CN104915473B - A method for measuring the distance between crystal surface structures - Google Patents

Abstract

A kind of method of distance between measurement Crystal surface structure, which solve existing measurement method physical significance is indefinite and the not high defect of accuracy.This method is according to geometrical symmetry and crystal periodicity principle, the measurement method that two o'clock is displaced in periodic spatial is invented, first to the mould progress square of the displacement vector of the atom of corresponding position in the space of two Crystal surface structures, then it sums, finally evolution seeks arithmetic square root again, to obtain the distance between two Crystal surface structures.

Description

A kind of method of distance between measurement Crystal surface structure

Technical field

The invention patent relates to a kind of methods of distance between measurement Crystal surface structure, for carrying out certainly to a large amount of structures Dynamic analysis, can measure the distance between two Crystal surface structures.

Background technique

Crystal surface structure has configuration complicated and changeable, currently, there are mainly two types of the spacing of measurement Crystal surface structure From method: (1) mutual distance between gauging surface atom and carry out Data Discretization and obtain that structure feature can be characterized Then " fingerprint " matrix calculates the COS distance of " fingerprint " between two structures, referred to as fingerprint COS distance (cosine- fingerprint-distance)；(2) Euclidean distance (Euclidean distance, euclidean-distance) method calculates two The arithmetic square root for the quadratic sum being displaced between atom in structure.But all there is certain limitation in both methods.Fingerprint skill Although art can difference between description scheme, it is weaker in terms of the configuration of expression structure, with structural difference Increase, fingerprint technique is unable to accurate response and goes out distance between structure, and its physical significance is not clear enough.Euclidean distance can It is truly reflected out distance between two structures, but the surface of crystal exists periodically, therefore in Euclidean distance, two knots Displacement in structure between the atom of corresponding position can not veritably reflect the practical shortest distance between atom, this can be to structure Between the measurement of distance cause big error.

Summary of the invention

In order to overcome the shortcomings of that the existing method for measuring distance between Crystal surface structure, the invention patent provide A kind of novel method carrys out the distance between two Crystal surface structures of accurately measure.

Below in conjunction with Fig. 1, the method in the present invention for measuring distance between two Crystal surface structures is introduced comprising Following steps.

Step 0: determining the Crystal surface structure of any two mutual distance to be measured.

Step 1: two Crystal surface structures to be measured are carried out with the reading and storage of information.Read Crystal surface structure Relevant information and store to an Array for structural body, these information include: (1) cell parameter (3 × 3 matrixes), and (2) are brilliant The type of atom intracellular, the number of (3) each type atom, the coordinate of (4) each atom, the energy of (5) structure.Pass through setting Total is divided into three parts, i.e. substrate layer area, superficial layer area, vacuum layer area by substrate zone thickness and rim surface zona thickness.By three Partial cell parameter and atomic coordinates is also respectively stored into Array for structural body.

Step 2: the arranging order of the atomic coordinates of Crystal surface structure.To two structures to be compared, table is selected Floor area and vacuum layer reconfigure, and obtain a new structure cell.The object of arranging order is the atomic coordinates recorded in structure cell Matrix (matrix of n × 3, n indicate the number of atom).Gridding is carried out to Crystal surface structure according to space geometry principle, i.e., M × N × L grid body is divided into entire structure cell, wherein M indicates the number of grid in the X-axis direction, and N is indicated in the Y-axis direction The number of grid, L indicate the number of the grid on Z axis.The side length of each grid cube is about 0.5 Ethylmercurichlorendimide, can with one group it is whole Number [m, n, l] indicates grid position, while according to grid position, seeing formula to the expression formula of each grid one serial number K, K (1).Grid position [m, n, l] and grid serial number K where calculating same type of all atoms respectively.Arbitrary atom (coordinate The acquiring method of grid where [x, y, z]) is set to example with X-direction online case (see formula (2)).According to each atom The serial number K of locating grid carries out arranging order to the coordinate of atom

(1)

(2)

Note: floor () is downward bracket function, such as floor (1.2)=1.

Step 3: the distance between two structures of measurement.According to geometrical symmetry and crystal periodicity principle in the present invention, The measurement method that two o'clock is displaced in periodic spatial is invented, as shown in formula (3).This new displacement measurement method can solve Certainly periodically influenced caused by distance between two atoms on measurement plane of crystal, it can be in the hope of shortest between two atoms Distance.By the mould progress square of the displacement vector of each atom of the space corresponding position between two structures, then sum, most Evolution seeks arithmetic square root again afterwards, can obtain the distance between two crystal structures, referred to as remainder Euclidean distance, see public affairs Formula (4),

(3)

(4)

In formula,

coor_{1_i}: the fractional coordinates of atom i in structure 1；

coor_{2_i}: the fractional coordinates of atom i in structure 2；

Lat: the vector matrix of cell parameter.Lat includes rim surface zona part and vacuum layer part, and vacuum layer is for blocking Influence of the complementation to atom Z axis coordinate difference；

V_{i_d}: the displacement vector between the atom i of two structure corresponding positions；

mod_dis: the distance between two structures, i.e. remainder Euclidean distance；

Mod (): complementation, note: for negative, complementation and positive number are slightly different, as mod (- 0.2,1)= 0.8；

Sign (): sign function.

Step 4: the measurement result of distance between two structures of output.Range measurements between two structures are exported, while defeated The reference format of two structures shows file out, and this document, which is loaded into common modeling software, can show the three of structure Tie up image.

Step 5: terminating.

Detailed description of the invention

Fig. 1 is flow chart of the invention.

Fig. 2 is for 4 structures in embodiment.4 structures in figure are (011) face of rutile titanium dioxide Structure, the top of each subgraph is divided into the front view of structure, and lower part is divided into the top view of structure, the atom of bottom in top view It is presented using dotted line mode.Black ball indicates that oxygen atom, Archon indicate titanium atom in figure.

Specific embodiment

Embodiment one: implement to carry out according to the following steps.

Step 0. determination will carry out range measurement to structure a and structure b.

Step 1. reads structure a, and the structural information of b is simultaneously stored to an Array for structural body, these information include: (1) crystalline substance Born of the same parents' parameter (3 × 3 matrixes), the type of atom in (2) structure cell, the number of (3) each type atom, (4) each atom Coordinate, the energy of (5) structure.By setting substrate zone thickness and rim surface zona thickness, total is divided into three parts, i.e. substrate Floor area, superficial layer area, vacuum layer area.The cell parameter of three parts and atomic coordinates are also respectively stored into Array for structural body.

Step 2. is to structure a, the coordinate arranging order of the surface atom of b.Select structure a, the rim surface zona and vacuum layer of b It reconfigures, obtains new structure cell, to matrix (matrix of n × 3, of n expression atom of the atomic coordinates in record structure cell Number) spatially position carry out arranging order.

Remainder Euclidean distance between step 3. measurement structure a and structure b.

The range measurements of step 4. export structure a and structure b, the distance between model a and model b are 2.530 angstroms Rice, and the reference format for exporting two structures shows file, this document, which is loaded into common modeling software, can show knot The 3-D image of structure.

Step 5. terminates.

Above step is repeated, acquiring the distance between structure a and structure c is 11.427 Ethylmercurichlorendimides.It can be obtained by calculated result Conclusion out: for comparing structure c, structure b and structure a are more like.

Embodiment two: step and the step in embodiment 1 are just the same.

In the embodiment, to model a, tri- structures of b, d are analyzed.Computation model a is at a distance from model b, model a The distance between model d and the distance between model b model d.

The result of output is that the distance between model a and model b are 2.530 Ethylmercurichlorendimides, the distance between model a and model d For 3.674 Ethylmercurichlorendimides, the distance between model b and model d are 2.460 Ethylmercurichlorendimides.In the front view in Fig. 2 a, Fig. 2 b and Fig. 2 d, Model a, b, configuration difference is not very big between d three, but in a top view, annular formed by three models is very different, Wherein model b is close compared with model d cyclization.It is analyzed from the distance between three is upper, also certain available conclusion model b ratio Model a is more close with model d.

Claims (1)

1. the method for distance, can calculate between two different crystal surface textures between a kind of measurement Crystal surface structure Distance, method the following steps are included:

Step 0: the Crystal surface structure of any two mutual distance to be measured；

Step 1: two Crystal surface structures to be measured are carried out with the reading and storage of information；

Step 2: the coordinate arranging order of the atom of Crystal surface structure；Atomic order is carried out using the method for grid dividing；It is right Two structures to be compared select rim surface zona and vacuum layer to reconfigure, obtain a new structure cell；Pair of arranging order As if the matrix of matrix n × 3 of the atomic coordinates in record structure cell, n indicate the number of atom；According to space geometry principle to crystalline substance Body surface texture carries out gridding, i.e., is divided into M × N × L grid body to entire structure cell, and wherein M indicates grid in the X-axis direction Number, N indicates the number of grid in the Y-axis direction, and L indicates the number of the grid on Z axis；The side length of each grid cube For 0.5 Ethylmercurichlorendimide, grid position can be indicated with one group of integer [m, n, l], while according to grid position, giving one sequence of each grid Number K, the expression formula of K are shown in formula (1)；Grid position [m, n, l] and grid where calculating same type of all atoms respectively Serial number K；Arbitrary atom coordinate is the acquiring method of grid where [x, y, z], and grid position is shown in formula (2) in X-direction；Grid Serial number is used for atomic order；

(1)

(2)

Note: floor () is downward bracket function；

Step 3: the remainder Euclidean distance between two structures of measurement；According to geometrical symmetry and crystal periodicity principle, invention The measurement method of two o'clock displacement in periodic spatial, as shown in formula (3)；This new displacement formula is able to solve periodicity It is influenced caused by distance between two atoms on measurement plane of crystal, it can be in the hope of shortest distance between two atoms；It will The mould progress square of the displacement vector of each atom of space corresponding position between two structures, then sums, finally opens again Side seeks arithmetic square root, can obtain the distance between two crystal structures, referred to as remainder Euclidean distance, see formula (4);

(3)

(4)

In formula,

coor_{1_i}: the fractional coordinates of atom i in structure 1；

coor_{2_i}: the fractional coordinates of atom i in structure 2；

Lat: the vector matrix of cell parameter；Lat includes rim surface zona part and vacuum layer part, and vacuum layer is for blocking remainder Influence of the operation to Z axis coordinate difference；

V_{i_d}: the displacement vector between the atom i of two structure corresponding positions；

mod_dis: the distance between two structures；That is remainder Euclidean distance

Mod (): complementation；

Sign (): sign function；

Step 4: the measurement result of distance between two structures of output；

Step 5: terminating.