Experimental setup for high-temperature in situ studies of crystallization of thin films with atmosphere control

A high-temperature setup is presented for in situ synchrotron scattering experiments on thin films, including high heating rates and atmosphere control.

Since the sample is translated downwards, the effective DTSD is decreased as the data were measured since the sample was tilted 2° initially and rotated Δ 1° during the measurement, as illustrated in the inset of Figure S2. When the sample was shifted downwards so much that the beam shoots above the sample, the effective footprint becomes smaller, and the change in DTSD deviates from being linear, and approaches a constant as the bottom of the beam reaches the upper edge of the sample. As long the refined DTSD follows the linear trend the dataset be used for further data treatment.

Figure S2
Refined detector-to-sample distance (DTSD) as function of height-offsets at different temperatures for a BTO sample on platinized Si. The straight lines are fits to the full colored data J. Synchrotron Rad. (2020). 27, doi:10.1107/S1600577520010140 Supporting information, sup-3 points, also indicated at the end of the label in the legend, e.g. the fitted line for 710 °C is only fitted for the 100-300 µm offset. For the datapoint at 400 µm for RT, the sample was completely out of the beam, hence no offset could be determined. The illustration at the bottom shows, how the DTSD decreases as the sample is translated downwards. The green line in the illustration represents the center of the X-ray beam.
The data in Figure S2 were measured as part of an in situ experiment with a heating ramp of 2 K s -1 and the temperatures are shown in Figure S3. By deciding which height offsets that still have the full footprint on the sample, more data points can be used, thereby giving more information than by just using one set of height offsets as the temperature increases. Using the thermal expansion coefficient for Pt, individual calibration files where generated for a set of height-offsets at ~ 400, 720 (when the constant temperature is reached), and 710 °C (at the end for the constant temperature), and the DTSDs were manually refined for all datasets, and shown in Figure S2, with the orange, green, and red data series, respectively.
A region in 2 for the full dataset series integrated with a DTSD set to the value at RT and 0 µm height offset, can be seen in Figure S4(a). The resulting effect of the change in DTSD can easily be seen from the five data series; the position of the peaks in the first dataset in each series should align at the same 2 -value if the DTSD was correct. The position of the (111) and (200) peaks for Pt at RT are indicated with red dashed lines. In Figure S4(b), the dataset series with corrected DTSD according to the linear trend in Figure S2 at RT can be seen. There is a clear change in the peak positions as the sample is heated, where the positions of the peaks move to higher 2 , which could be mis-interpreted as a unit-cell contraction. This effect arises from the thermal shift of the sample environment, the effect which was anticipated, and is the reason for performing the height-offset in the first place.
In Figure S2, the DTSD for the 100 µm offset series falls on the linear trendlines for the whole temperature range and can therefore be used as a starting point for correcting for the thermal shift of the setup. The green lines in Figure S4, indicate the maximum for the Bragg peaks expected as a result of the thermal expansion for Pt. To correct for the thermal shift, a pseudo-Voigt function was fitted to the data series for the (111) peak, to find the difference between the expected and the observed position. Since the data have been integrated using the DTSD for the first RT dataset, and are therefore in the 2 -space, an additional correction to the shift needs to be accounted for because the data are collected on a flat detector, resulting in a nonlinear shift in 2 -space. The situation is shown in Figure S5, where tan 2 , tan , where is the DTSD that was used for integrating the dataset before the height correction, is the new DTSD that is needed to integrate the data correctly, 2 is the calculated peak position at the temperature the dataset is measured at and corrected for thermal expansion, and is the peak position for the specific Bragg reflection integrated with . By isolating the correct DTSD, : the data can be reintegrated and used for further data treatment. This formulation was used for the 100 µm data series, and the results are shown in Figure S4(c).

Figure S4
Selection of the 2 range showing the (111) and (200)  The linear translation from Figure S2 can be applied to the DTSD for the 100 µm offset, corrected for thermal shift and expansion, to obtain the correction for all other heights. Here, the average of the slope of the dataset collected at elevated temperatures was -3.48(2) cm mm -1 . By fitting the position of the STO-(111) peak for the corrected data, the datasets that have a too large difference, can be excluded because they do not have the full footprint of the beam on the sample. In Figure S6(a), all the datasets corrected in this fashion are shown. Comparing Figure S6(b) to Figure S3, shows the data sampling interval and the regions where datasets are used. Figure S6(c) shows the final merged corrected datasets, which can be further processed as a regular time-resolved dataset from synchrotron in situ measurements. The (111) and (200) peaks for the STO substrate are indicated for comparison with Figure S4.
The adjustment in DTSD is effectively a remapping of the data bins for the scattering angle, which can easily be seen at the edge for the high-2θ region in Figure S6(c) as the fluctuations in the highest value for the datasets as function of time. At the same time, the scattering from the air in the low 2θregion varies for each height offset, giving rise to a non-continuous change in the background level as a function of time, which is accounted for in the subsequent data analysis.
For samples where the substrate is a standard single crystal, the availability of a Bragg reflection can be limited. The strategy for data measurements must account for this, since a reference peak is necessary for adjusting the DTSD. For the STO(100) substrate the {311} peaks fits well with an ω = 2-3° and the X-ray beam approximately parallel to the {100} side of the substrate. Since the Bragg reflections for single crystals, and especially large crystals, are a convolution of multiple components the resulting shape when the data are integrated can be complex. For the samples in this study, the position was found based on the smoothened first derivative of the data in a small region around the {311} peak in 2θ to find the edges of the peak and an average of those for the position.
The precision of the data after adjusting for the height offset, is estimated to be on the fourth digit, but significant differences in the peak profile for peaks for the thin film, can occur and could lead to a lower precision.

S3.1.1. Rietveld refinement
For the Rietveld refinement of the unfilled tetragonal tungsten bronze structure of SBN, the peak profile was refined using the Caglioti pseudo Voigt function with three and one terms for the Gaussian and Lorentzian contributions, respectively. The scale factor and zero-point offset were refined. For the structure, the unit cell parameters were refined along with texture as a two term March-Dollase model for the {100} and {001} families. The structural model for SBN is given in Table S1. The refined cell parameters where 12.4998(11) and 3.9637(3) Å for a and c, respectively.
The texture yielded 6.79 and 0.75 for the {100} and {001} families, revealing a small degree of preferred orientation. An R wp = 1.28 and a Goodness of fit (χ 2 ) = 0.44 were obtained. The obtained J. Synchrotron Rad. (2020). 27, doi:10.1107/S1600577520010140 Supporting information, sup-7 The low Goodness of fit is due to addition of the texture modeling adding several additional parameters (five more) to the refinement and the starting model based on a Rietveld refinement on a powder dataset measured on the calcined powder of the corresponding sol-gel. An χ 2 = 1.03 and R wp = 2.95 is obtain for a refinement with a polycrystalline texture model. The visual inspection of data ( Figure S8) compared to the refinement shown in Error! Reference source not found.(c), shows that the texture model is needed but do not hold any statistical significant information.