Calculated Vibrational Frequencies of a Wurtzite Crystal Structre CdSe Sphere

Last updated: January 23, 2008
Calculated Vibrational Frequencies of a Wurtzite Crystal Structure CdSe Sphere

Vibrational frequencies of a Wurtzite crystal structure Cadmium Selenide sphere are calculated based on the five bulk linear elastic constants. Comparison is made with an experiment on CdSe nanoparticles.

   The elastic properties of a crystal are not isotropic. Unlike polycrystalline materials such as metals, or disordered materials such as ceramics, glasses and plastics, a single crystal does not have a Young's modulus and Poisson ratio. Rather, the stress varies depending on the axis along which strain is applied.
   In bulk CdSe both the wurtzite and zinc blende forms are known. Nanocrystals of CdSe prepared at high temperatures manifest the wurtzite structure, while at low temperature they form in zinc blende. [Soloviev, Eichhofer, Fenske, Banin 2001 pdf ::].    There has been much interest in the observation and effects of low frequency phonon modes of spherical nanoparticles, and in particular nanoparticles made of Cadmium Selenide (CdSe), including experimental studies [Cerullo, De Silvestri & Banin 1999 pdf ::] and theoretical analysis [Ovsyuk and Novikov 1996] [Alcalde, Marques, Weber and Reinecke 2000 pdf ::].
   In order to estimate the vibrational frequencies of CdSe spheres, all this past work has begun with the approximation that CdSe is an isotropic, homogeneous, continuous, linear elastic material and referred to the original solution [Lamb 1881] as well as to more recent references incorporating restatements of the analysis [Nishiguchi and Sakuma 1981] [Tamura, Higeta and Ichinokawa 1982] [Fujii, Nagareda, Hayashi and Yamamoto 1991]. In practice, actual nanoparticles of CdSe deviate from this ideal in a number of ways: (1) diameter of the spheres varies within a sample; (2) they are not perfectly spherical; (3) they are not homogeneous, particularly at their surface [Tamura, Higeta and Ichinokawa 1982]; (4) they are often embedded in a glass or plastic matrix which damps and shifts the frequency of their vibration [Tamura, Higeta and Ichinokawa 1982] [Ovsyuk and Novikov 1996] [Alcalde, Marques, Weber and Reinecke 2000 pdf ::]; (5) the speed of sound is reduced at very high frequencies; (6) the elastic properties of the bulk material are not isotropic. It is this last issue, bulk material anisotropy, that is addressed here.
   Cadmium Selenide can exist in at least two structures. The first is the cubic zinc sulfide structure, reminiscent of a diamond crystal [Kittel, 4th ed., figure 30, page 31] with a cubic unit cell. The second is the hexagonal zinc sulfide structure, usually called the Wurtzite structure [Kittel, 4th ed., figure 31, page 32] with unit cell dimensions a = 0.430 nm and c = 0.702 nm [Kittel, 4th ed., page 33]. The Wurtzite structure is assumed in what follows.
   Computer programs (with listings written in C++) are available to accurately compute the vibrational frequencies of an anisotropic elastic sphere accurate to within the order of 1%. They are available for materials with cubic [Murray 2002] (C++ listing: cc3mod.cpp) and hexagonal [Murray 2002] (C++ listing: hc2mod.cpp) symmetry.
   Calculations have been made for spheres of CdS, Y₂O₃, Si, InAs, NaCl, CsBr and RbI.
   A separate computer program hex2.cpp is used to determined the five force constants starting from the five elastic constants of the material. The lattice used is hexagonal with lattice constants a = 1 and c = 0.93. The ratio c/a must be chosen so as to avoid having some negative force constants. The c/a ratio chosen for the lattice in the calculation is unrelated to the c/a ratio for the actual crystal structure, since only the bulk, low frequency, linear elastic constants are being simulated.
   Five different force constants are required in order to represent the general elasticity of a material with hexagonal symmetry. Such a material has five independent elastic constants, C₁₁, C₁₂, C₁₃, C₃₃ and C₄₄. Other elastic constants are dependent on these through: C₁₁=C₂₂=C₃₃, C₁₂=C₂₁, C₁₃=C₃₁=C₂₃=C₃₂, C₄₄=C₅₅, C₆₆=(C₁₁-C₁₂)/2. Finally, constants C_ij and C_ji with i=1,2,3 and j=4,5,6 are all 0.

Table I. Force constants for lattice simulation of hexagonal Cadmium Selenide Source for elastic constants: [Rabani 2002 pdf ::] (Using C++ program hex2.cpp.)
constant	units	value
a	(metres)	1
c	(metres)	0.93
ρ	(g/cc)	5.81
C₁₁	(GPa)	74.6
C₁₂	(GPa)	46.1
C₁₃	(GPa)	39.4
C₃₃	(GPa)	81.7
C₄₄	(GPa)	13.0
C₆₆	(GPa)	14.3
k_6pt	(???)	4.097e9
k_sp1	(N/m)	2.253e10
k_3pt	(???)	9.263e9
k_sp3	(N/m)	2.325e10
k_sp4	(N/m)	7.525e9

Table II. Vibrational frequencies (ω in rad/s) of a CdSe (Wurtzite form) nanosphere of radius R
mode type	angular momentum quantum number l	η	ω R	frequency, ν, for 10 nm diam. sphere (cm^-1)
sph	0	6.72	10046	10.67
sph	1	3.80	5681	6.03
sph	1	4.40	6578	6.98
sph	1	4.60	6877	7.30
sph	2	2.67	3992	4.24
sph	2	2.78	4156	4.41
sph	2	3.34	4993	5.30
sph	3	3.87	5786	6.14
sph	3	4.05	6055	6.43
sph	3	4.15	6204	6.59
sph	3	4.50	6728	7.14
sph	3	4.75	7101	7.54
tor	1	5.50	8222	8.73
tor	1	6.10	9119	9.68
tor	2	2.56	3827	4.06
tor	2	2.62	3917	4.16
tor	2	2.83	4231	4.49
tor	3	4.00	5980	6.35
tor	3	4.20	6279	6.67
tor	3	4.40	6578	6.98

Figure 1.Calculated vibrational spectrum for selected modes of a 10 nm diameter CdSe (Wurtzite crystal structure) nanoparticle
(hc2fmod.cpp cdse.frq readfrq3.cpp cdse10.scr s2g.cpp cdse10.gif)

Comparison with Experimental Data

Somebody has said [Ovsyuk & Novikov 1996, section III A] that only spheroidal peaks with even l and torsional peaks with odd l are Raman active. It has also been pointed out that the quadropolar modes have the greatest Raman activity [Portales et al. 2002 pdf ::].

Figure 2.Calculated vibrational spectrum for selected modes of a 3.6 nm diameter CdSe (Wurtzite crystal structure) nanoparticle, the same size as those observed experimentally [Cerullo, De Silvestri & Banin 1999 pdf ::].
(hc2fmod.cpp cdse.frq readfrq3.cpp cdse36.scr s2g.cpp cdse36.gif)

One earlier experiment [Cerullo, De Silvestri & Banin 1999 pdf ::] studied 3.6 nm diameter CdSe microcrystal using time domain femtosecond pump probe spectroscopy. Figure 6 of that paper shows the somewhat weak modulations, which when Fourier transformed have a peak at 22 cm^-1. Figure 2, above, shows the calculated spectrum for 3.6 nm diameter CdSe nanoparticles. The frequency of the breathing mode is 29.6 cm^-1. So the experimentally seen frequency is 26% lower. This can be attributed to two effects: (1) the surrounding matrix (a polymer film) will dampen and lower the vibration frequency; (2) the extremely short wavelength of the phonons means that the bulk static elastic constants will not give the right speed of sound.

References:

H. Lamb, "On the vibrations of an elastic sphere" Proc. London Math. Soc. 13, 189 (1881-1882).

N. Nishiguchi and T. Sakuma, "Vibrational spectrum and specific heat of fine particles" Solid State Comm. 38 (1981) 1073-1077.

A. Tamura, K. Higeta and T. Ichinokawa, "Lattice vibrations and specific heat of a small particle" J. Phys. C: Solid State Phys. 15 (1982) 4975-4991.

E. Duval, A. Boukenter, and B. Champagnon. "Vibration eigenmodes and size of microcrystallites in glass : observation by very-low-frequency raman scattering". Phys. Rev. Lett., 56, 2052, (1986). on-line summary

L. Saviot, B. Champagnon, E. Duval, I. Kudriavstev and A. Ekimov "Size dependence of acoustic and optical vibrational modes of CdSe nanocrystals in glasses" Journal of Non-Crystalline Solids vol. 197 (1996) 238-246 :: low freq Raman figure

M. Fujii, T. Nagareda, S. Hayashi and K. Yamamoto, "Low-frequency Raman scattering from small silver particles embedded in SiO₂ thin films" Phys. Rev. B 44 (1991) 6243-6248.

A. Tanaka. S. Onari and T. Arai, "Low-frequency Raman scattering from CdS microcrystals embedded in a germanium dioxide glass matrix" Phys. Rev. B 47 (1993) 1237-1243.

N. N. Ovsyuk and V. N. Novikov, "Influence of a glass matrix on acoustic phonons confined in microcrystals" Phys. Rev. B 53 (1996) 3113-3118.

G. Cerullo, S. De Silvestri and U. Banin "Size-dependent dynamics of coherent acoustic phonons in nanocrystal quantum dots" Phys. Rev. B volume 60 (July 15, 1999) pdf ::

A. M. Alcalde, G. E. Marques, G. Weber. T. L. Reinecke "Electron acoustic phonon scattering rates in II-IV quantum dots: contribution of the macroscopic deformation potential" Solid State Communications 116 (2000) 247-252 pdf ::

H. Portales, L. Saviot, E. Duval, M. Gaudry, E. Cottancin, M. Pellarin, J. Lermé and M. Broyer "Resonant Raman Scattering by Quadrupolar Vibrations of Ni-Ag Core-shell nanoparticles" (Preprint Mar 22 2002) pdf ::

V. N. Soloviev, A. Eichhofer, D. Fenske, U. Banin "Size-dependent optical spectroscopy of a homologous series of CdSe cluster molecules" J. Am. Chem. Soc. 123, 2354-2364 (2001) pdf ::

Eran Rabani "An interatomic pair potential for cadmium selenide" Journal of Chemical Physics vol. 116, no. 1 (2002) pdf ::

D. B. Murray "Molecular Dynamic Simulation of an Elastic Solid with Hexagonal Symmetry" link to article

D. B. Murray "Eight Point Force Molecular Dynamical Estimates of Vibrational Frequencies of an Isotropic Elastic Sphere" 2002 link to article

D. B. Murray "Breathing Mode Vibrations of an Isotropic Elastic Sphere Surrounded by a Fluid Medium" 2002 link to article

D. B. Murray "Vibrational Frequency of Silicon Nanoparticles" 2002 link to article

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 here.

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Chen, W. Q. and Ding, H. J. (2001) Free vibrations of multi-layered spherically isotropic hollow spheres. International Journal of Mechanical Science, Vol. 43(3), 667-680. ::

H. Cohen, A. H. Shah and C. V. Ramakrishnan 1972 Acustica 26 329-333, "Free Vibrations of a Spherically Isotropic Hollow Sphere"

P. R. Heyliger and A. Jilani 1992 International Journal of Solids and Structures 29 2689-2708 "The Free Vibrations of Inhomogeneous Elastic Cylinders and Spheres"

Chen, W. Q., Cai, J. B., Ye, G. R. and Ding, H. J. (2000) "On eigenfrequencies of an anisotropic sphere". ASME Journal of Applied Mechanics, Vol. 67(2), 422-424.

Chen, W. Q. "Effect of radial inhomogeneity on natural frequencies of an anisotropic hollow sphere" Journal of Sound and Vibration, Vol. 226(4), 787-794.(1999) ::

Chen, W. Q. and Ding, H. J. (1997) "On free vibrations of an embedded anisotropic spherical shell" ASME Journal of Pressure Vessel Technology, Vol. 119(4), 481-487.

Ding, H. J. and Chen, W. Q. (1996) "Natural frequencies of an elastic spherically isotropic hollow sphere submerged in a compressible fluid medium". Journal of Sound and Vibration, Vol. 192(1), 173-198.

W. Q. Chen and L. Z. Wang, "Free Vibrations of Functionally Graded Piezoceramic Hollow Spheres with Radial Polarization" Journal of Sound and Vibration vol. 251, pages 103-114 (2002) ::

W. Q. Chen, "Vibration Theory of Non-Homogeneous Spherically Isotropic Piezoelastic Bodies" Journal of Sound and Vibration" vol 236 pages 833-860 (2000) ::

Palko JW, Kriven WM, Sinogeikin SV, Bass JD, Sayir A "Elastic constants of yttria (Y₂O₃) monocrystals to high temperatures"
JOURNAL OF APPLIED PHYSICS 89 (12): 7791-7796 JUN 15 2001
http://hercules.geology.uiuc.edu/~stas/Abstracts/JAP01_89_7791.htm
Room temp: C₁₁=223.7(0.6) C₁₂=112.4(1.1) C₄₄=74.6(0.7) GPa K = 149.5(1.0) G_S=66.3(0.8) [Voigt-Reuss-Hill average]

Formula for Voigt and Reuss for cubic crystal (in french; has error in C' definition)
http://www.ens-lyon.fr/LST/WEBHP/elasticite/node2.html
G_V = (2C'+3C₄₄)/5 = Voigt Bound
G_R = 5C'C₄₄/(2C₄₄+3C') = Reuss Bound
G_S=(G_V+G_R)/2 = Voigt-Reuss-Hill average
C'=(C₁₁-C₁₂)/2
Also, for a cubic crystal, the VRH bulk modulus is (C₁₁+2C₁₂)/3

"Gas-phase-condensed Y2O3:Eu3+ nanoparticles of < 10 nm contain multiple phases: monoclinic Y2O3:Eu3+, cubic Y2O3:Eu3+, monoclinic Eu2O3, and a disordered phase. Larger particle sizes predominantly form in the metastable monoclinic phase" "Annealing as-prepared 4-nm Y2O3:Eu3+ at 500-900 C produces cubic-phase Y2O3:Eu3+ and removes all other phases. " link

Noninertial mechanism for electronic energy relaxation in nanocrystals Ho-Soon Yang,* Michael R. Geller, and W. M. Dennis Department of Physics and Astronomy, University of Georgia, Athens, Georgia 30602-2451 pdf ::

H. S. Yang, M. R. Geller Dennis, "New Mechanism for Electronic Energy Relaxation in nanocrystals" Aug 15 2000 preprint

H. S. Yang, M. R. Geller, W. M. Dennis, "Noninertial Mechanism for electronic energy relaxation in nanocrystals" Phys. Rev. B vol. 62 (2000) 9398. ::

T. Takagahara, J. Lumin. 70, 129-143 (1996)
"Electron-phonon interactions in semiconductor nanocrystals"

List of recent publications by Takagahara group (in Japanese)
http://www.hiei.kit.ac.jp/~takaghra/

http://www.chem.vt.edu/chem-dept/tissue/nano/

"While the elastic modes of spherical nanoparticles can be calculated analytically, this is not the case for nonspherical nanoparticles." "Visscher et al. ...mode structure for ellipsoidal nanoparticles..." ::

W. M. Visscher, A. Migliori, T. M. Bell and R. A. Reinhart, "The normal modes of free vibration of inhomogenous and anisotropic elastic objects" J. Acoust. Soc. 90 (1991) 2154-2161.

M. K�gl, L. Gaul A 3-D Boundary Element Method for Dynamic Analysis of Anisotropic Elastic Solids Computer Modeling in Engineering & Sciences, 1(4) (2000), pp. 27-43 abstract

U. Banin, G. Cerullo, et al. "Quantum confinement and ultrafast dephasing dynamics in InP " Phys Rev. B vol 55, March 1997 ::

Has general axis formula for Young's modulus!
1/E = (C₁₁+C₁₂) +...
http://www.crystran.co.uk/optics.htm
Sapphire Al₂O₃
C11=496
C12=164
C13=115
C33=498
C44=148
B = 240 GPa
http://www.tydex.ru/materials/materials2/sapphire.html
??? CdSe density 5.67 g/cc. !!!???
http://ncsr.csci-va.com/materials/cdse.asp
CdSe (Wurtzite) 5.81 g/cc

Article on CdSe modelled using pair potential
Table III gives calc and experi. elastic constants for wurtzite, zinc blende and rocksalt forms
CdSe Experimental values (Wurtzite = hexagonal):
C11 = 74.6 GPa
C12 = 46.1 GPa
C13 = 39.4 GPa
C33 = 81.7 GPa
C44 = 13.0 GPa
C66 = 14.3 GPa
B = 53.4 GPa
from: Eran Rabani "An interatomic pair potential for cadmium selenide" Journal of Chemical Physics vol. 116, no. 1 (2002) pdf ::

CdS colloidal quantum dots:
S. A. Empedocles, D. J. Norris, M. G. Bawendi, Phys. Rev. Lett 77, 3873 (1996).
Another experiment [Cerullo, De Silvestri & Banin 1999 pdf ::, see figure 6] used femtosecond pump-probe spectroscopy to look at a CdSe nanocrystal with diameter 3.6 nm in a polymer film. Excitation of the breathing (n=0 spheroidal) mode led to damped oscillations with frequency 21 cm^-1 and damping time 1.5 ps. This frequency corresponds to ω = 3.96×10¹² and ω R = 7120. But this is for CdSe and not for CdS.

http://www.spie.org/web/abstracts/2300/2362.html Paper #: 2362-33 Femtosecond pump-probe studies of CdSe microcrystals embedded in a germanium dioxide glass matrix, pp.304-311 Author(s): Toshihiro Arai, Univ. of Tsukuba, Tsukuba, Ibaraki, Japan; Akinori Tanaka, Univ. of Tsukuba, Sendai, Japan; Kiyoto Matsuishi, Univ. of Tsukuba, Tsukuba, Ibaraki, Japan; Seinosuke Onari, Univ. of Tsukuba, Tsukuba, Japan; Yoshihiro Maruyama, Hamamatsu Photonics KK, Tsukuba, Ibaraki, Japan; Mitsuru Ishikawa, Hamamatsu Photonics KK, Tsukuba, Ibaraki, Japan.
Abstract: We report here results of experiments on the transient absorption spectra of CdSe microcrystals embedded in a germanium dioxide glass matrix. The transient absorption spectra were measured by means of femtosecond pump-probe method. In the sample with the smaller microcrystal size within the category of the strong confinement regime (the individual particles confinement regime), the absorption bleachings due to the carrier dynamics in the quasi-zero- dimensional quantum confined states were observed. In the sample with the larger microcrystal size within the category of the weak confinement regime (the exciton confinement regime), the absorption bleachings due to the hot carrier in the 3D electronic states were studied at various excitation intensities.!31

E. P. Pokatilov, S. N. Klimin, V. M. Fomin, J. T. Devreese, and F. W. Wise "Multiphonon Raman scattering in semiconductor nanocrystals: Importance of nonadiabatic transitions" Physical Review B, Volume 65 pdf ::

Alivisatos - List of publications on nanocrystals:
http://www.cchem.berkeley.edu/~pagrp/publications.html

D. M. Mittleman, R. W. Schoenlein, J. J. Shiang, V. L. Colvin, A. P. Alivisatos, and C. V. Shank "Quantum Size Dependence of Femtosecond Electronic Dephasing and Vibrational Dynamics in CdSe Nanocrystals" Physical Review B - Condensed Matter, 49, 14,435 (May 15, l994
List of publications of... http://www.chem.ucla.edu/~craigim/publications.html
Shiang, JJ; Craig, IM; Alivisatos, AP; Resonance Raman depolarization in cadmium selenide nanocrystals. Z. Phys. D: At., Mol. Clusters 26(1-4), 358-60 (1993) "Resonance Raman intensity and depolarization of the LO mode fundamental ..."
http://pcml.univ-lyon1.fr/raman/resultats_eng.html CdSe-doped glasses... gif image of figure E, Duval, A. Boukenter, and B. Champagnon, Phys. Rev. Lett 56,2052 (1986)
(there is a picture of CdS Raman too) gif image of figure E. Duval, A. Boukenter, and B. Champagnon, Phys. Rev. Lett 56,2052 (1986)
On-line calculator of free sphere vibrational modes: (in terms of entered transverse and longitudinal sound velocities) French version: http://pcml.univ-lyon1.fr/raman/calcul.html
English version http://pcml.univ-lyon1.fr/raman/calcul_eng.html

Their recent papers: L Saviot, B Champagnon, E Duval, and A. I Ekimov, Phys. rev. B 57, 341 (1998)
Enjoy! And send your questions, remarks and any improvements to this english translation to [email protected] Long list of names and email addresses: http://pcml.univ-lyon1.fr/annuaire.html
arXiv:cond-mat/0204502 v1 23 Apr 2002 Comment on "Multi-phonon Raman scattering in semiconductor nanocrystals:Importance of non-adiabatic transitions" E. Men�endez-Proupin Institute of Materials and Reagents, University of Havana, San Lazaro y L, Vedado 10400, Havana, Cuba (Dated: April 23, 2002) In a recent paper [E. P. Pokatilov et al, Phys. Rev. B 65, 075316 (2002)] the Raman selection rules in spherical nanocrystals with a degenerate valence band are analyzed. Some precisions are... pdf ::

Seinosuke Onari webpage: http://www.ims.tsukuba.ac.jp/individual/onari.html
Dont know what this is: (in Japanese) (I can't read it because of Japanese font) www-dir.jst.go.jp/tenkai/scf/cz/cz-pdf/cz02.pdf ::
Lists of publications: http://phya.yonsei.ac.kr/ipap/lab/optics/publication.html
http://phya.yonsei.ac.kr/~optics/sub_0401.htm

Young-Nam Hwang, Seung-Han Park, Dongho Kim, "Size-dependent surface phonon mode of CdSe quantum dots", Phys. Rev. B59(11), 7285-7288 (1999).
Young-Nam Hwang, Sanghun Shin, Hong Lee Park, Seung-Han Park, Ung Kim, Hong Sik Jeong, Eun-joo Shin and Dongho Kim, "Effect of lattice contraction on the Raman shifts of CdSe quantum dots in glass matrices", Phys. Rev. B 54(21), 15120-15124 (1996).

Surface effects on phonon Energies of CdSe Quantum Dots in Glass Matrices, Y. N. Hwang, E. Shin, D. Kim, H. L. Park, S. H. Park, U. Kim, [Korean Journal Name] 5(S2), 57 (1996).

S. R. Emory and S. Nie "Screening and Enrichment of Metal Nanoparticles with Novel Optical Properities" J. Phys. Chem. B 1998 102 493-497. pdf ::

WANG J.C.; YAN Y.; ZHANG S.L.; ZHANG X.B. and HARK S.K. "Investigation of the Effect of Wavelength Selection in the Raman Scattering of CdSe Quantum Dots". Proceedings of the 17th International Conference on Raman Scattering ed.by ZHANG S.L., John Wiley & Suns(2000) pp.588-589. Beijing: John Wiley & Suns, 2000.08.
Group interested in CdSe nanoparticles (in German) (not much relevant) http://www.fzk.de/int/german/molekular/tc/main.html
http://mail.phy.pku.edu.cn/english/research/condense/raman.htm Beijing University physics dept: http://mail.phy.pku.edu.cn/english/research/condense/condense.htm
E. A. Menendez-Proupin (1), C. Trallero-Giner (1), A. Garcia-Cristobal "Resonant hyper-Raman scattering in spherical quantum dots" November 5, 1998 preprint ::

Two papers related to Quantum Dot of Zincblende CdS vibrational frequencies...
E. Roca, C.Trallero-Giner M. Cardona Phys. Rev. B 49, 13704 (1994)
[Ref [14] in Menendez-...]

M. P. Chamberlain, C. Trallero-Giner and M. Cardona Phys. Rev. B 51, 1680 (1995)
[Ref [15] in Menendez-...]

T. Toyoda "Effect of Size Confinement of CdSe Nanocrystals in a GeO2 Glass Matrix Characterized by Photoacoustic Spectroscopy" The Tenth International Conference on Phonon Scattering in Condensed Matter August 12 - 17, 2001 conf. info ::
[NANOLIST] [Nano-Tek Virtual Journal] http://www.nanojournal.org - Issue 36 - March 10, 2002
M. Claudia Troparevsky, Leeor Kronik, and James R. Chelikowsky "Ab initio absorption spectra of CdSe clusters" Phys. Rev. B 65, 2002, 033311
Steven R. Emory, Mingyong Han, and William Doering, and Shuming Nie, "BLINKING SURFACE-ENHANCED RAMAN SCATTERING OBSERVED IN SINGLE COLLOIDAL NANOCRYSTALS" *Department of Chemistry, Indiana University, Bloomington, IN 47405, USA e-mail: [email protected] pdf ::

Frank W. Wise "Lead salt quantum dots: The limit of strong confinement" March 23, 2000 Acc. Chem. Res. 2000, 33, 773-780 (2000) (Accounts of Chemical Research) pdf ::

http://www.webelements.com/webelements/compounds/text/Pb/Pb1S1-1314870.html PbS has NaCl structure, density 7600 kg/m^3, ("galena")
PbSe has NaCl structure, density 8100 kg/m^3,

Article on PbS and PbTe: ::
Table I: Bulk modulus for PbS is 53 to 70 GPa

Table of properties of semiconductors:
http://newton.ex.ac.uk/useful/scp.html
PbS has density 7.597 g/cc, Rocksalt structure.
PbSe has density 8.260 g/cc, rocksalt structure
PbTe has density 8.219 g/cc, rocksalt structure GaN Zincblende a=4.511
GaN Wurtz. a=3.1878 c=5.1850

http://www.hilger-crystals.co.uk/mat_nacl.htm
LiF C11=97.4 C12=40.4 C44=55.4 density=2.64 cubic
KI C11=27.4 C12=4.3 C44=3.7 density=3.12 FCC
KCl C11=39.8 C12=6.2 C44=6.2 density=1.99 Cubic
KBr C11=34.5 C12=5.4 C44=5.08 density=2.753 Cubic
CaF2 C11=164.0 C12=53.0 C44=33.7 density=3.18 Cubic

http://www.tydex.ru/materials/materials2/sapphire.html
mater. C11 C12 C13 C33 C44 density structure
Al2O3 496 164 115 498 148 3.98 g/cc hexagonal ("sapphire")
Quartz C11=87 C12=7 C44=58 C13=13 C14=18 C33=106 2.65 g/cc trigonal (SiO2)

http://www.macrooptica.com/materials.htm
mater. C11 C12 C13 C33 C44 density structure
MgF2 140.2 89.5 62.9 204.7 56.8 3.177 g/cc C66=95.7 tetragonal

V. N. Soloviev, A. Eichhofer, D. Fenske, U. Banin "Size-dependent optical spectroscopy of ... CdSe cluster molecules" J. Am. Chem. Soc. 2001, 123, 2354-2364
pdf ::

E. Duval, A. Boukenter, and B. Champagnon. "Vibration eigenmodes and size of microcrystallites in glass : observation by very-low-frequency raman scattering". Phys. Rev. Lett., 56, 2052, (1986).

CdS properties:
http://www.efunda.com/materials/piezo/material_data/matdata_output.cfm?Material_ID=CdS
Piezo Data: CdS
Hexagonal
??? density 5684 kg/m^3. ???? seems wrong
Compliance S_E 10^-12 m²/N: (inverse of 6x6 stiffness C matrix ! )
20.69 -9.99 -5.81 0 0 0
-9.99 20.69 -5.81 0 0 0
-5.81 -5.81 16.97 0 0 0
0 0 0 66.49 0 0
0 0 0 0 66.49 0
0 0 0 0 0 61.36
http://www.issp.ac.ru/lpcbc/DANDP/cds_adv.html
Density 4.825 g/cc (agrees) ???!!!!
Young's modulus 45 GPa
http://www.vidrine.com/iropmat3.htm
Gives density as 4.82 g/cc. (agrees)

Michael Conry "Notes on Wave propagation in anisotropic elastic solids"
CdS hexagonal
C11=90.7 GPa
C12=58.1 GPa
C33=93.8 GPa
C13=51.0 GPa
C44=15.04 GPa
Source: pdf ::

List of references: wwwraman.univ-lyon1.fr/raman/refnano.html E. Duval, A. Boukenter, and B. Champagnon, Phys. Rev. Lett 56,2052 (1986) B. Champagnon, B. Andrianasolo, and E. Duval, J. Chem. Phys. 94, 5327 (1991) B. Champagnon, B. Andrianasolo, and E. Duval, Mater. Sci. Eng. B 9, 417 (1991) E. Duval, Phys. Rev. B 46, 5795 (1992) B. Champagnon, B. Andrianasolo, A. Ramos, M. Gandais, M. Allais, and J. P. Benoit, J. Appl. Phys 73, 2775 (1993) L. Saviot, B. Champagnon, E. Duval I. A. Kudriavtsev, and A. I. Ekimov, J. Non-Cryst. Solids 197, 238 (1996) L. Saviot, B. Champagnon, E. Duval, and A. I. Ekimov, Phys. Rev. B 57, 341 (1998) Size-selective resonnant Raman scattering in CdS doped glasses, L. Saviot, B. Champagnon, E. Duval, A. I. Ekimov, Phys. Rev.B 57, 341 (1998) Comparative analysis of optical properties of gold and silver clusters embedded in aluminium matrix B. Prevel, B. Palpont, J. Lerm�, M. Pellarin, M. Treilleux, L. Saviot, E. Duval, A. Perez, M. Broyer, Nanostructures Materials, 12, 307 (1999) Observation of the quadrupolar vibrational modes of silver clusters by plasmon-assisted Raman Scattering, B. Palpant, H. Portales, L. Saviot, J. Lerm�, B. Pr�vel, M. Pellarin, E. Duval, A. Perez, M. Broyer, Phys. Rev. B. 60, 17107 (1999) Plasmon-Phonon coupling and resonant Raman Scattering of Silver clusters, B. Palpant, L. Saviot, J. Lerm�, B. Pr�vel, M. Pellarin, E. Duval, A. Perez, M. Broyer, Eur. Phys. J. D. 9, 585 (1999) Vibrations basses fr�quences dans les nanomat�riaux �tudi�s par spectroscopie Raman, L. Saviot, H. Portales, E. Duval, B. Champagnon, J. Phys. IV France 10, Pr8-73 (2000) Spatial Coherence effect on the resonant low-frequency Raman scattering from metallic nanoclusters, E. Duval, H. Portales, L. Saviot, M. Fujii, K. Sumitomo, S. Hayashi, Phys. Rev. B 63, 075405 (2001) Raman scattering by electron-hole excitations in silver nanocrystals, H. Portales, E. Duval, L. Saviot, M. Fujii, M. Sumitomo, S. Hayashi, Phys. Rev. B 63, 15 Avril (2001) 0101471.pdf Resonance and composition effects on the Raman scattering from silver-gold alloy clusters, H. Portales, L. Saviot, E. Duval, M. Gaudry, E. Cottancin, J. Lerm�, M. Pellarin, M. Broyer, B. Pr�vel, M. Terilleux, Eur. Phys. J. D soumis pour publication (2001) http://arxiv.org/find/cond-mat/1/au:+duval_e/0/1/0/past,all/0/1

"Raman scattering by electron-hole excitations in silver nanocrystals H. Portales, E. Duval, L. Saviot, M. Fujii, M. Sumitomo, S. Hayashi ::
H. Portales ,
E. Duval ,
L. Saviot , M. Fujii ,
M. Sumitomo ,
S. Hayashi
Back to Search form The URL for this search is http://arXiv.org/find/cond-mat/1/ti:+CdSe/0/1/0/all/0/1 Showing results 1 through 6 (of 6 total) for ti=CdSe 1. cond-mat/0207389 [abs , ps , pdf , other ] : Title: Size dependent tunneling and optical spectroscopy of CdSe quantum rods Authors: David Katz , Tommer Wizansky , Oded Millo , Eli Rothenberg , Taleb Mokari , Uri Banin Comments: Accepted to PRL (nearly final version). 4 pages in revtex, 4 figures Subj-class: Mesoscopic Systems and Quantum Hall Effect 2. cond-mat/0204614 [abs , pdf ] : Title: Transport properties of annealed CdSe nanocrystal solids Authors: M. Drndic , M. Vitasovic , N.Y. Morgan , M.A. Kastner , M.G. Bawendi Comments: 24 pages,4 figures, 1 table Subj-class: Mesoscopic Systems and Quantum Hall Effect 3. cond-mat/0204560 [abs , ps , pdf , other ] : Title: Electronic transport in films of colloidal CdSe nanocrystals Authors: Nicole Y. Morgan , C.A. Leatherdale , M. Drndic , Mirna Vitasovic , Marc A. Kastner , Moungi Bawendi Comments: 11 pages, 10 figures Subj-class: Mesoscopic Systems and Quantum Hall Effect 4. cond-mat/0111200 [abs , ps , pdf , other ] : Title: Electron (hole) paramagnetic resonance of spherical CdSe nanocrystals Authors: K. Gokhberg , A. Glozman , E. Lifshitz , T. Maniv , M.C. Schlamp , P. Alivisatos Comments: 4 pages, 2 figures Subj-class: Mesoscopic Systems and Quantum Hall Effect 5. cond-mat/0110134 [abs , ps , pdf , other ] : Title: Quantum confinement in CdSe nanocrystallites Authors: K. E. Andersen , C. Y. Fong , W. E. Pickett Comments: 15 pages, 4 figures, to be published in Journal of Non-Crystalline Solids Subj-class: Mesoscopic Systems and Quantum Hall Effect 6. cond-mat/0106108 [abs , ps , pdf , other ] : Title: Exciton states and optical properties of CdSe nanocrystals Authors: J. Perez-Conde (1), A. K. Bhattacharjee (2) ((1)Universidad Publica de Navarra, Pamplona, Spain, (2) Laboratoire de Physique des Solides, Orsay, France) Comments: Revtex, 24 pages, 7 Postscript figures Subj-class: Mesoscopic Systems and Quantum Hall Effect Journal-ref: Phys. Rev. B 63, 245318 (2001) Back to Search form Top of Form 1 Links to: arXiv , cond-mat , /find , /abs , /0208 , Bottom of Form 1
Size dependence of acoustic and optical vibrational modes of CdSe nanocrystals in glasses L. Saviota, B. Champagnona, *, E. Duvala, I. A. Kudriavtsevb and A. I. Ekimovb a Laboratoire de Physico-Chimie des Mat�riaux Luminescents, URA 442 CNRS, Universit� Lyon 1 69622 Villeurbanne cedex France b AF Ioffe Physico-Technical Institute 194021 St. Petersburg Russian Federation Received 28 September 1995; accepted 28 November 1995. Available online 8 February 1999. Abstract The size dependence of resonant Raman scattering from acoustic and optical vibrational modes in CdSe nanocrystals (size less than 10 nm) embedded in a glassy matrix has been investigated. In the low-frequency Raman scattering range (< 100 cm-1) a fine structure due to the confinement of acoustic modes is observed. The Raman line corresponding to the interaction with the optical modes (new 210 cm-1) shifts and widens with a decreasing of the particle size. These experimental results can be described by a single model based on the size dependence of the eigenvibration modes of spherical particles in a matrix. Corresponding author. This Document Abstract PDF (428 K) Journal of Non-Crystalline Solids Volume 197, Issues 2-3 , May 1996, Pages 238-246 ::

http://aapg.confex.com/aapg/cairo2002/techprogram/paper_65168.htm Heterogeneous Anisotropic Elastic Finite Difference Method for Irregular Grid Weitao Sun and Huizhu Yang. Dept. of Engineering Mechanics, Tsinghua University, Dept. of Engineering Mechanics, Beijing, 100084, China, phone: 86-10-62783149, fax: 86-10-62781824, [email protected]
http://aapg.confex.com/aapg/cairo2002/techprogram/paper_65881.htm Anisotropy: Who cares? Constantine Tsingas1, Don Pham2, Ruben Martinez2, and Maurice Gidlow3. (
http://www.wiley-vch.de/contents/jc_2232/2201.html J. Camacho, A. Cantarero Phonon Dispersion of Wurtzite CdSe: The Bond Charge Model phys. stat. sol. (b) 2000, 220, No. 1, 233-236
http://www.dartmouth.edu/~phonon/scientific.program4.html F. Vall�e Acoustic Vibration of Metal Nanoparticles: a Local Probe of their Environment :: abstract

www.edpsciences.com/articles/euro/abs/2001/21/6770/6770.html Europhys. Lett., 56 (3) , pp. 386-392 (2001) Investigation of confined acoustic phonons of tin nanoparticles during melting C. E. Bottani1, A. Li Bassi1, A. Stella2, P. Cheyssac3 and R. Kofman3
http://www.ioffe.rssi.ru/SVA/NSM/Semicond/InN/mechanic.html Wurtzite InN. Elastic constants at 300 K. C11 190 � 7 GPa Sheleg & Savastenko (1979) see also Wright (1997) ; Kim et al. (1996) C12 104 � 3 GPa C13 121 � 7 GPa C33 182 � 6 GPa C44 10 � 1 GPa

http://www.ioffe.rssi.ru/SVA/NSM/Semicond/AlN/mechanic.html Wurtzite AlN. Elastic constants at 300 K. C11 410 � 10 GPa McNeil (1993) see also Wright (1997) C12 149 � 10 GPa C13 99 � 4 GPa C33 389 � 10 GPa C44 125 � 5 GPa
http://nsr.mij.mrs.org/refs/prb/1996/53-16310.html {And also found at: http://els3.phys.cwru.edu/~kwiseon/nitprb/}
Elastic constants and related properties of tetrahedrally bonded BN, AlN, GaN, and InN Kwiseon Kim, Walter R. L. Lambrecht, Benjamin Segall Physical Review B 53(24), 16310 (1996).
http://nsr.mij.mrs.org/refs/jap/1997/82-2833.html Elastic properties of zinc-blende and wurtzite AlN, GaN, and InN AF Wright Journal of Applied Physics 82(6), 2833 (1997).
http://www.aps.org/BAPSMAR98/abs/S3150016.html Lattice Dynamics of Wurtzite Semiconductors: GaN and AlN Guanghong Wei, Jian Zi, Kaiming Zhang, Xide Xie (Surface Physics Laboratory, Fudan University, Shanghai 200433, P. R. China)
www.wsi.tu-muenchen.de/research/annual_reports/rep97/42-43.pdf
Misc Info about CdSe: http://ncsr.csci-va.com/materials/cdse.asp

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