CN107589135A - A kind of method and system for describing scattering shape - Google Patents
A kind of method and system for describing scattering shape Download PDFInfo
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- CN107589135A CN107589135A CN201610534988.9A CN201610534988A CN107589135A CN 107589135 A CN107589135 A CN 107589135A CN 201610534988 A CN201610534988 A CN 201610534988A CN 107589135 A CN107589135 A CN 107589135A
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Abstract
The present invention relates to a kind of method for describing scattering shape, this method comprises the following steps：The step of obtaining scattering shape initial value：The initial value of the size and dimension of material internal scattering object is obtained according to the electron micrology analysis method of material microstructure；The step of describing scattering object：Scattering object is described using super ellipsoids described function, is set according to above-mentioned initial value and changes the parameter in super ellipsoids described function, build the scattering object of the shape.The invention further relates to a kind of system for describing scattering shape.The present invention describes the scattering object in material using super ellipsoids described function, can change scattering shape by changing the function in super ellipsoids body, is brought great convenience for the calculating of two-dimensional scattering collection of illustrative plates.
Description
Technical field
The invention belongs to Advance of Small-angle X-ray Scattering Technique field, and in particular to a kind of to describe to scatter the method for shape and be
System.
Background technology
Small angle X ray scattering (SAXS) is a kind of method of nondestructive analysis micro-nano structure, is occurred near X ray direction
Electronics coherent scattering phenomenon in small angle range, it is poor that it comes from sample interior electron density, is that (one arrives research meso-scale
Hundreds of nanometers) important means of the interior structure of matter.Different from X-ray diffraction analysis crystal structure, SAXS is adapted to relatively low
The architectural feature of non-crystalline material is analyzed under resolution ratio, is widely used in parsing nanoscale electronic Density inhomogeneity material and (receives
Rice grain or nano aperture) physical dimension, than surface, pore-size distribution, interface information etc..The applicable sample scopes of SAXS are wide, do,
Wet, gaseous sample is all suitable for；Compared with conventional microstructure analysis, such as SEM, TEM, SAXS is almost not required to particular sample system
It is standby, the sample that TEM can not be measured can be characterized.SAXS can have preferable particle statistics evenness with direct measurement body phase material,
Chemistry, chemical industry, material science, molecular biology, medicine and pharmacology, Condensed Matter Physics etc. are multidisciplinary to be all widely used.Research object
Including with various nanostructureds, such as liquid crystal, the various phase changes of liquid crystal state biomembrane, lysotropic liquid crystal, micella, vesica, lipid
Body, surfactant associative structure, large biological molecule (protein, nucleic acid etc.), self-assembled supermolecular structure, micropore, crystal grain etc.,
Colloidal sol fractal structure and interface structure, polymer solution, crystalline orientation polymer (industrial fiber and film), block ion from
Microstructure of polymers etc..
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, SAXS data analyses need further to study, as
The N.Stribeck monographs at him in 2007《X-Ray Scattering of Soft Matter》(p15) pointed out in：" face
To anisotropy system, scientist faced isotropism system such as 1931 ".
At present, there is the two-dimensional scattering collection of illustrative plates that certain methods can calculate spheroid, cylinder, spheroid, but it is actual
Different scattering object particle in material be present, it is difficult to be described with spheroid, cylinder or spheroid, it is each how to describe shape
Different scattering object is a key issue in SAXS researchs.X-Y scheme can be effectively parsed using 2D SAXS analysis methods
Spectrum, but different systems is directed to, the different of scattering object is described, it is necessary to take different shapes the factor, especially
For some more complicated shapes, it is described it is difficult to find suitable function.
The content of the invention
In order to solve the above-mentioned technical problem, the present invention proposes a kind of method and system for describing scattering shape, utilizes
Super ellipsoids described function describes the scattering object in material, can change the scattering bodily form by changing the function in super ellipsoids body
Shape, brought great convenience for the calculating of two-dimensional scattering collection of illustrative plates.
A kind of method for describing scattering shape proposed by the present invention, this method comprise the following steps：
The step of obtaining scattering shape initial value：Material is obtained according to the electron micrology analysis method of material microstructure
Expect the initial value of the size and dimension of scattering-in body；
The step of describing scattering object：Scattering object is described using super ellipsoids described function, sets and changes according to above-mentioned initial value
The parameter become in super ellipsoids described function, build the scattering object of the shape.
Further, the electron density that microdefect is defined using super ellipsoids described function is poorBy being described to super ellipsoids
Parameter in function is regulated and controled, and generates the scattering object of the shape.
Further, electron density is poorSuper ellipsoids described function form such as following formula (1)：
In formula (1), e represents the round and smooth degree in horizontal direction, and n represents the round and smooth degree on vertical direction, R1、R2And R3
Span respectively in x, y and z axes.
Further, the shape of scattering object is changed by e, n and R1 in adjustment type (1), R2 and R3, by year-on-year
Parameter R in example adjustment type (1)1、R2And R3Value change the size of the scattering object.
Further, used scattering object described function also includes the deformation type of formula (1).
The invention also provides a kind of system for describing scattering shape, the system is included with lower module：
Obtain the module of scattering shape initial value：Material is obtained according to the electron micrology analysis method of material microstructure
Expect the initial value of the size and dimension of scattering-in body；
The module of scattering object is described：Scattering object is described using super ellipsoids described function, sets and changes according to above-mentioned initial value
The parameter become in super ellipsoids described function, build the scattering object of the shape.
Further, the electron density that microdefect is defined using super ellipsoids described function is poorBy being described to super ellipsoids
Parameter in function is regulated and controled, and generates the scattering object of the shape.
Further, electron density is poorSuper ellipsoids described function form such as following formula (1)：
In formula (1), e represents the round and smooth degree in horizontal direction, and n represents the round and smooth degree on vertical direction, R1、R2And R3
Span respectively in x, y and z axes.
Further, the shape of scattering object is changed by e, n and R1 in adjustment type (1), R2 and R3, by same
Parameter R in ratio adjustment type (1)1、R2And R3Value change the size of the scattering object.
Further, used scattering object described function also includes the deformation type of formula (1).
Beneficial effects of the present invention：The present invention uses super ellipsoids described function, by changing in super ellipsoids described function
Parameter e, n can change the shape of scattering object, and radius R1, R2, R3 or ɑ, b and the c by changing all directions can change scattered
The size of beam.The present invention can simulate variously-shaped scattering object by a kind of function, and continuous with parameter e, n
Change, the shape of scattering object can also consecutive variations, develop into 1,100 kinds of different scattering objects, be very easy to 2D
The calculating of scatter pattern in SAXS.
Brief description of the drawings
Fig. 1 is flow chart of the method for the present invention.
Fig. 2 is the system architecture diagram of the present invention.
Super ellipsoids described function shape (R when Fig. 3 is the different parameters of the present invention1=R2=R3=1) schematic diagram.
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.
A kind of method for describing scattering shape proposed by the present invention, applied to Advance of Small-angle X-ray Scattering Technique field, such as schemes
Shown in 1, comprise the following steps：
The step of obtaining scattering shape initial value：According to the micrology such as ESEM, transmission electron microscope method or other points
Analysis method obtains the initial value of the size and dimension of material internal scattering object；
The step of describing scattering object：Scattering object is described using super ellipsoids described function, sets and changes according to above-mentioned initial value
The parameter become in super ellipsoids described function, build the scattering object of the shape.
In the step of describing scattering object, to adapt to different systems, micropore of different shapes is simulated, is retouched using super ellipsoids
State function define microdefect electron density it is poorBy regulating and controlling to the parameter in super ellipsoids described function, generation is different
The scattering object of shape.
The form of super ellipsoids described function such as following formula (1) or formula (2) or its deformation type：
In formula (1), e represents the round and smooth degree in horizontal direction, and n represents the round and smooth degree on vertical direction, R1、R2And R3
Span respectively in x, y and z axes.
Super ellipsoids are a kind of multi-parameter functions, and variously-shaped scattering object can be obtained by adjusting parameter e and n, such as just
Cube, cylinder, spheroid, water chestnut cylinder etc..R in formula (1)1、R2And R3Equivalent to being stretched in the x, y and z directions respectively
Or compression.
Used scattering object described function is super ellipsoids described function and its deformation type.
The scattering object of various shapes can be constructed by the parameter e and n in adjustment type (1), as class cylinder, spheroid,
Octahedron etc..
The shape of scattering object is changed by e, n and R1 in adjustment type (1), R2 and R3, passes through adjustment type in proportion
(1) the parameter R in1、R2And R3Value can change the size of the scattering object.
The invention also provides a kind of system for describing scattering shape, applied to Advance of Small-angle X-ray Scattering Technique field, such as
Shown in Fig. 2, including following modules：
Obtain the module of scattering shape initial value：According to the micrology such as ESEM, transmission electron microscope method or other points
Analysis method obtains the initial value of the shape of material internal scattering object；
The module of scattering object is described：Scattering object is described using super ellipsoids described function, sets and changes according to above-mentioned initial value
The parameter become in super ellipsoids described function, build the scattering object of the shape.
Remaining content is identical with the content of the above method, repeats no more.
The following examples give the scattering object of some Common Shapes, as shown in figure 3, wherein R1=1, R2=1, R3=
1.Other shapes can be according to each parameter in actual conditions adjustment type (1) and formula (2).
Embodiment 1
Arrange parameter e=0.2；N=0.2, R1=1；R2=1；R3=1, obtain the scattering object as corresponded to parameter in Fig. 1.
Embodiment 2
Arrange parameter e=0.2；N=0.6, R1=1；R2=1；R3=1, obtain the scattering object as corresponded to parameter in Fig. 1.
Embodiment 3
Arrange parameter e=0.2；N=1.0, R1=1；R2=1；R3=1, obtain the scattering object as corresponded to parameter in Fig. 1.
Embodiment 4
Arrange parameter e=0.2；N=2.0, R1=1；R2=1；R3=1, obtain the scattering object as corresponded to parameter in Fig. 1.
Embodiment 5
Arrange parameter e=0.2；N=3.0, R1=1；R2=1；R3=1, obtain the scattering object as corresponded to parameter in Fig. 1.
Embodiment 6
Arrange parameter e=0.6；N=0.2, R1=1；R2=1；R3=1, obtain the scattering object as corresponded to parameter in Fig. 1.
Embodiment 7
Arrange parameter e=0.6；N=0.6, R1=1；R2=1；R3=1, obtain the scattering object as corresponded to parameter in Fig. 1.
Embodiment 8
Arrange parameter e=0.6；N=1.0, R1=1；R2=1；R3=1, obtain the scattering object as corresponded to parameter in Fig. 1.
Embodiment 9
Arrange parameter e=0.6；N=2.0, R1=1；R2=1；R3=1, obtain the scattering object as corresponded to parameter in Fig. 1.
Embodiment 10
Arrange parameter e=0.6；N=3.0, R1=1；R2=1；R3=1, obtain the scattering object as corresponded to parameter in Fig. 1.
Embodiment 11
Arrange parameter e=1.0；N=0.2, R1=1；R2=1；R3=1, obtain the scattering object as corresponded to parameter in Fig. 1.
Embodiment 12
Arrange parameter e=1.0；N=0.6, R1=1；R2=1；R3=1, obtain the scattering object as corresponded to parameter in Fig. 1.
Embodiment 13
Arrange parameter e=1.0；N=1.0, R1=1；R2=1；R3=1, obtain the scattering object as corresponded to parameter in Fig. 1.
Embodiment 14
Arrange parameter e=1.0；N=2.0, R1=1；R2=1；R3=1, obtain the scattering object as corresponded to parameter in Fig. 1.
Embodiment 15
Arrange parameter e=1.0；N=3.0, R1=1；R2=1；R3=1, obtain the scattering object as corresponded to parameter in Fig. 1.
Embodiment 16
Arrange parameter e=2.0；N=0.2, R1=1；R2=1；R3=1, obtain the scattering object as corresponded to parameter in Fig. 1.
Embodiment 17
Arrange parameter e=2.0；N=0.6, R1=1；R2=1；R3=1, obtain the scattering object as corresponded to parameter in Fig. 1.
Embodiment 18
Arrange parameter e=2.0；N=1.0, R1=1；R2=1；R3=1, obtain the scattering object as corresponded to parameter in Fig. 1.
Embodiment 19
Arrange parameter e=2.0；N=2.0, R1=1；R2=1；R3=1, obtain the scattering object as corresponded to parameter in Fig. 1.
Embodiment 20
Arrange parameter e=2.0；N=3.0, R1=1；R2=1；R3=1, obtain the scattering object as corresponded to parameter in Fig. 1.
Embodiment 21
Arrange parameter e=3.0；N=0.2, R1=1；R2=1；R3=1, obtain the scattering object as corresponded to parameter in Fig. 1.
Embodiment 22
Arrange parameter e=3.0；N=0.6, R1=1；R2=1；R3=1, obtain the scattering object as corresponded to parameter in Fig. 1.
Embodiment 23
Arrange parameter e=3.0；N=1.0, R1=1；R2=1；R3=1, obtain the scattering object as corresponded to parameter in Fig. 1.
Embodiment 24
Arrange parameter e=3.0；N=2.0, R1=1；R2=1；R3=1, obtain the scattering object as corresponded to parameter in Fig. 1.
Embodiment 25
Arrange parameter e=3.0；N=3.0, R1=1；R2=1；R3=1, obtain the scattering object as corresponded to parameter in Fig. 1.
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)
- A kind of 1. method for describing scattering shape, it is characterised in that this method comprises the following steps：The step of obtaining scattering shape initial value：Obtained according to the electron micrology analysis method of material microstructure in material The initial value of the size and dimension of portion's scattering object；The step of describing scattering object：Scattering object is described using super ellipsoids described function, is set and changed super according to above-mentioned initial value Parameter in ellipsoid described function, build the scattering object of the shape.
- 2. according to the method for claim 1, it is characterised in that the electronics that microdefect is defined using super ellipsoids described function is close Degree is poorBy regulating and controlling to the parameter in super ellipsoids described function, the scattering object of the shape is generated.
- 3. according to the method for claim 2, it is characterised in that electron density is poorSuper ellipsoids described function form Such as following formula (1)：<mrow> <mi>&rho;</mi> <mrow> <mo>(</mo> <mover> <mi>r</mi> <mo>&RightArrow;</mo> </mover> <mo>)</mo> </mrow> <mo>=</mo> <mi>&rho;</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msup> <mrow> <mo>(</mo> <mo>|</mo> <mfrac> <mi>x</mi> <msub> <mi>R</mi> <mn>1</mn> </msub> </mfrac> <msup> <mo>|</mo> <mrow> <mn>2</mn> <mo>/</mo> <mi>e</mi> </mrow> </msup> <mo>+</mo> <mo>|</mo> <mfrac> <mi>y</mi> <msub> <mi>R</mi> <mn>2</mn> </msub> </mfrac> <msup> <mo>|</mo> <mrow> <mn>2</mn> <mo>/</mo> <mi>e</mi> </mrow> </msup> <mo>)</mo> </mrow> <mrow> <mi>e</mi> <mo>/</mo> <mi>n</mi> </mrow> </msup> <mo>+</mo> <mo>|</mo> <mfrac> <mi>z</mi> <msub> <mi>R</mi> <mn>3</mn> </msub> </mfrac> <msup> <mo>|</mo> <mrow> <mn>2</mn> <mo>/</mo> <mi>n</mi> </mrow> </msup> </mrow> </mtd> <mtd> <mrow> <mi>r</mi> <mo>&le;</mo> <mn>1</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mi>r</mi> <mo>></mo> <mn>1</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>In formula (1), e represents the round and smooth degree in horizontal direction, and n represents the round and smooth degree on vertical direction, R1、R2And R3Respectively For the span in x, y and z axes.
- 4. according to the method for claim 3, it is characterised in that by e, n and R1 in adjustment type (1), R2 and R3 come Change the shape of scattering object, pass through the parameter R in adjustment type in proportion (1)1、R2And R3Value change the size of the scattering object.
- 5. the method according to claim 3 or 4, it is characterised in that used scattering object described function also includes formula (1) Deformation type.
- 6. a kind of system for describing scattering shape, it is characterised in that the system is included with lower module：Obtain the module of scattering shape initial value：Obtained according to the electron micrology analysis method of material microstructure in material The initial value of the size and dimension of portion's scattering object；The module of scattering object is described：Scattering object is described using super ellipsoids described function, is set and changed super according to above-mentioned initial value Parameter in ellipsoid described function, build the scattering object of the shape.
- 7. system according to claim 6, it is characterised in that the electronics that microdefect is defined using super ellipsoids described function is close Degree is poorBy regulating and controlling to the parameter in super ellipsoids described function, the scattering object of the shape is generated.
- 8. system according to claim 7, it is characterised in that electron density is poorSuper ellipsoids described function form Such as following formula (1)：<mrow> <mi>&rho;</mi> <mrow> <mo>(</mo> <mover> <mi>r</mi> <mo>&RightArrow;</mo> </mover> <mo>)</mo> </mrow> <mo>=</mo> <mi>&rho;</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msup> <mrow> <mo>(</mo> <mo>|</mo> <mfrac> <mi>x</mi> <msub> <mi>R</mi> <mn>1</mn> </msub> </mfrac> <msup> <mo>|</mo> <mrow> <mn>2</mn> <mo>/</mo> <mi>e</mi> </mrow> </msup> <mo>+</mo> <mo>|</mo> <mfrac> <mi>y</mi> <msub> <mi>R</mi> <mn>2</mn> </msub> </mfrac> <msup> <mo>|</mo> <mrow> <mn>2</mn> <mo>/</mo> <mi>e</mi> </mrow> </msup> <mo>)</mo> </mrow> <mrow> <mi>e</mi> <mo>/</mo> <mi>n</mi> </mrow> </msup> <mo>+</mo> <mo>|</mo> <mfrac> <mi>z</mi> <msub> <mi>R</mi> <mn>3</mn> </msub> </mfrac> <msup> <mo>|</mo> <mrow> <mn>2</mn> <mo>/</mo> <mi>n</mi> </mrow> </msup> </mrow> </mtd> <mtd> <mrow> <mi>r</mi> <mo>&le;</mo> <mn>1</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mi>r</mi> <mo>></mo> <mn>1</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>In formula (1), e represents the round and smooth degree in horizontal direction, and n represents the round and smooth degree on vertical direction, R1、R2And R3Respectively For the span in x, y and z axes.
- 9. system according to claim 8, it is characterised in that by e, n and R1 in adjustment type (1), R2 and R3 come Change the shape of scattering object, pass through the parameter R in adjustment type in proportion (1)1、R2And R3Value change the size of the scattering object.
- 10. system according to claim 8 or claim 9, it is characterised in that used scattering object described function also includes formula (1) deformation type.
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