1.1. INSIGHT

The new software In Situ GIXS Heuristic Tool (INSIGHT) addresses these newly emerging requirements of fast and flexible time-resolved GIXS data treatment. INSIGHT is a script-based and object-oriented Python package containing several modules and classes (see Section 3). It provides a comprehensive workflow customized for GISAXS/GIWAXS data reduction that accompanies the scientist from visualizing raw data to the final plotting or exporting of the reduced data. INSIGHT provides a program for easy-to-use, fast and flexible GISAXS/GIWAXS (batch) data processing that drastically reduces the scientist's time investment for data analysis and visualization while maximizing the data quality throughout the entire process. Reduced data can be easily exported to be treated in other specialized software, but GISAXS modeling is not included due to its high complexity and manifold approaches. The motivations for developing this new software are many, because during in situ studies the experimental geometry might change from frame to frame, requiring image-dependent processing parameters. For example, an expanding stage moves the X-ray footprint on the sample by several millimetres and this needs to be corrected (Reus et al., 2022). Varying the incident angle during scans or using flexible foils as substrates for roll-to-roll deposition requires frame-specific incident-angle parameter settings or corrections for the footprint movement. INSIGHT provides the functionality of defining frame-dependent parameters and offers a function to correct the sample-to-detector distance automatically for each frame. Furthermore, there may be a wish to export un-binned data for further processing, and having all raw and calculated data available in the powerful programming environment of Python offers a multitude of further processing options and great flexibility to the user.

Since 2022, multiple publications have used INSIGHT as the primary X-ray scattering data analysis tool. A brief overview of these publications is given here to demonstrate the capabilities of INSIGHT and its wide application range. For example, time-resolved phase- and orientation-dependent material quantities during the conversion of lead iodide and methyl ammonium iodide to perovskite were extracted from in situ GIWAXS synchrotron data obtained during annealing on the P03 beamline at PETRA III, DESY (Buffet et al., 2012; Reus et al., 2022). GIXS data of perovskite and organic solar cells were investigated after exposure to space conditions on a suborbital rocket flight (Reb et al., 2023). Grott et al. (2022) performed GISAXS line cuts and azimuthal GIWAXS integrations to investigate polymeric PBDB-T:ITIC {PBDB-T = poly[(2,6-{4,8-bis[5-(2-ethylhexyl)thiophen-2-yl]benzo[1,2-b:4,5-b′]dithiophene})-alt-(5,5-{1′,3′-di-2-thienyl-5′,7′-bis(2-ethyl­hexyl)benzo[1′,2′-c:4′,5′-c′]dithiophene-4,8-dione})]; ITIC = 3,9-bis{2-methylene-[3-(1,1-dicyanomethylene)indanone]}-5,5,11,11-tetrakis(4-hexylphenyl)dithieno[2,3-d:2′,3′-d′]-s-indaceno[1,2-b:5,6-b′]dithiophene} thin films for non-fullerene-based organic solar cells. Li and co-workers used INSIGHT to analyze GIWAXS images of solid-state dye-sensitized solar cells in operando degradation studies on the SAXS beamline at the ELETTRA synchrotron (Amenitsch et al., 1998; Li, Guo et al., 2022). Pole figures and orientation-dependent material quantities were accessed using INSIGHT by Heindl et al. (2022) in their work on induced circular dichroism in lead halide semiconducting materials. Ye et al. (2022) performed radial `cake' cuts, revealing a q shift of the perovskite nanocrystal h00 Bragg peaks. Sun et al. (2023) investigated the degradation in CsI bulk-modified perovskite materials and identified water-induced volume expansion and morphology changes by GISAXS/GIWAXS measurements. Recently, GIWAXS indexing using INSIGHT revealed changing quantum dot orientations during thin-film deposition and processing and showed the importance of carefully tuning each processing step (Reus et al., 2023).

The range of special features and possibilities for customized data treatment with INSIGHT has been growing steadily, as has the range of applications to various sample systems and data sets. During this process, concepts of data analysis have been standardized, raising the requirement to publish this detailed overview of its functionalities for further reference. The article is structured as follows. Section 2 gives an overview of the structure of the software package and Section 3 encompasses the main geometric definitions used in INSIGHT. Section 4 presents a suggested workflow for the analysis of GISAXS/GIWAXS data with INSIGHT and showcases special features and functions. Section 5 details the batch processing workflow routine and Section 6 comprises a discussion of crystallographic indexing. Section 7 presents previously published applications of INSIGHT.

The software is open source and freely available under the GNU General Public License version 3 as published by the Free Software Foundation, and is accompanied by documentation, example data and multiple demonstration scripts from the authors. Current information about the software can be found at https://www.ph.nat.tum.de/en/functmat/forschung-research/insight.

2.1. Coordinate systems and experimental geometry

To set up the geometric framework to transform the 2D detector scattering intensity data to reciprocal space, two right-handed and orthonormal coordinate systems are used to describe the experiment and the sample. An overview of the coordinate system's definitions can be found in Table 1. First, the laboratory reference frame (LRF) is defined. The direct beam is defined to travel along the x axis of the LRF in the positive direction, and the z axis points upwards, i.e. in the opposite direction to gravity.

The detector is initialized in the LRF with the primary beam pixel coordinates at the origin and the (planar) detector surface parallel to the yz plane. It then undergoes rotation according to the provided angles R_x, R_y, R_z, followed by a translation corresponding to the sample-to-detector distance (SDD) along the x direction. Here, we note that the SDD is defined as the distance from the LRF origin to the detector pixel aligned with the primary beam and that, depending on the detector orientation, other detector pixels will have a different distance. The detector can be freely positioned in the LRF and is not limited to standard geometries with normal primary beam incidence, as other software sometimes assumes.

The sample is placed at the origin of the LRF with its surface plane parallel to the xy plane and then rotated around the y axis by the incident angle. The X-ray point of incidence (or footprint center) on the sample surface is located at the LRF origin. Here, the sample reference frame (SRF) is introduced to describe scattering data with respect to the sample. The SRF shares the origin with the LRF, but the SRF is rotated together with the sample around the y axis by the incident angle. Hence, the sample surface is parallel to the xy plane of the SRF and the z axis of the SRF is the sample normal. The SRF is used to describe reciprocal scattering information.

2.2. Transformation to reciprocal space

To interpret 2D scattering images, the momentum transfer corresponding to each detector pixel needs to be calculated. The real-space angles of each pixel (in the LRF) provide the geometric basis for calculating the momentum transfer in reciprocal space (in the SRF).

First, the out-of-scattering-plane angle ϕ is calculated pixelwise, with the scattering plane being the xz plane, by

with the real-space coordinates (x, y, z). Here α_fosp denotes the out-of-scattering-plane angle in the SRF, which is identical to ϕ [ϕ is invariant in both the SRF and LRF and can be also expressed as ϕ = ]. Thereafter, the sample-to-pixel distance (SPD) is calculated for each pixel by taking the vector norm of its position. The angle α_Δk between the incoming and final wavevectors is calculated in the LRF pixelwise via

It translates to the out-of-sample-plane exit angle α_fs in the SRF as α_fs = α_Δk − α_i = , because to address the rotation of the sample around the y axis of the laboratory coordinate system, the incident angle α_i is subtracted from the angle between the incoming and final wavevectors (compare Fig. 1).

Each detector pixel position is linked to a particular momentum transfer q in reciprocal space, defined by the X-ray wavelength and experimental geometry. In the SRF, the incoming wavevector can be written as

The scattered exit (or final) wavevector can be written as

with the out-of-scattering-plane angle ϕ and the sample exit angle α_fs. Subtracting the incoming from the final wavevector yields the well known expression for the momentum transfer:

Using equations (1), (2) and (5), the momentum transfer xyz components in the SRF are calculated for each pixel. Equation (5) determines the components of the momentum transfer q_x, q_y, q_z of the scattered signal, describing points located on the curved Ewald sphere (Fig. 8). For in-plane powders, i.e. a thin film made of an ensemble of crystallites whose scattering pattern is invariant under rotation around the substrate normal (Baker et al., 2010), the in-plane components q_x, q_y are interchangeable, motivating the introduction of a single in-plane component , conserving the length of the in-plane component. Representing the curved Ewald wedge in the flat q_r, q_z coordinate system under conservation of the length of the momentum transfer causes distortions (see e.g. Fig. S1 in the supporting information).

4.1. Image data and experimental parameters

Two-dimensional GISAXS/GIWAXS data are loaded by providing a path to a .tif or .cbf file. The importing is done by the SingleImage class, which uses the FabIO package in the background (Sorensen et al., 2023). Raw data are stored as a static class attribute. Subsequent calculations on the intensity data are stored as new class attributes. A SingleImage instance always deals with one detector image only, as will be shown in detail in this section.

4.2. Transformation to reciprocal space and intensity corrections

To illustrate the workflow, example GIWAXS and GISAXS data from in situ spraying of a lead-free perovskite (methyl­ammonium bismuth iodide) collected at PETRA III (DESY, Germany) on the P03 beamline (Buffet et al., 2012) using a Lambda detector (X-Spectrum) are shown in Figs. 4 and 5, respectively. Because of the high angular resolution due to the small pixel size of only 0.055 × 0.055 mm and a large detector area of ca 260 × 175 mm, both GISAXS and GIWAXS signals were recorded simultaneously (SDD = 447 mm, λ = 1.0507 Å, α_i = 0.415°). Detailed experimental parameters will be published elsewhere. Before the reciprocal transformation function is called, geometric settings can be checked by plotting the specular beam, the horizon and the primary beam onto the original data, as shown in Fig. S1. All intensity correction maps are shown in Fig. S5. The transformation to reciprocal space can be performed by calling SingleImage.calculate_geometry(). This will calculate the geometric maps (e.g. SPD, position and pixel incident angles) and store them as attributes to the GeometryCalculations instance. Reciprocal information maps like q_x, q_y, q_z, q_r are stored as SingleImage attributes. Common intensity cor­rec­tions are applied by calling SingleImage.calculate_corrected_intensity(). This includes the geometric solid angle and air attenuation, as well as angular pixel sensitivity corrections (Buerger, 1940; Tolan, 1999; Smilgies, 2002; Renaud et al., 2009; Jiang, 2015). Reciprocal representations of the scattering data are shown in Figs. 4 and 5. GISAXS and GIWAXS data reduction and exporting as shown in Figs. 4 and 5 can be done simultaneously with one single transformation to reciprocal space, as the implemented scattering geometry is applicable to both GISAXS and GIWAXS. Plot and data export functions exist to save or plot the results, e.g. SingleImage.plot_reshaped_image() plots reshaped GISAXS/GIWAXS data and takes multiple arguments to customize the plotting. The function takes the argument folded=True to mirror data from negative and positive q values to fill detector gaps. This feature is only intended for visualization purposes and is demonstrated in Fig. S1. If the X-ray beam is horizontally or vertically polarized, this leads to an angle-dependent scattering intensity. INSIGHT offers corrections for non-polarized fully horizontal/vertical or fractional polarized light sources. Those corrections are already applied to the data shown in Fig. 4. For more information about the available intensity corrections see Appendix B. Additionally, INSIGHT offers pixel masks and flatfield corrections, which are explained in Appendix A.

Figure 4 Example GIWAXS data reduction performed in INSIGHT of spray-coated perovskite. (a) Image data transformed to reciprocal space. Cut outlines (i.e. contours) of the performed in-sample-plane radial `cake' cut (red) and the azimuthal `tube' cut (orange) are shown as overlays. The cut data are shown in (b) and (c), respectively, with cut parameters provided in Å−1. Detector gaps and the missing wedge are marked in shaded blue. Detailed cut parameters are given, and the influence of binning and gap effects was removed using an built-in INSIGHT function.

Figure 5 Example GISAXS data reduction performed in INSIGHT of spray-coated perovskite. (a) Two-dimensional GISAXS data transformed to reciprocal space. As is common, the data are shown as a qy–qz plot. INSIGHT offers the possibility of performing GISAXS horizontal cuts in qr space, if qx cannot be neglected. The transformed GISAXS image shows vertical and horizontal line-cut outlines in purple and green, respectively. The respective cut data are shown in (b) and (c). In panel (c), the data points of the left and right sides are plotted together, and establishing a common trend of both sides results from careful optimization of the geometric parameters used for the transformation. Note that such a combination is only meaningful in the case of a rotationally invariant (around the z axis) sample. In panels (b) and (c) the cut parameters are provided in nm−1.

4.3. Data reduction

The most common data reduction methods for GIWAXS data are azimuthal `tube' cuts and radial `cake' cuts. They provide information on texture and phase, respectively. In GISAXS analysis, horizontal and vertical line cuts are usually used to access mesostructural information (e.g. domain size, distance and shape) in the lateral and normal directions of the sample. In general, horizontal, vertical, azimuthal and radial cuts can be exported with built-in saving functions associated with the respective instance and directly loaded back into INSIGHT or processed further with third-party software. INSIGHT is a powerful tool that gives the user flexible control over the data processing workflow. Inherently, this comes with the risk of erroneous user input leading to faulty reduced data, especially for non-trivial and advanced features included in INSIGHT. Users must be aware that analysis of grazing-incidence scattering data is non-trivial and special care and plausibility checks must be performed by a knowledgeable user.

4.3.5. Local background subtraction, material quantity analysis and Lorentz representation

For advanced analysis, azimuthal tube cuts can be used to extract orientation-dependent material quantities, i.e. to create pole figures for rotation-symmetric samples around the z_q axis (2D in-plane powders) (Baker et al., 2010; Reus et al., 2022). The procedure is outlined in this section.

For demonstration purposes, 2D GIWAXS data of perov­skite quantum dots recorded on the P03 beamline of PETRA III [SDD = 212 mm, α_i = 0.2°, λ = 1.048 Å, Lambda 9M detector (X-spectrum)] are shown in Fig. 6(a). Further experimental details will be published elsewhere. The sharp Bragg spots show the highly oriented arrangement of the quantum dots. The cut outline of the 100 tube cut is shown in red in Fig. 6(a). The center of the ring-shaped cut is not restricted to the primary beam position in the origin at q_r = q_z = 0, but can be chosen freely to account for refraction and reflection of the primary beam. This becomes especially important for organic materials probed in the kinematic regime (α_{c, substrate} < α_i) close to the material's critical angle, where total external reflection at the film–substrate interface produces a strong reflected beam (Müller-Buschbaum, 2014; Mahmood & Wang, 2020).

Figure 6 Example INSIGHT workflow to extract material quantity from an azimuthal tube cut using the implemented local background subtraction method. (a) Two-dimensional GIWAXS data of perovskite quantum dots. The cut outline for the azimuthal tube cut of the 100 Bragg reflection is shown as solid red lines, and the outlines for the inner and outer tube cuts for interpolating background subtraction are shown as dashed red lines. (b) Uncorrected and background-corrected data are shown in purple and black, respectively, and the inner and outer cuts performed for interpolating the background intensity are shown in dashed and dotted red, respectively. The absence of a peak at χ ≃ 50° in the inner/outer annulus data shows no contamination with reflection signal, so no false intensity is subtracted. (c) Due to the z-axis rotational sample symmetry, the background-corrected cut data are used to create the orientation sphere. (d) To transform the signal intensity to a pole figure to quantify material amounts, the Lorentz factor is needed. The material quantity and signal intensity area are individually normalized to unity.

A scattering background is frequently present in the reflection data depending on the substrate and detailed experimental parameters, such as incident angle and biasing intensity values in the cut. This background can be approximated locally by a linear interpolation between two adjacent azimuthal cuts located symmetrically around the reflection (one inside, one outside). Subsequently, the result is subtracted for each azimuthal angle χ [SingleImage.CutWAXS.subtract_local_background()]. The width and distance from the central cut of these background annuli can be conveniently specified by the user in units of sigma (Gaussian) of the reflection under investigation. The local background-corrected data are shown in Fig. 6(b), together with the inner/outer annulus cuts. This step is essential to distinguish between background signal and isotropic scattering signal in azimuthal line cuts.

Using the reduced line cut (after subtracting the background intensity), the texture and relative orientation-dependent material distribution can be quantified by constructing the pole figure, as displayed in Figs. 6(c)–6(d). For this, we assume in-plane powders where the signal intensity does not depend on the longitude. In other words, a sample rotation around the z axis in the SRF does not change the observed scattering pattern. The scattered signal intensity at a given angle χ is proportional to the scattering volume probed, given by the intersection volume of the Ewald and orientation spheres. Since this scattering volume is constant to a first-order approximation, an isotropic crystal orientation distribution will give rise to a constant intensity as a function of χ. However, the total material amount (i.e. the orientation sphere surface) that contributes to the scattering is a function of latitude χ and scales (similar to spherical integration) with . Hence, in order to access the probed material quantity, the data must be multiplied by the Lorentz factor, which takes the form for a 2D in-plane powder in grazing-incidence geometry [Fig. 6(d)] (Buerger, 1940; Waser, 1951; Cser, 2001; Baker et al., 2010). The resulting curve (black) shows the area-normalized material quantity depending on the orientation χ. Extended examples of pole figures created with INSIGHT can be found in previous publications (Heindl et al., 2022; Reus et al., 2022).

5.1. Parallel image processing

The Batch class can be used for time-efficient data processing if a simple for loop is not feasible. This might be the case for extended batch sizes or if speed is of higher importance, e.g. for live processing. In its current state, it acts as a customizable wrapper to the SingleImage class and associated classes for intensity correction and the transformation to reciprocal space. The Batch class spawns multiple workers to handle multiple images in parallel (multi-threading), employing the threadpoolexecutor from concurrent.futures (de Groot, 2020). The Batch class then deals with the execution of the processing code (pythonic image processing instructions), including customizable pre- and post-characterization (e.g. rotation, masks, cuts, fits and data export). Scripts demonstrating the Batch capabilities are available from the authors. Interactive plotting is, however, not possible in this mode.

Speeds were tested on a server cluster (2 × 18-core Intel Xeon Gold 6154 at 3.00 GHz, 376 GB RAM) and the results are shown in Figs. 7(b) and 7(c). End-to-end processing includes the following functions: transpose(), delete_hot_pixels(), calculate_geometry(), calculate_corrected_intensity() and cleanup(). End-to-end processing of 128 Lambda 9M images is achievable in under 200 ms per image [dark-blue curve in Fig. 7(b)] with 16 workers (parallel processing threads). For 12 or more workers, 50 megapixel images can be processed in under 1 s. We estimate that GIXSGUI can achieve similar parallel image processing capabilities. The batch size significantly influences the speed, since process spawning, disk access and thread setup do not profit from the parallelization approach. Processing times decrease with batch size, as can be seen in Fig. 7(c), and times below 200 ns per pixel are feasible.

6.1. Implementation of Bragg reflection simulation

To simulate the position of a Bragg reflection in reciprocal space, the Laue condition is solved geometrically for a particular set of crystal lattice parameters and wavelength. A sketch of the geometric Laue condition as used in INSIGHT is shown in Fig. 8, which is very similar to the definitions used for the transformation to reciprocal space described in Section 2. The implementation is partially based on a previous publication by Breiby et al. (2008).

Figure 8 A two-dimensional geometric sketch of the Laue condition as used in INSIGHT for GIWAXS indexing and pattern simulation. The Laue condition is fulfilled if the superposition of ki and kf yields the reciprocal-lattice vector Ghkl (intersection of the Ewald sphere and orientation sphere in three dimensions). The involved momentum transfer with respect to the substrate (within the SRF) is q; the x and z components are shown in dark red. αi is the incidence angle and rotates the SRF around the y axis of the LRF.

The Ewald sphere radius is k = 2π/λ, from which it follows that the center of the Ewald sphere is at (−k, 0, 0) in the LRF or, transformed to the SRF, it reads

with the rotation matrix R_y(α_i) and incident angle α_i. The incident angle is used to calculate the missing wedge/eye (see Appendix C). The reciprocal-lattice vector G₀ for a given lattice plane (hkl) of the crystal is given by a linear combination of the scaled reciprocal-lattice vectors a*, b*, c*:

Crystallites are spawned with the (100) plane parallel to the substrate. From the user-provided orientation a 3 × 3 rotation matrix R_C is defined. This rotates the crystal into the desired orientation. Applying R_C to the reciprocal-lattice vector, the orientation of the reciprocal-lattice vector is finally calculated by

At the intersection of the orientation sphere with the Ewald sphere, the Laue condition G_hkl = q is fulfilled. The inter­section yields the momentum transfer and . Within the Born approximation, i.e. without considering refraction, q_r and q_z are independent of the incident angle.

6.2. Indexing and GIWAXS simulation example

As an example, simulated Bragg spot positions of a cubic crystal (space group No. 221, , a = 6.313 Å) are shown in Fig. 9(a). The wavelength for calculating the missing wedge is λ = 1.048 Å (Cu Kα₁). The raw data, flatfield and enlarged plots of the folded data are shown in Fig. S4. A pixel mask, a gap mask and a flatfield correction array were applied. Different crystal orientations are marked by (hkl)_||S, where the subscript indicates that the (hkl) plane is parallel to the substrate. The dotted circles represent the reflection sets and different orientations to the corresponding reflections are marked with respective symbols. Bragg spots within the missing wedge are shown but are usually inaccessible in real GIWAXS experiments unless extensive reflection broadening exists (weak texture or small crystallite sizes). The missing wedge depends on the wavelength and is shown for multiple incident angles in Fig. 9(a). For less oriented crystal ensembles, the tails might be visible, which is also the case for printed perovskite quantum dots, as shown in Fig. 9(b), and for the simulations in Fig. 9(c). The perovskite quantum dots exhibit identical crystal lattice parameters to those used for creating Fig. 9(a), and further experimental details will be published elsewhere. By comparing the diffraction pattern with the simulations of various orientations [Fig. 9(a)], it can be concluded that the orientations (100)_||S [(100) plane parallel to substrate surface] and (122)_||S explain all the Bragg spots in Fig. 9(b). This shows the fundamental advantage of 2D simulations over the analysis of 1D tube cuts, since it makes it easier to distinguish orientations [e.g. (112)_||S and (110)_||S] which appear almost identical in a (100) tube cut, because both yield peaks at χ ≃ 45°.

Figure 9 (a) Simulated Bragg spot positions for a cubic crystal (space group No. 221, , a = 6.313 Å) and different orientations (hkl)||S on a 2D GIWAXS area. The missing wedge was calculated for incident angles of 0 and 0.2° and a wavelength of 1.048 Å−1. (b) Indexed 2D GIWAXS data of in situ perovskite quantum dot printing at αi = 0.2°. Indexing is illustrated for the (122)||S orientation as an example. (c) INSIGHT GIWAXS simulations in two dimensions of a superposition of (100)||S and (122)||S oriented and isotropically distributed (100)||S crystallites.

Additionally, a weak (almost) isotropic signal is visible, which can be treated as a third orientation when commencing with a 2D simulation. The simulation result is shown in Fig. 9(c). The third orientation is treated as a strongly broadened (100)_||S orientation. The respective variation parameters for G_hkl (radial broadening) and χ (azimuthal broadening) are shown in Table 3. Recently, indexing of perovskite nanocrystal GIWAXS data using INSIGHT was reported (Reus et al., 2023) and this is discussed in Section 7.

7.1. Time-resolved phase and texture extraction from 2D GIWAXS data

First, INSIGHT was used to treat in situ data of perovskite annealing (Reus et al., 2022). In situ GIWAXS offers the opportunity to track the kinetics of thin-film formation, which in turn influences active layer morphology and crystallinity. Here, the interdiffusion solid-state reaction from methyl­ammonium iodide (MAI) and lead iodide (PbI₂) to methyl­ammonium lead iodide (MAPbI₃) via the intermediate (MA)₂(Pb₃I₈)·2DMSO state (DMSO is dimethyl sulfoxide) was observed by time-resolved GIWAXS.

The solid-state reaction was driven by heat, which led to an expansion of the stage. As shown in Fig. 10(b), this leads to a drift of the SDD during the experiment. INSIGHT was used to calibrate the SDD for each frame using the PbI₂ Bragg reflection, whose position can be taken as invariant over the observed temperature range [SingleImage.optimize_sdd(), Section 4.2.1]. By comparing the measured reflection position with XRD peak positions (or simulated positions from the literature), the true SDD can be found for each frame. The phase evolution shown in Fig. 10(a) (left) shows the emerging MAPbI₃ and the disintegration of the intermediate precursor–solvent complex, and reveals the reaction kinetics and transition temperature. After SDD calibration with an internal calibrant, the reflection positions were constant. Fig. 10(a) (right) shows the integrated peak area of the respective Bragg reflections. By using the LMFIT package (Newville et al., 2014), the cake cut of each frame was fitted by six Gaussian peaks and a background function to model the diffraction pattern. The respective areas were then evaluated, which shows in detail the synchronous decrease in precursor–solvent phases and the emergence of the perovskite phase.

Figure 10 INSIGHT application examples from the literature for 2D GISAXS/GIWAXS data reduction and analysis. (a) (Left) Time series of radial GIWAXS cuts showing the annealing of slot-die-coated perovskite. The SDD was corrected for all GIWAXS data using INSIGHT. (Right) Bragg peak area evolution of the intermediate (MA)2(Pb3I8)·2DMSO, MAPbI3 and PbI2 with the temperature in red. Adapted and reproduced with permission from Reus et al. (2022), copyright (2022) John Wiley and Sons Inc. (b) The mechanism of SDD changes during sample-stage heat expansion. The induced height change leads to a shift of the illuminated area, which results in an effective SDD change correctable by an INSIGHT function. The SDD for each frame was calculated from the temperature-invariant PbI2 Bragg reflection position. Adapted and reproduced with permission from Reus et al. (2022), copyright (2022) John Wiley and Sons Inc. (c) (Left) Azimuthal tube cut data with the fit (black) of the MAPbI3 110/002 Bragg reflection after the annealing process for a spin-cast sample. Intensities from isotropically and edge-on oriented crystallites are shown in green and red, respectively. (Middle) A pole figure created by multiplication by the Lorentz factor for 2D in-plane powders. (Right) Time series of the evolution of the material quantity of the respective orientations. Avrami model fits are shown as solid lines. Adapted and reproduced with permission from Reus et al. (2022), copyright (2022) John Wiley and Sons Inc. (d) (Left) Two-dimensional GISAXS data of the organic donor–acceptor system PTB7-Th:PCBM for organic solar cells. (Right) INSIGHT offers specialized cutting, graining, exporting and plotting functions to create and process horizontal (and vertical) line cuts. The horizontal line cuts were exported and modeled to access domain distances and sizes. Adapted and reproduced with permission from Reb et al. (2023), copyright (2023) John Wiley and Sons Inc. (e) (Left) Two-dimensional GIWAXS data of an organic PBDB-T:ITIC thin film spin-coated from chloroform. (Right) Radial cake cuts of the respective GIWAXS data for different solvents. Fits are shown as solid red lines. Black lines indicate the background (shaded area). Adapted and reproduced with permission from Grott et al. (2022), copyright (2022) John Wiley and Sons Inc. (f) (Top) Two-dimensional GIWAXS data of pristine and final slot-die-coated perovskite quantum dot layers. Bragg spot indexing was done using INSIGHT and the orientations are (001)||S and (111)||S, respectively. (Bottom) Schematic representations of the respective unit cells to show the orientations with respect to the substrate. Adapted and reproduced with permission from Reus et al. (2023), copyright (2023) John Wiley and Sons Inc.

Applying the Lorentz factor to the tube cut [Fig. 10(c), left], as explained in Section 4.3.5, gives access to orientation-dependent material quantities [Fig. 10(c), right], which can be accessed by creating pole figures (middle). This yields a linear proportionality between area and material quantity but is only valid for 2D in-plane powders that show rotational z symmetry. Three Gaussian peaks and a constant background were used to fit the tube cuts of each frame. Integration followed by area normalization led to the material quantity time evolution as shown in Fig. 10(c) (right). It was concluded that the majority of newly formed MAPbI₃ crystallizes in an isotropic orientation [green data in Fig. 10(c)]. Avrami (1939) model fits of the data (done with a customized fitting function in LMFIT) showed a reduced dimensionality for slot-die-coated films compared with spin-coated films. GIWAXS analysis by INSIGHT was able to explore a possible connection between crystal growth kinetics and the resulting texture in perovskite thin films for solar cell application.

7.2. GISAXS data reduction

Perovskite and organic solar cells were recently tested in space on a suborbital rocket flight, and post-flight characterization was focused on the structural and morphological impact of space conditions (Reb et al., 2023). Among others, organic solar cells with PTB7-Th:PCBM [PCBM = methyl 4-{3′-phenyl-3′H-cyclopropa[1,9](C60-Ih)[5,6]fulleren-3′-yl}butano­ate and PTB7-Th = poly({2,6′-4,8-di(5-ethylhexylthienyl)benzo[1,2-b;3,3-b]dithiophene}{3-fluoro-2[(2-ethylhexyl)carbonyl]thieno[3,4-b]thiophenediyl})] as the donor–acceptor system were tested. GISAXS data are shown in Fig. 10(d) (left). Vertical line cuts can help to identify the Yoneda region of the organic polymer (Yoneda, 1963), whereas horizontal line cuts help to analyze the lateral morphology (domain size and distance). Horizontal line cuts and corresponding model fits are shown in Fig. 10(d) (left). In INSIGHT, cuts were directly performed in q space on un-binned detector data. For display or export purposes, the data can be binned, which is fully customizable by the user. For horizontal GISAXS line cuts INSIGHT offers a graining function to merge intensity values accurately from the left and right sides of the detector (see Section 4.3.4 for more details). For the model a cylindrical domain shape within a 1D paracrystalline structure (Hosemann, 1950), the distorted-wave Born approximation and the local monodisperse approximation were assumed (Sinha et al., 1988; Holý & Baumbach, 1994; Lazzari, 2002).

7.3. Polymer orientation analysis

Grott et al. (2022) investigated non-fullerene acceptor-based organic solar cells by GIWAXS and GISAXS and showed that INSIGHT is perfectly usable for organic mater­ials as well. In their study three solvents were used to tailor the active layer morphology. The crystalline structure was probed by GIWAXS, and 2D GIWAXS data of thin films produced from chloroform are shown in Fig. 10(e) (left). Radial cuts showed the 100 Bragg peak of PBDB-T and the Bragg peak of ITIC at q = 0.3 and 1.7 Å⁻¹, respectively. From azimuthal tube cuts [Fig. 10(e), right] the orientation was determined to be face-on. Challenges arise when fitting tube-cut data over the missing wedge and detector gaps. However, from the results insights can be gathered about the center position and sharpness of the orientation (FWHM). Clean tube cuts were only obtained after local background subtraction, which is especially useful for weak scatterers like polymers. Binning artifacts were also removed and this further improved the quality of the cut data.

7.4. Bragg spot indexing

Bragg spot indexing with INSIGHT was used to follow the orientational changes of perovskite quantum dots (QDs) during the processing steps of creating the absorber layer of a solar cell (Reus et al., 2023). Three different QD layer configurations were investigated and the corresponding GIWAXS images with indexing are shown in Fig. 10(f). The pristine layer consists of as-prepared QDs. The final layer (green) consists of three QD layers, with an intermediate step to exchange long-chained ligands with short-chained lead nitrate, and an additional washing step of the QD ink to improve QD size homogeneity. For the pristine film a (001)_||S orientation was found, whereas the final film mainly showed a (011)_||S orientation. In the evaluation script, around a dozen different orientations were tested and compared with the 2D scattering pattern. Thus, within minutes it is possible to simulate, plot, compare and identify the correct indexing orientation. The lattice parameters can be taken from the literature, from specific measurements like XRD or single-crystal X-ray diffraction, or a combination thereof. In this study, lattice parameters were taken from the literature and checked against XRD measurements. Center positions and FWHM values of the 001 Bragg reflection were used to evaluate the impact on Bragg reflection broadening. GIWAXS in combination with Bragg spot indexing can be a powerful tool to learn about the orientation of QDs or related systems with respect to the substrate and investigate the influence of various processing factors on texture.