SLOWNESS SURFACES AND ENERGY FOCUSING PATTERNS OF AUXETIC CUBIC MEDIA
Paszkiewicz T. 1, Pruchnik M. 2, Wolski S. 1
1 Chair of Physics, Rzeszów University of Technology
W. Pola 2, PL-35-959 Rzeszów, Poland
2Institute of Theoretical Physics University of Wrocław
Pl. Maxa Borna 9, PL-50-204 Wrocław, Poland
Received:
Rec. 29 September 2004
DOI: 10.12921/cmst.2004.10.02.183-195
OAI: oai:lib.psnc.pl:570
Abstract:
We study properties of slowness surfaces and energy focusing patterns of cubic elastic media. We restricted ourselves to the region of the stability triangle where Poisson’s ratio σP of the specimen stretched in the [001] direction and measured for [100] is negative, i.e. we consider all cubic auxetic materials. We study properties of surfaces and energy focusing patterns for all elastic auxetic media characterized by σp = – 1/3.
References:
[1] R. H. Baughman, Auxetic materials: Avoiding the shrink, Nature 425, 667-670 (2003).
[2] R. S. Lakes and R. Witt, Making and Characterizing Negative Poisson’s Ratio Materials, International Journal of Mechanical Engineering Education 30, 50 (2002).
[3] K. E. Evans and A. Alderson, Auxetic materials: functional materials and structures from lateral thinking, in: Advanced Materials (Weinheim, Germany) 12, 617-628 (2000).
[4] R. H. Baughman, J. M. Shacklette, A. A. Zakhidov, and S. Stafström, Negative Poisson’s ratios as a common feature of cubic metals, Nature 392, 362-365 (1998).
[5] T. Paszkiewicz and M. Pruchnik, Acoustic phonons in cubic media: properies of their polarizations and the diffusion coefficient, Eur. Phys. J. B 24, 91-99 (2001).
[6] T. Paszkiewicz, M. Pruchnik, and P. Zieliński, Unified description of elastic and acoustic
properties of cubic media: elastic instabilities, phase transitions and soft modes, Eur. Phys. J. B
24, 327-338 (2001).
[7] T. Paszkiewicz, M. Pruchnik, and S. Wolski, Anisotropy of elastic characteristics of cubic media, in preparation.
[8] J. P. Wolfe, Imaging Phonons. Acoustic Wave Propagation in Solids, Cambridge University Press, Cambridge, 1998.
[9] T. Paszkiewicz and M. Pruchnik, Kinetic description of the phonon-pulse propagation and phonon images of crystalline solids, Physica 232, 747-768 (1996).
[10] D. Arbruster and G. Dangelmayr, Topological singularities, Z. Phys. B – Condensed Matter, 52, 87-94 (1983).
[11] A. G. Every, General closed-form expressions for acoustic waves in elastically anisotropic solids, Phys. Rev. B 22, 1746-1760 (1980).
[12] T. Paszkiewicz and M. Wilczyński, Scattering of long-wavelength acoustic phonons by isotopic impurities. Spectra of the collision integral and diffusion equation for crystalline media with cubic symmetry, Z. Phys. B 88, 5-15 (1992).
[13] T. Paszkiewicz and M. Wilczyński, Influence of isotopic and substitutional atoms on the propagation of phonons in anisotropic media, in: G. K. Horton, A. A. Maradudin (eds.), Dynamical Properties of Solids vol. 7, Phonon Physics, the Cutting Edge, North Holland, Amsterdam, pp. 257-348, 1995.
[14] U Schärer and P. Wachter, Negative elastic constants in intermediate valent SmxLa1_xS, Solid State Commun. 96, 497-500 (1995).
[15] W. M. Gancza, I. A. Obukhov, T. Paszkiewicz, and B. A. Danilchenko, Experiments on propagation and elastic scattering of down-converting beams ofphonons, Comp. Meth. Sci. Techn. 7, 7-46 (2001).
We study properties of slowness surfaces and energy focusing patterns of cubic elastic media. We restricted ourselves to the region of the stability triangle where Poisson’s ratio σP of the specimen stretched in the [001] direction and measured for [100] is negative, i.e. we consider all cubic auxetic materials. We study properties of surfaces and energy focusing patterns for all elastic auxetic media characterized by σp = – 1/3.
[1] R. H. Baughman, Auxetic materials: Avoiding the shrink, Nature 425, 667-670 (2003).
[2] R. S. Lakes and R. Witt, Making and Characterizing Negative Poisson’s Ratio Materials, International Journal of Mechanical Engineering Education 30, 50 (2002).
[3] K. E. Evans and A. Alderson, Auxetic materials: functional materials and structures from lateral thinking, in: Advanced Materials (Weinheim, Germany) 12, 617-628 (2000).
[4] R. H. Baughman, J. M. Shacklette, A. A. Zakhidov, and S. Stafström, Negative Poisson’s ratios as a common feature of cubic metals, Nature 392, 362-365 (1998).
[5] T. Paszkiewicz and M. Pruchnik, Acoustic phonons in cubic media: properies of their polarizations and the diffusion coefficient, Eur. Phys. J. B 24, 91-99 (2001).
[6] T. Paszkiewicz, M. Pruchnik, and P. Zieliński, Unified description of elastic and acoustic
properties of cubic media: elastic instabilities, phase transitions and soft modes, Eur. Phys. J. B
24, 327-338 (2001).
[7] T. Paszkiewicz, M. Pruchnik, and S. Wolski, Anisotropy of elastic characteristics of cubic media, in preparation.
[8] J. P. Wolfe, Imaging Phonons. Acoustic Wave Propagation in Solids, Cambridge University Press, Cambridge, 1998.
[9] T. Paszkiewicz and M. Pruchnik, Kinetic description of the phonon-pulse propagation and phonon images of crystalline solids, Physica 232, 747-768 (1996).
[10] D. Arbruster and G. Dangelmayr, Topological singularities, Z. Phys. B – Condensed Matter, 52, 87-94 (1983).
[11] A. G. Every, General closed-form expressions for acoustic waves in elastically anisotropic solids, Phys. Rev. B 22, 1746-1760 (1980).
[12] T. Paszkiewicz and M. Wilczyński, Scattering of long-wavelength acoustic phonons by isotopic impurities. Spectra of the collision integral and diffusion equation for crystalline media with cubic symmetry, Z. Phys. B 88, 5-15 (1992).
[13] T. Paszkiewicz and M. Wilczyński, Influence of isotopic and substitutional atoms on the propagation of phonons in anisotropic media, in: G. K. Horton, A. A. Maradudin (eds.), Dynamical Properties of Solids vol. 7, Phonon Physics, the Cutting Edge, North Holland, Amsterdam, pp. 257-348, 1995.
[14] U Schärer and P. Wachter, Negative elastic constants in intermediate valent SmxLa1_xS, Solid State Commun. 96, 497-500 (1995).
[15] W. M. Gancza, I. A. Obukhov, T. Paszkiewicz, and B. A. Danilchenko, Experiments on propagation and elastic scattering of down-converting beams ofphonons, Comp. Meth. Sci. Techn. 7, 7-46 (2001).
