Last updated: January 23, 2008
Soft Boundary Layer Effect on l = 1 Torsional
Amplitudes of a Si Nanoparticle in a SiO2 Matrix

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   When a nanoparticle is embedded in a glass matrix, a reasonable first approximation is that there is a sharp transition between the two materials. It is also natural to begin by assuming that the materials are tightly bonded. However, the nature of the boundary may be more complicated. What is the effect of a thin layer of softer material between the nanoparticle and the matrix? Figure 1 below explores the variation of the l = 1 torsional vibrational amplitude as the thickness is varied.


Figure 1: 3.5 nm diameter Si nanosphere in SiO2 matrix (C++ listing: scp70m.c)
** Sorry, but the vertical axis scale labels are wrong below! **
(a) Si nanosphere with very soft surrounding material. This is approaching the limit of an isolated sphere. The peak at 92 cm-1 corresponds to dimensionless frequency η=5.764 . This agrees with the exact solution for a free sphere (5.764 and 9.096 are exact solution).
(b) Si nanosphere with very soft surrounding material. This is approaching the limit of an isolated sphere. The peak at 92 cm-1 corresponds to dimensionless frequency η=5.764 . (9.096 is next exact solution) This agrees with the exact solution for a free sphere.
(c) Si nanosphere surrounded by 0.02 nm thick SiO2 layer, surrounded by SiO2 matrix (just a check on the correctness of the computer program) Compare to Fig 1(f) in md21.htm)
(d) soft 0.01 nm thick boundary
(e) soft 0.02 nm thick boundary
(f) soft 0.03 nm thick boundary
(g) soft 0.05 nm thick boundary
(h) soft 0.07 nm thick boundary
(i) soft 0.1 nm thick boundary
(j) soft 0.15 nm thick boundary
(k) soft 0.2 nm thick boundary
(l) soft 0.3 nm thick boundary
(m) soft 0.5 nm thick boundary


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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