Hostname: page-component-76fb5796d-45l2p Total loading time: 0 Render date: 2024-04-25T20:31:03.817Z Has data issue: false hasContentIssue false
  • English
  • Français

Strain in layered nanocrystals

Published online by Cambridge University Press:  01 October 2007

Y. BAE  and
R. E. CAFLISCH
Y. BAE
Affiliation:
ACMS, University of Arizona, Tucson, AZ, USA e-mail: byouri@acms.arizona.edu
R. E. CAFLISCH
Affiliation:
Department of Mathematics, UCLA, Los Angeles, CA, USA e-mail: caflisch@math.ucla.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

Layered nanocrystals consist of a core of one material surrounded by a shell of a second material. We present computation of the atomistic strain energy density in a layered nanocrystal, using an idealised model with a simple cubic lattice and harmonic interatomic potentials. These computations show that there is a critical size r*s for the shell thickness rs at which the energy density has a maximum. This critical size is roughly independent of the geometry and material parameters of the system. Interestingly, this critical size agrees with the shell thickness at which the quantum yield has a maximum, as observed in several systems and thus leads one to support the hypothesis that maximal quantum yield is strongly correlated with maximal elastic energy density.

Type
Papers
Information
European Journal of Applied Mathematics , Volume 18 , Issue 5 , October 2007 , pp. 571 - 582
Copyright
Copyright © Cambridge University Press 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Cao, Y. W. & Banin, B. (1999) Synthesis and characterization of InAs/InP and InAs/CdSe core–shell nanocrystals. Angew. Chem. Int. Ed. 38, 3692–3694.3.0.CO;2-W>CrossRefGoogle ScholarPubMed
[2]Connell, C. R., Caflisch, R. E., Luo, E. & Simms, G. (2006) The elastic field of a surface step: The Marchenko–Parshin formula in the linear case. J. Comp. Appl. Math. 196, 368–386.CrossRefGoogle Scholar
[3]Landau, L. D. & Lifschitz, E. M. (1959) Theory of Elasticity, Addison-Wesley.Google Scholar
[4]Manna, L., Schoer, E. C., Li, L. S. & Alivisatos, A. P. (2002) Epitaxial growth and photochemical annealing of graded CdS/ZnS shells on colloidal CdSe nanorods. J. Am. Chem. Soc. 124, 7136–7145.CrossRefGoogle ScholarPubMed
[5]Mokari, T. & Banin, U. (2003) Synthesis and properties of CdSe/ZnS core–shell nanorods. Chem. Mater. 15 (20), 3955–3960.CrossRefGoogle Scholar
[6]Peng, X., Schlamp, M. C., Kadavanich, A. V. & Alivisatos, A. P. (1997) Epitaxial growth of highly luminescent CdSe/CdS core–shell nanocrystals with photostability and electronic accessibility. J. Am. Chem. Soc. 119, 7019–7029.CrossRefGoogle Scholar
[7]Schindler, A. C., Gyure, M. F., Simms, G. D., Vvedensky, D. D., Caflisch, R. E., Connell, C. & Luo, E. (2003) Theory of strain relaxation in heteroepitaxial systems. Phy. Rev. B. 67, 075316.CrossRefGoogle Scholar