How to Select the Best Refractive Index

Transcription

1 How to Select the Best Refractive Idex Jeffrey Bodycomb, Ph.D. HORIBA Scietific HORIBA, Ltd. All rights reserved.

2 Outlie Laser Diffractio Calculatios Importace of Refractive Idex Choosig Refractive Idex Comparig Methods for Choosig Refractive Idex

3 Outlie Laser Diffractio Calculatios Importace of Refractive Idex Choosig Refractive Idex Comparig Methods for Choosig Refractive Idex

4 LA-950 Optics

5 Whe a Light beam Strikes a Particle Some of the light is: Diffracted Reflected Refracted Absorbed ad Reradiated Reflected Refracted Absorbed ad Reradiated Diffracted Small particles require kowledge of optical properties: Real Refractive Idex (bedig of light) Imagiary Refractive Idex (absorptio of light withi particle) Refractive idex values less sigificat for large particles Light must be collected over large rage of agles

6 Diffractio Patter

7 Usig Models to Iterpret Scatterig Scatterig data typically caot be iverted to fid particle shape. We use optical models to iterpret data ad uderstad our experimets.

8 The Calculatios There is o eed to kow all of the details. The LA-950 software hadles all of the calculatios with miimal itervetio.

9 Laser Diffractio Models Large particles -> Frauhofer More straightforward math Large, opaque particles Use this to develop ituitio All particle sizes -> Mie Messy calculatios All particle sizes

10 Frauhofer Approximatio dimesioless size parameter = D/; J 1 is the Bessel fuctio of the first kid of order uity. Assumptios: a) all particles are much larger tha the light wavelegth (oly scatterig at the cotour of the particle is cosidered; this also meas that the same scatterig patter is obtaied as for thi two-dimesioal circular disks) b) oly scatterig i the ear-forward directio is cosidered (Q is small). Limitatio: (diameter at least about 40 times the wavelegth of the light, or >>1)* If =650m (.65 m), the 40 x.65 = 26 m If the particle size is larger tha about 26 m, the the Frauhofer approximatio gives good results. Rephrased, results are isesitive to refractive idex choice.

11 Mie Scatterig a b x m S 1 1 1) ( 1 2 ),, ( a b x m S 1 2 1) ( 1 2 ),, ( ) '( ) ( ) '( ) ( ) '( ) ( ) '( ) ( mx x x mx m mx x x mx m a ) '( ) ( ) '( ) ( ) '( ) ( ) '( ) ( mx x m x mx mx x m x mx b : Ricatti-Bessel fuctios P 1 :1 st order Legedre Fuctios si ) (cos 1 P ) (cos 1 P d d ),, ( S S r k I x m I s Use a existig computer program for the calculatios!

12 Mie The equatios are messy, but require just three iputs which are show below. The ature of the iputs is importat. m x D p m Decreasig wavelegth is the same as icreasig size. So, if you wat to measure small particles, decrease wavelegth so they appear bigger. That is, get a blue light source for small particles. We eed to kow relative refractive idex. As this goes to 1 there is o scatterig. Scatterig Agle

13 Effect of Size As diameter icreases, itesity (per particle) icreases ad locatio of first peak shifts to smaller agle.

14 Mixig Particles? Just Add The result is the weighted sum of the scatterig from each particle. Note how the first peak from the 2 micro particle is suppressed sice it matches the valley i the 1 micro particle.

15 Outlie Laser Diffractio Calculatios Importace of Refractive Idex Choosig Refractive Idex Comparig Methods for Choosig Refractive Idex

16 What do we mea by RI? Optical properties of particle differet from surroudig medium Note that itesity ad wavelegth of light chages i particle (typical dispersats do ot show sigificat absorptio) Wavelegth chages are described by real compoet Itesity chages are described by imagiary compoet = i = 1 (for air)

17 Effect of RI: imagiary term As imagiary term (absorptio) icreases locatio of first peak shifts to smaller agle.

18 Effect of RI: Real Term It depeds.

19 Practical Applicatio: Glass Beads

20 Practical Applicatio: CMP Slurry

21 Effect of RI: Cemet Fixed absorbace, vary real Fixed real, vary absorbace

22 Refractive Idex Effect Most proouced whe: Particles are spherical Particles are trasparet RI of particle is close to RI of fluid Particle size is close to wavelegth of light source Least proouced whe: Particles are ot spherical Particles are opaque RI of particle is larger tha RI of the fluid Particle size is much larger tha wavelegth of the light source

23 Outlie Laser Diffractio Calculatios Importace of Refractive Idex Choosig Refractive Idex Comparig Methods for Choosig Refractive Idex

24 Dissolve sample at differet cocetratios Plot coc. vs. RI Extrapolate to ifiite cocetratio Abbe Refractometer 1.8 Refractive Idex Cocetratio

25 Becke Lies Bright lie is called the Becke lie ad will always occur closest to the substace with a higher refractive idex

26 Becke Lie Test As you move away from the thi sectio (raisig the objective or lowerig the stage), the Becke Lie appears to move ito the material with greater refractive idex. A particle that has greater refractive idex tha its surroudigs will refract light iward like a crude les. A particle that has lower refractive idex tha its surroudigs will refract light outward like a crude divergig les.

27 Becke Lie Test

28 Luxpop.com Note RI is depedet o wavelegth of light. Ca adjust RI for red & blue light, but oly eed to for small, absorbig particles.

29 Google Search

30 Usig R Value for i

31 What is R parameter? y i is the measured scatterig at detector I y(x i ) is the scatterig data at detector i calculated from the size distributio N is the umber of detector chaels used i the calculatio.

32 Chagig RI

33 Chagig RI

34 Chagig RI

35 Usig R Value for i Real compoet = 1.57 via Becke lie Vary imagiary compoet, miimize Chi square & R parameter

36 Automatio by Method Expert Aalytical coditios Calculatio coditios View Method Expert webiar TE004 i Dowload Ceter

37 Automated RI Computatio Real part study Need to fix imagiary part Set up to 5 real parts Software will compute all RI ad display R parameter variatio with RI selectio

38 Automated RI Computatio

39 Automated RI Computatio

40 Summary Measure sample, recalculate w/differet RI see how importat it is Use oe of the described approaches to determie the real compoet Recalculate usig differet imagiary compoet Choose result that miimizes R parameter, but also check if result makes sese You wish you had Method Expert by your side

41 Outlie Laser Diffractio Calculatios Importace of Refractive Idex Choosig Refractive Idex Comparig Methods for Choosig Refractive Idex

42 Study o TiO 2 Look up real refractive idex, use R parameter to fid imagiary.

43 Effect of RI o R parameter

44 Effect of RI o measured D50

45 Effect of RI o measured D10

46 Effect of RI o measured D90

47

48 Results Model D10, micros Differece from correct value D50, micros Differece from correct value D90, micros i (correct value) i % % % Frauhofer % % % Miimize R parameter ( i) % % % Differece from correct value

49 Recommedatios Use the Mie model whe evaluatig laser diffractio data. Search for literature for real ad imagiary refractive idex values or measure your sample yourself. If literature values are ot available, use the data to estimate values, it is better tha guessig or usig the Frauhofer model. Oce you choose a refractive idex value, stick with it.

50 Q&A Ask a questio at labifo@horiba.com Keep readig the mothly HORIBA Particle ewsletter! Visit the Dowload Ceter to fid the video ad slides from this webiar. Jeff Bodycomb, Ph.D. P: E: jeff.bodycomb@horiba.com

51 Thak you

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