Method for determining crystal structure and apparatus for carrying it out

Abstract

The present invention relates to a method for determining the crystal structure of a crystal (4) capable of electron diffraction, comprising the steps of acquiring a three-dimensional electron diffraction pattern and processing the data derived from the electron diffraction pattern. The essence of the invention is that the determination method consists in generating a virtual diffraction frame comprising a list of integrated scattered electron intensities. The dynamic diffraction theory is then used in the data processing step. In another embodiment, the invention provides a device capable of carrying out the method.

Description

Cross - reference to related applications

[0001] This application claims the benefit of priority of Czech Patent Application No. CZ2021 - 403, filed on September 1, 2021, and US Patent Application No. 17 / 565,624, filed on December 30, 2021, both of which are applications by the Fyzikalni ustav AV CR, v.v.i., a public research institution located in Prague, the Czech Republic.

Technical Field

[0002] The present invention relates to an invention implemented by a computer. More specifically, the present invention relates to the processing of rotational electron diffraction data of crystalline substances. In one embodiment, the present invention relates to a method for refining a crystal structure from rotational electron diffraction using dynamic refinement of data, which enables accurate determination of the atomic structure.

Background Art

[0003] Structure analysis is a method for obtaining information about the spatial arrangement of atoms in a crystal structure. The analysis includes several steps such as preparation of the crystal, acquisition of data, discovery of an initial structure model, and optimization of the structure model.

[0004] The structure model is optimized by a mathematical procedure called the least - squares method. In this procedure, experimental diffraction data is measured on the crystal and compared with theoretical diffraction data calculated based on the actual structure model. By adjusting the structure model, the difference between the experimental data and the theoretical data is minimized. For this procedure to succeed, the calculation of the theoretical data from the structure model must be accurate.

[0005] When electrons are used in the data acquisition step, it is known as an electron diffraction experiment. In this case, the calculation of the theoretical diffraction intensity is a complex method. The reason is the existence of the so - called "dynamic diffraction effect".

[0006] A method for calculating accurate theoretical diffraction data from electron diffraction, so-called refinement, is designed for a special case of precession electron diffraction data. There is still no method comparable to general electron diffraction data. SUMMARY OF THE INVENTION PROBLEMS TO BE SOLVED BY THE INVENTION

[0007] An object of the present invention is to provide a method for refining a crystal structure in view of the above-mentioned drawbacks, and since each step is executed by a computer, the method is suitable for obtaining good structure optimization not only for special cases of precession electron diffraction but also using general electron diffraction data.

[0008] A further object of the present invention is to provide a computer-implemented method capable of determining the electrostatic potential distribution and crystal structure of a wide range of compounds and crystal forms using a wide range of crystallographic calculations. MEANS FOR SOLVING THE PROBLEM

[0009] In a first aspect of the present invention, a method for determining a crystal structure model is provided. The method preferably includes, but is not limited to, organic crystals. The determination of the crystal structure can be carried out on inorganic crystals such as metal-containing compounds, such as hydrated cobalt and aluminum phosphate, or minerals such as quartz and natrolite, and organic crystals such as amino acids, hydrocarbons, and their derivatives, and many drugs such as abiraterone acetate. However, particular advantages are obtained with respect to the determination of protein structures and the crystal structures of antibodies, genes, and drug delivery samples.

[0010] The method is obtaining electron diffraction data from a crystal by three-dimensional electron diffraction, the data including information about the crystal diffraction pattern, each diffraction pattern including information about the scattered electron intensity and crystal orientation in each direction with respect to the incident electron beam during data acquisition, and the crystal rotating or tilting during the recording of the diffraction data. processing data that determines the crystal lattice parameters, the crystal orientation at the time of obtaining the diffraction pattern, the indices of each reflection, and the scattered electron intensity of each reflection on each diffraction pattern, thereby generating processed data; generating a virtual diffraction frame by a computer program, each virtual diffraction frame including a list of integrated scattered electron intensities in each direction, which is the sum of contributions from all experimental patterns forming one virtual frame, and the virtual diffraction frame being computationally formed from the provided three-dimensional electron diffraction data;

[0011] providing an approximate crystal structure model, and refining the approximate crystal structure model using dynamic diffraction theory wherein the refining step includes calculating the modeled intensity of scattered electrons using dynamic diffraction theory based on the approximate crystal structure model, and minimizing the difference between the experimentally determined scattered electron intensity and the modeled intensity, wherein the refined crystal structure model is the model having the minimum deviation including.

[0012] The method according to the present invention can determine the absolute structure of a non-centrosymmetric crystal that can be obtained by a crystal structure, preferably by dynamic refinement. Compared with the kinematic approximation, the method according to the present invention does not ignore the dynamic diffraction effect in the diffraction data, and thus it is possible to obtain more accurate information about the crystal structure. The combination of steps according to the method of the present invention is adapted to generate a so-called virtual diffraction frame, where the theoretical data corresponding to the experimental data within the virtual diffraction frame can be calculated more easily from the crystal structure model compared to the prior art methods where the virtual diffraction frame is not generated. As a result, a structure model can be obtained with an accuracy far superior to the procedures currently used for non-precession electron diffraction data, with an accuracy similar to that of the model established by precession electron diffraction. The advantages of the method using non-precession motion data compared to precession motion data are that it can be more easily utilized without the need for special equipment for the precession motion method, faster data processing, and a lower overall illumination of the electron crystal during data acquisition, which is advantageous especially for the analysis of organic materials sensitive to electron irradiation. Such an optimized structure model provides better insight into the crystal structure and also provides important information such as the absolute structure of crystals containing chiral molecules or the positions of light atoms, which are difficult to detect but are often important for the function and application of the material.

[0013] In a preferred embodiment, a method for determining the absolute structure of a non-centrosymmetric crystal is provided. The method comprises generating a model of the absolute structure opposite to the current approximate crystal structure model, thereby generating an inversion model, refining the approximate crystal structure model using dynamic diffraction theory for the inversion model, and comparing quality indicators of the inversion model, wherein the correct structure is the one with the minimum deviation between the experimental data and the data calculated based on the refined structure model comprising.

[0014] Another solution to the technical problem of obtaining a crystal structure is provided in a second aspect of the present invention. An alternative method for solving the same technical problem of determining the absolute structure of a non-centrosymmetric crystal capable of electron diffraction is disclosed herein. The method comprises obtaining electron diffraction data from a crystal by three-dimensional electron diffraction, wherein the data includes information regarding the crystal diffraction pattern, each diffraction pattern includes information regarding the scattered electron intensity in each direction with respect to the incident electron beam during data acquisition and the crystal orientation, and the crystal is rotating or tilting during data acquisition, and processing data for determining crystal lattice parameters, the crystal orientation at the time of acquisition of the diffraction pattern, the indices of each reflection, and the scattered electron intensity of each reflection on each diffraction pattern, thereby generating processed data, generating a virtual diffraction frame by a computer program, each virtual diffraction frame including a list of integrated scattered electron intensities in each direction, which is the sum of contributions from all experimental patterns forming one virtual frame, and the virtual diffraction frame being computationally formed from the provided three-dimensional electron diffraction data, providing an approximate crystal structure model; calculating a quality index of the approximate crystal structure model using the dynamic diffraction theory and calculating the model intensity, generating a model of the absolute structure opposite to the current approximate crystal structure model, thereby generating an inversion model; calculating a quality index of the inverted crystal structure model using the dynamic diffraction theory and calculating the model intensity, and comparing the quality indices of the inversion model and the non-inversion model, wherein the correct structure is the structure with the minimum deviation between the experimental data and the data calculated based on the refined structure model, is included.

[0015] Stepwise or continuous rotation means that the sample rotates around the axis of rotation within a certain preselected range, for example, stepwise from -50° to 50°, for example 1°, or continuously. The diffraction pattern is exposed either in "step" mode after each rotation or in continuous mode during crystal rotation. See, for example, Gemmi M, Mugnaioli E, Gorelik TE, Kolb U, Palatinus L, Boullay P, et al. 3D Electron Diffraction: The Nanocrystallography Revolution. ACS Cent Sci. 2019 Aug 28; 5 (8): 1315-29.

[0016] The diffraction pattern is a record of the direction and intensity of electrons scattered by the crystal and is usually obtained by an electronic device, i.e., an electron detector arranged such that the crystal is positioned between the electron source and the detector. The acquisition of the diffraction takes the form of an image, i.e., a two-dimensional record, and contains information about the intensity of the reflections. A typical example of diffraction acquisition is shown in Figure 1.

[0017] One skilled in the art understands a reflection as the location where the diffracted beam strikes the detector. See, for example, the text of Vaclav Valvoda, Milena Polcarova, Pavel Lukac, Zaklady strukturni analyzy, Karolinum, Prague, 1992, ISBN 80-200-0280-4.

[0018] An approximate crystal structure model is understood to be a list of atoms that includes the determination of the approximate positions and atom types within the unit cell of a crystal. This model can be obtained from the literature if it has already been published, or it can be obtained directly from diffraction data by established structure analysis methods. For example, see the text of Giacovazzo, C. (editor), Fundamentals of Crystallography, Third Edition, Oxford University Press, 2011, ISBN 9780199573653. In another embodiment, one of ordinary skill in the art can provide a pre-analysis of the data obtained from the experimental diffraction pattern and provide an estimate based on knowledge of the approximate crystal structure model.

[0019] The necessary information obtained from the diffraction data is a list of the parameters of the unit cell of the crystal, also known as the crystal lattice parameters, and the scattered electron intensities measured during the experiment and the standard deviations of all reflections. The reflections are characterized by three (or more in exceptional cases) integer indices that determine the positions within the reciprocal crystal lattice. For example, see the text of Vaclav Valvoda, Milena Polcarova, Pavel Lukac, Zaklady strukturni analyzy, Karolinum, Prague, 1992, ISBN 80-200-0280-4.

[0020] The refinement quality indicators are numerical values that estimate how good and reliable the refined structure model is. It may be advantageous for this quality indicator that the R factors R1, R2, and wR2 are defined as follows:

[0021]

Equation

[0022] Here, TIFF0007716579000002.tif6114

[0023] respectively TIFF0007716579000003.tif6114

[0024] are observed, and these are, respectively, the calculated intensities of specific diffracted electron beams characterized by diffraction vector g, where TIFF0007716579000004.tif6114

[0025] and TIFF0007716579000005.tif5114

[0026] are the following determined values: TIFF0007716579000006.tif6114

[0027] is the standard deviation of. The specific choice of quality indicator used is application-dependent and can be made by the user of the present invention based on expertise.

[0028] The present invention is particularly suitable for determining the absolute structure of crystals containing light atoms such as hydrogen, lithium, beryllium, or boron.

[0029] A further advantage of the present invention is that accurate atomic positions within the structure can be achieved with an average error of less than 0.005 nm.

[0030] Three-dimensional electron diffraction is a method of obtaining data, particularly the intensity of electrons scattered on a crystal under study, by rotating an electron beam and a crystal relative to each other. The rotation can be reliably performed by rotating the electron beam using the magnetic coils of a transmission electron microscope, or by rotating the crystal using a goniometer, or by combining both methods. In some embodiments, the rotation can be tilted.

[0031] In a preferred embodiment of the rotational diffraction data acquisition method, the electron scattering intensity is recorded in a series of continuous images, and after each diffraction pattern is acquired, the crystal is rotated by a certain angle about the axis of the goniometer. The magnitude of the rotation is usually between 0.1° and 1°. The total tilt of the crystal can typically range from ±60°, but in some embodiments it can be even larger.

[0032] In a preferred embodiment, the step of acquiring rotational electron diffraction data is a combination of the rotation of the electron beam and the tilt of the crystal, and several diffraction patterns for different tilts of the electron beam are recorded for each tilt of the crystal. Thus, the preferred embodiment has the advantage that the mutual orientation of the crystal and the beam is more accurate due to the fact that, in some cases, the tilt of the electron beam can be controlled with higher precision than the tilt of the goniometer.

[0033] In another preferred embodiment, the continuous tilt of the crystal is combined with the acquisition of continuous diffraction data. The crystal goniometer rotates continuously around the tilt axis during electron diffraction imaging. Each image of the rotational electron diffraction covers an angular range determined by the rotation speed of the goniometer and the exposure time. Different from sequential rotation, in continuous rotation, the integrated electron diffraction intensity is recorded. This preferred embodiment using the continuous tilt of the crystal provides the advantage of a simpler experimental plan, minimizing the electron irradiation of the crystal and acquiring the integrated intensity.

[0034] All of the above data acquisition methods by the rotational electron diffraction method are described in detail in M. Gemmi and A. Lanza: 3D electron diffraction techniques, Acta Crystallographica B, Vol. 75, pp. 495 - 504, year of publication 2019.

[0035] Data processing includes - the step of finding the maximum value of all diffraction patterns and determining the coordinates in reciprocal space, - Determining the parameters of the crystal lattice to determine the orientation of the crystal in space, i.e., determining the so-called orientation matrix; - Determining the diffraction intensity of all potentially excited reciprocal lattice points on all diffraction patterns; including.

[0036] The so-called virtual diffraction frame is generated as follows: · An appropriate number of consecutive experimental diffraction patterns are selected and combined into one virtual frame. The appropriate number is such that the total angular range covered by the virtual diffraction frame is preferably about 1° to 3°.

[0037] · It is found that all points of the reciprocal lattice are within the angular range covered by the virtual diffraction frame.

[0038] · For each point found, the diffraction intensities belonging to that point on all experimental diffraction patterns are summed.

[0039] · The list of acquired intensities belonging to the points of the reciprocal lattice forms a data set called the virtual diffraction frame.

[0040] · The orientation of the virtual diffraction frame is determined as the average of the orientations of all the experimental diffraction patterns that make it up.

[0041] · The angular difference between subsequent virtual diffraction frames is preferably selected such that the volumes of reciprocal space covered by adjacent virtual diffraction frames partially overlap.

[0042] In a preferred embodiment, the data processing also includes refinement of the diffraction geometry, i.e., refinement of the orientation of the crystal with respect to the incident electron beam.

[0043] Refinement is a general term used in the description of all operations necessary to develop a test model into a model that best fits the observed data, particularly the intensity of electrons scattered by a crystal. Refinement can be regarded as a series of mathematical procedures executed by a computer. The refinement of crystal structure determination according to the present invention utilizes the dynamic diffraction theory considering the multiple scattering of electrons by atoms within the crystal.

[0044] The step of determining the quality of the refined crystal structure model is preferably to determine the deviation between the observed quantity and the quantity simulated according to the crystal structure model using the parameter R. Even if the deviation is sufficiently small, the crystal structure model is considered accurate.

[0045] In another embodiment of the present invention, an apparatus suitable for determining the crystal structure model according to the present invention is described.

[0046] The apparatus comprises an electron source capable of emitting an electron beam, a crystal holder adapted to perform a rotational movement or a tiling movement together with the crystal, a detector for detecting electrons scattered from the crystal and the detector is connected to a data storage and processing unit wherein the processing unit is adapted to determine the crystal lattice parameters, the crystal orientation at the acquisition of the diffraction pattern, the indices of each reflection, and the scattered electron intensity of each reflection on each diffraction pattern, thereby generating the processed data, and generating a virtual diffraction frame by a computer program, each virtual diffraction frame including a list of integrated scattered electron intensities in each direction obtained by summing the contributions from all experimental patterns forming one virtual frame, and the virtual diffraction frame being formed by calculation from the provided three-dimensional electron diffraction data, The data storage is configured to provide an approximate crystal structure model, or the processing unit is adapted to perform an analysis of processing data leading to the acquisition of the approximate structure model, The processing unit is adapted to refine the structure model.

[0047] In a preferred embodiment, the processing unit is adapted to refine the approximate crystal structure model using the dynamical diffraction theory, where the processing unit, during the refinement, calculates the modeled intensity of scattered electrons using the dynamical diffraction theory based on the approximate crystal structure model, and minimizes the difference between the experimentally determined scattered electron intensity and the modeled intensity such that the refined crystal structure model is the model with the minimum deviation.

[0048] In another preferred embodiment, the processing unit is configured to determine the absolute structure of a non-centrosymmetric crystal, where the processing unit generates a model of the absolute structure opposite to the current approximate crystal structure model, thereby generating an inversion model, refines the inverted crystal structure model using the dynamical diffraction theory, and compares the quality indicators of the inversion model and the non-inversion model such that the correct structure is the structure with the minimum deviation between the experimental data and the data calculated based on the refined structure model.

[0049] In another preferred embodiment, the processing unit is adapted to refine the approximate crystal structure model, and the apparatus calculates the quality indicator of the approximate crystal structure model, and compares the quality indicators such that the correct crystal structure is considered to be the modeled crystal structure with the minimum deviation between the experimental data and the data calculated based on the refined structure model.

[0050] In another preferred embodiment, the processing unit is adapted to generate a virtual model of a crystal structure opposite to the structure of the current approximate crystal structure model, thereby generating an inversion model; the step of comparing quality indicators is the step of comparing the quality indicators of the inversion model and the experimental data, and the correct structure is the structure with the smallest deviation between them.

[0051] Preferably, the detector is set to collect data simultaneously with the rotation of the crystal.

[0052] In another preferred embodiment, the detector is set to collect data step by step during the rotation of the crystal.

Brief Description of the Drawings

[0053]

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Mode for Carrying Out the Invention

[0054] An embodiment corresponding to an apparatus for carrying out the method according to the present invention will be described with reference to FIG. 3.

[0055] FIG. 3 schematically shows a part of a transmission electron microscope further connected to a data storage and processing unit 8 using the determination or refinement method according to the present invention. FIG. 3 further shows a transmission electron microscope equipped with an electron source 1 which may be an electron gun, for example. The electron source 1 generates a primary electron beam 2. The electron beam 2 passes through a system of lenses 3 that focuses the primary electron beam 2 into a focused electron beam 4, and the focused electron beam 4 is directed onto a crystal 5 capable of electron diffraction. The inclination of the electron source 1 of the primary electrons 2, the lens 3, and preferably the crystal 5 can also be controlled by a control system. The scattered electrons 6 are detected by a detector 7, and this detector 7 is further connected to the data storage and processing unit 8. The data storage and processing unit 8 further comprises a database and a computer program that processes data so as to determine and / or refine the crystal structure of the measurement crystal 5 by the method according to the present invention.

[0056] In parallel with or subsequent to the measurement step, the calculation unit 8 can generate an initial inaccurate model of the crystal structure by analyzing the obtained data. In another embodiment, the computer programs and databases within unit 8 may include information regarding the structural model of crystal 5 estimated from other information sources such as X-ray diffraction. More specifically, the database may further include information regarding the crystal structure of crystal 5 determined by X-ray diffraction and / or theoretically predicted models. The structural models of crystal structure 5 obtained by these methods may be incomplete and / or inaccurate, and thus the technical problem is to refine this initially inaccurate structural model of crystal structure 5. The refined structural model of crystal 5 can be used to understand the physical, chemical, and pharmaceutical properties of the material, and thus is always used when knowledge of the properties of the material is useful or necessary. The use of rotational electron diffraction offers advantages over precession electron diffraction, especially when the experimental setup is simple, the experimental equipment is inexpensive, and the process of the experiment itself is simple. Thanks to the speed of data acquisition and the efficient use of the electron dose, rotational electron diffraction is also suitable for the study of materials that are very sensitive to electron irradiation. The dynamic diffraction theory is used to refine the crystal structure of crystal 5. In one embodiment, using the Bloch wave method for calculating diffraction intensities, the structural estimation using the dynamic diffraction theory can be refined. This method is described, for example, in the text of JCH Spence and JM Zuo, Electron microdiffraction, Plenum press, 21992, p.35.

[0057] In this way, the intensity of the scattered electrons 6 is determined according to a given model of the crystal structure of the crystal 5. Alternatively, the diffraction intensity using the dynamic diffraction theory can also be calculated using the multi-slice method that gives results equivalent to the Bloch wave method. The multi-slice method is described in more detail, for example, in the text of DB Williams and CB Carter, Transmission Electron Microscopy, 2nd Edition, Springer, 2009, p. 533.

[0058] Next, the calculated intensity values are compared with the measurement data, particularly the intensity of the scattered electrons 6.

[0059] The intensity calculated in the rotation data acquisition in a particular embodiment TIFF0007716579000007.tif5114

[0060] can be obtained by integrating all the calculated intensities in all possible orientations of the crystal 5 into a single virtual diffraction frame. The integration can be carried out numerically as the sum of the intensities calculated for a finite number of crystal orientations 5.

[0061] The refinement of the structure mainly consists of determining the structural parameters such as the positions of the atoms, the types of the atoms, and their scattering parameters. These parameters are changed to minimize the difference between the calculated intensity and the experimental intensity. The calculation may also include the parameters related to the crystal and its orientation, that is, the thickness of the crystal 5 and the mutual orientation between the primary electron beam 4 and the crystal 5. The calculation is also affected by the parameters that affect the calculation of the TIFF0007716579000008.tif6114

[0062] model intensity.

[0063] The crystal structure model of crystal 5 can be refined using the least squares method. In one embodiment, a standard Gauss-Newton algorithm can be used. This approach is sufficient for small residual problems where the starting point is close to the solution, i.e., the model is nearly accurate.

[0064] The step of determining the quality of the refined model includes verifying the correspondence between the refined model of the crystal structure and the observed quantities using a refinement quality metric. In one embodiment, the verification of the crystal structure model can be evaluated using one and / or the entire set of refinement quality metrics. The following equations apply to these metrics:

[0065]

Number

[0066] where TIFF0007716579000010.tif6114

[0067] respectively, TIFF0007716579000011.tif6114

[0068] are observed, and these are the calculated intensities of a specific diffracted electron beam 5 characterized by a diffraction vector g, respectively, TIFF0007716579000012.tif6114

[0069] and TIFF0007716579000013.tif6114

[0070] is the following decision value: TIFF0007716579000014.tif5114

[0071] is the standard deviation of.

[0072] When the coefficient wR2 reaches the minimum value, the crystal structure is considered to be refined. The R factor is also sensitive when determining the correct absolute crystal structure. By comparing the R factors of the two deformed structures of the absolute structure and selecting the deformed structure with the smaller R value, it becomes possible to clearly determine which of the two deformed structures is correct. Thereby, it becomes possible to determine the absolute structure of the crystal and, thus, the absolute configuration of the molecules contained in the crystal.

[0073] Therefore, the present embodiment provides a method for determining or refining the crystal structure of a crystal typically with an accuracy better than 0.05 Å.

[0074] The method according to the present invention will be described in detail in the mode of operation of the present invention considered to be the best mode. Those skilled in the art will further understand that the general method shown in FIG. 4 is useful.

[0075] Operation of the Invention Experimental Results The present invention has been tested on many materials, two of which (the inorganic crystal of sodium silicate (mineral natrolite) and the organic crystal of abiraterone acetate) are listed here.

[0076] Natrolite Natrolite is a mineral having a chemical composition of Na2(Al2Si3O 10 )(H2O)2. Its structure has a space group Fdd2, which means that it is reasonable to determine the absolute structure for this material.

[0077] A sample of natural natrolite from Mariánské Lázně, Ústí nad Labem, Czech Republic was ground into fine powder in an agate mortar. The powder was applied to a copper grid coated with a carbon film. This grid was placed in a sample holder for a transmission electron microscope and arranged in an FEI Tecnai G2 20 microscope with an acceleration voltage of 200 kV equipped with a LaB6 electron source and an SIS Veleta CCD detector.

[0078] The acquisition of electron diffraction data from crystals by three-dimensional electron diffraction was performed as follows: Several crystals were tested, and appropriate measurement candidates were selected by visually inspecting their diffraction patterns. The crystal goniometer was rotated to a position of -50°. The crystal was rotated by 0.6° at an angular velocity of 0.3° per second, and the diffraction pattern was recorded by the detector throughout the rotation. The obtained experimental diffraction patterns were saved on the hard disk of a computer. This diffraction pattern procedure was repeated with a further rotation of 0.6°. The total rotation of the crystal was 99.6°, and thus a total of 166 experimental diffraction patterns were obtained.

[0079] The obtained data were further processed with the computer program PETS2 (<http: / / pets.fzu.cz>). The data processing included the following steps: (For details, see, for example, Palatinus, L., Brazda, P., Jelinek, M., Hrda, J., Steciuk, G. & Klementova, M. (2019) Specifics of the data processing of precession electron diffraction tomography data and their implementation in the PETS2.0 program, Acta Cryst.B75, 512-522): - Finding the maximum value of all diffraction patterns and determining the coordinates in reciprocal space (see Figure 1); - Determining the orientation matrix, i.e., finding the parameters of the crystal lattice and determining the orientation of the crystal in space. The determined lattice parameters were a = 18.273 Å, b = 18.646 Å, c = 6.617 Å, α = 90°, β = 90°, γ = 90°; - Determining the diffraction intensities of all potentially excited reciprocal lattice points on all experimental diffraction patterns (see Figure 1); - Generating a virtual diffraction frame, whereby: ·One virtual frame covers an angular range of 1.2°, and thus was generated by combining two experimental diffraction patterns (see Fig. 2); ·All points of the reciprocal lattice within the angular range covered by the virtual diffraction frame were found.

[0080] ·For each found point of the reciprocal lattice, all diffraction intensities belonging to this point were summed over all experimental diffraction patterns.

[0081] ·The list of intensities thus obtained, belonging to the points of the reciprocal lattice, forms a data set called the virtual diffraction frame.

[0082] ·The orientation of the virtual diffraction frame was determined as the average of the orientations of the two experimental diffraction patterns that compose it.

[0083] ·Each subsequent virtual diffraction frame was shifted by one experimental diffraction pattern compared to the previous one. Thus, the angular overlap of two consecutive virtual diffraction frames was 0.6°.

[0084] ·The result of the whole procedure was a list of 48847 reflections on 165 virtual diffraction frames.

[0085] The output from the PETS program in the form of a list of reflections including refractive index, intensity, and standard deviation was further processed with the Jana2006 program (<http: / / jana.fzu.cz>) to find and refine the crystal structure model. This method includes the following steps: - Finding an approximate structure model containing a list of atoms in the structure and their approximate positions - Using the dynamical diffraction theory to calculate the theoretical diffraction intensities required for refinement while refining the structure model by the least-squares method. As a result of the refinement, the residual factors R1 = 0.0947 and wR2 = 0.0968 were obtained.

[0086] - Steps for determining the correct absolute structure, including the following steps: · Generating an inversion structure model, i.e., a model in which the coordinates of all atoms in the structure are replaced with coordinates having the same absolute value but opposite signs. · Refining the structure model in the same way as the refinement of the previous model.

[0087] · As a result of the refinement of the inversion model, residual factors R1 = 0.1559 and wR2 = 0.1663 were obtained. Since these values are more than 0.01 greater than the values of the non-inversion model, it is clearly determined by this procedure that the original non-inversion model corresponds to the correct absolute structure.

[0088] The obtained refined structure model was compared with the known reference structure of natrolite determined by X-ray single crystal diffraction. The average difference in interatomic distances was 0.0125 Å.

[0089] Abiraterone acetate Abiraterone acetate is an organic substance with medicinal efficacy. Its chemical formula is C 26 H 33 NO2. The molecule of abiraterone acetate is shown in Figure 7. This molecule is chiral and crystallizes in the P212121 space group, which means that it is reasonable to determine the absolute structure of this substance.

[0090] The white powder of abiraterone acetate was dissolved in distilled water. After 1 minute, 1 drop of the solution was dropped onto a carbon-coated copper grid. This grid was placed in a sample holder for a transmission electron microscope equipped with a cooling function, and arranged in an FEI Tecnai G2 20 microscope with an acceleration voltage of 200 kV, equipped with a LaB6 electron source and an SIS Veleta CCD detector. The sample was cooled to 100 K.

[0091] Data was acquired as follows: Crystals were tested, and suitable crystals for measurement were selected by visually inspecting their diffraction patterns. A total of five crystals were selected for measurement and further processing. For the first crystal, the goniometer containing the crystal was rotated to a position of -28.3°. Next, the crystal was rotated by 0.4° at an angular velocity of 0.465° per second, and its diffraction pattern was recorded by the detector throughout the rotation. The obtained experimental diffraction patterns were saved on the computer's hard disk. This diffraction pattern procedure was repeated with a further rotation of 0.4°. The total rotation of the crystal was 80°, and thus, a total of 200 experimental diffraction patterns were obtained.

[0092] The same procedure was repeated for the other four crystals. The rotation speed and the rotation angle range in one experiment remained the same. The total rotation ranges were 87.2°, 78.4°, 50.4°, and 54.0° for crystals 2, 3, 4, and 5, respectively.

[0093] The data obtained individually from each crystal were further processed with the computer program PETS2 (<http: / / pets.fzu.cz>). The data processing included the following steps (for details, see, for example, Palatinus, L., Brazda, P., Jelinek, M., Hrda, J., Steciuk, G. & Klementova, M. (2019) Specifics of the data processing of precession electron diffraction tomography data and their implementation in the PETS2.0 program, Acta Cryst.B75, 512 - 522): - Finding the maximum values of all diffraction patterns and determining the coordinates in reciprocal space (see Figure 1); - Determining the orientation matrix, i.e., finding the parameters of the crystal lattice and determining the orientation of the crystal in space. The determined lattice parameters were a = 7.470 Å, b = 9.689 Å, c = 30.20 Å, α = 89.96°, β = 89.98°, γ = 89.99°. - Determining the diffraction intensity of all potentially excited reciprocal lattice points on all experimental diffraction patterns (see Figure 1); - Generating a virtual diffraction frame, whereby: · One virtual frame covers an angular range of 2°, and thus was generated by a combination of five experimental diffraction patterns (see Figure 2); · All points of the reciprocal lattice within the angular range covered by the virtual diffraction frame were found.

[0094] · For each found reciprocal lattice point, the diffraction intensities belonging to this point were summed over all experimental diffraction patterns.

[0095] · The list of intensities thus obtained, belonging to the points of the reciprocal lattice, forms a data set called the virtual diffraction frame.

[0096] · The orientation of the virtual diffraction frame was determined as the average of all orientations of the five experimental diffraction patterns that make it up.

[0097] · Each subsequent virtual diffraction frame was shifted from the previous virtual diffraction frame by two experimental diffraction patterns for crystals 1, 2, 3 and by three experimental diffraction patterns for crystals 4 and 5. Thus, the angular overlap of two consecutive diffraction patterns was 1.2° and 0.8°, respectively.

[0098] · The result of the whole procedure was a list of 10957 reflections on 285 virtual diffraction frames.

[0099] The output from the PETS program in the form of a list of reflections including refractive index, intensity, and standard deviation is further processed by the Jana2006 program (<http: / / jana.fzu.cz>) to find and refine the crystal structure model. All data were read together and the structure model was refined for the data from all five crystals. This method includes the following steps: - Step of finding an approximate structural model including a list of atoms in the structure and their approximate positions - While calculating the theoretical diffraction intensities required for refinement using the dynamic diffraction theory, the structural model was refined by the least squares method. As a result of the refinement, residual factors R1 = 0.1242 and wR2 = 0.1354 were obtained.

[0100] Determining the correct absolute structure included the following steps: - Step of generating an inverted structural model, that is, a model in which the coordinates of all atoms in the structure are replaced by coordinates having the same absolute value but opposite signs; - Step of refining the structural model in the same manner as the refinement of the previous model.

[0101] - As a result of the refinement of the inverted model, residual factors R1 = 0.1560 and wR2 = 0.1721 were obtained. Since these values are more than 0.01 larger than the values of the non-inverted model, it is clearly determined by this procedure that the original non-inverted model corresponds to the correct absolute structure.

[0102] The obtained refined structural model was compared with the known reference structure of abiraterone acetate determined by X-ray single crystal diffraction. The average difference in interatomic distances was 0.0493 Å.

[0103] Industrial Applicability The present invention is applied to the field of computational crystallography. More precisely, the present invention can be applied to the determination of both the crystal structures of inorganic crystals and organic crystals, and the knowledge of crystal structures can be used in many fields such as the metallurgical or pharmaceutical industries.

Explanation of Signs

[0104] 1 Electron source 2 Electron beam 3 Lens 4 Focused electron beam 5 Measured crystal 6 Scattered electrons 7 Detector 8 Processing Unit

Claims

A method for determining a crystal structure model of a crystal, wherein the crystal is capable of electron diffraction, obtaining electron diffraction data from the crystal by three-dimensional electron diffraction, wherein the data includes information on a crystal diffraction pattern, and each diffraction pattern includes information on the scattered electron intensity and crystal orientation in each direction with respect to the incident electron beam during data acquisition, and the crystal is rotating or tilting during the recording of the diffraction data, and processing data for determining crystal lattice parameters, crystal orientation at the time of obtaining the diffraction pattern, indices of each reflection, and scattered electron intensity of each reflection on each diffraction pattern, thereby generating processed data, generating a virtual diffraction frame by a computer program, wherein each virtual diffraction frame includes a list of integrated scattered electron intensities in each direction obtained by summing contributions from all experimental patterns forming one virtual frame, and the virtual diffraction frame is formed by calculation from the provided three-dimensional electron diffraction data, providing an approximate crystal structure model, and refining the approximate crystal structure model using dynamic diffraction theory including, where the step of refining calculating the modeled intensity of scattered electrons using dynamic diffraction theory based on the approximate crystal structure model, and minimizing the difference between the experimentally determined scattered electron intensity and the modeled intensity, wherein the refined crystal structure model is the model with the minimum deviation including, a method. Claim 2 A method for determining the absolute structure of a non-centrosymmetric crystal, including the steps of claim 1, generating a model of the absolute structure opposite to the current approximate crystal structure model, thereby generating an inversion model, applying to the inversion model refining the approximate crystal structure model using dynamic diffraction theory, and comparing the quality indicators of the inversion model and the non-inversion model, wherein the correct structure is the structure with the minimum deviation between the experimental data and the data calculated based on the refined structure model including, a method. Claim 3 The method according to claim 1 or 2, wherein the step of obtaining electron diffraction data from the crystal by three-dimensional electron diffraction is a measurement of continuous crystal rotation. Claim 4 The method according to claim 1 or 2, wherein the step of obtaining electron diffraction data from the crystal by three-dimensional electron diffraction is a step of rotating the crystal.

5. The method according to claim 1 or 2, wherein the step of minimizing the difference between the experimentally determined scattered electron intensity and the modeled intensity includes a least squares calculation.

6. The method according to claim 1 or 2, wherein the step of providing the approximate crystal structure model is based on the analysis of experimental data.

7. An apparatus for determining a crystal structure model, comprising: an electron source capable of emitting an electron beam; a crystal holder adapted to perform a rotational or tiling movement together with the crystal; a detector for detecting scattered electrons by the crystal, a data storage and processing unit connected to the detector and including the processing unit being adapted to determine crystal lattice parameters, the crystal orientation at the time of obtaining the diffraction pattern, the indices of each reflection, and the scattered electron intensity of each reflection on each diffraction pattern, thereby generating processed data, and generating a virtual diffraction frame by a computer program, each virtual diffraction frame including a list of integrated scattered electron intensities in each direction, which is the sum of contributions from all experimental patterns forming one virtual frame, the virtual diffraction frame being computationally formed from the provided three-dimensional electron diffraction data; the data storage being configured to provide an approximate crystal structure model or the processing unit being adapted to perform an analysis of processing data leading to the acquisition of an approximate structure model, and the processing unit being adapted to refine the structure model. Apparatus.

8. The processing unit is adapted to refine the approximate crystal structure model using dynamic diffraction theory, and during the refinement, the processing unit calculates the modeled intensity of the scattered electrons using the dynamic diffraction theory based on the approximate crystal structure model, and minimizes the difference between the experimentally determined scattered electron intensity and the modeled intensity and is adapted such that the refined crystal structure model is the model having the minimum deviation. The apparatus according to claim 7.

9. The processing unit is configured to determine the absolute structure of a non-centrosymmetric crystal, and the processing unit Generate a model of the absolute structure that is the reverse of the structure of the current approximate crystal structure model, thereby generating an inversion model, Refine the approximate crystal structure model using the dynamic diffraction theory of the inversion model, and Compare the quality indicators of the inversion model and the experimental data is configured to, where the correct crystal structure is the one with the minimum deviation between them, The apparatus according to claim 7 or 8.

10. The processing unit is adapted to refine the approximate crystal structure model, and the apparatus calculates the quality indicator of the approximate crystal structure model, and compares the quality indicators is adapted to, where the correct crystal structure is regarded as a modeled crystal structure in which the deviation between the experimental data and the data calculated based on the refined structure model is minimized, The apparatus according to claim 9.

11. The processing unit is adapted to generate a model of the crystal structure that is the reverse of the current approximate crystal structure model, thereby generating an inversion model, and the step of comparing the quality indicators is a step of comparing the quality indicators of the inversion model and the non-inversion model, where the correct crystal structure is a structure in which the deviation between the experimental data and the data calculated based on the refined structure model is minimized, The apparatus according to claim 9.

12. The detector is set to collect data simultaneously with the rotation of the crystal, The apparatus according to claim 7 or 8.

13. The detector is set to collect data stepwise during the rotation of the crystal, The apparatus according to claim 7 or 8.

14. A method for determining a crystal structure model of a crystal, preferably the absolute structure of a non-centrosymmetric crystal, wherein the crystal is electron-diffractable, Obtaining electron diffraction data from the crystal by three-dimensional electron diffraction, the data including information on the crystal diffraction pattern, each diffraction pattern including information on the scattered electron intensity and crystal orientation in each direction with respect to the incident electron beam during data acquisition, the crystal rotating or tilting during data acquisition, step, and Processing the data to determine the crystal lattice parameters, the crystal orientation at the time of obtaining the diffraction pattern, the indices of each reflection, and the scattered electron intensity of each reflection on each diffraction pattern, thereby generating processed data A step of generating a virtual diffraction frame by a computer program, each virtual diffraction frame including a list of integrated scattered electron intensities in each direction, which is the sum of contributions from all experimental patterns forming one virtual frame, and the virtual diffraction frame being computationally formed from provided three-dimensional electron diffraction data, A step of providing an approximate crystal structure model, A step of calculating a quality index of the approximate crystal structure model using dynamic diffraction theory and calculating model intensities, A step of generating a model of the absolute structure opposite to the current approximate crystal structure model, thereby generating an inversion model, A step of calculating a quality index of the inversion model using dynamic diffraction theory and calculating model intensities, and A step of comparing the quality indices of the inversion model and the non-inversion model, wherein the correct structure is the one with the minimum deviation between the experimental data and the data calculated based on the refined structure model, A method comprising.

15. The method according to claim 14, wherein the step of obtaining electron diffraction data from the crystal by three-dimensional electron diffraction is a measurement of continuous crystal rotation.

16. The method according to claim 14 or 15, wherein the step of obtaining electron diffraction data from the crystal by three-dimensional electron diffraction is a step of rotating the crystal.

17. The method according to claim 14 or 15, wherein the step of providing an approximate crystal structure model is based on an analysis of experimental data.

Images