Accessing local electron-beam induced temperature changes during in situ liquid-phase transmission electron microscopy

A significant electron-beam induced heating effect is demonstrated for liquid-phase transmission electron microscopy at low electron flux densities using Au nanoparticles as local nanothermometers. The obtained results are in agreement with theoretical considerations. Furthermore, the impact of beam-induced heating on radiolysis chemistry is estimated and the consequences of the effect are discussed.


Thickness determination of the deposited carbon layer
For determination of the layer thickness of the amorphous carbon (a-C) film deposited on top of the liquid cell microchip, a similar a-C film was deposited onto a custom-made optical substrate using identical deposition parameters. It consists of a SiO 2 layer with a known thickness of 1.5 µm, which was grown via wet thermal oxidation on a single-crystalline silicon substrate. The film thickness was obtained by fitting a system corrected 27 physical model 28 to reflectance spectra measured via microspectroscopy by utilizing the layer thickness as the only fit parameter. Refractive index spectra of a-C and Si were taken from Arakawa S1 and Green S2 whereas the refractive index of silicon oxide was measured via spectroscopic ellipsometry. This procedure yielded a layer thickness of a-C of 9.8 nm. The results are shown in Supplementary Figure 1.

Contrast enhancement by energy filtering
As shown in Supplementary Figure 2, elastic filtering can be used to enhance the contrast of diffraction patterns during LPTEM. Elastic filtering was performed using a Gatan Image Filter (GIF) with a 10 eV energy slit around the zero loss peak.
Elastically filtered electron diffraction is especially suitable for investigation into specimen inside thick liquid pockets by enhancing the signal-to-background ratio (SBR, Au diffraction vs. diffuse scattering by water and membrane material). By comparing Supplementary Figures 2(a) and (b) it is clearly visible that the diffraction rings are more pronounced compared to unfiltered diffraction measurements.
When using the microscope setup described in the experimental section of the manuscript, elastic filtering comes at the cost of additional image distortion, a limited pixel resolution of 2k x 2k, and of shadowing a significant part of the pattern by the beam stopper due to the limited camera length available. As for layer thicknesses below the inelastic mean free path of water, the SBR of conventional diffraction is still sufficient for data analysis. Thus, we decided not to perform

Real space images
In Supplementary Figure 3 shows an elastically filtered measurement of a ramp up to 100°C. Here, the heating was not switched off after the plateau but the chip was set to cool down slowly. It is obvious, that both PBED measurements shown here do not settle at room temperature as in the case discussed in the main manuscript. It is furthermore evident that, for the present conditions, elastic filtering does not significantly alter the achievable temperature resolution. Nevertheless, elastic filtering is expected to enhance the signal-to-noise ratio and temperature resolution in LPTEM experiments conducted at thicker liquid films.
In Supplementary Figure 5(b) a failure of the used heating coil is documented, which is probably related to harsh thermal treatment of the chip during the dewetting process. It is clearly visible that the measured local temperature further decreases as expected, further emphasizing the power of local temperature measurement by PBED without relying on an external electronic readout.

Derivation of a dependency between electron flux density and dose rate
The dose rate ψ is defined as the amount of power absorbed by matter. This is fundamentally different from the electron flux density , which is measuring the amount of electrons n per time t and unit area . (1) With -e as electron charge and the negative sign to account for the flux direction of negative charges. (2) = J is defined as the amounts of electrons travelling through * during a time period t. This is easily convertible to electrons per area . ( This allows for calculating J as a function of : (4) = *

= =
When assuming a beam with cylindrical shape inciding normal to the sample (parallel beam), equals the product of a circular base area and the liquid thickness .
(5) = d is defined by the scattering events in liquid, which is reflected by the (inelastic) mean free path . If does not exceed a few microns, this can be described by first order approximation 4 :

= ( 1 + )
For an acceleration voltage of 300 kV, S amounts to 2.36 MeV(cm)²/g S4 , and is measured to be about 380 nm 42 . The resulting dose rates as a function of are plotted in Supplementary  Figure 6. For liquid layers that are significantly thinner than , Eq. (8) can be simplified to: (9) = This is in agreement with Alloyeau et al. 19 . In Supplementary  Figure 6(a) it is, however, evident that even for liquid layers with a thickness of tenths of nanometres this simplification introduces small errors, which can be easily avoided by using Eqation (8) instead.

Please do not adjust margins
Please do not adjust margins In Supplementary Figure 7, the in situ temperature profiles of constant illumination for five minutes at varying dose rates without external heating are shown. To ensure an ambient starting temperature, the beam was blanked for at least 10 min prior to every measurement. In lieu of benchmarking the relative radius change against a held set point temperature, the first 30 s of every measurement was set to 20 °C.
At the end of each measurement, a time window (shaded area) was chosen to calculate an averaged final temperature. The plateau was determined in order to try to minimize the trade-off between statistical fluctuation and possible continuation of the electron-beam induced heating. These averaged values are the basis for the data presented in Figure 3(b) in the main manuscript.
The data obtained at 0.7 show drastic -(Å 2 ) fluctuations and deviating trends, which may be attributed to the low dose rate used during data acquisition. This is believed to significantly reduce the achievable temporal resolution. In fact, a stable analysis of the {220} diffraction signal was only achieved by applying a floating average over two frames (the similar procedure was used for the second measurement at 1.3 ).
-(Å 2 ) At higher electron flux densities (1.3 and 3.0 ), the -(Å 2 ) trends remain consistent between the measurements, which in turn, underline the evidence of observed significant heating. During the last data acquired (3.0 ), the statistical fluctuation of the data is significantly enhanced. This is accompanied with a significant reduction of the relative Bragg peak intensity compared to the amorphous background contribution. This is most likely related to an increase in the dynamics of both, liquid and particle motion, which, in turn, result in flushing the particles out of the observed area. Thermal gradients caused by local heating could trigger these additional dynamics. It is noteworthy that the {311} signal is affected stronger than {220}. This may be related to the clipping of the radii chosen for observation discussed in the main manuscript, which results in a small intensity cut-off of the {311}-Voigt peak at its right flank (see Fig. 2(f) for illustration).

Estimation of temperature in the vicinity of a gas bubble in LPTEM
After Zheng et al. 8 the electron-beam induced heating of a Δ particle in a medium is given by Where h is the heat transfer coefficient of the surrounding material in . For liquid water, h amounts to 8 . In = For a single electron in Au, the total energy dissipation by the electron beam dE/dX is given by the product of the energy dissipation per nm and the particle radius r p . At 300 kV acceleration voltage, the following relation holds 8 : = ⋅ = 0.261 ⋅ is assumed as mean particle radius (see Suppl. Fig. 3(c)).
was calculated after N. Schneider 46 : and C p are the thermal diffusivity ( m²/s), and specific ℎ 1.4 ⋅ 10 -7 heat capacity of water (4.18 J/(g K)), respectively, and L is the liquid pocket side length of µm 46 . a is the beam radius (5 µm). In

T-dependent radiolysis simulations
A Python-based adaption of the reaction set developed by Ambrožič et al. 7 was used for simulation. We kindly ask the interested reader to refer to the original work for further information on the used reactions, kinetic constants, and G-values. Supplementary Figure 8 shows the absolute values of the equilibrium concentrations including a considered heating effect. The simulations were conducted until 10³ s.
Supplementary Figure 8: Absolute steady state values for radiolysis products of the utilized reaction set.