CN107590296A - A kind of Full _ pattern fitting method and system of small angle X ray scattering - Google Patents

A kind of Full _ pattern fitting method and system of small angle X ray scattering Download PDF

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CN107590296A
CN107590296A CN201610538586.6A CN201610538586A CN107590296A CN 107590296 A CN107590296 A CN 107590296A CN 201610538586 A CN201610538586 A CN 201610538586A CN 107590296 A CN107590296 A CN 107590296A
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scattering
mrow
spheroid
model
calculation formula
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朱才镇
海洋
崔可建
赵宁
徐坚
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Institute of Chemistry CAS
Shenzhen University
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Institute of Chemistry CAS
Shenzhen University
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Abstract

The present invention proposes a kind of small angle X ray scattering SAXS Full _ pattern fitting method, including：Obtaining step：Obtain the scattering strength experimental patterns of analysis object；Modeling procedure：The model of selective scattering body according to the characteristics of the feature of scattering strength experimental patterns and analysis object, so that it is determined that the scattered amplitude of scattering object, builds scattering strength calculation formula；Analyzing step：Adjust each adjustable parameter in the model so that the calculating collection of illustrative plates and the difference of the scattering strength experimental patterns obtained according to the scattering strength calculation formula is minimum, you can parses each parameter of the model；Wherein, the scattering object is spheroid.The invention also provides a kind of Full _ pattern fitting system of small angle X ray scattering.The present invention provides more preferable data support to carry out the Non-Destructive Testing of effectively observation material mesoscopic mesostructure using small angle X ray scattering.

Description

A kind of Full _ pattern fitting method and system of small angle X ray scattering
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 scattering Full _ pattern fitting method and system.
Background technology
Small angle X ray scattering refers to occur in the scattering phenomenon near incident beam in very little angular range, the production of scattering It is raw to come from the uneven of electron density in the range of sample interior one to hundreds of nanometers.Small angle X ray scattering is that research Jie sees chi The important means of the structure of matter in degree.The characteristics of being tested gas phase, liquid phase and solid phase liquid due to it, small angle X ray scattering is widely used in various fields, and its research object includes having various nanostructureds, as liquid crystal, liquid crystal state are given birth to The various phase changes of thing film, lysotropic liquid crystal, micella, vesica, liposome, surfactant associative structure, large biological molecule (albumen Matter, nucleic acid etc.), self-assembled supermolecular structure, micropore, crystal grain etc., colloidal sol fractal structure and interface structure, polymer solution, The microstructure etc. of crystalline orientation polymer (industrial fiber and film), block ion ionomeric.It is micro- relative to SEM, TEM etc. Electronic Speculum SAXS has that sample preparation is simple, and it is wide to be applicable sample scope, can obtain body phase information, have preferable particle statistics evenness The advantages that.
SAXS tests are simple, and data analysis is complicated, although by years of researches, SAXS theoretical analysis methods are still not It is perfect.SAXS model treatments are complicated, data analysis is difficult, and turning into influences its wide variety of main bottleneck and key scientific problems One of.For isotropism system, because the scattering phase of all directions is same, three-dimensional scattering intensity between emptying in spherical Distribution, whole scattered information can be reconstructed with a scattering curve.By the decades effort of researcher, to ergodicity The analysis of system has been achieved with breakthrough.But for oriented system, the problem of data analysis aspect still be present.
The content of the invention
To solve the above problems, the present invention proposes a kind of Full _ pattern fitting method and system of small angle X ray scattering, this hair The bright scattered amplitude calculating since a spheroid calculates setting about, and is finally derived by size and differs, orientation has distribution The scattering strength calculation formula of lax system, and calculating platform is established, two-dimensional scattering collection of illustrative plates is calculated by the method for model, adjusted Mould preparation shape parameter so that experimental patterns and the difference minimum for calculating collection of illustrative plates, you can parse model parameter, and standard sample can be passed through Verify the validity of model.
A kind of small angle X ray scattering SAXS proposed by the present invention Full _ pattern fitting method, comprises the following steps：
Obtaining step：Obtain the scattering strength experimental patterns of analysis object；
Modeling procedure：The mould of selective scattering body according to the characteristics of the feature of scattering strength experimental patterns and analysis object Type, so that it is determined that the scattered amplitude of scattering object, the model of structure scattering strength calculation formula；
Analyzing step：Adjust each adjustable parameter in the scattering strength calculation formula model so that according to the scattering The calculating collection of illustrative plates and the difference of the scattering strength experimental patterns that strength calculation formula obtains are minimum, you can it is strong to parse the scattering Spend each parameter of calculation formula model；
Wherein, the scattering object is spheroid.
Further, in the modeling procedure, the center of the spheroid is set as the origin of coordinates, then the spheroid Scattered amplitude F (q) calculation formula be：
F (q)=∫vρdVe-iqr (2)
Wherein, q is scattering vector, and V is the volume of spheroid, and ρ is the electron density of spheroid, and r is any on spheroid A little arrive the distance of the origin of coordinates.
Further, it is multiple in the quantity of the scattering object, when forming scattering system, in modeling procedure, structure Scattering strength I (q) calculation formula model is：
Wherein, q is vectorial for scattering, FnFor the scattered amplitude of n-th of scattering object in the scattering system, Fn’For the scattering The scattered amplitude of the n-th ' individual scattering object in system, N be the scattering system in scattering object quantity, rnFor in the scattering system The center of n-th of scattering object, rn'For the center of the n-th ' individual scattering object in the scattering system.
Further, differ, exist the lax system of orientation for size, in modeling procedure, according to dissipating for scattering object Amplitude and the Size Distribution and distribution of orientations according to scattering object are penetrated, to build the model of scattering strength calculation formula；
The model of constructed scattering strength calculation formula is：
Wherein, C1For constant, R1、R2、R3For three and half axial lengths of spheroid, f (R1)、f(R2) and f (R3) it is spheroid three The Size Distribution of individual axle, h (ω) are to be distributed along axis of orientation zenith angle,For azimuthal distribution, ω is represented along axis of orientation day Drift angle, ψ represent Scattering of Vector and qxThe angle of component direction,Represent azimuth.
Further, wherein, describe the zenith angle using Von Mises distribution functions and be distributed, functional form is as follows：
Wherein I0For the bessel functions of the rank of the first kind 0 amendment, ω0It is true by variance parameter к for average value, the variance of distribution It is fixed,It is defined as being uniformly distributed, ω0, κ be adjustable parameter.
Further, wherein describing the Size Distribution using log series model function, the form of log series model function is as follows Shown in formula (11)：
Wherein μ and σ is respectively the logarithmic average and logarithm standard deviation of logarithm normal distribution, its average value m and variance parameter υ Tried to achieve by following formula：
M=exp (μ+σ2/2) (12)
υ=exp (2 μ+σ2)(expσ2-1) (13)
μ and σ is adjustable parameter.
A kind of small angle X ray scattering SAXS proposed by the present invention Full _ pattern fitting system, including following modules：
Acquisition module：Obtain the scattering strength experimental patterns of analysis object；
Modeling module：The mould of selective scattering body according to the characteristics of the feature of scattering strength experimental patterns and analysis object Type, so that it is determined that the scattered amplitude of scattering object, the model of structure scattering strength calculation formula；
Parsing module：Adjust each adjustable parameter in the scattering strength calculation formula model so that according to the scattering The calculating collection of illustrative plates and the difference of the scattering strength experimental patterns that strength calculation formula obtains are minimum, you can it is strong to parse the scattering Spend each parameter of calculation formula model；
Wherein, the scattering object is spheroid.
Further, during the modeling module structure model, set the center of the spheroid as the origin of coordinates, then it is described The scattered amplitude F (q) of spheroid calculation formula is：
F (q)=∫vρdVe-iqr (2)
Wherein q is scattering vector, and V is the volume of spheroid, and ρ is the electron density of spheroid, and r is any one on spheroid Distance of the point to the origin of coordinates.
Further, it is multiple in the quantity of the scattering object, when forming scattering system, the scattering strength I's (q) of structure Calculation formula model is：
Wherein, q is vectorial for scattering, FnFor the scattered amplitude of n-th of scattering object in the scattering system, Fn’For the scattering The scattered amplitude of the n-th ' individual scattering object in system, N be the scattering system in scattering object quantity, rnFor in the scattering system The center of n-th of scattering object, rn'For the center of the n-th ' individual scattering object in the scattering system.
Further, differ, exist the lax system of orientation for size, according to the scattered amplitude of scattering object and according to The Size Distribution and distribution of orientations of scattering object, to build the model of scattering strength calculation formula；
The model of constructed scattering strength calculation formula is：
Wherein, C1For constant, R1、R2、R3For three and half axial lengths of spheroid, f (R1)、f(R2) and f (R3) it is spheroid three The Size Distribution of individual axle, h (ω) are to be distributed along axis of orientation zenith angle,For azimuthal distribution, ω is represented along axis of orientation zenith Angle, ψ represent Scattering of Vector and qxThe angle of component direction,Represent azimuth.
Further, wherein, describe the zenith angle using Von Mises distribution functions and be distributed, functional form is as follows：
Wherein I0For the bessel functions of the rank of the first kind 0 amendment, ω0It is true by variance parameter к for average value, the variance of distribution It is fixed,It is defined as being uniformly distributed, ω0, κ be adjustable parameter.
Further, wherein describing the Size Distribution using log series model function, the form of log series model function is as follows Shown in formula (11)：
Wherein μ and σ is respectively the logarithmic average and logarithm standard deviation of logarithm normal distribution, its average value m and variance parameter υ Tried to achieve by following formula：
M=exp (μ+σ2/2) (12)
υ=exp (2 μ+σ2)(expσ2-1) (13)
μ and σ is adjustable parameter.
The present invention since the scattered amplitude of spheroid calculate set about calculate, finally give size and differ and be orientated and deposit In the scattering strength calculation formula of the lax system of distribution, and calculating platform is established, calculating two dimension by the method for model dissipates Collection of illustrative plates is penetrated, adjusts model parameter so that experimental patterns and the difference minimum for calculating collection of illustrative plates, parses model parameter.The present invention is to take Calculating analysis to the two-dimensional scattering spectrogram of system provides strong method, so as to be to utilize small angle X ray scattering (SAXS) Non-Destructive Testing for carrying out effectively observation material mesoscopic mesostructure provides more preferable data support.
Brief description of the drawings
Fig. 1 is the flow chart of the Full _ pattern fitting method shown in the present invention；
Fig. 2 is the structured flowchart of the Full _ pattern fitting system shown in the present invention；
Fig. 3 is the phase difference schematic diagram of incident x-ray and scattered x rays in the spheroid shown in the present invention；
Fig. 4 is the schematic diagram of orientation scattering object each angular relationship in a coordinate system shown in the present invention；
Fig. 5 is the schematic diagram of the full spectral analysis method of two dimension shown in the present invention；
Fig. 6 a and Fig. 6 b are the Von Mises function curves under the different parameters shown in the present invention；
Fig. 7 is logarithm normal distribution function curve under the different parameters shown in the present invention.
Embodiment
For the object, technical solutions and advantages of the present invention are more clearly understood, below in conjunction with specific embodiment, and reference Accompanying drawing, the present invention is described in more detail.But those skilled in the art know, the invention is not limited in accompanying drawing and following reality Apply example.
As shown in figure 1, a kind of full spectrum digital simulation method of the invention for proposing small angle X ray scattering SAXS, including under Row step：
Obtaining step：Obtain the scattering strength experimental patterns of analysis object；
Modeling procedure：The mould of selective scattering body according to the characteristics of the feature of scattering strength experimental patterns and analysis object Type, so that it is determined that the scattered amplitude of scattering object, the model of structure scattering strength calculation formula；
Analyzing step：Adjust each adjustable parameter in the scattering strength calculation formula model so that according to the scattering The calculating collection of illustrative plates and the difference of the scattering strength experimental patterns that strength calculation formula obtains are minimum, you can it is strong to parse the scattering Spend each parameter of calculation formula model；
Wherein, the scattering object is spheroid.
In modeling procedure, the present invention analyzes the scattering object that volume is V first, it is assumed that its electron density be ρ (r)= ρ, the electron density outside scattering object is ρ (r)=0, then when beam of x-rays reaches the system, the electronics forced oscillation in scattering object It is dynamic, produce 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 scattering object can be written as：
F (q)=∫ ∫ ∫ dV ρ (r) eiqr (1)
It is abbreviated as：
F (q)=∫vρdVe-iqr (2)
Wherein, q is scattering vector, and V is the volume of spheroid, and ρ is the electron density of spheroid, and r is any on spheroid The distance of the origin of coordinates is a little arrived, i is imaginary unit.
If there is N number of spheroid in a system, center is located at r respectively1, r2, r3... rN, electron density can be written as ρn (r-rn), then the total electron density of system can be written as：
The scattered amplitude of system can be written as：
According to above-mentioned formula, the formula that scattering strength I (q) can be derived by modeling procedure is：
As n=n ',Above formula can be further written as：
Due to the size and heterogeneity of scattering object in lax system, the Size Distribution for defining three axles of scattering object is f (R1)、 f(R2) and f (R3), h (ω) is distributed as along axis of orientation zenith angle, azimuthal distribution isIts volume is V (R1, R2, R3).By Interference between the scattering object in lax system is very weak, therefore the Section 2 in above formula (6) is zero.
Above formula (6) can be further simplified as：
Then scattering the scattering strength of system can be written as：
There is following relation in above formula between each angle：
γ represents scattering object and the angle of X-axis, and ω represents that along axis of orientation zenith angle 2 θ are incident X-rays and scattered x-ray Angle, ψ represents Scattering of Vector and qxThe angle of component direction,Represent azimuth.
It is assumed that scattering object has rotational invariance, azimuthal distributionIt is defined as being uniformly distributed, is a constant.Zenith angle Distribution h (ω) is defined as Von Mises distributions, and functional form is as follows：
Wherein I0For the bessel functions of the rank of the first kind 0 amendment, ω0For average value, the variance of distribution is determined by к.
Von Mises distributions are the most frequently used circular distributions, and span is generally [0,2 π], are suitable for describing scattering object Distribution of orientations.As shown in figures 6 a and 6b, the Von Mises function curves under different parameters are described.
And the major axis and short-axis profile f (R) in the scattering strength in modeling procedure are defined as log distributions, functional form is such as Under
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 try to achieve：
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, the parameter of defect is given, you can two-dimensional scattering collection of illustrative plates corresponding to calculating；The scattering is strong The calculating collection of illustrative plates that degree calculation formula obtains is compared with the scattering strength experimental patterns, by constantly adjusting modeling parameters ω0, к, μ and σ make it that the two error is minimum, as shown in Figure 5, you can parse the parameter of model.In experimental patterns and calculate figure Before spectrum is compared, it is also necessary to experimental patterns are modified, deduct the shadow of laboratory apparatus and practical operation to experimental patterns Ring.First experimental patterns are carried out with various corrections, such as backscatter, dark current, beam shape correction, obtains high quality two dimension Test scatter pattern.Two-dimensional scattering collection of illustrative plates is calculated by the method for model again, adjusts model parameter so that experimental patterns and meter The difference of nomogram spectrum is minimum, you can parses model parameter, and the validity of model is verified by standard sample.
As shown in Fig. 2 the invention also provides the full spectrum digital simulation system of small angle X ray scattering SAXS a kind of, including Following modules：
Acquisition module：Obtain the scattering strength experimental patterns of analysis object；
Modeling module：The mould of selective scattering body according to the characteristics of the feature of scattering strength experimental patterns and analysis object Type, so that it is determined that the scattered amplitude of scattering object, the model of structure scattering strength calculation formula；
Parsing module：Adjust each adjustable parameter in the scattering strength calculation formula model so that according to the scattering The calculating collection of illustrative plates and the difference of the scattering strength experimental patterns that strength calculation formula obtains are minimum, you can it is strong to parse the scattering Spend each parameter of calculation formula model；
Wherein, the scattering object is spheroid.
In modeling module, the present invention analyzes the scattering object that volume is V first, it is assumed that its electron density be ρ (r)= ρ, the electron density outside scattering object is ρ (r)=0, then when beam of x-rays reaches the system, the electronics forced oscillation in scattering object It is dynamic, produce 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 scattering object can be written as：
F (q)=∫ ∫ ∫ dV ρ (r) eiqr (1)
It is abbreviated as,
F (q)=∫vρdVe-iqr (2)
Wherein, q is scattering vector, and V is the volume of spheroid, and ρ is the electron density of spheroid, and r is any on spheroid The distance of the origin of coordinates is a little arrived, i is imaginary unit.
If there is N number of spheroid in a system, center is located at r respectively1, r2, r3... rN, electron density can be written as ρn (r-rn), then the total electron density of system can be written as：
The scattered amplitude of system can be written as：
Wherein, q is scattering vector, and F is the scattered amplitude of the scattering object, and N is the number of scattering object in the scattering system Amount.
According to above-mentioned formula, the formula that scattering strength I (q) can be derived by modeling module is：
As n=n ',Above formula can be further written as：
Due to the size and heterogeneity of scattering object in lax system, the Size Distribution for defining three axles of scattering object is f (R1)、 f(R2) and f (R3), h (ω) is distributed as along axis of orientation zenith angle, azimuthal distribution isIts volume is V (R1, R2, R3). Interference in lax system between scattering object is very weak, and the Section 2 in above formula is zero.
Above formula can be further simplified as
Then scattering the scattering strength of system can be written as：
There is following relation in above formula between each angle：
Wherein γ represents scattering object and the angle of X-axis, and ω represents that along axis of orientation zenith angle 2 θ are incident X-rays and scattering X The angle of ray, ψ represent Scattering of Vector and qxThe angle of component direction,Represent azimuth.
It is assumed that scattering object has rotational invariance, azimuthal distributionIt is defined as being uniformly distributed, is a constant.Zenith angle Distribution h (ω) is defined as Von Mises distributions, and functional form is as follows：
Wherein I0For the bessel functions of the rank of the first kind 0 amendment, ω0For average value, the variance of distribution is determined by к.
Von Mises distributions are the most frequently used circular distributions, and span is generally [0,2 π], are suitable for describing scattering object Distribution of orientations.As shown in figures 6 a and 6b, the Von Mises function curves under different parameters are described.
And the major axis and short-axis profile f (R) in the scattering strength in modeling module are defined as log distributions, functional form is such as Under：
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 try to achieve：
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, the parameter of defect is given, you can two-dimensional scattering collection of illustrative plates corresponding to calculating；The scattering is strong The calculating collection of illustrative plates that degree calculation formula obtains is compared with the scattering strength experimental patterns, by constantly adjusting modeling parameters ω0, к, μ and σ make it that the two error is minimum, as shown in Figure 5, you can parse the parameter of model.In experimental patterns and calculate figure Before spectrum is compared, it is also necessary to experimental patterns are modified, deduct the shadow of laboratory apparatus and practical operation to experimental patterns Ring.First experimental patterns are carried out with various corrections, such as backscatter, dark current, beam shape correction, obtains high quality two dimension Test scatter pattern.Two-dimensional scattering collection of illustrative plates is calculated by the method for model again, adjusts model parameter so that experimental patterns and meter The difference of nomogram spectrum is minimum, you can parses model parameter, and the validity of model is verified by standard sample.
The embodiment of Von Mises function curves and Lognormal distribution curve under different parameters is given below.
Embodiment 1：
Arrange parameter ω0=-pi/2；κ=100, obtain the Von Mises function curves as corresponded to parameter in Fig. 6 a.
Embodiment 2：
Arrange parameter ω0=-π/4；κ=100, obtain the Von Mises function curves as corresponded to parameter in Fig. 6 a.
Embodiment 3：
Arrange parameter ω0=0；κ=100, obtain the Von Mises function curves as corresponded to parameter in Fig. 6 a.
Embodiment 4：
Arrange parameter ω0=π/4；κ=100, obtain the Von Mises function curves as corresponded to parameter in Fig. 6 a.
Embodiment 5：
Arrange parameter ω0=pi/2；κ=100, obtain the Von Mises function curves as corresponded to parameter in Fig. 6 a.
Embodiment 6：
Arrange parameter ω0=3 π/4；κ=100, obtain the Von Mises function curves as corresponded to parameter in Fig. 6 a.
Embodiment 7：
Arrange parameter ω0=0.95 π；κ=100, obtain the Von Mises function curves as corresponded to parameter in Fig. 6 a.
Embodiment 8：
Arrange parameter ω0=π；κ=100, obtain the Von Mises function curves as corresponded to parameter in Fig. 6 a.
Embodiment 9：
Arrange parameter ω0=0；κ=0, obtain the Von Mises function curves as corresponded to parameter in Fig. 6 b.
Embodiment 10：
Arrange parameter ω0=0；κ=4, obtain the Von Mises function curves as corresponded to parameter in Fig. 6 b.
Embodiment 11：
Arrange parameter ω0=0；κ=8, obtain the Von Mises function curves as corresponded to parameter in Fig. 6 b.
Embodiment 12：
Arrange parameter ω0=0；κ=12, obtain the Von Mises function curves as corresponded to parameter in Fig. 6 b.
Embodiment 13：
Arrange parameter ω0=0；κ=16, obtain the Von Mises function curves as corresponded to parameter in Fig. 6 b.
Embodiment 14：
Arrange parameter ω0=0；κ=20, obtain the Von Mises function curves as corresponded to parameter in Fig. 6 b.
Embodiment 15：
Arrange parameter ω0=0；κ=100, obtain the Von Mises function curves as corresponded to parameter in Fig. 6 b.
Embodiment 16：
Arrange parameter m=20；V=200, obtain the logarithm normal distribution function curve as corresponded to parameter in Fig. 7.
Embodiment 17：
Arrange parameter m=20；V=150, obtain the logarithm normal distribution function curve as corresponded to parameter in Fig. 7.
Embodiment 18：
Arrange parameter m=20；V=100, obtain the logarithm normal distribution function curve as corresponded to parameter in Fig. 7.
Embodiment 19：
Arrange parameter m=20；V=80, obtain the logarithm normal distribution function curve as corresponded to parameter in Fig. 7.
Embodiment 20：
Arrange parameter m=20；V=60, obtain the logarithm normal distribution function curve as corresponded to parameter in Fig. 7.
Embodiment 21：
Arrange parameter m=20；V=40, obtain the logarithm normal distribution function curve as corresponded to parameter in Fig. 7.
Embodiment 22：
Arrange parameter m=20；V=20, obtain the logarithm normal distribution function curve as corresponded to parameter in Fig. 7.
Embodiment 23：
Arrange parameter m=20；V=10, obtain the logarithm normal distribution function curve as corresponded to parameter in Fig. 7.
By setting different parameters, the zenith angle distribution of scattering object and being just distributed very much for major and minor axis are adjusted so that calculate The obtained error calculated between collection of illustrative plates and experimental patterns is minimum, you can parses model parameter, and is verified by standard sample The validity of model.Strong method is provided so as to the calculating analysis of the two-dimensional scattering spectrogram for oriented system.
More than, embodiments of the present invention are illustrated.But the present invention is not limited to above-mentioned embodiment.It is all Within the spirit and principles in the present invention, any modification, equivalent substitution and improvements done etc., it should be included in the guarantor of the present invention Within the scope of shield.

Claims (10)

  1. A kind of 1. small angle X ray scattering SAXS Full _ pattern fitting method, it is characterised in that this method comprises the following steps：
    Obtaining step：Obtain the scattering strength experimental patterns of analysis object；
    Modeling procedure：The model of selective scattering body according to the characteristics of the feature of scattering strength experimental patterns and analysis object, from And the scattered amplitude of scattering object is determined, build the model of scattering strength calculation formula；
    Analyzing step：Adjust each adjustable parameter in the scattering strength calculation formula model so that according to the scattering strength The calculating collection of illustrative plates and the difference of the scattering strength experimental patterns that calculation formula obtains are minimum, you can parse the scattering strength meter Calculate each parameter of formula model；
    Wherein, the scattering object is spheroid.
  2. 2. the method as described in claim 1, it is characterised in that in the modeling procedure, set the center of the spheroid For the origin of coordinates, then the scattered amplitude F (q) of spheroid calculation formula is：
    F (q)=∫vρdVe-iqr (2)
    Wherein, q is scattering vector, and V is the volume of spheroid, and ρ is the electron density of spheroid, and r is any point on spheroid To the distance of the origin of coordinates.
  3. 3. method as claimed in claim 2, it is characterised in that be multiple, composition scattering system in the quantity of the scattering object When, in modeling procedure, the scattering strength I (q) of structure calculation formula model is：
    Wherein, q is vectorial for scattering, FnFor the scattered amplitude of n-th of scattering object in the scattering system, Fn’For the scattering system In the n-th ' individual scattering object scattered amplitude, N be the scattering system in scattering object quantity, rnFor in the scattering system n-th The center of individual scattering object, rn'For the center of the n-th ' individual scattering object in the scattering system..
  4. 4. method as claimed in claim 3, it is characterised in that the lax system for the orientation that differs for size, exists, modeling In step, according to the scattered amplitude of scattering object and the Size Distribution and distribution of orientations according to scattering object, to build scattering strength The model of calculation formula；
    The model of constructed scattering strength calculation formula is：
    (8)
    Wherein, C1For constant, R1、R2、R3For three and half axial lengths of spheroid, f (R1)、f(R2) and f (R3) it is three axles of spheroid Size Distribution, h (ω) be along axis of orientation zenith angle be distributed,For azimuthal distribution, ω is represented along axis of orientation zenith angle, ψ Represent Scattering of Vector and qxThe angle of component direction,Represent azimuth.
  5. 5. method as claimed in claim 4, it is characterised in that wherein, the zenith is described using Von Mises distribution functions Angle is distributed, and functional form is as follows：
    Wherein I0For the bessel functions of the rank of the first kind 0 amendment, ω0For average value, the variance of distribution is determined by variance parameter к,It is defined as being uniformly distributed, ω0, κ be adjustable parameter；
    And/or
    The Size Distribution wherein is described using log series model function, shown in the form such as following formula (11) of log series model function：
    <mrow> <mi>f</mi> <mrow> <mo>(</mo> <mi>R</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mi>R</mi> <mi>&amp;sigma;</mi> <msqrt> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> </msqrt> </mrow> </mfrac> <msup> <mi>e</mi> <mfrac> <mrow> <mo>-</mo> <msup> <mrow> <mo>(</mo> <mi>ln</mi> <mi> </mi> <mi>R</mi> <mo>-</mo> <mi>&amp;mu;</mi> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> <mrow> <mn>2</mn> <msup> <mi>&amp;sigma;</mi> <mn>2</mn> </msup> </mrow> </mfrac> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> </mrow>
    Wherein μ and σ is respectively the logarithmic average and logarithm standard deviation of logarithm normal distribution, and its average value m and variance parameter υ pass through Following formula is tried to achieve：
    M=exp (μ+σ2/2) (12)
    υ=exp (2 μ+σ2)(expσ2-1) (13)
    μ and σ is adjustable parameter.
  6. 6. a kind of small angle X ray scattering SAXS Full _ pattern fitting system, it is characterised in that the system includes following modules：
    Acquisition module：Obtain the scattering strength experimental patterns of analysis object；
    Modeling module：The model of selective scattering body according to the characteristics of the feature of scattering strength experimental patterns and analysis object, from And the scattered amplitude of scattering object is determined, build the model of scattering strength calculation formula；
    Parsing module：Adjust each adjustable parameter in the scattering strength calculation formula model so that according to the scattering strength The calculating collection of illustrative plates and the difference of the scattering strength experimental patterns that calculation formula obtains are minimum, you can parse the scattering strength meter Calculate each parameter of formula model；
    Wherein, the scattering object is spheroid.
  7. 7. system as claimed in claim 6, it is characterised in that during the modeling module structure model, set the spheroid Center be the origin of coordinates, then the scattered amplitude F (q) of spheroid calculation formula is：
    F (q)=∫vρdVe-iqr (2)
    Wherein q is scattering vector, and V is the volume of spheroid, and ρ is the electron density of spheroid, and r is that any point is arrived on spheroid The distance of the origin of coordinates.
  8. 8. system as claimed in claim 7, it is characterised in that be multiple, composition scattering system in the quantity of the scattering object When, the scattering strength I (q) of structure calculation formula model is：
    Wherein, q is vectorial for scattering, FnFor the scattered amplitude of n-th of scattering object in the scattering system, Fn’For the scattering system In the n-th ' individual scattering object scattered amplitude, N be the scattering system in scattering object quantity, rnFor in the scattering system n-th The center of individual scattering object, rn'For the center of the n-th ' individual scattering object in the scattering system.
  9. 9. system as claimed in claim 8, it is characterised in that the lax system for the orientation that differs for size, exists, according to scattered The scattered amplitude of beam and the Size Distribution and distribution of orientations according to scattering object, to build the mould of scattering strength calculation formula Type；
    The model of constructed scattering strength calculation formula is：
    Wherein, C1For constant, R1、R2、R3For three and half axial lengths of spheroid, f (R1)、f(R2) and f (R3) it is three axles of spheroid Size Distribution, h (ω) be along axis of orientation zenith angle be distributed,For azimuthal distribution, ω is represented along axis of orientation zenith angle, ψ Represent Scattering of Vector and qxThe angle of component direction,Represent azimuth.
  10. 10. system as claimed in claim 9, it is characterised in that wherein, the day is described using Von Mises distribution functions Drift angle is distributed, and functional form is as follows：
    <mrow> <mi>h</mi> <mrow> <mo>(</mo> <mi>&amp;omega;</mi> <mo>|</mo> <msub> <mi>&amp;omega;</mi> <mn>0</mn> </msub> <mo>,</mo> <mi>&amp;kappa;</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <msup> <mi>e</mi> <mrow> <mi>&amp;kappa;</mi> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mrow> <mo>(</mo> <mi>&amp;omega;</mi> <mo>-</mo> <msub> <mi>&amp;omega;</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> </mrow> </msup> <mrow> <mn>2</mn> <msub> <mi>&amp;pi;I</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mi>&amp;kappa;</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow>
    Wherein I0For the bessel functions of the rank of the first kind 0 amendment, ω0For average value, the variance of distribution is determined by variance parameter к,It is defined as being uniformly distributed, ω0, κ be adjustable parameter；
    And/or
    The Size Distribution wherein is described using log series model function, shown in the form such as following formula (11) of log series model function：
    <mrow> <mi>f</mi> <mrow> <mo>(</mo> <mi>R</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mi>R</mi> <mi>&amp;sigma;</mi> <msqrt> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> </msqrt> </mrow> </mfrac> <msup> <mi>e</mi> <mfrac> <mrow> <mo>-</mo> <msup> <mrow> <mo>(</mo> <mi>ln</mi> <mi> </mi> <mi>R</mi> <mo>-</mo> <mi>&amp;mu;</mi> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> <mrow> <mn>2</mn> <msup> <mi>&amp;sigma;</mi> <mn>2</mn> </msup> </mrow> </mfrac> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> </mrow>
    Wherein μ and σ is respectively the logarithmic average and logarithm standard deviation of logarithm normal distribution, and its average value m and variance parameter υ pass through Following formula is tried to achieve：
    M=exp (μ+σ2/2) (12)
    υ=exp (2 μ+σ2)(expσ2-1) (13)
    μ and σ is adjustable parameter.
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Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112037183A (en) * 2020-08-12 2020-12-04 深圳大学 2D SAXS spectrum calculation method and device
CN112037181A (en) * 2020-08-12 2020-12-04 深圳大学 2D SAXS atlas analysis model training method and device
CN116067997A (en) * 2023-04-06 2023-05-05 中国科学院上海高等研究院 Liposome and method for detecting structure of liposome drug

Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105115998A (en) * 2015-08-20 2015-12-02 中国石油化工股份有限公司 Method for determining powder diffraction preferred orientation parameter

Patent Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105115998A (en) * 2015-08-20 2015-12-02 中国石油化工股份有限公司 Method for determining powder diffraction preferred orientation parameter

Non-Patent Citations (4)

* Cited by examiner, † Cited by third party
Title
BRIAN R. PAUW等: "Analysing the nanoporous structure of aramid fibres", 《JOURNAL OF APPLIED CRYSTALLOGRAPHY》 *
CAIZHEN ZHU等: "Relationship between performance and microvoids", 《JOURNAL OF APPLIED CRYSTALLOGRAPHY》 *
徐洪杰等编著: "《上海光源首批线站设计与研制》", 31 January 2015, 上海科学技术出版社 *
朱才镇: "取向体系的二维小角Ｘ射线散射分析理论研究进展", 《高分子通报》 *

Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112037183A (en) * 2020-08-12 2020-12-04 深圳大学 2D SAXS spectrum calculation method and device
CN112037181A (en) * 2020-08-12 2020-12-04 深圳大学 2D SAXS atlas analysis model training method and device
CN112037183B (en) * 2020-08-12 2023-07-28 深圳大学 2D SAXS map calculation method and device
CN112037181B (en) * 2020-08-12 2023-09-08 深圳大学 2D SAXS (three dimensional architecture) atlas analysis model training method and device
CN116067997A (en) * 2023-04-06 2023-05-05 中国科学院上海高等研究院 Liposome and method for detecting structure of liposome drug

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