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Investigation the effect of lattice angle on the band gap width in 3D phononic crystals with rhombohedral(I) lattice

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Abstract

In this paper, the propagation of acoustic waves in the phononic crystal of 3D with rhombohedral(I) lattice is studied theoretically. The crystal composite constituted of nickel spheres embedded in epoxy. The calculations of the band structure and density of states are performed with the plane wave expansion method in the irreducible part of Brillouin zone. In the present work, we have investigated the effect of lattice angle on the band structure and width of the band gap rhombohedral(I) lattice in the irreducible part of the first Brillouin zone and its planes separately. The results show that more than one complete band gape are formed in the four planes of the irreducible part. The most complete band gaps are formed in the (111) plane and the widest complete band gap in (443) with an angle greater than 80\(^{\circ }\). So, if the sound passes through the (111) and (443) planes for the lattice angle close to 90\(^{\circ }\), the crystal phononic displays the excellent insulation behavior. Moreover, in the other planes, the lattice angle does not affect on the width and the number of band gaps. Also, for the filling fraction 5 %, the widest complete band gap is formed. These results are consistent with the effect of symmetry on the band gap width, because the (111) plane has the most symmetry.

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References

  1. M.S. Kushwaha, P. Halevi, L. Dobrzynski, B. Djafari- Rouhani, Phys. Rev. Lett. 71, 2022 (1993)

    Article  ADS  Google Scholar 

  2. M. Kafesaki, M.M. Sigalas, N. Garcia, Phys. Rev. Lett. 85, 4044 (2000)

    Article  ADS  Google Scholar 

  3. C. Pachiu, V. Moagar, in SISOM 2011 and session of the commission of acoustics, Bucharest, 25–26 May (2011)

  4. J.O. Vasseur, P.A. Deymier, B. Chenni, B. Djafari-Rouhani, L. Dobrzynski, D. Prevost, Phys. Rev. Lett. 86, 3012 (2001)

    Article  ADS  Google Scholar 

  5. X.D. Zhang, Z.Y. Liu, Appl. Phys. Lett. 85, 341 (2004)

    Article  ADS  Google Scholar 

  6. M.Z. Ke, Z.Y. Liu, C.Y. Qiu, W.G. Wang, J. Shi, W.J. Wen, P. Sheng, Phys. Rev. B 72, 064306 (2005)

    Article  ADS  Google Scholar 

  7. L. Feng, X.P. Liu, M.H. Lu, Y.B. Chen, Y.F. Chen, Y.W. Mao, J. Zi, Y.Y. Zhu, S.N. Zhu, N.-B. Ming, Phys. Rev. Lett. 96, 014301 (2006)

    Article  ADS  Google Scholar 

  8. M.Z. Ke, Z.Y. Liu, P. Pang, W.G. Wang, Z.G. Cheng, J. Shi, X.Z. Zhao, W.J. Wen, Appl. Phys. Lett. 88, 263505 (2006)

    Article  ADS  Google Scholar 

  9. I. Sliwaa, M. Krawczykb, Acta Physica Polonica A 108, 6 (2005)

    Google Scholar 

  10. D.A. Parkhomenko, S.A. Kolenov, V.I. Grigoruk, N.N. Movchan, J. Exp. Theor. Phys. 112(5), 799–806 (2011)

    Article  ADS  Google Scholar 

  11. B. Djafari-Rouhani, L. Dobrzynski, O. Hardouin-Duparc, R.E. Camley, A.A. Maradudin, Phys. Rev. B 28, 1711 (1983)

    Article  ADS  Google Scholar 

  12. J.P. Dowling, J. Acoust. Soc. Am. 91, 2539 (1992)

    Article  ADS  Google Scholar 

  13. M.M. Sigalas, E.N. Economou, Solid State Commun. 86, 141 (1993)

    Article  ADS  Google Scholar 

  14. J.O. Vasseur, B. Djafari-Rouhani, L. Dobrzynski, M.S. Kushwaha, P. Halevi, J. Phys. Condens. Matter 6, 8759 (1994)

    Article  ADS  Google Scholar 

  15. M. Kafesaki, M.M. Sigalas, E.N. Economou, Solid State Commun. 96, 285 (1995)

    Article  ADS  Google Scholar 

  16. M.S. Kushwaha, B. Djafari-Rouhani, J. Appl. Phys. 80, 3191 (1996)

    Article  ADS  Google Scholar 

  17. J. F. Robillard, K. Muralidharan, J. Bucay, P. A. Deymier, Chin. J. Phys. 49, 1 (2011)

    Google Scholar 

  18. D. Caballero, J. Sanchez-Dehesa, R. Martnez-Sala, C. Rubio, J.V. Sanchez-Perez, L. Sanchis, F. Meseguer, Phys. Rev. B 64, 064303 (2001)

    Article  ADS  Google Scholar 

  19. L. Sanchis, F. Cervera, J. Sanchez-Dehesa, J.V. Sanchez-Perez, C. Rubio, R. Martinez-Sala, J. Acoust. Soc. Am. 109, 2598 (2001)

    Article  ADS  Google Scholar 

  20. Z. Liu, X. Zhang, Y. Mao, Y. Zhu, Z. Yang, C.T. Chan, P. Sheng, Science 289, 1734 (2000)

    Article  ADS  Google Scholar 

  21. M. Torres, F.R. Montero de Espinosa, J.L. Aragon, Phys. Rev. Lett. 86, 4282 (2001)

    Article  ADS  Google Scholar 

  22. F. Cervera, L. Sanchis, J.V. Sanchez-Perez, R. Martinez-Sala, C. Rubio, F. Meseguer, C. Lopez, D. Caballero, J. Sanchez-Dehesa, Phys. Rev. Lett. 88, 023902 (2002)

    Article  ADS  Google Scholar 

  23. L. Sanchis, A. Hakansson, F. Cervera, J. Sanchez-Dehesa, Phys. Rev. B 67, 035422 (2003)

    Article  ADS  Google Scholar 

  24. A. Khelif, P.A. Deymier, B. Djafari-Rouhani, J.O. Vasseur, L. Dobrzynski, J. Appl. Phys. 94, 1308 (2003)

    Article  ADS  Google Scholar 

  25. H. Ammari, H. Kang, H. Lee, Arch. Ration. Mech. Anal. 193, 679–714 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  26. J.H. Page, A. Sukhovich, S. Yang, M.L. Cowan, F. Van Der Biest, A. Tourin, M. Fink, Z. Liu, C.T. Chan, P. Sheng, Phys. Stat. Sol. (B) 241, 3454–3462 (2004)

    Article  ADS  Google Scholar 

  27. N. W. Ashcroft, N. D. Mermin, Solid State Physics (Holt-Saunders, Philadelphia, 1976), pp. 119–125

  28. W. Setyawan, S. Curtarolo, Cond-Mat-Mtrl-Sci 17 (2010)

  29. B. Luthi, Physical Acoustics in the Solid State (Springer-verlag, Berlin/Heidelberg, 2007)

  30. T. T. Wu, Z. G. Huang, S. Lin, Phys. Rev. B 69, 094301 (2004)

    Google Scholar 

  31. Y. Pennec, J. O. Vasseur, B. Djafari-Rouhani, L. Dobrzynski, A. Deymier, Surf. Sci. Rep. 65 (2010)

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Authors and Affiliations

  1. Department of Physics, Shahid Chamran University, Ahvaz, Iran

    H. Salehi, M. Aryadoust & M. Zargar Shoushtari

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  1. H. Salehi
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  2. M. Aryadoust
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  3. M. Zargar Shoushtari
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Correspondence to M. Aryadoust.

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Salehi, H., Aryadoust, M. & Shoushtari, M.Z. Investigation the effect of lattice angle on the band gap width in 3D phononic crystals with rhombohedral(I) lattice. Appl. Phys. A 116, 69–77 (2014). https://doi.org/10.1007/s00339-013-8084-6

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