A method for calibrating the absolute intensity of a sample at different locations in SAXS

Abstract

This invention provides a method for calibrating the absolute intensity of a sample at different locations in a SAXS (Scattered Optical Array) system, comprising: placing a sample and a standard sample at a first preset location and a second preset location, respectively, and measuring the relative intensity of the sample and the relative intensity of the standard sample; converting the relative intensity of the standard sample to the relative intensity of the standard sample corresponding to the first preset location based on a conversion formula, according to a first distance and a second distance; wherein the first distance is the distance from the first preset location to the detector, and the second distance is the distance from the second preset location to the detector; calculating an absolute intensity calibration factor using the scattering curve and the theoretical curve of the standard sample; and calculating the absolute intensity of the sample using the absolute intensity calibration factor and the relative intensity of the sample. This invention solves the problem in the prior art that methods cannot calibrate the absolute intensity of a sample by testing the sample and the standard sample at different locations.

Description

Technical Field

[0001] This invention relates to the field of scattering intensity calibration technology, and in particular to a method for calibrating the absolute intensity of a sample at different locations in a SAXS. Background Technology

[0002] Small-angle X-ray scattering (SAXS) is a physical technique and method for studying the submicroscopic structure and morphological characteristics of materials. It is applicable to both solid and liquid samples, requires small sample volumes, and is a precise and non-destructive analytical method widely used in research on polymers, biomacromolecules, nanomaterials, and porous materials.

[0003] A geometrical diagram of the SAXS experiment is shown below. Figure 2 As shown, the typical scattering angle 2θ ≤ 5°. The detector can be arranged symmetrically with respect to the direct light; for samples with isotropic scattered signals, it can also be biased, i.e., only half of the scattered signal is sampled. The advantage of this is that it can increase the measured scattering angle, which is particularly suitable for small-sized detectors.

[0004] In the experiment, the SAXS detector measures the relative scattering intensity of the sample (referred to as relative intensity), which depends not only on the sample structure but also on the instrument parameters and testing conditions. The differential scattering cross section of the sample is called the absolute scattering intensity (referred to as absolute intensity), which depends on the ratio of the scattered intensity to the incident intensity; that is, it depends only on the sample structure and is independent of the instrument parameters and testing conditions. From the relative intensity, the geometric parameters of the scatterers inside the sample (such as particles, pores, etc.), such as the fractal dimension, shape, size, and distribution of the scatterers, can be derived. To obtain parameters related to the sample's mass density, such as molecular weight and volume fraction (e.g., porosity of porous materials), absolute intensity must be used. Undoubtedly, absolute intensity calibration is of great significance.

[0005] Because absolute intensity depends on the ratio of scattered intensity to incident intensity, directly calculating this ratio requires precise measurement of the incident light intensity. However, due to the high intensity of the incident light, conventional detectors are limited by their dynamic range and cannot measure it effectively. Attenuation methods have been used to test the incident light intensity and then calculate the absolute intensity. The attenuation method involves mechanically attenuating the incident light intensity using absorbing sheets or foils of varying thicknesses (such as Ni or Si sheets) or a rotating disk, bringing it to a measurable range, and then extrapolating the incident light intensity. However, the attenuation method is cumbersome to operate, relatively complex to calculate, and has poor repeatability, and is rarely used in practice.

[0006] Another commonly used method for measuring the absolute intensity of a sample is called the standard sample method (or simply standard sample method). This method uses samples with known absolute strength, such as glassy carbon, water, silica suspension, gold sol, and polyethylene spheres, as standard samples. Under the same conditions as the experimental sample (also called the test sample) (including the testing instrument, experimental parameters, and the distance between the sample and the detector), the scattering intensity of the standard sample is measured, and the calibration factor is calculated. This calibration factor can then be used to convert the relative intensity of the test sample into absolute intensity. Compared to the attenuation method, the standard sample method is convenient to operate, simple to calculate, and provides stable results, making it widely applicable.

[0007] In 2016, the National Institute of Standards and Technology (NIST) introduced a new standard sample, glassy carbon SRM3600, such as... Figure 3 As shown, it is a black square sheet with a side length of 10 mm and a thickness of 1.055 mm, and has been widely used for the SAXS absolute strength calibration of samples measured at the same location. The theoretical absolute strength curve of this glassy carbon ( Σ / Ω)(1 / cm)~q(1 / nm) as Figure 4 As shown, where I a Where is the absolute intensity, q is the scattering vector, q = 4πsinθ / λ, 2θ is the scattering angle, and λ is the X-ray wavelength.

[0008] The main principle of calibrating absolute intensity using glassy carbon is to measure the SAXS signals of glassy carbon and the sample at the same location under the same conditions, compare the measured scattering curve of glassy carbon with its theoretical scattering curve, and calculate the absolute intensity calibration factor CF. The relative intensity of the sample is multiplied by this calibration factor and then divided by the product of the transmitted light intensity (usually the relative intensity recorded by a photodiode integrated into a through beam blocker) and the sample thickness to convert it into absolute intensity.

[0009] In the application of the standard sample method described above, it is particularly emphasized that the standard sample and the test sample must be tested under the same conditions. The same conditions mainly refer to using the same testing instruments, maintaining the same experimental parameters, and changing the sample in the same location. Under normal circumstances, these conditions are easy to meet. In a few cases, however, meeting the requirement of testing the standard sample and the test sample in the same location may be difficult. For example, the test sample may be tested within a cavity, but volume or environmental limitations may prevent the standard sample (such as glassy carbon) from fitting into the test sample cavity. Figure 5This image depicts an in-situ coal dry distillation experiment conducted at the SAXS experimental station of the 1W2A beamline at the Beijing Synchrotron Radiation Facility (BSRF). Due to the size limitation of the sample holder inside the high-temperature heating furnace, the standard sample, glassy carbon, cannot be placed inside. The existing method involves moving the furnace away from the optical path and installing another sample holder suitable for glassy carbon on the optical path, ensuring the distance from the standard sample to the detector is the same as the distance from the test sample to the detector, before testing the standard sample. This operation is cumbersome, inefficient, has poor repeatability, and significant errors. Is it possible to directly attach the glassy carbon to the direct X-ray exit port of the furnace for testing without moving the furnace? This method is simpler, but it requires converting the relative intensity of the standard sample tested at the furnace opening into the corresponding relative intensity at the test sample location.

[0010] In summary, the existing technology has the problem of not being able to test the specimens and standards at different locations to calibrate the absolute strength of the specimens. Summary of the Invention

[0011] In order to overcome the shortcomings of the prior art, the purpose of this invention is to provide a method for calibrating the absolute strength of a sample at different locations in a SAXS. This invention solves the problem that the prior art cannot test the sample and standard at different locations to calibrate the absolute strength of the sample.

[0012] To achieve the above objectives, the present invention provides the following solution:

[0013] A method for calibrating the absolute intensity of a sample at different locations in a SAXS system includes:

[0014] The sample and the standard were placed at a first preset position and a second preset position, respectively, and the relative strength of the sample and the relative strength of the standard were measured.

[0015] Based on the conversion formula, the relative intensity of the standard sample is converted into the relative intensity of the standard sample corresponding to the first preset position according to the first distance and the second distance; wherein, the first distance is the distance from the first preset position to the detector, and the second distance is the distance from the second preset position to the detector;

[0016] The absolute intensity calibration factor is calculated using the scattering curve and the theoretical curve of the standard sample.

[0017] The absolute strength of the specimen is calculated using the absolute strength calibration factor and the relative strength of the specimen.

[0018] Preferably, the conversion formula is as follows:

[0019] ;

[0020] in, I st, A (q) The relative intensity of the standard sample corresponding to the first preset position, I st,B (q) The relative intensity of the standard sample corresponding to the second preset position, L A The first distance, L B This is the second distance.

[0021] Preferably, the derivation process of the conversion formula is as follows:

[0022] The second sample intensity relationship is derived from the first sample intensity relationship and the spatial angle relationship.

[0023] The relative intensity relationship at the first preset position and the relative intensity relationship at the second preset position are obtained based on the second sample intensity relationship.

[0024] The pre-conversion formula is obtained based on the relative intensity relationship of the first preset position and the relative intensity relationship of the second preset position;

[0025] The conversion formula is obtained based on the pre-conversion formula.

[0026] Preferably, the relative intensity relationship of the first sample is:

[0027] ;

[0028] in, I(q) The relative scattering intensity of a sample after deducting background scattering, as measured by the detector; or simply relative intensity. I 0 The relative intensity of incident light (phs / mm) 2 / s); S The irradiated area of ​​the sample (cm²) 2 ); Ω The solid angle (sr) corresponding to a single pixel of the detector; η Detector efficiency (%); T The X-ray transmittance of the sample is expressed as a percentage (%). d Sample thickness (mm); ( Σ / Ω)(q) This refers to the absolute scattering intensity, or simply absolute intensity.

[0029] Preferably, the spatial angle relationship is:

[0030] Where L is the distance from the sample to the detector, pixel is the detector pixel size, 2θ is the scattering angle, and R is the distance from the sample to the top of a single pixel on the detector.

[0031] Preferably, the relative intensity relationship of the second sample is as follows:

[0032] .

[0033] Preferably, the relative intensity relationship at the first preset position is as follows:

[0034] ,in, I 0,A The relative intensity at the first preset position. L A The distance from the first preset position to the detector. I 0,B The relative intensity at the second preset position. L B This is the distance from the second preset position to the detector.

[0035] Preferably, the relative intensity relationship at the second preset position is as follows:

[0036] .

[0037] Preferably, the pre-conversion formula is:

[0038] .

[0039] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0040] This invention provides a method for calibrating the absolute strength of a sample at different locations in a SAXS system. The invention converts the relative strength of the standard sample at different locations into the relative strength of the corresponding sample location using a formula and obtains a calibration factor. The absolute strength of the sample is then obtained using the calibration factor. This invention improves the diversity and accuracy of absolute strength calibration and reduces calibration costs. Attached Figure Description

[0041] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0042] Figure 1A flowchart illustrating a method for calibrating the absolute intensity of a sample at different locations in a SAXS system, as provided in this embodiment of the invention;

[0043] Figure 2 This is a schematic diagram of the SAXS experiment provided in an embodiment of the present invention;

[0044] Figure 3 A schematic diagram of the novel standard sample glassy carbon SRM3600 provided in the embodiments of the present invention;

[0045] Figure 4 A schematic diagram of the theoretical absolute strength curve of the novel standard sample glassy carbon SRM3600 provided in the embodiments of the present invention;

[0046] Figure 5 A diagram illustrating an in-situ coal dry distillation experiment conducted at the 1W2A beamline SAXS experimental station of the Beijing Synchrotron Radiation Facility (BSRF) as provided in this embodiment of the invention.

[0047] Figure 6 This is a schematic diagram illustrating a method for calibrating the absolute intensity of a sample at different locations in a SAXS system, as provided in an embodiment of the present invention.

[0048] Figure 7 A schematic diagram illustrating the relative scattering intensity test between glassy carbon and the sample provided in an embodiment of the present invention;

[0049] Figure 8 This is a schematic diagram of the experimental measurement of standard samples and physical samples provided in the embodiments of the present invention;

[0050] Figure 9 This is a schematic diagram of the relative strength curves of the standard samples and specimens at various locations provided in the embodiments of the present invention;

[0051] Figure 10 This is a schematic diagram comparing the calculated location A data of the standard sample with the measured data provided in this embodiment of the invention;

[0052] Figure 11 The absolute intensity curve of the sample provided in the embodiment of the present invention. Detailed Implementation

[0053] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0054] The purpose of this invention is to provide a method for calibrating the absolute strength of a sample at different locations in a SAXS. This invention solves the problem in the prior art that it is impossible to test the sample and standard at different locations to calibrate the absolute strength of the sample.

[0055] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0056] like Figure 1 As shown, this invention provides a method for calibrating the absolute intensity of a sample at different locations in a SAXS, comprising:

[0057] Step 100: Place the sample and the standard sample at the first preset position and the second preset position respectively, and measure the relative strength of the sample and the relative strength of the standard sample;

[0058] Step 200: Based on the conversion formula, convert the relative intensity of the standard sample into the relative intensity of the standard sample corresponding to the first preset position according to the first distance and the second distance; wherein, the first distance is the distance from the first preset position to the detector, and the second distance is the distance from the second preset position to the detector;

[0059] Step 300: Calculate the absolute intensity calibration factor using the scattering curve of the standard sample and the theoretical curve of the standard sample;

[0060] Step 400: Calculate the absolute strength of the specimen using the absolute strength calibration factor and the relative strength of the specimen.

[0061] Furthermore, the conversion formula is as follows:

[0062] ;

[0063] in, I st , A (q) The relative intensity of the standard sample corresponding to the first preset position, I st,B (q) The relative intensity of the standard sample corresponding to the second preset position, L A The first distance, L B This is the second distance.

[0064] like Figure 6 As shown, the specific procedure for calibrating the absolute intensity of a sample at different locations in SAXS is as follows:

[0065] Measure the relative intensity of the sample and standard at different locations: Using the same SAXS instrument, measure the sample, standard (e.g., glassy carbon), and their back surfaces at different locations along the optical path. Figure 7 As shown, the sample and its backing were measured at position A, and the standard sample and its backing were measured at position B. The relative strength of the sample and the standard sample was obtained by subtracting the backing, denoted as I. s,A (q) and I st,B (q). Figure 7 The vacuum tube in the sample is used to protect the incident and scattered light. The slit upstream of the sample is used to block parasitic scattering. The ionization chamber is used to record the relative incident light intensity. The photodiode integrated in the direct beam blocker (also known as the beam blocker) is used to record the relative transmitted light intensity. The SAXS detector records the relative scattering signal.

[0066] Calculate the relative strength of the standard sample to the location of the specimen: that is, Figure 7 The relative intensity I of the standard sample measured at position B st,B (q) is converted into the relative intensity I corresponding to position A. st,A (q);

[0067] Calculate the absolute intensity calibration factor at the specimen location: compare the scattering curves of the standard specimens with those of the standard specimens. st,A (q) and its theoretical curve ( Σ / Ω) st (q) Figure 4 ), and calculate the absolute intensity calibration factor (CF).

[0068] Calculate the absolute strength of the sample: Based on the absolute strength calibration factor mentioned above, calculate the relative strength I of the sample measured at position A. s,A (q) is converted into absolute intensity ( Σ / Ω) s (q).

[0069] Furthermore, the derivation process of the conversion formula is as follows:

[0070] The second sample intensity relationship is derived from the first sample intensity relationship and the spatial angle relationship.

[0071] The relative intensity relationship at the first preset position and the relative intensity relationship at the second preset position are obtained based on the second sample intensity relationship.

[0072] The pre-conversion formula is obtained based on the relative intensity relationship of the first preset position and the relative intensity relationship of the second preset position;

[0073] The conversion formula is obtained based on the pre-conversion formula.

[0074] Preferably, the relative intensity relationship of the first sample is:

[0075] ;

[0076] in, I A (q) The relative scattering intensity of a sample after deducting background scattering, as measured by the detector; or simply relative intensity. I 0，A The relative intensity of incident light (phs / mm) 2 / s); S The irradiated area of ​​the sample (cm²) 2 ); Ω A The solid angle (sr) corresponding to a single pixel of the detector; η Detector efficiency (%); T The X-ray transmittance of the sample is expressed as a percentage (%). d Sample thickness (mm); ( Σ / Ω)(q) This refers to the absolute scattering intensity, or simply absolute intensity.

[0077] Furthermore, the spatial angle relationship is as follows:

[0078] Where L is the distance from the sample to the detector, pixel is the detector pixel size, 2θ is the scattering angle, and R is the distance from the sample to the top of a single pixel on the detector.

[0079] Furthermore, the relative intensity relationship of the second sample is as follows:

[0080] .

[0081] The same sample was placed at different positions along the optical path of the same SAXS instrument, such as position A and position B, and its scattering intensity was measured. The spatial angle relationships η, T, d, and pixel were then analyzed. Σ / Ω)(q) remains unchanged. For a parallel beam, S also remains unchanged; while for focused and diverging beams, theoretically S is not equal at different positions, but modern instruments have very small X-ray divergence and good collimation. When positions A and B are not too far apart (<0.1 m), S is approximately equal. Therefore, the relative intensity relationship at the first preset position is further obtained as follows:

[0082] ,in, I0,A The relative intensity at the first preset position. L A The distance from the first preset position to the detector. I 0,B The relative intensity at the second preset position. L B This is the distance from the second preset position to the detector.

[0083] The relative intensity relationship at the second preset position is:

[0084] .

[0085] Furthermore, dividing the relative intensity relationship at the second preset position by the relative intensity relationship at the first preset position yields a pre-conversion formula, which is:

[0086] .

[0087] For laboratory SAXS instruments with ordinary light sources and synchrotron radiation SAXS instruments in constant-intensity, constant-current top-up injection mode, I 0,A and I 0,B They are equal; however, for synchrotron radiation SAXS instruments in a gradually decaying periodic injection mode, they are not equal. When the incident light intensity is the same, the pre-conversion formula simplifies to the conversion formula.

[0088] The present invention also provides the following specific embodiments:

[0089] Standard sample: SRM3600 glassy carbon, in the form of a square sheet, 10 mm on each side and 1.055 mm thick.

[0090] Sample: Lean coal from Wuyang Coal Mine, Changzhi City, Shanxi Province, in the form of round flakes, 10 mm in diameter and 1 mm thick.

[0091] The SAXS experiment was conducted at the Shanghai Synchrotron Radiation BL16B1 small-angle scattering beamline station, with an incident light energy of 10 keV and a wavelength of 0.124 nm, using a Pilatus 2M detector. The two-dimensional scattering images were transformed into one-dimensional scattering curves using rectangular integration with Fit2d software (J. Appl. Crystallogr., 2016, 49, 646–652.). Relevant parameters were calculated from the data using S.exe software (Chinese Phys. C, 2013, 37, 110–115.).

[0092] The specific calibration and verification steps are as follows:

[0093] 1. Measure the scattering intensity of the sample and its background at position A (e.g., Figure 8The relative intensities of the standard sample (glassy carbon SRM3600) and its background were measured at locations A and B, respectively. The scattering curves of the standard sample and the sample after subtracting the background were denoted as I. st,A ´(q), I st,B ´(q), I s,A (q) (as in) Figure 9 ). Measure the distances L from positions A and B to the detector respectively. a =2020mm, L b =1910 mm. I st,B ´(q) is converted into the relative intensity I at position A. st,A (q):

[0094] The transformed curve I st,A (q) and the measured I at position A st,A ´(q) are drawn on a single graph for comparison, from Figure 10 It can be seen that the data calculated by the conversion formula at position B matches the measured data at position A well, proving the feasibility of the conversion formula.

[0095] Calculate the calibration factor from position B to position A, and compare it with the calibration factor calculated from the measured data at position A:

[0096]

[0097]

[0098] In the formula, CF is the calibration factor, and A and B correspond to... Figure 8 The position of k in the middle st+stb For diode counting of a standard sample with backscattering, d st The thickness of the standard sample is in mm. Σ / Ω) st (q) represents the absolute strength of glassy carbon.

[0099] CF B With CF A The relative error is 0.286%, which proves the feasibility of the conversion formula.

[0100] The absolute strength of the sample is calculated according to the following formula ( Σ / Ω) s,A (q), the result is as follows Figure 11 .

[0101]

[0102] In the formula k s+sb For the diode count of the sample and its back surface, ds The thickness of the sample.

[0103] The beneficial effects of this invention are as follows:

[0104] In this invention, calibrating the absolute scattering intensity at a certain distance is no longer limited to measuring the standard sample and the test sample at the same location; under the same test conditions, the relative intensity of the sample measured at a certain distance can be converted to the relative intensity at other distances. The calibration method of this invention is suitable for any standard sample location, requiring only precise knowledge of the distance from the standard sample to the test sample. This operation is simple, efficient, has good repeatability, and minimal error.

[0105] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0106] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A method for calibrating the absolute intensity of a sample at different positions in SAXS, characterized in that, include: The sample and the standard were placed at a first preset position and a second preset position, respectively, and the relative strength of the sample and the relative strength of the standard were measured. Based on the conversion formula, the relative intensity of the standard sample is converted into the relative intensity of the standard sample corresponding to the first preset position according to the first distance and the second distance; wherein, the first distance is the distance from the first preset position to the detector, and the second distance is the distance from the second preset position to the detector; The absolute intensity calibration factor is calculated using the scattering curve and the theoretical curve of the standard sample. The absolute strength of the specimen is calculated using the absolute strength calibration factor and the relative strength of the specimen. The specific conversion formula is as follows: ； wherein, I st，A (q) a relative intensity of a marker corresponding to the first pre-set position, I st,B (q) a relative intensity of a marker corresponding to the second pre-set position, L A is a first distance, L B is a second distance, The derivation process of the conversion formula is as follows: The second sample intensity relationship is derived from the first sample intensity relationship and the spatial angle relationship. The relative intensity relationship at the first preset position and the relative intensity relationship at the second preset position are obtained based on the second sample intensity relationship. The pre-conversion formula is obtained based on the relative intensity relationship of the first preset position and the relative intensity relationship of the second preset position; The conversion formula is obtained based on the pre-conversion formula. The relative intensity relationship of the first sample is: ； Wherein, I A (q) Relative scattering intensity of the sample measured by the detector after deducting the background scattering, referred to as relative intensity; I 0，A Relative intensity of incident light, phs / s / mm 2 ; S Irradiated area of the sample, cm 2 ; Ω A Solid angle corresponding to a single pixel of the detector, sr; η Efficiency of the detector, %; T Transmittance of the sample to X-rays, %; d Thickness of the sample, mm; Absolute scattering intensity, referred to as absolute intensity; The spatial angle relationship is as follows: ; where L is the distance from the sample to the detector, pixel is the detector pixel size, 2Q is the scattering angle, and R is the distance from the sample to the detector above a single pixel.

2. The method for calibrating the absolute intensity of a sample at different locations in a SAXS according to claim 1, characterized in that, The relative intensity relationship of the second sample is: 。 3. The method for calibrating the absolute intensity of a sample at different locations in a SAXS according to claim 2, characterized in that, The relative intensity relationship at the first preset position is as follows: ,in, I 0,A The relative intensity at the first preset position, L A The distance from the first preset position to the detector. I 0,B The relative intensity at the second preset position. L B This is the distance from the second preset position to the detector.

4. The method for calibrating the absolute intensity of a sample at different locations in a SAXS according to claim 3, characterized in that, The relative intensity relationship at the second preset position is: 。 5. The method for calibrating the absolute intensity of a sample at different locations in a SAXS according to claim 4, characterized in that, The pre-conversion formula is: 。

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