A method for calculating the reference intensity of an unknown crystalline phase and its application.

Abstract

This invention relates to a method for calculating the reference intensity of a crystal phase with an unknown structure and its application. The calculation method does not require complete crystal structure information. The reference intensity of the crystal phase can be calculated based only on the unit cell parameters, unit cell chemical composition, and diffraction intensity or relative diffraction intensity of the diffraction lines. It has high accuracy and does not require additional experimental work, thus providing a basis for quantitative phase analysis using reference intensity information.

Description

Technical Field

[0001] This invention relates to the field of X-ray crystallography, specifically to a method for calculating the reference intensity of a crystal phase with an unknown structure and its application. Background Technology

[0002] X-ray diffraction (XRD) is used to collect powder diffraction data of crystalline samples. This allows for the identification of the constituent phases of the sample and, based on the diffraction intensity of each phase, quantitative phase analysis to determine their content. The basic principle is that the XRD intensity of a phase is directly proportional to its content in the sample; the higher the relative content of a phase, the higher the intensity of its diffraction peak. However, different phases have different diffraction capabilities for incident X-rays. Therefore, the relative content of each phase in the sample cannot be determined by directly comparing their relative diffraction intensities.

[0003] Currently, commonly used quantitative analysis methods include the internal standard method, absorption-diffraction method, and standard addition method. These methods can perform quantitative phase analysis without knowing the crystal structure data of the phase being analyzed. However, in addition to performing diffraction experiments on the sample for quantitative analysis, it is also necessary to prepare standard samples and / or a series of samples doped with specific amounts of standard samples or target phases, collect diffraction data from each of these samples, and perform comprehensive analysis of the diffraction data from the series of samples in order to deduce the content of the target phase in the sample.

[0004] To reduce the experimental workload of quantitative phase analysis and facilitate phase analysis using diffraction methods, the International Centre for Diffraction Data (ICDD) proposed the reference intensity ratio (RIR) method. This method involves recording the powder diffraction pattern of each crystalline phase when it is mixed with a reference material at a 50%:50 mass ratio, and measuring the ratio of the strongest diffraction peak intensity of the mixed phase to that of the reference material. If RIR data are available for each phase in a mixed-phase sample, the diffraction pattern of the sample can be directly measured, and the quantitative phase analysis results can be obtained directly by combining the RIR data.

[0005] The essence of the reference intensity method is to determine the relative diffraction ability of each phase by comparing it with the same reference material, and then derive the content of each phase based on the ratio of the diffraction intensities of each phase in the diffraction spectrum of the mixed sample. If the RIR values ​​of all component phases in the sample are known, only one set of powder diffraction data needs to be measured for the sample. No additional auxiliary samples or auxiliary powder diffraction data need to be prepared, and the content of each component phase in the sample can be quickly determined. Therefore, compared with methods such as the internal standard method, the doping method, and the diffraction-absorption method, the reference intensity method is a more convenient and faster method for quantitative phase analysis, and it is widely used in many fields such as geology, materials, and medicine.

[0006] However, the Powder Diffraction File (PDF) database published by the International Powder Diffraction Data Center still lacks reference intensity information for many phases. If even one phase in a sample lacks reference intensity information, quantitative phase analysis using the reference intensity method becomes impossible. For phases with known crystal structures, the reference intensity can be calculated from the crystal structure data without experimental measurement. In fact, all powder diffraction data files in the PDF database published by the International Powder Diffraction Data Center, calculated from crystal structure information, already list the reference intensities calculated based on the structure data for the corresponding phases. However, many PDF entries in this database still lack both experimental reference intensities and the ability to calculate reference intensity values ​​due to the lack of structural information, causing significant inconvenience for quantitative phase analysis using the reference intensity method. Completing these missing reference intensity information through experimental measurement is undoubtedly a very time-consuming and laborious task. Furthermore, new phases are constantly being discovered in production and research activities, and the reference intensity information for these new phases also needs to be measured or calculated. To calculate the reference intensity of a new phase, its crystal structure must first be determined; to measure the reference intensity of a new phase, a pure-phase sample of that phase must first be isolated. Both methods are quite complex for new phases.

[0007] CN 115629091A discloses a method for determining the reference intensity of a phase. This method involves quantitatively analyzing the diffraction spectra of mixed samples with different contents using a full-spectrum fitting method to obtain the accurate content of each phase in the mixed sample. A curve is plotted based on the content ratio of the analyte phase to the standard phase and the intensity ratio of the strongest peak, and linear fitting is performed to obtain a fitting formula. The accurate reference intensity value is then calculated. However, this method requires known crystal structure data of each phase in the sample; otherwise, quantitative analysis is impossible.

[0008] Based on the previously proposed X-ray diffraction theory (Hui Li, Meng He and Ze Zhang, Method of calculating the coherent scattering power of crystals with unknown atomic arrangements and its application in the quantitative phase analysis, Powder Diffraction, 2022, 37(1), 34-39.), the inventors provide a method for calculating the reference intensity of a phase with unknown structure. Summary of the Invention

[0009] The purpose of this invention is to provide a method for calculating the reference intensity of a crystal phase with an unknown structure and its application. The reference intensity of the crystal phase can be calculated using the unit cell parameters, unit cell chemical composition and its X-ray powder diffraction data, and then applied to quantitative phase analysis.

[0010] To achieve this objective, the present invention adopts the following technical solution:

[0011] In a first aspect, the present invention provides a method for calculating the reference intensity of a crystalline phase with an unknown structure, the flowchart of which is shown below. Figure 1 As shown, the calculation method includes the following steps:

[0012] (1) Obtain the lattice parameters, unit cell chemical composition, and diffraction intensity or relative diffraction intensity of the diffraction lines of the unknown crystal phase.

[0013] (2) Calculate the reference intensity of the crystal phase according to the formula, which is as follows:

[0014]

[0015] or

[0016]

[0017] Among them: RIR j,f This represents the reference intensity of crystal phase j relative to the reference phase f, that is, the ratio of the diffraction intensity of a certain diffraction line of crystal phase j to the diffraction intensity of a certain diffraction line of reference phase f when crystal phase j and reference phase f are mixed at a mass ratio of 1:1; the certain diffraction line is usually the strongest diffraction line.

[0018] G j,h The Lorentz-polarization factor represents the diffraction line with diffraction index h corresponding to crystal phase j.

[0019] G f,H′The Lorentz-polarization factor represents the diffraction line with diffraction index H′ of the reference phase f.

[0020] ρ j and V j Let ρ represent the density and unit cell volume of phase j, respectively. f and V f These represent the density and unit cell volume of the reference phase f, respectively.

[0021] f j,i,h′ Let h′ represent the atomic scattering factor corresponding to the diffraction index h′ of the i-th atom in the unit cell of crystal phase j, where the diffraction index h′ corresponds to an imaginary crystal with the same unit cell as crystal phase j and atoms only at the origin of the unit cell.

[0022] I j,H and I j,h The diffraction intensities of H and h diffraction for phase j are represented respectively.

[0023] and These represent the relative diffraction intensities of H and h diffraction for crystal phase j, respectively.

[0024] H represents the diffraction index of the diffraction line of crystal phase j selected for comparison with the intensity of a specific diffraction line of the reference phase f. Conventionally, the strongest diffraction line of crystal phase j is selected for comparison with the intensity of a specific diffraction line of the reference phase.

[0025] |F f,H′ | represents the structural amplitude of the H′ diffraction of the reference phase f; H′ is the diffraction index of the diffraction line of the reference phase f selected for comparison with the intensity of the H diffraction line of the crystal phase j. By convention, the strongest diffraction line of the reference phase is selected for comparison with the intensity of a specific diffraction line of the crystal phase j.

[0026] m f,H′ This represents the multiplicity factor of the H′ diffraction of the reference phase f.

[0027] The calculation method provided by this invention can calculate the reference intensity of a crystal phase by using its cell parameters, cell chemical composition, and the diffraction intensity or relative diffraction intensity of the diffraction lines. The formula is derived through the following process:

[0028] For a semi-infinite thickness powder (polycrystalline) sample containing phase j, the integrated diffraction intensity measured by an X-ray powder diffractometer with a fixed-width receiving slit is (Jenkins, R. & Snyder, RL Introduction to X-Ray Powder Diffractometry, 1996, New York: John Wiley & Sons).

[0029]

[0030] Among them: I j,h The diffraction intensity of h-diffraction in phase j is given; e and m are the charge and mass of an electron, respectively; c is the speed of light; I0 ​​is the power of the incident X-ray; λ is the wavelength of the incident X-ray; R is the distance between the sample and the detector; G j,h μ represents the Lorentz-polarization factor corresponding to the diffraction line with diffraction index h for phase j; * x is the mass absorption coefficient of the sample; j ρ represents the mass fraction of crystalline phase j in the sample. j V j Represent the density and unit cell volume of phase j, respectively; |F j,h | represents the structural amplitude of the h diffraction of the reference crystal phase j; m j,h G is the multiplicity factor of h-diffraction for crystal phase j; when the incident light is unpolarized and there are no monochromators in either the incident or diffracted light paths, G j,h have The form, where θ j,h θ is the Bragg angle corresponding to the h diffraction of crystal phase j.

[0031] By definition, RIR j,f To determine the intensity ratio of diffraction lines between two phases in the X-ray powder diffraction pattern of a powder sample obtained by mixing crystalline phase j and reference phase f at a mass ratio of 1:1, the strongest diffraction line between the two phases is conventionally selected.

[0032]

[0033] Among them, I j,H I represents the diffraction intensity of the specified diffraction line H in the diffraction spectrum of the powder mixture, representing the phase j. f,H′ This indicates the diffraction intensity of the reference phase f in the powder diffraction spectrum of the mixture, specifying the diffraction line H′.

[0034] Substituting formula (3) into formula (4), we get

[0035]

[0036] Among them, G j,H The Lorentz-polarization factor represents the diffraction line with diffraction index H for phase j.

[0037] The inventors have demonstrated the following relationship for X-ray diffraction of crystals:

[0038]

[0039] For the proof of formula (6), please refer to the relevant literature (Hui Li, Meng He & Ze Zhang, Method of calculating the coherent scattering power of crystals with unknown atomic arrangementments and its application in the quantitative phase analysis, Powder Diffraction, 2022, 37(1), 34-39). Furthermore, the examples show that formula (6) is valid not only when the summation on both sides of the equal sign covers the entire reciprocal space, but also when it is well approximated within a sufficiently large finite reciprocal space.

[0040] From formula (3), it can be seen that there is the following relationship between the diffraction intensities of different diffraction lines H and h of phase j in the mixture:

[0041]

[0042] According to formula (7), we can obtain:

[0043]

[0044] Substituting formula (6) into formula (8), we get:

[0045]

[0046] Substituting formula (9) into formula (5), we obtain the aforementioned formula (1):

[0047]

[0048] And because

[0049]

[0050] Therefore, formula (1) can also be written in the form of formula (2), that is...

[0051]

[0052] As can be seen from the above derivation, the reference intensity of the unknown crystalline phase can be calculated using formula (1) or (2).

[0053] Preferably, the lattice parameters in step (1) are determined by powder diffraction data of the crystal phase.

[0054] Preferably, the chemical components in step (1) are determined by a micro-area chemical analysis device.

[0055] Preferably, the micro-area chemical analysis device includes an electron probe.

[0056] Preferably, the upper limit of the reciprocal space range occupied by the diffraction lines in step (1) is...

[0057] The reciprocal space occupied by the diffracted rays should be sufficiently large. Typically, the lower limit of the reciprocal space is... but If the lower limit of the reciprocal space range is increased, the upper limit of the reciprocal space range should also be increased accordingly to keep the reciprocal space range large enough.

[0058] Preferably, the wavelength of the incident X-ray is the characteristic wavelength of Cu Kα, and the reciprocal space range can be represented by the diffraction angle range, wherein the lower limit of the diffraction angle range is ≤10° and the upper limit of the diffraction angle range is ≥80°.

[0059] If the calculation method provided by this invention is applied within a small reciprocal space, the calculated RIR value may have a large deviation.

[0060] Secondly, the present invention provides an application of the calculation method as described in the first aspect, the calculation method being used in quantitative phase analysis.

[0061] The reference intensity obtained by the calculation method provided by this invention can be applied to quantitative phase analysis based on X-ray powder diffraction data.

[0062] Preferably, the quantitative phase analysis includes: sequentially calculating and quantitatively analyzing the reference intensity of the crystalline phases for which reference intensity information is missing.

[0063] The lack of reference intensity information refers to the absence of reference intensity (RIR) information in the PDF of the relevant crystal phase published by the International Powder Diffraction Data Center. As long as the cell parameters and cell chemical composition information of the crystal phase are available, the reference diffraction intensity of the crystal phase relative to the reference phase can be calculated based on the relative diffraction intensities of each diffraction line of the crystal phase, without any additional experimental work.

[0064] Preferably, the quantitative phase analysis includes: sequentially performing reference strength calculation and quantitative analysis on one component phase of the mixture.

[0065] One possible application scenario for the aforementioned reference intensity (RIR) calculation method is when a pure-phase sample of the studied phase is unavailable, and the phase exists only as one component phase in a mixture, with the content ratio of this phase to other component phases unknown. As long as the lattice parameters and unit cell chemical composition information of the phase are available, the reference intensity of the phase can be calculated using the X-ray powder diffraction spectrum containing that phase, and further quantitative analysis can be performed.

[0066] Another possible application scenario for the reference intensity (RIR) calculation method is when the phase under study is a pure phase, but for some reason, a reference phase cannot or is not desired to be incorporated into the sample. As long as the lattice parameters and unit cell chemical composition information of the phase exist, the reference intensity of the phase can be calculated using the X-ray powder diffraction data of the pure phase sample.

[0067] Compared with the prior art, the present invention has the following beneficial effects:

[0068] The calculation method provided by this invention does not require complete crystal structure information. It can calculate the reference intensity of a crystal phase based solely on the unit cell parameters, unit cell chemical composition, and diffraction intensity or relative diffraction intensity of the diffraction lines. It has high accuracy and requires no additional experimental work, thus providing a foundation for quantitative phase analysis using reference intensity information. Attached Figure Description

[0069] Figure 1 This is a flowchart illustrating the method for calculating the reference intensity of an unknown crystalline phase provided by the present invention.

[0070] Figure 2 The X-ray (Cu Kα) powder diffraction pattern of the three-phase mixture provided in Example 2 is shown. Detailed Implementation

[0071] The technical solution of the present invention will be further illustrated below through specific embodiments. Those skilled in the art should understand that the embodiments described are merely illustrative of the present invention and should not be construed as limiting the invention in any way.

[0072] Example 1

[0073] This embodiment calculates the reference intensity of cristobalite (PDF 82-1404) in the International Powder Diffraction Database. The quality label of this PDF file is "calculated", indicating that the powder diffraction file is calculated from crystal structure data. The corresponding crystal structure data comes from record 75484 in the Inorganic Crystal Structure Database (ICSD).

[0074] In this embodiment, the calculated PDF file is used to verify the calculation method provided by the present invention. On the one hand, the crystal structure data corresponding to the substance is known, and the RIR of the phase can be calculated based on the crystal structure data. The RIR obtained by the calculation method provided by the present invention is compared to verify the effectiveness of the method. On the other hand, the diffraction data in the PDF file calculated from the crystal structure data does not contain the interference of experimental factors, which can avoid the impact of inaccurate experimental data on the application effect of the method, and is more conducive to verifying the effectiveness of the calculation method provided by the present invention.

[0075] This embodiment provides a method for calculating the intensity of a crystal phase reference, the method comprising the following steps:

[0076] (1) Obtain the lattice parameters, unit cell chemical composition, and diffraction intensity or relative diffraction intensity of the tetragonal quartz phase. The information is as follows: tetragonal unit cell The chemical formula is SiO2, Z = 4. The X-ray powder diffraction data of cristobalite under the characteristic X-ray diffraction conditions of Cu Kα1 are shown in Table 1. The data in the three columns on the left of Table 1 are directly quoted from PDF 82-1404, “G j,h One column of data was calculated based on the data in the second column from the left, "2θ(°)". A series of data and "G" j,h "The results were obtained from the calculation of the two columns of data."

[0077] Table 1

[0078]

[0079]

[0080]

[0081] (2) Calculate the reference intensity of the crystal phase according to the formula, which is as follows:

[0082]

[0083] The following calculations are performed according to the formula (2) above. The specific calculation steps are as follows:

[0084] According to convention, the strongest diffraction peaks of cristobalite and the reference phase corundum are selected to calculate RIR, then H in formula (2) is 101 and H′ is 113.

[0085] Assuming the Lorentz polarization factor has In this case, based on the diffraction angle data of each diffraction line of the quartz, the corresponding G can be calculated. j,h Then, the value of each diffraction line can be calculated. Finally, the value of cubic quartz was determined. The value of the item is 15.7433;

[0086] quartz The unit cell volume is Density of cristobalite Where M j Z represents the chemical formula mass of SiO2. j ρ is the number of chemical formulas within the unit cell, which can be calculated. j =2.355g / cm 3 ;

[0087] Construct a hypothetical crystal containing only Si or O atoms at the origin of the unit cell. Calculate and sum the structural amplitudes of all possible diffractions of this hypothetical crystal within the same diffraction angle range as PDF 82-1404 (i.e., 0 < 2θ < 90°) to obtain the structural amplitudes. The numerical value of the term. Actual calculations show that for the O atom, For Si atoms For all atoms (8 O, 4 Si) within the unit cell Summing the terms yields the value of cubic quartz. The value of the item, i.e.

[0088] Corundum is used as a reference phase, and its crystal structure is known. This embodiment cites the crystal structure information of corundum given in ICSD record 92630: chemical formula Al2O3, Z=6, space group Lattice parameters Unit cell volume V f for density ρ f It is 3.986 g / cm³ 3 Al is located at position 12c, with coordinates (0, 0, 0.35217); O is located at position 18e, with coordinates (0.30634, 0, 1 / 4). Based on the structural information of corundum (the B values ​​of Al / O are both set to...), The structural amplitude of the strongest diffraction line 113 in the corundum powder diffraction spectrum can be calculated as |F f,H′ |=71.11, the multiplicity factor m of this diffraction f,H′ =12, G f,H′ =12.7122;

[0089] Substituting the above data into formula (2), we get

[0090]

[0091] The reference strength obtained from formula (5) and the crystal structure data of cristobalite is:

[0092]

[0093] The RIR value (5.72) of cristobalite obtained by the calculation method provided in this embodiment is in good agreement with the RIR value (5.10) calculated based on the crystal structure of cristobalite, with a deviation of about 12%, which verifies the effectiveness of the calculation method provided in this embodiment.

[0094] It is particularly important to note that the main source of the deviation is not the approximation of formula (6) on which this invention is based within a limited range of diffraction angles, but rather the inconsistency between the relative diffraction intensities of each diffraction line in the PDF file and the structural amplitudes of each diffraction line calculated based on the crystal structure data. In this embodiment, the sum of squares of the structure factors of cristobalite in the range of 0° < 2θ < 90° calculated according to the crystal structure model is:

[0095] ∑ h m j,h |F j,h | 2 =184113.8968

[0096] Based on the lattice parameters and the chemical composition of the unit cell, it was calculated that:

[0097]

[0098] The deviation between the two is only 1.6%. This shows that formula (6) holds well within the commonly used angle range of 0° < 2θ < 90° in practical X-ray powder diffraction experiments. Conversely, although formula (8) should strictly hold for different diffraction lines of the same phase j according to formula (3), calculations based on the cristobalite crystal structure data show that:

[0099]

[0100] Based on the relative diffraction intensities of each diffraction line of cristobalite given in the PDF file, the following calculations were performed:

[0101]

[0102] The deviation between the two is as high as 14%. The calculation method provided in this embodiment uses the diffraction intensity information from the PDF file to calculate... The term is used to replace the one that needs to be calculated from the crystal structure. The deviation between these two items constitutes the main source of RIR bias, indicating that the insufficient accuracy of the relative diffraction intensity of each diffraction line in the PDF file is the main cause of RIR bias.

[0103] Considering that PDF 82-1404 referenced in this embodiment is itself a set of powder diffraction patterns calculated based on crystal structure data, and The discrepancy may stem from two sources: 1) some rounding errors occurred when calculating the relative diffraction intensities in the PDF file; 2) in this embodiment, the calculation of F... j,h In this embodiment, the atomic scattering factor used differs slightly from that used by the International Powder Diffraction Data Center (IPDDC) when calculating PDF files. In this example, the atomic scattering factor for neutral atoms is used, and anomalous scattering effects are not considered.

[0104] Furthermore, it should be noted that RIR values ​​are easily affected by various factors such as sample preparation methods and micro-absorption effects, which can lead to significant deviations between RIR values ​​measured in different experiments. Even RIR values ​​calculated using crystal structure data can vary significantly depending on whether the scattering factor of neutral atoms or ions is used for calculation.

[0105] Even though the RIR values ​​calculated using this method may deviate from those calculated based on crystal structure data due to insufficient accuracy of the relative diffraction intensity in the PDF file, the degree of deviation is comparable to the deviation between the experimentally measured RIR values ​​and the calculated crystal structure values, and it still has reference value and practical value.

[0106] Example 2

[0107] This embodiment provides a method for calculating the intensity of a crystal phase reference, the method comprising the following steps:

[0108] (1) A three-phase mixture of Si, NaCl, and corundum (α-Al₂O₃) was prepared, with a mass ratio of 1:1:1. X-ray powder diffraction patterns of the mixture were collected within a 2θ angle range of 10-80°. Figure 2 As shown;

[0109] According to the definition of RIR and Chung's adiabatic principle (FHChung, Quantitative Interpretation of X-ray Diffraction Patterns of Mixtures. I1. Adiabatic Principle of X-ray Diffraction Analysis of Mixtures, J. Appl. Cryst., 1974, 7, 526-531), the ratio of the intensity of the strongest diffraction line of Si to that of corundum in the X-ray powder diffraction pattern of the mixture is the RIR value of Si. Using the lattice parameters of the three phases as constraints, the powder diffraction pattern of the mixture was decomposed. The integrated intensities of the strongest diffraction lines of Si and corundum obtained from the decomposition were 2492.3 and 544.4, respectively. Therefore,

[0110] Assuming that Si is a crystal with an unknown crystal structure, we can only obtain the lattice parameters of Si and the number of atoms in the unit cell;

[0111] (2) Calculate the reference strength of Si according to the formula, which is as follows:

[0112]

[0113] Therefore, the reference intensity of Si obtained by the calculation method provided in this embodiment deviates from the reference intensity of Si directly measured from actual diffraction data by less than 3.3%. Furthermore, in the powder diffraction data (PDF 27-1402) of silicon standard reference material (Standard Reference Material No. 640, SRM640) provided by the National Institute of Standards and Technology (NIST), the RIR value of Si is 4.70. Based on the crystal structure data of Si, the reference intensity of silicon calculated using formula (5) is 4.60. Both are very consistent with the RIR values ​​obtained by the calculation method provided in this embodiment.

[0114] Application Example 1

[0115] This application example provides an application of quantitative phase analysis using the calculation method provided in Example 2. The steps of the quantitative phase analysis include:

[0116] Consulting the international powder diffraction database PDF 72-1668, the RIR value of NaCl was found to be 4.56, and the RIR value of corundum was 1. Assuming that Si is a phase with an unknown crystal structure and its RIR is also unknown, the RIR value of Si was calculated to be 4.73 using the calculation method in Example 2. Using the RIR values ​​of Si, NaCl, and corundum, quantitative phase analysis was performed on the powder diffraction data of the three-phase mixture in Example 2, yielding the following results:

[0117]

[0118] Similarly, we can obtain

[0119] NaClwt%=35.9%, Al2O3wt%=32.6%.

[0120] Therefore, the results of quantitative phase analysis are in good agreement with the weighing value of the three phases in the mixture having a mass ratio of 1:1:1.

[0121] In summary, the calculation method provided by this invention does not require complete crystal structure information. It can calculate the reference intensity of a crystal phase based solely on the cell parameters, chemical composition of the cell, and the diffraction intensity or relative diffraction intensity of the diffraction lines. This method is highly accurate and requires no additional experimental work, thus providing a foundation for quantitative phase analysis using reference intensity information.

[0122] The above description is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Those skilled in the art should understand that any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention fall within the protection and disclosure scope of the present invention.

Claims

1. A method for calculating the reference intensity of a crystalline phase with unknown structure, characterized in that, The calculation method includes the following steps: (1) Obtain the lattice parameters, unit cell chemical composition, and diffraction intensity or relative diffraction intensity of the diffraction lines of the unknown crystal phase. (2) Calculate the reference intensity of the crystal phase according to the formula, which is as follows: or Among them: RIR j,f This represents the reference intensity of crystal phase j relative to the reference phase f, that is, the ratio of the diffraction intensity of a certain diffraction line of crystal phase j to the diffraction intensity of a certain diffraction line of reference phase f when crystal phase j and reference phase f are mixed at a mass ratio of 1:

1. G j,h The Lorentz-polarization factor represents the diffraction line with diffraction index h corresponding to crystal phase j. G f,H′ The diffraction index of the reference phase f is H. ′ The Lorentz-polarization factor corresponding to the diffraction lines; ρ j and V j Let ρ represent the density and unit cell volume of phase j, respectively. f and V f These represent the density and unit cell volume of the reference phase f, respectively. f j,i,h′ This represents the relationship between the i-th atom in the unit cell of crystal phase j and the diffraction index h. ′ The corresponding atomic scattering factor, where the diffraction index h ′ This corresponds to an imaginary crystal with the same unit cell as crystal phase j and atoms only at the origin of the unit cell; I j,H and I j,h The diffraction intensities of H and h diffraction for phase j are represented respectively. and These represent the relative diffraction intensities of H and h diffraction for crystal phase j, respectively. H represents the diffraction index of the diffraction line of crystal phase j, which is selected to be compared with the intensity of a specific diffraction line of reference phase f. |F f,H′ | Represents the H of the reference phase f ′ The structural amplitude of diffraction; H ′ The diffraction index of the diffraction line is selected as the reference phase f and compared with the intensity of the H diffraction line of the crystal phase j. m f,H′ H represents the reference phase f ′ The multiplicity factor of diffraction.

2. The calculation method according to claim 1, characterized in that, The difference between the upper and lower limits of the reciprocal space range occupied by the diffraction lines in step (1) is > 3. An application of the calculation method as described in claim 1 or 2, characterized in that, The calculation method is used in quantitative phase analysis.

4. The application according to claim 3, characterized in that, The quantitative phase analysis includes: sequentially calculating and quantitatively analyzing the reference intensity of crystalline phases for which reference intensity information is missing.

5. The application according to claim 3, characterized in that, The quantitative phase analysis includes: sequentially calculating and quantitatively analyzing the reference strength of one component phase in the mixture.

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