© 2013HORIBA, Ltd. All rights reserved.
How to Select the Best Refractive
Index
Jeffrey Bodycomb, Ph.D.
HORIBA Scientific
...
© 2013 HORIBA, Ltd. All rights reserved.
Outline
Laser Diffraction Calculations
Importance of Refractive Index
Choosing...
© 2013 HORIBA, Ltd. All rights reserved.
Outline
Laser Diffraction Calculations
Importance of Refractive Index
Choosing...
© 2013 HORIBA, Ltd. All rights reserved.
LA-950 Optics
© 2013 HORIBA, Ltd. All rights reserved.
When a Light beam Strikes a Particle
 Some of the light is:
 Diffracted
 Refle...
© 2013 HORIBA, Ltd. All rights reserved.
Diffraction Pattern
© 2013 HORIBA, Ltd. All rights reserved.
Using Models to Interpret
Scattering
Scattering data typically cannot be
inverte...
© 2013 HORIBA, Ltd. All rights reserved.
The Calculations
There is no need to know all of the
details.
The LA-950 softwa...
© 2013 HORIBA, Ltd. All rights reserved.
Laser Diffraction Models
Large particles -> Fraunhofer
More straightforward mat...
© 2013 HORIBA, Ltd. All rights reserved.
Fraunhofer Approximation
dimensionless size parameter  = D/;
J1 is the Bessel ...
© 2013 HORIBA, Ltd. All rights reserved.
Mie Scattering
 nnnn ba
nn
n
xmS  


 

1
1
)1(
12
),,(
 nnnn ba
nn
...
© 2013 HORIBA, Ltd. All rights reserved.
Mie

Dx 
m
p
n
n
m 
Decreasing wavelength is the same as
increasing size. So,...
© 2013 HORIBA, Ltd. All rights reserved.
Effect of Size
As diameter increases, intensity (per particle) increases
and loca...
© 2013 HORIBA, Ltd. All rights reserved.
Mixing Particles? Just Add
The result is the weighted sum of the scattering from ...
© 2013 HORIBA, Ltd. All rights reserved.
Outline
Laser Diffraction Calculations
Importance of Refractive Index
Choosing...
© 2013 HORIBA, Ltd. All rights reserved.
What do we mean by RI?
 Optical properties of particle different from surroundin...
© 2013 HORIBA, Ltd. All rights reserved.
Effect of RI: imaginary term
As imaginary term (absorption) increases location of...
© 2013 HORIBA, Ltd. All rights reserved.
Effect of RI: Real Term
It depends….
© 2013 HORIBA, Ltd. All rights reserved.
Practical Application: Glass Beads
© 2013 HORIBA, Ltd. All rights reserved.
Practical Application: CMP Slurry
© 2013 HORIBA, Ltd. All rights reserved.
Effect of RI: Cement
Fixed absorbance, vary real Fixed real, vary absorbance
© 2013 HORIBA, Ltd. All rights reserved.
Refractive Index Effect
Most pronounced when:
 Particles are spherical
 Particl...
© 2013 HORIBA, Ltd. All rights reserved.
Outline
Laser Diffraction Calculations
Importance of Refractive Index
Choosing...
© 2013 HORIBA, Ltd. All rights reserved.
Abbe Refractometer
 Dissolve sample at
different concentrations
 Plot conc. vs....
© 2013 HORIBA, Ltd. All rights reserved.
Becke Lines
Bright line is called the Becke line and will always occur closest to...
© 2013 HORIBA, Ltd. All rights reserved.
Becke Line Test
A particle that has greater refractive index than
its surrounding...
© 2013 HORIBA, Ltd. All rights reserved.
Becke Line Test
© 2013 HORIBA, Ltd. All rights reserved.
Luxpop.com
Note RI is dependent on
wavelength of light.
Can adjust RI for red &
b...
© 2013 HORIBA, Ltd. All rights reserved.
Google Search
© 2013 HORIBA, Ltd. All rights reserved.
Using R Value for i
© 2013 HORIBA, Ltd. All rights reserved.
What is R parameter?
yi is the measured scattering at detector I
y(xi) is the sca...
© 2013 HORIBA, Ltd. All rights reserved.
Changing RI
© 2013 HORIBA, Ltd. All rights reserved.
Changing RI
© 2013 HORIBA, Ltd. All rights reserved.
Changing RI
© 2013 HORIBA, Ltd. All rights reserved.
Using R Value for i
Real component = 1.57 via Becke line
Vary imaginary component...
© 2013 HORIBA, Ltd. All rights reserved.
Automation by Method Expert
 Analytical conditions  Calculation conditions
View...
© 2013 HORIBA, Ltd. All rights reserved.
Automated RI Computation
 Real part study
 Need to fix imaginary part
 Set up ...
© 2013 HORIBA, Ltd. All rights reserved.
Automated RI Computation
© 2013 HORIBA, Ltd. All rights reserved.
Automated RI Computation
© 2013 HORIBA, Ltd. All rights reserved.
Summary
 Measure sample, recalculate w/different RI –
see how important it is
 ...
© 2013 HORIBA, Ltd. All rights reserved.
Outline
Laser Diffraction Calculations
Importance of Refractive Index
Choosing...
© 2013 HORIBA, Ltd. All rights reserved.
Study on TiO2
Look up real refractive index, use R parameter to find imaginary.
© 2013 HORIBA, Ltd. All rights reserved.
Effect of RI on R parameter
© 2013 HORIBA, Ltd. All rights reserved.
Effect of RI on measured
D50
© 2013 HORIBA, Ltd. All rights reserved.
Effect of RI on measured
D10
© 2013 HORIBA, Ltd. All rights reserved.
Effect of RI on measured
D90
© 2013 HORIBA, Ltd. All rights reserved.
© 2013 HORIBA, Ltd. All rights reserved.
Results
Model D10,
microns
Difference
from
correct
value
D50,
microns
Difference
...
© 2013 HORIBA, Ltd. All rights reserved.
Recommendations
 Use the Mie model when evaluating laser
diffraction data.
 Sea...
© 2013 HORIBA, Ltd. All rights reserved.
Q&A
Ask a question at labinfo@horiba.com
Keep reading the monthly HORIBA Particle...
© 2013 HORIBA, Ltd. All rights reserved.
Thank you
© 2013 HORIBA, Ltd. All rights reserved.
Danke
Gracias
Большое спасибо
Grazie
‫ر‬ْ‫ك‬ُ‫ش‬‫ا‬ Σας ευχαριστούμε
감사합니다
Obriga...
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How to Select the Best Refractive Index for Particle Size Analysis

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Dr. Jeff Bodycomb discusses the process HORIBA uses to select the best possible refractive index. This information is valuable for anyone using any type of laser diffraction particle size analyzer regardless of manufacturer or model.

This presentation covers the following topics:

* Available resources and current thinking
* Automated RI determination with the Method Expert
* Effect on accuracy of using good, bad, and no refractive index

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How to Select the Best Refractive Index for Particle Size Analysis

  1. 1. © 2013HORIBA, Ltd. All rights reserved. How to Select the Best Refractive Index Jeffrey Bodycomb, Ph.D. HORIBA Scientific www.horiba.com/us/particle
  2. 2. © 2013 HORIBA, Ltd. All rights reserved. Outline Laser Diffraction Calculations Importance of Refractive Index Choosing Refractive Index Comparing Methods for Choosing Refractive Index
  3. 3. © 2013 HORIBA, Ltd. All rights reserved. Outline Laser Diffraction Calculations Importance of Refractive Index Choosing Refractive Index Comparing Methods for Choosing Refractive Index
  4. 4. © 2013 HORIBA, Ltd. All rights reserved. LA-950 Optics
  5. 5. © 2013 HORIBA, Ltd. All rights reserved. When a Light beam Strikes a Particle  Some of the light is:  Diffracted  Reflected  Refracted  Absorbed and Reradiated Reflected Refracted Absorbed and Reradiated Diffracted  Small particles require knowledge of optical properties:  Real Refractive Index (bending of light)  Imaginary Refractive Index (absorption of light within particle)  Refractive index values less significant for large particles  Light must be collected over large range of angles
  6. 6. © 2013 HORIBA, Ltd. All rights reserved. Diffraction Pattern
  7. 7. © 2013 HORIBA, Ltd. All rights reserved. Using Models to Interpret Scattering Scattering data typically cannot be inverted to find particle shape. We use optical models to interpret data and understand our experiments.
  8. 8. © 2013 HORIBA, Ltd. All rights reserved. The Calculations There is no need to know all of the details. The LA-950 software handles all of the calculations with minimal intervention.
  9. 9. © 2013 HORIBA, Ltd. All rights reserved. Laser Diffraction Models Large particles -> Fraunhofer More straightforward math Large, opaque particles Use this to develop intuition All particle sizes -> Mie Messy calculations All particle sizes
  10. 10. © 2013 HORIBA, Ltd. All rights reserved. Fraunhofer Approximation dimensionless size parameter  = D/; J1 is the Bessel function of the first kind of order unity. Assumptions: a) all particles are much larger than the light wavelength (only scattering at the contour of the particle is considered; this also means that the same scattering pattern is obtained as for thin two-dimensional circular disks) b) only scattering in the near-forward direction is considered (Q is small). Limitation: (diameter at least about 40 times the wavelength of the light, or  >>1)* If =650nm (.65 m), then 40 x .65 = 26 m If the particle size is larger than about 26 m, then the Fraunhofer approximation gives good results. Rephrased, results are insensitive to refractive index choice.
  11. 11. © 2013 HORIBA, Ltd. All rights reserved. Mie Scattering  nnnn ba nn n xmS        1 1 )1( 12 ),,(  nnnn ba nn n xmS        1 2 )1( 12 ),,( )(')()(')( )(')()(')( mxxxmxm mxxxmxm a nnnn nnnn n      )(')()(')( )(')()(')( mxxmxmx mxxmxmx b nnnn nnnn n      : Ricatti-Bessel functions Pn 1:1st order Legendre Functions    sin )(cos1 n n P   )(cos1    nn P d d   2 1 2 222 0 2 ),,( SS rk I xmIs  Use an existing computer program for the calculations!
  12. 12. © 2013 HORIBA, Ltd. All rights reserved. Mie  Dx  m p n n m  Decreasing wavelength is the same as increasing size. So, if you want to measure small particles, decrease wavelength so they “appear” bigger. That is, get a blue light source for small particles. The equations are messy, but require just three inputs which are shown below. The nature of the inputs is important. We need to know relative refractive index. As this goes to 1 there is no scattering.  Scattering Angle
  13. 13. © 2013 HORIBA, Ltd. All rights reserved. Effect of Size As diameter increases, intensity (per particle) increases and location of first peak shifts to smaller angle.
  14. 14. © 2013 HORIBA, Ltd. All rights reserved. Mixing Particles? Just Add The result is the weighted sum of the scattering from each particle. Note how the first peak from the 2 micron particle is suppressed since it matches the valley in the 1 micron particle.
  15. 15. © 2013 HORIBA, Ltd. All rights reserved. Outline Laser Diffraction Calculations Importance of Refractive Index Choosing Refractive Index Comparing Methods for Choosing Refractive Index
  16. 16. © 2013 HORIBA, Ltd. All rights reserved. What do we mean by RI?  Optical properties of particle different from surrounding medium  Note that intensity and wavelength of light changes in particle (typical dispersants do not show significant absorption)  Wavelength changes are described by real component  Intensity changes are described by imaginary component n = 1 (for air) n = 2-0.05i
  17. 17. © 2013 HORIBA, Ltd. All rights reserved. Effect of RI: imaginary term As imaginary term (absorption) increases location of first peak shifts to smaller angle.
  18. 18. © 2013 HORIBA, Ltd. All rights reserved. Effect of RI: Real Term It depends….
  19. 19. © 2013 HORIBA, Ltd. All rights reserved. Practical Application: Glass Beads
  20. 20. © 2013 HORIBA, Ltd. All rights reserved. Practical Application: CMP Slurry
  21. 21. © 2013 HORIBA, Ltd. All rights reserved. Effect of RI: Cement Fixed absorbance, vary real Fixed real, vary absorbance
  22. 22. © 2013 HORIBA, Ltd. All rights reserved. Refractive Index Effect Most pronounced when:  Particles are spherical  Particles are transparent  RI of particle is close to RI of fluid  Particle size is close to wavelength of light source Least pronounced when:  Particles are not spherical  Particles are opaque  RI of particle is larger than RI of the fluid  Particle size is much larger than wavelength of the light source
  23. 23. © 2013 HORIBA, Ltd. All rights reserved. Outline Laser Diffraction Calculations Importance of Refractive Index Choosing Refractive Index Comparing Methods for Choosing Refractive Index
  24. 24. © 2013 HORIBA, Ltd. All rights reserved. Abbe Refractometer  Dissolve sample at different concentrations  Plot conc. vs. RI  Extrapolate to infinite concentration 0 0.2 0.4 0.6 0.8 1.0 1.8 1.6 1.5 1.4 1.3 Concentration RefractiveIndex
  25. 25. © 2013 HORIBA, Ltd. All rights reserved. Becke Lines Bright line is called the Becke line and will always occur closest to the substance with a higher refractive index
  26. 26. © 2013 HORIBA, Ltd. All rights reserved. Becke Line Test A particle that has greater refractive index than its surroundings will refract light inward like a crude lens. A particle that has lower refractive index than its surroundings will refract light outward like a crude diverging lens. As you move away from the thin section (raising the objective or lowering the stage), the Becke Line appears to move into the material with greater refractive index.
  27. 27. © 2013 HORIBA, Ltd. All rights reserved. Becke Line Test
  28. 28. © 2013 HORIBA, Ltd. All rights reserved. Luxpop.com Note RI is dependent on wavelength of light. Can adjust RI for red & blue light, but only need to for small, absorbing particles.
  29. 29. © 2013 HORIBA, Ltd. All rights reserved. Google Search
  30. 30. © 2013 HORIBA, Ltd. All rights reserved. Using R Value for i
  31. 31. © 2013 HORIBA, Ltd. All rights reserved. What is R parameter? yi is the measured scattering at detector I y(xi) is the scattering data at detector i calculated from the size distribution N is the number of detector channels used in the calculation.
  32. 32. © 2013 HORIBA, Ltd. All rights reserved. Changing RI
  33. 33. © 2013 HORIBA, Ltd. All rights reserved. Changing RI
  34. 34. © 2013 HORIBA, Ltd. All rights reserved. Changing RI
  35. 35. © 2013 HORIBA, Ltd. All rights reserved. Using R Value for i Real component = 1.57 via Becke line Vary imaginary component, minimize Chi square & R parameter
  36. 36. © 2013 HORIBA, Ltd. All rights reserved. Automation by Method Expert  Analytical conditions  Calculation conditions View Method Expert webinar TE004 in Download Center
  37. 37. © 2013 HORIBA, Ltd. All rights reserved. Automated RI Computation  Real part study  Need to fix imaginary part  Set up to 5 real parts  Software will compute all RI and display R parameter variation with RI selection
  38. 38. © 2013 HORIBA, Ltd. All rights reserved. Automated RI Computation
  39. 39. © 2013 HORIBA, Ltd. All rights reserved. Automated RI Computation
  40. 40. © 2013 HORIBA, Ltd. All rights reserved. Summary  Measure sample, recalculate w/different RI – see how important it is  Use one of the described approaches to determine the real component  Recalculate using different imaginary component  Choose result that minimizes R parameter, but also check if result makes sense  You wish you had Method Expert by your side
  41. 41. © 2013 HORIBA, Ltd. All rights reserved. Outline Laser Diffraction Calculations Importance of Refractive Index Choosing Refractive Index Comparing Methods for Choosing Refractive Index
  42. 42. © 2013 HORIBA, Ltd. All rights reserved. Study on TiO2 Look up real refractive index, use R parameter to find imaginary.
  43. 43. © 2013 HORIBA, Ltd. All rights reserved. Effect of RI on R parameter
  44. 44. © 2013 HORIBA, Ltd. All rights reserved. Effect of RI on measured D50
  45. 45. © 2013 HORIBA, Ltd. All rights reserved. Effect of RI on measured D10
  46. 46. © 2013 HORIBA, Ltd. All rights reserved. Effect of RI on measured D90
  47. 47. © 2013 HORIBA, Ltd. All rights reserved.
  48. 48. © 2013 HORIBA, Ltd. All rights reserved. Results Model D10, microns Difference from correct value D50, microns Difference from correct value D90, microns Difference from correct value 2.7 - 0.001i (correct value) 0.30 0.42 0.80 2.6 - 0.001i 0.30 0% 0.45 7.1% 0.78 2.5% Fraunhofer 0.41 37% 0.57 36% 0.81 1.2% Minimize R parameter (3.25 - 0.1i) 0.26 13% 0.37 12% 0.72 10%
  49. 49. © 2013 HORIBA, Ltd. All rights reserved. Recommendations  Use the Mie model when evaluating laser diffraction data.  Search for literature for real and imaginary refractive index values or measure your sample yourself.  If literature values are not available, use the data to estimate values, it is better than guessing or using the Fraunhofer model.  Once you choose a refractive index value, stick with it.
  50. 50. © 2013 HORIBA, Ltd. All rights reserved. Q&A Ask a question at labinfo@horiba.com Keep reading the monthly HORIBA Particle e-mail newsletter! Visit the Download Center to find the video and slides from this webinar. Jeff Bodycomb, Ph.D. P: 866-562-4698 E: jeff.bodycomb@horiba.com
  51. 51. © 2013 HORIBA, Ltd. All rights reserved. Thank you
  52. 52. © 2013 HORIBA, Ltd. All rights reserved. Danke Gracias Большое спасибо Grazie ‫ر‬ْ‫ك‬ُ‫ش‬‫ا‬ Σας ευχαριστούμε 감사합니다 Obrigado Tacka 谢谢ขอบคุณครับ ありがとうございました धन्यवाद நன்ற Cảm ơn Dziękuję

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