CN101710085B - Electronic diffraction index calibrating method based on Matlab - Google Patents

Abstract

The invention belongs to the field of scientific analysis of materials, in particular to an electronic diffraction index calibrating method based on Matlab. The zero-order electronic pattern index calibration and the index calibration of electronic simulating diffraction spots of two substances with a specific orientation relationship are carried out on a sample material by using a transmission electronic microscope, a computer and Matlab software. The invention mainly relates to a calibrating method of a monocrystal diffraction spectrum and the drawing of a standard electronic diffraction spectrum. Compared with the traditional calibrating method, the invention saves more time, can conveniently draw a zero-order and high-order simulating spot chart and an orientation relationship chart of a second phase and a base body and provides the beneficial technical basis for the computer to recognize the monocrystal diffraction spectrum.

Description

Electronic diffraction index calibrating method based on Matlab

Technical field

The present invention relates to the scaling method of electronic diffraction index, be specifically related to a kind of electronic diffraction index calibrating method, belong to the material science analysis field based on Matlab.

Background technology

1, key concept

1.1 electron diffraction pattern

Usually seen electron diffraction pattern can divide for the single crystal diffraction spectrum and the polycrystalline list diffraction ring that are rearranged by spot.The monocrystalline electron diffraction pattern is divided into zeroth order Laue electron diffraction pattern and high-order Laue electron diffraction pattern again.The index of zeroth order Laue diffraction spot or reciprocal lattice point (hkl) should satisfy zone law (h*u+k*v+l*w=0).Zeroth order laue spot diffraction spectra is a kind of very useful diffraction information, not only can utilize it to identify the thing phase, also can estimate the useful data of sample at the thickness and the crystal orientation of electron beam incident direction.For the sample of unknown crystal structure, also comprise and determine the crystal lattice content.

Demarcate the index of all spots in the electron diffraction pattern, and then definite derivative be which kind of material and crystal type, this just passes through the beginning of TEM (transmission electron microscope) analysis of material.Whether correct the index of precision of each diffraction spot then become analysis key.

1.2 the electronics mould diffraction spot of two kinds of materials of specific orientation relation is arranged

In most of materials, when carrying out phase transformation matrix with second mutually, defer to the minimum principle of energy, always grow along each other certain crystallographic plane and certain crystallographic direction.Second usually shows constant orientation relationship with matrix, and electron diffraction pattern is equivalent to two kinds of differences and the stack on two reciprocal planes in the reciprocal lattice of fixed orientation relation is arranged.For example in the phase transition process of steel, the second phase martensite is separated out from the matrix austenite, and the Kurdjumov-Sachs relation (K-S) of formation, Nishiyama-Machlin relation (N-W) and Greninger-Troiano relation (G-T) are exactly best example.

Measure orientation relationship,, and material mechanical performance, resistance to oxidation, performance such as corrosion-resistant and wear-resisting had significance for the essence of understanding processes such as alloy phase change, epitaxial growth, oxidation and coating.For many years, new method, new way for seeking accurately to measure orientation relationship have become the problem that crystallography worker and material supplier author extremely pay close attention to.

2, the problem of prior art existence

2.1 zeroth order electron diffraction pattern

Trial-accounting method and standard style counter point are adopted in the analysis of electron diffraction pattern more, generally are divided into four steps:

(1) measure recently apart from the center spot, and the R value of the several spots on same straight line is not calculated the d value, with the comparison of standard d value, writes out (hkl);

(2) angle between the checking computations crystal face, further definite indices of crystal plane that produce these spots;

(3) determine the index of all the other spots;

(4) determine the zone axis index.

For a spot of electron diffraction pattern under the crystal lattice known case, determine its dot index or zone axis index, adopting said method is to be relatively easy to, if diffraction pattern quantity is many, it then is not an easy thing that thing phase number also adopts said method for a long time.Particularly under the crystal lattice condition of unknown, an electron diffraction diagram can have infinite cover calibration result, and in general, this demarcation is not easy to accomplish.

2.2 the electronics mould diffraction spot of two kinds of materials of specific orientation relation is arranged

According to the conventional method, determine the phase relation in the crystal, need do a large amount of TEM experiments, obtain many diffraction patterns, carry out series of analysis and calculating again, this is a quite complicated process.And might not photograph the electron diffraction pattern of required direction with transmission electron microscope, analyze intuitively, for the research work of reality brings convenience and can simulate the diffraction pattern that obtains required direction as required by this program.

At present, the electron diffraction pattern index calibrating is from slipstick, and counter is demarcated to develop into robot calculator and demarcated, thereby improves the speed and the accuracy of demarcating.Though just like BASAC, FORTRAN-M, related softwares such as Visual C++ are applied in and demarcate on the diffraction pattern, fail to make this scaling method to generalize, and are used widely, and can not obtain simulating spot accordingly with actual diffraction spot.Especially in the prior art, the index calibrating of electronics mould diffraction spot of two kinds of materials of specific orientation relation is arranged, disposal route complexity, loaded down with trivial details is difficult to simulate the electronics mould diffraction spot of two kinds of materials of separating out by the specific orientation relation.

And Matlab is the business mathematics software that U.S. MathWorks company produces, and is used for the advanced techniques computational language and the interactive environment of algorithm development, data visualization, data analysis and numerical evaluation.It has friendly workbench and programmed environment, is made up of a series of instruments, and what wherein many instruments adopted is graphic user interface.But the method that adopts Matlab programming carrying out electron diffraction pattern to demarcate still belongs to blank at home and abroad.

Summary of the invention

At the prior art above shortcomings, the object of the present invention is to provide a kind of man-machine interaction stronger, operate simpler, based on the electronic diffraction index calibrating method of Matlab, to simulate the electronics mould diffraction spot of two kinds of materials of separating out easily by specific orientation relation.

The object of the present invention is achieved like this: the electronic diffraction index calibrating method based on Matlab, it is characterized in that, and adopt transmission electron microscope, computing machine and Matlab software to carry out; Concrete steps comprise:

Zeroth order electronic pattern index calibrating: utilize transmission electron microscope to obtain sample electron diffraction pattern photo, measure two diffraction vector R the shortest of diffraction spectra characteristic parallelogram in the photo ₁And R ₂And their angle theta, with R ₁, R ₂, the camera constant K of θ, transmission electron microscope and the lattice constant input computing machine of sample, obtain each diffraction spot exponential sum zone axis index by the Matlab computed in software, and simulate the diffraction spot point diagram of zeroth order electronic pattern;

The index calibrating of electronics mould diffraction spot that two kinds of materials of specific orientation relation are arranged: obtain the sample matrices and second mutually the electron diffraction pattern photo by transmission electron microscope earlier, respectively the matrix diffraction spot in the comparison film with second mutually diffraction spot carry out zeroth order electronic pattern index calibrating, determine the matrix and second separately the indices of crystal plane mutually in the sample, indices of crystal direction and lattice constant, with gained data input Matlab software, utilize second to calculate second the transition matrix with respect to matrix with the parallel relation of matrix, and then obtain the angle of the second phase zone axis and matrix zone axis, simulate the diffraction spot point diagram of two kinds of materials of separating out by the specific orientation relation.

Compared to existing technology, the present invention has following beneficial effect:

(I) trial-accounting method, standard style comparison method are demarcated dot index and are compared than before, more save time, and demarcate face-centered cubic quickly and easily, body centred cubic, six sides and orthorhombic system zeroth order dot index and simulate standard diffraction pattern (simulation spot).

(II) general second can only see not having corresponding program to simulate out in the reality with the orientation relationship figure of matrix from the diffraction spot photo, and the present invention can simulate the respective orientation graph of a relation by incident crystal face as required.

Description of drawings

Fig. 1 is the synoptic diagram of diffraction spectra characteristic parallelogram;

Fig. 2 is the process flow diagram that the zeroth order electronic pattern is demarcated;

Fig. 3 is the process flow diagram of electronics mould diffraction spot index calibrating that two kinds of materials of specific orientation relation are arranged;

Fig. 4 is the zeroth order electron diffraction pattern photo (a) of magnesium metal and the diffraction spot point diagram (b) of the zeroth order electronic pattern that the Matlab software simulation goes out;

Fig. 5 is the zeroth order electron diffraction pattern photo (a) of body-centered cubic ferrite in the steel and the diffraction spot point diagram (b) of the zeroth order electronic pattern that the Matlab software simulation goes out;

Fig. 6 is the electronic diffraction spot figure of a kind of K-S orientation relationship of going out of Matlab software simulation.

Embodiment

The invention will be further described below in conjunction with the drawings and specific embodiments.

A kind of electronic diffraction index calibrating method based on Matlab adopts transmission electron microscope (TEM), computing machine and Matlab software to carry out.

1. zeroth order electron diffraction pattern index calibrating

Earlier obtain sample electron diffraction pattern photo, the diffraction pattern photo that the obtains ratio with 1: 1 is imported in the image processing software, measure two diffraction vector R the shortest of diffraction spectra characteristic parallelogram in the photo by TEM ₁And R ₂And their angle theta, as shown in Figure 1; The image processing software of measuring can adopt popular softwares such as Autocad, Potoshop; Then, inquiry related data and handbook obtain the camera constant K of transmission electron microscope and the lattice constant of sample, with R ₁, R ₂, the camera constant K of θ, transmission electron microscope and the lattice constant input Matlab software of sample simulates and data scaling.

For given crystal, crystal structure and lattice constant are known, concerning a certain definite zone axis [uvw], have only a cover electron diffraction pattern corresponding with it, so the calculation procedure of Matlab software is carried out according to the following procedure:

(1.1) produce an indices of crystal plane matrix:

The most diffraction spectra that obtain of electronic diffraction experiment all are low indexes.Therefore, utilize these characteristics to produce a matrix that comprises all common low indexes, to reduce the cycle index in the Computer Program Implementation Process.Produce an indices of crystal plane matrix [h by Matlab software _xk _xl _x], h wherein _x-5～5, k _x=-5～5, l _x-5～5.

For example produce matrix A in the following order: (555), (554), (553) ..., (554), (555), then A is the matrix of 1331 row * 3 row.

In the Matlab language, can quote arbitrary row of this matrix, as A (1 :)=(555), A (1331 :)=(555).

(1.2) the zone axis index of calculation sample:

From described indices of crystal plane matrix [h _xk _xl _x] in determine diffraction vector R ₁Crystal face (the h at place ₁k ₁l ₁) and R ₂Crystal face (the h at place ₂k ₂l ₂), and according to zone law by (h ₁k ₁l ₁) and (h ₂k ₂l ₂) the zone axis index [uvw] of cross product calculation sample; Described (h ₁k ₁l ₁) and (h ₂k ₂l ₂) meet the following conditions:

A) (h ₁k ₁l ₁) and (h ₂k ₂l ₂) interplanar distance d ₁, d ₂Satisfy: d ₁/ d ₂=R ₁/ R ₂

B) R ₁* d ₁=K, wherein K is the camera constant of transmission electron microscope;

C) utilize crystal face angle formula to calculate (h ₁k ₁l ₁) and (h ₂k ₂l ₂) the crystal face angle theta ₁₂Satisfy θ ₁₂=θ.

With above-mentioned matrix A is example, gets (h ₁k ₁l ₁) be A (1 :), interplanar distance is d ₁, (h ₂k ₂l ₂) be A (2 :), A (3 :) ..., A (1331 :), interplanar distance is d ₂Interplanar distance ratio d is satisfied in calculating ₁/ d ₂=R1/R2, the crystal face angle equals θ and R1*d ₁Two crystal faces of=K; Get (h again ₁k ₁l ₁) be A (2 :), (h ₂k ₂l ₂) be A (3 :), A (4 :) ..., A (1331 :); So circulation is so that get (h ₁k ₁l ₁) be that A (1330 :) is that A (1331 :) as above calculates (h2k2l2).Write the function of an abbreviation index, found like this might satisfy the index combination (h of above three conditions ₁k ₁l ₁) and (h2k2l2), by (h ₁k ₁l ₁) and (h ₂k ₂l ₂) cross product calculating zone axis [uvw].

(1.3) simulate the diffraction spot point diagram of zeroth order electronic pattern:

Set up the Cartesian plane rectangular coordinate system, with the some simulated diffraction spot in the Cartesian plane rectangular coordinate system, with R ₁For point (1,0), make Q=R ₂/ R ₁, R then ₂(m n) satisfies: m=Qcos θ, n=Qsin θ the coordinate of point;

Any one some R in all the other diffraction spots ₀In the Cartesian plane rectangular coordinate system, be expressed as:

R ₀=i * R ₁+ j * R ₂=i * (1,0)+j * (m, n)=(i+jm, jn), i wherein, j is an integer;

Be R ₀(ih ₁+ jh ₂, ik ₁+ jk ₂, il ₁+ jl ₂) in rectangular coordinate system corresponding to (i+jm, jn);

(1.4) utilize the operation result of step (1.3), in the Matlab language, can utilize loop statement and function plot to draw out sample with [uvw] diffraction spot point diagram as the zeroth order electronic pattern of zone axis.

Should be pointed out that and with the electronic diffraction delustring condition of different crystal structure output point to be limited, in the Matlab language, also be easy to realize.

The process flow diagram of zeroth order electronic pattern index calibrating is referring to Fig. 2.According to this method, only need in Matlab software, import R ₁, R ₂, θ, the camera constant K of transmission electron microscope and the lattice constant of sample, just can obtain the diffraction spot point diagram of the zone axis exponential sum zeroth order electronic pattern of sample.

Crystal for cubic structure, the change of lattice constant is to influence the diffraction pattern of same zone axis, and wait the crystal of other structures for HCP (close-packed hexagonal), the diffraction pattern of different lattice constants is different, does not also have the common low index zone axis standard electronic diffraction pattern about Mg (magnesium metal) in general documents and materials.

Can generate FCC (face-centered cubic) easily by this program, BCC (body centred cubic), and the diffraction spot point diagram of the common low index zone axis zeroth order electronic pattern of Mg.

Fig. 4 and Fig. 5 are the zeroth order electron diffraction pattern photo of magnesium metal and body-centered cubic ferrite and the diffraction spot point diagram that is obtained by the Matlab simulation, wherein:

Actual spot R among Fig. 4 (a) ₂/ R ₁=1, θ=60 °, uvw=[001] magnesium metal zeroth order electron diffraction pattern photo, Fig. 4 (b) is the simulation electronic diffraction spot point diagram of Fig. 4 (a);

Actual spot R among Fig. 5 (a) ₂/ R ₁=1.2247, θ=73.90 °, uvw=[012] the zeroth order electron diffraction pattern photo of body-centered cubic ferrite, Fig. 5 (b) is the simulation electronic diffraction spot point diagram of Fig. 5 (a).

2. the index calibrating of electronics mould diffraction spot that two kinds of materials of specific orientation relation are arranged

Earlier obtain the sample matrices and second mutually the electron diffraction pattern photo by transmission electron microscope, respectively the matrix diffraction spot in the comparison film with second mutually diffraction spot carry out zeroth order electronic pattern index calibrating, determine the matrix and second separately the indices of crystal plane mutually in the sample, indices of crystal direction and lattice constant, with gained data input Matlab software, utilize second to calculate second the transition matrix with respect to matrix with the parallel relation of matrix, and then obtain the angle of the second phase zone axis and matrix zone axis, simulate the diffraction spot point diagram of two kinds of materials of separating out by the specific orientation relation; In the calibration process, the computation process of Matlab software is as follows:

(2.1) respectively the matrix of sample is carried out zeroth order electronic pattern index calibrating mutually with second, obtain the indices of crystal plane and the zone axis [u of matrix ₁v ₁w ₁], and the indices of crystal plane of second phase and zone axis;

(2.2) when second generates from matrix, the crystal orientation [u of second phase ₁' v ₁' l ₁'] with the crystal orientation [u of matrix ₁v ₁w ₁] parallel, then second has three pairs of crystal faces to become parallel relation mutually with between the matrix, handles through normalizing, sets up equation with Matlab software:

$\left.\begin{array}{c}\left({{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="H200910250973XE00051.png"\; state="\{\{state\}\}">h</figure-callout>}}_1}^{\&prime;}{k_1}^{\&prime;}{{\mathrm{<figure-callout\; id="1"\; label="l"\; filenames="H200910250973XE00051.png"\; state="\{\{state\}\}">l</figure-callout>}}_1}^{\&prime;}\right)//\left(h_1{k}_1{l}_1\right)\\ \left({{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="H200910250973XE00051.png"\; state="\{\{state\}\}">h</figure-callout>}}_2}^{\&prime;}{k_2}^{\&prime;}{{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="H200910250973XE00051.png"\; state="\{\{state\}\}">l</figure-callout>}}_2}^{\&prime;}\right)//\left(h_2{k}_2{l}_2\right)\\ \left({{\mathrm{<figure-callout\; id="3"\; label="h"\; filenames="H200910250973XE00051.png"\; state="\{\{state\}\}">h</figure-callout>}}_3}^{\&prime;}{k_3}^{\&prime;}{{\mathrm{<figure-callout\; id="3"\; label="l"\; filenames="H200910250973XE00051.png"\; state="\{\{state\}\}">l</figure-callout>}}_3}^{\&prime;}\right)//\left(h_3{k}_3{l}_3\right)\end{array}\right\}---(2-1),$

Ask the transition matrix between them, (2-1) formula write:

$\left.\begin{array}{c}\frac{1}{\left|{{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="H200910250973XE00051.png"\; state="\{\{state\}\}">d</figure-callout>}}_1}^{\&prime;}\right|}[{{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="H200910250973XE00051.png"\; state="\{\{state\}\}">h</figure-callout>}}_1}^{\&prime;}{a_1}^{*\&prime;}+{{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="H200910250973XE00051.png"\; state="\{\{state\}\}">k</figure-callout>}}_1}^{\&prime;}{a2}^{*\&prime;}+{{\mathrm{<figure-callout\; id="1"\; label="l"\; filenames="H200910250973XE00051.png"\; state="\{\{state\}\}">l</figure-callout>}}_1}^{\&prime;}{a3}^{*\&prime;}]=\frac{1}{\left|{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="H200910250973XE00051.png"\; state="\{\{state\}\}">d</figure-callout>}}_1\right|}[h_1{a_1}^{*\&prime;}+k_1{a2}^{*\&prime;}+l_1{a3}^{*\&prime;}]\\ \frac{1}{\left|{{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="H200910250973XE00051.png"\; state="\{\{state\}\}">d</figure-callout>}}_2}^{\&prime;}\right|}[{{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="H200910250973XE00051.png"\; state="\{\{state\}\}">h</figure-callout>}}_2}^{\&prime;}{a_1}^{*\&prime;}+{{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="H200910250973XE00051.png"\; state="\{\{state\}\}">k</figure-callout>}}_2}^{\&prime;}{a2}^{*\&prime;}+{{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="H200910250973XE00051.png"\; state="\{\{state\}\}">l</figure-callout>}}_2}^{\&prime;}{a3}^{*\&prime;}]=\frac{1}{\left|{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="H200910250973XE00051.png"\; state="\{\{state\}\}">d</figure-callout>}}_2\right|}[h_2{a_1}^{*\&prime;}+k_2{a2}^{*\&prime;}+l_2{a3}^{*\&prime;}]\\ \frac{1}{\left|{{\mathrm{<figure-callout\; id="3"\; label="d"\; filenames="H200910250973XE00051.png"\; state="\{\{state\}\}">d</figure-callout>}}_3}^{\&prime;}\right|}[{{\mathrm{<figure-callout\; id="3"\; label="h"\; filenames="H200910250973XE00051.png"\; state="\{\{state\}\}">h</figure-callout>}}_3}^{\&prime;}{a_1}^{*\&prime;}+{{\mathrm{<figure-callout\; id="3"\; label="k"\; filenames="H200910250973XE00051.png"\; state="\{\{state\}\}">k</figure-callout>}}_3}^{\&prime;}{a2}^{*\&prime;}+{{\mathrm{<figure-callout\; id="3"\; label="l"\; filenames="H200910250973XE00051.png"\; state="\{\{state\}\}">l</figure-callout>}}_3}^{\&prime;}{a3}^{*\&prime;}]=\frac{1}{\left|{\mathrm{<figure-callout\; id="3"\; label="d"\; filenames="H200910250973XE00051.png"\; state="\{\{state\}\}">d</figure-callout>}}_3\right|}[h_3{a_1}^{*\&prime;}+k_3{a3}^{*\&prime;}+l_3{a3}^{*\&prime;}]\end{array}\right\}---(2-2),$

Wherein, d ₁, d ₂, d ₃Be respectively matrix crystal face (h ₁k ₁l ₁), (h ₂k ₂l ₂), (h ₃k ₃l ₃) interplanar distance; d ₁', d ₂' d ₃' be respectively the second phase crystal face (h ₁' k ₁' l ₁'), (h ₂' k ₂' l ₂'), (h ₃' k ₃' l ₃') interplanar distance; With (2-2) formula telogenesis matrix form be:

$\left(\begin{array}{ccc}{{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="H200910250973XE00051.png"\; state="\{\{state\}\}">h</figure-callout>}}_1}^{\&prime;}& {k_1}^{\&prime;}& {{\mathrm{<figure-callout\; id="1"\; label="l"\; filenames="H200910250973XE00051.png"\; state="\{\{state\}\}">l</figure-callout>}}_1}^{\&prime;}\\ {{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="H200910250973XE00051.png"\; state="\{\{state\}\}">h</figure-callout>}}_2}^{\&prime;}& {k_2}^{\&prime;}& {{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="H200910250973XE00051.png"\; state="\{\{state\}\}">l</figure-callout>}}_2}^{\&prime;}\\ {{\mathrm{<figure-callout\; id="3"\; label="h"\; filenames="H200910250973XE00051.png"\; state="\{\{state\}\}">h</figure-callout>}}_3}^{\&prime;}& {k_3}^{\&prime;}& {{\mathrm{<figure-callout\; id="3"\; label="l"\; filenames="H200910250973XE00051.png"\; state="\{\{state\}\}">l</figure-callout>}}_3}^{\&prime;}\end{array}\right)\left(\begin{array}{c}{a_1}^{*\&prime;}\\ {a_2}^{*\&prime;}\\ {a_3}^{*\&prime;}\end{array}\right)=\left(\begin{array}{ccc}\frac{d_1}{{{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="H200910250973XE00051.png"\; state="\{\{state\}\}">d</figure-callout>}}_1}^{\&prime;}}& 0& 0\\ 0& \frac{d_2}{{{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="H200910250973XE00051.png"\; state="\{\{state\}\}">d</figure-callout>}}_2}^{\&prime;}}& 0\\ 0& 0& \frac{d_3}{{{\mathrm{<figure-callout\; id="3"\; label="d"\; filenames="H200910250973XE00051.png"\; state="\{\{state\}\}">d</figure-callout>}}_3}^{\&prime;}}\end{array}\right)\left(\begin{array}{ccc}{h}_1& k_1& l_1\\ h_2& k_2& l_2\\ h_3& k_3& l_3\end{array}\right)\left(\begin{array}{c}{a_1}^{*}\\ {a_2}^{*}\\ {a_3}^{*}\end{array}\right)---(2-3),$

(2-3) formula is simply remembered work:

[H′][A ^*′]＝[J][H][A ^*] (2-4)，

Can get thus:

[A ^*′]＝[H′] ^-1[J][H][A ^*] (2-5)，

Make B=[H '] ^-1[J] [H] then has:

[A ^*′]＝B[A ^*] (2-6)，

That is:

$B={\left(\begin{array}{ccc}{{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="H200910250973XE00051.png"\; state="\{\{state\}\}">h</figure-callout>}}_1}^{\&prime;}& {k_1}^{\&prime;}& {{\mathrm{<figure-callout\; id="1"\; label="l"\; filenames="H200910250973XE00051.png"\; state="\{\{state\}\}">l</figure-callout>}}_1}^{\&prime;}\\ {{\mathrm{<figure-callout\; id="2"\; label="h"\; filenames="H200910250973XE00051.png"\; state="\{\{state\}\}">h</figure-callout>}}_2}^{\&prime;}& {k_2}^{\&prime;}& {{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="H200910250973XE00051.png"\; state="\{\{state\}\}">l</figure-callout>}}_2}^{\&prime;}\\ {{\mathrm{<figure-callout\; id="3"\; label="h"\; filenames="H200910250973XE00051.png"\; state="\{\{state\}\}">h</figure-callout>}}_3}^{\&prime;}& {k_3}^{\&prime;}& {{\mathrm{<figure-callout\; id="3"\; label="l"\; filenames="H200910250973XE00051.png"\; state="\{\{state\}\}">l</figure-callout>}}_3}^{\&prime;}\end{array}\right)}^{-1}\left(\begin{array}{ccc}\frac{d_1}{{{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="H200910250973XE00051.png"\; state="\{\{state\}\}">d</figure-callout>}}_1}^{\&prime;}}& 0& 0\\ 0& \frac{d_2}{{{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="H200910250973XE00051.png"\; state="\{\{state\}\}">d</figure-callout>}}_2}^{\&prime;}}& 0\\ 0& 0& \frac{d_3}{{{\mathrm{<figure-callout\; id="3"\; label="d"\; filenames="H200910250973XE00051.png"\; state="\{\{state\}\}">d</figure-callout>}}_3}^{\&prime;}}\end{array}\right)\left(\begin{array}{ccc}{h}_1& k_1& l_1\\ h_2& k_2& l_2\\ h_3& k_3& l_3\end{array}\right)---(2-7),$

Therefore, with B as the matrix and second mutually the transition matrix;

(2.3) with matrix zone axis [u ₁v ₁w ₁] convert the second phase zone axis to by transition matrix B:

$D=B\left[\begin{array}{c}{u}_1\\ v_1\\ w_1\end{array}\right]---(2-8),$

U11＝D(1，1)；V11＝D(2，1)；W11＝D(3，1)；

cosθ＝(U11*u ₁′+V11*v ₁′+W11*w ₁′)/sqrt((U11 ²+V11 ²+W11 ²)*(u ₁′ ²+v ₁′ ²+w ₁′ ²))

(2-9)，

Wherein, D is the matrix zone axis matrix after changing; U11, V11, W11 are the matrix dot index after changing, and with its dot index as second phase; θ be second with the angle of matrix;

(2.4) utilize the operation result of step (2.3), generate the diffraction spot point diagram of two kinds of materials of separating out by Matlab software by the specific orientation relation.

The process flow diagram of index calibrating of electronics mould diffraction spot of two kinds of materials that specific orientation relation is arranged is referring to Fig. 3.According to this method, the K-S orientation relationship is carried out the index calibrating and the simulation of electronic diffraction spot, obtain two groups of parallel crystal faces (111) _γ// (011) _αAnd two groups of parallel crystal orientation [011] _γ// [111] _αSimulation electronic diffraction spot point diagram, as shown in Figure 6, the black circle among the figure is the diffraction spot of K orientation, soft dot is the diffraction spot of S orientation, the angle theta of two-phase=0 degree.

Usually the electron diffraction pattern of seeing, the single crystal diffraction spectrum that can be divided into the polycrystalline diffraction ring and form by spot.The former scaling method is identical with the scaling method of X ray debye ring.The present invention does not relate to the scaling method of X ray debye ring, relates generally to the scaling method of single crystal diffraction spectrum and the drafting of standard electronic diffracting spectrum.

Adopt in the data and simulated diffraction spot figure storage and database of electronic diffraction index calibrating method acquisition of the present invention, can provide a large amount of reference datas and with reference to collection of illustrative plates, for computer Recognition single crystal diffraction spectrum provides favourable technical foundation for computer Recognition single crystal diffraction spectrum.

Need to prove that above embodiment is unrestricted the present invention with the explanation technical solution of the present invention only.Although the present invention is had been described in detail with reference to preferred embodiment, those of ordinary skill in the art is to be understood that, can make amendment or be equal to replacement technical scheme of the present invention, and not breaking away from the spirit and scope of technical solution of the present invention, it all should be encompassed among the claim scope of the present invention.

Claims (2)

1. based on the electronic diffraction index calibrating method of Matlab, it is characterized in that, adopt transmission electron microscope, computing machine and Matlab software to carry out; Concrete steps comprise:

Zeroth order electronic pattern index calibrating: utilize transmission electron microscope to obtain sample electron diffraction pattern photo, measure two diffraction vector R the shortest of diffraction spectra characteristic parallelogram in the photo ₁And R ₂And their angle theta, with R ₁, R ₂, the camera constant K of θ, transmission electron microscope and the lattice constant input computing machine of sample, obtain each diffraction spot exponential sum zone axis index by the Matlab computed in software, and simulate the diffraction spot point diagram of zeroth order electronic pattern;

The index calibrating of electronics mould diffraction spot that two kinds of materials of specific orientation relation are arranged: obtain the sample matrices and second mutually the electron diffraction pattern photo by transmission electron microscope earlier, respectively the matrix diffraction spot in the comparison film with second mutually diffraction spot carry out zeroth order electronic pattern index calibrating, determine the matrix and second separately the indices of crystal plane mutually in the sample, indices of crystal direction and lattice constant, with gained data input Matlab software, utilize second to calculate second the transition matrix with respect to matrix with the parallel relation of matrix, and then obtain the angle of the second phase zone axis and matrix zone axis, simulate the diffraction spot point diagram of two kinds of materials of separating out by the specific orientation relation;

In the index calibrating of the electronics mould diffraction spot of described two kinds of materials that specific orientation relation arranged, the calculation procedure of Matlab software comprises:

(2.1) respectively the matrix of sample is carried out zeroth order electronic pattern index calibrating mutually with second, obtain the indices of crystal plane and the zone axis index [u of matrix ₁v ₁w ₁], and the indices of crystal plane of second phase and zone axis index.

(2.2) second have three pairs of crystal faces to become parallel relation mutually with between the matrix, set up equation with Matlab software:

$\left.\begin{array}{c}\left({h_1}^{\&prime;}{k_1}^{\&prime;}{l_1}^{\&prime;}\right)//\left(h_1{k}_1{l}_1\right)\\ \left({h_2}^{\&prime;}{k_2}^{\&prime;}{l_2}^{\&prime;}\right)//\left(h_2{k}_2{l}_2\right)\\ \left({h_3}^{\&prime;}{k_3}^{\&prime;}{l_3}^{\&prime;}\right)//\left(h_3{k}_3{l}_3\right)\end{array}\right\}---(2-1),$

(2-1) formula is write:

$\left.\begin{array}{c}\frac{1}{\left|{d_1}^{\&prime;}\right|}[{h_1}^{\&prime;}{a_1}^{*\&prime;}+{k_1}^{\&prime;}{a2}^{*\&prime;}+{l_1}^{\&prime;}{a3}^{*\&prime;}]=\frac{1}{\left|d_1\right|}[h_1{a_1}^{*\&prime;}+k_1{a2}^{*\&prime;}+l_1{a3}^{*\&prime;}\\ \frac{1}{\left|{d_2}^{\&prime;}\right|}[{h_2}^{\&prime;}{a_1}^{*\&prime;}+{k_2}^{\&prime;}{a2}^{*\&prime;}+{l_2}^{\&prime;}{a3}^{*\&prime;}]=\frac{1}{\left|d_2\right|}[h_2{a_1}^{*\&prime;}+k_2{a2}^{*\&prime;}+l_2{a3}^{*\&prime;}\\ \frac{1}{\left|{d_3}^{\&prime;}\right|}[{h_3}^{\&prime;}{a_1}^{*\&prime;}+{k_3}^{\&prime;}{a2}^{*\&prime;}+{l_3}^{\&prime;}{a3}^{*\&prime;}]=\frac{1}{\left|d_3\right|}[h_3{a_1}^{*\&prime;}+k_3{a2}^{*\&prime;}+l_3{a3}^{*\&prime;}\end{array}\right\}---(2-2),$

Wherein, d ₁, d ₂, d ₃Be respectively matrix crystal face (h ₁k ₁l ₁), (h ₂k ₂l ₂), (h ₃k ₃l ₃) interplanar distance; d ₁', d ₂' d ₃' be respectively the second phase crystal face (h ₁' k ₁' l ₁'), (h ₂' k ₂' l ₂'), (h ₃' k ₃' l ₃') interplanar distance; With (2-2) formula telogenesis matrix form be:

$\left(\begin{array}{ccc}{h_1}^{\&prime;}& {k_1}^{\&prime;}& {l_1}^{\&prime;}\\ {h_2}^{\&prime;}& {k_2}^{\&prime;}& {l_2}^{\&prime;}\\ {h_3}^{\&prime;}& {k_3}^{\&prime;}& {l_3}^{\&prime;}\end{array}\right)\left(\begin{array}{c}{a_1}^{*\&prime;}\\ {a_2}^{*\&prime;}\\ {a_3}^{*\&prime;}\end{array}\right)=\left(\begin{array}{ccc}\frac{d_1}{{d_1}^{\&prime;}}& 0& 0\\ 0& \frac{d_2}{{d_2}^{\&prime;}}& 0\\ 0& 0& \frac{d_3}{{d_3}^{\&prime;}}\end{array}\right)\left(\begin{array}{ccc}{h}_1& k_1& l_1\\ h_2& k_2& l_2\\ h_3& k_3& l_3\end{array}\right)\left(\begin{array}{c}{a_1}^{*}\\ {a_2}^{*}\\ {a_3}^{*}\end{array}\right)---(2-3),$

(2-3) formula is simply remembered work:

[H′][A ^*′]＝[J][H][A ^*]?(2-4)，

Can get thus:

[A ^*′]＝[H′] ^-1[J][H][A ^*](2-5)，

Make B=[H '] ^-1[J] [H] then has:

[A ^*′]＝B[A ^*](2-6)，

That is:

$B={\left(\begin{array}{ccc}{h_1}^{\&prime;}& {k_1}^{\&prime;}& {l_1}^{\&prime;}\\ {h_2}^{\&prime;}& {k_2}^{\&prime;}& {l_2}^{\&prime;}\\ {h_3}^{\&prime;}& {k_3}^{\&prime;}& {l_3}^{\&prime;}\end{array}\right)}^{-1}\left(\begin{array}{ccc}\frac{d_1}{{d_1}^{\&prime;}}& 0& 0\\ 0& \frac{d_2}{{d_2}^{\&prime;}}& 0\\ 0& 0& \frac{d_3}{{d_3}^{\&prime;}}\end{array}\right)\left(\begin{array}{ccc}{h}_1& k_1& l_1\\ h_2& k_2& l_2\\ h_3& k_3& l_3\end{array}\right)---(2-7),$

Therefore, with B as the matrix and second mutually the transition matrix;

(2.3) with matrix zone axis index [u ₁v ₁w ₁] convert the second phase zone axis to by transition matrix B:

$D=B\begin{array}{c}\left[\begin{array}{c}{u}_1\\ v_1\\ w_1\end{array}\right]\end{array}---(2-8),$

U11＝D(1，1)；V11＝D(2，1)；W11＝D(3，1)；

cosθ＝(U11*u ₁′+V11*v ₁′+W11*w ₁′)/sqrt((U11 ²+V11 ²+W11 ²)*(u ₁′ ²+v ₁′ ²+w ₁′ ²))

(2-9)，

Wherein, D is the matrix zone axis matrix after changing; U11, V11, W11 are the matrix dot index after changing, and with its dot index as second phase; θ be second with the angle of matrix;

(2.4) utilize the operation result of step (2.3), generate the diffraction spot point diagram of two kinds of materials of separating out by Matlab software by the specific orientation relation.

2. the electronic diffraction index calibrating method based on Matlab according to claim 1 is characterized in that, in the described zeroth order electronic pattern index calibrating, the calculation procedure of Matlab software comprises:

(1.1) produce an indices of crystal plane matrix [h by Matlab software _xk _xl _x], h wherein _x=-5～5, k _x=-5～5, l _x=-5～5;

(1.2) from described indices of crystal plane matrix [h _xk _xl _x] in determine diffraction vector R ₁Crystal face (the h at place ₁k ₁l ₁) and R ₂Crystal face (the h at place ₂k ₂l ₂), and according to zone law by (h ₁k ₁l ₁) and (h ₂k ₂l ₂) the zone axis index [uvw] of cross product calculation sample; Described (h ₁k ₁l ₁) and (h ₂k ₂l ₂) meet the following conditions:

A) (h ₁k ₁l ₁) and (h ₂k ₂l ₂) interplanar distance d ₁, d ₂Satisfy: d ₁/ d ₂=R ₁/ R ₂

B) R ₁* d ₁=K, wherein K is the camera constant of transmission electron microscope;

C) utilize crystal face angle formula to calculate (h ₁k ₁l ₁) and (h ₂k ₂l ₂) the crystal face angle theta ₁₂Satisfy θ ₁₂=θ;

(1.3) simulate the diffraction spot point diagram of zeroth order electronic pattern: set up the Cartesian plane rectangular coordinate system, with the some simulated diffraction spot in the Cartesian plane rectangular coordinate system, with R ₁For point (1,0), make Q=R ₂/ R ₁, R then ₂(m n) satisfies: m=Qcos θ, n=Qsin θ the coordinate of point;

Any one some R in all the other diffraction spots ₀In the Cartesian plane rectangular coordinate system, be expressed as:

R ₀=i * R ₁+ j * R ₂=i * (1,0)+j * (m, n)=(i+jm, jn), i wherein, j is an integer;

Be R ₀(ih ₁+ jh ₂, ik ₁+ jk ₂, il ₁+ jl ₂) in rectangular coordinate system corresponding to (i+jm, jn);

(1.4) utilize the operation result of step (1.3), the diffraction spot point diagram of the zeroth order electronic pattern that generates by Matlab software.

Images