Time and space resolved modelling of the heating induced by synchrotron X-ray nanobeams

Abstract

X-ray synchrotron sources, possessing high power density, nanometric spot size and short pulse duration, are extending their application frontiers up to the exploration of direct matter modification. In this field, the use of atomistic and continuum models is now becoming fundamental in the simulation of the photoinduced excitation states and eventually in the phase transition triggered by intense X-rays. In this work, the X-ray heating phenomenon is studied by coupling the Monte Carlo method (MC) with the Fourier heat equation, to first calculate the distribution of the energy absorbed by the systems and finally to predict the heating distribution and evolution. The results of the proposed model are also compared with those obtained removing the explicit definition of the energy distribution, as calculated by the MC. A good approximation of experimental thermal measurements produced irradiating a millimetric glass bead is found for both of the proposed models. A further step towards more complex systems is carried out, including in the models the different time patterns of the source, as determined by the filling modes of the synchrotron storage ring. The two models are applied in three prediction cases, in which the heating produced in Bi2Sr2CaCu2O8+δ microcrystals by means of nanopatterning experiments with intense hard X-ray nanobeams is calculated. It is demonstrated that the temperature evolution is strictly connected to the filling mode of the storage ring. By coupling the MC with the heat equation, X-ray pulses that are 48 ps long, possessing an instantaneous photon flux of ∼44 × 1013 photons s−1, were found to be able to induce a maximum temperature increase of 42 K, after a time of 350 ps. Inversely, by ignoring the energy redistribution calculated with the MC, peaks temperatures up to hundreds of degrees higher were found. These results highlight the importance of the energy redistribution operated by primary and secondary electrons in the theoretical simulation of the X-ray heating effects.

Mapping of Structural Changes Induced by X-ray Nanopatterning via Nano-X-ray Diffraction and Corresponding Electrical Effects

“…This means that the irradiation has allowed releasing the local mechanical stress present in the crystal, which in turn implies a transient local change of the mechanical properties of the material occurred in the irradiated region only. The origin of this change could possibly be represented by thermal fatigue effects induced by the numerous (≈ 6 × 10 9 ) heating/cooling cycles with ΔT = 10–30 K locally induced by the X-ray nanobeam during the irradiation time Δt , which implies corresponding thermal dilation/contraction cycles or, alternatively, by transient local softening of the chemical bonds taking place during the irradiation pulses and inducing nonthermal melting in the system …”

“…Even though we have already extended this approach also to a semiconducting material like TiO 2 , nevertheless the microscopic mechanisms responsible for the material modifications are not known yet. Among the ones that we have already investigated, it has become increasingly clear that both the oxygen knock-on and the local heating induced by the photoelectron cascades can only play quite a limited role. , …”

Beam heating from a fourth-generation synchrotron source

“…Bonino et al used a more complex theoretical model using Monte Carlo (MC) simulations considering both photo-atomic and electron interactions to calculate the proportion of the incident X-ray beam converted into thermal energy in the sample (Bonino et al, 2020). Comparing explicit (using MC) to implicit modelling (using Beer-Lambert) of the experimental results of Snell et al (2007), Bonino et al find around 1 K difference between explicit and implicit models for a 5 to 10 K increase in the temperature of a glass bead in a 15 keV X-ray beam.…”

“…Consequently, we need to be able to understand and model beam heating to predict the severity of the problem and determine possible methods of mitigation. Past studies have investigated beam heating effects on samples, modelling the ISSN 1600-5775 effects of sample geometry, time, thermal conductivity, heat sinks and other parameters (Helliwell, 1984;Kuzay et al, 2001;Kriminski et al, 2003;Hopkins & Thorne, 2016;Wallander & Wallentin, 2017;Bonino et al, 2020). Some experimental investigations have shown increases in temperature in a thirdgeneration synchrotron beam (Snell et al, 2007;Rosenthal et al, 2014;Warren et al, 2019); however, these studies mostly consider only the implications for soft, biological samples and lack a clear comparison between model and experiment.…”

Functional Modifications Induced via X‐ray Nanopatterning in TiO2 Rutile Single Crystals

“…Actually, the microscopic mechanism responsible for these material modifications is not clear yet. Careful spaceand time-resolved numerical simulations of the interaction between the superconducting oxides and the X-ray nanobeam have shown that ordinary melting must be excluded, [32] leaving room for thermal fatigue or marginal non-thermal melting as two possible candidates (see also Supporting Information). [33][34][35][36] Nevertheless, the first indications that this mechanism could be relevant also for a transition metal oxide like TiO 2 were reported in the past for Pt/TiO 2 /Pt cells, where it was shown that prolonged, nonspatially controlled synchrotron irradiation acting in synergy with an applied DC electric field was able to induce structural changes corresponding to oxygen depletion and transition to the Ti 4 O 7 Magneli phase.…”