CN104915473A - Method for measuring distance between surface structures of crystals - Google Patents

Method for measuring distance between surface structures of crystals Download PDF

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Publication number
CN104915473A
CN104915473A CN201510245731.7A CN201510245731A CN104915473A CN 104915473 A CN104915473 A CN 104915473A CN 201510245731 A CN201510245731 A CN 201510245731A CN 104915473 A CN104915473 A CN 104915473A
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crystal
structures
grid
distance
atom
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CN104915473B (en
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龚学庆
丁攀
卢冠忠
胡培君
王海丰
曹宵鸣
郭杨龙
郭耘
王艳芹
王筠松
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East China University of Science and Technology
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East China University of Science and Technology
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Abstract

The invention provides a method for measuring distance between surface structures of crystals. The method for measuring the distance between the surface structures of the crystals solves the defects that an existing measuring method is ambiguous in physical significance and low in accuracy degree. According to the geometry symmetry and the crystal periodical theory, the measuring method for the displacement of two points in a periodical space is invented, models of displacement vectors of atoms on the corresponding positions in the space of the two surface structures of the crystals are squared, then summation is conducted, extraction of roots for obtaining arithmetic square roots are conducted finally, and therefore the distance between the two surface structures of the crystals is obtained.

Description

A kind of method measuring the spacing of Crystal surface structure
Technical field
Patent of the present invention relates to a kind of method measuring the spacing of Crystal surface structure, for carrying out automatic analysis to a large amount of structure, can measure the distance between two Crystal surface structures.
Background technology
Crystal surface structure has configuration complicated and changeable, at present, mainly contain the method for spacing that two kinds are measured Crystal surface structures: the phase mutual edge distance between (1) gauging surface atom and carry out that Data Discretization obtains can " fingerprint " matrix of characterisation of structures feature, then calculate the COS distance of " fingerprint " between two structures, be referred to as fingerprint COS distance (cosine-fingerprint-distance); (2) Euclidean distance (Euclidean distance, euclidean-distance) method, namely calculates the arithmetic square root of the quadratic sum of displacement between two structure Atoms.But all there is certain limitation in these two kinds of methods.Although fingerprint technique can difference between description scheme, weaker in the configuration of expression structure, along with the increase of structural difference, fingerprint technique can not go out the spacing of structure by accurate response, and its physical significance is clear and definite not.Euclidean distance can reflect the spacing of two structures truly, but the surface of crystal exists periodically, therefore in Euclidean distance, in two structures relevant position atom between displacement can not reflect actual bee-line between atom veritably, this can cause large error to the measurement of the spacing of structure.
Summary of the invention
In order to overcome the deficiency of the method for the existing spacing for measuring Crystal surface structure, patent of the present invention provides a kind of novel method to measure distance between two Crystal surface structures exactly.
Below in conjunction with Fig. 1, introduce for measuring the method for the spacing of two Crystal surface structures in the present invention, it comprises the steps.
Step 0: the Crystal surface structure determining any two phase mutual edge distances to be measured.
Step 1: reading and the storage of to be measured two Crystal surface structures being carried out to information.Read the relevant information of Crystal surface structure and be stored into an Array for structural body, these information comprise: (1) cell parameter (3 × 3 matrixes), the type of atom in (2) structure cell, the number of (3) every type atom, (4) coordinate of each atom, the energy of (5) structure.By setting substrate district thickness and rim surface zona thickness, total is divided into three parts, i.e. substrate layer district, superficial layer district, vacuum layer district.The cell parameter of three parts and atomic coordinates are also stored in Array for structural body respectively.
Step 2: the arranging order of the atomic coordinates of Crystal surface structure.To two structures that will compare, select rim surface zona and vacuum layer to reconfigure, obtain a new structure cell.The matrix (matrix of n × 3, n represents the number of atom) to the atomic coordinates liked in record structure cell of arranging order.Carry out gridding according to space geometry principle to Crystal surface structure, be namely divided into M × N × L grid body to whole structure cell, wherein M represents the number of grid in the X-axis direction, and N represents the number of grid in the Y-axis direction, and L represents the number of grid on Z axis.The cubical length of side of each grid is about 0.5 Ethylmercurichlorendimide, and available one group of integer [m, n, l] represents grid position, simultaneously according to grid position, sees formula (1) to the expression formula of each grid sequence number K, a K.Calculate all atoms grid position [m, n, l] at place and grid sequence number K separately of same kind.The acquiring method of arbitrary atom (coordinate is [x, y, z]) place grid, is set to example (see formula (2)) with X-direction online case.Residing for each atom, the sequence number K of grid carries out arranging order to the coordinate of atom
(1)
(2)
Note: floor () is downward bracket function, as floor (1.2)=1.
Step 3: measure the distance between two structures.According to geometrical symmetry and crystal periodically principle in the present invention, invent the measuring method of 2 displacements in periodic spatial, as shown in Equation (3).This new displacement measurement method can solve periodically on the impact that the spacing measuring two atoms on plane of crystal causes, can in the hope of distance the shortest between two atoms.Carried out by the mould of the displacement vector of each atom of the space correspondence position between two structures square, then sue for peace, finally evolution asks arithmetic square root again, just can obtain the distance between two crystal structures, be referred to as remainder Euclidean distance, sees formula (4),
(3)
(4)
In formula,
coor 1_i : the fractional coordinates of structure 1 Atom i;
coor 2_i : the fractional coordinates of structure 2 Atom i;
lat: the vector matrix of cell parameter. latcomprise rim surface zona part and vacuum layer part, vacuum layer is for blocking the impact of complementation on atom Z axis coordinate difference;
v i_d : the displacement vector between the atom i of two structure correspondence positions;
mod_dis: the distance between two structures, i.e. remainder Euclidean distance;
Mod (): complementation, note: for negative, complementation and positive number slightly different, as mod (-0.2,1)=0.8;
Sign (): sign function.
Step 4: the measurement result exporting the spacing of two structures.Export range measurements between two structures, export the standard format display file of two structures simultaneously, this file is loaded into the 3-D view that just can demonstrate structure in conventional modeling software.
Step 5: terminate.
Accompanying drawing explanation
Fig. 1 is process flow diagram of the present invention.
Fig. 2 is for the structure of 4 in embodiment.4 structures in figure are the structure in (011) face of rutile titanium dioxide, and the top of each subgraph is divided into the front elevation of structure, bottom to be divided into the vertical view of structure, and in vertical view, the atom of bottom adopts dotted line mode to present.In figure, black ball represents oxygen atom, and Archon represents titanium atom.
Embodiment
Embodiment one: implement according to the following steps to carry out.
step0. determines to carry out range observation to structure a and structure b.
step1. read structure a, b structural information and be stored into an Array for structural body, these information comprise: (1) cell parameter (3 × 3 matrixes), (2) type of atom in structure cell, (3) number of every type atom, the coordinate of (4) each atom, the energy of (5) structure.By setting substrate district thickness and rim surface zona thickness, total is divided into three parts, i.e. substrate layer district, superficial layer district, vacuum layer district.The cell parameter of three parts and atomic coordinates are also stored in Array for structural body respectively.
step2. the coordinate arranging order of the surface atom of couple structure a, b.Rim surface zona and the vacuum layer of choice structure a, b reconfigure, and obtain new structure cell, spatially carry out arranging order in position to the matrix (matrix of n × 3, n represents the number of atom) of the atomic coordinates in record structure cell.
step3. measure the remainder Euclidean distance between structure a and structure b.
step4. the range measurements of export structure a and structure b, the distance between model a and model b is 2.530 Ethylmercurichlorendimides, and exports the standard format display file of two structures, this file is loaded into the 3-D view that just can demonstrate structure in conventional modeling software.
step5. terminate.
Repeat above step, the distance of trying to achieve between structure a and structure c is 11.427 Ethylmercurichlorendimides.Can be reached a conclusion by result of calculation: compare structure c, structure b is more similar to structure a.
Embodiment two: the step in step and embodiment 1 is just the same.
In this embodiment, to model a, b, d tri-structures are analyzed.The distance of computation model a and model b, the distance between model a and model d, and the distance between model b model d.
The result exported is the distance between model a and model b is 2.530 Ethylmercurichlorendimides, and the distance between model a and model d is 3.674 Ethylmercurichlorendimides, and the distance between model b and model d is 2.460 Ethylmercurichlorendimides.In front elevation in Fig. 2 a, Fig. 2 b and Fig. 2 d, model a, between b, d three, configuration difference is not very large, but in a top view, formed by three models, annular has a great difference, and wherein model b becomes chain rate more close with model d.Analyze from the distance between three, also really can obtain conclusion model b more more close with model d than model a.

Claims (3)

1. measure a method for the spacing of Crystal surface structure, can measure the distance between two different crystal surface structures, method comprises the following steps:
Step 0: the Crystal surface structure of any two phase mutual edge distances to be measured;
Step 1: reading and the storage of to be measured two Crystal surface structures being carried out to information;
Step 2: the coordinate arranging order of the atom of Crystal surface structure;
Step 3: measure the remainder Euclidean distance between two structures;
Step 4: the measurement result and the display file of construction standard form that export the spacing of two structures;
Step 5: terminate.
2. method according to claim 1, is characterized in that: the measuring method of having invented 2 displacements in periodic spatial, and it can embody geometrical symmetry and the periodicity of plane of crystal.
3. method according to claim 1, is characterized in that: arrange in step at the atomic coordinates of Crystal surface structure, invented a kind of method that technology using gridding to divide is resequenced to the atomic coordinates in crystal structure; Carry out gridding according to space geometry principle to Crystal surface structure to divide, be divided into M × N × L grid body by whole structure cell, wherein M represents the number of grid in the X-axis direction, and N represents the number of grid in the Y-axis direction, and L represents the number of grid on Z axis; The cubical length of side of each grid is about 0.5 Ethylmercurichlorendimide, and available one group of integer [m, n, l] represents grid position, simultaneously according to grid position, to each grid sequence number K; The sequence number K of the grid residing for each atom carries out arranging order to atom.
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Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105527461A (en) * 2016-01-16 2016-04-27 北京工业大学 Material structure quantitative analysis method based on transmission electron microscope HAADF image
CN108268750A (en) * 2018-01-19 2018-07-10 吉林大学 Based on the imaginary Inorganic crystal structure Forecasting Methodology for enumerating Wyckoff position groupings
CN109002639A (en) * 2018-08-06 2018-12-14 北京航空航天大学 A kind of torsion and tilt boundary method for automatic modeling based on coincidence site lattice search

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US20140309971A1 (en) * 2013-04-15 2014-10-16 Sumitomo Rubber Industries, Ltd. Simulation method for macromolecular material

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Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105527461A (en) * 2016-01-16 2016-04-27 北京工业大学 Material structure quantitative analysis method based on transmission electron microscope HAADF image
CN108268750A (en) * 2018-01-19 2018-07-10 吉林大学 Based on the imaginary Inorganic crystal structure Forecasting Methodology for enumerating Wyckoff position groupings
CN109002639A (en) * 2018-08-06 2018-12-14 北京航空航天大学 A kind of torsion and tilt boundary method for automatic modeling based on coincidence site lattice search
CN109002639B (en) * 2018-08-06 2021-03-02 北京航空航天大学 Torsion and tilt crystal boundary automatic modeling method based on gravity lattice search

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