The crystal structure is FCC (for a perfect crystal the theoretical filling factor or volume fraction of particles should be 0.74), particles are silica with a refractive index of 1.42 and a particle size of 403 nm, they are surrounded by air, reflection wavelength was measure by a fiber spectrometer, and the crystal was receiving light at at an angle of 0 degree on the plane (111). Measured wavelength: 880 nm.
Soumia Cheddah While I cannot answer your question, I have one question for you. You are using an RI for silica of 1.42. Was this a measured value? Suggests a lot of water in the matrix if this is the case. The forms of SiO2 have RI's varying from ~ 1.46 (cristobalite) to quartz (1.554). Or does this reflect (bad pun) the wavelength at 880 nm?
Soumia Cheddah I have worked on packing volumes before. See these webinars (registration needed):
In pursuit of perfect packing
https://www.malvernpanalytical.com/en/learn/events-and-training/webinars/W151021PerfectPacking.html
Controlling powder bulk density by optimizing particle size and shape distribution
https://www.malvernpanalytical.com/en/learn/events-and-training/webinars/W161006PowderParticleSizeShape
Alan F Rawle Silica particles were purchased and the product data sheet indicates a value between 1.38 and 1.46 for the RI. I am planning to measure the RI to get a more accurate value, but since I needed to know its value urgently, I just estimated that is around 1.42 according to the transparency of a dispersion of particles in different solvents (RI matching, transparency in DMF with an RI of 1.42 at 25 deg). Moreover, similar values were reported for calcinated particles (mine were calcinated at 600 deg): García-Santamaría, F., et al., Refractive Index Properties of Calcined Silica Submicrometer Spheres. Langmuir, 2002. 18(5): p. 1942-1944.
I could not understand the second part of your question regarding the reflection at 880 nm.
Soumia Cheddah As the wavelength increases both the real and imaginary parts of the RI tend to decrease. I've examined the RI of silica and only see values this low (1.42) for hydrated systems (e.g. opal).
Soumia Cheddah See also the attached.
Also:
https://www.researchgate.net/post/What-is-the-refractive-index-and-absorption-of-silica-nanoparticles-MCM-41-when-I-am-testing-particle-size-and-zeta-potential-by-using-ZETASIZER
Soumia Cheddah I gave a webinar in 2013 on the topic. It's not available now but you may find the slides useful as reference.
BTW, I think there are simple/simpler ways of measuring the packing volume. For example, introducing a liquid and measuring the volume. Or looking at real and apparent densities.
Alan F Rawle Thank you very much for all the shared references.
I think my particles are hydrated, after calcination at 600 deg, we performed re-hydroxylation so the particles have silanol groups on their surface. I also found that in your slides there is a value of 1.39 for calcinated silica. I assume that regeneration of hydroxyl groups might not be complete and depends on the calcination temperature, therefore, the RI must be slightly different from the original fully hydrated particles.
Please, I would like to ask you what are the methods that I could use to measure RI and density of my silica particles. I really need accurate values for different particles calcinated at different temperatures.
Thank you
Soumia Cheddah Yes, I saw the same slide when going through my old talk. 'Silicalite' with a density of 1.70 g/cm3 and an RI of 1.39 (RI and density are intricately linked - look at the paper I did for WCPT7. The link is particularly good for silica) is basically a molecular sieve type material with a lot of air in the structure lowering the effective RI. See: https://www.nature.com/articles/271512a0
You can measure the density of your material with a gas pycnometer. Density and RI are closely aligned in SiO2. You can measure the RI reading through these 3 webinars (registration required):
Laser Diffraction Masterclass 3: Optical Properties - How Can Material Optical Properties be Measured
https://www.malvernpanalytical.com/en/learn/events-and-training/webinars/W200414OpticalProp.html
Masterclass 2: How Can Material Optical Properties be Calculated/Estimated
https://www.malvernpanalytical.com/en/learn/events-and-training/webinars/W200317LDBasics2.html
Laser Diffraction Masterclass 1: Why do you Need Material Optical Properties?
https://www.malvernpanalytical.com/en/learn/events-and-training/webinars/W200211LDBasics1.html
There's also a chapter that you can request from the author:
Chapter Refractive Index Measurements
Also re-read the paper attached.
Soumia Cheddah
You may also want to look at:
ISO/AWI TS 6857 Fine ceramics (advanced ceramics, advanced technical ceramics) — Physical properties of ceramic composites — Guidelines for determination of void and fiber contents in polished cross section by image analysis https://www.iso.org/standard/82406.html
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