[Gwyddion-users] Lateral grain statistics

[Daniil Bratashov]

We're now preparing an article about MRI contrasting by magnetite
nanoparticles and I'm puzzled, what kind of grain statistic can be used
to describe non-uniformity of lateral particle distribution. It can be
distribution of interparticle distances, some statistical parameters
from the distribution like minimal interparticle distance, average
particles cluster size, some thermodynamical parameters. For example,
with highly charged particles its distributed highly uniformly, then we
have small aggregates forming, then it's all one large aggregate. Is
there any parameters that reliably describe such processes, and which
literature can one recommend for such analysis?

WBR, Daniil Bratashov.

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[David Nečas (Yeti)]

Post by Daniil Bratashov
We're now preparing an article about MRI contrasting by magnetite
nanoparticles and I'm puzzled, what kind of grain statistic can be used
to describe non-uniformity of lateral particle distribution. It can be
distribution of interparticle distances, some statistical parameters
from the distribution like minimal interparticle distance, average
particles cluster size, some thermodynamical parameters. For example,
with highly charged particles its distributed highly uniformly, then we
have small aggregates forming, then it's all one large aggregate. Is
there any parameters that reliably describe such processes, and which
literature can one recommend for such analysis?

There are several, you can see a few for instance here: DOI:
10.1103/PhysRevE.92.062401, but for each method it is easy to construct
counterexamples where it does not work. Reducing the spatial
distribution to a single number is hard. So I would try to choose
(a) something that has physical meaning, i.e. it appears naturally in
other formulae you use
(b) something that correlates well with other quantities

Regards,

Yeti


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[Stefania Carapezzi]

Hi. If you are interested in characterizing the 2D spatial distribution of
your nanoparticles, you can apply statistical tools from spatial point
pattern analysis. A book on the topic I found clear and sufficiently
in-depth is Wiegand, Moloney, "Handbook of Spatial Point-Pattern Analysis
in Ecology". Especially, you can use the pair correlation function to test
if the distribution of your NPs is random (Poisson distribution), if it is
clustered or hyperdispersed, and also extract some informations like the
spatial range of clustering (in case of clustering). Some mateials-science
related literature: investigation of clustering in pits dislocations of GaN
surfaces (
M.A.Moram,R.A.Oliver,M.J.Kappers,C.J.Humphreys,Adv.Mater.21(38–39)
(2009)3941), analysis of breakdown spots patterns in Pt/HfO2/Pt structures
(Miranda et al., Journal of Applied Physics 115, 174502 (2014);
doi: 10.1063/1.4874740), analysis of clustering in Ni-Si microinslands
after temperature induced dewetting of Ni deposited on Si (Carapezzi et
al., J. Mater. Chem. C, 2016, 4, 8226) .
Best
Stefania Carapezzi

Post by Daniil Bratashov
We're now preparing an article about MRI contrasting by magnetite
nanoparticles and I'm puzzled, what kind of grain statistic can be used
to describe non-uniformity of lateral particle distribution. It can be
distribution of interparticle distances, some statistical parameters
from the distribution like minimal interparticle distance, average
particles cluster size, some thermodynamical parameters. For example,
with highly charged particles its distributed highly uniformly, then we
have small aggregates forming, then it's all one large aggregate. Is
there any parameters that reliably describe such processes, and which
literature can one recommend for such analysis?
WBR, Daniil Bratashov.
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[Daniil Bratashov]

On Wed, 14 Sep 2016 11:03:46 +0200

Post by Stefania Carapezzi
Hi. If you are interested in characterizing the 2D spatial
distribution of your nanoparticles, you can apply statistical tools
from spatial point pattern analysis. A book on the topic I found
clear and sufficiently in-depth is Wiegand, Moloney, "Handbook of
Spatial Point-Pattern Analysis in Ecology". Especially, you can use
the pair correlation function to test if the distribution of your NPs
is random (Poisson distribution), if it is clustered or
hyperdispersed, and also extract some informations like the spatial
range of clustering (in case of clustering). Some mateials-science
related literature: investigation of clustering in pits dislocations
of GaN surfaces
( M.A.Moram,R.A.Oliver,M.J.Kappers,C.J.Humphreys,Adv.Mater.21(38–39)
(2009)3941), analysis of breakdown spots patterns in Pt/HfO2/Pt
structures (Miranda et al., Journal of Applied Physics 115, 174502
(2014); doi: 10.1063/1.4874740), analysis of clustering in Ni-Si
microinslands after temperature induced dewetting of Ni deposited on
Si (Carapezzi et al., J. Mater. Chem. C, 2016, 4, 8226) . Best
Stefania Carapezzi

Thanks a lot, it seems to be the right statistical quantities in our
case. Also thanks to all who responded here and offlist, it was a very
productive discussion.

WBR, Daniil Bratashov.

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