluences. A close comparison between the expected variations in oxygen content and the experimental results allows determining the irradiation regime in which the knock-on mechanism can satisfactorily explain the observed changes. Finally, we estimate the threshold displacement energy of loosely bound oxygen atoms in this material $T_{d} = 0 . 15_{- 0.01}^{+ 0.025} eV$ .

Received 26 July 2017

DOI:https://doi.org/10.1103/PhysRevMaterials.2.014801

Physics Subject Headings (PhySH)

Electrical conductivity Impurities in superconductors Interstitials Irradiation effects Radiation damage

Condensed Matter, Materials & Applied PhysicsInterdisciplinary Physics

Authors & Affiliations

Daniele Torsello^1,2,3, Lorenzo Mino¹, Valentina Bonino¹, Angelo Agostino^4,5, Lorenza Operti⁴, Elisa Borfecchia⁴, Ettore Vittone^1,3, Carlo Lamberti^4,5,6, and Marco Truccato^1,3,5,*

¹Department of Physics, Interdepartmental Centre NIS, University of Torino, via P. Giuria 1, 10125 Torino, Italy
²Department of Applied Science and Technology, Politecnico di Torino, 10129 Torino, Italy
³Istituto Nazionale di Fisica Nucleare, Sez. Torino, via P. Giuria 1, 10125 Torino, Italy
⁴Department of Chemistry, Interdepartmental Centre NIS, University of Torino, via P. Giuria 7, 10125 Torino, Italy
⁵CrisDi Interdepartmental Center for Crystallography, University of Torino, Torino, Italy
⁶IRC “Smart Materials,” Southern Federal University, Rostov-on-Don, Russia

^*Corresponding author: marco.truccato@unito.it

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Vol. 2, Iss. 1 — January 2018

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Figure 1
Typical geometry (not to scale) of the irradiation mesh for each irradiation session. The beam is pointed onto the Bi-2212 sample on a spot for the selected irradiation time $Δ t$ , then moved in the $y$ direction to a second spot and so on. After a row is traced across the whole crystal, the beam is moved along the $z$ direction and the next row is drawn. $Δ y$ and $Δ z$ represent the mesh spacing between irradiation points in the two directions, respectively. The orange box represents the elementary unit on which calculations are carried out for each experimental setup, as explained in the text. The crystal $a$ , $b$ , and $c$ axes are parallel to the $z$ , $x$ , and $y$ direction, respectively.
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Figure 2
Typical energy distribution of the total electron fluence $Φ_{e} (E)$ calculated over an elementary unit of the sample (see Fig. 1). The results are normalized per source particle of the simulation and are therefore relative to a single incident photon. The parameters employed for this simulation correspond to the experimental conditions of the third irradiation session on sample WBAP13 ( $h ν = 17.05 keV$ ) and the results are qualitatively identical to all of the other studied sessions.
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Figure 3
Spatial distribution of the total electron fluence $Φ_{e} (x_{i}, y_{i}, z_{i}, E)$ for electrons with kinetic energy E between 16 and 17.05 keV (a), and between 7 and 8 keV (b), in the case of the data of Fig. 2. X rays come from left to right and impinge the crystal at $x = 0$ . Each electron distribution map is a $x y$ -plane cross section with a thickness of 50 nm in the $z$ direction, centered at an irradiation row position $z = z_{0}$ (1), at $z = z_{0} + 50 nm$ (2), at $z = z_{0} + 100 nm$ (3), at $z = z_{0} + 150 nm$ (4), and at $z = z_{0} + 200 nm$ (5). The results are normalized per source particle of the simulation and are therefore relative to a single incident photon.
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Figure 4
Spatial distribution of the fraction of displaced interstitial oxygen atoms $f_{a d} (x, y, z)$ corresponding to the data of Figs. 2 and 3, obtained using (a) $T_{d} = 0.93 eV$ and (b) $T_{d} = 0.073 eV$ . X rays come from left to right and impinge the crystal at $x = 0$ . The maps are $x y$ -plane cross sections with a thickness of 50 nm in the $z$ direction, centered at an irradiation row position $z = z_{0}$ (1), at $z = z_{0} + 50 nm$ (2), at $z = z_{0} + 100 nm$ (3), at $z = z_{0} + 150 nm$ (4), and at $z = z_{0} + 200 nm$ (5). Color scale is linear. Black solid contour lines are spaced by about (a) $8 \times 10^{- 5}$ and (b) $4.6 \times 10^{- 3}$ .
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Figure 5
Comparison between experimental and simulated δ values as a function of the photon cumulative fluence $Φ_{ph}$ for all the irradiation sessions on samples (a) WBAP13 (diamonds) and WBAP14 (squares) and (b) WBVB05 (circles) and WBVB10 (triangles). Black symbols indicate the experimental values, blue represents the values from simulations with $T_{d} = 0.93 eV$ , and red the values from simulations with $T_{d} = 0.073 eV$ .
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Figure 6
Comparison between experimental data (black) of samples WBAP13 (diamonds) and WBAP14 (squares) and simulated values (orange) obtained for the value of $T_{d}$ corresponding to minimization of $χ^{2}$ ( $T_{d} = 0 . 15_{- 0.01}^{+ 0.025} eV$ ). The inset shows the normalized $χ^{2}$ as a function of $T_{d}$ quantifying the agreement between experimental and simulated values calculated over the whole set of irradiations for samples WBAP13 and WBAP14. The solid curve is a guide for the eye.
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Physical Review Materials

Monte Carlo analysis of the oxygen knock-on effects induced by synchrotron x-ray radiation in the Bi2Sr2CaCu2O8+δ superconductor

Daniele Torsello, Lorenzo Mino, Valentina Bonino, Angelo Agostino, Lorenza Operti, Elisa Borfecchia, Ettore Vittone, Carlo Lamberti, and Marco Truccato

Phys. Rev. Materials 2, 014801 – Published 5 January 2018

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Monte Carlo analysis of the oxygen knock-on effects induced by synchrotron x-ray radiation in the $B i_{2} S r_{2} CaC u_{2} O_{8 + δ}$ superconductor