Updated: January 23, 2008
CdS in SiO2



ν = 0.01 S Clong / (2 a c)
a = radius of particle (m) = 3.3 nm
c = speed of light = 2.9979x108 m/s
Clong = longitudinal speed of sound = 4250 m/s
ν = 21.48 S

Approach A: Complex Frequency Modes

Table I:  Complex frequency modes
 type  l ν (cm-1)
for d=6.6 nm		Sprogrammethod
TOR110.6+1.50i  c:\nano\scp77c.cpp root searcher
TOR1 0.5+0.07ic:\nano\scp77.cpp graphical
SPH218.65+2.08i c:\nano\scp75d.cpp root searcher
SPH2 0.87+0.09ic:\nano\scp75d.cpp graphical
SPH021.7+3.98i c:\nano\scp73d.cpp root searcher

Approach B: Continuum Thermal Phonons From Matrix:

Figure 1
(a) c:\nano\scp80f.cpp 45a.gif
(large peak is rigid libration?)		 (b) c:\nano\scp79f.cpp 45b.gif
(breathing mode)		 (c) c:\nano\scp78i.cpp 45c.gif

Table II:  Comparison of approaches A and B
 approach Aapproach B
 type   l  Re(ν) Im(ν) peak ν HWHM
TOR1 10.6 1.50 10.0 1.5
SPH2 18.65 2.08 18.5 1.7
SPH0 21.7 3.98 20.5 4.1

   Generally, the results of approaches A and B agree quite well, both for the location of the peak as well as its width.

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

For a list of related articles click on the link.


Hosted by www.Geocities.ws

1