CN112304991A - Method for phase recognition using electron diffraction - Google Patents

Method for phase recognition using electron diffraction Download PDF

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CN112304991A
CN112304991A CN201910703052.8A CN201910703052A CN112304991A CN 112304991 A CN112304991 A CN 112304991A CN 201910703052 A CN201910703052 A CN 201910703052A CN 112304991 A CN112304991 A CN 112304991A
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施洪龙
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Minzu University of China
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Abstract

The invention provides a novel method for phase recognition by an electron diffraction pattern, which can be used for phase recognition of materials with known chemical components but with uncertain crystal structures, and is particularly suitable for occasions with difficult acquisition of a plurality of diffraction patterns. The invention has the advantages that: only one band-axis electron diffraction pattern containing a high-order Laue diffraction ring needs to be recorded or a zero-order Laue diffraction point pattern and a corresponding high-order Laue diffraction ring pattern are recorded on a crystal grain of the same crystal to be detected, although the Bravais lattice of the crystal to be detected cannot be completely determined, the measured radius of the high-order Laue diffraction ring and the volume of a primary protocell are compared with the calculation result of a target structure, so that the indexing accuracy can be improved, alternative phases which do not meet the conditions can be effectively filtered, and the accuracy of phase analysis is greatly improved; in the actual electron microscope experiment and data analysis, the working efficiency is obviously improved.

Description

Method for phase recognition using electron diffraction
Technical Field
The invention relates to a method for identifying crystal phases by using an electron diffraction pattern, belonging to the technical field of material microstructure characterization and crystal structure analysis.
Background
Phase recognition is a fundamental link in the preparation and characterization processes of materials, and solves the problem of 'what' the material to be detected is. The main means of phase recognition are X-ray powder diffraction and electron diffraction. The phase recognition of the X-ray Powder diffraction is to compare whether the diffraction peak of the Powder sample to be detected is matched with the diffraction peak on a standard card (PDF card for short). If the peak positions and peak intensities of all diffraction peaks can be matched with the PDF card in the experiment, the structure of the sample to be detected is consistent with the crystal structure represented by the PDF card.
A typical method for phase discrimination using electron diffraction is to record multiple (at least two) low-index, band-axis electron diffractions on the same crystal grain. If all the electron diffractions can be indexed by the same crystal structure, the measured crystal grain structure is consistent with the crystal structure. However, the increasingly emerging nano materials have the characteristics of small crystal grains, poor crystallinity, strong preferred orientation and the like, and only a small number of diffraction peaks appear in X-ray diffraction, even only broadened diffraction bulges appear, so that the accuracy of phase identification is greatly reduced; although these nanomaterials can be observed in real time by a transmission electron microscope, it is difficult to record a plurality of uniaxial electron diffraction patterns by tilting the same crystal grain in many cases, and accurate phase recognition is difficult.
Disclosure of Invention
In order to improve the technical problem, the invention provides a method for identifying material phases by using an electron diffraction pattern, which comprises the following steps:
step 1): recording a band-axis electron diffraction pattern containing a high-order laue diffraction ring, or a zero-order laue diffraction point pattern and a corresponding high-order laue diffraction ring pattern;
step 2): measuring the radius of a zero-order Laue diffraction point and a high-order Laue diffraction ring of the crystal to be measured;
step 3): calculating the primary primitive cell volume of the crystal to be detected by using the parameters obtained in the step 2);
step 4): calculating the volume of a primary primitive cell according to the lattice constant of the target crystal;
step 5): indexing the zero-order Laue diffraction points in the step 2) to determine band axis indexes;
step 6): calculating the radius of a high-order Laue diffraction ring of the target crystal by using the band axis index in the step 5);
step 7): if the electronic diffraction pattern of the crystal to be detected can not only be indexed by the target crystal structure, but also the initial primitive cell volume measured in the step 3) is calculated from the initial primitive cell volume in the step 4), and the radius of the high-order Laue diffraction ring measured in the step 2) is consistent with the radius of the high-order Laue diffraction ring of the target crystal, the crystal to be detected is consistent with the target crystal structure.
According to an embodiment of the invention, the method comprises the steps of:
step S1): recording a band axis electron diffraction pattern containing a high-order Laue diffraction ring of a crystal to be detected; or recording a zero-order Laue diffraction point pattern and a corresponding high-order Laue diffraction ring pattern on the same crystal to be detected;
step S2): the method for measuring the radius of the zero-order Laue diffraction point and the radius of the high-order Laue diffraction ring of the crystal to be measured comprises the following specific steps:
s21) measuring two-dimensional primary germ cells on zeroth-order laue diffraction: the transmission spot is the origin O of the two-dimensional primary primitive cell, and a parallelogram formed by two nearest neighbor diffraction points A and B as adjacent edges is used as the two-dimensional primary primitive cell: r1＝OA，R2＝OB，R3OC is a diagonal line of the parallelogram, and theta is equal to angle AOB; measuring the radius of the higher-order Laue diffraction Ring, denoted Robs；
S22) using the camera length L and the wavelength λ of the incident electron beam, the corresponding interplanar spacing d is calculated from the formula Rd — L λ1，d2，d3；
Step S3): calculating the initial primitive cell volume V of the crystal to be detected by using the parameters obtained in the step S2)obsThe calculation method comprises the following steps:
s31) from the radius R of the high-order Laue diffraction Ring in step S2)obsCalculating the layer spacing H of the reciprocal surface*：
Figure BDA0002151347760000031
λ is the wavelength of the incident electron beam;
s32) from d in step S2)1，d2And theta, and reciprocal plane layer spacing H*Calculating the volume V of the primordial germ cellsobs：
Figure BDA0002151347760000032
Step S4): calculating the volume V of primary primitive cell according to the lattice constant of target crystalcalcThe process is as follows:
s41) calculating the unit cell volume V from the lattice constants a, b, c, α, β, γ of the target crystal:
Figure BDA0002151347760000033
s42) determining the volume V of the primary primitive cell according to the lattice center of the target crystalcalc：
Vcalc＝V/M
Wherein M is a multiple caused by the center of the lattice and is determined by the following method:
center of lattice F A B C I P R
M 4 2 2 2 2 1 3 in the case of hexagonal system; rhombohedral crystal system is 1
；
Step S5): the zero-order Laue diffraction point is indexed to determine the band axis index, and the process is as follows:
s51) calculating a d-value table and a crystal face included angle theta list according to the lattice constants a, b, c, alpha, beta and gamma of the target crystal:
Figure BDA0002151347760000041
Figure BDA0002151347760000042
wherein ,
Figure BDA0002151347760000043
is unit cell volume, d1 and d2Is (h) of1k1l1) and (h2k2l2) The interplanar spacing of (a); sijThe matrix is defined as follows:
S11＝b2c2sin2α，S22＝a2c2sin2β，S33＝a2b2sin2γ
S12＝abc2(cosαcosβ-cosγ)，S23＝a2bc(cosβcosγ-cosα)
S13＝ab2c(cosγcosα-cosβ)；
s52) finding D in the d-value table1Matched crystal face index (h)1k1l1) (ii) a Find d in the table of d-values and the table of included angles of facets2Matched crystal face index (h)2k2l2) The angle between the two crystal faces is required to be consistent with the angle theta and the diagonal point d3Is just enough to satisfy (h)3k3l3)＝(h1k1l1)+(h2k2l2)；
S53) crystal face index (h)1k1l1) Cross multiplication (h)2k2l2) Obtaining the band axis index [ uv w ] of the crystal]：
Figure BDA0002151347760000044
Step S6) based on the tape axis index [ uv w ] determined in step S5)]Calculating radius R of high-order Laue diffraction ringcalc(ii) a The calculation steps are as follows:
s61) using the tape axis index [ uv w ] determined in step S5)]Calculating the layer spacing H of the reciprocal surface*：
Figure BDA0002151347760000045
Wherein a, b, c, alpha, beta and gamma are lattice constants of the target crystal;
s62) calculating the reciprocal face-layer spacing H according to the step S61)*Calculating radius R of high-order Laue diffraction ringcalc：
Figure BDA0002151347760000051
Wherein λ is the wavelength of the incident electron beam; n is an integer related to the extinction of the crystal system, determined by:
center of lattice F A B C I P R
N 2 2 2 2 2 1 3 in the case of hexagonal system; rhombohedral crystal system is 1
；
Step S7) if the band axis electron diffraction pattern of the crystal to be tested contains a high-order Laue diffraction ring; or the zero-order Laue diffraction point pattern and the corresponding high-order Laue diffraction ring pattern can not only be indexed by the target crystal structure, but also the volume V of the primordial primitive cell measured experimentallyobsHigh order, high orderRadius R of Laue diffraction RingobsCalculated result V of both and the target crystal structurecalc and RcalcAnd if so, indicating that the structure of the crystal to be detected is consistent with that of the target crystal, and confirming the structure of the crystal to be detected.
According to the embodiment of the invention, the crystal to be tested in step S1) is a crystal with a known chemical composition, but the crystal structure of the crystal cannot be determined, i.e. the lattice constant and the lattice center can be found through various crystal structure databases (such as PDF card library, ICDD database, ICSD database, etc.), documents, etc.;
according to the embodiment of the invention, the crystal to be measured in step S1) may be a bulk material, a powder, or a single crystal, a polycrystal, a microcrystal or a nanocrystal;
according to the embodiment of the invention, step S1) if the crystallinity of the crystal to be tested is better, recording a band axis electron diffraction pattern containing a high-order Laue diffraction ring; and if the crystallinity of the crystal to be detected is poor, recording a zero-order Laue diffraction point pattern and a corresponding high-order Laue diffraction ring pattern.
According to an embodiment of the invention, in step S1), a transmission electron microscope is used to record a band axis electron diffraction pattern containing a higher order laue diffraction ring of a crystal to be tested or a zeroth order laue diffraction point pattern and a corresponding higher order laue diffraction ring pattern are recorded on the same crystal to be tested; the electron diffraction of the transmission electron microscope can be selected area electron diffraction, precession electron diffraction, nano-beam electron diffraction, micro-beam electron diffraction or convergent beam electron diffraction;
according to an embodiment of the present invention, the on-axis electron diffraction pattern recorded in step S1) should be a low-index on-axis for indexing.
According to an embodiment of the present invention, the recorded band-axis electron diffraction pattern is not required to satisfy strict positive band-axis conditions in step S1).
According to the embodiment of the invention, in step S2), the area surrounded by the two-dimensional primordial germ cells should be the smallest.
According to an embodiment of the present invention, in step S2), the measured higher order laue diffraction loop should be the one with the smallest radius.
Advantageous effects
The invention provides a novel method for phase recognition by an electron diffraction pattern, which can be used for phase recognition of materials with known chemical components but with uncertain crystal structures, and is particularly suitable for occasions with difficult acquisition of a plurality of diffraction patterns. Compared with the prior art, the method has the advantages that: according to the method, only one band-axis electron diffraction pattern containing a high-order Laue diffraction ring is required to be recorded, or a zero-order Laue diffraction point pattern and a corresponding high-order Laue diffraction ring pattern are recorded on a crystal grain of the same crystal to be detected, although the Bravais lattice (lattice constant and lattice center) of the crystal to be detected cannot be completely determined, the measured radius of the high-order Laue diffraction ring and the volume of the primary primitive cell are compared with the calculation result of a target structure, so that the indexing accuracy can be improved, the alternative phases which do not meet the conditions can be effectively filtered, and the accuracy of phase analysis is greatly improved; in the actual electron microscope experiment and data analysis, the workload of the experiment and analysis can be greatly reduced, and the working efficiency is obviously improved.
The method can rapidly identify the phase of the material by utilizing selective area electron diffraction, precession electron diffraction, microbeam electron diffraction, nano-beam electron diffraction or convergent beam electron diffraction on a transmission electron microscope.
Drawings
FIG. 1a is a basic flow of conventional electronic diffraction indexing, and FIG. 1b is a flow chart of phase identification by electronic diffraction in examples 1 and 2 below;
FIG. 2 is a band axis electron diffraction pattern of titanium dioxide of example 1 (titanium dioxide gel sintered at 500 ℃ for 6 hours) containing a higher order Laue diffraction ring;
FIG. 3 is the diffraction patterns of the zeroth order Laue diffraction spot (a) and the corresponding higher order Laue diffraction ring (b) of the titanium dioxide nanocrystal of example 2.
Detailed Description
The technical solution of the present invention will be further described in detail with reference to specific embodiments. It is to be understood that the following examples are only illustrative and explanatory of the present invention and should not be construed as limiting the scope of the present invention. All the technologies realized based on the above-mentioned contents of the present invention are covered in the protection scope of the present invention.
Unless otherwise specified, the raw materials used in the following examples are all commercially available products or can be prepared by known methods.
Example 1 phase identification of titanium dioxide
1) The band axis electron diffraction pattern of titanium dioxide (titanium dioxide gel sintered at 500 ℃ for 6 hours) containing the higher order Laue diffraction ring was recorded as shown in FIG. 2. The electron diffraction pattern was recorded using a JEOL JEM-2100 transmission electron microscope at 200kV, with a camera length L of 100 mm.
2) Measuring the radius of the zero-order Laue diffraction point and the radius of the high-order Laue diffraction ring of the titanium dioxide;
the two-dimensional primitive cell is constructed by taking the transmission spot as the origin O of the two-dimensional primitive cell and taking the nearest neighbor diffraction points A and B as the adjacent edges, as shown in FIG. 2. Measuring OA, OB, OC (OC is diagonal) and angle AOB (wherein angle AOB is 72.2 DEG) and RobsThereby obtaining R1、R2、R3And theta. According to the formula Rd. L λ, wherein
Figure BDA0002151347760000071
Calculating the corresponding interplanar spacing d for the wavelength of 200kV electron beam1，d2，d3. The measurement and calculation results are shown in table 1.
3) Using the measurement parameter R in 2)obs＝23.57nm-1Calculating the layer spacing of the reciprocal surface as
Figure BDA0002151347760000072
Figure BDA0002151347760000073
wherein
Figure BDA0002151347760000074
A wavelength of 200kV electron beam; bonding of
Figure BDA0002151347760000075
Figure BDA0002151347760000081
Calculating the primary primitive cell volume of the crystal to be measured at 72.2 DEG theta
Figure BDA0002151347760000082
Figure BDA0002151347760000083
4) The common structures of titanium dioxide are three types, namely anatase, brookite and rutile phases. The unit cell volume of which is respectively
Figure BDA0002151347760000084
And
Figure BDA0002151347760000085
(wherein the unit cell volumes for the three crystal structures are calculated by the following formula:
Figure BDA0002151347760000086
wherein a, b, c, alpha, beta and gamma are lattice constants corresponding to the three structures);
then, the volume V of the primordial germ cells corresponding to the three crystal structures is calculated according to the following formulacalc
Vcalc＝V/M
Wherein M is a multiple caused by the center of the lattice and is determined by the following method:
Figure BDA0002151347760000087
the lattice centers of the three crystal forms are I (M is 2), P (M is 1) and P (M is 1), and the volumes V of the primary protocells corresponding to the three crystal structures are calculatedcalcAre respectively as
Figure BDA0002151347760000088
And
Figure BDA0002151347760000089
Figure BDA00021513477600000810
obviously, the initial germ cell volume obtained by the calculation of the crystal to be detected is closer to the anatase phase.
5) Based on the analysis result of 4), the crystal to be detected is assumed to be anatase (PDF #71-1167) and the lattice constant is
Figure BDA00021513477600000811
α ═ β ═ γ ═ 90 °, and the center of the lattice is I. The electron diffraction pattern can be indexed by anatase phase through indexing, band axis indexes are determined through calculation, the plane indexes of diffraction points A and B are (-110) and (12-1) respectively, and the band axis index is [ -1-1-3 [](ii) a The band axis index is calculated as follows
51) Calculating a d-value table and a crystal face included angle theta list according to the lattice constants a, b, c, alpha, beta and gamma of the target crystal:
Figure BDA0002151347760000091
Figure BDA0002151347760000092
wherein ,
Figure BDA0002151347760000093
is unit cell volume, d1 and d2Is (h) of1k1l1) and (h2k2l2) The interplanar spacing of (a); sijThe matrix is defined as follows:
S11＝b2c2sin2α，S22＝a2c2sin2β，S33＝a2b2sin2γ
S12＝abc2(cosαcosβ-cosγ)，S23＝a2bc(cosβcosγ-cosα)
S13＝ab2c(cosγcosα-cosβ)；
52) find and d in the d-value table1Matched crystal face index (h)1k1l1) (ii) a Find d in the table of d-values and the table of included angles of facets2Matched crystal face index (h)2k2l2) The angle between the two crystal faces is required to be consistent with the angle theta and the diagonal point d3Is just enough to satisfy (h)3k3l3)＝(h1k1l1)+(h2k2l2)；
53) Index of plane (h)1k1l1) Cross multiplication (h)2k2l2) Obtaining the band axis index [ uv w ] of the crystal]：
Figure BDA0002151347760000094
6) Using the tape axis index [ -1-1-3 ] determined in step 5)]Calculating the layer spacing of reciprocal surface as
Figure BDA0002151347760000095
Figure BDA0002151347760000096
Wherein a, b, c, alpha, beta and gamma are lattice constants of the target crystal: (
Figure BDA0002151347760000097
α ═ β ═ γ ═ 90 °). Then, the radius of the high-order Laue diffraction ring is calculated according to a formula
Figure BDA0002151347760000098
Where N is an integer related to the extinction of the crystal system, as known from the type of target crystal, N-2,
Figure BDA0002151347760000099
Figure BDA00021513477600000910
at a wavelength of 200kV electron beam.
Center of lattice F A B C I P R
N 2 2 2 2 2 1 3 in the case of hexagonal system; rhombohedral crystal system is 1
The results of the measurement and calculation in the above steps are shown in table 1,
TABLE 1
Figure BDA0002151347760000101
7) From the above results, it can be seen that the electron diffraction pattern of the titanium dioxide to be measured can not only be indexed by the target crystal structure, but also the experimentally measured primary primitive cell volume
Figure BDA0002151347760000102
And radius R of the higher order Laue diffraction Ringobs＝23.57nm-1All with anatase phase
Figure BDA0002151347760000103
and Rcalc＝23.41nm-1The high coincidence indicates that the crystal to be detected is in an anatase structure. Furthermore, d is measured in step 3)1，d2,θ and RobsCan calculate VobsEven if the indicator is not used, the brookite can be removed
Figure BDA0002151347760000104
And rutile phase
Figure BDA0002151347760000105
The analysis workload is greatly reduced.
Example 2 phase identification of titanium dioxide prepared by hydrothermal method
1) The titanium dioxide nanocrystalline prepared by the hydrothermal method has small crystal grains and poor crystallinity, and is difficult to record a zero-order Laue diffraction point and a high-order Laue diffraction ring on the same electron diffraction pattern. For this purpose, we recorded the zero-order Laue diffraction spot of the crystal with a JEOL JEM-2100 transmission electron microscope at 200kV using nanobeam electron diffraction, and the higher-order Laue diffraction ring with convergent beam electron diffraction, with a camera length L of 100mm, as shown in FIGS. 3 a-b.
2) Measuring the radius of a zero-order Laue diffraction point and a high-order Laue diffraction ring;
constructing a two-dimensional primary primitive cell by taking the transmission spot as the origin O of the two-dimensional primary primitive cell and taking the nearest neighbor diffraction points A and B as adjacent edgesPrimitive cell, as shown in FIG. 3 a. OA, OB, OC (OC is diagonal) and angle AOB (where angle AOB is 90.1 °) and R are measuredobsThereby obtaining R1、R2、R3And theta. The measurement results are shown in Table 2.
3) Using the measurement parameter R in 2)obs＝27.61nm-1Calculating the layer spacing of the reciprocal surface as
Figure BDA0002151347760000111
Figure BDA0002151347760000112
wherein
Figure BDA0002151347760000113
A wavelength of 200kV electron beam; bonding of
Figure BDA0002151347760000114
Figure BDA0002151347760000115
Calculating the primary primitive cell volume of the crystal to be measured at the angle of 90.1 DEG theta
Figure BDA0002151347760000116
Figure BDA0002151347760000117
4) Although the nanocrystals were reacted at 200 ℃ for 12 hours hydrothermally, either anatase or brookite structure could be formed (i.e., two-phase mixing). From the primary primitive cell volume V calculated in 3)obsIt is known that the crystal grains are consistent with brookite. The unit cell volume corresponding to three crystal structures of anatase, brookite and rutile is calculated by the following formula:
Figure BDA0002151347760000118
wherein a, b, c, alpha, beta and gamma are lattice constants corresponding to three structural crystal forms.
Then the volume V of the primordial germ cells corresponding to the three crystal structures is calculated according to the formulacalc
Vcalc＝V/M
Wherein M is a multiple caused by the center of the lattice and is determined by the following method:
Figure BDA0002151347760000119
the lattice centers of the three crystal forms are I (M is 2), P (M is 1) and P (M is 1), and the volumes V of the primary protocells corresponding to the three crystal structures are calculatedcalcAre respectively as
Figure BDA00021513477600001110
And
Figure BDA00021513477600001113
Figure BDA00021513477600001111
5) the crystal grain of the crystal to be detected is assumed to be a brookite structure (PDF #76-1934), and the lattice constant is
Figure BDA00021513477600001112
α ═ β ═ γ ═ 90 °, and the center of the lattice is P. The electron diffraction pattern can be indexed by brookite phase, and band axis index (band axis index [ -1-10 ]), wherein the plane indices of diffraction points A and B are (-110) and (00-1), respectively, and the band axis index is calculated and confirmed](ii) a The tape axis index is calculated as follows:
51) calculating a d-value table and a crystal face included angle theta list according to the lattice constants a, b, c, alpha, beta and gamma of the target crystal:
Figure BDA0002151347760000121
Figure BDA0002151347760000122
wherein ,
Figure BDA0002151347760000123
is unit cell volume, d1 and d2Is (h) of1k1l1) and (h2k2l2) The interplanar spacing of (a); sijThe matrix is defined as follows:
S11＝b2c2sin2α，S22＝a2c2sin2β，S33＝a2b2sin2γ
S12＝abc2(cosαcosβ-cosγ)，S23＝a2bc(cosβcosγ-cosα)
S13＝ab2c(cosγcosα-cosβ)；
52) find and d in the d-value table1Matched crystal face index (h)1k1l1) (ii) a Find d in the table of d-values and the table of included angles of facets2Matched crystal face index (h)2k2l2) The angle between the two crystal faces is required to be consistent with the angle theta and the diagonal point d3Is just enough to satisfy (h)3k3l3)＝(h1k1l1)+(h2k2l2)；
53) Index of plane (h)1k1l1) Cross multiplication (h)2k2l2) Obtaining the band axis index [ uv w ] of the crystal]：
Figure BDA0002151347760000124
6) Using the tape axis index [ -1-10 ] determined in step 5)]Calculating the layer spacing of reciprocal surface as
Figure BDA0002151347760000125
Figure BDA0002151347760000126
Wherein a, b, c, alpha, beta and gamma are lattice constants of the target crystal. Then, the radius of the high-order Laue diffraction ring is calculated according to a formula
Figure BDA0002151347760000131
Where N is an integer related to the extinction of the crystal system, as known from the type of target crystal, N1,
Figure BDA0002151347760000132
at a wavelength of 200kV electron beam.
Center of lattice F A B C I P R
N 2 2 2 2 2 1 3 in the case of hexagonal system; rhombohedral crystal system is 1
The measurement and examination results of the above steps are shown in table 2,
TABLE 2
Figure BDA0002151347760000133
7) From the above results, it can be seen that the electron diffraction pattern of the crystal grain to be measured can not only be indexed by the target crystal structure, but also the volume of the primordial primitive cell experimentally measured
Figure BDA0002151347760000134
And radius R of the higher order Laue diffraction Ringobs＝27.61nm-1Results of calculations both with brookite phase
Figure BDA0002151347760000135
and Rcalc＝27.34nm-1And (5) matching, which shows that the crystal to be detected is really the brookite structure. In addition, when d is measured1，d2,θ and RobsCan calculate VobsEven if the anatase is not indexed, the anatase can be removed
Figure BDA0002151347760000136
And rutile phase
Figure BDA0002151347760000137
Figure BDA0002151347760000138
The calculation time is greatly saved.
The embodiments of the present invention have been described above. However, the present invention is not limited to the above embodiment. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (10)

1. A method for phase recognition of a material by an electron diffraction pattern, comprising the steps of:
step 1): recording a band-axis electron diffraction pattern containing a high-order laue diffraction ring, or a zero-order laue diffraction point pattern and a corresponding high-order laue diffraction ring pattern;
step 2): measuring the radius of a zero-order Laue diffraction point and a high-order Laue diffraction ring of the crystal to be measured;
step 3): calculating the primary primitive cell volume of the crystal to be detected by using the parameters obtained in the step 2);
step 4): calculating the volume of a primary primitive cell according to the lattice constant of the target crystal;
step 5): indexing the zero-order Laue diffraction points in the step 2) to determine band axis indexes;
step 6): calculating the radius of a high-order Laue diffraction ring of the target crystal by using the band axis index in the step 5);
step 7): if the electronic diffraction pattern of the crystal to be detected can not only be indexed by the target crystal structure, but also the initial primitive cell volume measured in the step 3) is calculated from the initial primitive cell volume in the step 4), and the radius of the high-order Laue diffraction ring measured in the step 2) is consistent with the radius of the high-order Laue diffraction ring of the target crystal, the crystal to be detected is consistent with the target crystal structure.
2. Method according to claim 1, characterized in that step S1): recording a band axis electron diffraction pattern of a crystal to be detected, wherein the crystal to be detected contains a high-order Laue diffraction ring; or recording a zero-order Laue diffraction point pattern and a corresponding high-order Laue diffraction ring pattern on the same crystal to be detected;
step S2): the method for measuring the radius of the zero-order Laue diffraction point and the radius of the high-order Laue diffraction ring of the crystal to be measured comprises the following specific steps:
s21) measuring two-dimensional primary germ cells on zeroth-order laue diffraction: the transmission spot is the origin O of the two-dimensional primary primitive cell, and a parallelogram formed by two nearest neighbor diffraction points A and B as adjacent edges is used as the two-dimensional primary primitive cell: r1＝OA，R2＝OB，R3OC is a diagonal line of the parallelogram, and theta is equal to angle AOB; measuring the radius of the higher-order Laue diffraction Ring, denoted Robs；
S22) using the camera length L and the wavelength λ of the incident electron beam, the corresponding interplanar spacing d is calculated from the formula Rd — L λ1，d2，d3；
Step S3): calculating the initial primitive cell volume V of the crystal to be detected by using the parameters obtained in the step S2)obsThe calculation method comprises the following steps:
s31) from the radius R of the high-order Laue diffraction Ring in step S2)obsCalculating the layer spacing H of the reciprocal surface*：
Figure FDA0002151347750000021
λ is the wavelength of the incident electron beam;
s32) from d in step S2)1，d2And θ, reciprocal surface layer spacing H*Calculating the volume V of the primordial germ cellsobs：
Figure FDA0002151347750000022
Step S4): calculating the volume V of primary primitive cell according to the lattice constant of target crystalcalcThe process is as follows:
s41) calculating the unit cell volume V from the lattice constants a, b, c, α, β, γ of the target crystal:
Figure FDA0002151347750000023
s42) determining the volume V of the primary primitive cell according to the lattice center of the target crystalcalc：
Vcalc＝V/M
Wherein M is a multiple caused by the center of the lattice and is determined by the following method:
center of lattice F A B C I P R M 4 2 2 2 2 1 3 in the case of hexagonal system; rhombohedral crystal system is 1
；
Step S5): the zero-order Laue diffraction point is indexed to determine the band axis index, and the process is as follows:
s51) calculating a d-value table and a crystal face included angle theta list according to the lattice constants a, b, c, alpha, beta and gamma of the target crystal;
step S6) based on the tape axis index [ uv w ] determined in step S5)]Calculating radius R of high-order Laue diffraction ringcalc(ii) a The calculation steps are as follows:
s61) using the tape axis index [ uv w ] determined in step S5)]Calculating the layer spacing H of the reciprocal surface*：
Figure FDA0002151347750000031
Wherein a, b, c, alpha, beta and gamma are lattice constants of the target crystal;
s62) calculating the reciprocal face-layer spacing H according to the step S61)*Calculating radius R of high-order Laue diffraction ringcalc：
Figure FDA0002151347750000032
Wherein λ is the wavelength of the incident electron beam; n is an integer related to the extinction of the crystal system, determined by:
center of lattice F A B C I P R N 2 2 2 2 2 1 3 in the case of hexagonal system; rhombohedral crystal system is 1
；
Step S7) if the band axis electron diffraction pattern of the crystal to be tested contains a high-order Laue diffraction ring; or the zero-order Laue diffraction point pattern and the corresponding high-order Laue diffraction ring pattern can not only be indexed by the target crystal structure, but also the volume V of the primordial primitive cell measured experimentallyobsRadius R of the higher order Laue diffraction RingobsCalculated result V of both and the target crystal structurecalc and RcalcAnd if so, indicating that the structure of the crystal to be detected is consistent with that of the target crystal, and confirming the structure of the crystal to be detected.
3. The method according to claim 1 or 2, characterized in that the crystal to be tested in step S1) is a crystal of known chemical composition, but whose crystal structure cannot be determined.
4. The method according to any one of claims 1 to 3, wherein the crystal to be tested in step S1) is a bulk material, a powder, or a single crystal, a polycrystal, a microcrystal or a nanocrystal.
5. The method according to any one of claims 1 to 4, wherein step S1) is performed by recording a band axis electron diffraction pattern comprising a higher order Laue diffraction loop if the crystallinity of the crystal to be tested is good; and if the crystallinity of the crystal to be detected is poor, recording a zero-order Laue diffraction point pattern and a corresponding high-order Laue diffraction ring pattern.
6. The method according to any of claims 1 to 5, wherein in step S1) a transmission electron microscope is used to record a band axis electron diffraction pattern of the test crystal containing the higher order Laue diffraction rings or a zero order Laue diffraction spot pattern and a corresponding higher order Laue diffraction ring pattern on the same test crystal.
7. The method according to claim 6, wherein in step S1), the transmission electron microscope electron diffraction is selected area electron diffraction, precession electron diffraction, nanobeam electron diffraction, microbeam electron diffraction or convergent beam electron diffraction.
8. The method according to any one of claims 1 to 6, wherein in step S1), the recorded on-axis electron diffraction pattern is a low index on-axis for indexing.
9. The method according to any one of claims 1 to 8, wherein in step S1), the recorded on-axis electron diffraction pattern is not required to satisfy strict positive on-axis conditions.
10. The method according to any one of claims 1 to 9, wherein in step S2), the area enclosed by the two-dimensional primordial germ cells is the smallest;
preferably, in step S2), the measured higher order laue diffraction loop should be the one with the smallest radius.
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