Updated: January 28, 2008
Method B: Si in SiO2




All of this is with reference to: http://noee.u-bourgogne.fr/~saviot/dan/methodB/

In all cases, the nanoparticle diameter is 3.5 nm
ν = wavenumber in cm-1
η = ω R/Ctp
Ctp = transverse speed of sound in nanoparticle (5372 m/s for "average silicon")
ν = 16.3 η
η = 0.614 ν

Note that in these figures below, the vertical scale is surface displacement and not the square of surface displacement.

Average silicon (2.329 g/cc, 9017 m/s, 5372 m/s) has a Poisson ratio
ν = (1/2)(1-2(Ct/Cl)2)/(1-(Ct/Cl)2) = 0.2249.
The exact values of η for vibrational modes of an "average silicon" sphere are given in spectra13.txt

In all cases, the amplitude prefactor A for the incident wave is 1.

Table I
(a)
(SPH,l=0)
scp79f3.cpp 48d.gif

The peak positions and zero crossing
agree with Lucien's, but the ratio of
the peak heights disagrees strongly.
(b)
(TOR,l=1)
Silica matrix has
ρ=2.2 g/cc, Clm=5950 m/s, Ctm=3760 m/s.
48b.gif scp80g.cpp

Peak's are shifted relative to Lucien's.
(c)
(TOR,l=1)
"Light and soft" matrix has
ρ=1 g/cc, Clm=2000 m/s, Ctm=600 m/s.
48c.gif scp80g.cpp
ν (cm-1)94148
η 5.779.08
exact η5.7649.096
The peaks agree with the exact solution
for a free vibrating sphere.
(d)
(SPH,l=2)
scp78j.cpp 48e.gif

Shape is very different from Lucien's.
(e)
(SPH,l=2)
"Light and soft" matrix has
ρ=1 g/cc, Clm=2000 m/s, Ctm=600 m/s.
scp78j.cpp 48f.gif
ν (cm-1)4377133157
η 2.644.728.169.63
exact η2.6374.7928.2129.592
The peaks agree with the exact solution
for a free vibrating sphere.


Daniel Murray
Associate Professor
Math, Stats & Physics Unit
University of British Columbia - Okanagan
Kelowna, BC, Canada
daniel "dot" murray "at" ubc "dot" ca

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