research papers
UnitCell Tools, a package to determine unitcell parameters from a single electron diffraction pattern
^{a}School of Science, Minzu University, 27 Zhong guancun South Avenue, Haidian District, Beijing 100081, People's Republic of China, and ^{b}Institute of Physics, The Chinese Academy of Sciences, No. 8, 3rd South Street, Zhongguancun, Haidian District, Beijing 100190, People's Republic of China
^{*}Correspondence email: honglongshi@outlook.com, zali79@iphy.ac.cn
Electron diffraction techniques in _{2} nanorod using this package is also demonstrated. Should the parallelbeam, nanobeam and convergentbeam modes of the TEM be used flexibly, the software can determine unitcell parameters of unknownstructure crystallites (typically >50 nm).
(TEM) have been successfully employed for determining the unitcell parameters of crystal phases, albeit they exhibit a limited accuracy compared with Xray or neutron diffraction, and they often involve a tedious measurement procedure. Here, a new package for determining unitcell parameters from a single electron diffraction pattern has been developed. The essence of the package is to reconstruct a 3D reciprocal from a single electron diffraction pattern containing both zeroorder Laue zone and highorder Laue zone reflections. Subsequently, the can be reduced to the Niggli cell which, in turn, can be converted into the Using both simulated and experimental patterns, we detail the working procedure and address some effects of experimental conditions (diffraction distortions, misorientation of the and the use of highindex zone axis) on the robustness and accuracy of the software developed. The feasibility of unitcell determination of the TiOKeywords: unit cell; Bravais lattice; electron diffraction; SAED; HOLZ.
1. Introduction
Unitcell parameters and symmetry elements are two fundamental crystallographic quantities for characterizing a ; Williams & Carter, 2009; Young, 1995) or solving the of unknown crystals (Le Bail et al., 1988; David et al., 2006). Xray and neutron diffraction are two well established methods for the unitcell determination of singlephase materials. However, their broad irradiation beam makes them illsuited for probing finitesized samples (Baer et al., 2008), especially those in the form of nanoscale materials (Shi, Zou et al., 2019), inclusions or precipitates in alloys (Antion et al., 2003), and structurally modulated materials that are multiphase such as multilayers and superlattices (Collier et al., 1998). By contrast, highenergy electron diffraction in (TEM) can probe finitesized crystals, though the measurement precision of unitcell parameters is relatively poor for several practical reasons (Mugnaioli et al., 2009; Capitani et al., 2006; Hou & Li, 2008).
In a structural study, accurate measurement of unitcell parameters for a crystalline phase is considered to be the first step towards identifying a crystalline phase with known structures (Pecharsky & Zavalij, 2003Several approaches of electron diffraction in TEM for the unitcell determination of a crystal have been developed. The first employs (1) the search–match method (Lábár, 2008; Shi, Luo & Wang, 2019; Altomare et al., 2019; Zuo et al., 2018), which involves measuring dspacings of reflections in a powder electron diffraction pattern and comparing dspacings with those of the known structures in crystal databases; and (2) the patternindexing method (Williams & Carter, 2009; Shi, Luo & Wang, 2019),which involves measuring dspacings and interplanar angles in a zoneaxis diffraction pattern and performing the patternindexing procedure based on the known structures. However, this approach cannot be used in the case of unknown structures. The second approach is to construct a 3D reciprocal based on zoneaxis electron diffraction patterns: (1) the multipattern method (Zou et al., 2004) requires a tilt series of zoneaxis patterns (at least three) to reconstruct 3D using the geometric relationship of patterns; (2) the twopattern method (Li, 2019; Zhao et al., 2008) requires two zoneaxis patterns and their interzonal angles to determine unitcell parameters; and (3) the onepattern method is to construct a 3D reciprocal by making use of structural information present in the convergentbeam electron diffraction patterns (Ayer, 1989; Zuo, 1992, 1993). Some excellent electron diffraction software has been developed to determine unitcell parameters, e.g. TRICE (Zou et al., 2004), TEMUC3 (Li, 2019) and QtUCP (Zhao et al., 2008) etc. These analysis packages require at least two zoneaxis patterns recorded by a tilt series; however, this limits the application of the nanosized crystallite and the electronsensitive materials for the timeconsuming crystal tilting process.
In this work, we reexamine the geometrical description of the zoneaxis electron diffraction and develop the package `UnitCell Tools' to determine unitcell parameters from a single electron diffraction pattern with both ZOLZ and HOLZ reflections. We describe the working principles of the software and demonstrate the processes of constructing the 3D primitive reciprocal cell, converting the primitive reciprocal cell to the Niggli and then to the conventional using both simulated electron diffraction and experimental data. We also address the experimental aspects (diffraction distortion, zoneaxis misorientation and the use of highindex or arbitrary zoneaxis pattern) on the robustness and accuracy of the proposed software. Moreover, we experimentally test the applicability of the software to determine the unitcell parameters of nanocrystallites using diffraction patterns from both CBED and nanobeam electron diffraction (NBED) methods.
2. Fundamentals of the method
Fig. 1(a) presents the geometric descriptions of a 3D in the TEM diffraction setting. The zoneaxis electron diffraction pattern can contain both ZOLZ and HOLZ reflections as the intersects with the of the crystal, where the ZOLZ pattern is only a 2D of the but the HOLZ reflections can provide a wealth of 3D structural information.
2.1. The HOLZ ring and reciprocallattice layer spacing
The formula and illustrations of the geometrical descriptions on the HOLZ ring and the reciprocallayer spacing can be found in classic textbooks (De Graef, 2003; Williams & Carter, 2009). Here, we will describe in more detail how to derive this formula. Let us consider the layer spacing H^{*} between the ZOLZ and FOLZ (firstorder Laue zone) reciprocal layers along the incident beam direction [see Fig. 1(b)]. The layer spacing , where O′O is the radius of the and λ is the wavelength of the incident electron beam. Assuming 2θ is the full scattering angle of the FOLZ ring, H^{*} is rewritten as by considering and . According to Bragg's law , and assuming R_{H} = 1/d is the radius of the FOLZ ring, then H^{*} becomes
For other HOLZ rings with the order of the Laue zone N, the layer spacing becomes . In practice, by measuring the radius of the HOLZ ring R_{H} (the units are nm^{−1} or Å^{−1}), one can determine the reciprocallattice layer spacing H^{*} (the units are nm^{−1} or Å^{−1}) along the incident beam direction.
2.2. Determination of unitcell parameters from a single electron diffraction pattern
More importantly, HOLZ reflections are essentially replicas of the ZOLZ ones, and therefore a full layer of HOLZ reflections can be generated by vectoraddition of the basic vectors OA and OB which form the ZOLZ reflections, as shown in Fig. 1(c). Superimposing the full layer of FOLZ reflections onto the ZOLZ layer, one immediately recognizes that there must be a reflection C (in the FOLZ layer) that falls onto a position C_{1} within the 2D cell formed by vectors OA and OB in the ZOLZ layer.
The essence of the package UnitCell Tools is to establish a geometric relationship of a 3D reciprocal cell based on ZOLZ and HOLZ reflections [see Fig. 1(c)]. Since the line CC_{1} is perpendicular to the plane AOB, we write CC_{1}⊥OA. If we draw a line segment A_{1}C_{1} perpendicular to the line OA passing through the projection spot C_{1}, then the line OA_{1} is also perpendicular to the plane CA_{1}C_{1}. Similarly, line OB_{1} is perpendicular to the plane CB_{1}C_{1} when we draw a line segment B_{1}C_{1} perpendicular to the line OB. One can easily construct a 3D reciprocal cell from OA, OB, OA_{1}, OB_{1}, OC_{1} and CC_{1}, as expressed in Equation (2): (i) ZOLZ reflections define a 2D by a^{*} = OA, b^{*} = OB and ; (ii) The HOLZ ring defines the reciprocallayer spacing of CC_{1}; (iii) The HOLZ diffraction spot provides the remaining parameters ( c^{*}, and ) of a primitive cell.
defined in the RtΔOC_{1}C;
defined in the RtΔOB_{1}C;
defined in the RtΔOA_{1}C.
The constructed 3D reciprocal cell must be primitive if we choose a 2D ; Guo, 1978; GrosseKunstleve et al., 2004). In turn, the Niggli cell is uniquely converted to the of the by employing the relationships well documented in Volume A of International Tables for Crystallography: Space Group Symmetry (Wolff, 2006).
in the ZOLZ pattern and measure the innermost HOLZ ring. The constructed can be further reduced to a Niggli cell, which can provide a unique description of a lattice (Křivý & Gruber, 19762.3. Description of the software
2.3.1. Distribution and installation
UnitCell Tools is a package of the DigitalMicrograph software (https://www.gatan.com/products/temanalysis/gatanmicroscopysuitesoftware). The package can be provided via email upon reasonable request. The user should preinstall DigitalMicrograph software freely available at https://www.gatan.com/products/temanalysis/gatanmicroscopysuitesoftware.
To install the package into the DigitalMicrograph software, copy the file `UnitCell Tools.gtk' to `...\Gatan\DigitalMicrograph\PlugIns', a new item `UnitCell Tools' will be built on the menu bar. Click the item `UnitCell Tools/One Pattern' to enter the graphical user interface, as shown in Fig. 1(d).
2.3.2. Software overview
UnitCell Tools, as a package of DigitalMicrograph software, can determine unitcell parameters from electron diffraction patterns that contain ZOLZ reflections, HOLZ reflections and the HOLZ ring. It can process the native DM files (*.dm3) or other common greyscale images (JPG, TIF, BMP etc.). Before the pattern analysis, the diffraction pattern must be rigorously calibrated. The operation of the package is controlled via a graphical user interface [Fig. 1(d)], and processes for determining unitcell parameters are described as follows:
(i) ZOLZ reflections are measured by successively locating four diffraction spots (by pressing the SPACE bar) around the transmitted spot after clicking the `Z' button.
(ii) The HOLZ ring is measured by successively locating three points (by pressing the SPACE bar) on the HOLZ ring after clicking the `R' button.
(iii) The HOLZ spot is measured (by pressing the SPACE bar) after clicking the `H' button to construct a 3D primitive reciprocal cell. The three shortest vectors of the cell that meet the tolerant factors of `eps 1–3' will be listed in the `Reduced Cell List' box.
(iv) By choosing the appropriate basis vectors of the Niggli cell in the `Reduced Cell List' box, the
can be converted into the unit cells. Unit cells that meet the limit of `eps d/A' will be listed in the `Unit Cell List' box.(v) By picking the appropriate
in the `Unit Cell List' box, the simulated pattern based on the selected will be overlaid on the front pattern and the detailed parameters are output in the `Results' box and the `Result window'.Detailed operation of the package was documented in the user guide.
3. Results and discussion
In this section, we will first illustrate how to extract unitcell parameters from a simulated electron diffraction pattern based on the reported software, and then discuss some effects of experimental conditions (diffraction distortions, the misorientation of
and the use of highindex zone axis) on the robustness of the package, and demonstrate the application of unitcell determination of nanostructured materials. All experimental electron diffraction patterns were recorded on a JEM2100 (Jeol Inc.) working at 200 kV.3.1. Unitcell determination from a simulated pattern
Without loss of generality, we chose the monoclinic _{2}(Ti_{2}O_{7}) (the is listed in Table 1). Fig. 2(a) presents a simulated [211] zoneaxis electron diffraction pattern under the kinematic diffraction condition using the EDA software (Toshihiro, 2003), in which the firstorder Laue zone (FOLZ) reflections and the ring marked by a red circle are clearly observed. The analysis procedure of unitcell determination from a single electron diffraction pattern is as follows.
of La

First, clicking the `Z' button determines the 2D OA and OB in the ZOLZ layer [Fig. 2(b)] to be a^{*} = OA = 0.2289 (2) Å^{−1}, b^{*} = OB = 0.2221 (1) Å^{−1} and γ^{*} = ∠AOB = 70.09 (1)°. For the pattern, we always suggest choosing the two shortest nonlinear reflections to form the 2D details are discussed in Section S1 of the supporting information.
with basic vectors ofSecond, clicking the `R' button determines the radius R_{H} of the FOLZ ring [red circle in Fig. 2(a)] to be 1.7330 (1) Å^{−1}; according to Equation (1), CC_{1} = 0.0375 (1) Å^{−1}. Note that, if the HOLZ ring is split, we always use the innermost ring (Williams & Carter, 2009). For convenience to measure the HOLZ ring by employing the threepoint method, we suggest to acquire the HOLZ ring by selecting a large C_{2} aperture and focusing the beam. Details are discussed in Section S2 of the supporting information.
Third, clicking the `H' button to locate a FOLZ reflection, H (2402.1, 939.1 pixels), which is then vectorshifted by the integral multiplier of OA and OB to C_{1} (1408.8, 1247.1 pixels), i.e. shift 7 units for OA and 1 unit for OB, as denoted in Fig. 2(a). By a simple geometric calculation [see Equation (2)], one can obtain a 3D reciprocal with six parameters of a^{*}, b^{*}, c^{*}, α^{*}, β^{*} and γ^{*} (specific values are listed in Table 1).
Four, choosing three vectors in the `Reduced Cell List' box to form the e.g. , and [001]^{*}. The obtained reciprocal can then be converted to a realspace via relationships among the real and parameters. The realspace Niggli cell is finally converted to the by applying the NigglitoBravais cell transformation rule as tabulated in Volume A of International Tables for Crystallography: Space Group Symmetry (Wolff, 2006), and the cells which meet the limit of `eps d/A' are listed in the `Unit Cell List' box.
Five, picking the appropriate e.g. the mP cell, the simulated pattern based on the selected (symmetry constraint cell) is overlaid on the front pattern and the detailed parameters are output in the `Results' box and the `Output' window. In the present case, the Nigglimatrix elements of the realspace Niggli cell are = 61.0273, = 30.7419, = 168.2796, = −0.1869, = −15.1522 and = −0.0222; the reduced Niggli cell meets the condition of A ≠ B ≠ C, D = F = 0 (No. 33, mP) and the can be calculated by the corresponding matrix transformation to be a = 7.8120 (0), b = 5.5445 (5), c = 12.9723 (377) Å, α = 90.15 (15), β = 98.60 (6) and γ = 90.03 (3)°.
In order to estimate the accuracy of the cell, we separately evaluate the sum of the differences between the _{a} = 0.10% and FOM_{α} = 0.09%; the is [211], and the plane indices of the reflections A and B are and , which are consistent with the simulated parameters.
obtained and the standard Bravais as two figures of merit (FOM): one for unitcell lengths of and the other for unitcell angles of , where defines the absolute value of the relative error of unitcell parameters. In order to correctly choose the appropriate and the the simulated pattern based on the selected is overlaid on the front pattern; parameters of the symmetry constraint cell and its variants, the zoneaxis indices and the plane indices are listed in the `Results' box. In the present case, we obtain the values of FOMIt is worth noting that unitcell parameters can be determined from a monoclinic crystal in this example, indicating the proposed package can be used in the case of lowsymmetry crystal systems, e.g. the monoclinic and triclinic crystals. Instead, the tiltseries method is considered to be troublesome in the application for these two crystal systems (Li, 2019). As we will further demonstrate in real experimental data below, arbitrary zoneaxis diffraction patterns, either lowsymmetry or highsymmetry, can be used for unitcell determination.
3.2. Effects of experimental conditions on the unitcell determination
3.2.1. Diffraction distortions
We now proceed to the unitcell determination using experimental diffraction data. Fig. 3(a) shows a typical electron diffraction pattern of oriented silicon specimen recorded by a JEM2100 microscope operated at 200 kV, in which a set of FOLZ reflections and a FOLZ ring marked by a reddashed circle are clearly visible. Following the procedure detailed in the simulation case in the previous section, one can construct a 3D primitive reciprocal cell, the reciprocal Niggli cell, the realspace Niggli cell and the Bravaislattice In order to inspect the effects of diffraction distortions on the obtained unitcell parameters, in the present case, using a set of FOLZ reflections around the FOLZ ring and the 2D vectors OA and OB, one can obtain an angularly dependent set of OA_{1}, OB_{1} and OC_{1} [Fig. 3(b)] and the of parameters a, b, c, α, β and γ [Fig. 3(c)]. The open symbols represent the parameters of the uncorrected diffraction pattern, and the solid ones represent those of the ellipticaldistortion corrected pattern. Such angular variations in the 3D unitcell determination are actually found to exist, as the experimental diffraction pattern invariably bears diffraction distortions (Mugnaioli et al., 2009). The angularly fitted sinefunction curves in Fig. 3(b) also indicate that the dominant distortion in the electron diffraction pattern is elliptical, mainly due to twofold aberrations of the projection lens and/or objective lens – higher angle scattered electrons (e.g. HOLZ reflections) traveling close to the polepieces of the respective lens cause image distortions. Consequently, distortions of the diffraction pattern cause measurement errors in (i) the measurement of the HOLZ ring, which may cause an unreliable spacing of the reciprocal layer CC_{1} (it has a minor effect on the determined cell, details are discussed in Section S2 of the supporting information); (ii) measurement of the HOLZ diffraction spot, which may lead to inaccurate values of OA_{1}, OB_{1} and OC_{1}, in turn, affecting the determination of reciprocal parameters c^{*}, α^{*} and β^{*}. So, a highresolution diffraction pattern with well defined HOLZ reflections suffering minimal image distortions is essential to determine unitcell parameters.
Despite the presence of diffraction distortions, similar unitcell parameters [see open dots in Fig. 3(c)] are obtained, illustrating the robustness of the unitcell determination by employing single electron diffraction that contains HOLZ reflections. However, it is advised to accurately correct diffraction distortions prior to performing the unitcell determination, a more accurate can be determined using the corresponding HOLZ reflection after distortion correction [see the solid dots in Fig. 3(c)].
3.2.2. The misoriented zoneaxis pattern
We address the effect of electron diffraction patterns with slight misorientation of the et al., 2008; Li, 2019; Zou et al., 2004). Here, to inspect the effects of misorientation of on unitcell determination, we deliberately misoriented the Si specimen by ∼0.37° from its exact as shown in Fig. 4(a). Using this diffraction pattern, we carried out the procedure for unitcell determination as detailed in the previous section and tabulated the measured values of the 3D reciprocal the reciprocal Niggli cell, the realspace Niggli cell and the Bravaislattice in Table 1. When comparing the determined with the known lattice parameters of silicon, the low FOMs (FOM_{a} = 0.01% and FOM_{α} = 0.44%) indicate that the proposed software works well under even misoriented zoneaxis conditions. It should be noted that the intensities of ZOLZ reflections will be asymmetric when the incident beam deviates from the In this case, we suggest measuring highindex reflections (Nh Nk Nl) around the transmitted spot to reduce measurement errors of OA and OB resulting from the deviation vector.
on the robustness and accuracy of unitcell determination. In general, exactly oriented zoneaxis diffraction patterns are ideal for accurate unitcell determination. Such conditions are not always obtainable as they are either limited by the tilting accuracy of specimen holders or the difficulty in precise tilting of nanosized specimens (Zhao3.2.3. Highindex and lowsymmetry patterns
We next address the effect of using highindex and lowsymmetry zoneaxis electron diffraction patterns on unitcell determination. Conventional methods for unitcell determination require the use of major zoneaxis diffraction patterns, namely those with low index and higher symmetry (Zou et al., 2004; Li, 2019; Zhao et al., 2008). By contrast, the package also works well on arbitrary zoneaxis diffraction patterns as long as the patterns contain HOLZ reflections. In fact, in some cases, the use of a highindex and lower symmetry pattern is advantageous as HOLZ reflections and rings are close to the ZOLZ ones with higher visibility for easy and accurate measurements.
To illustrate the effect, we recorded a highindex (b)] and then performed the unitcell determination procedure. The resulting values are tabulated in Table 1. The low values of FOM (FOM_{a} = 0.55% and FOM_{α} = 0.31%) verify that the package can accurately determine unitcell parameters from highindex and lowsymmetry diffraction patterns.
pattern of the Si specimen [Fig. 43.2.4. Determination of unitcell parameters of small crystallites
The merit of the package can be best illustrated by the determination of unitcell parameters of small crystallites. As compared with Xray and neutron scattering methods of the broadbeam nature, electron diffraction in a TEM is a superior means for probing microstructures of finitesized specimens, such as nanoparticles, nanoscale inclusions or precipitates (Shi, Zou et al., 2019; Antion et al., 2003). However, the smallsized crystallites are difficult to tilt to multiple zoneaxis conditions, which greatly limits the use of the conventional reciprocalcell reconstruction method in the case of small crystallites.
We demonstrate the applicability of the package for determining unitcell parameters of TiO_{2} nanorods. Fig. 5(a) shows a convergentbeam electron diffraction pattern of TiO_{2} nanorods, in which FOLZ and SOLZ (secondorder Laue zone) rings are clearly visible. The radius of the FOLZ ring is used for determining the reciprocallattice layer spacing H^{*} along the electron beam direction. By keeping the diffraction condition but using a smaller condensed lens aperture (∼10 µm in diameter), nanobeam electron diffraction is produced as shown in Fig. 5(b), in which discrete ZOLZ and FOLZ reflections are clearly seen. Following the procedure from constructing a 3D reciprocal to the as detailed in the previous section, we obtained a set of unitcell values that are displayed in Table 1. The low FOM values (FOM_{a} = 0.67% and FOM_{α} = 0.90%) compared the experimentally determined with the known orthorhombic phase of TiO_{2} (PDF#76–1937, a = 5.472, b = 5.171, c = 9.211 Å, α = β = γ = 90°) indicate the examined TiO_{2} nanorods are of the brookite type. However, we note that FOM values are relatively higher, likely due to the larger measurement errors in the diffraction pattern, e.g. the poordefined and unsharp reflections, and the low signaltonoise ratio of the pattern.
3.2.5. Remarks on the recording of highquality electron diffraction patterns
The above examples indicate that unitcell parameters can be determined from a single electron diffraction pattern by employing the proposed software, although the accuracy of the determined parameters remains difficult to compare with those of the Xray method due to the unreliable camera constant and the aberrations present in the TEM (Mugnaioli et al., 2009). Here, we give some general remarks on the recording of highquality electron diffraction patterns with well defined ZOLZ and HOLZ reflections, accurately calibrated camera length, and minimal image distortions as follows:
(1) Prior to the electron diffraction pattern acquisition, one should perform standard microscope optical alignment procedures, including alignment of the illumination system, centering of the voltage/current, centering of the condenserlens/selectedarea aperture, correcting the condenser/diffractionlens astigmatism and adjustment of the sample eucentric height. An optimized electron optic is beneficial to obtain a sharp and well defined diffraction pattern.
(2) Calibration of the camera length with a standard specimen to set the correct image scale.
(3) Lowering the accelerating voltage of TEM can enhance the HOLZ reflections and increase the view of the pattern with the same camera length.
(4) Appropriate choice of camera length and exposure time for recording electron diffraction patterns with clear HOLZ reflections. In some cases, a doubleexposure method can be applied: short exposure time to obtain ZOLZ spots and long exposure time for HOLZ reflections.
(5) Lowering the temperature of the specimen can reduce the thermodiffusion scattering and hence enhance the HOLZ reflections.
(6) Mitigation of the imaging distortions from the intermediate and projection lenses by adjustment of their lens aberrations and misalignment using a clean diffraction pattern from standard specimens.
4. Conclusions
We developed an analysis package to determine unitcell parameters of crystals using a single electron diffraction pattern that contains both ZOLZ and HOLZ reflections. The proposed software was verified by a simulated electron diffraction pattern together with detailed working procedures. We then carried out experiments using diffraction data of the silicon specimen to evaluate the effects of diffraction distortions, the misorientation of the _{2} nanorods. In this particular case, it is advised to use convergentbeam electron diffraction to extract the radius of the FOLZ ring and nanobeam electron diffraction to locate the ZOLZ reflections and one of the HOLZ reflections.
the use of highindex and lower symmetry zoneaxis patterns on the robustness and accuracy of the unitcell determination. Moreover, we experimentally demonstrated the applicability of the proposed package for the unitcell determination of TiOCompared with other reciprocalspace reconstruction methods (Zhao et al., 2008; Zou et al., 2004; Li, 2019), our proposed method requires only one pattern that needs to not be in the exact zoneaxis condition and needs to not be a lowindex this will greatly simplify the TEM operation. The accuracy of the determined parameters is slightly better than the series tilt method (details are discussed in Section S3 of the supporting information) but are still not comparable with those of Xray methods; the parameters determined can be regarded as the first step and can be then refined by Xray or neutron diffraction. For complex materials of multiphases or small sizes (typically, 50–100 nm), this is probably the sole choice for the structural identification and determination of new crystal structures.
Supporting information
Demonstration for the package UnitCell Tools. DOI: https://doi.org/10.1107/S2052252521007867/gq5014sup1.wmv
The reported software. DOI: https://doi.org/10.1107/S2052252521007867/gq5014sup2.bin
The tested pattern. DOI: https://doi.org/10.1107/S2052252521007867/gq5014sup3.bin
Supporting figures and tables. DOI: https://doi.org/10.1107/S2052252521007867/gq5014sup4.pdf
Acknowledgements
We thank Yin Jia, Guling Zhang and Bin Zou of the Minzu University of China, and Minting Luo in the Institute of Process Engineering for their useful discussions.
Funding information
This work was supported financially by the National Natural Science Foundation of China (No. 11604394, 11974019, 11774403) and the Fundamental Research Funds for the Central Universities (grant No. 2020QNPY101).
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