Introduction to Laser Diffraction

Transcription

1 Itroductio to Laser Diffractio Jeffrey Bodycomb, Ph.D. HORIBA Scietific

2 0.001 Size: Particle Diameter (m) Methods Apps Sizes Nao-Metric Fie Coarse Colloidal Macromolecules Suspesios ad Slurries Powders Electro Microscope Acoustic Spectroscopy Sieves Light Obscuratio Laser Diffractio LA-960 Electrozoe Sesig DLS SZ-100 Sedimetatio Disc-Cetrifuge Optical Microscopy PSA300, Camsizer

3 Core Priciple Ca ivestigate a particle with light ad determie its size

4 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, wavelegth of light i particle) 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

5 LA-960 Optics

6 Diffractio Patter

7 Light Expressed i just i y-directio H E H E si( ky ) 0 t si( ky ) 0 t Oscillatig electric field Oscillatig magetic field (orthogoal to electric field) Complemets of weelookag.blogspot.com

8 Light: Iterferece Look at just the electric field. E E0 si( kxt ) Oscillatig electric field E E si( kx ) 0 t Secod electric field with phase shift

9 Path Legth Differece Path legth differece is s si( s r 0 Detector (far away)

10 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.

11 Laser Diffractio Models Large particles -> Frauhofer More straightforward math Large, opaque particles as 2-D disks Use this to develop ituitio All particle sizes -> Mie Messy calculatios All particle sizes as 3-D spheres

12 Frauhofer Approximatio dimesioless size parameter a = pd/l; 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 a >>1)* If l=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.

13 Frauhofer: Effect of Particle Size

14 Diffractio Patter: Large vs. Small Particles LARGE PARTICLE: Peaks at low agles Strog sigal Narrow Patter - High itesity Wide Patter - Low itesity SMALL PARTICLE: Peaks at larger agles Weak Sigal

15 Poll How may of you work with particles with sizes over 1 mm? How may of you work with particles with sizes over 25 micros? How may of you work with particles with sizes less tha 1 micro?

16 Mie Scatterig a b x m S p 1 1 1) ( 1 2 ),, ( a b x m S p 1 2 1) ( 1 2 ),, ( ),, ( S S r k I x m I s ) '( ) ( ) '( ) ( ) '( ) ( ) '( ) ( 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 p si ) (cos 1 P ) (cos 1 P d d Use computer for the calculatios!

17 Mie The equatios are messy, but require just three iputs which are show below. The ature of the iputs is importat. x pd l 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. m p m We eed to kow relative refractive idex. As this goes to 1 there is o scatterig. Scatterig Agle

18 Refractive Idex Real part-chage i wavelegth Imagiary partabsorptio i particle = i Good = 1 (for air)

19 Short Wavelegths for Smallest Particles By usig blue light source, we double the scatterig effect of the particle. This leads to more sesitivity. This plot also tells you that you eed to have the backgroud stable to withi 1% of the scattered sigal to measure small particles accurately.

20 Why 2 Wavelegths? 30, 40, 50, 70 m latex stadards Data from very small particles.

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

22 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.

23 Compariso, Large Particles For large particles, match is good out to through several peaks.

24 Compariso, Small Particles For small particles, match is poor. Use Mie.

25 Practical Applicatio: Glass Beads

26 Practical Applicatio: CMP Slurry

27 Aalyzig Data: Covergece

28 Other factors Size, Shape, ad Optical Properties also affect the agle ad itesity of scattered light Extremely difficult to extract shape iformatio without a priori kowledge Assume spherical model

29 Pop Quiz What particle shape is used for laser diffractio calculatios? A. Hard sphere B. Cube C. Triagle D. Easy sphere

30 Pop Quiz What particle shape is used for laser diffractio calculatios? A. Hard sphere B. Cube C. Triagle D. Easy sphere Either gets full credit!

31 Measuremet Workflow Prepare the sample Good samplig ad dispersio a must! May eed to use surfactat or admixture

32 Measuremet Workflow Prepare the system Alig laser to maximize sigal-to-oise Acquire blak/backgroud to reduce oise

33 Measuremet Workflow Itroduce sample Add sample to specific cocetratio rage Pump sample through measuremet zoe Fial dispersio (ultrasoic)

34 Flexible Sample Hadlers 10 ml 35 ml 200 ml powders Wide rage of sample cells depedig o applicatio High sesitivity keeps sample requiremets at miimum Techology has advaced to remove trade-offs

35 How much sample (wet)? It depeds o sample, but here are some examples. LA-950 Sample Hadlers Dispersig Volume (ml) Larger, broad distributios require larger sample volume Lower volume samplers for precious materials or solvets Aqua/SolvoFlow MiiFlow Fractio Cell 15 Small Volume Fractio Cell 10 Note: Fractio cell has oly magetic stir bar, ot for large or heavy particles Media (D50): 114 µm Sample Amout: 1.29 mg Media (D50): 35 m Sample Amout: 132 mg Media (D50): 9.33 µm Sample Amout: mg Bio polymer Colloidal silica Magesium stearate

36 How much sample (dry)? It depeds o sample.. Larger, broad distributios require larger sample quatity Ca measure less tha 5 mg (over a umber of particle sizes). Media (D50): 114 µm Sample Amout: 1.29 mg Media (D50): 35 m Sample Amout: 132 mg Media (D50): 9.33 µm Sample Amout: mg wet wet wet Bio polymer Colloidal silica Magesium stearate

37 Measuremet Workflow Measuremet Click Measure butto Hardware measures scattered light distributio Software the calculates size distributio

38 Pump? Dispersio? LA-960 Method Expert There are four importat tests Circulatio Cocetratio Dispersio Duratio

39 LA-960 Method Expert Method Expert guides user to prepare the LA-960 for each test Results displayed i multiple formats: PSD, D50, R-parameter

40 Reproducibility Mg Stearate dry, 2 bar

41 Cemet Dry D10 D50 d90 Portlad Cemet Portlad Cemet Portlad Cemet Average Std. Dev CV (%)

42 Cemet Wet Measure i isopropyl alcohol (IPA) (ot water) D10 D50 d90 Portlad Cemet Portlad Cemet Portlad Cemet Average Std. Dev CV (%)

43 Istrumet to istrumet variatio 20 istrumets, 5 stadards Sample CV D10 CV D50 CV D90 PS202 (3-30µm) 2% 1% 2% PS213 (10-100µm) 2% 2% 2% PS225 (50-350µm) 1% 1% 1% PS235 ( µm) 1% 1% 2% PS240 ( µm) 3% 2% 2% These are results from ruig polydisperse stadards o 20 differet istrumets

44 Istrumet to istrumet variatio Idustrial Samples 4 istrumets, real sample

45 Applicatio: Pigmet Hidig Power Operator depedet, eed to wait for dryig. Operator idepedet, o eed to wait for dryig.

46 Diffractio Drawbacks Volume basis by default Although excellet for mass balacig, caot calculate umber basis without sigificat error No shape iformatio Number Area Volume

47 The Beefits Wide size rage Most advaced aalyzer measures from 10 ao to 5 milli Flexible sample hadlers Powders, suspesios, emulsios, pastes, creams Very fast Allows for high throughput, 100 s of samples/day Easy to use May istrumets are highly automated with self-guided software Good desig = Excellet precisio Reduces uecessary ivestigatio/dowtime First priciple measuremet No calibratio ecessary Massive global istall base/history

48 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