X-ray diffraction method for analysis of amorphous and semi-crystalline materials

Abstract

To provide an apparatus and a method for performing X-ray diffraction analysis of an amorphous material and / or a semi-crystalline material.SOLUTION: A method includes the steps of: a) providing a sample, wherein the sample is a semi-crystalline material or an amorphous material, and the material comprises an amorphous region; b) providing a polychromatic X-ray source; c) collimating X-rays from the X-ray source into one or more pencil beams; d) diffracting the beams by exposing at least a region of the sample to the one or more pencil beams; e) collecting at least a portion of the diffracted beams at one or more energy dispersive 2D detectors to obtain one or more diffracted images; and f) analyzing the obtained diffracted images to determine internal strains and / or stresses in at least the exposed region of the sample, wherein the analysis comprises analyzing diffracted signals from the amorphous region of the sample.SELECTED DRAWING: Figure 1B

Description

[Technical Field]

[0001] The present disclosure relates to the field of X-ray diffraction, and in particular to methods and apparatus for performing X-ray diffraction analysis of amorphous and / or semi-crystalline materials. [Background technology]

[0002] Since the 1920s, X-ray diffraction has been the primary method for determining the arrangement of atoms in minerals and metals. X-ray diffraction probes interatomic distances. In crystalline materials, variations in interatomic distances represent elastic strain on larger length scales, which is relevant when assessing material strength. In the elastic regime, the relationship between stress and strain is given by a generalized version of Hooke's law. This law states that the strain (deformation) of an elastic object or material is proportional to the applied stress. By measuring multiple projections and combining this with X-ray imaging principles, maps of all six components of the strain tensor can be obtained.

[0003] Mapping elastic strain in 1D, 2D, or 3D is important because mechanical failure of a product typically occurs in regions of high strain. Macroscopic strain can be observed directly from the surface of a material or can be achieved using other tools. It is limited to an average of behavior throughout the bulk of the sample and very local behavior in the skin region. Therefore, we are more interested in mapping the microscopic strain of a material. Microscopic strain is the elongation of the atomic structure relative to a zero-strain state. The atomic structure consists of both intrachain bonds within a single molecule and interchain bonds between molecules. The intrachain bonds are usually shorter and stronger. The implication of microscopic strain is that because each bond has a preferred length, a force is required to stretch or compress the bonds away from their equilibrium state, thus indicating the presence of residual internal stress within the material.

[0004] Strain can be induced in a product during the manufacturing process or during use. Industry is often interested in mapping the internal stresses imposed during manufacturing. Internal stresses can affect atomic structures in two ways. First, bonds in the direction of the stress are stretched, while bonds perpendicular to the stress are compressed (the most common case of a positive Poisson's ratio). Second, molecules rotate to accommodate the stress; that is, they orient themselves so that the weakest bonds are in the direction of the highest stress. Therefore, there is interest in mapping the stress / strain distribution within a product during the design process and / or during manufacturing quality assurance and / or wear. Generally, the relationship between stress and strain is given by Hooke's Law. Therefore, internal stress can be inferred from internal strain, and vice versa.

[0005] However, not all materials are crystalline. As an example, most polymers are semi-crystalline or amorphous. Examples of semi-crystalline polymers include linear polyethylene (PE), polyethylene terephthalate (PET), polytetrafluoroethylene (PTFE), or isotactic polypropylene (PP). The crystallization of a polymer is a process associated with the partial alignment of its molecular chains. The ordered division of molecular chains within a polymer is characterized by its degree of crystallinity. Polymers can crystallize upon cooling from the melt, mechanical stretching, or solvent evaporation, and crystallization typically affects the polymer's optical, mechanical, thermal, and / or chemical properties.

[0006] Currently, there are no methods for determining strain maps for polymers similar to those for crystalline materials. Some information may be obtained from surface analysis or by destructive methods (e.g., by drilling holes). However, for all existing methods, it is not possible to obtain a complete, spatially resolved strain map. Therefore, there is a need for improved methods that can determine the global strain map of polymers.

[0007] To date, X-ray diffraction signals obtained from amorphous materials or the amorphous regions of semi-crystalline materials have not been considered suitable for obtaining strain maps with the accuracy necessary to determine the internal strain of the material. Prior art studies have considered only the strain in the crystalline phase of semi-crystalline materials, and the response of the amorphous phase of the material is usually inferred from model interpretations.

[0008] Therefore, there is a need for improved methods and analytical tools that can determine the elastic strain of amorphous regions of amorphous and / or semi-crystalline materials based on diffraction signals obtained from the materials, as well as apparatus that can provide an experimental platform for carrying out said methods. Summary of the Invention

[0009] The present disclosure addresses the aforementioned needs by providing a method and apparatus for X-ray diffraction analysis of amorphous and / or semi-crystalline materials, the method being capable of providing an internal strain map of at least exposed regions of the material, even in amorphous regions of the material.

[0010] This is achieved, among other things, by providing several unique and novel analytical methods capable of extracting material properties of semi-crystalline and amorphous materials based on the diffraction signals from the sample. Previous efforts have considered the diffraction signals from amorphous regions to be too broad or too weak to be used as a basis for analyzing the material properties of the investigated material. However, the inventors have found that material properties (e.g., internal strain) of amorphous materials or amorphous regions of semi-crystalline materials can be determined using the disclosed apparatus and methods. The ability to analyze the diffraction signals from amorphous regions is further facilitated by the use of one or more prior art energy dispersive detectors, which the inventors have found to be particularly well-suited for this purpose. This further allows for the use of polychromatic X-ray sources rather than the monochromatic X-ray sources typically encountered in X-ray diffraction experiments.

[0011] X-ray diffraction is typically used to study crystalline materials because the crystallinity of a material results in a diffraction pattern with distinct, sharp peaks from which material properties (e.g., lattice constants) can be inferred. In contrast, the diffraction signals from amorphous regions in amorphous or semi-crystalline materials are broader and weaker than those obtained from crystalline regions or materials. As a result, to date, it has not been possible to determine the molecular structure or internal strain of, for example, a semi-crystalline polymer based on an amorphous X-ray diffraction signal. However, by using the apparatus and methods described herein, information related to the material properties of amorphous or semi-crystalline materials (e.g., internal strain in semi-crystalline polymers) or biological tissues (e.g., implants and muscle) can be obtained.

[0012]

[0003] Accordingly, the present disclosure relates to an X-ray diffraction method for analyzing amorphous and / or semi-crystalline materials, the method comprising the steps of: preparing a sample, the sample being semi-crystalline or amorphous, the material containing at least one amorphous region; providing a polychromatic X-ray source; collimating X-rays from the X-ray source into one or more pencil beams; diffracting the beam(s) by exposing at least a region of the sample to the one or more pencil beams; collecting at least a portion of the diffracted beams in one or more energy-dispersive 2D detectors to obtain one or more diffraction images; and analyzing the obtained diffraction image(s) to determine internal strain and / or stress in at least the exposed region of the sample, the analysis including analyzing diffraction signals from the amorphous region of the sample. Any of the steps in the method may be optionally repeated to obtain one or more diffraction images from different regions of the sample or for different states of the sample. Furthermore, the steps of preparing the sample and the X-ray source may be performed in any order. The various conditions may relate to conditions in the environment of the sample (e.g., ambient temperature and / or humidity, or gases introduced into the environment of the sample), or the condition of the sample may relate to external strains imposed on the sample.

[0013] The internal strain of a sample may be extracted from a diffraction image in several ways according to the disclosed method. Typically, for all disclosed analytical methods, a characteristic pattern is obtained (e.g., similar to that shown in FIG. 7). As an example, the pattern may show the intensity of the diffraction signal versus the Q-factor. For crystalline samples, this pattern includes one or more sharp intensity peaks. For semi-crystalline or amorphous samples, the peaks are typically broader than those of crystalline samples (see FIG. 8, which shows data from an amorphous sample). The overall pattern can be attributed to a radial position, which is determined (alternatively, the position of one or more intensity peaks in the pattern is determined, e.g., the first and / or second diffraction peaks). This position directly correlates to the bond length in the sample. In some cases, the unstrained bond length of the sample material is known a priori. In such cases, the strain is determined directly by comparing the radial position of the pattern to the unstrained bond length. In other cases, the method and analysis are performed on multiple subvolumes of the sample. The position of the characteristic pattern is shown for each subvolume. By comparing the positions obtained for various volumes, it is possible to identify volumes within the sample where the strain is significantly higher or lower than the rest of the sample.

[0014] Thus, the disclosed method does not rely on imposing an external strain on the sample to assess internal strain. Instead, applicants have discovered that the location of intensity peaks (e.g., the first and / or second diffraction peaks) in characteristic patterns (e.g., those shown in Figures 7 and 8 ) can be used to infer internal strain (magnitude and / or direction). This can be done from a single measurement (i.e., a single diffraction image). Figure 9 shows how the location of the peak(s) varies among different levels of strain (the graph shows various curves for different values ​​of strain; the curve for no strain is subtracted from each curve to obtain a difference signal). Although the method works on a single diffraction image, applicants performed a series of experiments to verify the disclosed method by varying the internal strain (by imposing an external strain on the sample).

[0015] Another analytical method involves decomposing the azimuthal distribution of the diffraction signal. 1D diffraction patterns from orthogonal azimuthal angles arise from orthogonal bonds in the sample. The combined internal strain in three dimensions can be decomposed into a nine-component strain tensor with symmetry relative to six components. These components can be calculated from the azimuthal distribution of pattern positions. Therefore, the first part of the analytical method may include determining the radial position of the characteristic pattern obtained from the diffraction signal, since this position correlates with the bond length in the sample.

[0016] The second part of the analysis method involves determining the intensity of the characteristic pattern(s). By way of example, this can be achieved by determining the height of the peak(s) within the pattern(s), but also by determining the area of ​​the pattern (e.g., by integration). The intensity distribution is related to the scattering cross section of the material (i.e., how well the material scatters photons) and the density of bonds corresponding to that particular pattern. By determining the azimuthal distribution of intensity, the angular distribution of bonds can be determined. For each measurement interaction volume, the angular distribution is most often isotropic in the strain-free case. Therefore, an anisotropic distribution indicates internal strain.

[0017] Amorphous regions consist of molecules with the same atomic structure as crystalline regions, but the ordered molecules have shorter distances; that is, they are not aligned with each other in the same way in any significant region. Even if the molecules are not arranged in the same structure, they are still connected by molecular bonds. The bonds are usually observed to vary in length due to structural inconsistencies. On the other hand, because the molecules are not distributed completely randomly, bond lengths can be obtained from 1D diffraction patterns obtained from amorphous regions. However, the obtained bond lengths are usually associated with a larger uncertainty compared to crystalline regions.

[0018] All of the analytical methods disclosed herein can be used in the previously disclosed methods for analyzing semi-crystalline materials.

[0019] The present disclosure further relates to an apparatus for performing X-ray diffraction analysis of semi-crystalline materials, the apparatus including a polychromatic X-ray source, a collimator configured to collimate X-rays from the polychromatic X-ray source into one or more pencil beams, a stage for holding the sample, and one or more energy dispersive X-ray detectors. The apparatus may further include an optical element configured to be displaced along an optical axis 6 of the apparatus to provide depth information of the sample. The apparatus is preferably configured such that any of the X-ray diffraction methods for analyzing semi-crystalline materials disclosed herein may be performed using the apparatus.

[0020] The present disclosure further relates to a computer-implemented method for analyzing X-ray diffraction images of amorphous and / or semi-crystalline materials, the method comprising the steps of providing a plurality of X-ray diffraction images acquired from a semi-crystalline sample, optionally extracting one or more 1D diffraction patterns from said diffraction images, determining the positions of one or more intensity peaks in the diffraction images and / or 1D diffraction patterns, comparing said position(s) with similar intensity peaks acquired at different strain levels or in other regions of the sample, calculating the difference(s) between the positions of the peaks, and determining the internal strain in at least one region of the sample based on said difference(s).

[0021] The analysis preferably considers the entire diffraction pattern that may be formed from diffraction signals from all phases of the material (i.e., both the amorphous and crystalline phases of the material). The analytical methods of the present disclosure are preferably suitable for analyzing both the amorphous and crystalline phases of the material. 1D pattern(s) are preferably determined for multiple directions, and the difference(s) between the directions are preferably then analyzed as a signature for strain and structure within the material.

[0022] The present disclosure further relates to a computer-implemented method for analyzing X-ray diffraction images of amorphous and / or semi-crystalline materials, the method including providing one or more X-ray diffraction images acquired from the amorphous and / or semi-crystalline sample; extracting one or more azimuthal intensity distributions from the diffraction images; determining positions of one or more intensity peaks in the diffraction azimuthal intensity distributions, the positions specified by azimuthal angles; and determining an internal strain direction and / or an internal strain level in at least a region of the sample based on the positions of the intensity peak(s).

[0023] The present disclosure further relates to a computer program having instructions that, when executed by a computing device or system, cause the computing device or system to analyze an amorphous or semi-crystalline material by performing any of the computer-implemented methods for analyzing X-ray diffraction images of semi-crystalline materials disclosed herein. [Brief explanation of the drawings]

[0024] [Figure 1A] 1 is a schematic diagram of an apparatus for X-ray diffraction analysis according to the present disclosure. [Figure 1B] FIG. 1 is a schematic diagram of an apparatus for X-ray diffraction analysis according to the present disclosure, showing optical elements positioned in the beam path between the sample and the detector. [Figure 2] FIG. 1 shows the diffraction signal collected on an energy dispersive detector. [Figure 3] FIG. 10 illustrates how the diffraction signal can be acquired into the distinct energy bins required to analyze the diffraction signal. [Figure 4] Diffraction patterns collected on an energy dispersive detector for a range of energies, showing the radial direction r and the azimuthal direction η in 2D images. [Figure 5] FIG. 10 shows the intensity of the diffraction signal versus the diffraction angle for different energy bins. [Figure 6a]FIG. 1 shows how energy resolved signals can be ordered by their scattering vector length Q. In this illustration, the patterns for each energy bin are aligned. [Figure 6b] FIG. 1 shows how the diffraction signals from each energy bin can be combined into a single signal with increased signal-to-noise ratio by using the scattering vector Q. The graph is formed from a superposition of the signals from each energy bin, achieving increased signal-to-noise ratio. The intensity is a function of the common scattering vector Q. [Figure 7] 1 shows the diffraction signal from a polyethylene (PE) sample. The plot shows a graph of signal intensity versus Q value and indicates the numbering convention for the peaks in the diffraction pattern. [Figure 8] 1 shows the diffraction signal from an amorphous sample (atactic polystyrene), where the plot shows a graph of signal intensity versus Q value. [Figure 9a] 1 shows a series of diffraction signals from a PE sample taken at an azimuthal angle parallel to the stretch direction, where the sample was stretched in discrete steps and a diffraction signal was acquired at each step. Each plot is formed by subtracting the diffraction signal acquired for a particular strain level from the diffraction signal of the unstrained sample. [Figure 9b] Figure 1 shows a series of diffraction signals from an amorphous sample (atactic polystyrene) stretched in discrete steps, with each curve corresponding to a particular strain level (indicated by the grey scale) and the diffraction signal of the unstrained sample subtracted. [Figure 10] Zoom-in of the first diffraction peak (FDP) in Figure 7. The two curves correspond to two different strain values. The peak shifts to lower Q values ​​with increasing strain. [Figure 11] A zoom-in of the secondary diffraction peak (SDP) in Figure 7 is shown. The two curves correspond to two different strain values. The peak shifts to lower Q values ​​as the strain increases. [Figure 12]1 shows the experimental diffraction signal on an energy dispersive detector, the center of which is blocked by a beam stop to reduce unwanted scattering from the detector material. [Figure 13] Figure 11 shows the diffraction signal. An optical element (here a mask) was used to block a portion of the diffraction signal from the sample. This particular mask has an opening that allows scattering angles of 9 to 11.5 degrees through the mask. [Figure 14] FIG. 13 shows the intensity of the diffraction signal versus the azimuthal angle of the diffraction rings shown in FIG. 12 for various degrees of stretching of the sample. [Figure 15] The ratio of the azimuthally resolved shift in the diffraction peak between the intensity distributions for two different levels of engineering strain is plotted along with the fit of a sine function (solid curve). The factors of each term correspond to components in the strain tensor. [Figure 16] FIG. 15 shows the amplitude of the sinusoidal fitting function of FIG. 14 plotted as a function of macroscopic strain. A linear relationship is observed. [Figure 17] Figure 17 shows a plot similar to that shown in Figure 16, but with data from an amorphous sample. Thus, similar behavior is observed in the amorphous sample. [Figure 18] 1 shows experimental results achieved using a synchrotron as the X-ray source. The plot shows the relative shift in polymer chain link distance with respect to the internal strain direction of the material and with respect to the engineering strain of the sample. [Figure 19] Comparison of diffraction patterns obtained using two different experimental setups. Each setup contains a different X-ray source: one uses a synchrotron, the other a polychromatic laboratory X-ray source. The figure shows the contribution from the polychromatic source and the energy resolution of the detector in a less resolved diffraction pattern. [Figure 20] 10 is a schematic diagram of a mask design according to an embodiment of the optical element 7. FIG. [Figure 21]FIG. 1 shows an example of an array of four energy dispersive detectors, said array being compatible with the apparatus and methods of the present disclosure. [Figure 22] FIG. 10 shows the radial intensity of the diffraction signal on a portion of the detector versus the position of a mask placed in the beam path to block a particular portion of the diffraction signal. [Figure 23] FIG. 1 shows the diffraction signal from a point in a sample, where the signal has been reconstructed using a mask and a reconstruction algorithm. [Figure 24] FIG. 1 shows a series of diffraction signals where the beam size (BS) is varied between each successive diffraction signal.

[0025] definition A 2D diffraction pattern is understood to be a diffraction image formed by collecting the diffraction signals on a 2D detector.

[0026] A 1D diffraction pattern is understood as a 1D plot of the intensity of the diffraction signal collected at the detector. The intensity may be plotted against any suitable parameter (e.g., scattering angle, Q factor, direct spatial parameter, or azimuthal angle).

[0027] A strain map can be understood as a mathematical object with the same dimensions as the sample divided into smaller regions, each corresponding to a volume within the sample. Each region is assigned a strain tensor measured in the corresponding part of the sample. Collectively, the regions cover the entire volume of the sample.

[0028] The terms 2D diffraction pattern and diffraction image are used interchangeably.

[0029] The phrase "similar peaks" or "similar intensity peaks" refers to one or more peaks, each peak identified in at least two different diffraction patterns, wherein the location of said peaks is approximately the same between the at least two diffraction patterns.

[0030] Diffraction rings are understood to be approximately circular rings or annuli in a diffraction image. In other words, the term "diffraction rings," as used herein, is not limited to discrete lines formed in a circular shape, but may refer to annuli. DETAILED DESCRIPTION OF THE INVENTION

[0031] The present disclosure relates to an apparatus and an X-ray diffraction method for analyzing amorphous and / or semi-crystalline materials. The present disclosure further relates to a number of different analytical methods that may form part of the X-ray diffraction methods described herein.

[0032] Device The apparatus of the present disclosure preferably includes a polychromatic X-ray source 1 configured to emit X-rays 8, a collimator 2 configured to collimate the X-rays emitted from the source, a stage 4 for holding a sample 3, and one or more energy dispersive detectors 5. A schematic diagram of the apparatus is shown in FIG. 1A. The apparatus described herein is suitable for facilitating X-ray diffraction methods according to the present disclosure. That is, the apparatus is suitable for providing one or more diffraction images from a sample, as specified herein. The diffraction images may then be analyzed using novel analytical methods described below.

[0033] The X-ray source 1 is preferably a polychromatic X-ray source. An example of a suitable X-ray source is a 160 kV, 1.8 kW industrial X-ray tube (W tube) from COMET Industrial X-Ray. The use of a polychromatic X-ray source reduces the cost of the equipment, since high-energy monochromatic X-ray sources typically require synchrotron facilities, which often entail significant costs. The energy of the X-rays emitted by the source is typically in the range of 1-100 keV, depending on the thickness of the sample. The energy resolution is typically 1 x 10, depending on the energy used in the experiment. -2 The order is:

[0034] The collimator 2 for collimating the X-rays from the source may be a collimator, a condenser, a slit, or a combination thereof. The purpose of collimation is to collimate the X-rays from the X-ray source into one or more pencil beams, which are preferably substantially parallel to the optical axis 6 of the device.

[0035] The stage 4 for holding the sample 3 may be any platform suitable for this purpose. Preferably, however, the stage includes a goniometer that can rotate the sample to a precise angular position. The stage may also be an electromechanical goniometer stage. Preferably, the stage is further capable of providing a controlled environment (e.g., in terms of temperature, humidity, etc.).

[0036] detector The energy-dispersive detector(s) 5 used in the disclosed method and apparatus must be suitable for detecting X-rays impinging on the detector. Typically, X-rays emitted from a polychromatic X-ray source include a wide range of photon energies. As a result, the intensity distributions of diffraction signals associated with different scattering angles correspond to significant overlap in photon energies, as is evident from FIG. 5 . The inventors have realized that by using one or more energy-dispersive 2D detector(s), each capable of spectrally resolving the collected diffraction signal, the signal can be divided into multiple energy bins. The use of energy bins is advantageous when analyzing acquired diffraction patterns, especially when combined with the use of a Q-factor, which expresses energy and scattering angle in a single number given by the following equation:

[0037]

number

[0038] Preferably, the detector comprises an array of energy-dispersive detectors. The array may include multiple detectors, e.g., two, four, or more than four. Preferably, the detector sensitivity area is large enough to cover the entire first-order diffraction ring. Even more preferably, the detector is large enough to cover both the first-order and second-order diffraction rings. As an example, the device may include four energy-dispersive detectors arranged in an array (schematically shown in FIG. 19). Each detector may include a number of pixels defining a resolution. As an example, each detector may include 256 × 256 pixels, sufficient to cover the entire diffraction ring, corresponding to a spatial resolution of 0.5% and an energy resolution of approximately 2%. Preferably, when multiple detectors are arranged in an array, the detectors are arranged such that the center beam can pass uninterrupted through the detector array. This is due to the fact that the center beam is approximately 1000 times more intense than the beam scattered from the sample, and if the center beam were to strike the detector, unwanted scattering could occur from the detector material. Thus, the detector or array of detectors may include an aperture, which is preferably aligned to coincide with the central beam and / or optical axis 6 of the device. Alternatively, the device may include a beam stop configured to block the central beam, which beam stop is positioned on the optical axis 6 between the sample and the detector.

[0039] Preferably, the detector(s) used in the disclosed devices and methods are configured to simultaneously determine the detection of signals at adjacent pixels using very precise timing of the detected signals, allowing potential crosstalk to be weighed against fluorescence peaks to correct for charge sharing.

[0040] Optical elements The apparatus may further include an optical element 7 configured for displacement along the optical axis 6. Such a configuration is shown in FIG. 1B. The optical element may include an optical mask configured to block a portion of the diffracted X-rays 9 from the sample. The portion of the diffracted X-rays has a scattering angle greater than 0°. In one embodiment, the optical element is circularly symmetric, although other geometries may be used. The blocked portion of the diffracted X-rays may have a scattering angle greater than 0°, or greater than 2°, or greater than 5°, or greater than 10°, or greater than 20°, or greater than 30°, or a scattering angle greater than 40°. However, scattering angles typically encountered using the disclosed apparatus and methods are between 2 and 70°, preferably between 2 and 20°, or even more preferably between 2 and 50°. Thus, while the beam stop is configured to block the center beam, the optical elements disclosed herein are configured to block a portion of the diffraction pattern that would otherwise appear in the diffraction image on the detector. As an example, a mask pattern on an optical mask may include regions such as rings (shown as dark areas in FIG. 18 ). The regions are configured to block X-rays at specific scattering angles depending on the position of the mask. In one embodiment, the optical elements are configured to block approximately half of the radiation from the sample. The fact that not only a narrow angular range of the diffraction signal is allowed through means that there is ambiguity about where each photon in the signal originated from and at what angle (i.e., what angle was the diffracted X-ray defined by the photon at). To resolve the ambiguity, several acquisitions must be performed, each of which blocks a different part of the scattering cone and allows other parts through. As a result, the entire acquisition collects many more photons than existing approaches. The apparent loss of information due to collecting from multiple angles and depths can be resolved in the reconstruction step, thereby utilizing accessible computational power.

[0041] Thus, in one embodiment, the optical element is configured to translate along the optical axis 6 between the sample and the detector. As the position of the optical element changes, X-rays of different scattering angles are blocked by the optical element. As a result, the diffraction pattern on the detector changes with the position of the optical element. As an alternative to moving the optical element, other components of the apparatus (e.g., the detector(s) and / or the sample) may be moved (along the optical path or laterally). An important consideration in this regard is that as the optical element (or one of the other components) is translated / moved, the detector will capture different portions of the scattering cone. The variation in radial intensity of the diffraction signal on the detector with respect to the position of the optical element is shown in FIG. 20. By translating the optical element through the diffraction signal from the sample to acquire one or more diffraction images associated with each optical element position, the method enables spatial resolution in the dimension along the optical axis 6. FIG. 20 shows how the diffraction pattern changes with the position of the optical element. For each position, the diffraction pattern at various angles is blocked by the optical element depending on the depth into the sample from which the pattern originates. Each diffraction image contains information from a different volume in the sample, so the image contains all the information from the sample together, but the patterns from different depths are superimposed on each other.

[0042] Reconstruction The geometry of the instrument in FIG. 1B can be mathematically described by the positions of the optical elements. The description allows for mapping of the diffraction pattern from a specific depth in the sample to the pattern acquired by the detector. An iterative approach is used to evaluate different distributions of the diffraction pattern at various sample depths. By comparing the modeled results with the acquired data, the most likely distribution of the diffraction pattern in the sample can be inferred. Thus, the reconstruction algorithm can mathematically find a solution that matches the signal in the acquisition, but preferably the algorithm includes a physical model for the sample that constrains the possible solutions. As an example, the physical model can include information about the material and the expected strain range.

[0043] Mathematically, the reconstruction algorithm solves the equation P = Ax, where P is the acquired data, x represents the sample map, and A is the system matrix describing how radiation from the source travels through the device, is intercepted by the collimator, is scattered by the sample, and is detected by the detector. Solving this inverse problem can be done in several ways and is similar to problems encountered in tomography. The sample has three spatial dimensions and is associated with a vector describing the scattering factor for each Q value. The scattering vector combines the scattering angle and energy. Thus, by using the Q value, the number of extra dimensions beyond the spatial dimension is reduced from two to one. Finally, the azimuthal resolution is used to reduce the scattering factor to two dimensions, so both the scattering angle and the azimuthal angle are reconstructed. Mathematically, this means that the sample map is five-dimensional.

[0044] Depth resolution is a function of the aperture area of ​​the optical element and the number of images acquired at different positions. The method preferably allows for increasing either the acquisition rate or the depth resolution relative to the sample per measurement.

[0045] Thus, the device may be configured to provide depth information of the sample, said configuration being achieved by including optical elements within the device as described herein.

[0046] The present disclosure further relates to an X-ray diffraction method for analyzing amorphous and / or semi-crystalline materials (e.g., polymers). The method preferably includes the steps of: a) providing a sample, where the sample is an amorphous or semi-crystalline material; b) providing a polychromatic X-ray source; c) collimating X-rays from the X-ray source into one or more pencil beams; d) diffracting the beam(s) by exposing at least a portion of the sample to the one or more pencil beams; e) collecting at least a portion of the one or more diffracted X-rays in an energy dispersive detector to obtain one or more diffraction images; and f) analyzing the obtained diffraction image(s) to map internal strain and / or stress in at least a region of the sample. The disclosed method requires the acquisition of at least one diffraction image. However, multiple diffraction images may also be acquired, e.g., at least two diffraction images, or at least three diffraction images, or multiple diffraction images.

[0047] sample The disclosed apparatus and method can analyze semi-crystalline materials, which contain at least one amorphous region. Therefore, the sample 3 is preferably a semi-crystalline or amorphous material. The sample may include a semi-crystalline polymer, such as linear polyethylene (PE), polyethylene terephthalate (PET), polybutylene terephthalate (PBT), polyether ether ketone (PEEK), polytetrafluoroethylene (PTFE), or isotactic polypropylene (PP). The crystallinity of semi-crystalline polymers of interest typically ranges from 10% to 80%. The disclosed apparatus and method can determine the elastic strain of the amorphous region of the material. Therefore, the disclosed apparatus and method can be used to analyze semi-crystalline materials with a crystallinity level of less than 30%, or even less than 20%. Therefore, the disclosed apparatus and method are preferably suitable for analyzing semi-crystalline materials. The crystallinity of the analyzed material is less than 20%. It is even possible to analyze the amorphous region of a semi-crystalline material. Based on the analysis, it is possible to determine strain and / or stress in at least some regions of a sample containing a semi-crystalline material, even when the analysis is based on diffraction signals from amorphous regions within the sample. The determined strain / stress may be provided in the form of a strain map. The sample may be a thin film (2D) or a three-dimensional object. The sample may also be a biological sample, such as human tissue (e.g., muscle tissue). The method may preferably map muscle contraction at the myofibril level to provide local stress-strain levels. Through small muscle samples obtained by biopsy in humans, this may enable characterization of skeletal muscle in relation to rehabilitation, various diseases, and physical training. The sample may also include inorganic materials (e.g., glass or ceramic). These materials are increasingly being used for advanced applications due to their excellent strength, biocompatibility, and the possibility of tailoring electrical function. The lifetime of components depends on manufacturing that avoids the introduction of strain and stress, and the method may preferably be able to map these in detail.

[0048] method The method will now be described in more detail. A sample 3 is placed on a stage 4 so that the optical axis 6 of the instrument passes through at least a region of the sample. X-rays 8 are emitted from a polychromatic X-ray source 1. The emitted X-rays 8 are collimated into one or more pencil beams by a collimator 2. Exposing the sample to one or more pencil beams causes the beams to be diffracted. Diffracted X-rays 9 appear as diffraction cones. Each diffraction cone is described by a specific scattering angle 2θ according to diffraction theory. The diffraction cones appear as diffraction rings on a two-dimensional area detector 5, which is preferably perpendicular to the optical axis 6. As a result, the diffraction signals collected on the detector form a diffraction image containing one or more of the diffraction rings. A raw 2D diffraction pattern acquired on an energy-dispersive detector can be seen in Figure 2. Diffraction rings arise in semi-crystalline materials (or crystalline powders) due to the random orientation of crystalline regions. Each diffraction ring at a different scattering angle can be attributed to ordered regions with different lattice constants. As an example, a semi-crystalline polymer contains ordered domains, with polymer chains aligned with a separation distance indicated by the lattice constant. One or more 1D diffraction patterns may be obtained from the 2D diffraction pattern. The 1D diffraction pattern includes a graph of the intensity of the diffraction signal versus a related parameter (e.g., Q factor, scattering angle, or direct distance of the scattering center). Examples of 1D diffraction patterns are shown in Figures 6 and 7. An azimuthal intensity distribution may be obtained, showing the intensity variation along the azimuthal angle of the diffraction rings. Thus, the azimuthal intensity distribution is a 1D plot obtained from the 2D diffraction pattern. The present disclosure relates to several methods for analyzing such diffraction patterns or azimuthal intensity distributions and inferring information about the sample from said analysis. The information preferably includes strain and / or stress in at least a region of the sample (e.g., a small volume of the sample). Various analytical methods that form part of the X-ray diffraction methods of the present disclosure are described below.

[0049] Analysis method The analysis may include analyzing one or more diffraction images or one or more 1D diffraction patterns obtained from the diffraction images. The diffraction images may be obtained using methods of the present disclosure described elsewhere. The analysis may include analyzing one or more 1D diffraction patterns. The diffraction patterns include an intensity distribution. The intensity distribution is a 1D plot of the intensity of the diffraction signal versus a parameter selected from the group consisting of scattering angle, wavelength, energy, radial coordinate r, azimuthal coordinate η, or Q-factor. The Q-factor combines all the first three parameters into a single number via Bragg's law. The diffraction signal may alternatively be represented in direct space. This may be achieved using a Fourier transform. Rather than representing scattering characteristics, a direct space representation directly shows how structures of different lengths contribute to the signal. In a direct space representation, information from different energy bins of the detector can be aggregated to improve statistics.

[0050] The present disclosure relates to several analytical methods that may be part of the disclosed X-ray diffraction method, all for analyzing amorphous and / or semi-crystalline materials. At least one embodiment of the analytical method comprises analyzing the intensity distribution versus the Q-factor. Another embodiment comprises analyzing the azimuthal diffraction pattern. The analysis preferably further comprises determining the shift of one or more intensity peaks in the azimuthal diffraction pattern. The azimuthal diffraction pattern may be expressed in terms of the Q-factor shift versus the azimuthal coordinate η. Different embodiments are described in more detail below.

[0051] One embodiment of the analysis involves obtaining a 1D intensity distribution from one or more diffraction images. In the following description, the intensity distribution is expressed in terms of Q values, but one skilled in the art will recognize that similar results can be obtained using other parameters mentioned herein (e.g., scattering angle, radial coordinate r, or direct spatial parameters corresponding to lattice distance). An example intensity distribution is shown in FIG. 7. Preferably, the next step in the analysis is the identification of one or more diffraction peaks (e.g., first diffraction peaks (FDP) and / or second diffraction peaks (SDP)). The positions of these peaks are preferably recorded in terms of their Q values. The inventors have found that the internal strain of the sample is related to the position of the intensity peaks in the diffraction pattern. The inventors have also noticed that with larger strain values ​​in the direction of the external strain (corresponding to greater stretching of the sample), the positions of the peaks shift toward lower Q values, while the positions of the peaks in the transverse direction of the external strain shift toward higher Q values. This observation is illustrated in FIG. 8, which shows multiple diffraction signals for various values ​​of strain on the sample. Each diffraction signal has been subtracted from that of an unstrained sample. In this figure, lighter colors correspond to smaller strains on the sample, while darker colors correspond to larger strains. A value of zero indicates no change between the diffraction patterns of the strained versus unstrained sample. Thus, a positive value means that the intensity for a given Q value of the strained sample is lower compared to the intensity for a given Q value of the unstrained sample, and vice versa for a negative value. In other words, a positive peak at Q=1.5A -1 A negative peak appears around Q=1.6A. -1 The fact that the peak appears around Q=1.6A -1 So Q=1.5A -1 According to this embodiment, the analysis includes determining the positions and / or shifts in positions ΔQ of the diffraction peaks in one or more intensity distributions obtained from the diffraction image. The intensity distributions may be azimuthal or radial intensity distributions.

[0052] Diffraction images may be acquired from different regions of the sample (e.g., different volumes of the sample). The positions of one or more of the intensity peaks in different regions of the sample can then be compared to infer the strain level in the region or the relative difference in strain between different regions of the sample. Alternatively, the positions of the peaks may be compared to a reference sample (ideally unstrained). For amorphous regions, the diffraction pattern represented in either Q-space or direct space typically does not contain sharp peaks, but still contains information from one or more features of the pattern. The analysis may further include identifying one or more of such features. The features may be modeled using a function and then compared to a reference pattern acquired from a reference sample or to patterns acquired from one or more other regions of the sample.

[0053] As an example, multiple regions of a sample may be exposed. One or more diffraction images may be acquired for each region, and one or more 1D diffraction patterns may be acquired for each diffraction image, which may then be analyzed as described above. The location of one or more peaks in each 1D diffraction pattern may then be determined and recorded, for example, in terms of their Q-values. A region with a peak at a high Q-value indicates high strain in that region, while a region with a peak at a lower Q-value indicates lower strain in that region. The relative terms "high" and "low" should be understood relative to the median or average value of multiple regions within the sample. Thus, when multiple regions within a sample are measured, a "base level" may be established that indicates the average or median strain level. The magnitude and direction of strain can be inferred in relation to the azimuthal distribution of the shift compared to the base level. The base level may define a unit tensor, and other regions may then be classified as tensor maps of components relative to that unit tensor. This facilitates the creation of a strain map for the entire sample, or at least a representative portion of the sample. The strain map has a strain direction and a magnitude relative to the unit tensor of the reference or base level. When the analysis is compared to an unstrained reference sample, the absolute value of the internal strain and / or stress within the sample can be inferred.

[0054] Another embodiment of the analysis method will now be described. Similar to the first embodiment of the method, this embodiment involves obtaining a 1D intensity distribution from one or more diffraction images. The 1D intensity distribution in this embodiment is preferably an azimuthal intensity distribution, i.e., it represents the intensity of the diffraction signal as a function of azimuthal angle. In the case of diffraction rings, the azimuthal intensity distribution can be obtained by acquiring data (or selecting data from the raw data) along the azimuthal angle of each diffraction ring. This is feasible because diffraction patterns are typically approximately circularly symmetric and therefore typically lend themselves to characterizing the diffraction pattern in terms of polar coordinates (r, η), as shown in Figure 4. Alternatively, the azimuthal intensity distribution can be obtained by dividing the azimuthal range 0-2π into multiple segments (e.g., 24 segments) and then summing the contributions from each segment or integrating the intensity over the entire azimuthal range. Examples of azimuthal intensity distributions for various values ​​of sample strain are shown in Figures 13 and 14. The inventors have discovered that stretching the sample induces changes in the intensity of the diffraction rings along the azimuthal angle. Stretching a sample forces the polymer chains to align in the direction of strain, increasing the intensity of the diffraction rings in this direction. Therefore, by determining the location of the intensity peaks in the azimuthal intensity distribution, it is possible to infer the internal strain direction in exposed regions of the sample, even if the exposed regions are amorphous. Figure 13 shows the azimuthal intensity distributions for samples stretched to various degrees. It is observed that the amplitude of the intensity peaks increases with increasing levels of external strain. Figure 14 shows the ratio of the azimuthal integrated data of the strained and unstrained intensity distributions for two different levels of engineering strain, plotted along with a sinusoidal fit (solid curve). A ratio of 1 corresponds to an unstrained sample. Again, it is observed that the amplitude of the peaks increases with increasing levels of strain. This relationship is plotted in Figure 15, which shows a linear relationship between the amplitude of a sinusoidal fitting function applied to the data in Figure 14. The amplitude is plotted as a function of macroscopic strain (in percent).

[0055] Another embodiment of the analysis method will now be described. This particular embodiment requires that the apparatus include the optical element disclosed herein. Accordingly, this embodiment of the analysis method is suitable for use with the X-ray diffraction method of the present disclosure. An optical element is disposed in the beam path and configured to intercept a portion of the diffracted beam. The optical element should preferably be configured to be translated along the beam path, as shown in FIG. 1B . This facilitates that various portions of the diffraction signal can be intercepted by the optical element, and that the portions of the diffraction signal that are intercepted can be selected or changed by moving the optical element axially along the beam path. The method includes scanning / moving the optical element through the diffraction signal (e.g., from a first position closer to the sample to a second position closer to the detector). One or more diffraction images are captured by the detector for a plurality of different axial positions of the optical element. Additionally or alternatively, the optical element may be configured to be translated in a direction other than along the beam path (e.g., along a plane perpendicular to the beam path). Preferably, at least one diffraction image is acquired for each axial position of the optical element. The diffraction image may be analyzed using any of the analysis methods described herein, with the additional step of providing a novel reconstruction algorithm that can be used to provide depth information of the sample. In other words, the reconstruction algorithm facilitates obtaining a 3D distortion map of the sample. The spatial resolution of the distortion map in the depth direction (i.e., along the optical axis 6) can be dynamically improved or relaxed as needed during the measurement. Generally, more positions of the optical elements and the associated diffraction patterns increase the resolution. Similarly, reducing the beam size and / or reducing the divergence angle typically increases the accuracy of the reconstructed depth dimension. In most cases, the reconstruction is performed using a physical model of the measured material, imposing constraints on the solution and thereby improving the accuracy of the distortion map. In a preferred application of this method, the dimensions of the sample are known from other measurements, imposing further constraints on the solution.

[0056] Detailed Description of the Drawings FIG. 1A shows a schematic diagram of an apparatus for X-ray diffraction analysis according to the present disclosure. The apparatus includes a polychromatic X-ray source 1 configured to emit X-rays 8, a collimator 2 configured to collimate the X-rays 8 emitted from the X-ray source 1, a stage 4 for holding a sample 3, and a detector 5 for collecting at least a portion of the diffracted X-rays 9 from the sample 3. The apparatus may further include a beam stop (not shown) configured to block a central beam coincident with the optical axis 6. The central beam is not shown in this view because it coincides with the optical axis 6. Note that the apparatus is shown in cross section. In reality, the diffracted X-rays 9 are conical, and the diffraction pattern acquired on the detector 5 appears as diffraction rings (not visible in this cross-sectional view).

[0057] FIG. 1B shows a schematic diagram of an apparatus for X-ray diffraction analysis according to the present disclosure. An optical element 7 is positioned in the beam path between the sample 3 and the detector 5. The optical element 7 (illustrated here as a mask) can be used to reconstruct depth information of the sample 3. Images of the diffraction signal can be generated for each position of the mask as the mask is translated along the optical axis 6 between the sample 3 and the detector 5. For each depth of the sample 3 and each angular range of signals, the mask blocks the signal in some positions and collects the signal on the detector 5 in other positions. Using detailed knowledge of the apparatus geometry, the signals most likely emitted from each region of the sample 3 can be reconstructed from the collected data set.

[0058] 2 shows the diffraction signal collected on an energy dispersive detector 5. In this example, the detector 5 contains 256 x 256 pixels. The diffraction signal appears as diffraction rings on the detector 5.

[0059] Figure 3 shows how the diffraction signal can be divided into separate energy bins for analysis. The radius of the diffraction rings decreases with increasing energy. By separating the signal into multiple energy bins, higher order rings become visible on the detector 5.

[0060] Figure 4 shows the diffraction pattern collected on an energy dispersive detector 5 for a range of energies. The intensity plotted on the vertical scale indicates the scattering angle. The pattern can be described in terms of radial (r) and azimuthal (η) coordinates (r, η), where r is related to the radial distance in reciprocal space and is also referred to as the Q factor.

[0061] Figure 5 shows the intensity of the diffraction signal versus diffraction angle for various energies (energy bins). There is significant overlap between the curves, making them difficult to distinguish from one another. As a result, it is difficult to perform useful analysis based on this plot alone. The method of the present disclosure proposes how to transform the plot using the scattering vector length (Q value) to better distinguish the intensity peaks.

[0062] Figure 6a shows the same data as in Figure 5, but now displayed using Q-factors. That is, the graph shows intensity versus Q-factor (in units of 1 / A). The Q-factor combines the diffraction angle (2θ) and energy (wavelength) of the diffracted X-rays into a single metric, Q. Using the Q-factor has the advantage that the patterns for each energy bin are aligned with each other.

[0063] Figure 6b shows the same data as shown in Figure 6a. Here, the diffraction signals from each energy bin are combined (by superposition) into a single graph to achieve a higher signal-to-noise ratio. The intensity is a function of the common scattering vector Q. The position of the diffraction peaks in Q-space correlates to the bond length of the material and can therefore be used to map / determine the internal strain in the material.

[0064] Figure 7 shows the diffraction signal from a polyethylene (PE) sample 3. The plot shows a graph of signal intensity versus Q value. The diffraction pattern shows intensity peaks at several Q values. Therefore, this method can obtain diffraction information of semi-crystalline materials, even from the amorphous regions of the material.

[0065] Figure 8 shows the diffraction signal from an amorphous sample (atactic polystyrene). The plot shows a graph of signal intensity versus Q-value. Q-value is directly correlated to bond length. The diffraction pattern shows two intensity peaks at specific Q-values. Although the peaks are broader than those of semi-crystalline materials (see Figure 7), the positions of the peaks can be determined and strain can be inferred from their positions (Q-values). Therefore, this method can obtain diffraction information for amorphous materials.

[0066] Figure 9a shows a series of diffraction signals from PE sample 3. Sample 3 was stretched in separate steps, and a diffraction signal was acquired at each step. Each plot is formed by subtracting the diffraction signal acquired for a particular strain level from the diffraction signal of unstrained sample 3. As a result, it is easy to see how the peak position shifts towards lower Q values ​​at higher strain values. Lighter colors correspond to lower strain on sample 3, while darker colors correspond to higher strain. Note that at higher strain values ​​(corresponding to greater stretching of sample 3), the difference signal shows that the peak value shifts towards lower Q values. This is due to the presence of the first order peak (Q value of approximately 1.5A). -1 ) and secondary peak (approximately 1.7A -1 ) holds for both the internal strain and the Q-space. Therefore, the method is useful for determining internal strain because it directly correlates with the position of the intensity peak(s) in Q-space. The method does not rely on imposing external strain, as internal strain may arise during sample fabrication, etc. External strain is imposed only to validate the method.

[0067] Figure 9b shows a series of diffraction signals from an amorphous sample (atactic polystyrene). The sample was stretched in discrete steps, and diffraction signals were acquired at each step. Each plot is created by subtracting the diffraction signal acquired for a particular strain level from the diffraction signal of an unstrained sample. As a result, it is easy to see how the peak position shifts toward lower Q values ​​as strain values ​​increase. Lighter colors correspond to lower strain in the sample, while darker colors correspond to higher strain. Note that the difference signal shows that the peak position shifts toward lower Q values ​​as strain values ​​increase (corresponding to greater stretching of the sample). Therefore, this method is useful for determining internal strain within amorphous samples by correlating the position of one or more intensity peaks (e.g., in Q-space) with the bond length of the sample. Here, externally imposed strain serves only to validate the method. In practical applications, sample strain information can be inferred without imposing external strain. This is because the acquired curve(s) can be compared to a reference and / or multiple diffraction signals can be acquired from different volumes of the sample to obtain a relative distortion map.

[0068] Figure 10 shows a zoom-in of the first diffraction peak (FDP) from Figure 7. The two curves correspond to two different strain values. The peak shifts toward lower Q values ​​as strain increases. Therefore, internal strain can be inferred by determining the position of the FDP or the shift ΔQ in the Q value of the FDP between two different strain levels. The shift toward higher Q values ​​is observed at distinct angular positions (described by the azimuthal angle) around the diffraction ring. In other words, the internal strain direction within the material can be observed by observing the shift in the intensity peak of the diffraction ring(s).

[0069] Figure 11 shows a zoom-in of the second diffraction peak (SDP) from Figure 7. The two curves correspond to two different strain values. The peak shifts toward higher Q values ​​as strain increases. Therefore, internal strain can be inferred by determining the position of the SDP or the shift ΔQ in the Q value of the SDP between two different strain levels. The shift toward higher Q values ​​is observed at distinct angular positions (described by the azimuthal angle) around the diffraction ring. In other words, the internal strain direction within the material can be observed by observing the shift in the intensity peak of the diffraction ring(s).

[0070] Figure 12 shows the diffraction signal obtained from the experiment on the energy dispersive detector 5. The centre of the diffraction signal is blocked by a beam stop to reduce unwanted scattering from the detector 5 material.

[0071] Figure 13 shows the diffraction signal from Figure 11. An optical element 7 (here a mask) was used to block a portion of the diffraction signal from the sample 3. This particular mask has an opening that allows scattering angles of 9 to 11.5 degrees through the mask.

[0072] The shaded area indicates that this part of the diffraction signal was filtered / not considered in the analysis.

[0073] Figure 14 shows the intensity of the diffraction signal versus the azimuthal angle of the diffraction rings shown in Figure 12 for various degrees of stretching of Sample 3. It is observed that stretching induces a change in the intensity of the diffraction rings along the azimuthal angle. Stretching Sample 3 forces the polymer chains to align in the direction of strain, increasing the intensity of the diffraction rings in this direction.

[0074] Figure 15 shows the intensity ratio of the first diffraction peak (FDP) of the strained sample compared to the unstrained sample versus azimuthal angle (i.e., the angular distribution along the diffraction ring). It is observed that stretching induces a sinusoidal change in the intensity of the FDP compared to the unstrained case. The solid line is a sinusoidal fit to the data.

[0075] Figure 16 shows the amplitude of the sinusoidal fitting function of Figure 14 plotted as a function of engineering strain (macroscopic strain). A linear relationship is observed.

[0076] Figure 17 shows a plot similar to that shown in Figure 16, but shows data from an amorphous sample, so similar behavior is observed in the amorphous sample.

[0077] Figure 18 shows experimental results achieved using a synchrotron as the X-ray source 1. Sample 3 was placed in a strain apparatus so that X-ray diffraction images could be acquired while it was being stretched. The plot shows the relative shift in polymer chain link distance versus the internal strain direction (degrees) of the material and versus the engineering strain (per mil) of Sample 3. Sample 3 was a PE material. The radial shift of the first-order diffraction ring (i.e., the Q-factor shift) was observed for 37 different directions (azimuthal angles) and 18 different strain levels. The external strain directions were 20° and 200°. As the polymer chains were stretched, they became more tightly aligned in the transverse direction (darker colors) and more separated in the tensile direction (lighter colors).

[0078] Figure 19 shows a comparison of diffraction patterns obtained using two different experimental setups. Each setup includes a different X-ray source 1, one using a synchrotron and the other using a polychromatic laboratory X-ray source 1. The graph labeled "Lab" was obtained using the disclosed method and apparatus. It is observed that the main peak occurs at the same Q value for the two methods, confirming the validity of the present method using the laboratory X-ray source 1.

[0079] 20 shows a schematic diagram of a mask design according to an embodiment of optical element 7. The mask is configured such that certain diffraction rings (orders) are blocked in the beam path, preventing one portion of the diffraction signal from reaching detector 5 and allowing another portion to pass through the mask.

[0080] Figure 21 shows an example of an array of four energy dispersive detectors 5, said array being compatible with the apparatus and methods of the present disclosure.

[0081] Figure 22 shows the radial intensity of the diffraction signal on a portion of the detector 5 versus the position of a mask placed in the beam path to block a particular portion of the diffraction signal. Data is selected from an annular sector of the detector 5. Radial intensity refers to the intensity measured radially outward from the center of the beam. As the distance from the center increases, more diffraction orders appear. The horizontal axis corresponds to the position of the mask. The mask can be placed anywhere between the sample 3 and the detector 5. This plot is shown for a particular energy value of the X-ray beam. However, the plot can be extended into a third dimension to include the diffraction signal versus energy.

[0082] Figure 23 shows the diffraction signal from a point within the sample 3. The signal has been reconstructed using a mask and a reconstruction algorithm. The signal has been reconstructed for 10 sections of the sample 3. In the two other dimensions, the beam width / height defines the area of ​​the sample 3 included in the reconstruction. The data used in the reconstruction is based on 25 different positions of the mask. It is observed that the reconstructed signal is similar to the ground truth.

[0083] Figure 24 shows a series of diffraction signals. The beam size (BS) was varied between each successive diffraction signal. Thus, the differences between the graphs show the effect of increasing the beam size. With larger beam sizes, the beam produces diffraction from other regions within the sample 3 with internal structures that alter the diffraction signal. However, with larger beams, diffraction also emanates from a larger volume, increasing ambiguity in the reconstruction.

[0084] reference numbers 1.X-ray source 2. Collimator 3. Sample 4. Stage 5. Detector 6. Optical axis 7. Optical Elements 8. Emitted X-rays 9. X-ray diffraction

[0085] Further details of the invention The list of items below should not be construed as claims.

[0086] 1. An X-ray diffraction method for carrying out said analysis of amorphous and / or semi-crystalline materials, comprising: a) providing a sample, said sample being a semi-crystalline or amorphous material, said material including at least one amorphous region; b) providing a polychromatic X-ray source; c) collimating the x-rays from the x-ray source into one or more pencil beams; d) diffracting the beam(s) by exposing at least an area of ​​the sample to the one or more pencil beams; e) collecting at least a portion of the diffracted beam on one or more energy dispersive 2D detectors to obtain one or more diffraction images; f) analyzing the acquired diffraction image(s) to determine the internal strain and / or stress in at least the exposed region of the sample.

[0087] 2. The method of claim 1, wherein the analysis comprises analyzing a diffraction signal from the amorphous region of the sample.

[0088] 3. The method of any of the preceding items, wherein the one or more pencil beams are substantially parallel to the optical axis of the system.

[0089] 4. The method of any of the preceding items, wherein the crystallinity of the material being analyzed is less than 20%.

[0090] 5. The method of any of the preceding items, wherein the material is a semi-crystalline polymer.

[0091] 6. The method of any of the preceding items, wherein the material is amorphous.

[0092] 7. A method according to any preceding claim, wherein at least four energy dispersive detectors are arranged in an array.

[0093] 8. The method of any preceding claim, wherein each of the energy dispersive detectors comprises a plurality of pixels.

[0094] 9. A method according to any preceding claim, comprising providing an optical element in the beam path, said optical element being configured to intercept a portion of said diffracted beam.

[0095] 10. A method according to any preceding claim, wherein the optical element is a mask.

[0096] 11. The method of claim 9, wherein the optical element is configured to intercept a selected subset of the diffracted beams, the beams having a scattering angle less than 0°.

[0097] 12. The method of claim 11, wherein the obstructed subset is correlated to the position of the optical element, and the subset can be selected by displacing the optical element on an axis along the beam path.

[0098] 13. The method according to any of items 9 to 12, wherein the optical element is displaced along the optical axis in a series of diffraction measurements and the diffraction signal is imaged for each position of the optical element.

[0099] 14. The method of claim 13, wherein a computer-implemented algorithm is used to analyze the acquired diffraction images to infer depth information of the sample, the depth information relating to the internal strain and / or stress in the sample.

[0100] 15. The diffraction images are obtained from at least two different strain levels of the sample, and the analysis further comprises: a) extracting at least one 1D diffraction pattern for each distortion level from the diffraction image; b) determining the location of one or more diffraction peaks for each of said 1D diffraction patterns; c) determining the difference(s) in the positions of the peaks between the 1D diffraction patterns; and d) correlating the difference(s) to the internal strain in the exposed area of ​​the specimen.

[0101] 16. The method according to item 15, wherein the one or more diffraction peaks include a first diffraction peak (FDP) and / or a second diffraction peak (SDP).

[0102] 17. A method according to any of the preceding items, wherein the analysis comprises determining the position of one or more intensity peaks in the diffraction image(s) and / or in 1D diffraction pattern(s) obtained from the image(s), and the internal strain in the exposed region of the sample can be inferred from said positions.

[0103] 18. A method according to any preceding item, wherein at least two distinct regions of the sample are exposed and at least one diffraction image is obtained for each of the regions.

[0104] 19. The method according to item 18, wherein the analysis comprises determining the positions of one or more intensity peaks in the diffraction image or a 1D diffraction pattern obtained from the image, and the internal strain in the exposed region of the sample can be inferred from the positions.

[0105] 20. A method according to any preceding item, wherein the position of the intensity peak is compared to a reference sample to determine the internal strain of the exposed region of the sample.

[0106] 21. A method according to any of the preceding items, wherein the analysis includes determining the positions of one or more diffraction peaks, comparing the positions with a reference sample, and determining the internal strain in the exposed region of the sample based on the comparison.

[0107] 22. The method of any preceding claim, wherein the one or more diffraction peaks include a first diffraction peak (FDP) and / or a second diffraction peak (SDP).

[0108] 23. A method according to any of the preceding items, wherein the analysis includes determining the position of one or more intensity peaks in the azimuthal intensity distribution of one or more diffraction rings formed on the diffraction image(s).

[0109] 24. The method of claim 23, wherein the position of the intensity peak (the position being specified by the azimuthal angle) is used to determine the internal strain direction in the exposed region of the sample.

[0110] 25. An apparatus for performing X-ray diffraction analysis of semicrystalline materials, comprising: a) a polychromatic X-ray source configured to emit X-rays; b) a collimator configured to collimate the x-rays from said polychromatic x-ray source into one or more pencil beams; c) a stage for holding the sample; d) an optical element configured to be displaced along an optical axis of the device to provide depth information of the sample; e) one or more energy dispersive X-ray detectors.

[0111] 26. The apparatus of item 25, wherein the apparatus includes at least four detectors arranged in an array, each detector including a plurality of pixels.

[0112] 27. The apparatus according to item 25, wherein the collimator for collimating the X-rays comprises a condenser and / or at least one slit.

[0113] 28. The device according to item 25, wherein the device is configured to perform the method according to item 1.

[0114] 29. A computer-implemented method for analyzing X-ray diffraction images of semicrystalline materials, comprising: a) providing a plurality of X-ray diffraction images acquired from a semi-crystalline sample; b) optionally extracting one or more 1D diffraction patterns from said diffraction image; c) determining the location of one or more intensity peaks in the diffraction image and / or the 1D diffraction pattern; d) comparing said position(s) with similar intensity peaks acquired at different strain levels or in other regions of the sample, and calculating the difference(s) between said position(s) of said peaks; e) determining the internal strain in at least one region of the sample based on the difference(s).

[0115] 30. The method of claim 29, wherein the X-ray diffraction images are obtained from at least two distinct regions of the sample.

[0116] 31. The method according to any one of items 29 to 30, wherein the X-ray diffraction image is obtained from an amorphous region of the sample.

[0117] 32. A computer-implemented method for analyzing X-ray diffraction images of semicrystalline materials, comprising: a) providing one or more X-ray diffraction images obtained from a semi-crystalline sample; b) extracting one or more azimuthal intensity distributions from the diffraction image; c) determining the positions of one or more intensity peaks in the diffracted azimuthal intensity distribution, the positions being specified by azimuthal angles; and d) determining the internal strain direction and / or the internal strain level of at least a region of the sample based on the position of the intensity peak(s).

Claims

1. 1. An X-ray diffraction method for the analysis of amorphous and / or semi-crystalline materials, comprising: a) providing a sample, said sample being a semi-crystalline or amorphous material, said material including at least one amorphous region; b) providing a polychromatic X-ray source; c) collimating the x-rays from said x-ray source into one or more pencil beams; d) diffracting the beam(s) by exposing at least an area of ​​the sample to the one or more pencil beams; e) collecting at least a portion of the diffracted beam on one or more energy dispersive 2D detectors to obtain one or more diffraction images; f) analyzing the acquired diffraction image(s) to determine internal strain and / or stress in at least the exposed region of the sample, wherein the analysis comprises analyzing diffraction signals from the amorphous region of the sample.

2. The method of claim 1, wherein the material being analyzed has a crystallinity of less than 20%.

3. 10. A method according to any preceding claim, wherein the material is a semi-crystalline polymer.

4. 10. A method according to any preceding claim, wherein the one or more energy-dispersive 2D detectors comprise a two-dimensional grid of pixels, e.g. a rectangular grid.

5. The method of claim 4 , wherein the energy-dispersive 2D detector(s) comprise 256×256 pixels.

6. 10. A method according to any preceding claim, comprising providing an optical element in the beam path, said optical element being arranged to intercept a portion of said diffracted beam.

7. The method of claim 6 , wherein the optical element is configured to block approximately half of the diffracted x-rays.

8. 8. A method according to any one of claims 6 to 7, wherein the optical element is configured to intercept a selected subset of the diffracted beams, the beams having a scattering angle greater than 0°, the subset being correlated with the position of the optical element, and the subset can be selected by displacing the optical element on axis along the beam path.

9. A method according to any one of claims 6 to 8, wherein the optical element is displaced along the optical axis in a series of diffraction measurements, and the diffraction signal is imaged for each position of the optical element.

10. 10. The method of claim 9, wherein a computer-implemented algorithm is used to analyze the acquired diffraction images to infer depth information of the sample, the depth information relating to the internal strains and / or stresses in the sample.

11. 10. The method of any preceding claim, wherein the analysis comprises determining positions of one or more intensity peaks in the diffraction image(s) and / or in 1D diffraction pattern(s) obtained from the image(s), comparing the positions with a reference sample, and determining the internal strain of the analyzed sample based on the comparison.

12. 10. A method according to any preceding claim, comprising exposing at least two distinct regions of the sample and obtaining at least one diffraction image for each of said regions.

13. 13. The method of claim 12, wherein the analysis further comprises obtaining one or more 1D diffraction patterns from the diffraction image, determining positions of one or more intensity peaks in the 1D diffraction patterns, and determining the difference(s) between positions of similar peaks obtained in different regions of the sample to obtain a relative strain map of the sample.

14. The method of claim 13 , wherein the intensity peaks include a first diffraction peak (FDP) and / or a second diffraction peak (SDP).

15. 10. A method according to any preceding claim, wherein the analysis comprises determining the position of one or more intensity peaks in the azimuthal intensity distribution of one or more diffraction rings formed on the diffraction image(s).

16. 16. The method of claim 15, wherein the position of the intensity peak, the position specified by the azimuthal angle, is used to determine the internal strain direction in the exposed region of the specimen.

17. 1. An apparatus for performing X-ray diffraction analysis of semi-crystalline materials, comprising: a polychromatic X-ray source; a collimator configured to collimate the x-rays from the polychromatic x-ray source into one or more pencil beams; a stage for holding the sample; an optical element configured to be displaced along an optical axis of the device to provide depth information of the sample; one or more energy dispersive X-ray detectors.

18. The apparatus of claim 17, wherein the apparatus is configured to perform at least steps b) to e) of the method of claim 1.

19. 1. A computer-implemented method for analyzing an X-ray diffraction image of a semi-crystalline material, comprising: providing a plurality of X-ray diffraction images acquired from a semi-crystalline sample; extracting one or more diffraction patterns from the diffraction image; determining the location of one or more intensity peaks in the diffraction image and / or the diffraction pattern; comparing the position(s) with similar intensity peaks acquired at different strain levels or in other regions of the sample, and calculating the difference(s) between the position(s) of the peaks; and determining an internal strain in at least one region of the specimen based on the difference(s).

20. 20. The method of claim 19, wherein the X-ray diffraction images are obtained from at least two distinct regions of the sample.

21. 21. The method of any of claims 19 to 20, wherein the X-ray diffraction image is obtained from an amorphous region of the sample.

22. 1. A computer-implemented method for analyzing an X-ray diffraction image of a semi-crystalline material, comprising: Providing one or more X-ray diffraction images obtained from a semi-crystalline sample; extracting one or more azimuthal intensity distributions from the diffraction image; determining the positions of one or more intensity peaks in the diffracted azimuthal intensity distribution, the positions being specified by azimuthal angles; and determining an internal strain direction and / or an internal strain level of at least a region of the sample based on the position of the intensity peak(s).

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