A Modeling recoil track diffusion modification in aerogels?

[karen01]

TL;DR Summary

Recoil of 224Ra->220Rn in a UO3 aerogel likely typically penetrates 1 or more pores before coming to rest in the matrix, but how to model diffusion rate changes due to the track damage?

I'm working on a theoretical analysis of a thin 232U UO3 aerogel layer (5-20nm feature size, granular, crystalline, ~98% porosity) in a vacuum in GEANT4, with the desired goal of losing most of the 220Rn (and thus the hard gamma from 208Tl and the residual 208Pb mass). GEANT4 handles the particle physics, but I obviously have to model the diffusion myself. 220Rn has a half life of 55,6s, while modeled diffusion times through the pores are typically on the order of a few hundred milliseconds, so no issues there.

The issue becomes the time for diffusion from the matrix into the pore space. With varying assumptions, in an unmodified bulk solid, I get solid diffusion times on the order of a couple minutes to an hour or more - too long, but tantalizingly close when dealing with systems where variations in rates tend to be on order-of-magnitude scales. And there is a serious complication: the damage to the matrix from the deceleration of the recoiling 220Rn (~100keV).

1) My understanding from research in bulk solids is that preexisting tracks in crystalline oxides tend to be immobilizing to diffusion, but for a very brief period, the track is a hot, chaotic mess before it cools and the bond structure stabilizes. I don't expect the daughters to go far during this (incredibly brief) period, but then again, they don't have far to go.

2) When dealing with aerogels, we're dealing with an incredibly fine, delicate structure to begin with, which raises the question of localized diffusion enhancement mechanisms, such as microcracking (indeed, there's a question of microcracks to begin with...), voids, etc. Also, UO3 is chemically disfavored at elevated temperatures (will lose oxygen at 750°C even in pure O2 at 5ATM), so there's the possibility of UO2 or U3O8 formation with free oxygen and grain boundaries.

Any idea how I could reasonably model this, or am I basically SOL without experimental data? My attempts to dig up preexisting research haven't proved fruitful.

(Precision isn't needed, but order-of-magnitude is. In all likelihood, it's "nearly all diffuses into the pore space" or "nearly none diffuses into the pore space")

 

[bob012345]

It seems like you are saying whatever gets into the pores quickly diffuses out and whatever is in the matrix very slowly leaves making the dominant position in the matrix to first order? I would define the matrix/pore geometry for a test volume, assume initial distributions and diffusion rates and code the net diffusion over time and plot that. Start simple then add refinements and see how things act.

 

[karen01]

It seems like you are saying whatever gets into the pores quickly diffuses out and whatever is in the matrix very slowly leaves making the dominant position in the matrix to first order? I would define the matrix/pore geometry for a test volume, assume initial distributions and diffusion rates and code the net diffusion over time and plot that. Start simple then add refinements and see how things act.

More specifically, I can be confident at how quickly whatever gets into the pores diffuses out, but I cannot be confident at how quickly whatever is in the matrix leaves, because it's not simple bulk solid diffusion, but rather diffusion through a delicate fine structure that just got blasted by a recoil track, and I would not expect that to have the same diffusion properties (or even close) to those of bulk solid diffusion (of which diffusion data exists).

How can I assume the solid diffusion rate in this circumstance?

 

[bob012345]

More specifically, I can be confident at how quickly whatever gets into the pores diffuses out, but I cannot be confident at how quickly whatever is in the matrix leaves, because it's not simple bulk solid diffusion, but rather diffusion through a delicate fine structure that just got blasted by a recoil track, and I would not expect that to have the same diffusion properties (or even close) to those of bulk solid diffusion (of which diffusion data exists).

How can I assume the solid diffusion rate in this circumstance?

You can simulate with different values and ultimately see which values match any measured data you have. This assumes you have a reasonable model for the relative sizes and proportions of the matrix and pores.

 

[karen01]

The problem is that this is a theoretical study. Working with 232U directly is highly nontrivial and beyond the scope of the study. The aerogel structure is at least well modeled (with natural uranium) - but not radon diffusion within it (the generation rate would be too slow for practical measurements).

Unfortunately, I'm kind of rather suspecting that I'm either going to have to limit the scope and utility of the study (adding explicit premises about diffusion requiring validation) or that it would require deliberate bombardment of a sample from an external radon ion source (prob. not practical for my budget).

 

[karen01]

For anyone encountering this thread: I'm having to abandon this approach. Data from porous crystalline silicon bombardment with heavy noble gas ions at recoil energies shows that while the gases do enter the pore space, sputtering steadily closes the pores and densifies the material. Larger pores take longer to close, so an aerogel would remain porous for significantly longer than the study materials, but ultimately sputtering would destroy its properties.