Accurate extrinsic and intrinsic peak broadening modelling for time-resolved in situ ball milling reactions via synchrotron powder X-ray diffraction

Accurate extrinsic and intrinsic peak broadening modelling for time-resolved in situ ball milling reactions via synchrotron powder X-ray diffraction† Paolo P. Mazzeo, * ab Giulio I. Lampronti, * c Adam A. L. Michalchuk, d Ana M. Belenguer, e Alessia Bacchi ab and Franziska Emmerling d Received 16th May 2022, Accepted 12th July 2022 DOI: 10.1039/d2fd00104g The debate on the mechanisms which underpin mechanochemical reactions via ball mill grinding is still open. Our ability to accurately measure the microstructural (crystal size and microstrain) evolution of materials under milling conditions as well as their phase composition as a function of time is key to the in-depth understanding of the kinetics and driving forces of mechanochemical transformations. Furthermore, all ball milling reactions end with a steady state or milling equilibrium –represented by a specificphase composition and relative microstructure –that does not change as long as the milling conditions are maintained. The use of a standard sample is essential to determine the instrumental contribution to the X-ray powder diffraction (XRPD) peak broadening for time-resolved in situ (TRIS) monitoring of mechanochemical reactions under in operando conditions. Using TRIS-XRPD on a ball milling setup, coupled with low-energy synchrotron radiation, we investigated different data acquisition and analysis strategies on a silicon standard powder. The diffraction geometry and the microstructural evolution of the standard itself have been studied to model the instrumental contribution to XRPD peak broadening throughout the grinding activity. Previously proposed functions are here challenged and further developed. Importantly, we show that minor drifts of the jar position do not affect the instrumental resolution function significantly. We here report and discuss the results of such investigations and their application to TRIS-XRPD datasets of inorganic and organic ball mill grinding reactions. a Department of Chemistry, Life Sciences and Environmental Sustainability, University of Parma, Parco Area Delle Scienze 17/A, Parma 43124, Italy. E-mail: paolopio.mazz[email protected] b Biopharmanet-TEC, University of Parma, Parco Area Delle Scienze 27/A, Parma 43124, Italy c Department of Materials Science & Metallurgy, University of Cambridge, 27 Charles Babbage Rd, Cambridge CB3 0FS, UK. E-mail: [email protected] d BAM Federal Institute for Materials Research and Testing, Richard-Willst¨ atter-Straße 11, D-12489 Berlin, Germany e Yusuf Hamied Department of Chemistry, University of Cambridge, Lenseld Road, Cambridge CB2 1EW, UK †Electronic supplementary information (ESI) available. See https://doi.org/10.1039/d2fd00104g Thisjournalis©TheRoyalSocietyofChemistry2023 Faraday Discuss.,2023,241,289–305 | 289 Faraday Discussions Cite this: Faraday Discuss.,2023,241,289 PAPER Published on 12 July 2022. Downloaded by Bundesanstalt fuer Materialforschung und -pruefung on 10/31/2025 12:34:28 PM. View Article Online View Journal | View Issue Introduction The ability to drive chemical transformation by means of mechanical force has been recently rediscovered as an attractive and cost-effective tool 1–4 for the synthesis of organic, 5–10 metal–organic 11–16 and inorganic compounds and materials. 17–20 Many traditional solution-based chemical reactions can be performed via mechanochemistry with no (or minimal) use of solvent. 1,21–23 Providing a sustainable and cheaper strategy for synthesis as compared with traditional solution methods, mechanochemistry was selected by the International Union of Pure and Applied Chemistry (IUPAC) as one of “the 10 chemical innovations that will change our world”. 24 Although mechanically induced reactions have been known since prehistoric times, the eld of mechanochemistry remained largely a curiosity until the end of the 19th century, expanding as a scientic discipline through the 20th century. 25 Mechanochemistry is still conned to specialized laboratories, and despite its clear environmental benets, the lack of fundamental knowledge of mechanochemical transformation poses signicant limitation to its application across the academic and industrial communities. Mechanistic understanding of mechanochemical reactions is sparse in modern literature, 26–29 usually investigated by stepwise ex situ studies, wherein the reaction is stopped and the material is removed from the reactor for analysis. 4,30 The evidence of ex situ analyses relies on the stability of products under atmospheric conditions so that they undergo no change when removed from the grinding jar. If these conditions are not met, the ex situ analysis provides only a partial interpretation of the system under investigation. Furthermore, examples are known where the stop–start ex situ approach results in the system evolving via adifferent pathway than the unperturbed reaction, 11,30 or continuing to transform aer milling is stopped. 31 The unambiguous investigation of such reactions can only be achieved by directly probing the reaction in situ while the mechanical treatment is ongoing. Time-resolved in situ (TRIS) monitoring approaches have opened the door to extraordinary detail in mechanochemical transformations. 32 Mechanochemistry is primarily a solidstate synthetic technique, and therefore TRIS X-ray powder diffraction (XRPD) remains a pivotal tool to investigate mechanochemical transformations. A typical TRIS-XRPD ball milling set-up is based on a vibratory mill with either vertical or horizontal trajectory, accelerating a jar loaded with the reagent(s) and milling bodies. The jar intercepts the path of the X-ray beam, with diffraction collected on a detector placed behind the jar. Ideal diffraction occurs from a single point. However, when TRIS-XRPD is performed in a typical set-up, the beam passes through an elongated sample volume causing broadening and ultimately splitting of the diffracted peaks. 26 The use of high energy radiation mitigates the peak splitting by compressing the diffraction prole. 33 This has allowed various groups to identify unexpected and short-lived intermediates and begin to discuss the macroscopic dynamics of chemical and physical transformations under mechanochemical conditions. 33 Despite the growing number of TRIS-XRPD studies being reported, 4,19,34–39 the collection of quality diffraction data suitable for microstructural investigation remains a challenging task with conventional setups and data collection strategies. This challenge has hindered robust analysis of TRIS-XRPD, thus limiting the Faraday Discussions Paper 290 |Faraday Discuss.,2023,241,289–305 This journal is © The Royal Society of Chemistry 2023 Published on 12 July 2022. Downloaded by Bundesanstalt fuer Materialforschung und -pruefung on 10/31/2025 12:34:28 PM. View Article Online mechanochemical investigation to a mere phase identication process. For a complete mechanistic understanding of a mechanochemical process, microstructural information cannot be neglected in the overall XRPD analysis. We recently proposed a novel approach for TRIS-XRPD under ball milling conditions by implementing an optimized milling jar set-up, and innovative strategy for X-ray beam alignment, data acquisition and data processing. Our approach offers important improvements on the diffraction peak shape and signalto-noise ratio 26 and extending TRIS-XRPD acquisition and analysis towards accurate microstructural investigations over the course of a mechanochemical transformation. 26 Importantly, the use of a standard sample (e.g. silicon) is essential to determine the instrumental contribution to the XRPD peak broadening for TRIS monitoring of mechanochemical reaction under in operando conditions. Following from our recent advances on data collection and analysis for TRISXRPD, we questioned the limits of the functions that we used for data analysis and, in particular, how the output values extracted by the Rietveld renements are affected by the jar alignment. We here report a detailed study on the instrumental resolution function for TRIS milling experiments (IRF, the function that denes the instrumental contribution to the peak widths as a function of the Bragg angle) 40 using data collected from a standard material under the same experimental conditions. We describe how our IRF leads to robust data analysis strategies for the evaluation of the microstructural parameters of milling reactions and transformations. Importantly, we show that the IRF can be reliably estimated even when the jars that contain the standard material and those containing the sample do not sit at the same alignment position. This is of fundamental importance because we have evidence that the jar position can experience minor dris during the milling experiment (vide infra). Finally, we report on the aberration due to use of a large at area detector that affects the peak positions at higher 2qvalues, and we provide a new peak displacement function that includes an empirical correction for this problem. Experimental Ball milling setup Ball milling reactions were performed using a Fritsch Pulverisette 23 vertical vibratory ball mill. This mill has a xed amplitude of 9 mm and adjustable frequency from 15 Hz to 50 Hz with an adjustable timer. A 2.3 mL jar was custom designed at BAM and consists of three pieces, two stainless steel or polyvinyl chloride (PVC) end pieces and a transparent Perspex middle segment of 0.75 mm thickness. The overall size of the jar is 40 mm with an internal diameter of 12 mm (see ESI†for details). Synchrotron TRIS-XRPD data acquisition TRIS-XRPD monitoring was performed at mSpot (BESSY-II; Helmholtz-Zentrum Berlin) using a 150 mm beam monochromated (with Si(111) monochromator) to 17 keV. Scattering was acquired using an Eiger 9M detector, placed at ca. 250 mm from the sample. Scattering data were integrated using the DPDAK soware. NIST Si640d 41 was used as a standard for the careful characterization of the Instrumental Resolution Function (IRF) under the same experimental conditions used for TRIS monitoring of the samples under investigation. Paper Faraday Discussions Thisjournalis©TheRoyalSocietyofChemistry2023 Faraday Discuss.,2023,241,289–305 | 291 Published on 12 July 2022. Downloaded by Bundesanstalt fuer Materialforschung und -pruefung on 10/31/2025 12:34:28 PM. View Article Online General Rietveld renement details The evolution of the phases through the reaction was followed by Quantitative Phase Analysis (QPA) 42 via Rietveld Renement performed on TOPAS-Academic V6. 43,44 The structural models were retrieved from either the CSD or the ICSD databases. XRPD datasets were t sequentially, with a convergence criterion of 0.0005 and a maximum number of iterations of 1000. Our TRIS setup induces aberration in terms of the peak prole and peak positions (i.e. the actual 2qpeak position with respect to the expected Bragg reection; vide infra). The background is dened taking into account the experimental contribution coming from the empty jar (included in the Rietveld renement) together with a seventh-order Chebychev polynomial function. Custom-built TOPAS macros are available in the ESI.†Datasets were sequentially rened in order to have the output parameters as starting values for the following one. In-house XRPD Ex situ powder diffraction data were collected on specimens of Si640d NIST 41 standard powder before and aer milling. The two specimens were individually mixed with LaB 6 660b NIST 45 standard in approximately equal volume and spread on a at sample holder for measurement. Data were collected in Bragg–Brentano geometry on a D8 Bruker Advance diffractometer equipped with a Mo Kaprimary beam and a LYNXEYE XE-T position sensitive detector. Collections conditions were: 12–90in 2q, 0.01step size, variable counting rate (1 to 6 seconds per step), divergence slit 0.2 mm. Output values from the Rietveld renement are reported in the ESI.† TRIS-XRPD monitoring of NIST Si640d Data collection was performed with ca. 80 mg of Si and one 5 mm stainless steel ball bearing. The milling experiment was performed at 50 Hz for 30 min with the jar aligned in 5 different positions with respect to the beam path. Starting from a position tangential to the internal wall of the jar, we moved the jar horizontally in 100 mm steps across the beam path. XRPD patterns were acquired with a collecting time of 5 s. Results and discussion The success of a TRIS-XRPD mechanochemical experiment requires that the Xrays travel through the milling jar to the detector (Fig. 1a). In doing so, the Xrays scatter from both jar walls and the powder (and ball bearing) that is contained within the jar. To ensure useful signals, particularly at lower incident energies, e.g. 17 keV, it is therefore essential to minimize scattering from the jar walls, whilst maximising scattering from the powder. To achieve this, we previously designed custom-made Perspex jars with exceptionally thin (0.75 mm) walls which were used also in this work (Fig. 1b). 26 Jar alignment and data collection strategy We previously outlined an effective strategy to align the milling jar in the X-ray beam and optimize the quality of collected data; we summarise the strategy Faraday Discussions Paper 292 |Faraday Discuss.,2023,241,289–305 This journal is © The Royal Society of Chemistry 2023 Published on 12 July 2022. Downloaded by Bundesanstalt fuer Materialforschung und -pruefung on 10/31/2025 12:34:28 PM. View Article Online here for completeness. 26 To evaluate the evolution of microstructural parameters, both the standards and the sample under investigation must be measured under the same experimental conditions. To achieve this, the sample jar was carefully aligned before each TRIS-XRPD experiment. A photodiode was placed behind the milling jar and the intensity of the impinging X-ray beam was measured as the jar was moved in 100 mm steps across the beam path using a motorized translational stage. At each step, the X-ray intensity on the diode was measured thereby mapping the absorption of radiation by the jar itself (Fig. 1c). With a beam size of 150 mm, this step size ensured overlap between adjacent sampling points for best coverage of the jar geometry. The jar walls are clearly visible on both sides of the jar, where the material density increases and hence the diode reading decreases. We mapped the peak shape functions at different jar positions by collecting XRPD data from NIST Si640d 41 whilst milling at 50 Hz to reect experimental conditions. 2D X-ray diffraction proles were collected at each 100 mm step through the milling jar (Fig. 1c), exactly reproducing the map across the empty vessel. A quasisingle Bragg reection of the Si standard is only observed at the extreme edges of the vessel. Splitting of the reections increases quickly as the beam is moved away from the extreme edge, morphing into the more complex diffraction prole (Fig. 2 and 3). This is because some of the milled powder adheres to the jar wall during Fig. 1 Schematic representation of the milling setup used in this study. (a) The PMMA jar is used with the Fritsch P23 ball mill. The primary X-ray beam ~ p(yellow dashed line) passes through the jar and is diffracted by the sample contained within, scattering onto the 2D Xray detector. (b) Details of the PMMA jars. (c) Photodiode alignment of the custom-built Perspex milling jar in the X-ray beam, superimposed with the diffraction profile collected from NIST Si640d at the corresponding jar position. The milling jar is mapped by the absorption of X-ray intensity as it passes through the milling jar and is scanned along a horizontal path across the jar diameter. Paper Faraday Discussions Thisjournalis©TheRoyalSocietyofChemistry2023 Faraday Discuss.,2023,241,289–305 | 293 Published on 12 July 2022. Downloaded by Bundesanstalt fuer Materialforschung und -pruefung on 10/31/2025 12:34:28 PM. View Article Online ball milling, and hence the amount of sample in the X-ray beam (and hence scattering) increases. The agglomeration of powder on the jar wall gives rise to the splitting of diffraction peaks into three main components, with each component originating from multiple scattering centres. The inner and outer scattering components arise from powder adhered to the front and back walls of the milling jar, while the scattered intensity between these extremes arises from the powder which ows freely within the jar (Fig. 3 and 4). Instrumental resolution function (IRF) The accurate denition of instrumental resolution function (IRF, the function that denes the instrumental contribution to the peak widths as a function of the Bragg angle) 40,47–49 is essential to model the complex diffraction peak instrumental aberrations in a Rietveld renement. NIST Si640d 41 standard powder is typically used to evaluate the extrinsic (i.e. instrumental) contribution to peak broadening in standard XRPD data acquisition since it is assumed to have no intrinsic contribution to the peak broadening. However, we expected its microstructure to change over time as a function of the grinding process due to powder comminution under the experimental milling conditions. To conrm the progressive silicon comminution during the milling, Si640d powder was loaded into the milling jar with one 5 mm stainless steel ball bearing and a grinding experiment was performed with a vertical shaker-mill for 30 minutes at 50 Hz, simulating the typical milling conditions used in our TRIS data collection. Some silicon powder was sampled from the jar at the end of the milling time and blended with untreated NIST LaB 6 660b standard. 45 Milled Si640d was then compared with nonmilled material. XRPD patterns were collected on conventional source instrumentation in Bragg–Brentano geometry. Aer 30 minutes of grinding, the peak broadening of Si640d had signicantly increased (Fig. 5). The crystal size was found to be in the order of hundreds of nm, and the microstrain, 3, in the order of 10 4 . However, TRIS-XRPD monitoring of the line prole of the Si640d suggests that (i) the effects of powder comminution to the peak width become evident only aer several minutes of grinding (see ESI†) and (ii) some tens of seconds were necessary to allow the Si powder to adhere to the internal walls of the jar and thus Fig. 2 Orthogonal schematic representation of the jar alignment with respect to the X-ray beam path ~ p. Peak shape differs as a function of the jar position returning an emphasized peak split when the jar is investigated closer to the centre. This effect is sensibly mitigated if the jar is crossed closer to the edge (a). Diffraction with the set-up in (b) and (c) results in splitting of each Bragg reflection into a convolution of 2qpositions as the powder inside the jar is distributed across different locations and hence a range of sample-to-detector distances. Faraday Discussions Paper 294 |Faraday Discuss.,2023,241,289–305 This journal is © The Royal Society of Chemistry 2023 Published on 12 July 2022. Downloaded by Bundesanstalt fuer Materialforschung und -pruefung on 10/31/2025 12:34:28 PM. View Article Online generate a split peak that is consistent in shape over time. For these reasons, we encourage to dene the instrumental resolution function by rening an XRPD pattern acquired aer a couple of minutes from the beginning of the grinding experiment. This protocol guarantees the standard material to be clearly adhered to the jar walls and with a still negligible intrinsic contribution to the peak width. To dene the IRF for TRIS-XRPD setup by using a standard material, we had to concomitantly model all the instrumental aberrations that consist of the peak position and peak prole deviation from the ideal diffraction denition. Peak position aberration Our TRIS setup induces aberrations in terms of the peak prole and peak positions (i.e. the actual 2qpeak position with respect to the expected Bragg reection). As such, the nal XRPD pattern results from a convolution of the scattering Fig. 3 Rietveld plot of the Si640d NIST standard collected with the beam path intersecting the milling jar at different positions, namely (a) tangent to the jar and (b) in a general position across the jar diameter. For both patterns, the calculated profile is given (red line) against experimental data (black dots) and the difference pattern is shown (grey line). The peak split arises as a function of the jar alignment. The primary beam ~ p(yellow line) passes through the jar and is diffracted by the sample contained within. The contribution to the overall peak shape of the sample distributed within the jar is highlighted in the insets with different colours: the scattering vectors are produced by the sample located at the jar wall closer to the source (~ s 1 , green line), the wall nearer the detector (~ s 3 , blue line), and by the sample distributed randomly within the jar (~ s 2 , pink line). The difference in 2qangle between scattering vectors ~ s 1 and ~ s 3 is larger when the jar is in a general position with respect to the primary beam ~ p(b). The difference in 2qangle is minimised when the jar is accurately aligned (a), with negligible scattering contribution from the sample distributed within the jar (~ s 2 ). Paper Faraday Discussions Thisjournalis©TheRoyalSocietyofChemistry2023 Faraday Discuss.,2023,241,289–305 | 295 Published on 12 July 2022. Downloaded by Bundesanstalt fuer Materialforschung und -pruefung on 10/31/2025 12:34:28 PM. View Article Online that originates from the sample attached to the jar walls (namely ~ s 1 and ~ s 3 ) and from the sample randomly distributed within the jar ~ s 2 (Fig. 3). In Debye–Scherrer (transmission) geometry, the offset of the sample with respect to the ideal centre of the goniometer causes a nonlinear shiin the 2q positions 49,50 calculated as D2qsd ¼arcsindL RDS sin2qarcsindV RDS cos2q(1) Fig. 4 Empty jar profile superimposed with the Si640d profile collected in the different jar positions progressively moved apart from the tangent position with respect to the beam path. Fig. 5 Cascade superimposition of Rietveld refinement plots performed on XRPD pattern collected with Mo Karadiation for NIST Si640d blended with LaB 6 . (a) Native Si640d and (b) Si640d after 30 min of milling with one 5 mm stainless steel ball bearing at 50 Hz. Calculated pattern (red curves) against experimental data. Y obs Y calc differential patterns are reported in orange. Sticks at the bottom represent the calculated angular positions of silicon (green sticks) and LaB 6 (blue sticks). Inset: silicon reflections (111) (12.98 2q, left) and (311) (24.98 2q, right) are reported with the closest LaB 6 peaks emphasizing the peak broadening of the milled silicon (red curve) with respect to the native silicon (blue curve). Patterns in the insets were individually normalized to the Si peak intensity. Faraday Discussions Paper 296 |Faraday Discuss.,2023,241,289–305 This journal is © The Royal Society of Chemistry 2023 Published on 12 July 2022. Downloaded by Bundesanstalt fuer Materialforschung und -pruefung on 10/31/2025 12:34:28 PM. View Article Online where d L and d V denote, respectively, the displacement of the sample in the direction of the beam and perpendicular to it and R DS is the sample-to-detector distance. In the Rietveld renement, each scattering contribution is dened as a unique phase with the lattice parameters constrained to be identical among them. A longitudinal sample displacement correction d L is individually applied for each scattering contribution. Assuming the powder distributes homogeneously along the vertical direction (i.e. the axis of the jar vibration), the vertical sample displacement does not inuence the angular offset. Correspondingly, the nal correction is applied according to the simplied eqn (2). D2qhkl ¼arcsindL RDS sin2qhkl (2) For all silicon data, we observed a slight mismatch between the modelled curveandtheexperimentaldataathigher angular values. This misinterpretation of the angular position, due to the parallax effect observed with the large at area detector, 40,51 is particularly evident for patterns acquired with a high sample displacement, namely when the jar is aligned signicantly far from the ideal tangential position to the beam path. To overcome this problem, an empirical correction has been added to the sample displacement function as follows: D2qhkl ¼arcsindL RDS sin2qhkl þm$tan2ð2qhkl Þ(3) The corrected peak split function models this further aberration in excellent detail (Fig. 6). It is worth noting that this further geometrical misalignment was only detected with sharp silicon peaks, while it has never been observed with real samples of either organic or inorganic materials. With the peak position ultimately inuenced by the sample displacement, we additionally observed a progressive increase of the peak split as a function of milling time during the TRIS-XRPD monitoring of the Si640d, which is symptomatic of a jar drifrom the ideal alignment position (Fig. 7; see ESI†for details). The use of an independent sample displacement correction for each Bragg phase according to eqn (3), individually rened for each TRIS-XRPD pattern, is advised as it also compensates for any jar driwith respect to the beam path. In fact, Rietveld renements performed on silicon data showed that the IRF calculated for the jar aligned in different positions is virtually identical. The same IRF function was obtained for silicon data collected across a wide range of jar positions, spanning lengths much larger than intrinsic errors associated with jar alignment (vide infra). Peak shape denition The peak split due to the geometrical constraints imposed by our milling setup, mirrors the aberration of the prole full-width-at-half-maximum (FWHM) as a function of 2qdegrees, 52 that was described with a modied Thompson–Cox– Hastings pseudo-Voigt TCHZ function 47 (see ESI†for details). 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