Phononic crystals of spherical particles: A tight binding approach

Journal of Chemical Physics

Volumn 139, Issue 17, 2013, Pages

  Mattarelli, M ^a   Secchi, M ^b,c   Montagna, M ^c  

^a UNIVERSITY OF PERUGIA   (Italy)

^b FONDAZIONE BRUNO KESSLER   (Italy)

^c UNIVERSITY OF TRENTO   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

ATOMIC WAVE FUNCTION; DENSITY OF PHONON STATE; ELECTRON WAVE FUNCTIONS; PHONON DISPLACEMENT; SINGLE-PARTICLE MODEL; TIGHT BINDING MODEL; TIGHT-BINDING APPROACHES; VIBRATIONAL DYNAMICS;

ACOUSTIC IMPEDANCE; ATOMS; PHONONS; VIBRATIONS (MECHANICAL); WAVE FUNCTIONS;

SPHERES;

EID: 84903363842     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.4828436     Document Type: Article

References (43)

1. 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, 2052-2055 (1986). 10.1103/PhysRevLett. 56.2052
2. G. Mariotto, M. Montagna, G. Viliani, E. Duval, S. Lefrant, E. Rzepka, and C. Mai, " Low-energy Raman scattering from silver particles in alkali halides.," Europhys. Lett. 6, 239-243 (1988). 10.1209/0295-5075/6/3/009
3. 2 thin films.," Phys. Rev. B 44, 6243-6248 (1991). 10.1103/PhysRevB.44.6243
4. H. Portales, L. Saviot, E. Duval, M. Fujii, S. Hayashi, N. Del Fatti, and F. Vallée, " Resonant Raman scattering by breathing modes of metal nanoparticles.," J. Chem. Phys. 115, 3444-3447 (2001). 10.1063/1.1396817
5. 2 glass system.," J. Appl. Phys. 90, 2522-2527 (2001). 10.1063/1.1365426
6. 3+ doped ultra-transparent oxy-fluoride glass-ceramics for application in the 1.54 μm telecommunication window.," J. Mater. Sci. Lett. 21, 293-295 (2002). 10.1023/A:1017919719782
7. M. Montagna, E. Moser, F. Visintainer, M. Ferrari, L. Zampedri, A. Martucci, M. Guglielmi, and M. Ivanda, " Nucleation of titania nanocrystals in silica titania waveguides.," J. Sol-Gel Sci. Technol. 26, 241-244 (2003). 10.1023/A:1020755200573
8. 1-x quantum dots embedded in a glass matrix.," Phys. Rev. B 67, 235329 (2003). 10.1103/PhysRevB.67.235329
9. M. Ivanda, A. Hohl, M. Montagna, G. Mariotto, M. Ferrari, Z. Crnjak Orel, A. Turkovic, and K. Furic, " Raman scattering of acoustical modes of silicon nanoparticles embedded in silica matrix.," J. Raman Spectrosc. 37, 161-165 (2006). 10.1002/jrs.1445
10. 3+ activated silica-hafnia glass-ceramics planar waveguides.," Proc. SPIE 6183, 61831W (2006). 10.1117/12.664610
11. M. Ivanda, K. Furic, S. Music, M. Ristic, M. Gotic, D. Ristic, A. M. Tonejc, I. Djerdj, M. Mattarelli, M. Montagna, F. Rossi, M. Ferrari, A. Chiasera, Y. Jestin, G. C. Righini, W. Kiefer, and R. R. Gonçalves, " Low wavenumber Raman scattering of nanoparticles and nanocomposite materials.," J. Raman Spectrosc. 38, 647-659 (2007). 10.1002/jrs.1723
12. E. Duval, " Far-infrared and Raman vibrational transitions of a solid sphere: Selection rules.," Phys. Rev. B 46, 5795-5797 (1992). 10.1103/PhysRevB.46.5795
13. M. Montagna and R. Dusi, " Raman scattering from small spherical particles.," Phys. Rev. B 52, 10080-10089 (1995). 10.1103/PhysRevB.52.10080
14. M. Montagna, " Brillouin and Raman scattering from the acoustic vibrations of spherical particles with a size comparable to the wavelength of the light.," Phys. Rev. B 77, 045418 (2008). 10.1103/PhysRevB.77.045418
15. M. Mattarelli and M. Montagna, " Comment on 'Selection rules for Brillouin light scattering from eigenvibrations of a sphere' [Chem. Phys. Lett. 461, 111 (2008)].," Chem. Phys. Lett. 524, 112-115 (2012). 10.1016/j.cplett.2011.12.027
16. M. Mattarelli, M. Montagna, F. Rossi, A. Chiasera, and M. Ferrari, " Mechanism of low-frequency Raman scattering from the acoustic vibrations of dielectric nanoparticles.," Phys. Rev. B 74, 153412 (2006). 10.1103/PhysRevB.74.153412
17. Y. Li, H. S. Lim, S. C. Ng, Z. K. Wang, and M. H. Kuok, " Selection rules for Brillouin light scattering from eigenvibrations of a sphere.," Chem. Phys. Lett. 461, 111-113 (2008). 10.1016/j.cplett.2008.07.003
18. T. Still, M. Mattarelli, D. Kiefer, G. Fytas, and M. Montagna, " Eigenvibrations of submicrometer colloidal spheres.," J. Phys. Chem. Lett. 1, 2440-2444 (2010). 10.1021/jz100774b
19. T. Still, R. Sainidou, M. Retsch, U. Jonas, P. Spahn, G. P. Hellmann, and G. Fytas, " The 'music' of core-shell spheres and hollow capsules: Influence of the architecture on the mechanical properties at the nanoscale.," Nano Lett. 8, 3194-3199 (2008). 10.1021/nl801500n
20. T. Still, W. Cheng, M. Retsch, U. Jonas, and G. Fytas, " Colloidal systems: A promising material class for tailoring sound propagation at high frequencies.," J. Phys.: Condens. Matter 20, 404203 (2008). 10.1088/0953-8984/20/40/404203
21. W. Cheng, J. J. Wang, U. Jonas, W. Steffen, G. Fytas, R. S. Penciu, and E. N. Economou, " The spectrum of vibration modes in soft opals.," J. Chem. Phys. 123, 121104 (2005). 10.1063/1.2046607
22. T. Still, M. Retsch, U. Jonas, R. Sainidou, P. Rembert, K. Mpoukouvalas, and G. Fytas, " Vibrational eigenfrequencies and mechanical properties of mesoscopic copolymer latex particles.," Macromolecules 43, 3422-3428 (2010). 10.1021/ma1001589
23. R. S. Penciu, H. Kriegs, G. Petekidis, G. Fytas, and E. N. Economou, " Phonons in colloidal systems.," J. Chem. Phys. 118, 5224-5240 (2003). 10.1063/1.1553763
24. M. H. Kuok, H. S. Lim, S. C. Ng, N. N. Liu, and Z. K. Wang, " Brillouin study of the quantization of acoustic modes in nanospheres.," Phys. Rev. Lett. 90, 255502 (2003). 10.1103/PhysRevLett.90.255502
25. M. Mattarelli, M. Montagna, T. Still, D. Schneider, and G. Fytas, " Vibration spectroscopy of weakly interacting mesoscopic colloids.," Soft Matter 8, 4235-4243 (2012). 10.1039/c2sm07034k
26. H. Lamb, " On the vibrations of an elastic sphere.," Proc. London Math. Soc. 13, 189-212 (1882). 10.1112/plms/s1-13.1.189
27. L. Saviot and D. Murray, " Acoustic vibrations of anisotropic nanoparticles.," Phys. Rev. B 79, 214101 (2009). 10.1103/PhysRevB.79.214101
28. A. E. H. Love, A Treatise on the Mathematical Theory of Elasticity (Cambridge University Press, 1944).
29. J. Gale, " GULP: A computer program for the symmetry-adapted simulation of solids.," J. Chem. Soc., Faraday Trans. 93, 629-637 (1997). 10.1039/a606455h
30. S. Altmann and C. Bradley, " On the symmetries of spherical harmonics.," Philos. Trans. R. Soc. London, Ser. A 255, 199 (1963). 10.1098/rsta.1963.0002
31. A. Ayouch, X. Dieudonné, G. Vaudel, H. Piombini, K. Vallé, V. Gusev, P. Belleville, and P. Ruello, " Elasticity of an assembly of disordered nanoparticles interacting via either van der Waals-bonded or covalent-bonded coating layers.," ACS Nano 6, 10614-10621 (2012). 10.1021/nn303631d
32. J. Israelachvili, Intermolecular and Surface Forces (Academic Press, London, 1985).
33. E. Lifshitz, " The theory of molecular attractive forces between solids.," Sov. Phys. JETP 2, 73-83 (1956).
34. D. Hough and L. White, " The calculation of Hamaker constants from Liftshitz theory with applications to wetting phenomena.," Adv. Colloid Interface Sci. 14, 3-41 (1980). 10.1016/0001-8686(80)80006-6
35. V. Parsegian and G. Weiss, " Spectroscopic parameters for computation of van der Waals forces.," J. Colloid Interface Sci. 81, 285-289 (1981). 10.1016/0021-9797(81)90325-8
36. B. Derjaguin, " Untersuchungen über die Reibung und Adhäsion, IV. Theorie des Anhaftens kleiner Teilchen.," Kolloid-Z. 69, 155-164 (1934). 10.1007/BF01433225
37. K. Johnson, K. Kendall, and A. Roberts, " Surface energy and the contact of elastic solids.," Proc. R. Soc. London, Ser. A 324, 301-313 (1971). 10.1098/rspa.1971.0141
38. M. Kafesaki and E. Economou, " Interpretation of the band-structure results for elastic and acoustic waves by analogy with the LCAO approach.," Phys. Rev. B 52, 13317-13331 (1995). 10.1103/PhysRevB.52.13317
39. L. Saviot and D. Murray, " Vibrations of weakly coupled nanoparticles.," Phys. Rev. B 81, 235432 (2010). 10.1103/PhysRevB.81.235432
40. P. Benassi, O. Pilla, V. Mazzacurati, M. Montagna, G. Ruocco, and G. Signorelli, " Disorder-induced light scattering in solids: Microscopic theory and applications to some model systems.," Phys. Rev. B 44, 11734-11742 (1991). 10.1103/PhysRevB.44.11734
41. M. Montagna, G. Ruocco, G. Viliani, R. Dell'Anna, R. Di Leonardo, R. Dusi, G. Monaco, M. Sampoli, and T. Scopigno, " Elastic constant inhomogeneity and the broadening of the dynamic structure factor in one-dimensional disordered systems.," Phys. Rev. Lett. 83, 3450-3453 (1999). 10.1103/PhysRevLett.83.3450
42. S. Taraskin and S. Elliott, " Spectral density of vibrational excitations in lattices with force-constant disorder.," Philos. Mag. B 81, 1263-1272 (2001). 10.1080/13642810108205806
43. L. Yang, N. Yang, and B. Li, " Reduction of thermal conductivity by nanoscale 3D phononic crystal.," Sci. Rep. 3, 1143 (2013). 10.1038/srep01143