CN109632603A - A kind of the specific surface area calculation method and system of foam metal - Google Patents
A kind of the specific surface area calculation method and system of foam metal Download PDFInfo
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- 239000006260 foam Substances 0.000 title claims abstract description 197
- 229910052751 metal Inorganic materials 0.000 title claims abstract description 165
- 239000002184 metal Substances 0.000 title claims abstract description 165
- 238000004364 calculation method Methods 0.000 title claims abstract description 34
- PXHVJJICTQNCMI-UHFFFAOYSA-N Nickel Chemical compound [Ni] PXHVJJICTQNCMI-UHFFFAOYSA-N 0.000 claims abstract description 28
- 239000004411 aluminium Substances 0.000 claims abstract description 16
- 229910052782 aluminium Inorganic materials 0.000 claims abstract description 16
- XAGFODPZIPBFFR-UHFFFAOYSA-N aluminium Chemical compound [Al] XAGFODPZIPBFFR-UHFFFAOYSA-N 0.000 claims abstract description 16
- RYGMFSIKBFXOCR-UHFFFAOYSA-N Copper Chemical compound [Cu] RYGMFSIKBFXOCR-UHFFFAOYSA-N 0.000 claims abstract description 15
- 229910052802 copper Inorganic materials 0.000 claims abstract description 15
- 239000010949 copper Substances 0.000 claims abstract description 15
- 229910052759 nickel Inorganic materials 0.000 claims abstract description 14
- 239000000463 material Substances 0.000 claims description 41
- 238000000034 method Methods 0.000 claims description 33
- 238000012937 correction Methods 0.000 claims description 16
- 238000003860 storage Methods 0.000 claims description 9
- NAWXUBYGYWOOIX-SFHVURJKSA-N (2s)-2-[[4-[2-(2,4-diaminoquinazolin-6-yl)ethyl]benzoyl]amino]-4-methylidenepentanedioic acid Chemical compound C1=CC2=NC(N)=NC(N)=C2C=C1CCC1=CC=C(C(=O)N[C@@H](CC(=C)C(O)=O)C(O)=O)C=C1 NAWXUBYGYWOOIX-SFHVURJKSA-N 0.000 claims description 6
- 238000004590 computer program Methods 0.000 claims description 6
- 238000004519 manufacturing process Methods 0.000 claims description 6
- 239000012530 fluid Substances 0.000 claims description 4
- PCHJSUWPFVWCPO-UHFFFAOYSA-N gold Chemical compound [Au] PCHJSUWPFVWCPO-UHFFFAOYSA-N 0.000 claims description 3
- 229910052737 gold Inorganic materials 0.000 claims description 3
- 239000010931 gold Substances 0.000 claims description 3
- 150000002739 metals Chemical class 0.000 abstract description 6
- -1 foam copper Chemical class 0.000 abstract description 4
- 210000004027 cell Anatomy 0.000 description 63
- 239000011148 porous material Substances 0.000 description 16
- 238000005259 measurement Methods 0.000 description 5
- 230000008569 process Effects 0.000 description 5
- 238000002474 experimental method Methods 0.000 description 4
- 239000006262 metallic foam Substances 0.000 description 4
- 238000002360 preparation method Methods 0.000 description 4
- 238000010586 diagram Methods 0.000 description 3
- 238000009826 distribution Methods 0.000 description 3
- 238000004070 electrodeposition Methods 0.000 description 3
- 230000006872 improvement Effects 0.000 description 3
- 238000011160 research Methods 0.000 description 3
- 238000001179 sorption measurement Methods 0.000 description 3
- 238000003775 Density Functional Theory Methods 0.000 description 2
- 238000010521 absorption reaction Methods 0.000 description 2
- 238000005266 casting Methods 0.000 description 2
- 238000011156 evaluation Methods 0.000 description 2
- 238000012986 modification Methods 0.000 description 2
- 230000004048 modification Effects 0.000 description 2
- 238000009715 pressure infiltration Methods 0.000 description 2
- 239000007787 solid Substances 0.000 description 2
- 239000000243 solution Substances 0.000 description 2
- 230000000153 supplemental effect Effects 0.000 description 2
- 238000012360 testing method Methods 0.000 description 2
- 238000004458 analytical method Methods 0.000 description 1
- 238000007630 basic procedure Methods 0.000 description 1
- 230000008901 benefit Effects 0.000 description 1
- 210000005056 cell body Anatomy 0.000 description 1
- 238000004587 chromatography analysis Methods 0.000 description 1
- 238000004891 communication Methods 0.000 description 1
- 238000007405 data analysis Methods 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 238000001914 filtration Methods 0.000 description 1
- 238000002347 injection Methods 0.000 description 1
- 239000007924 injection Substances 0.000 description 1
- 230000001788 irregular Effects 0.000 description 1
- QSHDDOUJBYECFT-UHFFFAOYSA-N mercury Chemical compound [Hg] QSHDDOUJBYECFT-UHFFFAOYSA-N 0.000 description 1
- 229910052753 mercury Inorganic materials 0.000 description 1
- 239000000203 mixture Substances 0.000 description 1
- 239000002086 nanomaterial Substances 0.000 description 1
- 230000009467 reduction Effects 0.000 description 1
- 238000006722 reduction reaction Methods 0.000 description 1
- 230000000630 rising effect Effects 0.000 description 1
- 238000000926 separation method Methods 0.000 description 1
- 230000003068 static effect Effects 0.000 description 1
- 239000000126 substance Substances 0.000 description 1
Classifications
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N15/00—Investigating characteristics of particles; Investigating permeability, pore-volume or surface-area of porous materials
- G01N15/08—Investigating permeability, pore-volume, or surface area of porous materials
- G01N15/088—Investigating volume, surface area, size or distribution of pores; Porosimetry
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- Life Sciences & Earth Sciences (AREA)
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- Biochemistry (AREA)
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Abstract
The invention discloses the specific surface area calculation methods and system of a kind of foam metal, the specific surface area calculation method of foam metal of the present invention is tested the aperture d and porosity θ of foam metal by obtaining, the aperture d of tested foam metal and porosity θ is substituted into the specific surface area computation model of tetrakaidecahedron model, the specific surface area of tested foam metal is calculated, the specific surface area computing system of foam metal of the present invention includes the corresponding system of specific surface area calculation method of foam metal of the present invention.The present invention can be realized that structure is simple, precision is higher, the smaller foam metal specific area measuring of error, and the present invention can be realized the specific surface areas of the foam metals such as foam copper, foamed aluminium, nickel foam and calculate.
Description
Technical field
The present invention relates to the specific area measuring technologies of foam metal, and in particular to a kind of specific surface area meter of foam metal
Method and system are calculated, the specific surface area that can be used for the foam metals such as foam copper, foamed aluminium, nickel foam calculates.
Background technique
Foam metal (porous metals) because its with the excellent performances such as high porosity, high-specific surface area, bulk density be small,
Function and structure double attribute is had both, aerospace, electronics and communication, building and electrochemical field are widely used in, and
Noise reduction, separation, filtering, heat exchange, electrochemical process and in terms of outstanding representation then depend on it is more
The structural form on mesoporous metal surface and the specific surface area of porous material.Therefore, the specific area measuring of foam metal is also increasingly
Cause the attention of related scholar.
The method of measurement porous material specific surface area mainly has gas adsorption method, mercury injection method and fluid penetrant method etc. at present.
The aperture of porous material and porosity are his essential attributes, can directly determine or simply measure to obtain (Ding Yi nanoporous
Metal: a kind of new energy nano material [J] journal of Shandong university (Edition), 2011,46 (10): 121-133.).Currently,
Some scholar has done foamed material specific surface area and has calculated the research of aspect, but has some limitations in terms of practical application
(the specific surface area calculation method of Zhuan Shijian porosu solid newly visits [J] chromatography, 1986,4 (1): 89-92；Guan Yue, Sun Qinlian, Wu
A row man of virtue and ability waits specific surface area and pore-size distribution to measure improvement [J] chemistry journal with calculation method, 1990,48 (5): 424-
430.).Liu et al. (Liu P S.A new method for calculating the specific surface area of
Porous metal foams [J] .Philosophical Magazine Letters, 2010,90 (6): 447-453.) with just
Based on octahedra ideal model, the specific surface area of foam metal is calculated, but in the space that precision aspect is also improved.
(Duan D L, Zhang R L, Ding X J, the et al.Calculation of specific surface area such as Duan
Of foam metals using dodecahedron model [J] .Metal Science Journal, 2006,22 (11):
Based on 1364-1367.) using dodecahedron model, a kind of method for calculating foam metal specific surface area is provided, but it is this
Method needs the width of first measured hole rib, and it is cumbersome to calculate step.
Summary of the invention
The technical problem to be solved in the present invention: in view of the above problems in the prior art, a kind of ratio table of foam metal is provided
Area computation method and system, the present invention can be realized that structure is simple, precision is higher, the smaller foam metal specific surface area of error
Measurement, the specific surface area that can be realized the foam metals such as foam copper, foamed aluminium, nickel foam calculate.
In order to solve the above-mentioned technical problem, the technical solution adopted by the present invention are as follows:
A kind of specific surface area calculation method of foam metal, implementation steps include:
1) the aperture d and porosity θ of tested foam metal are obtained；
2) the aperture d of tested foam metal and porosity θ is substituted into the specific surface area computation model of tetrakaidecahedron model, meter
It calculates and obtains the specific surface area of tested foam metal.
Preferably, the tetrakaidecahedron model is constituted by fixing rib length, and hole rib is cylindrical body, and top to bottom, left and right, front and rear six
It is square structure on a direction, and four hexagonal structures for being surrounded by total side of each square structure.
Preferably, in step 2) the specific surface area computation model of tetrakaidecahedron model calculating function expression such as formula (1)
It is shown；
In formula (1), svFor the specific surface area for being tested foam metal, d is the aperture of tested foam metal, and θ is tested foam
The porosity of metal, α are the material constant of tested foam metal, and β is the single unit body structural constant of tested foam metal.
Preferably, the tested foam metal is one of foam copper, foamed aluminium, nickel foam.
Preferably, the determination step of the specific surface area computation model of the tetrakaidecahedron model includes:
S1) tetrakaidecahedron model is carried out to be reduced to unit cell tetrakaidecahedron model, the unit cell tetrakaidecahedron model is by solid
Determine the long composition of rib, hole rib is cylindrical body, and is square structure on the six direction of top to bottom, left and right, front and rear, and each is square
Four hexagonal structures for being surrounded by total side of shape structure, the hole rib radius of unit cell tetrakaidecahedron model is determined according to formula (2)
r；
In formula (2), l is that the rib of unit cell tetrakaidecahedron model is long, and the value that the rib of unit cell tetrakaidecahedron model is long isθ is the porosity of tested foam metal, and a is the cube side length comprising unit cell tetrakaidecahedron model；
S2 the orthographic projection of plane, the positive throwing of any node where) combining any square structure of unit cell tetrakaidecahedron model
Shadow estimates the long l ' of practical rib of unit cell tetrakaidecahedron model as shown in formula (3)；
In formula (3), θ is the porosity of tested foam metal, and a is the cube side length comprising unit cell tetrakaidecahedron model；
S3) according to hole rib radius r, the long l ' of practical rib of unit cell tetrakaidecahedron model, ten four sides of unit cell is calculated according to formula (4)
Total external surface area S of body Model；
In formula (4), θ is the porosity of tested foam metal, and a is the cube side length comprising unit cell tetrakaidecahedron model；
S4 it) is calculated according to formula (5) after total external surface area S of unit cell tetrakaidecahedron model is ignored the surface area inside the rib of hole
Obtain the specific surface area S of unit cell tetrakaidecahedron modelv；
In formula (5), θ is the porosity of tested foam metal, and a is the cube side length comprising unit cell tetrakaidecahedron model；
S5 the frontal projected area S of plane where) combining any square structure of unit cell tetrakaidecahedron modelEightAnd hole rib
Projected area SRib, the equivalent area of a circle S of orthographic projection is calculated using formula (6)Diameter；
In formula (6), SEightFor the frontal projected area of plane where any square structure of unit cell tetrakaidecahedron model, SRibFor hole
The projected area of rib, a are the cube side length comprising unit cell tetrakaidecahedron model, and r is the hole rib half of unit cell tetrakaidecahedron model
Diameter；
S6) in the equivalent area of a circle S for obtaining orthographic projectionDiameterOn the basis of, the equivalent circular aperture of orthographic projection is calculated according to formula (7)
d'；
In formula (7), SDiameterFor the equivalent area of a circle of orthographic projection, d' is the equivalent circular aperture of orthographic projection；
S7) convolution (2) determines the equivalent circular aperture d' of orthographic projection, the cube side length comprising unit cell tetrakaidecahedron model
Shown in the relation function expression formula such as formula (8) of both a；
In formula (8), d' is the equivalent circular aperture of orthographic projection, and θ is the porosity of tested foam metal, and a is to include unit cell ten
The cube side length of tetrahedral model；
The influence that will receive porous body cell structure when S8) in view of inside fluid flow through porous body is introduced according to formula (9)
The equivalent circular aperture of correction factor ε orthographic projection obtains the aperture d of tested foam metal；
D=ε d'(9)
In formula (9), d' is the equivalent circular aperture of orthographic projection, and ε is correction factor；
S9) it is derived by the equivalent circular of the cube side length a comprising unit cell tetrakaidecahedron model and revised orthographic projection
Shown in the relation function expression formula such as formula (10) of aperture d；
In formula (10), a is the cube side length comprising unit cell tetrakaidecahedron model, and d is the aperture of tested foam metal, ε
For correction factor, θ is the porosity of tested foam metal；
S10) the specific surface area S of convolution (10) and calculating unit cell tetrakaidecahedron modelvFormula (5), simplify simultaneously approximate
The specific surface area S of new unit cell tetrakaidecahedron model is obtained after arrangementvCalculating formula such as formula (11) shown in；
In formula (11), ε is correction factor, and d is the aperture of tested foam metal, and θ is the porosity of tested foam metal；
S11 it) on the basis of formula (11), introduces and is modified depending on the material technological coefficient δ of material and manufacture craft,
Obtain the specific surface area S of new unit cell tetrakaidecahedron modelvCalculating formula such as formula (12) shown in；
In formula (12), ε is correction factor, and δ is material technological coefficient, and d is the aperture of tested foam metal, and θ is tested bubble
The porosity of foam metal；
The ε δ of α=3.893 is enabled, the specific surface area S of new unit cell tetrakaidecahedron model is obtainedvCalculating formula such as formula (13) institute
Show；
In formula (13), the ε of α=3.893 δ, ε are correction factor, and δ is material technological coefficient, and d is the hole of tested foam metal
Diameter, θ are the porosity of tested foam metal；
S12 material coefficient β) is introduced to wherein (1- θ) on the basis of formula (13) and carries out index amendment, obtains the tetrakaidecahedron
Shown in the calculating function expression such as formula (1) of the specific surface area computation model of model；
In formula (1), svFor the specific surface area for being tested foam metal, d is the aperture of tested foam metal, and θ is tested foam
The porosity of metal, α are the material constant of tested foam metal, and β is the single unit body structural constant of tested foam metal, and
The single unit body structural constant β of the material constant α, tested foam metal that are wherein tested foam metal are obtained by experimental fit
It arrives.
The present invention also provides a kind of specific surface area computing systems of foam metal, including computer equipment, it is characterised in that:
The computer equipment is programmed to perform the step of specific surface area calculation method of foregoing foams metal of the present invention.
The present invention also provides a kind of specific surface area computing systems of foam metal, including computer equipment, it is characterised in that:
The specific surface area calculating for being programmed to perform foregoing foams metal of the present invention is stored on the storage medium of the computer equipment
The computer program of method.
The present invention also provides a kind of computer readable storage mediums, it is characterised in that: the computer readable storage medium
On be stored with the computer program for being programmed to perform the specific surface area calculation method of foregoing foams metal of the present invention.
The present invention also provides a kind of specific surface area computing systems of foam metal, comprising:
Structural parameters capture program unit, for obtaining the aperture d and porosity θ of tested foam metal；
Specific surface area calculation procedure unit, for the aperture d of tested foam metal and porosity θ to be substituted into preset unit cell
The specific surface area computation model of tetrakaidecahedron model, is calculated the specific surface area of tested foam metal.
Preferably, the tetrakaidecahedron model that the specific surface area calculation procedure unit uses is constituted by fixing rib length, hole rib
It for cylindrical body, and is square structure on the six direction of top to bottom, left and right, front and rear, and the surrounding of each square structure is set
There are four hexagonal structures on total side.
Compared to the prior art, the present invention has an advantage that
1, the present invention is by obtaining the aperture d and porosity θ of tested foam metal, by the aperture d of tested foam metal and
Porosity θ substitutes into the specific surface area computation model of tetrakaidecahedron model, and the specific surface area of tested foam metal is calculated, can
Realize that structure is simple, precision is higher, the smaller foam metal specific area measuring of error.
2, the specific surface area that the present invention can be realized the foam metals such as foam copper, foamed aluminium, nickel foam calculates.
Detailed description of the invention
Fig. 1 is the electromicroscopic photograph of foam copper in the embodiment of the present invention one.
Fig. 2 is the basic procedure schematic diagram of one method of the embodiment of the present invention.
Fig. 3 is the structural schematic diagram of tetrakaidecahedron model in the embodiment of the present invention one.
Fig. 4 is the model unit cell orthographic projection of tetrakaidecahedron model in the embodiment of the present invention one.
Fig. 5 is the node sectional view of tetrakaidecahedron model in the embodiment of the present invention one.
Fig. 6 is the pore analysis schematic diagram of tetrakaidecahedron model in the embodiment of the present invention one.
Specific embodiment
Embodiment one:
Hereafter by by taking the foam copper obtained with electrodeposition process as an example, to the specific surface area calculation method of foam metal of the present invention
And system is described in further detail, the electromicroscopic photograph of foam copper is as shown in Figure 1.It should be noted that foam of the present invention
The specific surface area calculation method and system of metal are not limited only to foam copper, can also be applied to foamed aluminium (embodiment
Two) with nickel foam (embodiment three), unquestionably, the specific surface area calculation method and system of foam metal of the present invention can also be fitted
For other types of foam metal, the accuracy that only difference in microstructure may result in calculating be might have centainly
Difference.
As shown in Fig. 2, the implementation steps of the specific surface area calculation method of the present embodiment foam metal include:
1) the aperture d and porosity θ of tested foam metal are obtained；
2) the aperture d of tested foam metal and porosity θ is substituted into the specific surface area computation model of tetrakaidecahedron model, meter
It calculates and obtains the specific surface area of tested foam metal.
As shown in figure 3, tetrakaidecahedron model is constituted by fixing rib length in the present embodiment, hole rib is cylindrical body, and upper and lower, left
It is square structure on right, front and back six direction, and four hexagons for being surrounded by total side of each square structure
Structure.Effective ratio area is the sum of wire surface product of tetrakaidecahedron model and the ratio of corresponding porous volume.
In the present embodiment, the calculating function expression such as formula of the specific surface area computation model of tetrakaidecahedron model in step 2)
(1) shown in；
In formula (1), svFor the specific surface area for being tested foam metal, d is the aperture of tested foam metal, and θ is tested foam
The porosity of metal, α are the material constant of tested foam metal, and β is the single unit body structural constant of tested foam metal.
In the present embodiment, the determination step of the specific surface area computation model of tetrakaidecahedron model includes:
S1) tetrakaidecahedron model is carried out to be reduced to unit cell tetrakaidecahedron model, as shown in figure 3, unit cell tetrakaidecahedron mould
Type is constituted by fixing rib length, and hole rib is cylindrical body, and is square structure on the six direction of top to bottom, left and right, front and rear, and each
Four hexagonal structures for being surrounded by total side of a square structure, the hole of unit cell tetrakaidecahedron model is determined according to formula (2)
Rib radius r；
In formula (2), l, which is that the rib of unit cell tetrakaidecahedron model is long, (shown in the L in referring to fig. 4, does not consider that the wide ideal of rib is long
Degree), the value that the rib of unit cell tetrakaidecahedron model is long isθ is the porosity of tested foam metal, and a is to include unit cell
The cube side length (referring to fig. 4) of tetrakaidecahedron model；
S2 the orthographic projection (as shown in Figure 4) of plane where) combining any square structure of unit cell tetrakaidecahedron model, arbitrarily
The long l ' of practical rib (considering the wide ideal length of rib) of the orthographic projection of node estimation unit cell tetrakaidecahedron model (as shown in Figure 5) is such as
Shown in formula (3)；
In formula (3), θ is the porosity of tested foam metal, and a is the cube side length comprising unit cell tetrakaidecahedron model；
The orthographic projection (as shown in Figure 4) of plane, the positive throwing of any node in conjunction with where unit cell tetrakaidecahedron model any square structure
Shadow (as shown in Figure 5) is it is found that l' ≈ l-AB, and wherein l is that the rib length of unit cell tetrakaidecahedron model (does not consider that the wide ideal of rib is long
Degree), AB is that duplicate length is calculated at rib node (referring to Fig. 5)；
S3) according to hole rib radius r, the long l ' of practical rib of unit cell tetrakaidecahedron model, ten four sides of unit cell is calculated according to formula (4)
Total external surface area S of body Model；
In formula (4), θ is the porosity of tested foam metal, and a is the cube side length comprising unit cell tetrakaidecahedron model；
S4 it) is calculated according to formula (5) after total external surface area S of unit cell tetrakaidecahedron model is ignored the surface area inside the rib of hole
Obtain the specific surface area S of unit cell tetrakaidecahedron modelv；
In formula (5), θ is the porosity of tested foam metal, and a is the cube side length comprising unit cell tetrakaidecahedron model；
Since rib body interior surface area is less and smaller on the influence of porous specific surface area relevant property on the whole, formula (5) is in formula (4)
On the basis of have ignored surface area inside unit cell body cylinder rib.
S5 the frontal projected area S of plane where) combining any square structure of unit cell tetrakaidecahedron modelEightAnd hole rib
Projected area SRib, the equivalent area of a circle S of orthographic projection is calculated using formula (6)Diameter；
In formula (6), SEightFor the frontal projected area of plane where any square structure of unit cell tetrakaidecahedron model, SRibFor hole
The projected area of rib, a are the cube side length comprising unit cell tetrakaidecahedron model, and r is the hole rib half of unit cell tetrakaidecahedron model
Diameter；The orthographic projection of plane where any square structure of unit cell tetrakaidecahedron model in figure with L as shown in fig. 6, wherein l (being indicated)
Long (not considering the wide ideal length of rib), the orthographic projection of tetrakaidecahedron model as shown in Figure 6 for the rib of unit cell tetrakaidecahedron model,
The projected area of the unit tetrakaidecahedron can be calculated, equivalent circular aperture can be calculated by projected area.
S6) in the equivalent area of a circle S for obtaining orthographic projectionDiameterOn the basis of, the equivalent circular aperture of orthographic projection is calculated according to formula (7)
d'；
In formula (7), SDiameterFor the equivalent area of a circle of orthographic projection, d' is the equivalent circular aperture of orthographic projection；
S7) convolution (2) determines the equivalent circular aperture d' of orthographic projection, the cube side length comprising unit cell tetrakaidecahedron model
Shown in the relation function expression formula such as formula (8) of both a；
In formula (8), d' is the equivalent circular aperture of orthographic projection, and θ is the porosity of tested foam metal, and a is to include unit cell ten
The cube side length of tetrahedral model；
The influence that will receive porous body cell structure when S8) in view of inside fluid flow through porous body is introduced according to formula (9)
The equivalent circular aperture of correction factor ε orthographic projection obtains the aperture d of tested foam metal；
D=ε d'(9)
In formula (9), d' be orthographic projection equivalent circular aperture, ε be correction factor (depending on material material and its made
Journey can pass through fitting or empirical value value)；
S9) it is derived by the equivalent circular of the cube side length a comprising unit cell tetrakaidecahedron model and revised orthographic projection
Shown in the relation function expression formula such as formula (10) of aperture d；
In formula (10), a is the cube side length comprising unit cell tetrakaidecahedron model, and d is the aperture of tested foam metal, ε
For correction factor, θ is the porosity of tested foam metal；
S10) the specific surface area S of convolution (10) and calculating unit cell tetrakaidecahedron modelvFormula (5), simplify simultaneously approximate
The specific surface area S of new unit cell tetrakaidecahedron model is obtained after arrangementvCalculating formula such as formula (11) shown in；
In formula (11), ε is correction factor, and d is the aperture of tested foam metal, and θ is the porosity of tested foam metal；
S11 it) on the basis of formula (11), introduces and is modified depending on the material technological coefficient δ of material and manufacture craft,
Obtain the specific surface area S of new unit cell tetrakaidecahedron modelvCalculating formula such as formula (12) shown in；
In formula (12), ε is correction factor, and δ is material technological coefficient, and d is the aperture of tested foam metal, and θ is tested bubble
The porosity of foam metal；Due to actual hole rib and the cylindrical body of Non-smooth surface, but a kind of irregular triangular prism column type, because of material
The difference of matter and preparation process can take on any of a number of shapes variation, and correspond to different surface state, go out so as to cause surface area
Now different degrees of increase, formula (11) Ying Zengjia mono- depend on material and the material technological coefficient δ of manufacture craft is modified；
The ε δ of α=3.893 is enabled, the specific surface area S of new unit cell tetrakaidecahedron model is obtainedvCalculating formula such as formula (13) institute
Show；
In formula (13), the ε of α=3.893 δ, ε are correction factor, and δ is material technological coefficient, and d is the hole of tested foam metal
Diameter, θ are the porosity of tested foam metal；
S12 material coefficient β) is introduced to wherein (1- θ) on the basis of formula (13) and carries out index amendment, obtains the tetrakaidecahedron
Shown in the calculating function expression such as formula (1) of the specific surface area computation model of model；
In formula (1), svFor the specific surface area for being tested foam metal, d is the aperture of tested foam metal, and θ is tested foam
The porosity of metal, α are the material constant of tested foam metal, and β is the single unit body structural constant of tested foam metal, and
The single unit body structural constant β of the material constant α, tested foam metal that are wherein tested foam metal are obtained by experimental fit
It arrives.D (mm) is porous body aperture, and α is the material constant of the material and technique depending on rib diameter.Shown by experimental data in reality
It tests in the data area of selection, is verified with actual result, it is known that the varying aperture of material is little, but specific surface area is with hole
The raising of rate and increased dramatically, it is seen that formula (13) and actual conditions are not met simultaneously, therefore are introduced modifying factor and usually carried out to formula
Amendment type (13), to meet the specific surface area situation of practical porous material.In view of porous material specific surface area by material,
The influence of the factors such as preparation and geometry, introducing material constant α (material constant related with preparation method with material itself),
Single unit body structural constant β (constant related with the regularity of the single unit body of porous material and geometry).This two
A material constant is influenced by material preparation process.Theoretically, for theoretic porous material, β value is zero.
In the present embodiment, the aperture d and porosity θ for obtaining tested foam metal use laboratory apparatus for the U.S.
2020 Full-automatic physical chemical adsorption instrument of Micromeritics ASAP, instrument can carry out single-point, multiple spot BET specific surface area,
Langmuir specific surface area, BJH mesoporous, pore size distribution, Kong great little and total pore volume and area, Density Functional Theory (DFT), absorption
The working principle of a variety of data analysis instrument of hot and average pore size etc. is the static volumetric method of isothermal physical absorption.This reality
It applies using the dimensional parameters of BET gas adsorption method measurement foam copper, including specific surface area and average pore size etc. in example, according to sinus
Deng (Dou Zhifeng, Yu Wenhui, Feng Yuhong porous material specific surface area and pore-size distribution uncertainty of measurement evaluation the Hainan [J] it is big
Learn journal (natural science edition), 2009,27 (4): 353-357.) uncertain evaluation, go in measurement result most accurate value, remember
Record is in table 1.
Table 1: the relevant experimental data and theoretical calculation data of foam copper.
For the foam copper data in experiment, α=101.1, β=- 0.6289 are taken in gained formula.Come from experimental result
See, there is biggish differences for 3 in table 1 foam copper sample, but calculated result in experimental result we can see
Out, calculated result extremely meets the resulting data of experiment, and Error Absolute Value is there are 1.2% hereinafter, illustrating that formula accuracy is higher.
The present embodiment also provides a kind of specific surface area computing system of foam metal, including computer equipment, feature exist
In: computer equipment is programmed to perform the step of specific surface area calculation method of the present embodiment foregoing foams metal.
The present embodiment also provides a kind of specific surface area computing system of foam metal, including computer equipment, feature exist
In: the specific surface area calculating for being programmed to perform the present embodiment foregoing foams metal is stored on the storage medium of computer equipment
The computer program of method.
The present embodiment also provides a kind of computer readable storage medium, it is characterised in that: on computer readable storage medium
It is stored with the computer program for being programmed to perform the specific surface area calculation method of the present embodiment foregoing foams metal.
The present embodiment also provides a kind of specific surface area computing system of foam metal, comprising:
Structural parameters capture program unit, for obtaining the aperture d and porosity θ of tested foam metal；
Specific surface area calculation procedure unit, for the aperture d of tested foam metal and porosity θ to be substituted into preset unit cell
The specific surface area computation model of tetrakaidecahedron model, is calculated the specific surface area of tested foam metal.
In the present embodiment, the tetrakaidecahedron model that aforementioned specific surface area calculation procedure unit uses is constituted by fixing rib length,
Hole rib is cylindrical body, and is square structure on the six direction of top to bottom, left and right, front and rear, and the four of each square structure
Week is equipped with four hexagonal structures on side altogether.
Embodiment two:
The present embodiment is basically the same as the first embodiment, and distinctive points are that foam metal is the bubble that high pressure infiltration casting obtains
Foam aluminium.Related supplemental characteristic in the present embodiment for foamed aluminium is by document (Ma L, He D.Fabrication and pore
structure control of new type aluminium foams[J].Chinese Journal of Material
Research, 1994.) and document ([13] Liu P S.Anew method for calculating the specific
Surface area of porous metal foams [J] .Philosophical Magazine Letters, 2010,90
(6): 447-453. it) provides, experimental result is recorded in table 2.Relevant parameter is substituted into fitting in formula (1), obtains correspondence
α, β value, calculated result is recorded in table last line, is compared with experimental data Sv.Document (Liu is based in the present embodiment
The magnetic property of rising sun brightness porous foam metal and experimental study [J] foundry engieering that magnetic field is influenced, 2011,32 (6): 815-
817.) the foamed aluminium data in are fitted, and the document gives the aperture d and porosity θ of foamed aluminium and the ratio of foamed aluminium
Surface area sv, α=43.5119, β=0.11 are obtained after fitting, and resulting data will be calculated according to formula (1) and be recorded in table 2.
Table 2: the relevant experimental data and theoretical calculation data of foamed aluminium.
Embodiment three:
The present embodiment is basically the same as the first embodiment, and distinctive points are that foam metal is the foam obtained with electrodeposition process
Nickel.
Related supplemental characteristic in the present embodiment for nickel foam is by document (Ma L, He D.Fabrication and
pore structure control of new type aluminium foams[J].Chinese Journal of
Material Research, 1994.) and document ([13] Liu P S.Anew method for calculating the
specific surface area of porous metal foams[J].Philosophical Magazine
Letters, 2010,90 (6): 447-453.) it provides, experimental result is recorded in table 2.Relevant parameter is substituted into formula (1)
Middle fitting obtains corresponding α, β value, and calculated result is recorded in table last line, is compared with experimental data Sv.This implementation
Document (Liu P S.Anew method for calculating the specific surface area of is based in example
Porous metal foams [J] .Philosophical Magazine Letters, 2010,90 (6): 447-453.) bubble
Foam nickel data are fitted, and the document gives the aperture d and porosity θ of nickel foam and the specific surface area s of nickel foamv, intend
α=30.03, β=- 1.4979 are obtained after conjunction, and resulting data will be calculated according to formula (1) and be recorded in table 3.
Table 3: the relevant experimental data and theoretical calculation data of nickel foam.
It is counted it can be seen from the corresponding data of three kinds of porous material specific surface areas of above three embodiments with formula (1)
There is basic consistency between the notional result and actual experiment result of calculating.The mean error of three groups of data all exists
1.2% hereinafter, and worst error be no more than 1.8%, it is good to demonstrate the accuracy of formula.In the situation that two value of α, β is constant
Under, it is substituted into formula and is compared with the experimental data for having neither part nor lot in fitting, the calculated specific surface area of discovery formula and reality
It tests data quite to coincide, it was demonstrated that this formula can apply to the foam metal of the same race under same process.
In conclusion previous embodiment discloses a kind of short-cut method for calculating foam metal specific surface area, by building out
A kind of novel tetrakaidecahedron ideal model based on foam metal practical structures, can easily calculate foam metal whereby
Specific surface area, Binding experiment data comparison demonstrates the foam gold that resulting expression formula can obtain with a variety of methods well
True border specific surface area is adapted, the foam that the nickel foam and foam copper and high pressure infiltration casting obtained such as electrodeposition process obtains
Aluminium.Also, the actual error of expression formula obtained by the method is smaller, there is preferable practicability.
The above is only a preferred embodiment of the present invention, protection scope of the present invention is not limited merely to above-mentioned implementation
Example, all technical solutions belonged under thinking of the present invention all belong to the scope of protection of the present invention.It should be pointed out that for the art
Those of ordinary skill for, several improvements and modifications without departing from the principles of the present invention, these improvements and modifications
It should be regarded as protection scope of the present invention.
Claims (10)
1. a kind of specific surface area calculation method of foam metal, it is characterised in that implementation steps include:
1) the aperture d and porosity θ of tested foam metal are obtained；
2) the specific surface area computation model that the aperture d of tested foam metal and porosity θ is substituted into tetrakaidecahedron model, calculates
To the specific surface area of tested foam metal.
2. the specific surface area calculation method of foam metal according to claim 1, it is characterised in that: the tetrakaidecahedron mould
Type is constituted by fixing rib length, and hole rib is cylindrical body, and is square structure on the six direction of top to bottom, left and right, front and rear, and each
Four hexagonal structures for being surrounded by total side of a square structure.
3. the specific surface area calculation method of foam metal according to claim 1, it is characterised in that: ten four sides in step 2)
Shown in the calculating function expression such as formula (1) of the specific surface area computation model of body Model；
In formula (1), svFor the specific surface area for being tested foam metal, d is the aperture of tested foam metal, and θ is tested foam metal
Porosity, α are the material constant of tested foam metal, and β is the single unit body structural constant of tested foam metal.
4. the specific surface area calculation method of foam metal according to claim 1, it is characterised in that: the tested foam gold
Belong to is one of foam copper, foamed aluminium, nickel foam.
5. the specific surface area calculation method of foam metal described according to claim 1~any one of 4, it is characterised in that:
The determination step of the specific surface area computation model of the tetrakaidecahedron model includes:
S1) tetrakaidecahedron model is carried out to be reduced to unit cell tetrakaidecahedron model, the unit cell tetrakaidecahedron model is by fixing rib
Long to constitute, hole rib is cylindrical body, and is square structure on the six direction of top to bottom, left and right, front and rear, and each square knot
Four hexagonal structures for being surrounded by total side of structure determine the hole rib radius r of unit cell tetrakaidecahedron model according to formula (2)；
In formula (2), l is that the rib of unit cell tetrakaidecahedron model is long, and the value that the rib of unit cell tetrakaidecahedron model is long isθ
For the porosity for being tested foam metal, a is the cube side length comprising unit cell tetrakaidecahedron model；
S2 the orthographic projection of plane, the orthographic projection of any node are estimated where) combining any square structure of unit cell tetrakaidecahedron model
The long l ' of practical rib of unit cell tetrakaidecahedron model is calculated as shown in formula (3)；
In formula (3), θ is the porosity of tested foam metal, and a is the cube side length comprising unit cell tetrakaidecahedron model；
S3) according to hole rib radius r, the long l ' of practical rib of unit cell tetrakaidecahedron model, unit cell tetrakaidecahedron mould is calculated according to formula (4)
Total external surface area S of type；
In formula (4), θ is the porosity of tested foam metal, and a is the cube side length comprising unit cell tetrakaidecahedron model；
S4 it) is calculated according to formula (5) and is obtained after total external surface area S of unit cell tetrakaidecahedron model is ignored the surface area inside the rib of hole
The specific surface area S of unit cell tetrakaidecahedron modelv；
In formula (5), θ is the porosity of tested foam metal, and a is the cube side length comprising unit cell tetrakaidecahedron model；
S5 the frontal projected area S of plane where) combining any square structure of unit cell tetrakaidecahedron modelEightAnd the projection of hole rib
Area SRib, the equivalent area of a circle S of orthographic projection is calculated using formula (6)Diameter；
In formula (6), SEightFor the frontal projected area of plane where any square structure of unit cell tetrakaidecahedron model, SRibFor hole rib
Projected area, a are the cube side length comprising unit cell tetrakaidecahedron model, and r is the hole rib radius of unit cell tetrakaidecahedron model；
S6) in the equivalent area of a circle S for obtaining orthographic projectionDiameterOn the basis of, the equivalent circular aperture d ' of orthographic projection is calculated according to formula (7)；
In formula (7), SDiameterFor the equivalent area of a circle of orthographic projection, d ' is the equivalent circular aperture of orthographic projection；
S7) convolution (2) determines the equivalent circular aperture d ' of orthographic projection, the cube side length a two comprising unit cell tetrakaidecahedron model
Shown in the relation function expression formula such as formula (8) of person；
In formula (8), d ' is the equivalent circular aperture of orthographic projection, and θ is the porosity of tested foam metal, and a is comprising ten four sides of unit cell
The cube side length of body Model；
The influence that will receive porous body cell structure when S8) in view of inside fluid flow through porous body is introduced according to formula (9) and is corrected
The equivalent circular aperture of coefficient ε orthographic projection obtains the aperture d of tested foam metal；
D=ε d'(9)
In formula (9), d ' is the equivalent circular aperture of orthographic projection, and ε is correction factor；
S9) it is derived by the equivalent circular aperture d of the cube side length a comprising unit cell tetrakaidecahedron model and revised orthographic projection
Relation function expression formula such as formula (10) shown in；
In formula (10), a is the cube side length comprising unit cell tetrakaidecahedron model, and d is the aperture of tested foam metal, and ε is to repair
Positive coefficient, θ are the porosity of tested foam metal；
S10) the specific surface area S of convolution (10) and calculating unit cell tetrakaidecahedron modelvFormula (5), simplify and it is approximate arrange after
Obtain the specific surface area S of new unit cell tetrakaidecahedron modelvCalculating formula such as formula (11) shown in；
In formula (11), ε is correction factor, and d is the aperture of tested foam metal, and θ is the porosity of tested foam metal；
S11 it) on the basis of formula (11), introduces and is modified depending on the material technological coefficient δ of material and manufacture craft, obtained
The specific surface area S of new unit cell tetrakaidecahedron modelvCalculating formula such as formula (12) shown in；
In formula (12), ε is correction factor, and δ is material technological coefficient, and d is the aperture of tested foam metal, and θ is tested foam gold
The porosity of category；
The ε δ of α=3.893 is enabled, the specific surface area S of new unit cell tetrakaidecahedron model is obtainedvCalculating formula such as formula (13) shown in；
In formula (13), the ε of α=3.893 δ, ε are correction factor, and δ is material technological coefficient, and d is the aperture of tested foam metal, and θ is
The porosity of tested foam metal；
S12 material coefficient β) is introduced to wherein (1- θ) on the basis of formula (13) and carries out index amendment, obtains tetrakaidecahedron model
Specific surface area computation model calculating function expression such as formula (1) shown in；
In formula (1), svFor the specific surface area for being tested foam metal, d is the aperture of tested foam metal, and θ is tested foam metal
Porosity, α are the material constant of tested foam metal, and β be the single unit body structural constant for being tested foam metal, and wherein by
The single unit body structural constant β of the material constant α, tested foam metal that survey foam metal are obtained by experimental fit.
6. a kind of specific surface area computing system of foam metal, including computer equipment, it is characterised in that: the computer equipment
The step of being programmed to perform the specific surface area calculation method of foam metal described in any one of Claims 1 to 5.
7. a kind of specific surface area computing system of foam metal, including computer equipment, it is characterised in that: the computer equipment
Storage medium on be stored with the specific surface area meter for being programmed to perform foam metal described in any one of Claims 1 to 5
The computer program of calculation method.
8. a kind of computer readable storage medium, it is characterised in that: be stored with and be programmed on the computer readable storage medium
With the computer program of the specific surface area calculation method of foam metal described in any one of perform claim requirement 1~5.
9. a kind of specific surface area computing system of foam metal, comprising:
Structural parameters capture program unit, for obtaining the aperture d and porosity θ of tested foam metal；
Specific surface area calculation procedure unit, for the aperture d of tested foam metal and porosity θ to be substituted into preset unit cell 14
The specific surface area computation model of face body Model, is calculated the specific surface area of tested foam metal.
10. the specific surface area computing system of foam metal according to claim 9, it is characterised in that: the specific surface area
The tetrakaidecahedron model that calculation procedure unit uses is constituted by fixing rib length, and hole rib is cylindrical body, and top to bottom, left and right, front and rear six
It is square structure on a direction, and four hexagonal structures for being surrounded by total side of each square structure.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2021082277A1 (en) * | 2019-10-29 | 2021-05-06 | 沈阳铸造研究所有限公司 | High melting point kelvin structure lattice metal and preparation method therefor and application thereof |
| WO2021129315A1 (en) * | 2019-12-26 | 2021-07-01 | 中国科学院广州能源研究所 | Method for calculating pore distribution of marine sediment layer |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101566553A (en) * | 2009-04-09 | 2009-10-28 | 北京师范大学 | Computing method for specific surface area of foamed nickel |
| CN104032157A (en) * | 2014-06-10 | 2014-09-10 | 深圳先进技术研究院 | Regular porous metal material as well as preparation method and application thereof |
| CN104646669A (en) * | 2013-11-25 | 2015-05-27 | 广州中国科学院先进技术研究所 | Biomedical porous pure-titanium implant material and preparation method thereof |
-
2019
- 2019-01-04 CN CN201910006863.2A patent/CN109632603A/en active Pending
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101566553A (en) * | 2009-04-09 | 2009-10-28 | 北京师范大学 | Computing method for specific surface area of foamed nickel |
| CN104646669A (en) * | 2013-11-25 | 2015-05-27 | 广州中国科学院先进技术研究所 | Biomedical porous pure-titanium implant material and preparation method thereof |
| CN104032157A (en) * | 2014-06-10 | 2014-09-10 | 深圳先进技术研究院 | Regular porous metal material as well as preparation method and application thereof |
Non-Patent Citations (3)
| Title |
|---|
| H.P.蒂吉斯切 等: "《多孔泡沫金属》", 31 January 2005, 化学工业出版社 * |
| 刘培生: "多孔金属比表面积的计算方法", 《材料研究学报》 * |
| 屠永清 等: "闭孔泡沫铝材料十四面体模型的改进", 《计算力学学报》 * |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2021082277A1 (en) * | 2019-10-29 | 2021-05-06 | 沈阳铸造研究所有限公司 | High melting point kelvin structure lattice metal and preparation method therefor and application thereof |
| EP4052817A4 (en) * | 2019-10-29 | 2023-04-26 | Shenyang Research Institute of Foundry Co., Ltd. | High melting point kelvin structure lattice metal and preparation method therefor and application thereof |
| WO2021129315A1 (en) * | 2019-12-26 | 2021-07-01 | 中国科学院广州能源研究所 | Method for calculating pore distribution of marine sediment layer |
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