CN101055241B - Multiple-passage dispersion reverse deduction microgranule tri-dimensional shape detector and detection method - Google Patents

Abstract

The invention discloses a kind of detector and detection method using multiple-passage dispersion reverse deduction microgranule tri-dimensional shape,Experiment carries out in spherical shape scattering chamber,Scatter chamber feature be at 30 °~150 ° of polar angle,In the space that azimuth is 360 °,Every 15 ° of settings, four fiber optic hubs,9 azimuth discs being parallel to each other are formed,It could also say that form 4 pairs of symmetrical circular conical surfaces of azimuth disc about 90 ° of polar angle directions; 36 fiber optic hubs also form two orthogonal discs for respectively containing 18 fiber optic hubs simultaneously,The angle of disc and the sample introduction particle beams is 45 °. Every measurement point radius size of particle is extracted using scattered signal, then the method for line obtains the shape information of particle, and the measurement point radius size of particle is obtained by mature Mie scattering theory inverting:

Wherein the π r/ of α=2 λ, r are the fiber optic point respective radius of particle.

Description

Multiple-passage dispersion reverse deduction microgranule tri-dimensional shape detector and detection method

Technical field

The present invention relates to the particle optical field, specifically is to utilize multiple-passage dispersion reverse deduction microgranule tri-dimensional shape detector

Background technology

Particle shape and granularity are the important parameters that influences the microparticle physical characteristics, are the basic references that characterizes its characteristic.The granulometry technology is quite ripe, and existing at present multiple technologies are applied to laboratory or actual online detection.With respect to granulometry, it is many that the development that particle shape is measured will lag behind, at present the domestic report that is not seen in as yet.Only there is sreen analysis relatively, can provides the more information of horn of plenty for process kinetics research by the data of measuring particle shape and granularity.The influence of considering the particle shape parameter in process of production can the monitoring product quality, reduce production costs, as industries such as pharmacy, papermaking, cement.Thereby particle shape can also be reacted effectively control pollution of source to a certain extent.The deposition location of imbedibility particle is closely related with particle shape, can make the relation between imbedibility gasoloid and the disease more clear for the detailed monitoring of particle shape.Therefore the research of particle shape has very wide prospect.Analyze for particle shape, the past is difficult to a kind of quick and conventional instrument of development and reaches.Traditionally, microscope is commonly used to carry out this work, and as the unique instrument that can observe independent particle and analyze its size and shape, because its absoluteness, microtechnic is commonly used to confirm the result of other technologies.Yet, obtain significative results on the statistics, must require a great deal of time and carry out specimen preparation, manual observation.The scattered light of particle is the function of a plurality of factors such as particle shape, can fast inversion coating of particles information, but technology of having reported or constant bearing angle research polar angle, fixedly polar angle is studied the position angle, and the scattering of particle is three-dimensional, and having only starts with from the inverting of multi-faceted scattered information just might obtain the accurate information of particle shape.

Summary of the invention

Purpose of the present invention provides a kind of fast inversion micro-particles shapes detector, and the present invention is by collecting 36 orientation of flight particle scattered intensity information, and the way of filling a vacancy with similar fixed point arrives the 3D shape of particle fast.This invention technical scheme mature and reliable is a kind of practicable method.

Technical scheme of the present invention

Multiple-passage dispersion reverse deduction microgranule tri-dimensional shape detector, it is characterized in that including the scattering cavity, its inside surface is handled through blackout, the outer wall profile fiber jack of scattering cavity, sampling optical fiber is installed in the fiber optic hub, scattering cavity top is linked with the incident pipe of the sample introduction particle beams, its below is linked with the exit tube of the sample introduction particle beams that is positioned on the same axis, sheath stream pipe is arranged on the sidewall of the incident pipe of the sample introduction particle beams, but a plurality of Modulating Diode Laser modulators are installed on the sidewall of scattering cavity, the emitting light path of each laser modulator all intersects at from described incident pipe and enters the sample introduction particle beams in the scattering cavity, and the opposite of each laser modulator is equipped with the light absorption pipe.

Described scattering cavity is a spherical cavity, the incident pipe of the described sample introduction particle beams and the axis of exit tube pass the centre of sphere of scattering cavity, but described Modulating Diode Laser modulator is two, its emitting light path is vertical mutually, and its installed surface is the diametric plane of scattering cavity, vertical with the sample introduction particle beams, 30 °～150 ° of polar angles, the position angle is in 360 ° the space, every 15 ° four fiber optic hubs are set, forming 9 position angle discs that are parallel to each other, promptly is to form 4 pairs of circular conical surfaces about the position angle disc symmetry of 90 ° of polar angle directions; 36 fiber optic hubs have also formed two orthogonal discs that respectively contain 18 fiber optic hubs simultaneously, and the angle of the disc and the sample introduction particle beams is 45 °; The termination of sampling optical fiber is equipped with lenticule, places in the scattering chamber, and the other end of 36 optical fiber directly enters on the reception target surface of ICCD, by by root optical fiber mark, obtains each corresponding angle particle scattered light electric signal and distributes.

Hyperchannel scattered information inverting microparticle 3D shape detection method is characterized in that may further comprise the steps:

(1), design a scattering cavity, its inside surface is handled through blackout, the outer wall of scattering cavity is distributed with several fiber optic hubs, sampling optical fiber is installed in the fiber optic hub, scattering cavity top is linked with the incident pipe of the sample introduction particle beams, its below is linked with the exit tube of the sample introduction particle beams that is positioned on the same axis, sheath stream pipe is arranged on the sidewall of the incident pipe of the sample introduction particle beams, but a plurality of Modulating Diode Laser modulators are installed on the sidewall of scattering cavity, the emitting light path of each laser modulator all intersects at from described incident pipe and enters the sample introduction particle beams in the scattering cavity, and the opposite of each laser modulator is equipped with the light absorption pipe;

(2), purge the scattering inside cavity with pure air, till experiment not being brought the particle of influence, regulate the airshed of the injector at scattering cavity top, cooperate sheath stream, both ratios are reached about 1: 6, produce individual particle corpuscullar flow along axial line rectilinear flight;

(3) but semiconductor laser modulation sends the light beam of 650nm, the laser beam after the modulation enters the scattering chamber, the optical fiber that the light scattering signal of particle is distributed on the scattering cavity inner wall is collected simultaneously in different positions;

(4), the light-emitting window of fibre bundle is arranged on the light-sensitive surface of ICCD successively, scattered light signal becomes pulse electrical signal through ICCD, if the scattered signal that this position optical fiber is collected is identical at the scattered signal of this position with the spheric grain of a certain yardstick, this scattered signal also can be drawn by the Mie scattering theory, then think the scale size of this position correspondence of particle, several fiber position has just formed several and has represented the point of radius size like this, these points are coupled together, just formed the 3D shape of particle.

1. the processing of parts

This instrument is used for monitoring the faint scattered signal of particle, should be as far as possible little by the reflection that the scattering inner cavity surface itself brings, so the mode that mould is used in the scattering chamber processes, and cavity integral body especially inside surface will be done blackout and handles, so comparatively suitable with cast aluminium.The internal diameter in scattering chamber is 24mm, and external diameter is 38mm.It is characterized in that 30 °～150 ° of polar angles, the position angle is in 360 ° the space, four fiber optic hubs are set every 15 °, form 9 position angle discs that are parallel to each other, also can be described as and form 4 pairs of circular conical surfaces about the position angle disc symmetry of 90 ° of polar angle directions; 36 fiber optic hubs have also formed two orthogonal discs that respectively contain 18 fiber optic hubs simultaneously, and the angle of the disc and the sample introduction particle beams is 45 °.The junction of other parts and scattering inner cavity surface also should be done blackout and be handled, and considers the weight of instrument, selects for use duralumin to get final product.

2. the assembling of instrument

The junction in scattering chamber itself and all and scattering chamber is all sealed, in order to avoid external interference.The standard that equals air output with air inflow is checked the seal degree based on the instrument in scattering chamber.

3. the calibration of instrument

At first purge inside, scattering chamber, till the particle that experimental result is not brought influence exists with pure dry air.Adopt the optical fiber of the poly-stupid ethene ball sizing instrument of standard then, because the slight errors during machining or optical fiber are installed, the scattered signal difference that may cause the same latitude angle of standard spheric grain by calibration, makes the ability of reception light scattering of same angle of latitude identical.

4. scattered signal obtains

Because the detection of a target is locked in the inhalable particle of particle, the especially PM2.5～PM10 of 1～20um, be the sensitivity that strengthens low light level scattered signal, added the convex lens of φ 2.5 at the light inlet of optical fiber, the collection solid angle of optical fiber is about 6 ° like this.The light-emitting window of fibre bundle is arranged on the light-sensitive surface of ICCD successively, and scattered light signal becomes pulse electrical signal through ICCD, and the threshold value of choose reasonable pulse electrical signal is to eliminate the influence of dark current.During to the influencing of result, should readjust the threshold value of pulse electrical signal at the light of measuring different polarization states.

3. the inverting of particle shape

For reducing workload, the corresponding relation of optical fiber measurement point and software inverse point is fixed.The corresponding angle of each root optical fiber, if the scattered signal that this position optical fiber is collected and the scattered signal of spheric grain in this position identical (this scattered signal also can be drawn by the Mie scattering theory) of a certain yardstick, then think the scale size of this position correspondence of particle, such 36 positions have just formed 36 points of representing radius size, these points are coupled together, just formed the 3D shape of particle.Granularity and particle shape have confidential relation, in the process of inverting shape, consider the influence of granularity.

Advantage of the present invention

1. ultimate principle is ripe Mie scattering theory

2.36 the method that the orientation fixed point is filled a vacancy is simple

3. the particle shape inverting quick and precisely

Description of drawings

Fig. 1 is a scattering cavity body structure synoptic diagram of the present invention.

Fig. 2 is a particle shape inverting synoptic diagram.

Fig. 3 is a workflow diagram of the present invention.

Fig. 4 is the diameter equivalent sphere synoptic diagram of particle.

Fig. 5 is aerosol particle Mie scatter intensity distribution figure.

Fig. 6 is the calculating of Feret.

Embodiment

Multiple-passage dispersion reverse deduction microgranule tri-dimensional shape detector, it is characterized in that including scattering cavity 1, its meat surface is handled through blackout, the outer wall profile fiber jack 2 of scattering cavity 1, sampling optical fiber 3 is installed in the fiber optic hub 2, scattering cavity 1 top is linked with the incident pipe 4 of the sample introduction particle beams, its below is linked with the exit tube 5 of the sample introduction particle beams that is positioned on the same axis, sheath stream pipe 6 is arranged on the sidewall of the incident pipe 4 of the sample introduction particle beams, but a plurality of Modulating Diode Laser modulators 7 are installed on the sidewall of scattering cavity 1, the emitting light path of each laser modulator 7 all intersects at from described incident pipe and enters the sample introduction particle beams in the scattering cavity 1, and the opposite of each laser modulator 7 is equipped with light absorption pipe 8.

Described scattering cavity 1 is a spherical cavity, the incident pipe 4 of the described sample introduction particle beams and the axis of exit tube pass the centre of sphere of scattering cavity 1, but described Modulating Diode Laser modulator 7 is two, its emitting light path is vertical mutually, and its installed surface is the diametric plane of scattering cavity 1, vertical with the sample introduction particle beams, 30 °～150 ° of polar angles, the position angle is in 360 ° the space, every 15 ° four fiber optic hubs 3 are set, forming 9 position angle discs that are parallel to each other, promptly is to form 4 pairs of circular conical surfaces about the position angle disc symmetry of 90 ° of polar angle directions; 36 fiber optic hubs have also formed two orthogonal discs that respectively contain 18 fiber optic hubs 3 simultaneously, and the angle of the disc and the sample introduction particle beams is 45 °; The termination of sampling optical fiber 3 is equipped with lenticule, places in the scattering cavity 1, and an end of the outside of 36 optical fiber directly enters on the reception target surface of ICCD, by by root optical fiber mark, obtains each corresponding angle particle scattered light electric signal and distributes.

Concrete structure:

One, the junction of sealing scattering chamber parts and the junction of scattering chamber and laser modulator 7, light absorption pipe 8, air inlet and outlet pipe make the scattering chamber not be subjected to the influence of ambient atmosphere.Purge scattering inside by force with pure air, till experiment not being brought the particle of influence.Regulate the airshed of the injector of scattering top of chamber, cooperate sheath stream, make both ratios reach (ratio of reference particle counter) about 1: 6, produce individual particle corpuscullar flow along axial line rectilinear flight.

But two semiconductor laser modulations send the light beam of 650nm, behind laser modulation device, beam shape becomes the rectangle (or ellipse of minor axis 0.3mm, major axis 1.6mm) of high 0.3mm, wide 1.6mm, why modulate like this, reason is: 1. spacing is very little on the corpuscullar flow macroscopic view of individual particle flight, for guaranteeing to collect the scattered signal of individual particle, the height of laser beam (minor axis) is in that satisfy should be as far as possible little under the prerequisite of measurement requirement; 2. the microparticle of individual particle flight flows to end the restriction that pipe has sheath stream, disalignment line a little still, and in order to ensure the collection of particle scattered signal, it is longer slightly that width of light beam (major axis) should be done.

Three, the laser beam after the modulation enters the scattering chamber, and the interior external diameter in scattering chamber is respectively 24mm, 38mm, and for preventing the reflection of inside, scattering chamber, cavity is all done blackout with the part that gos deep into inside cavity and handled.The 36 root distance chamber equidistant optical fiber of the heart that the light scattering signal of particle is distributed on the cavity are collected simultaneously in different positions.

Four, the light-emitting window of fibre bundle is arranged in (see figure 1) on the light-sensitive surface of ICCD successively, scattered light signal becomes pulse electrical signal through ICCD, if the scattered signal that this position optical fiber is collected and the scattered signal of spheric grain in this position identical (this scattered signal also can be drawn by the Mie scattering theory) of a certain yardstick, then think the scale size (seeing Fig. 3,4) of this position correspondence of particle, such 36 positions have just formed 36 points of representing radius size, these points are coupled together, just formed the 3D shape of particle.

Five, polarisation of light influences the scattering nature of particle, thereby the equipment of measuring particle shape adopts circularly polarized light usually, but the realization polarization state is not seen report as yet to the influence of particle scattering nature in same equipment, and the pulsed light beam that the present invention utilizes two bundles to focus on the centre of sphere has simultaneously been realized this point.

Measuring principle

The Mie scattering theory has been inquired into the light scattering problem of the even spheroidal particle of any size and refractive index.Optical wavelength and particle size have determined the PHASE DISTRIBUTION in the particle, and hypothetical particle is spherical, and the ratio of particle size and wavelength is dimensionless scale parameter α:

$\mathrm{\α}=\frac{2\mathrm{\πr}}{\mathrm{\λ}}---\left(1\right)$

Can be divided into two mutually perpendicular polarized components by a particle scattering to the scattered light I (θ) of θ direction, its intensity is respectively I

(θ) and I _// (θ).The former is perpendicular to plane of vision, and the latter is parallel to plane of vision, they respectively with two intensity distribution function i ₁And i ₂Be directly proportional.i ₁And i ₂Provide by following formula:

$i_1(\mathrm{\α},m,\mathrm{\θ})={\left|S_1\right|}^2={\left|\underset{n=1}{\overset{\∞}{\mathrm{\Σ}}}\frac{2n+1}{n(n+1)}(a_n{\mathrm{\π}}_n+b_n{\mathrm{\τ}}_n)\right|}^2={|\mathrm{Re}\left(S_1\right)+\mathrm{Im}\left(S_2\right)|}^2---\left(2\right)$

$i_2(\mathrm{\α},m,\mathrm{\θ})={\left|S_2\right|}^2={\left|\underset{n=1}{\overset{\∞}{\mathrm{\Σ}}}\frac{2n+1}{n(n+1)}(a_n{\mathrm{\τ}}_n+b_n{\mathrm{\π}}_n)\right|}^2={|\mathrm{Re}\left(S_2\right)+\mathrm{Im}\left(S_1\right)|}^2---\left(3\right)$

S ₁And S ₂Be that intensity is I

(θ) and I _//The nondimensional complex amplitude value of scattering wave (θ), m is a complex index of refraction.

$S_1\left(\mathrm{\θ}\right)=\underset{n=1}{\overset{\∞}{\mathrm{\Σ}}}\frac{2n+1}{n(n+1)}[a_n{\mathrm{\π}}_n\left(\cos \mathrm{\θ}\right)+b_n{\mathrm{\τ}}_n\left(\cos \mathrm{\θ}\right)]---\left(4\right)$

$S_2\left(\mathrm{\θ}\right)=\underset{n+1}{\overset{\∞}{\mathrm{\Σ}}}\frac{2n+1}{n(n+1)}[b_n{\mathrm{\π}}_n\left(\cos \mathrm{\θ}\right)+a_n{\mathrm{\τ}}_n\left(\cos \mathrm{\θ}\right)]---\left(5\right)$

Scattering wave is to be made of the subwave that the various multipoles that electric charge in the particle constitutes are launched.First is a dipole radiation, and second portion is the quadrapole radiation, by that analogy to more senior multipole.N electricity part and n magnetic part wave amplitude are used amplitude function a respectively _nAnd b _nExpression.a _nAnd b _nBy the decision of Riccati-Bessel function, be the function of scale parameter α and complex index of refraction m, irrelevant with scatteringangle.π _n(cos θ) and τ _n(cos θ) is only relevant with angle, and it is n rank Legendres (Legendre) the polynomial expression P of argument that the both comprises with cos θ _nThe single order and the second derivative of (cos θ):

$a_n=\frac{{\mathrm{\ψ}}_n^{\′}\left(y\right){\mathrm{\ψ}}_n\left(x\right)-m{\mathrm{\ψ}}_n\left(y\right){\mathrm{\ψ}}_n^{\′}\left(x\right)}{{\mathrm{\ψ}}_n^{\′}\left(y\right){\mathrm{\ζ}}_n\left(x\right)-m{\mathrm{\ψ}}_n\left(y\right){\mathrm{\ζ}}_n^{\′}\left(x\right)}---\left(6\right)$

$b_n=\frac{m{\mathrm{\ψ}}_n^{\′}\left(y\right){\mathrm{\ψ}}_n\left(x\right)-{\mathrm{\ψ}}_n\left(y\right){\mathrm{\ψ}}_n^{\′}\left(x\right)}{m{\mathrm{\Ψ}}_n^{\′}\left(y\right){\mathrm{\ζ}}_n\left(x\right)-{\mathrm{\ψ}}_n\left(y\right){\mathrm{\ζ}}_n^{\′}\left(x\right)}---\left(7\right)$

${\mathrm{\π}}_n\left(\cos \mathrm{\θ}\right)=\frac{{\mathrm{dP}}_n\left(\cos \mathrm{\θ}\right)}{d\left(\cos \mathrm{\θ}\right)}---\left(8\right)$

${\mathrm{\τ}}_n\left(\cos \mathrm{\θ}\right)=\cos \mathrm{\θ}\·{\mathrm{\π}}_n\left(\cos \mathrm{\θ}\right)-{\sin }^2\mathrm{\θ}\frac{{\mathrm{d\π}}_n\left(\cos \mathrm{\θ}\right)}{d\cos \mathrm{\θ}}---\left(9\right)$

ψ in the formula _n(z), χ _n(z) and ζ _n(z) be the Riccati-Bessel function:

ψ _n(z)＝zj _n(z)＝(πz/2) ^1/2J _n+1/2(z)＝S _n(z) (10)

χ _n(z)＝-zn _n(z)＝-(πz/2) ^1/2N ^n+1/2(z)＝C _n(z) (11)

ζ _n(z)＝ψ _n(z)+iχ _n(z) (12)

x＝α＝2πr/λ (13)

y＝mkr (14)

J _N+1/2And N _N+1/2Be respectively half odd-order Bessel (Bessel) function and half odd-order Neumann (Neunann) function, belong to first kind Bessel function and bessel function of the second kind respectively.J _-(n+1/2)Be negative odd-order Bessel function.They are provided by formula (16)-(19) respectively:

$J_{\frac{2n+1}{2}}\left(x\right)={(-1)}^n\sqrt{\frac{2}{\mathrm{\π}}}{x}^{\frac{2n+1}{2}}\frac{d^n}{{\left(\mathrm{xdx}\right)}^n}\left(\frac{\sin x}{x}\right)---\left(15\right)$

$J_{\frac{2n+1}{2}}\left(x\right)=\sqrt{\frac{2}{\mathrm{\π}}}{x}^{\frac{2n+1}{2}}\frac{d^n}{{\left(\mathrm{xdx}\right)}^n}\left(\frac{\cos x}{x}\right)---\left(16\right)$

$N_{\frac{2n+1}{2}}\left(x\right)=-{(-1)}^n{J}_{-\frac{2n+1}{2}}\left(x\right)=-{(-1)}^n\sqrt{\frac{2}{\mathrm{\π}}}{x}^{\frac{2n+1}{2}}\frac{d^n}{{\left(\mathrm{xdx}\right)}^n}\left(\frac{\cos x}{x}\right)---\left(17\right)$

Wherein, n is an integer.So (10) and (11) can be transformed to:

${\mathrm{\ψ}}_n\left(z\right)={(-1)}^n{x}^{n+1}\frac{d^n}{{\left(\mathrm{xdx}\right)}^n}\left(\frac{\sin x}{x}\right)---\left(18\right)$

${\mathrm{\χ}}_n\left(z\right)={(-1)}^n{x}^{n+1}\frac{d^n}{{\left(\mathrm{xdx}\right)}^n}\left(\frac{\cos x}{x}\right)---\left(19\right)$

$P_n\left(\cos \mathrm{\θ}\right)=\underset{k=1}{\overset{n}{\mathrm{\Σ}}}{A}_k{A}_{n-k}\cos (2k-\mathrm{\θ})---\left(20\right)$

Wherein, $A_k=\frac{\left(2k\right)!}{{(2^{k}k!)}^2}.$

The scattering efficiency factor Q of Mie scattering theory _s(α m) is provided by formula (22):

$Q_s(\mathrm{\α},m)=\frac{2}{{\mathrm{\α}}^2}\underset{n=1}{\overset{\∞}{\mathrm{\Σ}}}(2n+1)({\left|a_n\right|}^2+{\left|b_n\right|}^2)---\left(21\right)$

Under the fixing situation of wavelength, because being the dimensionless of particle radius, scale parameter α represents, so the distribution of α just becomes the scale (see figure 5) of particle radius.

When obtaining the scattered signal of certain position optical fiber, can relatively draw the radius that this position produces the spheric grain of onesize scattering, this radius is exactly a particle radius corresponding herein, so obtain the radius of 36 positions of particle, the fixed point of these 36 radiuses is connected in turn, has just formed the three-dimensional picture of particle.

From the above, onesize particle shape difference can cause the difference of scatter distributions, the change of particle direction will cause the change of scatter intensity distribution, and scale size is judged by scatter distributions, so contain certain relation between particle scale and the shape will, therefore independent diameter with projected area or volume inverting is inaccurate, in the present invention, introduces the notion (see figure 6) of average Fei Leite (Feret) diameter:

$F=\frac{F1+F2+F3+...+F36}{36}$

Claims (1)

1. hyperchannel scattered information inverting microparticle 3D shape detection method is characterized in that may further comprise the steps:

(1), design a scattering cavity, its inside surface is handled through blackout, the outer wall of scattering cavity is distributed with several fiber optic hubs, sampling optical fiber is installed in the fiber optic hub, scattering cavity top is linked with the incident pipe of the sample introduction particle beams, its below is linked with the exit tube of the sample introduction particle beams that is positioned on the same axis, sheath stream pipe is arranged on the sidewall of the incident pipe of the sample introduction particle beams, but a plurality of Modulating Diode Laser modulators are installed on the sidewall of scattering cavity, the emitting light path of each laser modulator all intersects at from described incident pipe and enters the sample introduction particle beams in the scattering cavity, and the opposite of each laser modulator is equipped with the light absorption pipe;

(2), purge the scattering inside cavity with pure air, till experiment not being brought the particle of influence, regulate the airshed of the injector at scattering cavity top, cooperate sheath stream, both ratios are reached about 1: 6, produce individual particle corpuscullar flow along axial line rectilinear flight;

(3) but the Modulating Diode Laser modulator sends the light beam of 650nm, the laser beam after the modulation enters the scattering chamber, the optical fiber that the light scattering signal of particle is distributed on the scattering cavity inner wall is collected simultaneously in different positions;

(4), the light-emitting window of fibre bundle is arranged on the light-sensitive surface of ICCD successively, scattered light signal becomes pulse electrical signal through ICCD, if the scattered signal that this position optical fiber is collected is identical at the scattered signal of this position with the spheric grain of a certain yardstick, this scattered signal is drawn by the Mie scattering theory, then think the scale size of this position correspondence of particle, just having formed several and represent the point of radius size of several fiber position couples together these points like this, just formed the 3D shape of particle.

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