CN112151122A - Method for calculating diffraction capability of crystal with unknown structure and method for quantitatively analyzing phase - Google Patents
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Abstract
The invention provides a method for calculating diffraction capability of a crystal with an unknown structure and a method for quantitatively analyzing a phase, which comprise the following steps: s1, constructing a hypothetical crystal which has the same unit cell parameters as the crystal under study and only has one atom at the original point of the unit cell of the hypothetical crystal, wherein the kind of the atom is the same as that of one atom in the unit cell of the crystal under study, and calculating the diffraction capability of the unit cell of the hypothetical crystal on X-rays; s2, executing the calculation process of S1 on each atom in the unit cell of the crystal to be researched, and accumulating the diffraction capacities of the unit cells of all the hypothetical crystals on the X-rays to obtain the diffraction capacity of the unit cells of the crystal to be researched on the X-rays. The calculation method provided by the invention can be used for carrying out phase quantitative analysis on the mixed substance containing the crystal phase with unknown structure by utilizing X-ray powder diffraction data.
Description
Technical Field
The invention relates to the technical field of X-ray crystallography, in particular to a method for calculating diffraction capacity of a crystal with an unknown structure and a method for quantitatively analyzing a phase.
Background
The method comprises the steps of collecting powder (polycrystal) diffraction data of a crystal sample by utilizing an X-ray diffraction technology, identifying composition phases of the sample according to the diffraction data, and carrying out phase quantitative analysis on the sample according to the diffraction intensity of each phase of the composition sample to determine the content of each composition phase in the sample. The technology for phase identification and quantitative analysis by using X-ray polycrystalline diffraction data has been widely applied to scientific research and production after more than 100 years of development, and is the most widely applied and authoritative phase quantitative analysis technology.
The basic principle of quantitative phase analysis by using X-ray diffraction data is that the X-ray diffraction intensity of a phase is in direct proportion to the content of the phase in a sample, and the higher the relative content of the phase in the sample is, the higher the intensity of the diffraction peak of the phase is correspondingly improved. However, the diffraction power of different phases with respect to incident X-rays is different, and therefore the relative amounts of the various phases in the sample cannot be determined by directly comparing the relative diffraction intensities of the different phases. To solve this problem, many methods have been developed, such as absorption-diffraction method, standard addition method (incorporation method), internal standard method, and the like. These methods can perform quantitative analysis of the phase without knowing the crystal structure data of the phase to be analyzed, but not only do diffraction experiments on the samples to be quantitatively analyzed, but also prepare standard samples and/or a series of samples doped with a specific amount of standard samples or target phases, collect diffraction data for the series of samples one by one, and comprehensively analyze the diffraction data of the series of samples, thereby deriving the content of the target phase in the samples. In order to reduce The experimental workload of phase quantification and facilitate The phase quantification by Diffraction methods, The International Diffraction Data Centre (abbreviated to ICDD) proposes a reference intensity method (RIR method), in which for each crystal phase, The phase is recorded in 50% relationship with a reference substance (usually corundum): the powder diffraction pattern when mixed at 50% mass ratio was measured as the ratio of the intensity of the most intense diffraction peak of the phase to the reference substance and recorded as RIR. If each phase in a sample of a mixture phase has corresponding RIR data, the diffraction spectrum of the sample of the mixture phase can be directly measured, and the phase quantitative analysis result can be directly obtained by combining the RIR data. The essence of the reference intensity method is that the relative diffraction power of each phase is actually determined by comparing with the same reference substance, and then the content of each phase is obtained according to the ratio of the diffraction intensity of each phase in the diffraction spectrum of the mixed sample. The limitations of this approach are: firstly, RIR of each phase needs to be measured one by one through experiments and collected and arranged in a database, RIR data of a plurality of phases are missing, particularly the RIR data cannot exist in an unknown new phase, and the RIR data cannot be used for quantitative analysis of the phases; secondly, the analysis method only utilizes the strongest diffraction peak to determine RIR and carry out quantitative analysis, the quantitative accuracy is poor, and particularly when a certain phase in a sample has a problem of preferred orientation, the quantitative analysis result can seriously deviate from a true value.
In addition to the above-described method for quantitative analysis of phase using X-ray polycrystalline diffraction data, if the crystal structure data of each phase in a sample is known, the diffraction ability of the unit cell of each phase to X-rays can be calculated using the crystal structure data, and then quantitative analysis of phase 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. The method is usually combined with a full spectrum fitting or full spectrum decomposition technology, the obtained quantitative analysis result is more reliable, and the phase quantitative analysis can be carried out without carrying out additional experimental work like an absorption-diffraction method, an internal standard method, a standard addition method and the like. 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.
In actual work, a sample often contains a phase with an unknown crystal structure, particularly in the process of development, a new crystal phase is often encountered, and the crystal structure of the new crystal phase is less likely to be known. However, in many cases, although the crystal structure of a certain phase is unknown, the lattice parameter and the unit cell chemical composition thereof are known. Even if the new phase has never been reported, the lattice parameter can be usually determined by the index technique using the powder diffraction data, and the chemical composition can be determined by the chemical analysis technique, especially by the micro-area chemical analysis tool such as an electron probe.
Disclosure of Invention
The embodiment of the invention provides a method for calculating the diffraction capacity of a crystal with an unknown structure and a method for quantitatively analyzing a phase, which are used for solving the defect that the diffraction capacity of a unit cell of the crystal with the unknown structure on X-rays cannot be calculated in the prior art and can calculate the diffraction capacity of the unit cell of the crystal with the unknown structure on the X-rays.
The embodiment of the invention provides a method for calculating diffraction capacity of a crystal with an unknown structure, which comprises the following steps:
s1, constructing a hypothetical crystal, wherein the hypothetical crystal has the same unit cell parameters as the crystal with unknown structure and only has one atom at the original point of the unit cell of the hypothetical crystal, the kind of the atom is the same as that of one atom in the unit cell of the crystal with unknown structure, and calculating the diffraction capability of the unit cell of the hypothetical crystal on X-rays;
s2, executing the calculation process of S1 on each atom in the unit cell of the crystal with unknown structure, and accumulating the diffraction ability of the unit cell of each hypothetical crystal on the X-ray to obtain the diffraction ability of the unit cell of the crystal with unknown structure on the X-ray.
The embodiment of the invention also provides a phase quantitative analysis method, for a mixed substance containing a plurality of crystal phases, for the crystal phase with unknown structure, calculating the diffraction capability of the unit cell of the crystal phase with unknown structure to X-rays by adopting the calculation method of the diffraction capability of the crystal with unknown structure as claimed in claim 1; the volume fraction or mass fraction of each crystal phase in the mixed substance is calculated based on the diffraction ability of the unit cell of each crystal phase to X-rays and experimentally observed X-ray polycrystalline diffraction data.
The method provided by the embodiment of the invention can calculate the diffraction capability of the crystal unit cell to X-ray and perform phase quantitative analysis on a sample containing a crystal phase with an unknown structure only by knowing the unit cell parameters and the chemical composition of the unit cell of the crystal and not knowing the space distribution condition of atoms.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and those skilled in the art can also obtain other drawings according to the drawings without creative efforts.
FIG. 1 is a schematic flow chart of a method for calculating diffraction power of a crystal with an unknown structure according to an embodiment of the present invention;
FIG. 2 is a schematic flow chart of a method for quantitative analysis of a phase according to an embodiment of the present invention;
fig. 3 shows a mixture of the following components in a mass ratio of 1: 1: 1 silicon (Si), common salt (NaCl), and corundum (. alpha. -Al2O 3).
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Based on the defect that the diffraction capability of a unit cell of a crystal with an unknown structure on X-rays cannot be calculated in the prior art, the embodiment of the invention provides a method for calculating the diffraction capability of the crystal with the unknown structure, wherein the structure of the crystal is unknown, namely the coordinate position of each atom in the crystal is unknown, 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 the number of atoms of each atom in the unit cell. Knowing the unit cell parameters of the crystal and the chemical composition in the unit cell, the diffraction capability of the unit cell of the crystal to X-rays can be calculated by the embodiment of the invention.
Assuming a crystal with an electron density distribution function in its unit cell of ρ (r), the structure factor F of the crystalhIs the fourier transform of the electron density distribution function in the unit cell, i.e.:
Fh＝∫Vρ(r)exp(i2πh·r)dv； (1)
where V is the unit cell volume, r is the position vector, h is the diffraction vector, and for crystals, h is also its reciprocal lattice vector.
According to the Parceval theorem, there are:
∑h|Fh|2＝∫Vρ2(r)dv。 (2)
since only the shell electrons participate in the bonding when the atoms form a crystal, the extra-nuclear electron density distribution of the atoms participating in the bonding is only very slightly changed from that of the free atoms, and the difference between the two is usually indistinguishable in conventional X-ray powder diffraction experiments. Thus, the electron density distribution in a crystal unit cell can be viewed approximately as a simple superposition of the extra-nuclear electron densities of a series of free atoms at different specific positions. Since the extra-nuclear electrons of atoms are mainly located near the nucleus, there is little overlap of extra-nuclear electron clouds of different atoms, or it is said that the overlap of electron clouds between different atoms is almost negligible with respect to the detection capability of X-ray powder diffraction. This can result in:
wherein r isiIs the coordinate of the ith atom in the unit cell, pi(ri) Is located at riThe electron density distribution function of the ith atom in (b), and n is the number of atoms in the unit cell.
Imagine a hypothetical crystal with a lattice parameter identical to that of the crystal under study, in which only one atom is present in the crystal cell and is located at the cell origin, the atomic species being the same as the second in the crystal cell discussed abovei atoms being identical and having an atomic scattering factor fi(s), s is a scattering vector. Then the structure factor F of the hypothetical crystal according to the definition of the structure factori,h′Comprises the following steps:
Fi,h′＝∑fi(h′)exp(i2πh′·r′)＝fi(h′)≡fi,h′； (5)
where h 'and r' are the diffraction vector and position vector, respectively, of the hypothetical crystal.
At the same time, the structure factor F of the hypothetical crystali,h′The fourier transform of the electron density distribution function in the hypothetical crystal cell can also be written as:
Fi,h′＝∫Vρi(r′)exp(i2πh′·r′)dv； (6)
the Parceval theorem is utilized again to obtain:
∑h′|Fi,h′|2＝∫Vρi 2(r′)dv； (7)
according to the formulae (5) and (7), it is possible to obtain:
and because the extra-nuclear electron density distribution function of the same atom is not dependent on its coordinates in the unit cell, or ρi(r') and ρi(ri) Only one positional shift therebetween. The formula (2), (4) and (8) can be used for obtaining:
according to the formula (9), a method of calculating the diffraction ability of one cell of a crystal to X-rays without knowing the atomic coordinates in the cell and only knowing the lattice parameters and the chemical composition of the cell can be obtained, wherein,
is the ith in the unit cellThe contribution of atoms to the X-ray diffraction power of the unit cell,
n is the total number of atoms in the unit cell, which is the diffraction capability of the entire cell for X-rays. The specific calculation steps can be seen in fig. 1, which is:
s1, constructing a hypothetical crystal, wherein the hypothetical crystal has the same unit cell parameters as the crystal with unknown structure and only has one atom at the original point of the unit cell of the hypothetical crystal, the kind of the atom is the same as that of one atom in the unit cell of the crystal with unknown structure, and calculating the diffraction capability of the unit cell of the hypothetical crystal on X-rays;
s2, executing the calculation process of S1 on each atom in the unit cell of the crystal with unknown structure, and accumulating the diffraction ability of the unit cell of each hypothetical crystal on the X-ray to obtain the diffraction ability of the unit cell of the crystal with unknown structure on the X-ray.
The calculation method provided by the embodiment of the invention can calculate the diffraction capability of the crystal unit cell to X-rays only by knowing the unit cell parameters and the chemical composition of the unit cell of the crystal and not knowing the space distribution condition of atoms, and can perform phase quantitative analysis on a sample containing a crystal phase with an unknown structure on the basis.
Referring to fig. 2, there is provided a method of quantitative phase analysis comprising: s1', calculating the diffraction ability of the unit cell of the crystal phase with unknown structure to the X-ray by using the method for calculating the diffraction ability of the unit cell of the crystal with unknown structure to the X-ray according to claim 1; s2', calculating the volume fraction or mass fraction of each crystal phase in the mixed material according to the diffraction ability of the crystal phase to X-ray and the experimentally observed polycrystalline diffraction data of X-ray.
It is understood that, for a mixed substance containing a plurality of crystal phases, if a crystal phase with unknown structure is contained therein, the calculation method of the diffraction ability of the unit cell of the crystal with unknown structure to X-rays provided in the foregoing embodiment can be used to calculate the diffraction ability of the unit cell of the crystal with unknown structure to X-rays, and for a crystal with known structure, the conventional method can be used to calculate the diffraction ability of the unit cell of the crystal with unknown structure to X-rays. According to the diffraction capacity 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 further the mass fraction of each crystal phase in the mixed substance can be calculated, namely, the quantitative analysis is carried out on various crystal phases in the mixed substance.
Wherein, for the mixed substance containing J crystal phases, the diffraction intensity of the J crystal phase with the diffraction index h is Ij,hComprises the following steps:
wherein K is a proportionality constant, vjIs the volume fraction of the j phase crystal, VjIs the unit cell volume, G, of the j phase crystalj,hIs a parameter dependent on the diffraction angle determined by the diffraction geometry, from which G can be calculatedj,h，Fj,hIs a structural factor.
As can be seen from equation (10), the sum of the diffraction intensities of all diffractions of the j-th phase crystal is:
transforming equation (11) yields:
substituting equation (9) into equation (12) yields:
in equations (12), (13), K can be determined from the sum of the volume fractions of the respective crystal phases in the sample being 1, only if the proportionality constant K is unknown, i.e.:
and calculating K and the volume fraction of each crystal phase according to the formula.
The content of the jth crystal phase in the mixed substance can also be expressed as a mass fraction wj：
Wherein M isj、ZjFor the phase crystals having a known crystal structure in the sample, sigma in the formula (9) can be used, as the formula mass of the j-th phase crystal and the number of the formula contained in the unit cell, respectivelyh|Fj′,h|2Instead of in equation (15)
Three common crystal phases of silicon (Si), common salt (NaCl) and corundum (. alpha. -Al2O3) are exemplified below. The crystal structure data of the three crystal phases mentioned above are known, with each crystal cell having the ability to diffract X-rays (i.e.Sigma)h|Fh|2) Can be calculated from the respective crystal structure data. In the present examples, it is assumed that the crystal structure (atomic coordinates) is unknown but the lattice parameters and the unit cell chemical composition are known, and then the diffraction ability of one cell to X-rays, i.e., the diffraction ability of one cell to X-rays, is calculated using the method provided in the present examples
The validity of the method for calculating the X-ray diffraction capacity of the unit cell of the crystal with unknown structure provided by the embodiment of the invention is verified by checking the consistency of the unit cells calculated by two different ways on the X-ray diffraction capacity.
Crystal structure data of silicon (Si) are cited in the literature: parrish, W., Acta Crystallographics, (1960),13, 838-.
ICSD database record number: 150530, the crystal structure data for silicon is as follows: the chemical formula is as follows: si, cubic system, space group:
(227), a: 0.54305(2) nm, unit cell volume 0.16015(1) nm3The number of the formula in the unit cell: 8, independent atomic coordinates: si: (0,0,0).
The crystal structure data of common salt (NaCl) are cited in the literature: swanson, h.e.; fuyat, R.K., National Bureau of Standards (U.S.), Circular (1953),539, 41-43.
ICSD database record number: 655785, the crystal structure data for table salt is as follows: the chemical formula is as follows: NaCl, cubic, space group:
(No.225), a-0.56402 nm, unit cell volume: 0.17943nm3The number of the formula in the unit cell: 4, independent atomic coordinates: na: (0.5,0.5,0.5), Cl: (0,0,0).
The crystal structure data of corundum (. alpha. -Al2O3) are cited in the literature: bellet, s.; souhassou, m.; lecote, c.; schwarz, k.; blaha, p.; rerat, m.; lichanot, a.; roveri, P., Acta Crystallographics A, (2001),57, 290-.
ICSD database record number: 92630, the crystal structure data for corundum is as follows: the chemical formula is as follows: al (Al)2O3Trigonal, space group:
(No.167), a-0.47602 (4) nm, c-1.2993 (2) nm, unit cell volume: 0.25497(5) nm3The number of the formula in the unit cell: 6, independent atomic coordinates: al: (0,0,0.35217), O: (0.30634,0,1/4).
Theoretically, formula (9) of the embodiment of the present invention, namely:
this is only true if all diffraction indices are summed. Experimentally, however, only a range of diffraction data can be collected, and to verify the validity of equation (9) in different data collection ranges, Σ in different diffraction index ranges was calculated for each of the three crystal phasesh|Fh|2And
atomic scattering factors are a function of both wavelength and diffraction angle. In this example, the atomic scattering factor corresponding to the Cu K α wavelength (0.15418nm) most frequently selected in the actual X-ray powder diffraction experiment was used for calculation.
The sigma of the three crystals at four conditions of the highest diffraction angle (the included angle between the incident X-ray and the emergent X-ray, commonly called 2 theta angle) of 60 DEG, 80 DEG, 100 DEG and 120 DEG is calculated respectivelyh|Fh|2And
wherein, under the condition that the crystal structure is known, the calculation process of the diffraction capacity of one crystal cell to X-ray is as follows:
(1) according to the wavelength of the incident X-ray and the selected upper limit of the 2 theta angle, the lower limit d of the interplanar spacing corresponding to the upper limit of the 2 theta angle is calculated by a Bragg formulamin；
(2) Calculating the distance between crystal faces to be larger than d according to the symmetry and lattice parameters of the crystalminThe diffraction indexes of all possible diffraction lines and the corresponding interplanar spacings thereof;
(3) determining the diffraction angle of each diffraction line through a Bragg formula according to the wavelength and the calculated interplanar spacing of each diffraction line;
(4) according to atomic scattering factor pair
Calculating the dependency of each component atom of the crystalAn atomic scattering factor corresponding to the selected wavelength and bragg location;
(5) deriving all atomic positions in the unit cell according to the independent atomic coordinates of the atoms and the symmetry operations of the crystal space group;
(6) using the formula of structural factors
The structure factor of each possible diffraction is calculated. Wherein F represents a structural factor, h represents a diffraction index, h represents a reciprocal form corresponding to the diffraction index, r represents an atom position vector, j represents an atom number in a unit cell, n is the total number of atoms in the unit cell, Fj,hDenotes an atomic scattering factor of the jth atom in the unit cell corresponding to a diffraction line with a diffraction index h, and i denotes an imaginary unit.
(7) For all FhObtaining | Fh|2And are added to obtain sigmah|Fh|2。
The calculation of the diffraction power of a cell on X-rays, with unknown atomic coordinates but known lattice parameters and cell chemistry, is as follows:
(1) according to the wavelength of the X-ray and the selected upper limit of the 2 theta angle, the lower limit d of the interplanar spacing corresponding to the upper limit of the 2 theta angle is calculated by a Bragg formulamin；
(2) A hypothetical crystal was constructed with exactly the same lattice parameters as the crystal under study, with only one atom in the unit cell and at the origin of the unit cell, the atom being of the same species as the jth atom in the unit cell of the crystal under study.
(3) Calculating the interplanar spacing of the hypothetical crystal to be greater than dminThe diffraction indexes of all possible diffraction lines and the corresponding interplanar spacings thereof;
(4) determining the diffraction angle of each diffraction line through a Bragg formula according to the wavelength and the calculated interplanar spacing of each diffraction line;
(5) according to atomic scattering factor pair
Calculating the atomic scattering factors of the atoms contained in the virtual crystal corresponding to the selected wavelength and Bragg position;
(6) calculate out
Wherein h' represents a diffraction index, fj,h′The atomic scattering factor of the atom corresponding to the diffraction line with the index of diffraction h' is shown.
(7) Repeating the above steps 2) -6) for all atoms in the unit cell of the crystal under study, to obtain a series of
(8) For all
Adding to obtain
I.e., the ability of one cell of the crystal of unknown structure under study to diffract X-rays, where n is the total number of atoms in the unit cell of the crystal under study.
The results obtained in this example are shown in table 1, where table 1 shows the X-ray diffraction ability of one cell of silicon, common salt and corundum and the correspondence between the two cells (wavelength:. lambda.: 0.15418nm) calculated by two different methods.
As can be seen from table 1, for the X-ray diffraction of the copper target with a wavelength of 0.15418nm, when the upper diffraction limit angle of the three crystals of silicon, common salt and corundum is 80 ° or more, the X-ray diffraction ability of one cell calculated by using only the lattice parameters and the cell chemical composition is relatively consistent with the X-ray diffraction ability of one cell calculated by using the crystal structure data (atomic coordinates) without using the atomic coordinates provided by the present invention.
The following is an example illustrating the method for quantitative analysis of a multiphase mixed sample containing phases with unknown crystal structures provided in the embodiments of the present invention.
In this example, a sample of a three-phase mixture of silicon, common salt and corundum was selected as an example. Wherein corundum is assumed to be a phase with an unknown crystal structure, and silicon and common salt are assumed to be phases with a known crystal structure. Silicon, salt and corundum which are equal in mass are taken, mixed and ground to a particle size suitable for X-ray powder diffraction measurement. The diffraction pattern of the three-phase mixed sample is collected by a Bragg-Brentano type quasi-focusing diffraction geometrical powder diffractometer which is commonly used in a laboratory, the radiation source is Cu Ka, the wavelength is 0.15418nm, the collection range of diffraction data is 20-125 degrees (2 theta), the obtained experimental pattern is shown in figure 3, and figure 3 is a graph obtained by mixing the following components according to the mass ratio of 1: 1: 1 silicon (Si), common salt (NaCl) and corundum (. alpha. -Al)2O3) X-ray powder diffraction pattern of the three-phase mixture. The three vertical lines at the bottom represent the Bragg diffraction positions of silicon, salt and corundum respectively from top to bottom.
TABLE 1
The specific process of the quantitative analysis is as follows:
(1) comparing the experimental spectrum with a powder diffraction data file (PDF) in an international powder diffraction data center (ICDD) database, and identifying diffraction peaks of the salt and the silicon. Data file retrieval and comparison are currently available in sophisticated methods and software.
(2) By utilizing a powder diffraction spectrum indexing technology, diffraction peaks which do not belong to common salt and silicon are tried to be indexed, lattice parameters a-b-0.4760 nm and c-1.3048 nm of an unknown phase (corundum) are obtained,
from the extinction law of the diffraction index, a possible space group is deduced to be R3c (No.161) or
(No.167)。
(3) Chemical analysis (such as XRF, ICP-OES, electron probe, etc.) is used to infer that the chemical formula of the unknown phase is Al2O3。
(4) It is concluded from the lattice parameters and the possible space groups that the unit cell should contain 6 formulae: from the lattice parameters, it can be concluded that the number of oxygen anions contained in the cell is about 15, and that the space group requires that the number of each atom in the cell should be a multiple of 6, from which it can be concluded that the cell should contain 6 chemical formulae.
(5) The X-ray diffraction power of one cell of a phase of unknown structure (corundum) was calculated from the lattice parameters and the chemical composition of the unit cell according to the method described in example 1:
(6) the total coherent scattering power of each unit cell was calculated according to the method shown in example 1, using the crystal structure data of common salt and silicon: sigmah|FNaCl,h|2Sum Σh|FSi,h|2。
(7) Obtaining integral intensity I of each diffraction line of each phase from the experimental data of powder diffractionj,h. The acquisition of the integrated diffraction intensities, including the separation of the integrated intensities of the overlapping diffraction peaks, is currently available in well-established methods and corresponding software.
(8) Calculating G corresponding to each diffraction linej,h. In this example, the powder diffraction data was collected using a Bragg-Brentano type quasi-focused diffraction geometry diffractometer, Gj,h＝(1+cos22θj,h)/(sin2θj,hcosθj,h) Wherein thetaj,hIs the bragg angle with the jth phase diffraction index h.
(9) The mass fraction of each phase was calculated by the formula (15).
The analyzed mass percentages of the silicon, the salt and the corundum are respectively 35.6%, 32.6% and 31.8%. As a control, the mass percentages of silicon, salt, and corundum, using the crystal structure information of the three component phases and the full spectrum Rietveld refinement method, were 34.0%, 35.7%, and 30.3%, respectively. From the above experimental results, it can be seen that the quantitative analysis result obtained by the method of the present invention is consistent with the phase ratio of the sample, and the quality of the quantitative analysis result is even better than that obtained by the Rietveld structure refinement method.
According to the method for calculating the diffraction capability of the crystal with the unknown structure and the method for quantitatively analyzing the phase, provided by the embodiment of the invention, the diffraction capability of one crystal cell of the crystal to X-rays can be calculated only by knowing the unit cell parameters and the chemical composition of the unit cell of the crystal and without knowing the space distribution condition of atoms, and the phase of a sample containing the crystal phase with the unknown structure is quantitatively analyzed on the basis.
Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.
Claims (3)
1. A method for calculating the diffraction capability of a crystal with an unknown structure is characterized by comprising the following steps:
s1, constructing a hypothetical crystal, wherein the hypothetical crystal has the same unit cell parameters as the crystal with unknown structure and only has one atom at the original point of the unit cell of the hypothetical crystal, the kind of the atom is the same as that of one atom in the unit cell of the crystal with unknown structure, and calculating the diffraction capability of the unit cell of the hypothetical crystal on X-rays;
s2, executing the calculation process of S1 on each atom in the unit cell of the crystal with unknown structure, and accumulating the diffraction ability of the unit cell of each hypothetical crystal on the X-ray to obtain the diffraction ability of the unit cell of the crystal with unknown structure on the X-ray.
2. A method for quantitative phase analysis, comprising:
calculating the diffraction power of the unit cell of the unknown-structure crystal phase to X-rays for a mixed substance containing a plurality of crystal phases for the unknown-structure crystal phase therein by using the calculation method of the diffraction power of the unknown-structure crystal according to claim 1;
the volume fraction or mass fraction of each crystalline phase in the mixed substance is calculated from the diffraction power of the unit cell of each crystalline phase in the mixed substance to X-rays and the experimentally observed X-ray powder diffraction intensity.
3. The method for quantitative phase analysis according to claim 2, wherein the calculating of the volume fraction or mass fraction of the unit cell of each crystal phase based on its diffraction ability for X-rays and the experimentally observed X-ray powder diffraction intensity in the mixed material comprises:
for a mixed material containing J crystal phases, the diffraction intensity of the J crystal phase with the diffraction index h is Ij,hComprises the following steps:
wherein K is a proportionality constant, vjIs the volume fraction of the j phase crystal, VjIs the unit cell volume, G, of the j phase crystalj,hIs a parameter dependent on the diffraction angle determined by the diffraction geometry, from which G can be calculatedj,h，Fj,hIs a structural factor;
the sum of all diffracted diffraction intensities for the j-th crystalline phase is:
transforming the formula to obtain:
wherein if the structure of the j-th crystal phase is known, the corresponding sigmah|Fj,h|2Can be calculated according to the crystal structure; if the structure of the j-th crystalline phase is unknown, using
In place of its corresponding ∑h|Fj,h|2；
accordingly, if the structure of the j-th crystalline phase is unknown, its volume fraction in the mixed material is:
wherein, the sum of the volume fractions of all crystal phases in the mixed substance is 1, namely:
and calculating K and the volume fraction of each crystal phase according to the formula.
Mass fraction w of jth crystal phase in mixed substancejComprises the following steps:
wherein M isj、ZjFor the crystal phase having a known crystal structure in the sample, Sigma can be used, as the chemical formula mass of the j-th crystal phase and the number of the chemical formulas contained in the unit cell, respectivelyh|Fj′,h|2Instead of the former
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