First created: Nov. 6, 2003    Updated: Nov. 17, 2003
4. Actual material combinations
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1. Equal Poisson ratio
2. Poisson ratio of nanoparticle greater than matrix
3. Poisson ratio of matrix greater than nanoparticle
These are examples for combinations
of nanoparticle and matrix materials:
Ag (Silver)
Figure 4(a)
sph0cn15.cpp
md54sq.gif md54sk.gif

The Poisson ratios correspond to a Ag nanoparticle in SiO2 and also GeO2. The actual relative parameters of Ag in SiO2 and Ag in GeO2 are plotted as crosses. (The Poisson ratio of GeO2 is 0.18, while the Poisson ratio of SiO2 is 0.17)
Figure 4(b)
sph0cn16.cpp
md54aq.gif md54ak.gif

The Poisson ratios correspond to an Ag nanoparticle in Al2O3, TiO2 and ZrO2. The actual relative parameters of Ag in the matrices are shown as a cross.
Figure 4(c)
sph0cn16.cpp
md54eq.gif md54ek.gif

The Poisson ratios correspond to an Ag nanoparticle in BaO-P2O5, Y2O3 and MgF2. The actual relative parameters of Ag and the matrices are plotted as plus symbols.
Au (Gold)
Figure 4(d)
sph0cn15.cpp
md54fq.gif md54fk.gif

The Poisson ratios correspond to an Au nanoparticle in diamond. The actual relative parameters of Au and diamond are plotted as a white symbol. At right, note the continuous transition of ξ from FSM to BSM.
Figure 4(e)
sph0cn15.cpp
md54vq.gif md54vk.gif

The Poisson ratios correspond to an Au nanoparticle in SiO2 and GeO2. The actual relative parameters of Au and the matrices are plotted as plus symbols.
Figure 4(f)
sph0cn16.cpp
md54cq.gif md54ck.gif

The Poisson ratios correspond to an Au nanoparticle in TiO2, Al2O3 and ZrO2. The actual relative parameters of Au and the matrices are plotted as plus symbols.
Figure 4(g)
sph0cn15.cpp
md54wq.gif md54wk.gif

The Poisson ratios correspond to an Au nanoparticle in BaO-P2O5, Y2O3 and MgF2. The actual relative parameters of Au and the matrix is plotted as a plus symbol.
Silicon
Figure 4(h)
sph0cn16.cpp
md54dq.gif md54dk.gif

The Poisson ratios correspond to an Si nanoparticle in diamond.

Figure 4(i)
sph0cn16.cpp
md54bq.gif md54bk.gif

The Poisson ratios correspond to an Si nanoparticle in TiO2, Al2O3 and ZrO2, all of which have nearly the same Poisson ratio.

Figure 4(j)
sph0cn15.cpp
md54iq.gif md54ik.gif

The Poisson ratios correspond to an Si nanoparticle in Hg. The actual relative parameters of Si-in-Hg is plotted as a plus symbol.
Figure 4(k)
sph0cn15.cpp
md54xq.gif md54xk.gif

The Poisson ratios correspond to an Si nanoparticle in BaO-P2O5. This is a special situation since the Poisson ratio of Si is lower than that of the matrix. ( Ignore the TiO2 data point )

Others (...under construction...)
Figure 4(l)
sph0cn10.cpp
md54gw.gif md54gf.gif

The Poisson ratios correspond to a CdS or CdSe nanoparticle in TiO2 or BaO-P2O5. The actual relative parameters are plotted as white symbol.
Figure 4(m)
sph0cn12.cpp
md54kw.gif md54kf.gif

The Poisson ratios correspond to an Si nanoparticle in SiO2. The actual relative parameters of and Si in SiO2 is plotted as a cross.

Material Property References:

Y2O3  "Elastic Moduli of Transparent Yttria," O. Yeheskel and O. Tevet, Journal of the American Ceramic Society, Vol. 82 [1], pp. 136-144 (1999), published by American Ceramic Society. found at www.ceramics.nist.gov/srd/scd/Z00639.htm.

ZrO2  "Engineering Properties of Zirconia," R. Stevens, Engineered Materials Handbook, Vol. 4, pp. 775-786 (1991), edited by S.J. Schneider, Jr., published by ASM International. www.ceramics.nist.gov/srd/scd/Z00097.htm

TiO2  "Elastic Properties of Polycrystalline TiO2-x," W.P. Minnear and R.C. Bradt, Journal of the American Ceramic Society, Vol. 60 [9], pp. 458-459 (1977), published by American Ceramic Society. www.ceramics.nist.gov/srd/scd/Z00451.htm

Al2O3  R. G. Munro, Journal of the American Ceramic Society, vol. 80, pp. 1919-1928 (1997).

MgF2  www.crystran.co.uk/mgf2data.htm  and  www.almazoptics.com/MgF2.htm

Diamond  H. J. McSkimin and W. L. Bond, J. Appl. Phys. 43, 2944-2948 (1972), C11=1079 C12=124 C44=578

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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