WO2025141291A1 - Methods for reducing the contribution of aberrations in the diffraction pattern using neural networks - Google Patents

Abstract

Method for improving the resolution of diffraction measurements using neural networks. A method for obtaining diffractograms with a smaller contribution of aberration, using neural networks, where the diffractogram with a smaller contribution of aberration is determined from the diffractogram with a greater contribution of aberration using neural networks previously trained on a set of pairs consisting of a diffractogram with a greater contribution of aberration and corresponding target diffractogram with a smaller contribution of aberration, where, for each individual crystal structure, diffractograms with a greater contribution of aberration are computed from known crystal structures, and precalculated target diffractogram with a smaller contribution of aberration are used for the diffractogram with a smaller contribution of aberration, with prior adjustment of the model by optimizing the loss function.

Description

Short description of the invention :

Methods for reducing the contribution of aberrations in the diffraction pattern using neural networks.

INVENTION TITLE: Methods for Reducing the Contributi on of

Aberrations in the Diffract i o n Pattern U s i ng Neu r a 1 Network s

FIELD OF TECHNOLOGY TO WHICH THE INVENTION RELAT E S

The present invention relates to methods for reducing the contribution of aberrations in the diffraction pattern, arising from the properties and geometry of the instrument, sample properties, and measurement settings, particularly in the case of powder diffraction patterns, by utilizing neural networks.

INTRODUCTION

The resolution of diffraction measurements is crucial for a more reliable characterization of samples. Diffraction measurement results in a dif f ractogram or a diffraction pattern consisting of bands (or diffraction peaks) of intensity as a function of angle and/or energy, which have certain widths, leading to the potential overlap of adjacent diffraction peaks. The overlap of peaks results in a less precise determination of the position and intensity of individual peaks, and in the context of this invention, a diffraction pattern with higher peak overlap is considered to have lower resolution, i.e. a greater contribution of aberrations. Higher and superior resolution implies less overlap of peaks. Generally, if the peak widths are smaller, the overlap of adjacent peaks is reduced, resulting in a more. resolved diffraction pattern, i . e . a lower contribution of aberrations . Conversely, if the peak widths are larger, the overlap of adjacent peaks increases, leading to a dif fractogram of lower resolution, i . e . a dif fractogram of greater contribution of aberrations .

Diffraction measurement techniques are analytical methods based on the interaction of electromagnetic or other radiation, such as neutron radiation, with a sample . Among these techniques are, but not limited to, X-ray powder diffraction, X-ray diffraction on a single crystal, and Laue diffraction. Diffraction measurement techniques yield a dif fractogram representing the radiation intensity after interaction with the sample, depending on the direction of radiation scattering.

X-ray powder diffraction (PXRD) is an analytical technique used for the characterization of crystalline samples or materials . This includes the identification of the number and types of components in the sample . Identification refers to determining the phase in a sample characterized by its chemical formula, crystal structure, set of characteristic diffraction peak positions, or any other common method that can specifically determine a particular phase . The analyzed sample or material, if necessary, is crushed and homogenized, and by interacting X- rays with the powdered sample, measurements are obtained that are used for, but not limited to :

(i) Identifying crystalline materials in the sample (e . g. , minerals, inorganic compounds, organic materials, pharmaceutical active ingredients) ,

( ii) Determining the composition of samples,

(iii ) Determining the unit cell of individual materials or chemical compounds in the sample, (iv) Identifying new crystalline materials or compounds,

(v) Determining the unit cell and the crystal structure of new chemical compounds and materials, and

(vi) Determining particle size and strain of crystal, domains in chemical compounds and materials in the sample .

Characterizing solid substances through powder diffraction is crucial for research in geology, environmental science, materials science, chemistry, physics, engineering, biology, pharmaceutical development, and related branches .

X-ray powder diffraction is a technique or method for material characterization, performed using an instrument called a powder diffractometer . This instrument typically consists of an X-ray source, a sample holder, an X-ray detector, and is equipped with a computer . In this process, the sample on the sample holder is exposed to X-rays of a specific wavelength from the X-ray source . The interaction between the sample and X-rays is then measured by the X-ray detector . The instrument and measurements are usually controlled by a computer . The powder sample is placed on the sample holder and illuminated with X-rays so that the detector measures the intensity of scattered X-rays as a function of the angle between the direction of incident radiation and the direction of scattered radiation . This angle is known as the diffraction angle and is typically denoted as 2Theta .

Observing the diffractogram of the sample in its entirety, in the experimentally measured diffractogram of the crystalline powder sample, diffraction bands (peaks) are identified, each at a specific 2Theta position. The diffraction bands have certain widths, resulting from the characteristics of the diffractometer and the sample itself , leading to partial overlap of adjacent bands i f the separation between thei r maxima in 2Theta is small enough . The overlap of the intensities of adj acent bands is greater if their widths are larger and if their peak maxima are closer in 2Theta .

When comparing two diffraction patterns of the same sample , it i s generally stated that the one with a smaller contribution of aberrations has higher resolution, and conversely, the diffraction pattern with a greater contribution of aberrations is said to have lower resolution . A diffraction pattern with a greater contribution of aberrations typically exhibits Bragg peaks that overlap to a greater extent and is therefore described as having lower resolution . Conversely, a diffraction pattern with a smaller contribution of aberrations usually has Bragg peaks with less overlap and is described as having higher resolution ,

In most analyses of dif f ractograms , it is preferable to have a di f fractogram with a smaller contribution of aberrations , i . e . , a dif f ractogram with hi gher resolution compared to other peaks in the dif fractogram. In the subj ect invention, it is understood that a dif f ractogram with less overlap between peaks is of higher resolut ion, i . e . such a dif fract ion pattern has a smaller contribution of aberrations ari s ing from the properties of the sample as well as the properties and characteristics of the instrument . Smaller contribution of aberrations in the dif fractogram allow for clearer differentiation of adj acent diffract ion bands , representing an improvement for determining the unit cell of a crystal sample and determining the intensity of individual dif fraction peaks , and, therefore , the determination of crystal structures from a dif fractogram with smaller contribution of aberrations is improved, i . e . it i s of higher resolution . Powder dif f ractograms with the smallest contribution of aberrations are typically measured using diffractometers equipped with a synchrotron X-ray source. One such diffractometer is, for example, found at the ID22 - High- resolution powder diffraction beamline at the European Synchrotron Radiation Facility (ESRF) in Grenoble, France (as of April 2023) . The resolution of a measurement that can be achieved on the ID22 setup cannot be attained with laboratory diffractometers. However, synchrotron measurements are (i) less accessible and unsuitable for everyday use in sample characterization, and additionally, (ii) measurements in certain cases must be fast, and under these conditions, measurement of high-resolution dif f ractograms may not be achievable even on a synchrotron diffractometer.

Reducing the contribution of aberrations in a diffraction pattern., arising from the properties and geometry of the instrument as well as the properties of the sample, is considered a challenging problem [A. Coelho, J. Appl . Cryst. 2018, 51, 112-123; abstract on p. 112] . While it is possible to experimentally measure the contribution of the instrument to the measured diffraction pattern of a powder sample to deconvolute its impact, the contribution of sample-induced aberrations remains unknown. Aberrations contribute to the broadening of Bragg peaks, increasing their overlap, which exacerbates the. inherent issue of powder diffraction with peak overlap, thereby complicating powder diffraction data analysis: "...what is known as the main problem of powder diffraction: the accidental and systematic overlap of peaks caused by the projection of the three-dimensional reciprocal space onto a one-dimensional axis..." [Dinnebier, Billinge, Powder Diffraction, Theory and Practice, The Royal Society of Chemistry 2008; p. v] .

Definitions of Terms: For the purposes of this patent application, the foll owing terms have the following meanings :

Width of Diffraction bands, often expressed as the full width at half maximum ( FWHM) , depends on sampl e characteristics , diffractometer features , measurement settings , and may depend on the diffraction angle . Generally, the widths of diffraction bands increase with an increase in the diffraction angle 2Theta, and th is increase may or may not be monotonic .

Di ff ractogram with a smaller contribution of aberrations refers to the measured or simulated dif f ractogram in which the widths ( FWHM) and shapes of diffraction bands are influenced by aberrations in a manner that is known in the art . .Aberrations can result from sample features ., diffractometer features , as is the case in dif f ractograms measured on laboratory instruments , and from the features of the measurement settings , which are known to an expert s killed in the art .

Di ff ractogram with a greater contribution of aberrations is determined in relation to the measured or s imu lated dif f ractogram containing aberration contributions , where the contribution of some or several aberrations is smaller compared to the contribution of aberrations in the corresponding measured or simulated dif f ractogram. A. smaller contribution of aberrations generally corresponds to na rrower widths ( FWHM) of the diffraction bands , whereby for the comparison of the width in 2Theta with the dif f ractogram with a greater contribution the dependencies of the position s of diffraction peaks in 2Theta on the wavelengths of radiation in both dif f ractograms is taken into account , in a manner known in the art , as well as the possible symmetric shapes ( for example , but not limited to, Gaussian di stribution , Lorentzian distribution, Voigt profile , or delta functi on ) of the diff raction peaks in the diff ractogram with a smaller contribution of aberrati ons compared to the corresponding band in the dif f ractogram with a greater contribution of aberration, as recognized by an expert skilled in the art . Other differences between lower and higher resolution dif f ractograms are also possible due to the smaller contribution of aberrations in the higher resolution dif f r a c t oar am .

Example : Based on a known crystal structure , a pair of dif f ractograms with a smaller contribution of aberrations and greater contribution of aberrations are simulated, as known to an expert skilled in the art . The dif f ractogram with a greater contribution of aberration is simulated with an average crystal domain size of 40 nm. and instrument characteristics of a l aboratory diffractometer equipped with an X-ray tube featuring a copper anode and an emission spectrum corresponding to copper Ka radiation . Such a dif f ractogram in the angular range of 2Theta above 30 ° typically contains diffraction bands with widths ( FWHM) of 0 . 30 ° in 2Theta or more. The di f f ractogram with a smaller contribution of aberrat ion is simulated with an average crystal domain si ze of 1000 nm and instrument characteristics of a laboratory diffractometer equipped with an X-ray tube with a copper anode with an emission spectrum corresponding to copper Kai radiation . Such a dif f ractogram typically conta ins dif fract ion bands with widths ( FWHM) less than 0 . 05 ° in 2Theta in the same angular range . These two simulated dif f ractograms represent an example pair of dif f ractograms with a smaller and greater contribution of aberrations .

Other pairs of dif f ractograms with smaller and greater contributions of aberration can be created wit h differently selected sample features , diffractometer features, or measurement settings , so that , typically, the dif f ractogram with a smaller contribution of aberration has a smaller overall contribution of aberrations than the dif f ractogram with

greater contribution of aberration.

Example: A dif f ractogram with a greater contribution of aberration of a sulfadiazine sample is measured on a laboratory diffractometer equipped with an X-ray tube with a copper anode with an emission spectrum corresponding to copper Kai radiation. Such a dif f ractogram with a greater contribution of aberration for a given sulfadiazine sample has a diffraction peak at approximately 29.5° 2Theta with an asymmetric shape and a width (FWHM) of approximately 0.13° in 2Theta. A dif f ractogram with a smaller contribution of aberration of the same sample is measured on the ID22 beamline at the ESRF synchrotron with a radiation wavelength of 0.035 nm, which has reduced aberrations of the measuring device compared to the laboratory diffractometer equipped with an X-ray tube with a copper anode. Such a dif f ractogram with a smaller contribution of aberration contains less asymmetric diffraction peaks., and, after considering the wavelength of radiation inherent to each dif f ractogram for the purpose of comparison in a manner known in the art, the corresponding diffraction peak has a full width at half maximum of approximately 0.03°.

A dif f ractogram with a greater contribution of aberration typically contains diffraction bands that overlap with adjacent bands due to a significant influence of aberrations. Diffraction bands in dif f ractogram with a smaller contribution of aberration typically overlap less than in dif f ractograms with a greater contribution of aberration, due to reduced aberration effects. A diffraction pattern with a greater contribution of aberrations, in the context of this invention, also implies a diffraction pattern that is processed using the method of the present invention, resulting in a diffraction pattern with a smaller contribution of aberrations . In the dif f ractograms produced by the method of the subj ect invention, the overlap of adj acent diffraction bands is reduced compared to the overlap in the dif f ractograms with a greater contribution of aberration .

Contributions to diffraction bands arising from crystal structure denote measured or simulated intensities of diffracted X-rays resulting from the periodic electronic density of a component of the measured or simulated sample .

The noise contribution to the dif f ractogram signifies random deviations from the ideal value of the measured or simulated intensity, distributed according to a probabi lity density function, which may include , but is not limited to , Gaussian or Poisson distribution . Noise typically arises in processes involving photon counting, for example , in the mea surement of photon counts in diffraction experiments .

The background of a dif f. ractogram refers to the measured or simulated intensities of X-ray radiation which are not contributions to the diffracti on peaks originating f rom the crystal structure . Common sources of the background are radiation scattered on optical elements , air , sample holder , non-crystal line components of the sample , and background radiation .

Aberra tion arising from the properties of the sample signifies every influence of the sample on the width and/or shape of diffraction peaks resulting from any deviations of the sample from the ideal crystal structure , manifested through , but not limited to , the distribution of crystal domain si zes , strain within crystal domains , any other types of defects in crystal domains , as well as the. thermal motion of atoms within the crystal domains of the measured sample . Aberration arising from the features of the diffractometer denotes any broadening, shape alteration, or modification of the measured area of diffraction bands resulting from the features of the diffractometer and the measurement settings. Furthermore, this term encompasses any contribution of noise or background curve arising from the features of the diffractometer and the measurement settings. Diffractometer features and measurement settings are, but are not limited to, imperfections in the used diffractometer, characteristics of the divergent slit, receiving slit, Seller slits, spectral characteristics of the X-ray source, characteristics of the used detector, features of the choice of the angular measurement range, choice of the angular measurement step, choice of the exposure time per measurement point, choice of the sample holder, choice of the measurement geometry, and other parameters of the chosen measurement method related to the diffractometer and the measurement settings.

TECHNICAL PROBLEM FOR WHICH PATENT PROTECTION IS CLAIMED

The present invention addresses the problem of reducing the contribution of aberrations in a diffraction pattern, arising from the properties and geometry of the instrument as well as the properties of the sample, which is considered a challenging issue [A. Coelho, J. Appl. Cryst. 2018, 51, 112-123; abstract on p. 112] , While it is possible to experimentally measure the contribution of instrument-induced aberrations in the measured diffraction pattern of a powder sample to deconvolute their effect, the contribution of sample-induced aberrations remains unknown. This invention provides a solution to this problem by utilizing a neural network trained to reduce the contribution of aberrations arising from the instrument, the sample, or both. Aberrations contribute to the broadening of Bragg peaks, increasing their overlap, which emphasizes the inherent issue of powder diffraction with peak overlap, making the analysis of powder diffraction data more difficult: " . . .what is known as the main problem of powder diffraction: the accidental and systematic overlap of peaks caused by the projection of the three-dimensional reciprocal space onto a one-dimensional axis. . ." [Dinnebier, Billinge, Powder Diffraction, Theory and Practice, The Royal Society of Chemistry 2008; p. v] .

State of the art

Powder X-ray diffraction, X-ray powder diffraction, or X-ray diffraction on a powdered sample (PXRD) , is a technique or a method for material characterization. It is performed using an instrument called a powder diffractometer or a diffractometer for powdered samples, typically consisting of an X-ray source, a sample holder, an X-ray detector, and it is equipped with a computer, while the sample on the sample holder is illuminated with X-rays of a specific wavelength from an X-ray source, and the interaction between the sample and X-rays is measured using an X-ray detector. The instrument and measurements are usually controlled by a computer. A powdered sample is placed on the sample holder and illuminated with X-rays, allowing the detector to measure, the intensity of scattered X-ray radiation as a function of the angle between the vector describing the direction of incident radiation and the vector describing the direction of scattered radiation. This angle is known as the diffraction angle and is typically denoted as 2Theta.

A typical diffractogram of a powdered crystalline material, recorded in a computer-usable file in any format or form known in the art, consists of a series of points where each individual 2Theta value is assigned an intensity of scattered radiation. Observing the entire dif fractogram in the angular range of 2Theta, for example, from 2° to 70°, distinct bands (peaks or maxima) are noticeable in the dif fractogram of a crystalline powdered sample, each at a specific 2Theta position. These bands have certain widths in 2Theta, which can lead to the overlapping of intensities between adjacent bands if the distance between their maxima is small enough in the 2Theta angles. The degree of overlap increases when the widths of adjacent bands are larger. It is desirable to have a dif fractogram with a larger number of bands that are well-resolved from other bands in the dif fractogram, meaning that the overlap is minimized. It is also known in the art that at lower 2Theta values, diffraction bands overlap less than at higher 2Theta values. In the subject invention, it is implied that the dif fractogram with sharper and better-separated diffraction bands is of higher resolution, i.e. with smaller contribution of aberrations. For most dif fractogram analyses performed in the art, it is desirable to have access to a dif fractograms with a smaller contribution of aberration.

In the context of this invention, a synchrotron beamline for high-resolution powder diffraction is considered a diffractometer capable of providing dif fractograms with the highest experimentally achievable resolution, in terms of minimal practically achievable overlap of diffraction bands. Achieving high-resolution dif fractograms , as would be obtained on a synchrotron beamline, is generally not possible using only a laboratory powder diffractometer.

The dif fractogram of a sample or material consists of diffraction bands (also known as Bragg peaks, Bragg maxima, or Bragg reflections) , which arise due to coherent interference of radiation resulting from its diffraction on the sample, as well as background and noise, which arises from random deviations during measurement due to the stochastic nature of the interaction between radiation and material at the quantum level , as wel l as stochastic processes inherent to measurement equipment , such as thermal and electronic noise in radiation detectors . The signal consist s of bands and background, carrying useful information about the sample , while noise is undesirable , introducing random deviations into the signa l . Since noise is random, longer or repeated measurements allow for a reduction in the level of noise compared to the useful signal , as random noise deviations tend to average out over multiple measurements , leading to an improved signal-to-noise ratio . Shorter measurements result in a less favorable signal-to-noise ratio compared to longer measurements , with all other settings of the used diffractometer and measurement conditions on the same sample being equal . It is also known that measuring a dif f ractogram with a smaller contribution of aberration typically requi res a longer time period for measurement .

However , in some applications of powder diff raction , such as studies with time-resolved measurements where the measured sample changes over time in any way, extended measurement of individual diffraction patterns may not be feasible if the sample itself undergoes significant changes during measurement . Such measurements necessitate short measurement times for individual di ffraction patterns , resulting in lower resolution and a less favorable signal-to-noise ratio . Compromises between various experimental limitations can, therefore , constrain the reliable determination of sample properties from such lower- quality diffraction data . The method or methods described in the present invention have the capabil ity to enhance the quality of diffraction data by decreasing the contribution of aberrat ions of the dif fractogram, improving the signal-to-noise ratio , and reducing the impact of aberrations to a level not achievable by any modifications avai lable on the used diffractometer . When comparing two diffraction patterns of the same sample , it is commonly stated that the one with a smaller contribution of aberrations has higher resolution, and conversely, the diffraction pattern with a greater contribution of aberrations is said to have lower resolution . A dif fraction pattern with a greater contribution of aberrations typical ly exhibits Bragg peaks that overlap to a great er extent and is therefore described as having lower resolution . Conversely, a diffraction pattern with a smaller contribution of aberrations usually exhibi ts Bragg peaks with less overlap and is described as having higher resolution .

Among other methods used to achieve sharper and better-resolved bands is , for example, the method of weighted subtraction of the second derivative . This method has been extended to incorporate higher-order even derivatives , but it is known to be limited in its ability to sharpen a peak or a band due to the presence of noi se in the measured dif f ractogram, as wel l a s the complex interplay of aberrations ari s ing f rom sample features and diffractometer characteristics .

Experimental methods on the diffractometer involve replacing optical elements with element s that impose stricter conditions for the passage of X-rays f rom the radiation source to the detector, such as divergent s lits on the source side and receiving slits on the detector s ide, and Seller slits . Imposing stricter conditions for the passage of X-rays from the detector to the sample reduces the radiation intensity reaching the detector, and the measurement duration is increasingly prolonged as stricter conditions are set . A longer measurement duration is more favorable as it achieves a better signal-to-noise ratio in the measured dif f ractogram. Reducing the contribution of aberrations in a diffraction pattern, arising from the properties and geometry of the instrument as well as the properties of the sample, is considered a challenging problem [A. Coelho, J. Appl.

2018, 51, 112-123; abstract on p, 112] . While it is possible to experimentally measure the contribution of instrument- induced aberrations in the measured diffraction pattern of a powder sample to deconvolute their effect, the contribution of sample- induced aberrations remains unknown. Aberrations contribute to the broadening of Bragg peaks, increasing their overlap, which highlights the inherent problem of powder diffraction with peak overlap, complicating the analysis of powder diffraction data: "...what is known as the main problem of powder diffraction: the accidental and systematic overlap of peaks caused by the projection of the three-dimensional reciprocal space onto a onedimensional axis..." [Dinnebier, Billings, Powder Diffraction, Theory and Practice, The Royal Society of Chemistry 2008; p. v] .

Closest pr i o r art

US2021302332A1 discloses a trained convolutional neural network using input intensities to provide crystal structure as output. The method used in this patent extracts atomic coordinates from X-ray diffraction data. Precise definitions of X-ray diffraction data are not provided within the patent itself, nor are they tied to specific experimental (instrumental) . It is clear to one skilled in the art that in the patent US2021302332A1, X-ray diffraction data refers to pairs of so-called Miller indices and their corresponding intensities or equivalent pairs, rather than experimentally measured X-ray powder diffraction patterns. Furthermore, an expert skilled in the art would understand that the method described in the patent US2021302332A1 cannot be directly applied to X-ray powder diffraction patterns without additional preprocessing. This preprocessing represents a known issue in the prior art and is condit ioned by the resolution of the experimenta l di f fra ctogram, sample properties , and the in strument . The subj ect invention described in the present patent precisely addresses this issue .

CN109725013A (X-ray diffraction data analysis system) describes a computer syst em for processing dif f ractograms of powdered crystal samples . The patent acknowledges the need for automating dif fractagram analysis but does not disclose methods for determining dif f ractograms with a smaller contribution of aberration from dif fractogram with a greater contribution of aberration, dist inguishing it. from the subj ect invention .

WO2018025618A1 (Material structure searching method and X-ray structural analysis system used in sa id method) describes a system for structural characterization of samples that does not require expert knowledge . The patent recognizes the need for automating dif f ractogram analysis , but it does not disclose methods for determining dif f ractogram with a smal ler contribution of aberration from dif f ractogram with a greater contribution of aberration, distinguishing it from the subj ect invention .

JP2020134382A (CRYSTAL STRUCTURE ANALYSIS METHOD USING MACHINE LEARNING) outlines a machine learning-based method for extracting the positions of peaks from dif f ractograms , thereby improving success in s tructural analysis . Enhanced peak position extraction improves the ability to determine the sample ' s unit cell , Invention JP2020134382A describes that machine lea rning can be used to more reliably determine the positions of diffraction peaks in a powder dif f ractogram, thereby improving the chances of successfully solving the crystal struc ture based on the powder dif fractogram. Invention JP2020134382A employs machine learning to obtain the positions of diffraction peaks , hile in other segments of the procedure for solving crystal structure from powder dif f ractogra®, it utilizes methods known and common in the prior art., applying them to the originally measured dif f ractogram. Although the method of the present invention also uses dif f ractograms of different band widths as input for training the machine learning model, the training objective is not isolated peak positions. Instead, the goal of training is a new overall higher-resolution dif f ractogram, i.e., the intensity of the output radiation as a function of the diffraction angle. The new dif fractogram obtained by the method of the present invention comprises narrower bands compared to the bands in the experimental, dif fractogram, but their relative intensities are preserved, which is crucial for a precise determination of the crystal structure. The dif fractogram with a smaller contribution of aberration, i.e. higher-resolution dif fractogram obtained by the method of the present invention, there is a higher success rate in determining the crystal structure using direct methods, a capability not provided by the invention -JP2020134382A, as every processing step after the extraction of peak positions is performed on the originally measured dif fractogram. The present invention does not rely on or involve the extraction of peak positions using machine learning methods. The subject invention achieves the generation of a high-resolution dif fractogram, typically achievable onlywith diffractometers utilizing synchrotron radiation sources, such as the ID22 beamline at the ESRF synchrotron. The subject invention also improves the signal-to-noise ratio. The subject invention simulates target dif f ractograms used in training the machine learning model to be free from instrumental aberrations. When applying the model to real experimental data, this allows for a reduction in these instrumental contributions, including contributions from the Ka2 line or axial divergence, for example. This is something that the invention JP2020134382A does not achieve. B. Sullivan et al. in J. Appl. Cryst. 2019, 52, 8.54-863 describe a neural network for predicting the positions and shapes of diffraction peaks to improve accuracy in integration. However, it does not disclose a method for determining higher-resolution d i f f r a c t o g r am s f r om 1 o w er-r e solut io n ones.

In the state of the art,, machine learning has been applied to crystallography problems for classifying crystal structures and determining spatial groups, as seen in works such as F. Oviedo et al, npj Computational Materials, 2019, 5, 1-9; N. J, Szymanski, npj Computational Materials , 2023, 9, 31; B. D, Lee, Advanced Intelligent Systems, 2022, 4, 2200042.

Machine learning has also been used to solve crystal structures directly from measured intensities, obtaining 3-dimensional electron density maps (Madsen et.al. DOI: 10.26434 /chemrxiv- 2023-f cdps-v2) where the neural network is used to solve the problem of reconstructing the phases of complex structural factors from experimentally measured intensities of individual diffraction peaks obtained by X-ray diffraction on a single crystal. An expert skilled in the art understands that the disclosed prior art cannot be directly applied to lower- resolution powder dif f ractograms . Furthermore, the disclosed prior art does not reveal a method for determining higher- resolution dif f ractograms from lower-resolution dif f ractograms .

G. Guo et al. (arXiv: 2312.15136) describe a machine learningbased method that reconstructs electron density maps from simulated dif f ractograms of simple cubic and trigonal crystal structures. However, it does not disclose a method for determining higher-resolution dif f ractograms from lower- resolution ones.

Uncovering the Essence of the Invention : The invention describes methods for achieving di f f ractogram with a smaller contribution of aberration of powder dif f ractograms based on machine learning . In the first step, the machine learning model is trained using pairs of data , where the input is a simulated dif f ractogram with a greater contribution of aberration, and the target is a simulated dif f ractogram with a smaller contribution of aberration .

In the second step, the trained model is then provided with an experimentally measured dif f ractogram with a greater contribut ion of aberration as input ., and the result is a new dif f ractogram wi th a smaller contribution of aberration .

By appropriately sel ecting pairs of simulated dif f ractogram with a greater contribution of aberration and dif f ractogram with a smaller contribution of aberration during the training process of the machine learning model , the resolution of dif f ractograms obtained by processing through the model is determined . In this way, it is possible to achieve higher resolution than what is experimentally achievable on the diffractometer used t o obtain the input measured dif f ractogram . By increasing the resolution of the powder dif f ractogram using the methods of the subj ect invention , the obtained dif f ractogram faithfully reproduces essent ial features of the measured dif f ractogram in the sense that the positions of diffraction bands in the dif f ractogram with a greater contribution of aberration are close to those in the measured dif f ractogram and that the band area rat ios in the dif f ra ctogram with a smaller contribution of aberration are similar to the corresponding ratios in the dif f ractogram with a greater contribution of aberrat ion . In the dif f ractogram with a smaller cont ribution of aberration , diffraction bands are better separated f rom neighboring diffraction bands , increasing the success rate of determining the sample ' s unit cell and solving its crys tal structure . Additionally, the dif f ractogram with a greater contribution of aberration obtained by the methods of the present invention reveals diffraction bands , their positions , intensities , and shapes that are not di stinguishable or clearly visible in the input measured lower-resolution dif fractogram due to aberrat ions arising from sample properties , aberrations ari sing from diffractometer features , or measurement settings .

Figures and Brief Description Thereof

FIGURE 1. Example of a measured diffractogram with a greater contribution of aberration processed using the second derivative method and the method of the subject invention to obtain a diffractogram with a smaller contribution of aberration.

FIGURE 2. A narrower angular range with an example of a measured diffractogram with a greater contribution of aberration processed using the 2nd derivative method and the method of the subject invention to obtain a diffractogram with a smaller contribution of aberration.

FIGURE 3. A high-angle range with an example of a measured diffractogram with a greater contribution of aberration processed using the 2nd derivative method and the method of the subject invention to obtain a diffractogram with a smaller contribution of aberration.

FIGURE 4. Significant reduction of the contribution of the Ka2 line and improvement in resolution by processing the measured diffractogram with a greater contribution of aberration using the method of the subject invention.

FIGURE 5. The crystal structure of the sample obtained by applying the direct method of crystal structure determination to the measured diffractogram with a greater contribution of aberration, in which structurally meaningful parts cannot be recognized or interpreted.

FIGURE 6. The crystal structure of the sample obtained by applying the direct method of crystal structure determination to the diffractogram with a smaller contribution of aberration obtained using the method of the subject invention on the measured diffractogram with a greater contribution of aberration , which was used to obtain the results shown in Figure 5 . In this case, it is possible to interpret the crystal structure , and it is consistent with the expected molecular structure of silver sulfadiazine .

FIGURE 7 . The crystal structure of the sample obtained by applying the direct method of crystal structure determination to the measured dif f ractogram with a greater contribution of aberration, in which structurally meaningful parts cannot be recognized or interpreted .

FIGURE 8 . The crystal structure of the sample obtained by applying the direct method of crystal structure determination to the dif f ractogram with a smaller contribution of aberration obtained using the method of the subj ect invention on the measured dif f ractogram with a greater contribution of aberration , which was used to obtain the results shown in Figure 7 .

FIGURE 9 . The molecular structural formula for the chemical compound 4~amino~N~ [2- ( 3-aminopropanoylamino) ethyl ] butanamide dihydrochloride .

FIGURE 10 . The crystal structure of the sample i s success ful ly determined using the direct method for solving crystal structures on the di f f ractogram with a smal ler contribution of aberration obtained by applying the method of the subj ect inventi on to the measured dif f ractogram with a greater contribut ion of aberration .

TABLE 1 . Comparison of unit cel l parameters and their standard deviations given in parentheses obta ined from the refinement of unit cell parameters on the measured dif f ractogram sample containing the greater contribution of aberration , the dif f ractogram with a smal ler contribution of aberrat ion obtained using the method of the subj ect invention, on the seine measured di.f f ractograift sample containing a greater cont ribution of aberration , and on the dif f ractograra measured at a synchrotron beamline on the same sample .

Detailed Description of the Invention

Subject invention utilizes a .laboratory X-ray powder diffractometer equipped with an X-ray radiation source, sample holder, detector, and a computer for measuring di f f ractogram samples containing a greater contribution of aberration, which are then processed by the methods of the subject invention using machine learning, such as neural networks, to obtain corresponding diff ractogram with a smaller contribution of aberration. Therefore, this invention's method can be used to determine higher resolution dif f ractograms that could not be achieved using the mentioned diffractometer.

The improved or higher resolution dif f ractogram, determined by applying the methods of this invention, is manifested by reduced contributions of aberrations to the diffraction patterns in the higher resolution dif f ractogram obtained using the subject invention's method. This is evident in, but not limited to, narrower band widths, less asymmetry in the diffraction bands, reduced overlap of diffraction bands with neighboring ones, and reduced noise in the dif f ractogram.

By using the dif f ractogram with a smaller contribution of aberration obtained with the subject invention's method, it is possible to conduct analyses with a higher degree of success, especially in determining the crystal structure of the sample, compared to analyses conducted using the original measured lower- resolution powder dif f ractogram with a greater contribution of aberration, which served as the basis for determining the new powder di ff ractogram with a smaller contribution of aberration using the method of the subject invention.

The method of this invention characterized by the following components : (i) a machine learning model such as a neural network that is

(ii) trained with an optimization algorithm (optimizer) on

(iii) a set of pairs, consisting of one simulated dif f ractogram with a greater contribution of aberration and one simulated dif f ractogram with a smaller contribution of aberration. Both dif fractograms are calculated for the same crystal structure and take into account contributions to the diffraction patterns, including but not limited to aberrations arising from sample properties, aberrations arising from diffractometer features, and features of the simulated measurement settings. The optimization goal is to

(iv) minimize their distance by minimizing the loss function between the output higher resolution dif f ractogram obtained by applying the machine learning model to the simulated lower resolution dif f ractogram and the target simulated higher resolution dif f ractogram, and

(v) the thus trained machine learning model is then applied to process the measured dif f ractogram with a greater contribution of aberration and determine the higher resolution dif f ractogram with reduced contributions of aberrations.

The first step in implementing the method of this invention is to prepare a training dataset for the model. Based on publicly available crystal structures (for example,, in the Crystallography Open Database (COD, http://vrww.crystallography.net/cod/ (23. 11. 2023.) ) . Simulated diffraction patterns are calculated, and multiple ones for each crystal structure are considered, taking into account that the widths and shapes of the bands corresponding to the selected contribution of aberrations are not the same in each calculated diffraction pattern. Simulated diffraction patterns are calculated using methods known in the art , and available computer programs can be employed for this purpose . These simulated diffraction patterns serve as input dif f ractogram pat terns with a greater contribution of aberration for training the model . For each crystal structure , a corresponding target diffraction pattern of smaller aberration contribution is calculated, forming a pair with the simulated di ffra ction pattern of greater aberrat ion contribution which is calculated from the same crystal structure . Ideal ly, the target simulated diffraction pattern of a smaller aberration contribution is calculated to have greater resolution ( less aberration contribution) than what is achievable through measurements on the laboratory diffractometer for wh ich the model is trained . The training process involves comparing the target simulated diffraction pattern with the model output and adj usting the model with the ultimate goal of minimizing their difference .

Training the machine learning model is done through an optimi zation process where the model is provided simulated dif f ractogram with a greater contribution of aberration as input , and the distance or loss function between the model output and the target simulated dif f ractogram with a smal ler contribution of aberration is calculated . Using optimization algorithms known to those s killed in the art, model parameters are adj usted so that the cal culated loss function is minimal for all pairs of input and target simulated dif f ractograms .

Training the machine learning model is finished when the distance , determined by the loss function , between the target simulated dif f ractogram with a smaller contribution of aberrat ion and the corresponding output dif f ractogram with a smal ler contribution of aberration provided by the model , ceases to signif icantly decrease, typically after multiple passes through all pairs of input and target dif f ractograms , as i s common in the art . In this way , the trained model predicts or calculates the output dif f ractogram for each input dif f ractogram in the training set that is as close, as possibl e or ideall y identical to the target di f f ractogram with a smaller contribution of aberration . The machine learning model trained in this way can increase the resolut ion of even those dif f ractogram with a greater contribution of aberrati on that were not used during its optimization process in training .

Subsequently, the trained model is given a measured dif f ractogram with a greater contribution of aberration, which could have been recorded on a laboratory diffractometer, and the model yields a dif f ractogram with a smaller contribution of aberration as a result . The obtained dif f ractogram with a smaller contribution of aberration is then used for sample characterization, including but not limited to component identi fication, determining sample composition, determining unit cells of sample components , refining crystal st ructures of known compounds and materials , determining crystal st ructures of new compounds and materials , and other applications known in the art . This characterization of the sample is more reliable and improved by using the dif f ractogram with a smaller contribution of aberration obtained by the method of the. subj ect invention .

Detai ls about preparing the. da taset for trai ning the mad line learning model

The dataset used for training the machine learning model is computed from known and/or simulated crystal structures . For each crystal structure , multiple, simulated di f f . ractogram with a greater contribution of aberration are calculated for various values of simulated contributions from the sample, instrument, and (simulated) instrument usage regarding the widths, shape, and intensity of diffraction peaks.

Computer programs commonly used in the art, such as GSAS, Fullprof, Fox, or custom-made programs, can be utilized to calculate simulated pairs of greater and smaller aberration contributions by appropriately selecting parameters for particle properties of the sample and contributions from the diffractometer to the widths and shapes of diffraction peaks.

Crystal structures for calculating simulated dif f ractograras are taken from publicly available databases such as the Crystallography Open Database or Bilbao Crystallographic Server, From the publicly available crystal structures dataset, it is advantageous to exclude those where atomic coordinates are not defined. Additionally, crystal structures with atomic arrangements that are deemed unexpected or non-physical by an expert skilled in the art should be removed. Furthermore, crystal structures of related substances, materials, or compounds the measured diffraction patterns of which are used in validating the model training should be omitted. Generating more than one dif f ractogram with a greater contribution of aberration for each individual crystal structure, with variations in peak widths or shapes, is advantageous for obtaining a larger dataset for training the model. This approach increases the number of pairs of diffraction patterns used for training the machine learning model, enhancing its overall performance. From the calculated pairs of simulated dif f raction patterns, additional pairs can be computed by calculating their linear combinations, simulating diffraction patterns of mixtures of crystal substances in appropriate ratios.

For training machine learning models with specific and specialized purposes, it is possible to limit the set of crystal structures . For example, one can choose only crystal structures that do not contain metal atoms with the goal of training a model specialized in improving the resolution, of dif f raction patterns of organic crystal substances . Similarly, it is possible to restrict the set of crystal structures to only those cont aining metal atoms , aiming to train a model speciali zed in enhancing the resolution of dif f ractograms of organometallic and metal-organic compounds and materials .

Apart from sorting by types of compounds and materials , pairs consisting of one simulated dif f ractogram with a greater contribution of aberration and one simulated dif f ractogram with a smaller contribution of aberration can be tailored for specific purposes and instruments by considering specific features of experimental measurements and specific properties or settings of the instrument . For example, simulated dif f ractogram ’with a great er contribution of aberration can be calculated for specif ic conf igurations of a chosen diffractometer, such as the Empyrean diffractometer from Panalytical . This allows obtaining a model tailored for processing input of dif f ractograms with a greater contribution of aberration measured with a specific diffractometer and its specific settings . The parameter values for the contributions of individual aberrations in the training dataset are selected to encompass expected values for samples whose measured dif f ractograms wil l be processed by the trained machine learning model . Without limiting to the mentioned aspects , the model can be specialized in mitigating specif ic aberrations or a set of aberrations to reduce the overlap of diffraction pea ks , for example , reducing the contribution of Kc<2 radiation in the diffract ion pattern, mitigating axial divergence to decrease the asymmetry of dif fraction peaks , or reducing the contribution of crystal domain size and strain . In one embodiment of the invention, when calculating the contribution of particle si ze to band widths , simulated dif f ractogram with a greater contribution of aberration are computed for crystal domain sizes randomly selected from the range of 40-250 nm . Similarly, values are chosen f or other cont ributions to widths , shapes , and intensities of diffraction bands aris ing from the sample , such as strain in the sample ( range of values from 0 to 0 . 005 radians ) or those arising from the instrument , such as the exposure time or recording time of the dif f ractogram, which is proportional to the total intensity of the di f fractogram and each individual band, the contribution of Ka2 radiation ( for instance , for radiation generated using an X-ray tube with a copper anode and a nickel foi l filter, the emission profile consists of two bands centered approximately at 1 . 541 A and 1 , 545 A . The intensity ratio is such that the first band is approximately twice as intense as the second one ) axia l divergence , the height, of the divergent and receiving slits , and other contributions known to an expert skilled in the art . Random values from the selected interval f or each parameter of the contribution of each aberration can be uniformly distributed or fol low another distribution within the chosen value range , such as , but not l imited to, Gaussian distribution or triangular distribution . In this way, various input s of dif fractogram with a greater contribution of aberrati on dif f ractograms are calculated from a single crystal structure which are paired with their corresponding simulated dif fractogram with a smaller contribution of aberration , In other embodiments of the invention, it is possible to choose different ranges of sample and instrument parameter values , as well as different distributions for the values of these parameters .

Pairs of dif f ractograms for training a machine learning model can be prepared to simulate a mixture of substances . The dif f ractogram, which simulates a mixture of substances , is a linear combination of simulated dif fractograms of pure substances in randomly chosen ratios . The target dif f ractogram is simulated with the a ssumption of an equal composition in the mixture as in the di f f ractogram with a greater contribution of aberration . By using such simulated dif fractograms of mixture samples , the variability in the set of training pa irs for the model is further increased . In one embodiment of the invent ion, to simulate di f fractograms of mixture samples , linear combinations of simulated dif fractograms from one , two, three , and four pure crystal phases are used . The ratios are randomly selected f rom a Dirichlet distribution, and the number of phases used in the mixture is randoml y chosen from the four mentioned possibilities .

Training pairs for the machine learning model can be prepared by adding a computationally generated background to the input of dif f ractogram with a greater contribution of aberration, aiming to simulate a dif f ractogram resembling a measured di f f ractogram. The target dif f ractogram with a smaller contribut ion of aberration may or may not have an added background, or the background may not need to be added to . In one embodiment of the invention, a background is added, having a constant i ntensity at all points of the dif f ractogram, and the ratio of the intensity of the generated background to the average intensity of the total dif f ractogram is randomly chosen from a range of possible values , where the l imits of the interval are estimated based on the ratio of the average intensity of the background to the average intensity representative of experimental dif fractograms to be processed by the model trained in this way .

Simulated pairs of dif fractograms for training the machine learning model may also include a contribution of simulated noise . The target dif f ractogram with a smal ler contribution of aberration is simulated without noise . Each experimental measu rement of a dif f ractogram also i ncludes a noise contribution, so it is advantageous to prepare an input of simulated dif f ractogram with a greater contribution of aberration with noise . Typically, this is noise corresponding to a Poi sson distribution parameterized by the measured intensity of each point of the dif f ractogram and is inherent to the process of measurement by detectors that count photons . The noise level used in calculating the simulated input dif f ractogram with a greater contribution of aberration is determined by randomly selecting values from the Poisson distribution based on the intensity value of each point of the dif f ractogram . Other types of noi se , such as but not limited to , Gaussian noise or uniform random noise , can a lso be used for training model purposes , Different combinations and ratios of these and other types of noise can also be used .

In one embodiment o± the subj ect invention, a model that is a neural network is trained using pairs of simulated dif fractograms , where noise is computationally generated on the dif fractogram with a greater contribution of aberration , which is provided as input to the neural network, whi le the target dif fractogram with a smaller contribution of aberration is simulated without computationally generated noise . In thi s way, the model is trained to ef fectively reduce or eliminate the contribution of noise when given as input a dif fractogram with a greater contribution of aberration containing noise .

Details about the machine learning model

The machine learning model used in the subj ect invention for processing the experimental powder dif f ractogram with a greater contribution of aberration of a sample and determining the output dif f ractogram with a sma ller contribution of aberration can be a neural network that can consist of convolutional and transposed convolutional layers , transformer encoder layers with self -attention mechanism, perceptron ( fully connected feedforward) layers , normalization layers , and non-linearity layers , among others . These layers can be chosen and connected in various ways . The model can also be based on an ensemble of multiple individual model s , such as the so-called "mixture of experts" , known to experts s ki lled in the art . In one embodiment of the invention , an ensemble of neural networks is used, trained on the same dataset . The dif f ractogram with a smaller contribution of aberration is determined as the average or median of the dif fractograms obtained by processing the input dif f ractogram with a greater contribution of aberration with the ensemble of neural networks . In the same embodiment of the invention, an ensemble of neural networks is used, where each network consists of the following sequence of layers :

• a sequence consisting of a Id convolutional layer, which maps intensity, log-intensity , and 2Theta to 256 channel s with a kernel si ze of 5 and stride of 1 , a ReLU nonlinearity, and batch normal i z a t. i o n ,

4 sequences each consisting of a Id convolutional layez from 256 to 256 channels with kernel size of 5 and stride of 2 , a ReLU nonlinearity, and batch normalization,

• a sequence consisting of 16 transformer encoder layers , each with a multi-head self -attention mechanism with 16 heads , a dimension of 256 , a feedforward layer with a hidden dimension of 1024 , and layer normalization,

• 5 sequences each consisting of Id transposed convolutional layers from 256 to 256 channels wi th kernel si ze of 5 and stride of 2 , a ReLU nonlinearity, and batch normalization, - a Id transposed convolutional layer from 256 to 2 channels with a stride of 1 and a kernel size of 5, with Softplus nonlinearity: two output channels represent intensity and uncertainty for each point in the dif fractogram predicted by th neural network at its output.

Details about the loss function

The training process also involves a loss function for optimizing the machine learning model, with the aim to minimize the distance computed by the loss function based on the model's output and the corresponding target dif fractogram with a smaller contribution of aberration. The loss function can be selected from various distance functions, such as conventional metrics like LI and L2, the R_wp function, or the so-called negative loglikelihood (NLL) . In one embodiment of the subject invention, the R_wp function was used as the loss function, taking the form o f :

where the summation is over jy points of the dif fractogram, the index targ denotes the intensity values of the target dif fractogram with a smaller contribution of aberration, and the index pred denotes the intensity values of the dif fractogram with a smaller contribution of aberration predicted by applying the machine learning model to the corresponding input dif fractogram with a greater contribution of aberration. In addition to the above, it is possible to use other loss functions; for example, to train a model that, in addition to ypred,i, also provides uncertainty factors o_Pred. i, the NLbRwp loss function was used, taking the form of

Details about the optimize

The optimizer of the loss function used in model training is an algorithm designed to reduce the value of the loss function by adjusting the model, i.e. , its internal parameters. It can be chosen from optimizers known in the art, such as, for example, but not limited to, SGD, Adam, or Adagrad. In one embodiment of the subject invention, the AdamW optimizer is used.

Details a b o u t app 1 yi n g the trained machine learning model to the measured dif f ractogram with a greater contribution ot aberration

In the application of this invention's method, the experimental dif f ractogram is collected and forwarded to the model (or ensemble of models) to determine the corresponding dif f ractogram with a smaller contribution of aberration. The obtained dif f ractogram with a smaller contribution of aberration is then utilized, for example, but not limited to, the analysis of the sample's crystal structure, qualitative or quantitative sample analysis, or other analyses known in the art (such as, but not limited to, unit cell refinement, crystal structure determination, crystal structure refinement) . In one embodiment of the subject invention, before being forwarded to the model, which is a neural network, the experimental dif f ractogram is processed by algorithms known to experts skilled in the art to remove the background, and instead of the removed background, a background of constant intensity, equal to the average intensity of the removed background, is added to the processed exp e r ime n t a 1 d 1. f f r a c t o g r am .

The invention enables obtaining a dif f ractogram with a smaller contribution of aberration based on the measured dif f ractogram wi th a greater contribution of aberration . The resulting higher- resolution dif fractogram, with reduced aberration contributions , cannot be obtained by measurement on the same diffractometer . In the existing state of the art , the identification of sample components and the structural characterization of these components are limited by the loss of information due to aberration contributions to diffraction peaks and the overlap of neighboring di ffraction peaks . By applying the methods of this invention, the obtained higher-resolution dif fractogram has reduced aberration contributions and reduced overlap of neighboring diffraction peaks . In comparison to the existing state of the art, this allows for an improved analysis of sampl es .

EXAMPLE 1

In one embodiment of the invent ion for processing experimental dif fractogram with a greater contributi on of aberration samples measured on the laboratory diffractometer Empyrean by Malvern Panalytical , the following contributions are used for calculating simulated dif f ractograms with a greater contribution of aberration for training the model , which is a neural network :

A set of Gaussian distributions in the domain of angular frequencies defined by :

where co is the angular frequency, 9 is half the 2Theta value, g_s is equal to 5.0.10"¹⁶, X is the wavelength of the emission line radiation, g_c is a value chosen front a triangular distribution with a left boundary and mode equal to 4.0.10^-8 and a right boundary equal to 2.5-10"⁷, and g_s is a value chosen from a triangular distribution with a left boundary and mode equal to 0, and a right boundary equal to 5.0.10”'*.

A set of Lorentz (Cauchy) distributions in the domain of angular frequencies defined by:

where c is the angular frequency, 9 is half of the 2Theta value, le 5.0-10”¹⁴, A is the wavelength of the emission line, l_c is the value chosen from a triangular distribution with left boundary and mode equal to 4.0-10"⁸ and right boundary equal to 2.5-10“', and Is is the value chosen from a triangular distribution with left boundary and mode equal, to 0, and right boundary equal to

set of emission orofile distributions defined

where i represents the ordinal number of the emission line, G previously defined Gaussian distribution, L previously defined Lorentz distribution, and the number of emission lines and the l_if /p g_ei? ? . values are known in the art; and specific to the emission profile obtained using an X-ray tube with a coppe anode

A set of axial divergence distributions defined at each 2Theta point (20_o)as:

where is 29 _o the 2Theta angle, y is the horizontal deviation of incident radiation,

is the axial angle of incident radiation, y is the axial angle of diffracted radiation, 29 is the equatorial angle of diffracted radiation, $ is the Dirac delta function, and £ is the transmission function of the optical elements of the diffractometer, which depends on the choice of optical elements, in this embodiment,

is chosen as the product of a triangular distribution with a mode of 0 and boundaries of ^=-0.04 and (p =0.04, and a triangular distribution with a mode of 0 and boundaries of y^:::-n and y^:::n, where n is a value chosen from a triangular distribution with a left boundary of 0.0367, a mode of 0.0401, and a right boundary of 0.0698.

A set of distributions of absorption aberration defined in the uencies by:

and where & is the angular frequency, 0 is half of the 2Theta angle, R is equal to 0.240, T is chosen from a uniform distribution with the left boundary equal to 1.0-10"⁴ and the right boundary equal to 2.0.10^-3 and u is chosen from a uniform distribution with the left boundary equal to 1.0-10² and the right boundary equal to 1.5-10³.

Temperature scaling factor, defined as:

where t i s chosen from a triangular distribution with a eft boundary and mode equal to 0, and a right boundary equal to 100 , an where is the wavelength of incident radiation and

f; is half of the 2Theta value.

EXAMPLE 2

The sample of sulfadiazine ( 4-amino-N-pyrimidift-2~yl- benzenesulfonamide) was gently homogenized in an agate mortar. The homogenized sample, was loaded into a 0.5 mm diameter Lindemann glass capillary for X-ray diffraction. Diffracted intensities were recorded on a laboratory diffractometer, Empyrean by Malvern Panalytical, with the following settings:

Trie collected intensities were recorded in the xrdml file format, and a file for the measured dif f ractogram was prepared using the instrument's software interface in the xy format suitable for evaluation with the trained machine learning model.

By the method of the subject invention, using the measured lower-resolution dif fractogram as input, a higher-resolution dif fractogram (hereinafter: enhanced dif fractogram) has been determined, as shown in Figures 1, 2, and 3.

To an expert skilled in the art, it is evident that the enhanced dif fractogram obtained by the method of the subject invention does not contain, or contains to a lesser extent, artifacts, aberrations, or undesirable contributions typically present in measured di f fractograms . Additionally, to an expert skilled in the art, it is clear that the enhanced dif f ractogram contains fewer artifacts , aberrations , or undes irable contributi ons ( such as the contribution of the wavelength of the Kct2 radiation ) compared to the results of the state of the art method based on subtracting the weighted second derivative , as shown in Figure

4 . This example demonstrates the advantage of the invention over the state of the art .

EXAMPLE 3

A diffractogram with a greater contribution of aberration was measured, and by applying the method of the subj ect invention, an enhanced diffractogram with a smaller contribution of aberration was determined as in Example 2 . Additionally, a diffractogram with a smaller contribution of aberration was measured compared to the measured diffractogram with a greater contribution of aberration using the ID22 instrument at the ESRF synchrotron ( hereinafter ref erred to as the synchrotron diffractogram) . Using known techniques (Rietveld refinement ) , the unit cell parameters of the crystal structure of sul fadiazine were refined against the measured, enhanced, and synchrotron dif f ractograms , and the standard deviat ions of these parameters were cal culated, as shown in Table 1 . From the refinement results , it is evident to an expert skil led in the art that the standard deviat ions of the parameter va lues obtained by refining against the enhanced diffractogram are more favorable than those obtained by refining against the measured diffractogram, and they are comparable to those obtained by refining against the synchrotron diffractogram. Furthermore , the unit cel l pa rameter values obtained by refining against the enhanced diffractogram are closer to the values obta ined by refining aga inst the synchrotron dif fractogram . Therefore , it fol lows that sources of uncertainty ( i . e . , aberrations ) typically present in the measured dif f ractogram with a greater contribution of aberration are significantly reduced in the enhanced dif fractogram. This example demonstrates the appli cation of the invention in producing data of smaller contribution of aberration, accuracy, and reli ability than is achievable solely using a laboratory instrument .

EXAMPLE 4

A dif fractogram with a greater contribution of aberration was measured, and by applying the method of the subj ect invention, an enhanced dif fractogram with a smaller contribution of aberrat ion was determined as in Example 2 , but using a sample of silver sulfadiazine ( silver ( 4 -aminophenyl ) sulf onyl-pyrimidin~2- ylazanide ) .

Furthermore, using methods known in the art, automatic indexing, peak position and intensity extract ion of diffraction peaks , and solving the crystal structure using the direct method, specifically the resolution bias modification, were performed . This was implemented in the computer program Expo2014 , using commands Intreor, %extraction, and %alltrials , with the composition of the unit cell Ag4C40H36N16O8S4 .

For the measured dif fractogram with a greater cont ribution of aberration, a crystal structure with a residual structure factor (RF) of 0 . 4169 was obtained, and the three-dimensional arrangement of atoms is shown in Figure 5.

For the enhanced dif fractogram with a smaller contributi on of aberration , whi ch was obtained us ing the method of the subj ect invention ,

crystal structure with a residual structure factor (RF) of 0 . 2925 was obtained, and the three-dimensional arrangement of atoms is shown in Figure 6 .

To an expert ski l led in the art, it is evident from the presentation in Figure 5 that the crystal structure obtained f rom the measured dif f ractogram with a greater contribution of aberration does not represent a phys ically meaningful crystal structure or chemical species , while the crystal structure shown in Figure 6 obtained from the di f f ractogram with a smaller contribution of aberration using the method of the subj ect invention represents a physically meaningful crystal pha se and the specif i c chemical species of silver sulfadiazine , with minor variations in atomic positions and identities of atoms with close atomi c numbers (e . g . , nitrogen, carbon, oxygen ) expected by an expert skilled in the art . This example also demonstrates the application of the subj ect invention in identifying unknown powder samples and determining new crystal structures .

EXAMPLE 5

A dif f ractogram with a greater contribution of aberration was measured, and by applying the method of the subj ect invention, an dif f ractogram with a smaller contribution of aberration was determined as in Example « , but with modified diff ractometer settings :

The further procedure is the same as in Example 4 .

For the measured dif f ractogram with a greater contribution of aberration , a crystal structure with a residual structure factor (RF) of 0. 4171 was obtained , and the three-dimensional arrangement of atoms is shown in Figure 7 .

For the di f fractogram with a smaller contribution of aberration of higher resolution , a crystal structure with a residual structure factor (RF) of 0 . 4032 was obtained , and the three- dimensional arrangement of atoms is shown in Figure 8 .

As in Example 4 , it is clear to an expert skilled in the art from the presentation that the crystal structure obtained from the measured dif f ractogram with a greater contribution of aberration does not represent a physically meaningful crystal structure, whi le the crystal structure obtained from the dif fractogram with a smaller contribut ion of aberration using the method of the present invention represents a phys ica lly meaningful crysta l phase and the specific chemical species of silver sulfadiazine , with minor variations in atomic positions , atomi c arrangement , and identities of atoms of chemical elements with close atomic numbers ( such as nitrogen, carbon, oxygen ) expected in the art . This example demonstrates the industrial application of the invention in faster identifi cation of unknown samples , even with an exceptional ly short measurement time of 5 minutes , which is considered extremely short by an expert s killed in the art and results in high noise in the dif f ractogram with a greater contribut ion of aberration .

EXAMPLE 6 A dif f ractogram with a greater contribution of aberration was measured for the sample of 4-amino-N-[2-(3- aminopropanoylamino) ethyl] butanamide dihydrochloride (Figure 9) , for which, to the best of knowledge of the authors, the crystal structure has never been determined and using the method of the subject invention, an enhanced dif f ractogram with a smaller contribution of aberration was determined, The assumed unit cell composition was C18O4N8C14H46.

The further procedure for solving the crystal structure was the

S3rn S 3-S in Example 5

For the measured dif f ractogram with a greater contribution of aberration, the structure-solving procedure failed because no unit cell describing the positions of diffraction peaks was found.

For the enhanced dif f ractogram with a smaller contribution of aberration, a unit cell with parameters a = 16.5715 A, b = 8.9909 A, c - 4.7023 A, a - 102.23° , p == 95.59°, y - 78.91° was obtained, and the crystal structure with a residual structure factor (RF) of 0.4912, and the three-dimensional arrangement of atoms is shown in Figure 10.

As in Example 3, it is evident to an expert skilled in the art that the crystal structure obtained from the dif f ractogram with a smaller contribution of aberration represents a physically meaningful crystal phase and the specific chemical species close to the dif f ractogram with a greater contribution of aberration, with minor variations in atomic positions, atomic arrangement, and identities of atoms of chemical elements with close atomic numbers (e.g, , nitrogen, carbon, oxygen) that are expected by an expert skilled in the art. This example demonstrates the industrial application of the subject invention in rapid (-5 min) identification, and characterization of unknown samples, intermediates , impurities , etc . , which is essential in the chemical and pharmaceut ical industries . Final ly, to an expert skilled in the art , the advantage of the invent ion over conventional, powder X-ray diffraction analysis methods using 1 a b o r a to r y .1 n s t r ume n t s .1 s e v i d e n t .

EXAMPLE 7

The number of crystal structures used to calculate pairs of simulated dif f ractograms is greater than 100 000 , and the total number of pairs of simulated dif f ractograms for training the model is greater than 1 , 000 000 .

EXAMPLE 8

The number of crystal structures used to calculate pairs of simulated dif f ractograms is greater than 500 000 , and the total number of pairs of simulated dif fractograms for training the model is greater than 50 000 000 .

INDUSTRIAL APPLICATION OF THE INVENTION

The invention i s applicable to the analysis of powder dif f ractograms for the purpose of identifying sample components, determining sample composition, refining or determining the unit cell of sample components , refining or determining the crystal structure of sample components, and other macroscopic and microscopic properties of crystal l ine substances , mixtures of crystalline substances , or mixtures of crysta ll ine and noncrystalline substances in the pharmaceutical industry, chemical industry, f ood indust ry, metallurgy, and related industries . Furthermore , the invention is appl icable in research and development aspects related to industry and science, indue ling issues in analytical chemistry, materials chemistry, solid-state chemistry, organic chemistry, inorganic chemistry, solid-st late physics, and related fields.

Example: The methods of the subject invention are applied in the analysis of drug samples to determine the crystal structure of the active substance, impurities remaining in the active substance from production, undesired changes in the active substance resulting, for example, from moisture absorption, chemical degradation, oxidation, or changes in polymorphic form.

Example: The methods of the subject invention are used in high- throughput methods for optimizing the synthesis process, searching for solid forms of pharmacologically active substances, pesticides, herbicides, conductors, semiconductors, superconducting materials, composite materials, photovoltaics , luminescent materials, photochromic and thermochromic materials, catalysts, precursors, ionic compounds, salts, covalent compounds, metals and alloys, multicomponent solid substances, and other substances.

Example: The methods of the subject invention are used in the process monitoring of the identity and composition of a solid product over time in mechanochemical reactions, reactions in suspension, and similar processes.

Example: The methods of the subject invention are used in the process monitoring of the identity and composition of a sample as a function of temperature, pressure, atmosphere, magnetic field, electric field, or other external parameter. Example: The methods of the subject invention are used in the analysis of newly synthesized ceramics to determine the phase composition, size of crystalline domains, and stresses.

Example: The methods of the subject invention are used in the analysis of geological samples, minerals _f and other samples of natural origin, not necessarily from planet Earth.

Example: The methods of the subject invention are used in the analysis of materials from various machines and devices.

Claims

PATENT CLAIMS

1. A method for reducing aberrati on contributions in a dif fraction pattern , characteri zed by :

( a ) A neural network trained using pairs of simulated dif f ractograms consisting of dif f ractograms with a greater contribut ion of aberrat ions and target dif f ractogram with a smaller contribution of aberrations ,

(b) In the process of training the neural network, simulated dif f ractograms with a greater contribution of aberrations are provided to the model as input , and the loss function i s calculated between the model ’ s output and the corresponding simulated target dif f ractogram with a smaller contribution of aberrations ,

(c) The neural network is adj usted during the training process to optimize the loss f unction,

(d) The measured dif f ractogram with a greater contribution of aberrations is provided as input to the neural network, which determines the dif f ractogram with a smaller c o n t r i b u t ion of aberrations . The method according to claim 1 , characteri zed in that the diff ractogram with a greater contribution of aberrations within each training pair for the neura l network is calculated taking into account the contributions of dif fraction peaks originating from the crystal structure .

The method according to claims 1 and 2 , characterized in that the dif f ractogram with a greater contribution of aberrations within each training pai r for the neural network is calcu lated taking into account the f eatures of the diffractometer and the characteristics of the diffractometer .

4 The method according to cl a ims to 3 , characterized in that the dif f ractogram with a greater contribution of aberrations within each training pair for the neural network is calculated taking into account the geometry of the diffractometer .

The method according to claims 1 to 4 , characteri zed in that the dif f ractogram with a greater contribution of aberrations ’within each training pair for the neural network is cal c u 1 a t e d t a k i n g into account the measurement settings of the d i f f r a c t ome t e r . The method according to claims 1 to .5 , characterized in that the dif f ractogram with a greater contribution of aberrations within each training pair for the neural network is calculated taking into account the features of the part icle properties of the sample .

The method according to claims 1 to 6 , characterized in that the dif fractogram with a greater contribution of aberrations and dif fractogram with a smaller contribution of aberrations are prepared as mixtures of more than one crystal l ine phase .

The method according to claims 1 to 1 , characterized in that a background is added to the dif f ractogram with a greater contribution of aberrations within each training pair for the neural network .

The method according to claims 1 to >3 , characterized in that the dif fractogram with a greater contribution of aberrations and dif fractogram with a smaller contribution of aberrations within each training pair for the neural network has an added background . The method according to claims 1 to 9 , characteri zed in that the dif fractogram with a greater contribution of aberrations within each tra ining pair for the neural network has added noise .

11 . The method according to claims 1 to 10 , characterized in that the dif fractogram with a greater contribution of aberrations has added noise, and the target dif f ractogram with a smaller contribution of aberrations is the same dif fractogram without added noise .

12 . The method according to claims 1 to 11 , characterized in that the dif fractogram with a greater contribution of aberrations contains simulated aberrat ion arising from sample features or dif fractometer features, and the dif fractogram with a smaller contribution of aberrations does not contain aberration arising from sample features or dif fractometer features .

13 . The method according to claims 1 to 12 , characterized in that the dif fractogram with a greater contribution of aberrat ions is simulated taking into account the features of a specific di ffractometer and measurement method .

14 . The method according to claims 1 to 13 , characterized in that it uses the dif fractogram with a smaller contribution of aberrations for the purpose of identi fying the components of the sample .

15 . The method according to claims 1 to 14 , characteri zed in that it uses the dif fractogram with a smaller contribution of aberrations for the purpose of determining and refining the unit cell of components in the measured sample .

16. The method according to claims 1 to 15 , characteri zed in that it uses the dif f ractogram with a smaller contribution of aberrations for the purpose of solving the crystal structure from powder dif f ractograms .

17 . The method according to claims 1 to 16 , characterized in that it uses the dif f ractogram with a smaller contribution of aberrations for the purpose of refining the crystal structure of the components of the sample .

18 . The method according to claims 1 to 17 , characterized in that the sample dif f ractogram is measured on a device equipped with an X-ray source, a sample holder, an X-ray detector, and a computer for device control . The sample on the sample holder is irradiated with X-rays from the X-ray source, and the intensity of radiation is measured as a function of scattering angle using the X-ray detector .