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What does SAS Profile say

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j_    a if-u ti

Intensity

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Fg. a) arid b): Lucjan Pijak, ‘Nanostruktora wybrarg*h...” 1998

How SAS can see fractals?

Measrred intensityof i>yVS. can be npproximnted by:

I(q)<x Apfr^(r)^Sin^^r dr

i v

, whcro:

o diaiuełer of a particie (e.g. in agdouieiaie)

•\p - iii ffcxnce iii cl cc Iron dcnsily of a mnlcrial fc.g. SiC) and il.s stirrotmding (e.p. vacmun>

f>(r) - correlatlon 1'unctlon of the scatterlnp particie

Nnlicc:    sincc scallcrinj: inlcnsily ilcjwnds on <hf$erenct of c cclroi

densities. the scatterers can be both: particles i.e.p. SiC crains) or pores. SAS experiment iiself can t determine l)]ic of llic scallcrcr.

Then. the correlation tunctiou we can expres$ as:

g(r)oc f(_r)p(r)

, wliere:

fir) - shaj» funclion i:f llicagglimicniic (ilocsn'l niallcr licrc)

;'(r) - denslty of the aęglomerate

Agglmneralcs grown as fraclal siruclurcs havc llic corrclaliori tainctio.t:

g(r) oc f(r)r^p^

miii ihcy scali er likc:

/(#)<* q

tor 1/A < q < Ha. wt.ere:

A diameter of neglomerate a - diumcler oL pnmary pimiclc

Jt means: we can determlue mass fractal dfnienslon L>„ oi agglnmcralc by .slmplc mcasurcmcnl of slopc of scallcring curvc.