Research Article The Magnetic Nanoparticle Movement in

Research ArticleThe Magnetic Nanoparticle Movement in Magnetic FluidCharacterized by the Laser Dynamic Speckle Interferometry

Xijun Wang

Changchun Institute of Optics Fine Mechanics and Physics State Key Laboratory of Applied Optics Chinese Academy of SciencesChangchun 130033 China

Correspondence should be addressed to Xijun Wang xjwangciompaccn

Received 16 July 2013 Revised 25 December 2013 Accepted 9 January 2014 Published 24 February 2014

Academic Editor Rakesh Joshi

Copyright copy 2014 Xijun Wang This is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

A dual scanning laser speckle interferometry experiment was designed to observe the dynamic behavior of the magnetic fluidactuated by a magnetic field In order to improve the spatial resolution of the dynamic speckle measurement the phase delayscanning was used to compensate the additional phase variation which was caused by the transverse scanning The correlationcoefficients corresponding to the temporal dynamic speckle patternswithin the same time interval scattering from the nanoparticleswere calculated in the experiment on nanoscale magnetic clusters In the experiment the speckle of the magnetic nanoparticlefluid movement has been recorded by the lens unmounted CCD within the interferometry strips although the speckle led to thedistinguished annihilation of the light coherenceThe results have showed that the nanoparticle fluid dynamic properties appearedsynergistically in the fringe speckles The analyses of the nanoparticlersquos relative speed and the speckle pattern moving amount inthe fringes have proved the nanoparticlersquos movement in a laminar flow in the experiment

1 Introduction

Amagnetic fluid is a colloidal suspension of the paramagneticnanoparticles in a liquid carrier which can be easily actuatedby applying a magnetic field [1] Therefore the applicationareas have been widened into the nanotechnologies suchas nanogenerators nanopumps and nanomotors and manyother nanodevices with a variety ofmagnetic fluids have beencoming of age [2ndash4]

The dynamic property of magnetic fluids in combinationwith high absorption coefficient to visible light has beenfound useful in optical device applications such as informa-tion displays and light modulators [5ndash8]

Because the performance of magnetic-fluid-based opticaldevices will depend on the movement of magnetic fluidresponding to the applied magnetic field it is significantlycrucial to characterize the behavior of the magnetic particlesin a magnetic field However the dynamics of magneticparticles in magnetic fluid unlike the nanoparticles fixed ina solid bulk material is difficult to characterize by adoptingthe conventional methods such as AFM and SEM Instead

it is possible to use noncontact and nondestructive methodbased on the laser speckle technique [9ndash12]

Although the light scattering method has discoveredapplications in the characterizations of the dynamic laserspeckle from a magnet fluibuiltd [13 14] the contrast of thespeckle or the scattering intensity may open only a generalobservation to the bulk magnet solution The magneticnanoparticles were also covered in the fluid that could notbe observedThe average signal of the PMT (photomultipliertube) or photodiode is too deficient to meet the requirementfor the nanoparticle movement in the solution when theexerted magnetic field drives the magnetic particles rotatingaligning or piling up So the speckle images captured byCCDimage sensor will record an array of optoelectronic data of thespeckle in each equal interval

How to coordinate the speckle movement from a vari-ation of the surface profile resulted in the solution of themoving magnetic particles which could be driven by anelectromagnetic tesla coil array The optical interferometrythat the crucial component works in an AFM is the firstchoice to build up the coordinates in the speckle images

Hindawi Publishing CorporationJournal of NanomaterialsVolume 2014 Article ID 287813 7 pageshttpdxdoiorg1011552014287813

2 Journal of Nanomaterials

Gap

A A998400

(a)

GapInsulator

Channel Mesa

Electrode(II)

Electrode(I)Ferromagnetic layer substrate

(b)

Figure 1 (a) Top view of the device with the spiral electrode coils and the rectangular magnetic gaps (b) Cross-sectional view of the devicewith a magnified view to the vertical layer structure

In order to make stationary interferometry strips the twoquestions should be answered that the higher-order interfer-ometer speckle decreases the coherence of the scattering lightso significantly that the strips could not be found while thetransverse scanning find a uniform view field the nonlinearadditional phase should be compensated by the phase delayto make the strip ldquostillrdquo

While a dual scanning laser speckle interferometry toobserve the dynamic behavior of the magnetic fluid actuatedby amagnetic field was built up the experimental results werediscussed to characterize themovement of the granules in themagnetic fluid

2 Experimental Setup

21 Magnetic Fluid and the Device In the experimentmagnetite Fe

3O4nanoparticles were from the F2+ and F3+

precipitation with the F2+F3+ molar rate 1 18 acting tem-perature 80∘C [15] and keeping pH 9sim10 by gradually drop-ping the concentrated ammonia into the agitation solutionThe magnetite Fe

3O4particles were separated by a magnet

directly The average particle size was around 40 nm by AFMand the saturation magnetization was around 70 emug Themagnetite particles were coated with sodium oleate keepingpH 5sim6 and dispersed in n-nonane (C

9H20) which was one

clear ingredient of commercial keroseneThe operation of a magnetic fluid display device relied

on the modulation of the thickness of a magnetic fluid layerwhich was placed on the substrate and the characterizationwas focused on a magnetic fluid actuator to form a pixelof a display device The actuator consisted of two unitseach with an area of 15 times 05mm2 formed by a thin layerof ferromagnetic thin film enclosing a spiral conductorelectrode which could be manipulated easily by controllingthe current going through the spiral coils in Figure 1(a) [8]The channel stored the magnet fluid and formed the effectivepath to the mesa The length of the channel was 15mm and

its width was the same as the gap in the mesa so the widthwas 15 micron in the design

Most of the magnetic fluid would initially stay in thechannel around the mesa due to the capillarity when noelectric field was applied and only a minute thin solutionlayer of the liquid would reside on top of the mesa area inFigure 1(b)

The thickness of the magnetic fluid was modulated bythe step magnetic field which was generated by the electriccurrent pulse through the circuit underneath the actuatormesa The magnetic force exerted by the electric field drovethe ferrofluids into the region of strong magnetic intensityand made the display pixel darker When the current was offon the other hand the surface tension of the fluid restoredthe force of the liquid back to the original state and the pixelbecame brighter in which the light and dark states of the pixelcould be thereby produced correspondingly

22 Experimental Design The scanning interferometer useda He-Ne laser with the beam collimating expanding split-ting and combining to generate the reference and objectlight to create interferometer patterns practicably Two nearlyparallel light beams one as the object beam was incident tothe magnetic unit containing magnetic fluid and scattered bythe magnetic particles to form a speckle field and the otheras the reference beam was incident to the speckle field whichgenerated interferometer fringes in the speckle field

The transverse scanning device that was a spinningoptical parallel plate keeping the incident angle invariablealigned the object light to the pixel mesa by transversescanning precisely with an additional phase The phase delaywas used to compensate the variation of the additional phasecaused by the view field requirement of the object light Theexperimental setup was shown in Figure 2

Adjusting the angle of the two light beams could changethe interferometer fringe spacing and the fringe contrast inthe laser speckle field Assuming that the object light and

Journal of Nanomaterials 3

Transverse scanning

PS

BS

M4

M2

Sample

Phase

M1

M3

CCD

120596

He-NE laser

Figure 2 Schematic of a dual-scan laser speckle interferometerexperiment

120596120573

B

C

F

A

120579

Dt

120572

E

Figure 3 Transverse scanning plate to subjoin phase delay

reference light were in the same incident angle 119894 and sym-metrically incident to CCD the spacing of the interferometerfringe was given by

Δ119909 =

120582

2 sin 119894 (1)

23 Phase Compensation An additional phase shift was intothe object light path while using a transverse scanning plateas shown in Figure 3 where 120572 was the incidence angle of theplate and 120573 was the refraction angle in Snellrsquos law 119899 sdot sin120573 =sin120572 where 119899was the refractive index of the plate and the airrefractive index was 10

The optical path length 119871 from the incidence point A thatwas the spinning center on the transverse scanning plate tothe point C on the sample surface was given by

119871 = 119899AB + BC = 119899AB + (AD minus AF + CE)

AB = 119905cos120573

AF = AB sdot cos (120572 minus 120573)

CE = AB sdot sin (120572 minus 120573) cot 120579

(2)

where 120579 was the incident light angle of the ferrofluids samplesurface Thus the optical path length could be written as

119871 = AD + 119899 minus cos (120572 minus 120573) + sin (120572 minus 120573) cot 120579 sdot 119905cos120573

(3)

where AD and 120579 were invariants in the experimental setupThe derivative of 119871 versus 120572 which gave the changing rate ofthe optical path length varied with the spinning angle of thetransverse scanning plate Consider119889119871

119889120572

=

119905 sin120573 cos120572119899 cos3120573

[119899 minus cos (120572 minus 120573) + sin (120572 minus 120573) cot 120579]

+

119905 (119899 cos120573 minus cos120572)119899 cos2120573

[sin (120572 minus 120573) + cos (120572 minus 120573) cot 120579]

(4)

The rotation of the transverse scanning plate was drivenby a stepper motor with a miniature step angle 0009∘ OPD(optical path difference) from transverse scanning could beobtained by formulas (3) and (4)TheOPD curve was showedin Figures 4(a) and 4(b) while the thickness of the parallelplate is 05mm

The transverse scanning could be controlled in half wave-length in the setup and Figure 4(a) showed that the tendencyof the OPD varied with the spinning angle depending onformula (4) which is symmetrical with the spinning anglesand nonlinear in the angle range The ferrofluids incidentangle 120579 became smaller and the OPD varied faster So theincident angle was around 2∘ in the experiment

Nearby the spinning angle zero location the curvebecame linear But some light might have reflected back thelaser source and made some noise in the zero angle so inthe experiment the transverse scanning would deviate a littlemore to get the higher resolution in tens nanometers

The optical path of the reference light was adjusted usinga 180∘ prism phase compensation device driven by anotherstepper motor in a straight line reciprocating motion TheOPD created by the phase delay was twice the movementdistance

For a given incidence angle 120572 of the transverse scanningplate a certain amount of phase compensation was to bedetermined so as to determine the rotation angle of the phasedelay stepmotor and also to synchronize the phase delay withthe transverse scanning by creating the driving parameters forboth of the step motors controlled by microcomputer units

3 Experimental Results

He-Ne laser with an output power of 3mW at 6328 nm wasused as the light source and a magnetic fluid film with athickness of about 20120583m was used as the device for test Themagnetic fluid display cell was driven by step rectangularpulses with a duty ratio of 1 2 and a pulse width of 100msThe response time of the device was measured to be around400ms with a driving current of 70mA The device wasplaced horizontally in the optical path

To get an unlimited localization of the speckle image theunmounted lens CCD and the free space propagation model


0

10

20

30

0 20 40 60minus60 minus40 minus20

Spinning angle 120572 (deg measure)

The O

PD in

the s

pinn

ing

(mm

)

Ferrofluids incident angle 05∘Ferrofluids incident angle 1∘Ferrofluids incident angle 2∘

Ferrofluids incident angle 025∘

(a)

0

001

002

003

004

005

0 01 02 03

The O

PD in

the s

pinn

ing

(mm

)




(b)

Figure 4 The OPD induced from the transverse scanning in all angle range (b) was the OPD linear in small angle

were adopted The CCD was placed at 30 cm vertically abovethe sample surface

The energy ratio between the object and the referencelight was adjusted to balance each other using polarizers inorder to produce visible interferometer fringes

The speckle patterns were recorded continuously by theCCD camera with a frame rate of 25 fps and an image size of640 times 480 pixels and the CCD operation was synchronizedwith the electric current pulse driving the magnetic fluidWhile the incident angle in which the light beams shinedupon the CCD was one degree the fringe spacing wasestimated to be 19 120583m by formula (1) The incident angleincreased twice on the contrary the fringe space decreasedtwice nearly

Because the speckle was the highest order coherent ofthe laser beam the interferometry fringe would not be easyto capture even if the laser had an excellent coherenceMaking the two beams equal was the first step to utilize thepolarization method

After the speckle had appeared in the object a beamshined on themagnet fluid device and it was necessary to finda zero order fringe by the detailed adjusting phase delay withminiature step driving In spite of the probably appearingfringes interferometer strip is difficult to observe in nakedsight because of the lesser strip contrast within backgroundnoises

Partly the unstable fringes were captured with the CCDuntil the transverse scanning both stabilized with the magnetparticle movement and synchronized with the phase delay

A set of laser speckle interferometer fringes in the sameintervals recorded by the CCDwas showed from Figures 4(a)to 4(b)

The thin and crowed strips with an arc were the interfer-ometry fringes reflected by the surfaces of the multiple lensesand became main noises

The intensity relation correlation coefficient in neighbornamed ldquoneighbor coefficientrdquo that means the coefficientcalculation as the pairwise correlation From Figures 5(a) to5(f) the neighbor coefficient was respectively 05197 0432905340 08125 and 02175 in Figures 5(a)sim5(f) sequence

The coefficient showed that Figure 5(b) compared withFigure 5(a) began to change as the coefficient decreasedFigure 5(c) compared with Figure 5(b) changed intensivelyas the coefficient became less Figure 5(d) compared withFigure 5(c) began to change slowly as the coefficient recov-ered Figure 5(e) compared with Figure 5(d) tended to stopthe movement as the coefficient became more Figure 5(f)compared with Figure 5(e) stopped the movement as thecoefficient jumped when the driving current of the coil wasoff

To study the speckle profile movement the centerlinesand laser speckle interferometer bright fringes were extractedsimply by the wavelet denoising the contrast enhancementand the binarization algorithm in a MATLAB software Thecalculation from Figure 5 is converted to Figure 6

With the center line of the interferometer bright strip-swere as a calibration and the lower left corner of the centerline from article 1 interferometer fringe calibration to 1 to


(a) (b)

(c) (d)

(e) (f)

Figure 5 The sequent patterns of the dual-scan laser speckle interferometry

the upper right corner to the center line of the interferometerfringes in turn calibration for 2 3

A speckle pattern was identified and circled as a referencefor tracking as shown in Figures 6(a)sim6(f) where the numbernext to the circle represents the relative position of the specklewith respect to an interferometer fringe The black mark inthe middle of the reference speckle was the centroid of thespeckle The origin of the graph corresponds to Figure 6(a)The marked number 39 in Figure 6(a) was shown as thespeckle and strip tracking coordinates

To calculate the speckle movement from Figures 6(a) to6(b) the speckle movement was 07 strip and the otherswere 11 10 minus06 and minus16 strips The speckle movedforward or backward in the interferometry strips because thenanoparticles were driven by the coil current in on or offstate

The speckle patternmoving amount in the fringes showedthat the nanoparticles moved quicker in the piling up thanin the quitting in the same time intervals Therefore theelectromagnetic force was less than the gravity and capillarityto keep laminar flow of the nanoparticle fluid but not theturbulence flow of the solution

Every strip reflected light expressed twice OPD of onewavelength 6328 nm so one strip is related to 63282 =3164 nm variation of the magnetic nanoparticles in theinterval 125 second Furthermore the nanoparticle pilingrate is around 76 micron per second The mesa area was15 times 05mm2 and the effective ldquochannelrdquo area was 15 times0015mm2 so the relative speed between nanoparticles in thechannel was 03mms In other words one step pulse madethe nanoparticle move sim0325mm (12 micron) in which thedistance was far less than the path length of the solution


39

(a)

46

(b)

57

(c)

67

(d)

61

(e)

45

(f)

Figure 6 Image binarization and tracking of the speckle pattern movement

Furthermore the nanoparticlersquos relative speed variation alsoproved that the nanoparticlersquos movement in the experimentwas a laminar flow

4 Conclusions

Although the laser speckle was a higher order coherentphenomenon and the speckle led to the distinguished anni-hilation of the light coherence the speckle of the magneticnanoparticle fluid movement would be recorded by CCDwithin the interferometry strips The development of themagnetic nanoparticle fluid characterization focused on adynamic interaction of the magnet nanoparticles

It was obvious that the scanning interferometry specklecould capture the nanoparticle and nanostructurersquos move-ments which was different from the light scatting studies

which focused on measuring the scattering intensity with astatistical averaged calculation in contrast with the patternsor with a phase microscope method in a static microndimension of the speckle patterns [13 14]

The experiment showed that the nanoparticles fluiddynamic properties could synergistically appear in the fringespeckles The analysis of the nanoparticle relative speedand the speckle pattern moving amount in the fringesproved the nanoparticlesrsquo movement in a laminar flow in theexperiment

Conflict of Interests

The author declares that there is no conflict of interestsregarding the publication of this paper


Acknowledgments

The author is fully grateful for the support of the study by theNational Science Fund of China (NSFC) (no 60748026) andKorea Science and Engineering Foundation (KOSEF) (Grantno F01-2005-000-10169-0)

References

[1] B M Berkovsky V F Medvedev and M S Krakov MagneticFluids Engineering and Applications Oxford University PressOxford UK 1993

[2] M Zahn ldquoMagnetic fluid and nanoparticle applications tonanotechnologyrdquo Journal of Nanoparticle Research vol 3 no 1pp 73ndash78 2001

[3] K Nakatsuka ldquoTrends of magnetic fluid applications in JapanrdquoJournal of Magnetism and Magnetic Materials vol 122 no 1ndash3pp 387ndash394 1993

[4] K Raj B Moskowitz and R Casciari ldquoAdvances in ferrofluidtechnologyrdquo Journal of Magnetism and Magnetic Materials vol149 no 1-2 pp 174ndash180 1995

[5] J-W Seo and S J Park ldquoAn experimental study of light mod-ulator using magnetic fluid for display applicationsrdquo Journal ofMagnetism andMagnetic Materials vol 192 no 3 pp 499ndash5041999

[6] J-W Seo S-M Jeon S J Park and H-S Lee ldquoAn experimentaland numerical investigation of flat panel display cell usingmagnetic fluidrdquo Journal of Magnetism and Magnetic Materialsvol 252 pp 353ndash355 2002

[7] J-W Seo H Kim and S Sung ldquoDesign and fabrication of amagnetic microfluidic light modulator using magnetic fluidrdquoJournal of Magnetism and Magnetic Materials vol 272ndash276 ppE1787ndashE1789 2004

[8] J-W Seo and X-J Wang ldquoMagnetic-fluid microelectrorne-chanical light modulatorrdquoOptics and Precision Engineering vol13 no 5 pp 542ndash547 2005

[9] C A Thompson K J Webb and A M Weiner ldquoDiffusivemedia characterization with laser specklerdquo Applied Optics vol36 no 16 pp 3726ndash3734 1997

[10] R-S Lu G-Y Tian D Gledhill and SWard ldquoGrinding surfaceroughness measurement based on the co-occurrence matrix ofspeckle pattern texturerdquoAppliedOptics vol 45 no 35 pp 8839ndash8847 2006

[11] W-W Feng M-J Liu X-Q Wang F-R Shi J Zhang and R-X Jiang ldquoFeature extraction and recognition of laser speckle forspecialmaterial surfacerdquo Infrared and Laser Engineering vol 36no 2 pp 186ndash188 2007 (Chinese)

[12] X-F Li J Xu J-J Luo L Cao and S Zhang ldquoNoise analyzingand denoising of intensity image for laser active imagingsystemrdquo Infrared and Laser Engineering vol 40 no 2 pp 332ndash337 2011 (Chinese)

[13] J Philip and J M Laskar ldquoOptical properties and applicationsof ferrofluidsmdasha reviewrdquo Journal of Nanofluids vol 1 no 1 pp3ndash20 2012

[14] S Brojabasi and J Philip ldquoMagnetic field dependant backscat-tering of light in water based ferrofluid containing polymercovered Fe

3O4nanoparticlesrdquo Journal of Applied Physics vol

113 Article ID 054902 2013[15] S Wu A-Z Sun F-Q Zhai et al ldquoFe

3O4magnetic nanopar-

ticles synthesis from tailings by ultrasonic chemical co-precipitationrdquo Materials Letters vol 65 no 12 pp 1882ndash18842011

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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CompositesJournal of

NanoparticlesJournal of



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NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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CrystallographyJournal of


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research



MetallurgyJournal of


BioMed Research International

MaterialsJournal of


Nano

materials


Journal ofNanomaterials


Gap

A A998400

(a)

GapInsulator

Channel Mesa

Electrode(II)

Electrode(I)Ferromagnetic layer substrate

(b)

Figure 1 (a) Top view of the device with the spiral electrode coils and the rectangular magnetic gaps (b) Cross-sectional view of the devicewith a magnified view to the vertical layer structure

In order to make stationary interferometry strips the twoquestions should be answered that the higher-order interfer-ometer speckle decreases the coherence of the scattering lightso significantly that the strips could not be found while thetransverse scanning find a uniform view field the nonlinearadditional phase should be compensated by the phase delayto make the strip ldquostillrdquo

While a dual scanning laser speckle interferometry toobserve the dynamic behavior of the magnetic fluid actuatedby amagnetic field was built up the experimental results werediscussed to characterize themovement of the granules in themagnetic fluid

2 Experimental Setup

21 Magnetic Fluid and the Device In the experimentmagnetite Fe

3O4nanoparticles were from the F2+ and F3+

precipitation with the F2+F3+ molar rate 1 18 acting tem-perature 80∘C [15] and keeping pH 9sim10 by gradually drop-ping the concentrated ammonia into the agitation solutionThe magnetite Fe

3O4particles were separated by a magnet

directly The average particle size was around 40 nm by AFMand the saturation magnetization was around 70 emug Themagnetite particles were coated with sodium oleate keepingpH 5sim6 and dispersed in n-nonane (C

9H20) which was one

clear ingredient of commercial keroseneThe operation of a magnetic fluid display device relied

on the modulation of the thickness of a magnetic fluid layerwhich was placed on the substrate and the characterizationwas focused on a magnetic fluid actuator to form a pixelof a display device The actuator consisted of two unitseach with an area of 15 times 05mm2 formed by a thin layerof ferromagnetic thin film enclosing a spiral conductorelectrode which could be manipulated easily by controllingthe current going through the spiral coils in Figure 1(a) [8]The channel stored the magnet fluid and formed the effectivepath to the mesa The length of the channel was 15mm and

its width was the same as the gap in the mesa so the widthwas 15 micron in the design

Most of the magnetic fluid would initially stay in thechannel around the mesa due to the capillarity when noelectric field was applied and only a minute thin solutionlayer of the liquid would reside on top of the mesa area inFigure 1(b)

The thickness of the magnetic fluid was modulated bythe step magnetic field which was generated by the electriccurrent pulse through the circuit underneath the actuatormesa The magnetic force exerted by the electric field drovethe ferrofluids into the region of strong magnetic intensityand made the display pixel darker When the current was offon the other hand the surface tension of the fluid restoredthe force of the liquid back to the original state and the pixelbecame brighter in which the light and dark states of the pixelcould be thereby produced correspondingly

22 Experimental Design The scanning interferometer useda He-Ne laser with the beam collimating expanding split-ting and combining to generate the reference and objectlight to create interferometer patterns practicably Two nearlyparallel light beams one as the object beam was incident tothe magnetic unit containing magnetic fluid and scattered bythe magnetic particles to form a speckle field and the otheras the reference beam was incident to the speckle field whichgenerated interferometer fringes in the speckle field

The transverse scanning device that was a spinningoptical parallel plate keeping the incident angle invariablealigned the object light to the pixel mesa by transversescanning precisely with an additional phase The phase delaywas used to compensate the variation of the additional phasecaused by the view field requirement of the object light Theexperimental setup was shown in Figure 2

Adjusting the angle of the two light beams could changethe interferometer fringe spacing and the fringe contrast inthe laser speckle field Assuming that the object light and


Transverse scanning

PS

BS

M4

M2

Sample

Phase

M1

M3

CCD

120596

He-NE laser


120596120573

B

C

F

A

120579

Dt

120572

E



Δ119909 =

120582

2 sin 119894 (1)




AB = 119905cos120573



(2)



(3)


119889120572

=

119905 sin120573 cos120572119899 cos3120573


+

119905 (119899 cos120573 minus cos120572)119899 cos2120573


(4)










0

10

20

30



The O

PD in

the s

pinn

ing

(mm

)



(a)

0

001

002

003

004

005

0 01 02 03

The O

PD in

the s

pinn

ing

(mm

)




(b)















(a) (b)

(c) (d)

(e) (f)








39

(a)

46

(b)

57

(c)

67

(d)

61

(e)

45

(f)



4 Conclusions








Acknowledgments


References


























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




Transverse scanning

PS

BS

M4

M2

Sample

Phase

M1

M3

CCD

120596

He-NE laser


120596120573

B

C

F

A

120579

Dt

120572

E



Δ119909 =

120582

2 sin 119894 (1)




AB = 119905cos120573



(2)



(3)


119889120572

=

119905 sin120573 cos120572119899 cos3120573


+

119905 (119899 cos120573 minus cos120572)119899 cos2120573


(4)










0

10

20

30



The O

PD in

the s

pinn

ing

(mm

)



(a)

0

001

002

003

004

005

0 01 02 03

The O

PD in

the s

pinn

ing

(mm

)




(b)















(a) (b)

(c) (d)

(e) (f)








39

(a)

46

(b)

57

(c)

67

(d)

61

(e)

45

(f)



4 Conclusions








Acknowledgments


References


























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




0

10

20

30



The O

PD in

the s

pinn

ing

(mm

)



(a)

0

001

002

003

004

005

0 01 02 03

The O

PD in

the s

pinn

ing

(mm

)




(b)















(a) (b)

(c) (d)

(e) (f)








39

(a)

46

(b)

57

(c)

67

(d)

61

(e)

45

(f)



4 Conclusions








Acknowledgments


References


























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




(a) (b)

(c) (d)

(e) (f)








39

(a)

46

(b)

57

(c)

67

(d)

61

(e)

45

(f)



4 Conclusions








Acknowledgments


References


























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




39

(a)

46

(b)

57

(c)

67

(d)

61

(e)

45

(f)



4 Conclusions








Acknowledgments


References


























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




Acknowledgments


References


























CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials










CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials



Documents

Research Article The Magnetic Nanoparticle Movement in