CN111122623A - Method for realizing rapid tilting crystal tape shaft - Google Patents

Method for realizing rapid tilting crystal tape shaft Download PDF

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CN111122623A
CN111122623A CN201911390891.5A CN201911390891A CN111122623A CN 111122623 A CN111122623 A CN 111122623A CN 201911390891 A CN201911390891 A CN 201911390891A CN 111122623 A CN111122623 A CN 111122623A
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crystal
rod
axis
diffraction
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CN111122623B (en
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马延航
严睿文
张韵豪
孙凸
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ShanghaiTech University
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Abstract

The invention relates to a method for realizing rapid tilting of crystal belt axes, which adopts different methods for processing when a crystal is not on a designated belt axis or when the crystal is close to one belt axis but slightly deviated in orientation. The invention also provides an application of the method for realizing the rapid tilting of the crystal ribbon axis, which is characterized in that the method for realizing the rapid tilting of the crystal ribbon axis is realized by utilizing computer program programming. The invention discloses a thought for calculating the rotation direction and angle of a double-inclined sample rod in a transmission electron microscope, which can use a program to judge the band axis of the current crystal by utilizing an electron diffraction pattern, quickly calculate the tilting angle of the double-inclined rod required by rotating to a specified band axis, and adjust the crystal slightly deviating from the band axis to a correct position according to a Laue ring.

Description

Method for realizing rapid tilting crystal tape shaft
Technical Field
The invention provides a method for rapidly rotating a crystal to a specific band axis when a transmission electron microscope is used for shooting an electron diffraction pattern and a high-resolution image, and belongs to the technical field of transmission electron microscopy.
Background
Transmission electron microscopes have been widely used in materials, chemistry, biology and other fields, the two main functions of which are to capture a selected area electron diffraction pattern and a high resolution image, and the prerequisite for achieving both functions is to rotate the crystal to a specific band axis. In most cases, the operator tilts the crystal empirically, which not only takes a lot of time and effort, but also the long-time electron beam irradiation may damage the crystal.
In previous reports, researchers have determined the band axes of crystals using convergent electron beam diffraction methods, but strong electron beams can disrupt the structure of some crystals. American scientists developed a tool known as "KSpaceNavigator" to determine the crystallographic band axis by comparing simulated and experimental selected area electron diffraction patterns and to determine the sample rod rotation angle using a reconstructed three-dimensional reciprocal sphere. Furthermore, a similar method was recently developed by the university of saudi arabia KAUST, but this method is only applicable to the case where the crystal band axis deviates plus or minus 5 degrees.
Disclosure of Invention
The invention aims to provide a method capable of quickly calibrating an electron diffraction sample and automatically calculating the rotation angle of a double-inclined rod to a specific belt axis.
In order to achieve the above object, the present invention provides a method for rapidly tilting a ribbon axis of a crystal, wherein the crystal is not on a designated ribbon axis, the method comprising the following steps:
step 1, calculating theoretical interplanar distances of crystal planes corresponding to diffraction points according to an interplanar distance calculation formula and input unit cell parameters a, b, c, α, β and gamma, wherein each diffraction point is represented by a interplanar index H, K, L, and H, K, L is an integer;
step 2, analyzing the diffraction pattern shot in the experiment, determining the pixel coordinates of the transmission spot O, the two nonlinear diffraction spots P and the diffraction spot Q in the experiment diffraction pattern, and calculating the length L from the diffraction spot P to the transmission spot OPAnd the length L of the diffraction spot Q to the transmission spot OQAnd calculating the interplanar space corresponding to the diffraction spot P according to the pixel length P of the experimental diffraction patternDistance value dPInterplanar spacing values d corresponding to diffraction spots QQ，dP＝1/(LP×p)，dQ＝1/(LQ×p)；
Step 3, searching all theoretical interplanar distances obtained by calculation in step 1 and interplanar distance value dPAnd interplanar spacing value dQThe matched value is the index H of the crystal face of the diffraction spot P corresponding to the index H, K, L of the crystal face corresponding to the matched theoretical interplanar spacing1、K1、L1And the index H of the crystal plane of the diffraction spot Q2、K2、L2Thereby obtaining a vector [ H ]1K1L1]And vector [ H2K2L2]Will vector [ H1K1L1]And vector [ H2K2L2]Cross multiplication to obtain current ribbon axis
Figure BDA0002344904240000021
Step 4, setting the vector of the target crystal band axis direction as
Figure BDA0002344904240000022
Establishing a sample rod coordinate system, wherein in the sample rod coordinate system, the X rod direction OX of the sample rod is an S axis, and the Y rod initial direction OY of the sample rod0Is T axis, and the direction perpendicular to the plane of the X rod and the Y rod is defined as R axis, then:
target ribbon axis
Figure BDA0002344904240000023
The coordinates in the sample rod coordinate system are:
Figure BDA0002344904240000024
in the formula (1), the reaction mixture is,
Figure BDA0002344904240000025
and
Figure BDA0002344904240000026
are identical to each other，
Figure BDA0002344904240000027
And
Figure BDA0002344904240000028
in the same way, the first and second,
Figure BDA0002344904240000029
Figure BDA00023449042400000210
and comprises the following components:
Figure BDA00023449042400000211
Figure BDA00023449042400000212
in the formula (2), the reaction mixture is,
Figure BDA00023449042400000213
in the formula (3), S11＝b2c2sin2α，S22＝a2c2sin2β，S33＝a2b2sin2γ，S12＝abc2(cosαcosβ-cosγ)，S23＝a2bc(cosβcosy-cosα)，S13＝b2ac(cosacosγ-cosβ)，d1And d2Represents two crystal planes (h)1k1l1) And (h)2k2l2) The distance between the crystal planes of (a),
Figure BDA00023449042400000214
(h1k1l1) And (h)2k2l2) Indices OF crystal planes represented by crystal planes perpendicular to the OX and OF directions, respectively;
current ribbon axis
Figure BDA00023449042400000215
The coordinates in the sample rod coordinate system are:
Figure BDA0002344904240000031
in the formula (4), the reaction mixture is,
Figure BDA0002344904240000032
step 5, calculating to obtain an X rod rotation angle delta X required by rotating the direction of the current crystal band shaft to the direction of the target crystal band shaft and a Y rod rotation angle delta Y required by rotating the current direction to the target direction, wherein the X rod rotation angle delta X comprises the following steps:
Figure BDA0002344904240000033
Figure BDA0002344904240000034
in the formulae (5) and (6), x1The angle shown for the X-bar below the current ribbon axis.
Preferably, in step 3, if there are a plurality of interplanar spacing values dPAnd interplanar spacing value dQCalculating all theoretical angles of the crystal faces matched with the diffraction spots P and Q according to the formula of the angle of the crystal faces, and screening out the value with the angle difference within a set value as the value d of the distance between the crystal faces and the crystal face by taking ∠ POQ on the experimental diffraction pattern as referencePAnd interplanar spacing value dQMatched theoretical interplanar spacings.
The invention also provides an application of the method for realizing the rapid tilting of the crystal ribbon axis, which is characterized in that the method for realizing the rapid tilting of the crystal ribbon axis is realized by utilizing computer program programming.
Another aspect of the present invention is to provide a method for rapidly tilting a ribbon axis of a crystal, the crystal being adjacent to a ribbon axis but slightly misaligned in orientation, comprising the steps of:
step 1, identifying diffraction points in a diffraction pattern image shot in an experiment, extracting coordinates of the diffraction points on the image, and fitting a Laue ring according to the positions and distribution of the diffraction points;
step 2, determining the circle center O of the Laue ringLAnd a radius RLEstablishing a sample rod coordinate system, wherein in the sample rod coordinate system, the X-rod direction OX of the sample rod is an S axis, and the Y-rod initial direction OY of the sample rod0Is T axis, and the direction perpendicular to the plane of the X rod and the Y rod is defined as R axis, then:
current ribbon axis
Figure BDA0002344904240000035
The coordinates in the sample rod coordinate system are:
Figure BDA0002344904240000036
in the formula (7), λ is an electron wavelength, and p is a pixel length of an experimental diffraction pattern;
target ribbon axis
Figure BDA0002344904240000037
The coordinates in the sample rod coordinate system are:
Figure BDA0002344904240000041
in formula (8), ∠ XOOLIs the direction of the X rod and the circle center O of the connecting Laue ringLAngle to the straight line of the centre point, ∠ Y0OOLIs the direction of the initial position of the Y rod and the circle center O of the connecting Laue ringLAngle to the straight line of the center point;
step 3, calculating to obtain an X rod rotation angle delta X required by rotating the direction of the current crystal band shaft to the direction of the target crystal band shaft and a Y rod rotation angle delta Y required by rotating the current direction to the target direction, wherein the X rod rotation angle delta X comprises the following steps:
Figure BDA0002344904240000042
Figure BDA0002344904240000043
in the formulae (9) and (10), x1The angle shown for the X-bar below the current ribbon axis.
Preferably, in step 1, as many diffraction points as possible fall on the circumference of the laue ring.
The invention also provides an application of the method for realizing the rapid tilting of the crystal ribbon axis, which is characterized in that the method for realizing the rapid tilting of the crystal ribbon axis is realized by utilizing computer program programming.
The invention discloses a thought for calculating the rotation direction and angle of a double-inclined sample rod in a transmission electron microscope, which can use a program to judge the band axis of the current crystal by utilizing an electron diffraction pattern, quickly calculate the tilting angle of the double-inclined rod required by rotating to a specified band axis, and adjust the crystal slightly deviating from the band axis to a correct position according to a Laue ring.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a schematic view of the actual rotation of the double-tilting lever;
FIG. 3 is a double-tilting-lever rotating model;
FIG. 4 is a geometric model from the Laue ring to the positive band axis;
FIG. 5 is an example of an LTA molecular sieve photographed using the method provided by the present invention.
Detailed Description
The invention will be further illustrated with reference to the following specific examples. It should be understood that these examples are for illustrative purposes only and are not intended to limit the scope of the present invention. Further, it should be understood that various changes or modifications of the present invention may be made by those skilled in the art after reading the teaching of the present invention, and such equivalents may fall within the scope of the present invention as defined in the appended claims.
The method for realizing the rapid tilting of the crystal ribbon axis can rapidly calculate the position of the double-tilting sample rod corresponding to the ribbon axis for researchers according to the input electron diffraction pattern and the sample structure information.
Specifically, the method provided by the invention can realize the following two functions: (A) when the crystal is not on the designated belt axis, calibrating the current electron diffraction pattern to obtain the orientation of the current crystal, and further calculating the rotation angle of the double-inclined sample rod corresponding to the rotation to the designated belt axis; (B) when the crystal is close to one band axis but slightly off-set in orientation, the corresponding sample rod position at the time of alignment is calculated from the laue ring appearing on the diffraction pattern.
In order to realize the function (A) and the function (B), the invention constructs a mathematical model of the rotation of the double-inclination sample rod, which comprises a sample rod rotation matrix related to the initial position of the double-inclination rod, a space vector to be rotated and a function of the rotation angle of the double-inclination rod, and finally derives a simplified equation applicable to both the function (A) and the function (B).
In order to realize the function (A), the invention constructs a program processing method for automatically calibrating an electron diffraction pattern, which comprises the following steps:
step 1, calculating theoretical interplanar distances of the corresponding crystal planes of each diffraction point according to a known interplanar distance calculation formula and input unit cell parameters a, b, c, α, β and gamma, and storing the theoretical interplanar distances as a database to be retrieved, wherein each diffraction point is represented by a interplanar index H, K, L, and H, K, L is an integer.
And 2, analyzing the diffraction patterns shot in the experiment. The diffraction pattern shot by the experiment mainly comprises a transmission spot and a plurality of diffraction spots, and the pixel coordinates of the transmission spot O, two nonlinear diffraction spots P and two nonlinear diffraction spots Q in the experiment diffraction pattern are determined by the automatic identification function or the manual point selection function of a program. Calculating the length L from the diffraction spot P to the transmission spot OPAnd the length L of the diffraction spot Q to the transmission spot OQ(expressed in pixels), and the interplanar spacing value d corresponding to the diffraction spot P is calculated from the pixel length P of the experimental diffraction patternPInterplanar spacing values d corresponding to diffraction spots QQ，dP＝1/(LP×p)，dQ＝1/(LQX.p). The pixel length p is a fixed value for a particular experimental diffraction pattern.
Step 3, searching a matched value (deviation error can be set, such as +/-10%) in the interplanar spacing database calculated in the step 1, and taking the interplanar index H, K, L corresponding to the matched theoretical interplanar spacing as the interplanar index H of the diffraction spot P1、K1、L1And the index H of the crystal plane of the diffraction spot Q2、K2、L2Thereby obtaining a vector [ H ]1K1L1]And vector [ H2K2L2]. Using the tape axis theorem, vector [ H ]1K1L1]Sum vector [ H2K2L2]Cross multiplication to obtain current ribbon axis
Figure BDA0002344904240000061
In this step, a plurality of theoretical calculation values may be matched with the experimental values, in order to further reduce errors, theoretical angles of crystal planes matched with the diffraction spots P and Q are calculated according to a formula of the included angle of the crystal plane, and a value with an angle difference within 3 degrees (a set value) is screened out by taking ∠ POQ on the experimental diffraction pattern as a reference.
Step 4, the position of the diffraction point selected in step 2, the position of the rotating shaft of the double-inclined sample rod in the diffraction pattern (a fixed value for a specific device) obtained in other experiments, and the current zone axis calculated in step 3
Figure BDA0002344904240000062
And target ribbon axis
Figure BDA0002344904240000063
The geometric relationship between them, a calculation formula is derived because
Figure BDA0002344904240000064
And
Figure BDA0002344904240000065
in crystalsIn the coordinate system, in the actual calculation process, the two vectors need to be put into the coordinate system of the sample rod for calculation, and according to the sample rod tilting model shown in fig. 3, the two vectors can be deduced
Figure BDA0002344904240000066
And
Figure BDA0002344904240000067
coordinates in the sample rod coordinate system.
Step 5, through the working principle of the sample rod, the rotation matrix is deduced, and the current crystal band axis of the crystal is calculated according to the rotation matrix
Figure BDA0002344904240000068
Rotate to the target ribbon axis
Figure BDA0002344904240000069
A simplified equation for the required rotation angle, which requires the values calculated in step 4.
The specific formulas and derivation processes involved in steps 4 and 5 are described below.
(I) construction of double-inclined-rod rotation model
The double tilt rod allows the sample to be rotated in two mutually perpendicular directions. At the same time, due to the particularity of its design, the two levers are not completely independent in rotation. When the double-inclined rod tilts, the two rods meet the following geometrical relationship:
(1) the center point O is not moved in any rotation process;
(2) the direction of the X rod is unchanged in any rotation process;
(3) the X and Y bars remain vertical at all times (OX and OY are the axes of rotation of the X and Y bars, respectively);
(4) the direction of the Y-bar changes during rotation and the initial position of the Y-bar (denoted as Y)0) Is theta.
The position of the Y-bar affects the result, so calculations must be made taking into account variations in the Y-bar position. Namely, a model shown in fig. 3 is established, wherein the included angle between the Y-bar and the initial position is the rotation angle of the current X-bar.
(II) Dual Tilt Lever rotation matrix derivation
By T1(Δ x) and T2(Δy，x1) The bars represent the X-bar rotation matrix and the Y-bar has an X-bar rotation angle1The rotation matrix of time, the above process can be expressed as the following equation:
Figure BDA0002344904240000071
by simple derivation, T can be obtained1(x) And when x0In the special case of 0, T2(y, 0), which is specifically:
Figure BDA0002344904240000072
Figure BDA0002344904240000073
by definition, T2(Δy，x1) The corresponding rotational effects in practice are: at an X-bar inclination of X1The Y-bar is rotated by an angle Δ Y. Since the Y-axis is not in the original position, if T is derived directly by means of solid geometry2(Δy，x1) It would be very troublesome. Therefore, consideration is not given to linear algebra.
From the mechanical design of the double-inclined rod, the rotating operation of the double-inclined rod should have the following properties:
(1) the position of the Y-bar can affect the rotating effect;
(2) the rotation sequence of the two rods does not influence the result;
(3) after any rod rotates for a certain angle, the rod rotates for a certain angle, and the effect is equivalent to the sum of the two angles of the rod;
(4) after any rod rotates for a certain angle, the rod rotates for the angle opposite to the angle, and the position of the vector cannot be changed in a comprehensive mode.
Converting these properties into a mathematical language, then the correspondence is:
T1(Δx)·T2(Δy，x1)≠T2(Δy，x1)·T1(Δx) (1-4)
T1(Δx)·T2(Δy，x1)＝T2(Δy，x1+Δx)·T1(Δx) (1-5)
T(θ1)·T(θ2)＝T(θ1+θ2) (1-6)
T1(Δx)·T1(-Δx)＝T2(Δy)·T2(-Δy)＝I (1-7)
the above mathematical formula also hides an important property, namely: the rotating effect of the double-tilting lever is process-independent. Mathematically, this property can be written as:
Tany path＝T1(x2-x1)T2(y2-y1，x1)＝T1(Δx3′)T1(Δx2′)T2(Δy2′，x1+Δx1′)T1(Δx1′)T2(Δy1′，x1) (1-8)
wherein the variables satisfy:
∑Δxi′＝x2-x1(1-9)
∑Δyi′＝y2-y1(1-10)
then, the formula (1-8) is simplified, and the formula (1-5) is brought into the formula (1-8) to obtain:
Tany path＝T1(Δx3′)T1(Δx2′)T1(Δx1′)T2(Δy2′，x1)T2(Δy1′，x1) (1-11)
and bringing formula (1-6) into formula (1-11):
Tany path＝T1(Δx1′+Δx2′+Δx3′)T2(Δy1′+Δy2′，x1) (1-12)
t can also be found by the formula (1-8)2(Δy，x1) The relationship with the two special rotation matrices in the foregoing, namely:
T2(Δy，x1)＝T1(x1)·T2(y1，0)·T1(-x1) (1-13)
the rotation matrix of the Y-bar can be obtained by simplification:
Figure BDA0002344904240000081
now we have T1(Δ x) and T2(Δy，x1) The mathematical expression of (1), then we need to extrapolate
Figure BDA0002344904240000082
And
Figure BDA0002344904240000083
derivation of calculation formula of rotation angle of (III) double-inclined rod
Determining the current spool Direction as described above
Figure BDA0002344904240000084
And target ribbon axis
Figure BDA0002344904240000085
Are all based on a coordinate system of a crystal, and in the actual calculation process, we want to use
Figure BDA0002344904240000086
And
Figure BDA0002344904240000087
the calculation is performed in the coordinate system of the sample rod, since the purpose of the calculation is to know the rotation angle of the sample rod. In the sample rod coordinate system, the X-rod direction OX of the sample rod is the S-axis, and the Y-rod initial direction OY of the sample rod0Is the T axis, and the direction vertical to the plane of the X rod and the Y rod is defined as the R axis.Assuming a target vector
Figure BDA0002344904240000088
And the current direction
Figure BDA0002344904240000089
The coordinates in the sample rod coordinate system are:
Figure BDA00023449042400000810
Figure BDA00023449042400000811
in the formula (1-15), the metal oxide,
Figure BDA00023449042400000812
and
Figure BDA00023449042400000813
in the same way, the first and second,
Figure BDA00023449042400000814
and
Figure BDA00023449042400000815
in the same way, the first and second,
Figure BDA00023449042400000816
Figure BDA00023449042400000817
and since the two modulo lengths are equal, the two vectors should have a relationship:
Figure BDA0002344904240000091
the problem then becomes to utilize1v1w1]And [ u ]2v2w2]Finding ∠ MON and ∠ XOF has the following relationship:
Figure BDA0002344904240000092
in the formula (1-18), the metal oxide,
Figure BDA0002344904240000093
Figure BDA0002344904240000094
in the formula (1-20), S11＝b2c2sin2α，S22＝a2c2sin2β，S33＝a2b2sin2γ，S12＝abc2(cosαcosβ-cosγ)，S23＝a2bc(cosβcosγ-cosα)，S13＝b2ac(cosαcosγ-cosβ)，d1And d2Represents two crystal planes (h)1k1l1) And (h)2k2l2) The distance between the crystal planes of (a),
Figure BDA0002344904240000095
(h1k1l1) And (h)2k2l2) Are the indices OF the crystal planes represented by the crystal planes perpendicular to the OX and OF directions, respectively.
By this step, s, t, r and r' are solved.
Due to the fact that
Figure BDA0002344904240000096
Two of the coordinates of (a) are zero, so it is more convenient to calculate the product of the matrix and it. Thus, the entire process can be viewed as if it were
Figure BDA0002344904240000097
Is rotated to
Figure BDA0002344904240000098
But the rotation angle would be exactly opposite to the result of the calculation in the model. Mathematically, i.e. using a double-pitch lever turn previously derivedAnd a rotation matrix (1-7) for rewriting the formula (1-1) as:
Figure BDA0002344904240000099
the method is simplified and can be obtained:
Figure BDA00023449042400000910
in the formulae (1-21) and (1-22), x1The angle displayed for the X rod under the current ribbon axis; Δ x ═ x2-x1，x2An inclination angle of an X rod under a target crystal band axis is obtained, and delta X is an X rod rotation angle required by rotating from the current direction to the target direction; y is2-y1，y2Is the target tape axis lower Y-bar tilt angle, Y1And the angle displayed by the Y rod under the current crystal band axis is delta Y which is the rotation angle of the Y rod required by rotating from the current direction to the target direction.
Solving equations (1-22) yields the tilt angle calculation for both rods:
Figure BDA0002344904240000101
Figure BDA0002344904240000102
to achieve function (B), the present invention constructs a programmed process for crystal orientation shift correction using a laue ring, comprising the steps of:
step 1, identifying diffraction points in a diffraction pattern image shot in an experiment, extracting coordinates of the diffraction points on the image, and fitting a Laue ring according to the positions and the distribution of the diffraction points. As many diffraction points as possible fall on the laue circle circumference.
Step 2, determining the circle center O of the Laue ringLAnd a radius RLAnd bringing the current orientation of the ribbon axis into the sample rod coordinate system derived above
Figure BDA0002344904240000103
And a target direction
Figure BDA0002344904240000104
Is described in (1).
As shown in FIG. 4, OEIs the center of the Evalad sphere,
Figure BDA0002344904240000105
corresponds to the above
Figure BDA0002344904240000106
Corresponds to the above
Figure BDA0002344904240000107
Comprises the following steps:
Figure BDA0002344904240000108
Figure BDA0002344904240000109
in the formula (1-26), λ represents the wavelength of electrons.
Figure BDA00023449042400001010
And 3, calculating the rotation angle required by rotating to the target direction by using the formulas (1-23) and (1-24) derived in the above.
In order to facilitate the operation of an operator, the LabView-based user interaction panel is designed, and a user can directly install the user interaction panel for use.

Claims (6)

1. A method of effecting rapid tilting of a ribbon axis of a crystal, the crystal not being on a given ribbon axis, comprising the steps of:
step 1, calculating theoretical interplanar distances of crystal planes corresponding to diffraction points according to an interplanar distance calculation formula and input unit cell parameters a, b, c, α, β and gamma, wherein each diffraction point is represented by a interplanar index H, K, L, and H, K, L is an integer;
step 2, analyzing the diffraction pattern shot in the experiment, determining the pixel coordinates of the transmission spot O, the two nonlinear diffraction spots P and the diffraction spot Q in the experiment diffraction pattern, and calculating the length L from the diffraction spot P to the transmission spot OPAnd the length L of the diffraction spot Q to the transmission spot OQAnd calculating the interplanar spacing value d corresponding to the diffraction spot P according to the pixel length P of the experimental diffraction patternPInterplanar spacing values d corresponding to diffraction spots QQ，dP＝1/(LP×p)，dQ＝1/(LQ×p)；
Step 3, searching all theoretical interplanar distances obtained by calculation in step 1 and interplanar distance value dPAnd interplanar spacing value dQThe matched value is the index H of the crystal face of the diffraction spot P corresponding to the index H, K, L of the crystal face corresponding to the matched theoretical interplanar spacing1、K1、L1And the index H of the crystal plane of the diffraction spot Q2、K2、L2Thereby obtaining a vector [ H ]1K1L1]And vector [ H2K2L2]Will vector [ H1K1L1]And vector [ H2K2L2]Cross multiplication to obtain current ribbon axis
Figure FDA0002344904230000011
Step 4, setting the vector of the target crystal band axis direction as
Figure FDA0002344904230000012
Establishing a sample rod coordinate system, wherein in the sample rod coordinate system, the X rod direction OX of the sample rod is an S axis, and the Y rod initial direction OY of the sample rod0Is T axis, and the direction perpendicular to the plane of the X rod and the Y rod is defined as R axis, then:
target ribbon axis
Figure FDA0002344904230000013
The coordinates in the sample rod coordinate system are:
Figure FDA0002344904230000014
in the formula (1), the reaction mixture is,
Figure FDA0002344904230000015
and
Figure FDA0002344904230000016
in the same way, the first and second,
Figure FDA0002344904230000017
and
Figure FDA0002344904230000018
in the same way, the first and second,
Figure FDA0002344904230000019
Figure FDA00023449042300000110
and comprises the following components:
Figure FDA00023449042300000111
Figure FDA00023449042300000112
in the formula (2), the reaction mixture is,
Figure FDA0002344904230000021
in the formula (3), S11＝b2c2sin2α，S22＝a2c2sin2β，S33＝a2b2sin2γ，S12＝abc2(cosαcosβ-cosγ)，S23＝a2bc(cosβcosγ-cosα)，S13＝b2ac(cosαcosγ-cosβ)，d1And d2Represents two crystal planes (h)1k1l1) And (h)2k2l2) The distance between the crystal planes of (a),
Figure FDA0002344904230000022
(h1k1l1) And (h)2k2l2) Indices OF crystal planes represented by crystal planes perpendicular to the OX and OF directions, respectively;
current ribbon axis
Figure FDA0002344904230000023
The coordinates in the sample rod coordinate system are:
Figure FDA0002344904230000024
in the formula (4), the reaction mixture is,
Figure FDA0002344904230000025
step 5, calculating to obtain an X rod rotation angle delta X required by rotating the direction of the current crystal band shaft to the direction of the target crystal band shaft and a Y rod rotation angle delta Y required by rotating the current direction to the target direction, wherein the X rod rotation angle delta X comprises the following steps:
Figure FDA0002344904230000026
Figure FDA0002344904230000027
in the formulae (5) and (6), x1The angle shown for the X-bar below the current ribbon axis.
2. A method of effecting a fast tilting crystal ribbon axis as claimed in claim 1 wherein in step 3, if there are a plurality of interplanar spacing values dPAnd interplanar spacing value dQThe matched theoretical interplanar spacing is calculated according to the interplanar angle formulaThe theoretical included angle of the crystal face matched with the diffraction spots P and Q is selected, and the value with the angle difference within a set value is selected as the value d between the value and the crystal face distance by taking ∠ POQ on the experimental diffraction pattern as referencePAnd interplanar spacing value dQMatched theoretical interplanar spacings.
3. Use of the method of claim 1 for achieving a fast tilting crystal ribbon axis, wherein the method of claim 1 is implemented by computer program programming.
4. A method of effecting rapid tilting of the ribbon axis of a crystal adjacent to a ribbon axis but slightly offset in orientation, comprising the steps of:
step 1, identifying diffraction points in a diffraction pattern image shot in an experiment, extracting coordinates of the diffraction points on the image, and fitting a Laue ring according to the positions and distribution of the diffraction points;
step 2, determining the circle center O of the Laue ringLAnd a radius RLEstablishing a sample rod coordinate system, wherein in the sample rod coordinate system, the X-rod direction OX of the sample rod is an S axis, and the Y-rod initial direction OY of the sample rod0Is T axis, and the direction perpendicular to the plane of the X rod and the Y rod is defined as R axis, then:
current ribbon axis
Figure FDA0002344904230000031
The coordinates in the sample rod coordinate system are:
Figure FDA0002344904230000032
in the formula (7), λ is an electron wavelength, and p is a pixel length of an experimental diffraction pattern;
target ribbon axis
Figure FDA0002344904230000033
The coordinates in the sample rod coordinate system are:
Figure FDA0002344904230000034
in formula (8), ∠ XOOLIs the direction of the X rod and the circle center O of the connecting Laue ringLAngle to the straight line of the centre point, ∠ Y0OOLIs the direction of the initial position of the Y rod and the circle center O of the connecting Laue ringLAngle to the straight line of the center point;
step 3, calculating to obtain an X rod rotation angle delta X required by rotating the direction of the current crystal band shaft to the direction of the target crystal band shaft and a Y rod rotation angle delta Y required by rotating the current direction to the target direction, wherein the X rod rotation angle delta X comprises the following steps:
Figure FDA0002344904230000035
Figure FDA0002344904230000036
in the formulae (9) and (10), x1The angle shown for the X-bar below the current ribbon axis.
5. A method of effecting fast tilt crystal ribbon axes as claimed in claim 4 wherein in step 1 as many diffraction points as possible are made to fall on the circumference of the Laue ring.
6. Use of the method of claim 4 for achieving a fast tilting crystal ribbon axis, wherein the method of claim 4 is implemented by computer program programming.
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