Electron crystallography\(\def\hfill{\hskip 5em}\def\hfil{\hskip 3em}\def\eqno#1{\hfil {#1}}\)

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3D electron diffraction techniques

aCenter for Nanotechnology Innovation@NEST, Istituto Italiano di Tecnologia, Piazza San Silvestro 12, Pisa, 56127, Italy
*Correspondence e-mail: mauro.gemmi@iit.it

Edited by L. Palatinus, Czech Academy of Sciences, Czech Republic (Received 30 January 2019; accepted 23 May 2019; online 1 August 2019)

3D electron diffraction is an emerging technique for the structural analysis of nanocrystals. The challenges that 3D electron diffraction has to face for providing reliable data for structure solution and the different ways of overcoming these challenges are described. The route from zone axis patterns towards 3D electron diffraction techniques such as precession-assisted electron diffraction tomography, rotation electron diffraction and continuous rotation is also discussed. Finally, the advantages of the new hybrid detectors with high sensitivity and fast readout are demonstrated with a proof of concept experiment of continuous rotation electron diffraction on a natrolite nanocrystal.

1. Introduction

The availability of a single crystal electron diffraction (ED) technique is completely changing the crystallography scenario. While, in the past, the crystallographic information obtained from a transmission electron microscope (TEM) was essentially two-dimensional, with data derived from high-resolution images or zone axis diffraction patterns, now it is possible to use a TEM as a single-crystal diffractometer for nanocrystals in a way which is approaching the accuracy of X-rays. This means bringing the well established tools of single-crystal diffraction at least two order of magnitude further deep into the nanoworld, and making accessible to crystallographers many open problems that could not be solved for the lack of probe resolution of the standard diffraction techniques. Such revolution has been possible thanks to two bright ideas: the invention of precession electron diffraction (Vincent & Midgley, 1994[Vincent, R. & Midgley, P. A. (1994). Ultramicroscopy, 53, 271-282.]) and the idea of mapping reciprocal space through a sequence of non-oriented patterns, originally named automated electron diffraction tomography (ADT) (Kolb et al., 2007[Kolb, U., Gorelik, T. E., Kübel, C., Otten, M. T. & Hubert, D. (2007). Ultramicroscopy, 107, 507-513.]). It is with the combination of these two techniques that Mugnaioli et al. (2009[Mugnaioli, E., Gorelik, T. & Kolb, U. (2009). Ultramicroscopy, 109, 758-765.]) demonstrated that ADT collected in precession electron diffraction mode provides, at the same time, a large coverage of reciprocal space and quasi-kinematical ED intensities, suitable for structure solution. Since this seminal result, the number of crystal structures solved with ED have started to increase constantly every year and new variations of the original experimental protocol appeared on the scene. The first alternative to ADT was brought about by Zhang et al. (2010[Zhang, D., Oleynikov, P., Hovmöller, S. & Zou, X. (2010). Z. Kristallogr. 225, 94-102.]) with the so-called rotation electron diffraction (RED). In RED, the patterns are collected in standard parallel illumination and the reciprocal space is sampled with a fine slicing obtained through small electrical beam tilts. The last and more recent version of the technique was the introduction of continuous data collection modes (Nederlof et al., 2013[Nederlof, I., van Genderen, E., Li, Y.-W. & Abrahams, J. P. (2013). Acta Cryst. D69, 1223-1230.]) known as MicroED (Nannenga et al., 2014[Nannenga, B. L., Shi, D., Leslie, A. G. W. & Gonen, T. (2014). Nat. Methods, 11, 927-930.]), IEDT (Gemmi et al., 2015[Gemmi, M., La Placa, M. G. I., Galanis, A. S., Rauch, E. F. & Nicolopoulos, S. (2015). J. Appl. Cryst. 48, 718-727.]) and cRED (Wang et al., 2018[Wang, Y., Yang, T., Xu, H., Zou, X. & Wan, W. (2018). J. Appl. Cryst. 51, 1094-1101.]), in which the patterns are collected while the crystal is rotated, analogously to what is common practice for single-crystal X-ray diffraction, and more specifically to `shutterless' data collection modes (Hasegawa et al., 2009[Hasegawa, K., Hirata, K., Shimizu, T., Shimizu, N., Hikima, T., Baba, S., Kumasaka, T. & Yamamoto, M. (2009). J. Appl. Cryst. 42, 1165-1175.]). While ADT and RED were originally very solid for inorganic and beam resistant crystals, the introduction of the continuous methods, combined with the availability of hybrid single electron detectors (Nederlof et al., 2013[Nederlof, I., van Genderen, E., Li, Y.-W. & Abrahams, J. P. (2013). Acta Cryst. D69, 1223-1230.]) has extended the application of the technique to beam-sensitive materials such as metal–organics (Wang et al., 2017[Wang, Y., Takki, S., Cheung, O., Xu, H., Wan, W., Öhrström, L. & Inge, A. K. (2017). Chem. Commun. 53, 7018-7021.]; Portolés-Gil et al., 2018[Portolés-Gil, N., Lanza, A., Aliaga-Alcalde, N., Ayllón, J. A., Gemmi, M., Mugnaioli, E., López-Periago, A. M. & Domingo, C. (2018). ACS Sustainable Chem. Eng. 6, 12309-12319.]; Yuan et al., 2018[Yuan, S., Qin, J. S., Xu, H. Q., Su, J., Rossi, D., Chen, Y., Zhang, L., Lollar, C., Wang, Q., Jang, H., Son, D. H., Xu, H., Huang, Z., Zou, X. & Zhou, H. C. (2018). ACS Cent. Sci. 4, 105-111.]) organics (Das et al., 2018[Das, P. P., Mugnaioli, E., Nicolopoulos, S., Tossi, C., Gemmi, M., Galanis, A., Borodi, G. & Pop, M. M. (2018). Org. Process Res. Dev. 22, 1365-1372.]) and proteins (Yonekura et al., 2015[Yonekura, K., Kato, K., Ogasawara, M., Tomita, M. & Toyoshima, C. (2015). Proc. Natl Acad. Sci. USA, 112, 3368-3373.]; Sawaya et al., 2016[Sawaya, M. R., Rodriguez, J., Cascio, D., Collazo, M. J., Shi, D., Reyes, F. E., Hattne, J., Gonen, T. & Eisenberg, D. S. (2016). Proc. Natl Acad. Sci. USA, 113, 11232-11236.]; Clabbers et al., 2017[Clabbers, M. T. B., van Genderen, E., Wan, W., Wiegers, E. L., Gruene, T. & Abrahams, J. P. (2017). Acta Cryst. D73, 738-748.]; Xu et al., 2018[Xu, H., Lebrette, H., Yang, T., Srinivas, V., Hovmöller, S., Högbom, M. & Zou, X. (2018). Structure, 26, 667-675.]; Lanza et al., 2019[Lanza, A., Margheritis, E., Mugnaioli, E., Cappello, V., Garau, G. & Gemmi, M. (2019). IUCrJ, 6, 178-188.]). The variety of names given to these techniques suggests that there are several ways in which a data collection can be performed and implemented in a standard TEM. For the sake of simplicity, we will join all these techniques under the name 3D ED. In this paper, we would like to identify the key points that have to be faced for 3D ED to be successful in structure solution and we will describe how the different data collection types meet these requirements. The final goal will be to provide the fundamental details for implementing the method in any TEM: not only on instruments having the most advanced add-ons, but also on those with the most standard goniometer settings, sample holders, detectors, and illumination conditions. We believe 3D ED technology has matured sufficiently to allow its routine application, especially when only sub-micron crystals are available.

2. The challenges

The chance of solving a crystal structure using ED data relies on the collection of a complete three-dimensional set of ED intensities proportional to the square modulus of the structure factors, thus abiding the approximation of kinematical scattering. This requires electron crystallography methods to deal and possible solve the following problems:

(1) Dynamical scattering: the assumption of single kinematic scattering, on which traditional X-ray crystallography is based, is not valid for ED, therefore the linear relation between the reflection intensity and the square modulus of the structure factor is often violated;

(2) Excitation error: due to the limited diffracting area and its shape, the reflections have a non-negligible volume in reciprocal space and if a reflection is measured out of its exact Bragg conditions, severe underestimation of the intensity occurs;

(3) Coverage: with common TEMs it is not trivial to collect enough data for structure solution, as the accessibility of reciprocal space is hampered by hardware constraints;

(4) Beam damage: many samples are beam sensitive and a strong or prolonged illumination can induce their decomposition or amorphization, at times even under cryogenic conditions.

Dynamical scattering and excitation error, in particular, cannot be overcome by technological developments, as they are intrinsic consequences of the very nature of electrons and the short wavelengths at play.

The problem of dynamical scattering has been considered for years the main obstacle for the use of ED in structure solution and derives from the strong interaction of electrons with matter. An electron beam traveling inside a crystal can be easily diffracted several times leading to a redistribution of the diffracted intensities among the excited reflections. This spoils the linear relation between intensities and squared structure factor amplitudes (kinematical scattering), strongly hampering the symmetry determination, structure solution and above all structure refinement. The theory of dynamical diffraction is available (Spence & Zuo, 1992[Spence, J. C. H. & Zuo, J. M. (1992). Electron Microdiffraction. New York: Plenum Press.]); however, the different contributions are difficult to deconvolve without any prior knowledge of the structure, as their dependence on thickness, orientation, chemical composition and atomic arrangement of the sample is highly nonlinear.

The excitation error problem is more subtle but no less severe. It is connected to the fact that the reflections have a certain extension in reciprocal space due to the shape of the diffracting area and the crystal mosaicity. If we model a crystal as a slab of thickness t, in kinematical approximation the reflection intensities must be calculated as

[I({\bf q})\sim\left|F({\bf h})\right|^{2}\left[{ {\sin^{2}\left(\pi ts_{h} \right)} \over {s_{h}^{2}}}\right],]

where F(h) is the structure factor, the sinc function sin(πtsh)/sh is the Fourier transform of the shape function of the crystal and sh = qh is known as the excitation error. A plot of the square of the sinc function for different thicknesses (see Fig. S1) shows how extended the reflection is in reciprocal space and how its intensity is damped by departing from an exact Bragg condition (increasing excitation error). To have an idea of the impact of excitation error on the correct estimation of the structure factor amplitude, it suffices to calculate how far from a perfect Bragg condition the intensity drop off by 50%. In the case of t = 200 Å, an optimal thickness for an ED experiment, this happens for sh = 0.0022 Å−1. Such an excitation error corresponds to a tilt of 0.35° off from Bragg condition for a reflection of 3 Å periodicity and to smaller tilts for higher resolution reflections (see supplementary information). For thicker crystals these angles are even smaller. Therefore, correctly estimating |F(h)|2 from single patterns is very problematic, since orientations differing for a fraction of degree produces completely different intensities. In X-ray crystallography data reduction programs, the intensity of partially recorded reflections due to the excitation error is usually corrected by refining and integrating several empirical profile fitting functions, instead of summing the partial measurements of the intensities. This approach however relies on a complete, redundant and good quality data set.

Traditionally, electron crystallography consisted in the acquisition and analysis of oriented zone axis patterns. However, a useful 3D set of ED data cannot simply be obtained by merging together intensities collected in different zones, as oriented patterns indeed feature and enhance all the above-mentioned pitfalls. In zone axis the presence of a large number of reflections close to a Bragg condition maximizes the possibility of multiple scattering aggravating the dynamical effects, while any small deviation from a perfect zone axis orientation will produce significant and random deviations from |F(h)|2 even in the case of a negligible dynamical scattering. Despite pioneering efforts in using zone axis patterns for structure solution (Dorset, 1995[Dorset, D. (1995). Structural Electron Crystallography. New York: Plenum Press.]; Nicolopoulos et al., 1995[Nicolopoulos, S., González-Calbet, J. M., Vallet-Regi, M., Corma, A., Corell, C., Guil, J. M. & Perez-Pariente, J. (1995). J. Am. Chem. Soc. 117, 8947-8956.]), both the dynamical and the excitation error problem were an insurmountable obstacle, hence very few structures have been solved in this way (Gemmi et al., 2000[Gemmi, M., Righi, L., Calestani, G., Migliori, A., Speghini, A., Santarosa, M. & Bettinelli, M. (2000). Ultramicroscopy, 84, 133-142.]; Weirich et al., 2000[Weirich, T. E., Zou, X. D., Ramlau, R., Simon, A., Cascarano, G. L., Giacovazzo, C. & Hovmöller, S. (2000). Acta Cryst. A56, 29-35.]).

Electron crystallography developed further in order to minimize these problems, and at the same time to overcome some apparently trivial issues, such as the insufficient coverage and positional instability of the crystal. These latter depend on technical limits of TEM instruments which are not (yet) conceived as diffractometers. Among the several solutions that have been implemented, one can identify two main concepts and combinations thereof: (i) moving away from a zone axis orientation (beam precession or tilting); (ii) adopting strategies for sampling the reciprocal space.

2.1. Precession electron diffraction

A big step forward was the invention of the precession technique (Vincent & Midgley, 1994[Vincent, R. & Midgley, P. A. (1994). Ultramicroscopy, 53, 271-282.]; Midgley & Eggeman, 2015[Midgley, P. A. & Eggeman, A. S. (2015). IUCrJ, 2, 126-136.]) whose primary goal was to reduce dynamical scattering, but at the same time it turned out to be also the first solution to the excitation error problem. The precession electron diffraction (PED) technique was originally devised as a zone axis pattern technique. In PED a crystal is first oriented in zone axis, then the beam is precessed on a cone surface having the vertex fixed on the sample plane. In order to have a stationary spot pattern, the diffracted beams are also precessed in the opposite way (descan). Although an apparently normal diffraction pattern is obtained, what is registered is a sum of different diffraction conditions corresponding to off-axis orientations. In off axis orientation only those reflections that are close to the Laue circle are excited (compared to a standard SAED zone axis pattern), thus the non-systematic dynamical effects are strongly reduced. PED patterns are therefore quasi-kinematical and contain clear information about systematic absences and symmetry that in traditional zone axis patterns is usually lost due to dynamical scattering (multiple diffraction). The precession movement also causes the Ewald sphere to sweep a reciprocal space sector around the zone axis plane, thus integrating all the reflection in this sector over the excitation error. The different speed at which reflections at different scattering angles pass through the Ewald sphere causes an underestimation of high-resolution intensities which requires an ad hoc Lorentz correction (Gemmi & Nicolopoulos, 2007[Gemmi, M. & Nicolopoulos, S. (2007). Ultramicroscopy, 107, 483-494.]). While PED tackles both the dynamical and excitation error problems, low coverage remains an issue [Fig. 1[link](a)], unless several PED patterns are collected from different zones. A 3D set of reflection intensities can be built by merging data from different zone axes and several structures could be solved in this way (Gjønnes et al., 1998[Gjønnes, J., Hansen, V., Berg, B. S., Runde, P., Cheng, Y. F., Gjønnes, K., Dorset, D. L. & Gilmore, C. J. (1998). Acta Cryst. A54, 306-319.]; Gemmi et al., 2003[Gemmi, M., Zou, X. D., Hovmöller, S., Migliori, A., Vennström, M. & Andersson, Y. (2003). Acta Cryst. A59, 117-126.], 2010[Gemmi, M., Klein, H., Rageau, A., Strobel, P. & Le Cras, F. (2010). Acta Cryst. B66, 60-68.]; Boullay et al., 2009[Boullay, P., Dorcet, V., Pérez, O., Grygiel, C., Prellier, W., Mercey, B. & Hervieu, M. (2009). Phys. Rev. B, 79, 184108.]; Hadermann et al., 2010[Hadermann, J., Abakumov, A. M., Tsirlin, A. A., Filonenko, V. P., Gonnissen, J., Tan, H., Verbeeck, J., Gemmi, M., Antipov, E. V. & Rosner, H. (2010). Ultramicroscopy, 110, 881-890.], 2012[Hadermann, J., Abakumov, A., Van Rompaey, S., Perkisas, T., Filinchuk, Y. & Van Tendeloo, G. (2012). Chem. Mater. 24, 3401-3405.]; Klein, 2011[Klein, H. (2011). Acta Cryst. A67, 303-309.]). However, orienting the crystal in many different zone axes is tedious and time consuming. Moreover, in order to reach an acceptable coverage, data often need to be collected on different crystals, thus complicating the data merging procedure. These facts have always been an unavoidable hindrance for zone axis PED to become a routine technique. An alternative solution to the coverage problem had to be found.

[Figure 1]
Figure 1
Sketch of a data collection made of single zone axes (a) versus an ADT data collection (b) where a sequence of patterns is collected by rotating the goniometer in steps.

2.2. Reciprocal space exploration

An obvious solution for the coverage problem would be to collect a sequence of patterns while tilting the sample around the goniometer axis. This solution was proposed for the first time in 2007 (Kolb et al., 2007[Kolb, U., Gorelik, T. E., Kübel, C., Otten, M. T. & Hubert, D. (2007). Ultramicroscopy, 107, 507-513.]) and originally named automated diffraction tomography [ADT; Fig. 1[link](b)]. ADT gives a volume rendering of a large portion of reciprocal space that, depending on the microscope model and on the sample holder, varies between 60° and more than 120°. It has the advantage that the patterns are randomly oriented, i.e. most of the time far from main zone axis orientations, which guarantees a minimization of dynamical scattering. However, data collection has to face the problem of the crystal movement during tilt. In fact, in most of the microscopes it is almost impossible to avoid an appreciable crystal movement for the entire tilt range of the goniometer, even after setting very precisely the eucentric height. The standard solution to this problem is to check the crystal position, when needed, by taking an image and by recentering it under the beam. The type and the frequency of the images depends on the chosen illumination and will be discussed in a dedicated paragraph.

While the data collection is relatively easy and can be performed in every microscope, the interpretation of the data collection requires an offline data reduction procedure based on ad hoc software. At the present there are several software programs that can handle ED data. Some of them are designed specifically for electrons such as ADT3D (Kolb et al., 2011[Kolb, U., Mugnaioli, E. & Gorelik, T. E. (2011). Cryst. Res. Technol. 46, 542-554.]), PETS (Palatinus et al., 2019[Palatinus, L., Brázda, P., Jelínek, M., Hrdá, J., Steciuk, G. & Klementová, M. (2019). Acta Cryst. B75, 512-522.]), EDTProcess (Gemmi & Oleynikov, 2013[Gemmi, M. & Oleynikov, P. (2013). Z. Kristallogr. Cryst. Mater. 228, 51-58.]) and RED (Wan et al., 2013[Wan, W., Sun, J., Su, J., Hovmöller, S. & Zou, X. (2013). J. Appl. Cryst. 46, 1863-1873.]), while others were developed for X-ray diffraction DIALS (Waterman et al., 2013[Waterman, D. G., Winter, G., Parkhurst, J. M., Fuentes-Montero, L., Hattne, J., Brewster, A., Sauter, N. K. & Evans, G. (2013). CCP4 Newsl. Protein Crystallography, 49, 16-19.]; Clabbers et al., 2018[Clabbers, M. T. B., Gruene, T., Parkhurst, J. M., Abrahams, J. P. & Waterman, D. G. (2018). Acta Cryst. D74, 506-518.]), MOSFLM (Leslie & Powell, 2007[Leslie, A. G. W. & Powell, H. R. (2007). Evolving Methods for Macromolecular Crystallography. Dordrecht: Springer.]) and XDS (Kabsch, 2010[Kabsch, W. (2010). Acta Cryst. D66, 125-132.]).

Once provided with a suitable software, a simple sequence of patterns collected every degree can be used to get the unit-cell parameters and the extinction symbol of the analyzed crystal (Kolb et al., 2008[Kolb, U., Gorelik, T. E. & Otten, M. T. (2008). Ultramicroscopy, 108, 763-772.]) but very rarely it is suitable for structure solution (Shi et al., 2013[Shi, D., Nannenga, B. L., Iadanza, M. G. & Gonen, T. (2013). eLife, 2, e01345.]; Fan et al., 2013[Fan, J., Carrillo-Cabrera, W., Akselrud, L., Antonyshyn, I., Chen, L. & Grin, Y. (2013). Inorg. Chem. 52, 11067-11074.]), since the gaps between consecutive patterns leave the excitation error problem unsolved.

3. 3D electron diffraction

3.1. Precession-assisted electron diffraction tomography (PEDT)

The first solution to the excitation error problem for a sequence of patterns came by collecting the patterns in precession mode, in a kind of `precession-assisted electron diffraction tomography' (PEDT; Mugnaioli et al., 2009[Mugnaioli, E., Gorelik, T. & Kolb, U. (2009). Ultramicroscopy, 109, 758-765.]). In PEDT the patterns are collected in steps, usually of 1°, with a precession semi-angle comparable with the angular step. In this way the Ewald sphere sweeps the reciprocal space between the collected orientations integrating the reflections over the excitation error [Fig. 2[link](a)]. The simultaneous solution of the main problems enabled PEDT to be the first 3D ED technique with a high chance of success in structure solution (Kolb et al., 2011[Kolb, U., Mugnaioli, E. & Gorelik, T. E. (2011). Cryst. Res. Technol. 46, 542-554.]). The ED intensities collected in this way give a large reciprocal space coverage and can be successfully used in ab initio structure solution methods, such as direct methods or charge flipping (Palatinus et al., 2011[Palatinus, L., Klementová, M., Dřínek, V., Jarošová, M. & Petříček, V. (2011). Inorg. Chem. 50, 3743-3751.]) just as they were kinematical. Although beam precession requires a special external device to be connected to the TEM, the method resulted to be portable on different instruments and has proved to work in a high voltage range between 120 and 300 kV [examples of structures solved at 300 kV with a FEI Tecnai F30 are given by Kolb et al. (2011)[Kolb, U., Mugnaioli, E. & Gorelik, T. E. (2011). Cryst. Res. Technol. 46, 542-554.]; at 200 kV with a Tecnai F20, in Gemmi et al. (2012)[Gemmi, M., Campostrini, I., Demartin, F., Gorelik, T. E. & Gramaccioli, C. M. (2012). Acta Cryst. B68, 15-23.]; at 200 kV with a Jeol 2010 given by Rozhdestvenskaya et al. (2017)[Rozhdestvenskaya, I. V., Mugnaioli, E., Schowalter, M., Schmidt, M. U., Czank, M., Depmeier, W. & Rosenauer, A. (2017). IUCrJ, 4, 223-242.]; at 120 kV with an energy-filtered Zeiss Libra 120 given by Gemmi & Oleynikov (2013)[Gemmi, M. & Oleynikov, P. (2013). Z. Kristallogr. Cryst. Mater. 228, 51-58.]; at 120 kV with a Philips CM120 given by Boullay et al. (2013[Boullay, P., Palatinus, L. & Barrier, N. (2013). Inorg. Chem. 52, 8-10.])]. PEDT data can be also successfully modeled taking into account the residual dynamical effects. In this way, through a least square procedure the crystal structure can be refined with accuracies comparable with single-crystal X-ray diffraction (Palatinus et al., 2015a[Palatinus, L., Petrícek, V. & Corrêa, C. A. (2015a). Acta Cryst. A71, 235-244.],b[Palatinus, L., Corrêa, C. A., Steciuk, G., Jacob, D., Roussel, P., Boullay, P., Klementová, M., Gemmi, M., Kopeček, J., Domeneghetti, M. C., Cámara, F. & Petříček, V. (2015b). Acta Cryst. B71, 740-751.]; Colmont et al., 2016[Colmont, M., Palatinus, L., Huvé, M., Kabbour, H., Saitzek, S., Djelal, N. & Roussel, P. (2016). Inorg. Chem. 55, 2252-2260.]; Gemmi et al., 2016[Gemmi, M., Merlini, M., Palatinus, L., Fumagalli, P. & Hanfland, M. (2016). Am. Mineral. 101, 2645-2654.]; Mugnaioli et al., 2016[Mugnaioli, E., Gemmi, M., Merlini, M. & Gregorkiewitz, M. (2016). Acta Cryst. B72, 893-903.]) and light elements, such as hydrogen, can be detected and refined (Palatinus et al., 2017[Palatinus, L., Brázda, P., Boullay, P., Perez, O., Klementová, M., Petit, S., Eigner, V., Zaarour, M. & Mintova, S. (2017). Science, 355, 166-169.]).

[Figure 2]
Figure 2
Sketch of a PEDT data collection (a) and RED data collection (b). In PEDT, reciprocal space is sampled by a conical movement of the Ewald sphere (green cones), while in RED by fine electrical beam tilts (red lines).

3.2. Rotation electron diffraction (RED)

An alternative solution to the excitation error problem can be found by fine sampling reciprocal space through very small angular steps instead of using the precession movement. The method, called rotation electron diffraction (RED), was first proposed by Zhang et al. (2010[Zhang, D., Oleynikov, P., Hovmöller, S. & Zou, X. (2010). Z. Kristallogr. 225, 94-102.]) and simply requires an ad hoc designed software plug-in to control and synchronize the beam tilt with the microscope hardware and the detector. In fact, for a proper sampling of reciprocal space, the tilt step between the patterns should be less than 0.1°, which is beyond the mechanical precision of standard goniometers, but it can be implemented through electron beam tilt. Thus, for covering the entire angular range of the goniometer, the data collection is designed as a combination of coarse mechanical steps of about 1°–3° and fine electron beam tilts in between [Fig. 2[link](b)]. The angular range sampled by beam tilt is slightly larger than the mechanical tilt angle, in order to avoid any gap. During the beam tilts, since there are no mechanical movements, there is no need for crystal recentering, which is instead often needed after mechanical tilt. The total data collection consists of a larger number of patterns, around 1000 compared to the 100 of PEDT. As in PEDT, ED intensities collected with RED can be used as kinematical in structure solution with direct methods or other structure solution methods developed for X-ray diffraction. The quality of the data is also suitable for kinematical refinement that in some cases can give very detailed structural information such as partial occupancies (Guo et al., 2016[Guo, P., Strohmaier, K., Vroman, H., Afeworki, M., Ravikovitch, P. I., Paur, C. S., Sun, J., Burton, A. & Zou, X. (2016). Inorg. Chem. Front. 3, 1444-1448.]). The RED method has been mainly implemented in Jeol microscopes, but there are no reasons why it cannot be performed on other instruments.

The solution of the excitation error problem in 3D ED by RED and PEDT opened ED to the possibility to solve crystal structures of different types of materials: inorganic crystals (PEDT: Mugnaioli et al., 2012[Mugnaioli, E., Andrusenko, I., Schüler, T., Loges, N., Dinnebier, R. E., Panthöfer, M., Tremel, W. & Kolb, U. (2012). Angew. Chem. Int. Ed. 51, 7041-7045.]; RED: Mayence et al., 2014[Mayence, A., Navarro, J. R. G., Ma, Y., Terasaki, O., Bergström, L. & Oleynikov, P. (2014). Inorg. Chem. 53, 5067-5072.]; Yun et al., 2014[Yun, Y., Wan, W., Rabbani, F., Su, J., Xu, H., Hovmöller, S., Johnsson, M. & Zou, X. (2014). J. Appl. Cryst. 47, 2048-2054.]), mesoporous materials (PEDT: Jiang et al., 2011[Jiang, J., Jorda, J. L., Yu, J., Baumes, L. A., Mugnaioli, E., Diaz-Cabanas, M. J., Kolb, U. & Corma, A. (2011). Science, 333, 1131-1134.]; Mugnaioli & Kolb, 2013[Mugnaioli, E. & Kolb, U. (2013). Microporous Mesoporous Mater. 166, 93-101.]; RED: Martínez-Franco et al., 2013[Martínez-Franco, R., Moliner, M., Yun, Y., Sun, J., Wan, W., Zou, X. & Corma, A. (2013). Proc. Natl Acad. Sci. 110, 3749-3754.]), metal–organic frameworks (PEDT: Feyand et al., 2012[Feyand, M., Mugnaioli, E., Vermoortele, F., Bueken, B., Dieterich, M., Reimer, T., Kolb, U., de Vos, D. & Stock, N. (2012). Angew. Chem. Int. Ed. 51, 10373-10376.]), covalent organic framework (RED: Zhang et al., 2013[Zhang, Y., Su, J., Furukawa, H., Yun, Y., Gándara, F., Duong, A., Zou, X. & Yaghi, O. M. (2013). J. Am. Chem. Soc. 135, 16336-16339.]; Liu et al., 2019[Liu, Y., Diercks, C. S., Ma, Y., Lyu, H., Zhu, C., Alshmimri, S. A., Alshihri, S. & Yaghi, O. M. (2019). J. Am. Chem. Soc. 141, 677-683.]) modulated structures (PEDT: Palatinus et al., 2011[Palatinus, L., Klementová, M., Dřínek, V., Jarošová, M. & Petříček, V. (2011). Inorg. Chem. 50, 3743-3751.]), new minerals (PEDT: Rozhdestvenskaya et al., 2010[Rozhdestvenskaya, I., Mugnaioli, E., Czank, M., Depmeier, W., Kolb, U., Reinholdt, A. & Weirich, T. (2010). Mineral. Mag. 74, 159-177.]; Gemmi et al., 2012[Gemmi, M., Campostrini, I., Demartin, F., Gorelik, T. E. & Gramaccioli, C. M. (2012). Acta Cryst. B68, 15-23.]; Capitani et al., 2014[Capitani, G. C., Mugnaioli, E., Rius, J., Gentile, P., Catelani, T., Lucotti, A. & Kolb, U. (2014). Am. Mineral. 99, 500-510.]; Plášil et al., 2014[Plášil, J., Palatinus, L., Rohlícek, J., Houdková, L., Klementova, M., Goliáš, V. & Škácha, P. (2014). Am. Mineral. 99, 276-282.]; Németh et al., 2018[Németh, P., Mugnaioli, E., Gemmi, M. & Czuppon, G. (2018). Sci. Adv. 4, eaau6178.]) organic crystals (PEDT: Gorelik et al., 2016[Gorelik, T. E., Czech, C., Hammer, S. M. & Schmidt, M. U. (2016). CrystEngComm, 18, 529-535.]) and biominerals (PEDT: Mugnaioli et al., 2014[Mugnaioli, E., Reyes-Gasga, J., Kolb, U., Hemmerlé, J. & Brès, É. (2014). Chem. Eur. J. 20, 6849-6852.]), to name only a small selection of all publications.

3.3. Centering methods and different illumination conditions

Both in PEDT and RED the patterns can usually be collected in either of two different illumination conditions: in selected area electron diffraction (SAED) mode or in nanodiffraction mode. In SAED, the diffracting area is selected through a diaphragm. The displacement of the crystal in this case can be controlled by switching between diffraction and image mode and eventually removing the SAED aperture if necessary (Palatinus et al., 2011[Palatinus, L., Klementová, M., Dřínek, V., Jarošová, M. & Petříček, V. (2011). Inorg. Chem. 50, 3743-3751.]; Gemmi et al., 2012[Gemmi, M., Campostrini, I., Demartin, F., Gorelik, T. E. & Gramaccioli, C. M. (2012). Acta Cryst. B68, 15-23.]; Wan et al., 2013[Wan, W., Sun, J., Su, J., Hovmöller, S. & Zou, X. (2013). J. Appl. Cryst. 46, 1863-1873.]). SAED is the simplest mode implementable in any TEM which allows parallel beam diffraction with possibly very low dose conditions. SAED has the drawback that the illuminated area is larger than the diffracting area, thus, if the sample is beam sensitive, the beam damages all the crystal and not only the area visible inside the SAED aperture. Secondly, it suffers from the error in the localization of the SAED aperture due to the spherical aberration of the objective lens. Because of this error, the electrons contributing to low- and high-resolution reflections come from displaced areas of the sample. The effect is more significative with small SAED apertures and limit the spatial resolution of the technique (Williams & Carter, 1996[Williams, D. B. & Carter, C. B. (1996). Transmission Electron Microscopy. New York: Plenum Press.]).

In nanodiffraction mode the diffracting area is selected by illuminating the sample with a parallel beam having a size in the 50–200 nm range. It avoids at the same time to damage the crystal beyond the diffracting area and the problems connected to the spherical aberration. However, such a nanobeam makes it extremely challenging to perform the crystal centering in standard TEM imaging mode; therefore, two alternative ways are followed.

One possibility is to strongly defocus the ED pattern until an image of the crystal is visible inside the central spot and use this one for the centering (Wan et al., 2013[Wan, W., Sun, J., Su, J., Hovmöller, S. & Zou, X. (2013). J. Appl. Cryst. 46, 1863-1873.]).

Alternatively, a scanning transmission electron microscopy (STEM) image can be taken to visualize the crystal position, if this mode is available on the microscope (Kolb et al., 2007[Kolb, U., Gorelik, T. E., Kübel, C., Otten, M. T. & Hubert, D. (2007). Ultramicroscopy, 107, 507-513.]). This can be performed without changing the optical configuration, making a blurred image with the parallel nanobeam (Mugnaioli & Gemmi, 2018[Mugnaioli, E. & Gemmi, M. (2018). Z. Kristallogr. 233, 163-178.]), or in standard STEM configuration with a convergent beam. The use of STEM in collecting the images is extremely valuable because it reduces the total dose on the sample. One can record an image with just one scan, freeze it, blank the beam and finally select where to position the beam directly on the frozen image, while the sample is not exposed to the beam. The effectiveness of STEM imaging in keeping the dose limited is confirmed by the structure determination of a new polymorph of lysozyme by PEDT (Lanza et al., 2019[Lanza, A., Margheritis, E., Mugnaioli, E., Cappello, V., Garau, G. & Gemmi, M. (2019). IUCrJ, 6, 178-188.]).

4. Towards a fast and automated 3D electron diffraction

PEDT and RED solved the problem of structure solution with ED data, however both techniques are difficult to be completely automated and the crystal centering procedure is a limiting step which increases the dose making the observation of very beam-sensitive samples problematic.

4.1. Continuous rotation methods (cRED, MicroED, IEDT)

Beam-sensitive materials and automation pushed 3D ED towards data collection in continuous rotation. Collecting the patterns during the rotation of the sample and not in steps is an obvious approach for X-ray crystallographers, but it relies completely on the mechanical stability of the goniometer. Ideally, the sphere of confusion should be smaller than the illuminated area or the crystal size in order to allow a sequence of patterns to be collected automatically according to a programmed data collection strategy. In reality, often TEM sample stages do not have the necessary stability and the crystal can drift significantly during rotation, thus allowing continuous data collection only in finite angular ranges. Depending on the microscope characteristics (sample holder model, goniometer, objective pole pieces), this ranges are variable from a few tens of degrees to 120° or more.

In continuous rotation methods, the excitation error problem is solved by sampling reciprocal space during the exposure time (texp). At the end the data collection is made by a sequence of patterns that are integrated portions of reciprocal space of angular thickness ηexp = ω*texp (ω being the angular speed of the goniometer). The speed of the detector is crucial as, in fact, during the detector readout time (tdead), the information contained in an angular range ηdead = ω*tdead is lost (Fig. 3[link]). While tdead is almost negligible in modern detectors, this method can also be implemented if the detector is relatively slow (e.g. a CCD). Possible strategies that can be followed to reduce the ηdead gaps are: (i) to speed up the readout (i.e. reduce tdead) by binning the detector; (ii) to collect the patterns in precession mode. A discussion of these strategies is given by Gemmi et al. (2015[Gemmi, M., La Placa, M. G. I., Galanis, A. S., Rauch, E. F. & Nicolopoulos, S. (2015). J. Appl. Cryst. 48, 718-727.]).

[Figure 3]
Figure 3
Sketch of a continuous data collection. The green sectors correspond to the portion of reciprocal space sampled during the exposure of the detector (ηexp). The light-brown sectors correspond to the missed gaps of reciprocal space swept by the Ewald sphere during the detector readout time (ηdead).

The continuous method has the further advantage that, apart from a stable goniometer, it does not require any external device or plugin to be realized.

This method of data collection was first proposed in 2013 for studying protein crystals (Nederlof et al., 2013[Nederlof, I., van Genderen, E., Li, Y.-W. & Abrahams, J. P. (2013). Acta Cryst. D69, 1223-1230.]) and it is now known with several acronyms as MicroED (Nannenga et al., 2014[Nannenga, B. L., Shi, D., Leslie, A. G. W. & Gonen, T. (2014). Nat. Methods, 11, 927-930.]), IEDT (Gemmi et al., 2015[Gemmi, M., La Placa, M. G. I., Galanis, A. S., Rauch, E. F. & Nicolopoulos, S. (2015). J. Appl. Cryst. 48, 718-727.]), cRED (Wang et al., 2017[Wang, Y., Takki, S., Cheung, O., Xu, H., Wan, W., Öhrström, L. & Inge, A. K. (2017). Chem. Commun. 53, 7018-7021.]). Continuous rotation data collection has been a second revolution for 3D ED making it possible to perform single-crystal studies on very beam-sensitive compounds that could only be synthesized in nanocrystalline form such as zeolites (Simancas et al., 2016[Simancas, J., Simancas, R., Bereciartua, P. J., Jorda, J. L., Rey, F., Corma, A., Nicolopoulos, S., Pratim Das, P., Gemmi, M. & Mugnaioli, E. (2016). J. Am. Chem. Soc. 138, 10116-10119.]; Bieseki et al., 2018[Bieseki, L., Simancas, R., Jordá, J. L., Bereciartua, P. J., Cantín, Á., Simancas, J., Pergher, S. B., Valencia, S., Rey, F. & Corma, A. (2018). Chem. Commun. 54, 2122-2125.]), pharmaceuticals (van Genderen et al., 2016[Genderen, E. van, Clabbers, M. T. B., Das, P. P., Stewart, A., Nederlof, I., Barentsen, K. C., Portillo, Q., Pannu, N. S., Nicolopoulos, S., Gruene, T. & Abrahams, J. P. (2016). Acta Cryst. A72, 236-242.]; Jones et al., 2018[Jones, C. G., Martynowycz, M. W., Hattne, J., Fulton, T. J., Stoltz, B. M., Rodriguez, J. A., Nelson, H. M. & Gonen, T. (2018). ACS Cent. Sci. 4, 1587-1592.]), organics (Sawaya et al., 2016[Sawaya, M. R., Rodriguez, J., Cascio, D., Collazo, M. J., Shi, D., Reyes, F. E., Hattne, J., Gonen, T. & Eisenberg, D. S. (2016). Proc. Natl Acad. Sci. USA, 113, 11232-11236.]) and proteins (Nannenga et al., 2014[Nannenga, B. L., Shi, D., Leslie, A. G. W. & Gonen, T. (2014). Nat. Methods, 11, 927-930.]; Yonekura et al., 2015[Yonekura, K., Kato, K., Ogasawara, M., Tomita, M. & Toyoshima, C. (2015). Proc. Natl Acad. Sci. USA, 112, 3368-3373.]).

Although the continuous rotation had a lot of success in the case of beam-sensitive samples, if the goniometer is stable there is no reason why a stepwise data collection cannot be performed in an automatic way. A sequence of tilt and pattern recording steps can be programmed through an external script which can control at the same time the microscope and the detector hardware. If the beam is blanked during the tilting step the dose is comparable to the continuous rotation mode. An example of a stepwise low-dose procedure is given by Kodjikian & Klein (2019[Kodjikian, S. & Klein, H. (2019). Ultramicroscopy, 200, 12-19.]).

4.2. Fast detectors

Pushed by the cryoEM revolution and by the ambition to perform live in situ experiments in a TEM, the detector technology evolved in the production of fast and very sensitive detectors based on hybrid pixel technology (Georgieva et al., 2011[Georgieva, D., Jansen, J., Sikharulidze, I., Jiang, L., Zandbergen, H. W. & Abrahams, J. P. (2011). J. Instrum. 6, C01033.]; Tinti et al., 2018[Tinti, G., Fröjdh, E., van Genderen, E., Gruene, T., Schmitt, B., de Winter, D. A. M., Weckhuysen, B. M. & Abrahams, J. P. (2018). IUCrJ, 5, 190-199.]). Besides being radiation hard and thus specific for diffraction, these detectors are sensitive to single electrons, allowing diffraction experiments at doses that can be lower than 0.01 el s−1Å−2. Hybrid pixel detectors are also extremely fast, with readout times of the order of several milliseconds. The latest models are able to work in continuous counting mode, ruling out any read out time problem. The combination of high dynamic range, sensitivity and speed makes them the first choice for continuous 3D ED on beam-sensitive materials. Thanks to hybrid detectors it has been possible to solve the crystal structure of very beam-sensitive materials even at room temperature such as pharmaceuticals (Das et al., 2018[Das, P. P., Mugnaioli, E., Nicolopoulos, S., Tossi, C., Gemmi, M., Galanis, A., Borodi, G. & Pop, M. M. (2018). Org. Process Res. Dev. 22, 1365-1372.]; Gruene et al., 2018[Gruene, T., Wennmacher, J. T. C., Zaubitzer, C., Holstein, J. J., Heidler, J., Fecteau-Lefebvre, A., De Carlo, S., Müller, E., Goldie, K. N., Regeni, I., Li, T., Santiso-Quinones, G., Steinfeld, G., Handschin, S., van Genderen, E., van Bokhoven, J. A., Clever, G. H. & Pantelic, R. (2018). Angew. Chem. Int. Ed. 57, 16313-16317.]) or MOFs (Yuan et al., 2018[Yuan, S., Qin, J. S., Xu, H. Q., Su, J., Rossi, D., Chen, Y., Zhang, L., Lollar, C., Wang, Q., Jang, H., Son, D. H., Xu, H., Huang, Z., Zou, X. & Zhou, H. C. (2018). ACS Cent. Sci. 4, 105-111.]; Portolés-Gil et al., 2018[Portolés-Gil, N., Lanza, A., Aliaga-Alcalde, N., Ayllón, J. A., Gemmi, M., Mugnaioli, E., López-Periago, A. M. & Domingo, C. (2018). ACS Sustainable Chem. Eng. 6, 12309-12319.]). Other interesting results have been obtained at low temperature in continuous rotation, again on pharmaceuticals (Wang et al., 2017[Wang, Y., Takki, S., Cheung, O., Xu, H., Wan, W., Öhrström, L. & Inge, A. K. (2017). Chem. Commun. 53, 7018-7021.]) and on cryoplunged samples of proteins (Clabbers et al., 2017[Clabbers, M. T. B., van Genderen, E., Wan, W., Wiegers, E. L., Gruene, T. & Abrahams, J. P. (2017). Acta Cryst. D73, 738-748.]; Xu et al., 2018[Xu, H., Lebrette, H., Yang, T., Srinivas, V., Hovmöller, S., Högbom, M. & Zou, X. (2018). Structure, 26, 667-675.]; Lanza et al., 2019[Lanza, A., Margheritis, E., Mugnaioli, E., Cappello, V., Garau, G. & Gemmi, M. (2019). IUCrJ, 6, 178-188.]).

5. Different data collection types with a fast detector

The availability of detectors with a negligible readout time opens many possibilities for different data collection types in continuous rotation, provided the rotation speed of the goniometer can be tuned in a wide range (0.1° s−1 to 5° s−1). We are going to show the results of an experiment where we have been able to perform three different data collections in continuous rotation on the same crystal: one at the fastest speed, one at a slow speed that mimics a RED, and one at a slow speed in combination with beam precession. Finally one ADT-like and one PEDT-like data sets were obtained from the same crystal, to compare continuous rotation data with stepwise data. The experiments have been performed on a Zeiss Libra 120 operating at 120 kV and equipped with in-column omega energy filter, a high-angular annular dark-field detector for HAADF STEM imaging and a Nanomegas Digistar P1000 device for PED. The data were acquired with an ASI Timepix single electron detector 512 × 512 pixels, which has a tread = 7 ms. The Libra 120 has the possibility of tuning the tilt speed between 0.15° s−1 and 3° s−1. As test sample we selected a microcrystalline powder of the natural zeolite natrolite (Na2Al2Si3O10·2H2O). Natrolite is an orthorhombic structure with a = 18.2930 (2) Å, b = 18.6430 (5) Å, c = 6.5860 (5) Å, space group Fdd2 with ten non-hydrogen atoms in the asymmetric unit, two Si, one Al, one Na, five O and one water molecule.

5.1. Fast continuous rotation

A fast data collection has the purpose of minimizing the exposure of the sample to the beam. The sample has to rotate at the maximum speed, while the excitation error problem is solved by integrating reciprocal space during the exposure. In our case we rotated the goniometer at a speed ω = 2.9° s−1. At this speed, with an exposure of 0.6 s, the detector was integrating a reciprocal space wedge of ηexp = 1.76° with gaps of 0.02°. The total experimental time for was only 27 s for ca 80° rotation.

5.2. RED-like

If the sample is rotated very slowly and the detector collects patterns with a short exposure time, the data collection will be similar to a RED, since the reciprocal space integration during the exposure will be minimal. We implemented this data collection by rotating at the slowest speed of ω = 0.15° s−1. The exposure time of 0.6 s gave an integrated wedge of ηexp = 0.09°. The ηdead is obviously negligible. The total experimental time was almost 10 min.

5.3. Continuous PEDT

As a proof of concept we tried also a slow data collection but with the beam in precession mode. The rotation speed and the reciprocal space integration were the same as in the RED-like data collection (ω = 0.15° s−1, ηexp = 0.09°). The semi-angle of the precession cone was set to 1°. For the sake of simplicity we will call this data collection cPEDT (continuous precession electron diffraction). In cPEDT we have a clear oversampling of reciprocal space which is redundant, however it is an automatic and operator free way to collect PEDT data avoiding the centering procedure. The total experimental time was almost 10 minutes.

5.4. Stepwise data collections

In order to compare continuous with stepwise data collections we formed two different data sets extracting one pattern per degree from the RED-like and cPEDT continuous data collections. Due to the thin reciprocal space integration (only 0.09 degrees per frame), both these data sets can be considered as stepwise. The one extracted from the RED-like corresponds to an ADT data collection without precession, whereas the one extracted from cPEDT corresponds to a PEDT.

5.5. Comparison

A summary of the different data sets can be found in Table 1[link]. A comparison between single patterns of the fast continuous rotation, the RED-like and cPEDT is displayed in Fig. 4[link]. In the selected orientation the reflections are concentrated around two circular arcs corresponding to two different Laue zones cut by the Ewald sphere. These arcs are thinner in RED data due to a smaller reciprocal space integration with respect to the other two techniques. The difference between cPEDT and fast continuous is tiny since the precession amplitude of 2° is comparable with the integration angle due to the goniometer rotation in fast continuous rotation.

Table 1
Summary of the details of the different data collections performed with the ASI Timepix detector in continuous rotation on the same crystal of natrolite

Data Speed (° s−1) Total angular range (°) No. of patterns Angular step (°) Precession angle (°) Total time (s)
Continuous 2.9 79 46 1.78 0 27
RED-like 0.15 88 983 0.09 0 585
ADT-like 0.15 88 89 1 0 -
cPEDT 0.15 88.5 980 0.09 1 590
PEDT-like 0.15 88 89 1 1 -
[Figure 4]
Figure 4
Single diffraction patterns collected on the same natrolite crystal in almost identical orientations but during different data collections. The larger reciprocal space integration in the fast continuous (top) and the cPEDT (bottom) data collections with respect to the RED-like (middle) is shown by the higher number of reflections.

The patterns have been processed with the program PETS for indexing and intensity integration (Palatinus et al., 2019). We used as integration routine the integrated profile option which takes into account the angular distance in reciprocal space of reflection replicas that appear in consecutive patterns. The total intensity is calculated as the integration of the recorded replicas on consecutive patterns over the excitation error which automatically considers and corrects the oversampling of reflections that are close to the rotation axis with respect to those that are far apart (Lorentz correction). We tried to process the same data collections also by the program XDS and obtained very similar results. The visualization of the reconstructed 3D reciprocal volume has been performed with the software ADT3D (Kolb et al., 2011[Kolb, U., Mugnaioli, E. & Gorelik, T. E. (2011). Cryst. Res. Technol. 46, 542-554.]) and one reconstruction of the continuous data collection can be seen in Fig. 5[link]. All the intensity data sets were analyzed with the direct methods program SIR2014 (Burla et al., 2015[Burla, M. C., Caliandro, R., Carrozzini, B., Cascarano, G. L., Cuocci, C., Giacovazzo, C., Mallamo, M., Mazzone, A. & Polidori, G. (2015). J. Appl. Cryst. 48, 306-309.]) with a standard run for structure solution. The obtained structural models were refined with Jana2006 (Petříček et al., 2014[Petříček, V., Dušek, M. & Palatinus, L. (2014). Z. Kristallogr. 229, 345-352.]) using a kinematical approximation. As reference structure of natrolite we used the structure published by Capitelli & Derebe (2007[Capitelli, F. & Derebe, M. G. (2007). J. Chem. Crystallogr. 37, 583-586.]). The comparison among the structural models refined with Jana2006 is reported in Table 2[link].

Table 2
Comparison between the reference structure of natrolite (Capitelli & Derebe, 2007[Capitelli, F. & Derebe, M. G. (2007). J. Chem. Crystallogr. 37, 583-586.]) and the structural models obtained ab initio from the different 3D ED data collections

For each atom the shift (in Å) from the reference position is reported. dmax and dav are the maximum and the average shift of structural model. The measure of similarity (Δ) (Bergerhoff et al., 1999[Bergerhoff, G., Berndt, M., Brandenburg, K. & Degen, T. (1999). Acta Cryst. B55, 147-156.]) is a function of the differences in atomic positions (weighted by the multiplicities of the sites) and the ratios of the corresponding lattice parameters of the structures. The comparison of structural models was performed with the COMPSTRU program of the Bilbao Crystallographic server (de la Flor et al., 2016[Flor, G. de la, Orobengoa, D., Tasci, E., Perez-Mato, J. M. & Aroyo, M. I. (2016). J. Appl. Cryst. 49, 653-664.]). Rint is the internal R factor of the intensity data sets calculated on symmetry equivalent intensities. RSIR is the agreement factor given by the SIR2014 program after ab initio structure solution. R1obs and R1all are the agreement factors calculated by Jana2006 on the observed and on all the reflections respectively.

  Continuous RED-like ADT cPEDT PEDT-like
Si1 0.094 0.052 0.025 0.062 0.081
Si2 0.072 0.067 0.038 0.049 0.070
Al1 0.128 0.062 0.075 0.051 0.056
Na1 0.048 0.039 0.060 0.039 0.043
O1 0.077 0.075 0.179 0.023 0.043
O2 0.107 0.086 0.076 0.114 0.129
O3 0.177 0.046 0.136 0.066 0.094
O4 0.074 0.059 0.111 0.043 0.087
O5 0.117 0.054 0.086 0.045 0.066
O6 0.145 0.089 0.158 0.088 0.105
           
dmax (Å) 0.177 0.089 0.179 0.114 0.129
dav (Å) 0.104 0.063 0.098 0.058 0.077
Δ 0.014 0.009 0.012 0.008 0.010
           
Rint (%) 37 31 64 25 26
RSIR (%) 28.4 26.4 38.6 20.9 21.8
R1obs (Jana) (%) 32.2 26.8 39.4 21.1 21.2
R1all (Jana) (%) 41.9 32.6 46.9 27.3 29.0
[Figure 5]
Figure 5
Reciprocal space reconstruction obtained with the software ADT3D (Kolb et al., 2011[Kolb, U., Mugnaioli, E. & Gorelik, T. E. (2011). Cryst. Res. Technol. 46, 542-554.]) for the continuous data collection on natrolite. The projections along the three main reciprocal directions are displayed together with a projection along the rotation axis direction to outline the covered angular range (top right). A 6 × 6 reciprocal unit cells grid is drawn on three views to show F centering of the lattice.

Interestingly the structure has been solved and refined with all data sets. The most accurate structure were obtained by RED, PEDT and cPEDT. In terms of agreement factors the lowest is obtained with PEDT and cPEDT, which apparently provide the best sampling of the intensities. The very high similarity of all quality parameters for the models obtained with PEDT and cPEDT suggests that the integration of reciprocal space by beam precession is generally enough, as no additional benefit seems to be provided by the concomitant integration of reciprocal space along the scan direction.

The fast data collection and the ADT-like (without precession) give similar accuracies. However ADT has much higher agreement factors with an Rint higher than 60% which indicates problems in correctly estimating the reflection intensities as expected by the excitation error problem. With such a high internal R value a high percentage of failure in the structure solution is expected, especially if there are numerous atoms in the asymmetric unit. However, our results demonstrate that it is still worth trying even if experimental limitations are present (e.g. instabilities of the goniometer, the absence of the hardware or software control needed for beam precession or RED).

The intermediate quality of the solution obtained with our example of continuous data collection is probably a consequence of the coarse angular step we chose, which can cause noisier data.

Nevertheless it is highly remarkable that with a data collection obtained in only 27 s, we get a solution with an acceptable accuracy and an agreement factor around 30%. Reliable structure solution data in a few seconds means small total doses and accessibility to structural problems that normally are considered out of reach for ED because the crystals are too beam sensitive [see Yuan et al. (2018[Yuan, S., Qin, J. S., Xu, H. Q., Su, J., Rossi, D., Chen, Y., Zhang, L., Lollar, C., Wang, Q., Jang, H., Son, D. H., Xu, H., Huang, Z., Zou, X. & Zhou, H. C. (2018). ACS Cent. Sci. 4, 105-111.]) for an example of a fast low-dose data collection].

In order to have an estimate of the total dose in equivalent experiments performed in low-illumination condition, the reader has to consider that with a detector such as ASI Timepix, we can measure an acceptable diffraction signal with doses of the order of 0.01 el s−1 Å−2 (Lanza et al., 2019[Lanza, A., Margheritis, E., Mugnaioli, E., Cappello, V., Garau, G. & Gemmi, M. (2019). IUCrJ, 6, 178-188.]). Therefore the total dose, in the case of minimum illumination, in our experimental configurations varies between 0.5 el Å−2 for the fastest, up to 10 el Å−2 for RED-like and cPEDT, which are values one order of magnitude lower than single particle cryo-EM optimal doses (Cheng et al., 2015[Cheng, Y., Grigorieff, N., Penczek, P. A. & Walz, T. (2015). Cell, 161, 438-449.]). It is obvious, however, that reducing the dose and speeding up the data collection means having weaker reflections that are sampled for less time, therefore their intensity estimation can become critical posing a intrinsic limit to the method.

6. Conclusions

All methods described above demonstrate how 3D ED is at an advanced stage of development and must be considered as the key structure solution technique for micro- or nanocrystalline samples. Although it can be easily implemented in any microscope, it still suffers from the absence of TEM specifically designed for ED. The key points that require specific improvements are the stability of the goniometer, the flexibility in the illumination conditions and specific low-dose procedures for sample searching.

The goniometer should be designed to minimize the sample movement below a few hundred nm in a rotation range of more than 100°, and its rotation speed should be synchronized with the detector exposure to implement any desired data collection type.

The illumination system should allow parallel nanobeams of variable size in a range from ten nanometres to a few hundred nanometres with the possibility of reducing the intensity of the beam to doses smaller than 0.01 el s−1 Å−2.

The inspection of the sample for seeking a suitable crystal should be carried out in STEM mode. However, the sensitivity of STEM detectors should be improved in order to perform imaging with weak beams, with the final goal of making the dose received by the sample during crystal search negligible. A microscope with these characteristics equipped with a single electron detector could be employed as an electron diffractometer on a wide spectrum of samples from inorganic to macromolecules.

Waiting for such a machine, the degree of development reached by 3D ED opens a new chapter in crystallography: crystallography at the nanometre scale. Before 3D ED any crystallographic information with a complete reciprocal space coverage and high structural details was coming from techniques with a probe resolution in the micron size range. With 3D ED for the first time we can have this information two order of magnitudes lower and on very different type of samples. We expect a great impact on all the fields where the crystallization is an issue. If even grains that are invisible at the optical microscope can be analyzed as single crystals with 3D ED, crystallization efforts will become less demanding. Pharmaceutical chemistry, macromolecular chemistry but also materials chemistry will all greatly benefit from the option of such a nanocrystallography technique. Kinetics studies will also change in view of the possibility to follow the nucleation and growth of a crystal at the nanometre scale with the structural details given by 3D ED. All the structural problems that lay unsolved because the ordered domains are nanometric and are hidden in a disordered or multi-twinned matrix can be eventually unveiled. Finally, the advent of very sensitive detectors will bring electron diffraction into new fields where the weakness of bonds has so far prevented this technique to go beyond qualitative and low-resolution observations. We see organic chemistry as the most promising of these fields.

Supporting information


Funding information

The following funding is acknowledged: Regione Toscana (grant No. Por CREO FESR 2014–2020).

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