Calculation method of diffraction ability of crystals with unknown structure and quantitative analysis method of phase

Abstract

The present invention provides a method for calculating the diffraction ability of a crystal with an unknown structure and a method for quantitative phase analysis, the method comprising: S1, constructing a hypothetical crystal, the hypothetical crystal having the same unit cell parameters as the crystal under study, and having only one atom at the unit cell origin of the hypothetical crystal, the type of the atom being the same as the type of one of the atoms in the unit cell of the crystal under study, and calculating the diffraction ability of the unit cell of the hypothetical crystal to X-rays; S2, executing the calculation process of S1 for each atom in the unit cell of the crystal under study, accumulating the diffraction abilities of the unit cells of all hypothetical crystals to X-rays, and obtaining the diffraction ability of the unit cell of the crystal under study to X-rays. The calculation method provided by the present invention can use X-ray powder diffraction data to perform quantitative phase analysis on a mixed substance containing a crystal phase with an unknown structure.

Description

Technical Field

[0001] The present invention relates to the technical field of X-ray crystallography, and in particular to a method for calculating the diffraction ability of a crystal with an unknown structure and a method for quantitatively analyzing a phase. Background Art

[0002] By using X-ray diffraction technology to collect powder (polycrystalline) diffraction data of crystal samples, the constituent phases of the sample can be identified based on the diffraction data. The sample can also be quantitatively analyzed based on the diffraction intensity of each phase that makes up the sample to determine the content of each constituent phase in the sample. This technology of using X-ray polycrystalline diffraction data for phase identification and quantitative phase analysis has been developed for more than 100 years and has been widely used in scientific research and production. It is already the most widely used and authoritative phase quantitative analysis technology.

[0003] The basic principle of using X-ray diffraction data for quantitative phase analysis is that the X-ray diffraction intensity of a phase is proportional to its content in the sample. The higher the relative content of a phase in the sample, the higher the intensity of the diffraction peak of the phase. However, the diffraction ability of different phases to the incident X-ray is different, so the relative content of each phase in the sample cannot be determined by directly comparing the relative diffraction intensity of different phases. In order to solve this problem, people have developed many methods, such as absorption-diffraction method, standard addition method (incorporation method), internal standard method, etc. These methods do not require the knowledge of the crystal structure data of the analyzed phase to perform phase quantitative analysis, but in addition to the need to perform diffraction experiments on the samples for quantitative analysis, it is also necessary to prepare standard samples and / or a series of samples doped with a specific amount of standard samples or target phases, and collect diffraction data for the above series of samples one by one, and conduct a comprehensive analysis of the diffraction data of the series of samples, so as to derive the content of the target phase in the sample. In order to reduce the experimental workload of phase quantitative analysis and facilitate phase quantitative analysis by diffraction method, the International Centre for Diffraction Data (ICDD) proposed the reference intensity ratio method (RIR method), that is, for each crystalline phase, record the powder diffraction spectrum of the phase and the reference material (usually corundum) mixed at a mass ratio of 50%:50%, measure the ratio of the strongest diffraction peak intensity of the phase and the reference material, and record it as RIR. If each phase in a mixed phase sample has corresponding RIR data, the diffraction spectrum of the mixed phase sample can be directly measured, and the phase quantitative analysis results can be directly obtained by combining the RIR data. The essence of the reference intensity method is actually to determine the relative diffraction ability of each phase by comparing with the same reference material, and then obtain the content of each phase based on the ratio of the diffraction intensity of each phase in the diffraction spectrum of the mixed sample. The limitations of this method are: first, the RIR of each phase needs to be measured one by one in the experiment and collected and organized into a database. The RIR data of many phases are missing, especially for unknown new phases, which are even less likely to have RIR data. In this case, the RIR data cannot be used for quantitative analysis of the phases. Second, this analysis method only uses the strongest diffraction peak to determine the RIR and perform quantitative analysis. The quantitative accuracy is relatively poor, especially when a phase in the sample has a problem of preferential orientation, the quantitative analysis results will seriously deviate from the true value.

[0004] In addition to the above-mentioned method of using X-ray polycrystalline diffraction data for phase quantitative analysis, if the crystal structure data of each phase in the sample are known, the crystal structure data can be used to calculate the diffraction ability of the unit cell of each phase to X-rays, and then the phase quantitative analysis can be performed based on the diffraction ability of the unit cell of each phase to X-rays and the powder diffraction data of the mixture. This method is usually combined with full spectrum fitting or full spectrum decomposition technology, and the quantitative analysis results obtained are more reliable, and no additional experimental work such as absorption-diffraction method, internal standard method, standard addition method, etc. is required to perform phase quantitative analysis. However, this method requires that the crystal structure data of each phase in the sample is known, otherwise the diffraction ability of the unit cell of the corresponding phase to X-rays cannot be calculated, and thus quantitative analysis cannot be performed.

[0005] In actual work, samples often contain phases with unknown crystal structures. Especially in the process of research and development, new crystal phases are often encountered, and their crystal structures are even less likely to be known. However, in many cases, although the crystal structure of a phase is unknown, its lattice parameters and unit cell chemical composition are known. Even for new phases that have never been reported before, the indexing technology of powder diffraction data can usually determine its lattice parameters, and chemical analysis technology, especially micro-area chemical analysis tools such as electron probe, may be able to determine its chemical composition. Summary of the invention

[0006] The embodiments of the present invention provide a method for calculating the diffraction ability of a crystal with an unknown structure and a method for quantitative analysis of a phase, so as to solve the defect in the prior art that the diffraction ability of a unit cell of a crystal with an unknown structure to X-rays cannot be calculated, and the diffraction ability of a unit cell of a crystal with an unknown structure to X-rays can be calculated.

[0007] The embodiment of the present invention provides a method for calculating the diffraction ability of a crystal with unknown structure, comprising:

[0008] S1, constructing a hypothetical crystal, wherein the hypothetical crystal has the same unit cell parameters as the crystal of unknown structure, and has only one atom at the unit cell origin of the hypothetical crystal, and the type of the atom is the same as the type of one of the atoms in the unit cell of the crystal of unknown structure, and calculating the diffraction ability of the unit cell of the hypothetical crystal to X-rays;

[0009] S2, executing the calculation process of S1 for each atom in the unit cell of the crystal with unknown structure, accumulating the diffraction ability of the unit cell of each hypothetical crystal to X-rays, and obtaining the diffraction ability of the unit cell of the crystal with unknown structure to X-rays.

[0010] An embodiment of the present invention also provides a method for quantitative analysis of physical phases. For a mixed substance containing multiple crystal phases, for a crystal phase with an unknown structure therein, the above-mentioned method for calculating the diffraction ability of a crystal with an unknown structure is used to calculate the diffraction ability of a unit cell of the crystal phase with an unknown structure to X-rays; based on the diffraction ability of the unit cell of each crystal phase to X-rays and the experimentally observed X-ray polycrystalline diffraction data, the volume fraction or mass fraction of each crystal phase in the mixed substance is calculated.

[0011] The method provided in the embodiment of the present invention only requires knowing the unit cell parameters and unit cell chemical composition of the crystal, without knowing the spatial distribution of atoms, and can calculate the diffraction ability of the unit cell of the crystal to X-rays, and perform quantitative phase analysis on samples containing crystal phases with unknown structures. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0013] Figure 1 A schematic flow chart of a method for calculating the diffraction ability of a crystal with unknown structure provided by an embodiment of the present invention;

[0014] Figure 2 It is a schematic flow chart of a phase quantitative analysis method provided by an embodiment of the present invention;

[0015] Figure 3 This is the X-ray powder diffraction pattern of a three-phase mixture of silicon (Si), salt (NaCl) and corundum (α-Al2O3) in a mass ratio of 1:1:1. DETAILED DESCRIPTION

[0016] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0017] Based on the defect in the prior art that the diffraction ability of the unit cell of a crystal with an unknown structure to X-rays cannot be calculated, an embodiment of the present invention provides a method for calculating the diffraction ability of a crystal with an unknown structure, wherein the structure of the crystal is unknown, that is, the coordinate position of each atom in the crystal is unknown, and only the unit cell parameters of the crystal and the chemical composition in the unit cell are known, and the chemical composition in the unit cell refers to the type and number of atoms in the unit cell. Knowing the unit cell parameters of the crystal and the chemical composition in the unit cell, the diffraction ability of the unit cell of the crystal to X-rays can be calculated by the embodiment of the present invention.

[0018] Assuming that the electron density distribution function in the unit cell of a crystal is Δ(r), the structure factor of the crystal is F h is the Fourier transform of the electron density distribution function in the unit cell, that is:

[0019] F h =∫ V ρ(r)exp(i2πh·r)dv; (1)

[0020] Among them, V is the unit cell volume, r is the position vector, and h is the diffraction vector. For a crystal, h is also its reciprocal lattice vector.

[0021] According to Parseval's theorem, we have:

[0022] ∑ h |F h | 2 =∫ V ρ 2 (r)dv. (2)

[0023] Because when atoms form crystals, only the outer shell electrons participate in bonding, the electron density distribution of the atoms involved in bonding has only changed very slightly compared to that of free atoms, and the difference between the two is usually indistinguishable in conventional X-ray powder diffraction experiments. Therefore, the electron density distribution in the crystal unit cell can be approximately regarded as a simple superposition of the electron density of a series of free atoms in different specific positions. Since the electrons of atoms are mainly located near the nucleus, the electron clouds of different atoms have almost no overlap, or the overlapping electron clouds between different atoms are almost negligible relative to the detection capability of X-ray powder diffraction. It can be concluded that:

[0024]

[0025]

[0026]

[0027] Among them, r i is the coordinate of the i-th atom in the unit cell, ρ i(r i ) is located at r i is the electron density distribution function of the i-th atom at location, where n is the number of atoms in the unit cell.

[0028] Imagine a hypothetical crystal with the same lattice parameters as the crystal under study. There is only one atom in the crystal unit cell, and it is located at the origin of the unit cell. The type of atom is the same as the i-th atom in the crystal unit cell discussed above, and its atomic scattering factor is f i (s), s is the scattering vector. According to the definition of structure factor, the structure factor F of the hypothetical crystal is i,h′ for:

[0029] F i,h′ =∑f i (h′)exp(i2πh′·r′)=f i (h′)=f i,h′ ; (5)

[0030] where h′ and r′ are the diffraction vector and position vector of the imaginary crystal respectively.

[0031] At the same time, the structure factor F of the hypothetical crystal i,h′ It can also be written as the Fourier transform of the electron density distribution function in the hypothetical crystal unit cell, that is:

[0032] F i,h′ =∫ V ρ i (r′)exp(i2πh′·r′)dv; (6)

[0033] Using Parseval's theorem again, we get:

[0034] ∑ h′ |F i,h′ | 2 =∫ V ρ i 2 (r′)dv; (7)

[0035] According to equations (5) and (7), we can obtain:

[0036]

[0037] Because the electron density distribution function of the same atom does not depend on its coordinates in the unit cell, or in other words, Δ i (r′) and ρ i (r i ) differ only by a position shift. From equations (2), (4), and (8), we can obtain:

[0038]

[0039] According to formula (9), a method can be obtained to calculate the diffraction ability of a crystal unit cell to X-rays without knowing the atomic coordinates in the unit cell, but only needing to know the lattice parameters and the chemical composition of the unit cell, where: is the contribution of the i-th atom in the unit cell to the X-ray diffraction ability of the unit cell, is the diffraction capacity of the entire unit cell for X-rays, and n is the total number of atoms in the unit cell. The specific calculation steps can be found in Figure 1 ,for:

[0040] S1, constructing a hypothetical crystal, wherein the hypothetical crystal has the same unit cell parameters as the crystal of unknown structure, and has only one atom at the unit cell origin of the hypothetical crystal, and the type of the atom is the same as the type of one of the atoms in the unit cell of the crystal of unknown structure, and calculating the diffraction ability of the unit cell of the hypothetical crystal to X-rays;

[0041] S2, executing the calculation process of S1 for each atom in the unit cell of the crystal with unknown structure, accumulating the diffraction ability of the unit cell of each hypothetical crystal to X-rays, and obtaining the diffraction ability of the unit cell of the crystal with unknown structure to X-rays.

[0042] The calculation method provided in the embodiment of the present invention only requires knowing the unit cell parameters and unit cell chemical composition of the crystal, without knowing the spatial distribution of atoms, and can calculate the diffraction ability of the unit cell of the crystal to X-rays, and on this basis, perform quantitative phase analysis on samples containing crystal phases of unknown structure.

[0043] See also Figure 2 , a method for quantitative analysis of physical phases is provided, comprising: S1', for a mixed substance of multiple crystal phases, for a crystal phase with an unknown structure, the diffraction ability of the crystal cell of the unknown crystal phase to X-rays is calculated by using the above-mentioned method for calculating the diffraction ability of the crystal cell of the unknown crystal phase to X-rays; S2', according to the diffraction ability of the crystal cell of each crystal phase to X-rays and the experimentally observed X-ray polycrystalline diffraction data, the volume fraction or mass fraction thereof in the mixed substance is calculated.

[0044] It is understandable that, for a mixed substance containing multiple crystal phases, if a crystal phase with an unknown structure is included therein, the method for calculating the diffraction ability of the unit cell of a crystal with an unknown structure to X-rays provided in the above embodiment can be used to calculate the diffraction ability of the unit cell of the crystal with an unknown structure to X-rays, and for a crystal with a known structure, the traditional method can be used to calculate the diffraction ability of its unit cell to X-rays. According to the diffraction ability of the unit cell of each crystal phase to X-rays, the volume fraction of each crystal phase in the mixed substance can be calculated, and then the mass fraction of each crystal phase in the mixed substance can be calculated, that is, the various crystal phases in the mixed substance can be quantitatively analyzed.

[0045] Among them, for a mixed material containing J crystal phases, the diffraction index of the jth crystal phase is h and the diffraction intensity is I j,h for:

[0046]

[0047] Where K is the proportional constant, v j is the volume fraction of the jth phase crystal, V j is the unit cell volume of the jth phase crystal, G j,h It is a parameter related to the diffraction angle and determined by the diffraction geometry. G can be calculated based on the diffraction geometry and the lattice parameters of the jth phase. j,h , F j,h is the structure factor.

[0048] From formula (10), we can know that the sum of the diffraction intensities of all diffraction of the j-th phase crystal is:

[0049]

[0050] Transforming formula (11) yields:

[0051]

[0052] Substituting formula (9) into formula (12), we can obtain:

[0053]

[0054] In formulas (12) and (13), only the proportional constant K is an unknown number, which can be determined based on the fact that the sum of the volume fractions of each crystal phase in the sample is 1, that is:

[0055]

[0056] According to the above formula, K and the volume fraction of each crystal phase are calculated.

[0057] The content of the jth crystal phase in the mixture can also be expressed as the mass fraction w j :

[0058]

[0059] Among them, M j , Z j are the chemical formula mass of the jth phase crystal and the number of chemical formulas contained in the unit cell. For the phase crystals in the sample with known crystal structures, the ∑ h |F j′,h | 2 Substituting the formula (15)

[0060] The following three common crystal phases are taken as examples: silicon (Si), salt (NaCl) and corundum (α-Al2O3). The crystal structure data of the above three crystal phases are all known, and the diffraction ability of each unit cell to X-rays (i.e. ∑ h |F h | 2 ) can be calculated based on their respective crystal structure data. In the embodiment of the present invention, it is assumed that the crystal structure (atomic coordinates) is unknown, but the lattice parameters and unit cell chemical composition are known, and then the diffraction ability of each unit cell to X-rays is calculated using the method provided in the embodiment of the present invention, that is, The effectiveness of the method for calculating the X-ray diffraction ability of a unit cell of a crystal with an unknown structure proposed in an embodiment of the present invention is verified by examining the consistency of the X-ray diffraction ability of the unit cell calculated by two different approaches.

[0061] The crystal structure data of silicon (Si) is cited from the literature: Parrish, W., Acta Crystallographica, (1960), 13, 838-850.

[0062] ICSD database record number: 150530, the crystal structure data of silicon is as follows: Chemical formula: Si, cubic system, space group: a=0.54305(2)nm, unit cell volume is 0.16015(1)nm 3 ,Number of chemical formulas in the unit cell: 8, independent atomic coordinates: Si: (0,0,0).

[0063] The crystal structure data of common salt (NaCl) are cited from the literature: Swanson, HE; ​​Fuyat, RK, National Bureau of Standards (US), Circular (1953), 539, 41-43.

[0064] ICSD database record number: 655785, the crystal structure data of table salt are as follows: Chemical formula: NaCl, cubic system, space group: a=0.56402nm, unit cell volume: 0.17943nm 3 , Number of chemical formulas in the unit cell: 4, independent atomic coordinates: Na: (0.5, 0.5, 0.5), Cl: (0, 0, 0).

[0065] The crystal structure data of corundum (α-Al2O3) are cited from the literature: Pillet, S.; Souhassou, M.; Lecomte, C.; Schwarz, K.; Blaha, P.; Rerat, M.; Lichanot, A.; Roversi, P., Acta Crystallographica A, (2001), 57, 290-303.

[0066] ICSD database record number: 92630, the crystal structure data of corundum are as follows: Chemical formula: Al2O3, trigonal system, space group: a=0.47602(4)nm,c=1.2993(2)nm,unit cell volume is:0.25497(5)nm 3 ,Number of chemical formulas in the unit cell: 6, independent atomic coordinates: Al: (0,0,0.35217), O: (0.30634,0,1 / 4).

[0067] Theoretically, the formula (9) of the embodiment of the present invention is:

[0068]

[0069] This is only true when all diffraction indices are summed. However, in experiments, only diffraction data within a certain range can be collected. In order to verify the validity of formula (9) in different data collection ranges, ∑ h |F h | 2 and

[0070] The atomic scattering factor is a function of both wavelength and diffraction angle. In this embodiment, the atomic scattering factor corresponding to the Cu Kα wavelength (0.15418 nm) most commonly used in actual X-ray powder diffraction experiments is used for calculation.

[0071] The ∑ θ values ​​of the three crystals were calculated for the four cases where the highest diffraction angle (the angle between the incident X-ray and the outgoing X-ray, usually called the 2θ angle) was 60°, 80°, 100° and 120°. h |F h | 2 and

[0072] Among them, when the crystal structure is known, the calculation process of the diffraction ability of a unit cell to X-rays is as follows:

[0073] (1) Based on the wavelength of the incident X-ray and the selected upper limit of the 2θ angle, the lower limit of the interplanar spacing d corresponding to the upper limit of the 2θ angle is calculated using the Bragg formula. min ;

[0074] (2) According to the symmetry and lattice parameters of the crystal, calculate the interplanar spacing greater than d min The diffraction indices of all possible diffraction lines and their corresponding crystal plane spacings;

[0075] (3) determining the diffraction angle of each diffraction line by using the Bragg formula according to the wavelength and the calculated interplanar spacing of each diffraction line;

[0076] (4) According to the atomic scattering factor The atomic scattering factors of each constituent atom of the crystal corresponding to the selected wavelength and Bragg position are calculated.

[0077] (5) Based on the independent atomic coordinates of atoms and the symmetry operations of the crystal space group, all atomic positions in the unit cell are derived;

[0078] (6) Using the definition of structure factor Calculate the structure factor of each possible diffraction. Where F represents the structure factor, h represents the diffraction index, h represents the reciprocal format corresponding to the diffraction index, r represents the atomic position vector, j represents the atomic number in the unit cell, n is the total number of atoms in the unit cell, and f j,h It represents the atomic scattering factor of the jth atom in the unit cell corresponding to the diffraction line with diffraction index h, and i represents the imaginary unit.

[0079] (7) For all F h Request|F h | 2 , and add them together to get ∑ h |F h | 2 .

[0080] When the atomic coordinates are unknown but the lattice parameters and the chemical composition of the unit cell are known, the calculation process of the diffraction ability of a unit cell for X-rays is as follows:

[0081] (1) Based on the wavelength of the X-ray and the selected upper limit of the 2θ angle, the lower limit of the interplanar spacing d corresponding to this upper limit of the 2θ angle is calculated using the Bragg formula. min ;

[0082] (2) Construct a hypothetical crystal whose lattice parameters are exactly the same as those of the crystal being studied. There is only one atom in the unit cell and it is located at the origin of the unit cell. The type of this atom is the same as the jth atom in the unit cell of the crystal being studied.

[0083] (3) Calculate the interplanar spacing of the above hypothetical crystal to be greater than d min The diffraction indices of all possible diffraction lines and their corresponding crystal plane spacings;

[0084] (4) determining the diffraction angle of each diffraction line by using the Bragg formula according to the wavelength and the calculated interplanar spacing of each diffraction line;

[0085] (5) According to the atomic scattering factor The atomic scattering factors corresponding to the selected wavelength and Bragg position of the atoms contained in the above hypothetical crystal are calculated based on the dependence of

[0086] (6) Calculate Where h' represents the diffraction index, f j,h′ It represents the atomic scattering factor of the atom corresponding to the diffraction line with the diffraction index h'.

[0087] (7) Repeat the above steps 2)-6) for all atoms in the unit cell of the crystal under study to obtain a series of

[0088] (8) For all Add and we get That is, the diffraction ability of a unit cell of the unknown crystal under study to X-rays, where n is the total number of atoms in the unit cell of the crystal under study.

[0089] The results obtained in this example are shown in Table 1, which shows the diffraction ability of a unit cell of silicon, salt and corundum to X-rays calculated using two different methods and the consistency between the two (wavelength: ).

[0090] It can be seen from Table 1 that for the copper target X-ray diffraction with a wavelength of 0.15418 nm, when the diffraction upper limit angle of the three crystals of silicon, salt and corundum is 80° or above, the diffraction ability of a unit cell to X-rays calculated by using only lattice parameters and unit cell chemical composition without atomic coordinates provided by the present invention is relatively consistent with the diffraction ability of a unit cell to X-rays calculated using crystal structure data (atomic coordinates).

[0091] The following is an example to illustrate the method for quantitative analysis of a multiphase mixed sample containing a phase with unknown crystal structure provided by an embodiment of the present invention.

[0092] This embodiment selects a three-phase mixture sample of silicon, salt and corundum as an example. It is assumed that corundum is a phase with unknown crystal structure, and silicon and salt are phases with known crystal structure. Take equal masses of silicon, salt and corundum, mix them, and grind them to a particle size suitable for X-ray powder diffraction measurement. The diffraction spectrum of the three-phase mixed sample is collected using a Bragg-Brentano type quasi-focusing diffraction geometry powder diffractometer commonly used in laboratories. The radiation source is Cu Kα, the wavelength is 0.15418nm, and the collection range of diffraction data is 20-125° (2θ). The obtained experimental spectrum is as follows: Figure 3 As shown, Figure 3 This is the X-ray powder diffraction pattern of a three-phase mixture of silicon (Si), salt (NaCl) and corundum (α-Al2O3) in a mass ratio of 1:1:1. The three vertical lines at the bottom represent the Bragg diffraction positions of silicon, salt and corundum from top to bottom.

[0093] Table 1

[0094]

[0095]

[0096] The specific process of quantitative analysis is as follows:

[0097] (1) Compare the experimental spectrum with the powder diffraction data file (PDF) in the International Powder Diffraction Data Center (ICDD) database to identify the diffraction peaks of salt and silicon. Currently, there are mature methods and software available for data file retrieval and comparison.

[0098] (2) Using the powder diffraction spectrum indexing technique, we attempted to index the diffraction peaks that did not belong to salt and silicon, and obtained the lattice parameters of the unknown phase (corundum) a = b = 0.4760 nm, c = 1.3048 nm, According to the extinction law of the diffraction index, the possible space group is inferred to be R3c (No.161) or

[0099] (3) Using chemical analysis (such as XRF, ICP-OES, electron probe, etc.), it is inferred that the chemical formula of the unknown phase is Al2O3.

[0100] (4) Based on the lattice parameters and possible space groups, it can be inferred that the unit cell should contain 6 chemical formulas: From the lattice parameters, it can be inferred that the number of oxygen anions contained in the unit cell is about 15, and the space group requires that the number of each type of atom in the unit cell should be a multiple of 6, so it can be inferred that the unit cell should contain 6 chemical formulas.

[0101] (5) Based on the lattice parameters and unit cell chemical composition of the unknown phase (corundum), the diffraction ability of a unit cell of this phase to X-rays is calculated according to the method provided by the present invention:

[0102] (6) According to the method provided by the present invention, the total coherent scattering ability of each unit cell is calculated using the crystal structure data of salt and silicon: ∑ h |F NaCl,h | 2 and∑ h |F Si,h | 2 .

[0103] (7) From the powder diffraction experimental data, obtain the integrated intensity I of each diffraction line of each phase j,h There are currently mature methods and corresponding software available for obtaining the integrated diffraction intensity, including the separation of the integrated intensity of overlapping diffraction peaks.

[0104] (8) Calculate G corresponding to each diffraction line j,h In this embodiment, the powder diffraction data were collected using a Bragg-Brentano type quasi-focusing diffraction geometry diffractometer, G j,h =(1+cos 2 2θ j,h ) / (sin 2 θ j,h cosθ j,h ), where θ j,h is the Bragg angle of the jth phase with diffraction index h.

[0105] (9) Use formula (15) to calculate the mass fraction of each phase.

[0106] The mass percentages of silicon, salt and corundum analyzed are 35.6%, 32.6% and 31.8% respectively. As a comparison, the mass percentages of silicon, salt and corundum obtained by using the crystal structure information of the three component phases and the full spectrum Rietveld refinement method are 34.0%, 35.7% and 30.3% respectively. From the above experimental results, it can be seen that the quantitative analysis results obtained by the method provided by the present invention are consistent with the phase ratio of the sample, and the quality of the quantitative analysis results is even better than the quantitative analysis results obtained by the Rietveld structure refinement method.

[0107] The embodiments of the present invention provide a method for calculating the diffraction ability of a crystal with an unknown structure and a method for quantitative phase analysis. Only the unit cell parameters and the unit cell chemical composition of the crystal are needed, without knowing the spatial distribution of atoms. The diffraction ability of a unit cell of the crystal to X-rays can be calculated, and on this basis, quantitative phase analysis can be performed on samples containing a crystal phase with an unknown structure.

[0108] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for calculating the diffraction ability of a crystal with unknown structure, characterized in that: include: S1, construct a hypothetical crystal, the hypothetical crystal has the same unit cell parameters as the unknown crystal j, and has only one atom at the unit cell origin of the hypothetical crystal, the atom is located at the unit cell origin, the type of the atom is the same as the type of the i-th atom in the unit cell of the unknown crystal j, calculate the diffraction ability of the unit cell of the hypothetical crystal to X-rays The unknown structure crystal j is a crystal with unknown atomic coordinates but known unit cell parameters and chemical composition in the unit cell. The chemical composition in the unit cell refers to the type and number of atoms in the unit cell; f j,i,h′ represents the structure factor of the hypothetical crystal with diffraction index h′, represents f j,i,h′ The sum of the squares of h′; S2, execute the calculation process of S1 for each atom in the unit cell of the unknown crystal j, and obtain the diffraction ability of each unit cell of the hypothetical crystal to X-rays Accumulate and obtain the diffraction ability of the unit cell of the crystal with unknown structure to X-rays Among them, F j,h The structure factor of the crystal phase j with diffraction index h, ∑ h |F j,h | 2 Indicates F j,h The sum of the squares of the modulus values ​​for h, where n is the number of atoms in a unit cell in the crystal j of the unknown structure.

2. A phase quantitative analysis method, characterized in that: include: For a mixed substance containing multiple crystal phases, for a crystal phase with an unknown structure, the method for calculating the diffraction ability of a crystal with an unknown structure as described in claim 1 is used to calculate the diffraction ability of a unit cell of the crystal phase with an unknown structure to X-rays; The volume fraction or mass fraction of each crystal phase in the mixed substance is calculated based on the X-ray diffraction ability of the unit cell of each crystal phase in the mixed substance and the experimentally observed X-ray powder diffraction intensity.

3. The method for quantitative phase analysis according to claim 2, characterized in that: The calculation of the volume fraction or mass fraction of each crystal phase in the mixed material based on the X-ray diffraction capability of the unit cell of each crystal phase and the experimentally observed X-ray powder diffraction intensity includes: For a mixed material containing J crystal phases, the diffraction index of the jth crystal phase is h and the diffraction intensity is I j,h for: Where K is the proportional constant, v j is the volume fraction of the jth phase crystal, V j is the unit cell volume of the jth phase crystal, G j,h It is a parameter related to the diffraction angle and determined by the diffraction geometry. G can be calculated based on the diffraction geometry and the lattice parameters of the jth phase. j,h , F j,h is the structure factor; The sum of the diffraction intensities of all diffractions of the jth crystal phase is: Transforming the formula we get: If the structure of the jth crystal phase is known, then its corresponding ∑ h |F j,h | 2 Can be calculated based on the crystal structure; if the structure of the jth crystal phase is unknown, then Instead of its corresponding ∑ h |F j,h | 2 ; is the diffraction ability of the unit cell of the crystal with unknown structure to X-rays, where f j,i,h′ an atomic scattering factor representing the diffraction of the i-th atom in the unit cell of the crystal j of unknown structure corresponding to the diffraction index h′ of the hypothetical crystal described in claim 1; Correspondingly, if the jth crystal phase structure is unknown, its volume fraction in the mixed material is: Among them, the sum of the volume fractions of each crystal phase in the mixed substance is 1, that is: K and the volume fraction of each crystal phase are calculated according to the above formula; The mass fraction w of the jth crystal phase in the mixture j for: Among them, M j , Z j are the chemical formula mass of the jth crystal phase and the number of chemical formulas contained in the unit cell. For the crystal phase with known crystal structure in the sample, ∑ h |F j′,h | 2 replace

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