Choosing a Refractive Index

The accuracy of your laser diffraction particle size measurement depends by varying degrees upon the accuracy of your choice of refractive index. How to identify good refractive index from bad is one of the most common questions (and most common headaches) of the typical laser diffraction user.

Why is Refractive Index Important?

One of the key factors affecting the accuracy of many laser diffraction particle size measurements is the choice of refractive index (RI).  Consisting of real and imaginary components the RI describes how light interacts with a material.  The real component is often either listed in the software library, located through a literature or internet search, or can be directly measured. The imaginary component, or i term is a value between 0.0 and 10.0 that correlates to the degree of difference between a transparent and opaque particle. The i term is sometimes easy to deduce - for example samples that are transparent and spherical and therefore have an imaginary value of zero. For non-transparent particles the i term is a non-trivial selection and directly affects result accuracy.  The LA-960 Method Expert software provides a structured, automated approach with expert advice to choose the optimum i term.

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The LA-960 Method Expert: Guided, Automated Method Development Software
The LA-960 Method Expert: Guided, Automated Method Development Software

Choosing the Optimum Imaginary Component

The raw data for the experiment is the scattered light measured on the instrument detectors. This scattered light is then used to calculate the particle size distribution (PSD). An error calculation called the R parameter quantifies the error when converting from the raw data to the PSD. This error calculation can be used to select the optimum i term; the lower the R parameter, the better the calculation (result). The i term generating the lowest R parameter is then used for all future measurements of this sample.

Automation by Method Expert

The sample is measured once and then this raw data is used for optimization in the Method Expert. The real component of RI is kept fixed and the i term is varied as determined by the user – typically 0, 0.01, 0.1, 1, and 10. A screen shots from the wizard set up is shown below.

Setup screen for the Method Expert Imaginary Refractive Index Wizard
Click image to enlarge: Setup screen for the Imaginary RI Wizard

After the calculations are completed a summary report is generated the displays the following information as seen below:

  • PSD for each calculation
  • D90, D50, D10 vs. RI
  • R parameter vs. RI
The LA-950 Method Expert Imaginary Refractive Index Result screen
Click image to enlarge: Result screen for the Imaginary RI Wizard

For this and every test the Method Expert provides the user with Expert Advice containing guidance on how to make the best possible choice.

The LA-950 Method Expert provides Expert Advice for every test
Click image to enlarge: Expert Advice for Imaginary RI Wizard

In this case the user should select 1.0 as the best i term for this sample and can choose from a number of options to report the results.

The same wizard can also be used to select the optimum real RI component while keeping the i term fixed. This approach works for the majority of samples, but the user must still also decide that the result generated meets expectations or correlates to another technique or product performance.

The user can then perform the other automated tests within the Method Expert software including structured tests to select the optimum:

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