CN107589136B - A kind of the dual model approximating method and system of small angle X ray scattering - Google Patents
A kind of the dual model approximating method and system of small angle X ray scattering Download PDFInfo
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Abstract
The invention proposes a kind of dual model approximating methods of small angle X ray scattering, comprising: obtaining step: obtaining the scattering strength experimental patterns of analyzed object；Modeling procedure: according to the feature construction dual model of scattering strength experimental patterns；Analyzing step: each adjustable parameter in the scattering strength calculation formula model of isotropic scatter and the scattering strength calculation formula model of orientation scatterer is adjusted, so that the difference of obtained calculating map and the scattering strength experimental patterns is minimum after the scattering strength calculation formula model of isotropic scatter and the scattering strength calculation formula model of orientation scatterer are added, the parameter of each model can be parsed.The invention also provides a kind of dual models of small angle X ray scattering to be fitted system.The present invention provides better data support for the non-destructive testing for carrying out effectively observation material mesoscopic mesostructure using small angle X ray scattering.
Description
Technical field
The invention belongs to small angle X ray scattering (SAXS) theoretical calculation field more particularly to a kind of small angle X ray scatterings
Dual model approximating method and system.
Background technique
Small angle X ray scattering (SAXS) is the effective laboratory facilities for probing into meso-scale structure, and essence is in scatterer
In one to hundreds of nanometers range electron density unevenly caused by scattering phenomenon.Since SAXS scattering has sample preparation simple, gas phase,
The measurable feature of liquid phase, solid phase is widely used in chemistry, chemical industry, material science, molecular biology, medicine and pharmacology, coagulates
In the multi-disciplinary researchs such as poly- state physics.Research object include have various nanostructures, as liquid crystal, liquid crystal state biomembrane it is each
Kind of phase change, surfactant associative structure, large biological molecule (protein, nucleic acid etc.), self-assembled supermolecular structure, micropore,
Colloidal sol fractal structure and interface structure, polymer solution, crystalline orientation polymer (industrial fiber and film), block ion from
The microstructure etc. of polymers.
SAXS has the features such as preferable particle statistics evenness because it can directly measure body phase material, micro- in fiber
There is the unrivaled advantage of micro- Electronic Speculum in terms of seeing the measurement of hole configurations, to obtain in the microtexture measurement of fiber
Pay attention to and is widely applied.Since micropore is in the presence of orientation in its system in the SAXS analysis of fibrous material, to be dissipated using two dimension
The method for penetrating spectrogram fitting carries out modeling analysis.The existing hole for stretching orientation in fiber is found in a large amount of experimental analysis,
Also there is non-oriented spherical hole, selecting the scatterer being individually orientated to carry out digital simulation, there are biggish errors.
Summary of the invention
To solve the above problems, the invention proposes the dual model approximating method and system of a kind of small angle X ray scattering, root
It is modeled respectively according to the different scattering properties of scatterer, the digital simulation for SAXS two-dimensional scattering map provides more accurately data.
A kind of dual model approximating method of small angle X ray scattering proposed by the present invention, this method include the following steps:
Obtaining step: the scattering strength experimental patterns of analyzed object are obtained；
Modeling procedure: according to the feature construction dual model of scattering strength experimental patterns, specifically: the analyzed object
Scattering system has isotropic scatter and is orientated the scatterer of scatterer both types, chooses isotropic scatter structure
The scattering strength calculation formula model of isotropic scatter is built, the scattering strength of orientation scatterer building orientation scatterer is chosen
Calculation formula model；Wherein, the scattering strength calculation formula model of isotropic scatter is spherical model, is orientated scatterer
Scattering strength calculation formula model is stick model；
Analyzing step: the scattering for adjusting the scattering strength calculation formula model and orientation scatterer of isotropic scatter is strong
Each adjustable parameter in calculation formula model is spent, so that the scattering strength calculation formula model of isotropic scatter and orientation dissipate
The difference of obtained calculating map and the scattering strength experimental patterns is minimum after the scattering strength calculation formula model of beam is added,
The parameter of each model can be parsed.
Further, in modeling procedure, the scattering strength calculation formula model of isotropic scatter and orientation scattering
The scattering strength calculation formula model of body is equal are as follows:
Wherein, q is scattering vector, FnFor the scattered amplitude of n-th of scatterer, Fn’It shakes for the scattering of the n-th ' a scatterer
Width, N are the quantity of scatterer, rnFor the center of n-th of scatterer, rn'For the center of n-th ' a scatterer.
Further, in the modeling procedure, set the center of the scatterer as coordinate origin, then it is described respectively to same
Property scatterer and it is described orientation scatterer scattered amplitude F (q) calculation formula are as follows:
F (q)=∫vρdVe-iqr (2)
Wherein, q is scattering vector, and V is the volume of scatterer, and ρ is the electron density of scatterer, and r is any on scatterer
A little arrive the distance of coordinate origin.
Further, in modeling procedure, according to the scattered amplitude of scatterer and according to the size of scatterer distribution and
Distribution of orientations, to construct above-mentioned scattering strength calculation formula model；
Constructed scattering strength calculation formula model are as follows:
Wherein, C1For constant, R1、R2、R3For three and half axial lengths of scatterer,WithFor scatterer
The size distribution of three axis, h (ω) are to be distributed along axis of orientation zenith angle,For azimuthal distribution, ω is indicated along axis of orientation day
Apex angle, ψ indicate Scattering of Vector and qxThe angle of component direction,Indicate azimuth；
For being orientated scatterer, in formula (8), R1、R2、R3Value be all different, or both wherein identical, third
Person is different from the two；
For isotropic scatter, in formula (8), R1=R2=R3, h (ω) is constant, and azimuthal distribution is constant.
Further, wherein for being orientated scatterer, the zenith angle is described using Von Mises distribution function and is distributed,
Functional form is as follows:
Wherein I0For the modified bessel function of 0 rank of the first kind, ω0Variance for average value, distribution is true by variance parameter к
It is fixed,It is defined as being uniformly distributed；In formula (10), ω0, κ be adjustable parameter.
Further, wherein describe the axis of the orientation scatterer using log series model function and the isotropism dissipates
The radius of beam, shown in the form such as following formula (11) of the log series model function:
Wherein μ and σ is respectively the logarithmic average and logarithm standard deviation of logarithm normal distribution, average value m and variance parameter υ
It is acquired by following formula:
M=exp (μ+σ2/2) (12)
υ=exp (2 μ+σ2)(expσ2-1) (13)
In formula (11), μ and σ are adjustable parameter.
A kind of dual model of small angle X ray scattering proposed by the present invention is fitted system, which includes following modules:
It obtains module: obtaining the scattering strength experimental patterns of analyzed object；
Modeling module: according to the feature construction dual model of scattering strength experimental patterns, specifically: the analyzed object
Scattering system has isotropic scatter and is orientated the scatterer of scatterer both types, chooses isotropic scatter structure
The scattering strength calculation formula model of isotropic scatter is built, the scattering strength of orientation scatterer building orientation scatterer is chosen
Calculation formula model；Wherein, the scattering strength calculation formula model of isotropic scatter is spherical model, is orientated scatterer
Scattering strength calculation formula model is stick model；
Parsing module: the scattering for adjusting the scattering strength calculation formula model and orientation scatterer of isotropic scatter is strong
Each adjustable parameter in calculation formula model is spent, so that the scattering strength calculation formula model of isotropic scatter and orientation dissipate
The difference of obtained calculating map and the scattering strength experimental patterns is minimum after the scattering strength calculation formula model of beam is added,
The parameter of each model can be parsed.
Further, in modeling module, the scattering strength calculation formula model of isotropic scatter and orientation scattering
The scattering strength calculation formula model of body is equal are as follows:
Wherein, q is scattering vector, FnFor the scattered amplitude of n-th of scatterer, Fn’It shakes for the scattering of the n-th ' a scatterer
Width, N are the quantity of scatterer, rnFor the center of n-th of scatterer, rn'For the center of n-th ' a scatterer.
Further, in the modeling module, set the center of the scatterer as coordinate origin, then it is described respectively to same
Property scatterer and it is described orientation scatterer scattered amplitude F (q) calculation formula are as follows:
F (q)=∫vρdVe-iqr (2)
Wherein, q is scattering vector, and V is the volume of scatterer, and ρ is the electron density of scatterer, and r is any on scatterer
A little arrive the distance of coordinate origin.
Further, in modeling module, according to the scattered amplitude of scatterer and according to the size of scatterer distribution and
Distribution of orientations, to construct above-mentioned scattering strength calculation formula model；
Constructed scattering strength calculation formula model are as follows:
Wherein, C1For constant, R1、R2、R3For three and half axial lengths of scatterer,WithFor scatterer
The size distribution of three axis, h (ω) are to be distributed along axis of orientation zenith angle,For azimuthal distribution, ω is indicated along axis of orientation
Zenith angle, ψ indicate Scattering of Vector and qxThe angle of component direction,Indicate azimuth；
For being orientated scatterer, in formula (8), R1、R2、R3Value be all different, or both wherein identical, third
Person is different from the two；
For isotropic scatter, in formula (8), R1=R2=R3, h (ω) is constant, and azimuthal distribution is constant.
Further, wherein for being orientated scatterer, the zenith angle is described using Von Mises distribution function and is distributed,
Functional form is as follows:
Wherein I0For the modified bessel function of 0 rank of the first kind, ω0Variance for average value, distribution is true by variance parameter к
It is fixed,It is defined as being uniformly distributed；In formula (10), ω0, κ be adjustable parameter.
Further, wherein describe the axis of the orientation scatterer using log series model function and the isotropism dissipates
The radius of beam, shown in the form such as following formula (11) of the log series model function:
Wherein μ and σ is respectively the logarithmic average and logarithm standard deviation of logarithm normal distribution, average value m and variance parameter υ
It is acquired by following formula:
M=exp (μ+σ2/2) (12)
υ=exp (2 μ+σ2)(expσ2-1) (13)
In formula (11), μ and σ are adjustable parameter.
Beneficial effects of the present invention: the present invention is according to the meter for establishing spherical and rodlike dual model in fiber the characteristics of scatterer
Calculation method, obtain the accurate hole information of fibrous inside, the further expansion scope of application of model.
Detailed description of the invention
Fig. 1 is the flow chart of dual model approximating method shown in the present invention；
Fig. 2 is the structural block diagram that dual model shown in the present invention is fitted system；
Fig. 3 is the phase difference schematic diagram of incident X-rays and scattered x-ray in scatterer shown in the present invention；
Fig. 4 is the schematic diagram of orientation scatterer each angular relationship in a coordinate system shown in the present invention；
Fig. 5 is the schematic diagram of two dimension dual model analysis method shown in the present invention；
Fig. 6 a and Fig. 6 b are the Von Mises function curve under different parameters shown in the present invention；
Fig. 7 is logarithm normal distribution function curve under different parameters shown in the present invention；
Fig. 8 is the small angle X ray scattering experimental patterns that the present invention is directed to；
Fig. 9 is the double model structure schematic diagram that the present invention proposes scatterer；
Figure 10 is the two-dimensional scattering map of dual model digital simulation of the invention.
Specific embodiment
To make the objectives, technical solutions, and advantages of the present invention clearer, below in conjunction with specific embodiment, and reference
Attached drawing, the present invention is described in more detail.But as known to those skilled in the art, the invention is not limited to attached drawings and following reality
Apply example.
As shown in Figure 1, the invention proposes the dual model approximating method of small angle X ray scattering SAXS a kind of, including it is following
Step:
Obtaining step: the scattering strength experimental patterns of analyzed object are obtained, as shown in Figure 8；
Modeling procedure: according to the feature construction dual model of scattering strength experimental patterns, specifically: the analyzed object
Scattering system has isotropic scatter and is orientated the scatterer of scatterer both types, chooses isotropic scatter structure
The scattering strength calculation formula model of isotropic scatter is built, the scattering strength of orientation scatterer building orientation scatterer is chosen
Calculation formula model；Wherein, the scattering strength calculation formula model of isotropic scatter is spherical model, is orientated scatterer
Scattering strength calculation formula model is stick model, as shown in figure 9, the present invention uses the dual model of spherical model and stick model
Two-dimensional scattering map is calculated, the scope of application of model is expanded, improves the accuracy of fitting；
Analyzing step: the scattering for adjusting the scattering strength calculation formula model and orientation scatterer of isotropic scatter is strong
Each adjustable parameter in calculation formula model is spent, so that the scattering strength calculation formula model of isotropic scatter and orientation dissipate
The difference of obtained calculating map and the scattering strength experimental patterns is minimum after the scattering strength calculation formula model of beam is added,
The parameter of each model can be parsed.
In modeling procedure, the present invention analyze first a volume be V scatterer, it is assumed that its electron density be ρ (r)=
ρ, the electron density outside scatterer is ρ (r)=0, then when beam of x-rays reaches the system, scatters intracorporal electronics forced oscillation
It is dynamic, it generates secondary wave (scattered wave).The phase difference schematic diagram of its incident X-rays and scattered x-ray is as shown in Figure 3.
The scattered amplitude of scatterer is writeable are as follows:
F (q)=∫ ∫ ∫ dV ρ (r) eiqr (1)
It writes a Chinese character in simplified form are as follows:
F (q)=∫vρdVe-iqr (2)
Wherein, q is scattering vector, and V is the volume of scatterer, and ρ is the electron density of scatterer, and r is any on scatterer
The distance of coordinate origin is a little arrived, i is imaginary unit.
If having N number of scatterer in a system, center is located at r1, r2, r3... rN, electron density can be written as ρn
(r-rn) then the total electron density of system it is writeable are as follows:
The scattered amplitude of system is writeable are as follows:
According to above-mentioned formula, the scattering strength I (q) of spherical model and stick model can be derived by modeling procedure
Formula are as follows:
As n=n ',Above formula can be further written as:
The size and orientation of scatterer in system are introduced into when calculating scattering strength, wherein define three axis of scatterer
Size is distributed asWithIt is distributed as h (ω) along axis of orientation zenith angle, azimuthal distribution isIts
Volume isDue to very weak in the interference in lax system between scatterer, in above formula (6) second
Item is zero.
Above formula (6) can be further simplified are as follows:
Then the scattering strength of spherical model and stick model is writeable are as follows:
There is following relationship in above formula between each angle:
γ indicates that the angle of scatterer and X-axis, ω indicate that, along axis of orientation zenith angle, 2 θ are incident X-rays and scattered x-ray
Angle, ψ indicates Scattering of Vector and qxThe angle of component direction,Indicate azimuth.For being orientated the scattering strength meter of scatterer
Calculate formula model, i.e. stick model, R1、R2、R3Value be all different, or it is both wherein identical, the third party and both no
Together；For the scattering strength calculation formula model of isotropic scatter, i.e. spherical model, R1=R2=R3, h (ω) is constant,
Azimuthal distribution is constant.
It is assumed that orientation scatterer has rotational invariance, azimuthal distributionIt is defined as being uniformly distributed, is a constant.It
Apex angle distribution h (ω) is defined as Von Mises distribution, and functional form is as follows:
Wherein I0For the modified bessel function of 0 rank of the first kind, ω0Variance for average value, distribution is determined by к.
Von Mises distribution is most common circular distribution, and value range is generally [0,2 π], is suitable for describing scatterer
Distribution of orientations.As shown in figures 6 a and 6b, the Von Mises function curve under different parameters is described.
The axis R being orientated in modeling procedure in scatterer1、R2、R3Logarithm normal distribution f (R) is obeyed, isotropism dissipates
Axis in beam, that is, the radius R of sphere also obey logarithm normal distribution f (R), and functional form is as follows:
Wherein μ and σ is respectively the logarithmic average and logarithm standard deviation of logarithm normal distribution, and average value m and variance v can lead to
Following formula is crossed to acquire:
M=exp (μ+σ2/2) (12)
υ=exp (2 μ+σ2)(expσ2-1) (13)
As shown in Figure 7, it is shown that logarithm normal distribution function curve under different parameters.
In analyzing step, each adjustable parameter value is given, the corresponding two-dimensional scattering map of each model can be calculated, is such as schemed
Shown in 10；The calculating map that described two scattering strength calculation formula are added and the scattering strength experimental patterns carry out
Compare, by adjusting the parameter ω of the parameter μ of size, σ and direction of adjustment angle0, к it is strong come the scattering for adjusting stick model
Angle value adjusts the scattering strength value of spherical model by adjusting the parameter μ of size, σ, so that stick model dissipates
Penetrate both scattering strengths for calculating map and experimental patterns that intensity value is added with the scattering strength value of spherical model error
Minimum, as shown in figure 5, the parameter of two models can be parsed.Before experimental patterns and calculating map are compared, also need
Experimental patterns are modified, deduct the influence of laboratory apparatus and practical operation to experimental patterns.First to experimental patterns into
The various corrections of row, such as backscatter, dark current, beam shape correction, obtain high quality two dimension experiment scatter pattern.Pass through again
The method for constructing two models calculates two-dimensional scattering map, adjusts the parameter of each model, so that experimental patterns and calculating map
Difference it is minimum, the parameter of each model can be parsed, and pass through the validity of standard sample verifying model.
The invention also provides the dual model digital simulation systems of small angle X ray scattering SAXS a kind of, as shown in Fig. 2, packet
Include following modules:
It obtains module: obtaining the scattering strength experimental patterns of analyzed object, as shown in Figure 8；
Modeling module: according to the feature construction dual model of scattering strength experimental patterns, specifically: the analyzed object
Scattering system has isotropic scatter and is orientated the scatterer of scatterer both types, chooses isotropic scatter structure
The scattering strength calculation formula model of isotropic scatter is built, the scattering strength of orientation scatterer building orientation scatterer is chosen
Calculation formula model；Wherein, the scattering strength calculation formula model of isotropic scatter is spherical model, is orientated scatterer
Scattering strength calculation formula model is stick model, as shown in figure 9, the present invention uses the dual model of spherical model and stick model
Two-dimensional scattering map is calculated, the scope of application of model is expanded, improves the accuracy of fitting；
Parsing module: the scattering for adjusting the scattering strength calculation formula model and orientation scatterer of isotropic scatter is strong
Each adjustable parameter in calculation formula model is spent, so that the scattering strength calculation formula model of isotropic scatter and orientation dissipate
The difference of obtained calculating map and the scattering strength experimental patterns is minimum after the scattering strength calculation formula model of beam is added,
The parameter of each model can be parsed.
In modeling module, the present invention analyze first a volume be V scatterer, it is assumed that its electron density be ρ (r)=
ρ, the electron density outside scatterer is ρ (r)=0, then when beam of x-rays reaches the system, scatters intracorporal electronics forced oscillation
It is dynamic, it generates secondary wave (scattered wave).The phase difference schematic diagram of its incident X-rays and scattered x-ray is as shown in Figure 3.
The scattered amplitude of scatterer is writeable are as follows:
F (q)=∫ ∫ ∫ dV ρ (r) eiqr (1)
It writes a Chinese character in simplified form are as follows:
F (q)=∫vρdVe-iqr (2)
Wherein, q is scattering vector, and V is the volume of scatterer, and ρ is the electron density of scatterer, and r is any on scatterer
The distance of coordinate origin is a little arrived, i is imaginary unit.
If having N number of scatterer in a system, center is located at r1, r2, r3... rN, electron density can be written as ρn
(r-rn) then the total electron density of system it is writeable are as follows:
The scattered amplitude of system is writeable are as follows:
According to above-mentioned formula, the scattering strength I (q) of spherical model and stick model can be derived by modeling module
Formula are as follows:
As n=n ',Above formula can be further written as:
The size and orientation of scatterer in system are introduced into when calculating scattering strength, wherein define three axis of scatterer
Size is distributed asWithIt is distributed as h (ω) along axis of orientation zenith angle, azimuthal distribution isIts
Volume isDue to very weak in the interference in lax system between scatterer, in above formula (6) second
Item is zero.
Above formula (6) can be further simplified are as follows:
Then the scattering strength of spherical model and stick model is writeable are as follows:
There is following relationship in above formula between each angle:
γ indicates that the angle of scatterer and X-axis, ω indicate that, along axis of orientation zenith angle, 2 θ are incident X-rays and scattered x-ray
Angle, ψ indicates Scattering of Vector and qxThe angle of component direction,Indicate azimuth.For being orientated the scattering strength meter of scatterer
Calculate formula model, i.e. stick model, R1、R2、R3Value be all different, or it is both wherein identical, the third party and both no
Together；For the scattering strength calculation formula model of isotropic scatter, i.e. spherical model, R1=R2=R3, h (ω) is constant,
Azimuthal distribution is constant.
It is assumed that orientation scatterer has rotational invariance, azimuthal distributionIt is defined as being uniformly distributed, is a constant.It
Apex angle distribution h (ω) is defined as Von Mises distribution, and functional form is as follows:
Wherein I0For the modified bessel function of 0 rank of the first kind, ω0Variance for average value, distribution is determined by к.
Von Mises distribution is most common circular distribution, and value range is generally [0,2 π], is suitable for describing scatterer
Distribution of orientations.As shown in figures 6 a and 6b, the Von Mises function curve under different parameters is described.
And the axis R in scatterer is orientated in modeling module1、R2、R3Logarithm normal distribution f (R) is obeyed, isotropism dissipates
Axis in beam, that is, the radius R of sphere also obey logarithm normal distribution f (R), and functional form is as follows:
Wherein μ and σ is respectively the logarithmic average and logarithm standard deviation of logarithm normal distribution, and average value m and variance v can lead to
Following formula is crossed to acquire:
M=exp (μ+σ2/2) (12)
υ=exp (2 μ+σ2)(expσ2-1) (13)
As shown in Figure 7, it is shown that logarithm normal distribution function curve under different parameters.
In parsing module, each adjustable parameter value is given, the corresponding two-dimensional scattering map of each model can be calculated, is such as schemed
Shown in 10；The calculating map that described two scattering strength calculation formula are added and the scattering strength experimental patterns carry out
Compare, by adjusting the parameter ω of the parameter μ of size, σ and direction of adjustment angle0, к it is strong come the scattering for adjusting stick model
Angle value adjusts the scattering strength value of spherical model by adjusting the parameter μ of size, σ, so that stick model dissipates
Penetrate both scattering strengths for calculating map and experimental patterns that intensity value is added with the scattering strength value of spherical model error
Minimum, as shown in figure 5, the parameter of two models can be parsed.Before experimental patterns and calculating map are compared, also need
Experimental patterns are modified, deduct the influence of laboratory apparatus and practical operation to experimental patterns.First to experimental patterns into
The various corrections of row, such as backscatter, dark current, beam shape correction, obtain high quality two dimension experiment scatter pattern.Pass through again
The method for constructing two models calculates two-dimensional scattering map, adjusts the parameter of each model, so that experimental patterns and calculating map
Difference it is minimum, the parameter of each model can be parsed, and pass through the validity of standard sample verifying model.
The embodiment of Von Mises function curve and Lognormal distribution curve under different parameters is given below.
Embodiment 1:
Parameter ω is set0=-pi/2；κ=100 obtain the Von Mises function curve as corresponded to parameter in Fig. 6 a.
Embodiment 2:
Parameter ω is set0=-π/4；κ=100 obtain the Von Mises function curve as corresponded to parameter in Fig. 6 a.
Embodiment 3:
Parameter ω is set0=0；κ=100 obtain the Von Mises function curve as corresponded to parameter in Fig. 6 a.
Embodiment 4:
Parameter ω is set0=π/4；κ=100 obtain the Von Mises function curve as corresponded to parameter in Fig. 6 a.
Embodiment 5:
Parameter ω is set0=pi/2；κ=100 obtain the Von Mises function curve as corresponded to parameter in Fig. 6 a.
Embodiment 6:
Parameter ω is set0=3 π/4；κ=100 obtain the Von Mises function curve as corresponded to parameter in Fig. 6 a.
Embodiment 7:
Parameter ω is set0=0.95 π；κ=100 obtain the Von Mises function curve as corresponded to parameter in Fig. 6 a.
Embodiment 8:
Parameter ω is set0=π；κ=100 obtain the Von Mises function curve as corresponded to parameter in Fig. 6 a.
Embodiment 9:
Parameter ω is set0=0；κ=0 obtains the Von Mises function curve as corresponded to parameter in Fig. 6 b.
Embodiment 10:
Parameter ω is set0=0；κ=4 obtain the Von Mises function curve as corresponded to parameter in Fig. 6 b.
Embodiment 11:
Parameter ω is set0=0；κ=8 obtain the Von Mises function curve as corresponded to parameter in Fig. 6 b.
Embodiment 12:
Parameter ω is set0=0；κ=12 obtain the Von Mises function curve as corresponded to parameter in Fig. 6 b.
Embodiment 13:
Parameter ω is set0=0；κ=16 obtain the Von Mises function curve as corresponded to parameter in Fig. 6 b.
Embodiment 14:
Parameter ω is set0=0；κ=20 obtain the Von Mises function curve as corresponded to parameter in Fig. 6 b.
Embodiment 15:
Parameter ω is set0=0；κ=100 obtain the Von Mises function curve as corresponded to parameter in Fig. 6 b.
Embodiment 16:
Parameter m=20 is set；V=200 obtains the logarithm normal distribution function curve as corresponded to parameter in Fig. 7.
Embodiment 17:
Parameter m=20 is set；V=150 obtains the logarithm normal distribution function curve as corresponded to parameter in Fig. 7.
Embodiment 18:
Parameter m=20 is set；V=100 obtains the logarithm normal distribution function curve as corresponded to parameter in Fig. 7.
Embodiment 19:
Parameter m=20 is set；V=80 obtains the logarithm normal distribution function curve as corresponded to parameter in Fig. 7.
Embodiment 20:
Parameter m=20 is set；V=60 obtains the logarithm normal distribution function curve as corresponded to parameter in Fig. 7.
Embodiment 21:
Parameter m=20 is set；V=40 obtains the logarithm normal distribution function curve as corresponded to parameter in Fig. 7.
Embodiment 22:
Parameter m=20 is set；V=20 obtains the logarithm normal distribution function curve as corresponded to parameter in Fig. 7.
Embodiment 23:
Parameter m=20 is set；V=10 obtains the logarithm normal distribution function curve as corresponded to parameter in Fig. 7.
By the way that different parameters are arranged, the zenith angle distribution and the normal distribution of major and minor axis of scatterer are adjusted, so that passing through
What two models were added calculates the error minimum between map and experimental patterns, can parse the parameter of each model.Root
It is modeled according to the feature of scattering strength experimental patterns, so that the Porous Characteristic expression of fibrous material is more accurate.
More than, embodiments of the present invention are illustrated.But the present invention is not limited to above embodiment.It is all
Within the spirit and principles in the present invention, any modification, equivalent substitution, improvement and etc. done should be included in guarantor of the invention
Within the scope of shield.
Claims (10)
1. a kind of dual model approximating method of small angle X ray scattering, which is characterized in that this method includes the following steps:
Obtaining step: the scattering strength experimental patterns of analyzed object are obtained；
Modeling procedure: according to the feature construction dual model of scattering strength experimental patterns, specifically: the scattering of the analyzed object
System has isotropic scatter and is orientated the scatterer of scatterer both types, and it is each to choose isotropic scatter building
To the scattering strength calculation formula model of same sex scatterer, the scattering strength for choosing orientation scatterer building orientation scatterer is calculated
Formula model；Wherein, the scattering strength calculation formula model of isotropic scatter is spherical model, is orientated the scattering of scatterer
Strength calculation formula model is stick model；
Analyzing step: the scattering strength calculation formula model of isotropic scatter and the scattering strength meter of orientation scatterer are adjusted
Each adjustable parameter in formula model is calculated, so that the scattering strength calculation formula model of isotropic scatter and orientation scatterer
Scattering strength calculation formula model be added after the difference of obtained calculating map and the scattering strength experimental patterns minimum
Parse the parameter of each model.
2. the method as described in claim 1, which is characterized in that in modeling procedure, the scattering strength of isotropic scatter
The scattering strength calculation formula model of calculation formula model and orientation scatterer is equal are as follows:
Wherein, q is scattering vector, FnFor the scattered amplitude of n-th of scatterer, Fn’For the scattered amplitude of the n-th ' a scatterer, N is
The quantity of scatterer, rnFor the center of n-th of scatterer, rn'For the center of n-th ' a scatterer, i is imaginary unit.
3. method according to claim 2, which is characterized in that in the modeling procedure, set the center of the scatterer
For coordinate origin, then the calculation formula of the scattered amplitude F (q) of the isotropic scatter and the orientation scatterer are as follows:
F (q)=∫vρdVe-iqr (2)
Wherein, q is scattering vector, and V is the volume of scatterer, and ρ is the electron density of scatterer, and r is any point on scatterer
To the distance of coordinate origin.
4. method as claimed in claim 3, which is characterized in that in modeling procedure, according to the scattered amplitude of scatterer and
According to the distribution of the size of scatterer and distribution of orientations, to construct above-mentioned scattering strength calculation formula model；
Constructed scattering strength calculation formula model are as follows:
Wherein, C1For constant, R1、R2、R3For three and half axial lengths of scatterer, f (R1)、f(R2) and f (R3) it is three axis of scatterer
Size distribution, h (ω) be along axis of orientation zenith angle be distributed,For azimuthal distribution, ω is indicated along axis of orientation zenith angle, ψ
Indicate Scattering of Vector and qxThe angle of component direction,Indicate azimuth；
For being orientated scatterer, in formula (8), R1、R2、R3Value be all different, or it is both wherein identical, the third party with
The two is different；
For isotropic scatter, in formula (8), R1=R2=R3, h (ω) is constant, and azimuthal distribution is constant.
5. method as claimed in claim 4, which is characterized in that wherein, for being orientated scatterer, be distributed using Von Mises
Function describes the zenith angle distribution, and functional form is as follows:
Wherein I0For the modified bessel function of 0 rank of the first kind, ω0Variance for average value, distribution is determined by variance parameter к；?
In formula (10), ω0, κ be adjustable parameter；
And/or
Wherein, the axis of the orientation scatterer and the radius R of the isotropic scatter, institute are described using log series model function
Shown in the form such as following formula (11) for stating log series model function:
Wherein μ and σ is respectively the logarithmic average and logarithm standard deviation of logarithm normal distribution, and average value m and variance parameter υ pass through
Following formula acquires:
M=exp (μ+σ2/2) (12)
υ=exp (2 μ+σ2)(expσ2-1) (13)
In formula (11), μ and σ are adjustable parameter.
6. a kind of dual model of small angle X ray scattering is fitted system, which is characterized in that the system includes following modules:
It obtains module: obtaining the scattering strength experimental patterns of analyzed object；
Modeling module: according to the feature construction dual model of scattering strength experimental patterns, specifically: the scattering of the analyzed object
System has isotropic scatter and is orientated the scatterer of scatterer both types, and it is each to choose isotropic scatter building
To the scattering strength calculation formula model of same sex scatterer, the scattering strength for choosing orientation scatterer building orientation scatterer is calculated
Formula model；Wherein, the scattering strength calculation formula model of isotropic scatter is spherical model, is orientated the scattering of scatterer
Strength calculation formula model is stick model；
Parsing module: the scattering strength calculation formula model of isotropic scatter and the scattering strength meter of orientation scatterer are adjusted
Each adjustable parameter in formula model is calculated, so that the scattering strength calculation formula model of isotropic scatter and orientation scatterer
Scattering strength calculation formula model be added after the difference of obtained calculating map and the scattering strength experimental patterns minimum
Parse the parameter of each model.
7. system as claimed in claim 6, which is characterized in that in modeling module, the scattering strength of isotropic scatter
The scattering strength calculation formula model of calculation formula model and orientation scatterer is equal are as follows:
Wherein, q is scattering vector, FnFor the scattered amplitude of n-th of scatterer, Fn’For the scattered amplitude of the n-th ' a scatterer, N is
The quantity of scatterer, rnFor the center of n-th of scatterer, rn'For the center of n-th ' a scatterer.
8. system as claimed in claim 7, which is characterized in that in the modeling module, set the center of the scatterer
For coordinate origin, then the calculation formula of the scattered amplitude F (q) of the isotropic scatter and the orientation scatterer are as follows:
F (q)=∫vρdVe-iqr (2)
Wherein, q is scattering vector, and V is the volume of scatterer, and ρ is the electron density of scatterer, and r is any point on scatterer
To the distance of coordinate origin, i is imaginary unit.
9. system as claimed in claim 8, which is characterized in that in modeling module, according to the scattered amplitude of scatterer and
According to the distribution of the size of scatterer and distribution of orientations, to construct above-mentioned scattering strength calculation formula model；
Constructed scattering strength calculation formula model are as follows:
Wherein, C1For constant, R1、R2、R3For three and half axial lengths of scatterer, f (R1)、f(R2) and f (R3) it is three axis of scatterer
Size distribution, h (ω) be along axis of orientation zenith angle be distributed,For azimuthal distribution, ω is indicated along axis of orientation zenith angle,
ψ indicates Scattering of Vector and qxThe angle of component direction,Indicate azimuth；
For being orientated scatterer, in formula (8), R1、R2、R3Value be all different, or it is both wherein identical, the third party with
The two is different；
For isotropic scatter, in formula (8), R1=R2=R3, h (ω) is constant, and azimuthal distribution is constant.
10. system as claimed in claim 9, which is characterized in that wherein, for being orientated scatterer, be distributed using Von Mises
Function describes the zenith angle distribution, and functional form is as follows:
Wherein I0For the modified bessel function of 0 rank of the first kind, ω0Variance for average value, distribution is determined by variance parameter к；It is public
In formula (10), ω0, κ be adjustable parameter；
And/or
Wherein, the axis of the orientation scatterer and the radius R of the isotropic scatter, institute are described using log series model function
Shown in the form such as following formula (11) for stating log series model function:
Wherein μ and σ is respectively the logarithmic average and logarithm standard deviation of logarithm normal distribution, and average value m and variance parameter υ pass through
Following formula acquires:
M=exp (μ+σ2/2) (12)
υ=exp (2 μ+σ2)(expσ2-1) (13)
In formula (11), μ and σ are adjustable parameter.
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