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Original Articles

Ultrasonic investigation of the vibrational modes of a sintered glass-bead percolation system

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Pages 361-386 | Received 01 Feb 1996, Published online: 19 Aug 2006

References

  • Deptuck , D , Harrison , J D and Zawadzki , P . 1985 . Measurement of elasticity and conductivity of a three-dimensional percolation system . Phys. Rev. Lett. , 54 : 913 – 6 .
  • Kantor , Y and Webman , I . 1984 . Elastic properties of random percolating systems . Phys. Rev. Lett. , 52 : 1891 – 4 .
  • Maliepaard , M C , Page , J H , Harrison , J P and Stubbs , R J . 1985 . Ultrasonic studies of the vibrational modes of sintered metal powders . Phys. Rev. , B 32 : 6261 – 71 .
  • Page , J H and McCulloch , R D . 1986 . Ultrasound propagation in sintered metal powder: evidence of a crossover from phonons to fractons . Phys. Rev. Lett. , 57 : 1324 – 7 .
  • Nakayama , T , Yakubo , K and Orbach , R L . 1994 . Dynamical properties of fractal networks: scaling, numerical simulations, and physical realizations . Rev. Mod. Phys. , 66 : 381 – 443 .
  • Vacher , R , Woignier , T , Pelous , J and Courtens , E . 1988 . Structure and self-similarity of silica aerogels . Phys. Rev. , B 37 : 6500 – 3 .
  • Courtens , E , Pelous , J , Phalippou , J , Vacher , R and Woignier , T . 1987 . Brillouin-scattering measurements of phonon-fracton crossover in silica aerogels . Phys. Rev. Lett. , 58 : 128 – 31 .
  • Courtens , E , Vacher , R , Pelous , J and Woignier , T . 1988 . Observation of fractons in silica aerogels . Europhys. Lett. , 6 : 245 – 50 .
  • Courtens , E and Vacher , R . 1992 . Structure and dynamics of silica aerogels . Phil. Mag. , B 65 : 347 – 55 .
  • Stoll , E and Courtens , E . 1990 . Connectivity and the fractal dimension of percolation clusters . Z. Phys. , B 81 : 1 – 2 .
  • Pachet , N and Page , J H . 1989 . “ Ultrasonic velocity and attenuation in a glass-bead percolation system ” . In Phonons 89 , Edited by: Hunklinger , S . 679 – 81 . Singapore : World Scientific .
  • Schriemer , H P and Page , J H . 1992 . “ Ultrasonic investigation of acoustic phonons at megaHertz frequencies in sintered glass-bead networks ” . In Phonon Scattering in Condensed Matter VII , Edited by: Meisser , M and Pohl , R O . 281 – 2 . Berlin : Springer . Springer Series in Solid State Sciences
  • Stauffer , D . 1985 . Introduction to Percolation Theory , London : Taylor and Francis .
  • Roux , S and Guyon , E . 1986 . “ Transport exponents in percolation ” . In On Growth and Form , Edited by: Stanley , E and Ostrowsky , N . 273 – 7 . Dordrecht : Nijhoff .
  • Alexander , A and Orbach , R . 1982 . Density of states on fractals: ‘fractons’ . J. Physique , 43 : 625 – 31 .
  • Rammal , R and Toulouse , G . 1983 . Random walks on fractal structures and percolation clusters . J. Physique Lett. , 44 : L13 – 22 .
  • Aharony , A , Alexander , S , Entin-Wohlman , O and Orbach , R . 1986 . Scattering of fractons, the Ioffe-Regel criterion, and the 4/3 conjecture . Phys. Rev. Lett. , 58 : 132 – 5 .
  • Stauffer , D . 1986 . “ Percolation and cluster size distribution ” . In On Growth and Form , Edited by: Stanley , E and Ostrowsky , N . 79 – 100 . Dordrecht : Nijhoff .
  • Webman , I and Grest , G S . 1984 . Dynamic behaviour of fractal structures . Phys. Rev. , B 31 : 1689 – 92 .
  • Born , M and Huang , K . 1954 . Dynamical Theory of Crystal Lattices , New York : Oxford University Press .
  • Sahimi , M and Arbabi , S . 1993 . Mechanics of disordered solids. II. Percolation on elastic networks with bond-bending forces . Phys. Rev. , B 47 : 703 – 12 .
  • Feng , S , Sen , P N , Halperin , B I and Lobb , C J . 1984 . Percolation on two-dimensional elastic networks with rotationally invariant bond-bending forces . Phys. Rev. , B 30 : 5386 – 9 .
  • Feng , S and Sahimi , M . 1985 . Position-space renormalization for elastic percolation networks with bond-bending forces . Phys. Rev. , B 31 : 1671 – 3 .
  • Bergman , D J . 1985 . Elastic moduli near percolation: universal ratio and critical exponent . Phys. Rev. , B 31 : 1696 – 8 .
  • Roux , S . 1986 . Relation between elastic and scalar transport exponent in percolation . J. Phys. A: Math. Gen. , 19 : L351 – 6 .
  • Sahimi , M . 1986 . Relation between the critical exponent of elastic percolation networks and the conductivity and geometrical exponents . J. Phys. C: Solid State Phys. , 19 : L79 – 83 .
  • Zabolitsky , J G , Bergman , D J and Stauffer , D . 1986 . Precision calculation of elasticity for percolation . J. Stat. Phys. , 44 : 211 – 23 .
  • Arbabi , S and Sahimi , M . 1988 . Elastic properties of three dimensional percolation networks with stretching and bond-bending forces . Phys. Rev. , B 38 : 7173 – 6 .
  • Ioffe , A F and Regel , A R . 1960 . Prog. Semicond. , 4 : 237
  • Song , Y , Noh , T W , Lee , S and Gaines , J R . 1986 . Experimental study of the three-dimensional AC conductivity and dielectric constant of a conductor-insulator composite near the percolation threshold . Phys. Rev. , B 33 : 904 – 8 .
  • Page , J H and McCulloch , R D . 1986 . “ Phase-insensitive measurements of ultrasonic attenuation near the phonon-fracton crossover in sintered powder ” . In Phonon Scattering in Condensed Matter V , Edited by: Anderson , A C and Wolfe , J P . 221 – 3 . Berlin : Springer . Springer Series in Solid-State Sciences
  • Cohen , M H , Jortner , J and Webman , I . 1977 . Electrical Transport and Optical Properties of Inhomogeneous Media , Edited by: Garland , J C and Tanner , D B . New York : AIP .
  • Liebovitch , L S and Toth , T . 1989 . A fast algorithm to determine fractal dimensions by box counting . Phys. Lett. , 141A : 386 – 90 .
  • Huang , Q , Lorch , J R and Dubes , R C . 1994 . Can the fractal dimension of images be measured? . Pattern Recog. , 27 : 339 – 49 .
  • Pachet , N G . 1990 . “ Ultrasonic velocity and attenuation in a glass-bead percolation system ” . In MSc Thesis , Winnipeg : University of Manitoba .
  • Paul , A . 1982 . Chemistry of Glasses , London : Chapman and Hall .
  • Alexander , A . 1984 . Is the elastic energy of amorphous materials rotationally invariant? . J. Physique , 45 : 1939 – 45 .
  • Halperin , B I , Feng , S and Sen , P N . 1985 . Differences between lattice and continuum percolation transport exponents . Phys. Rev. Lett. , 54 : 2391 – 4 .
  • Ye , L , Weitz , D A , Sheng , P , Bhattacharya , S , Huang , J S and Higgins , M J . 1989 . Dynamics rigidity percolation in inverted micelles . Phys. Rev. Lett. , 63 : 263 – 6 .
  • Bergman , D J and Kantor , Y . 1984 . Critical properties of an elastic fractal . Phys. Rev. Lett. , 53 : 511 – 4 .
  • Bogardus , E H . 1965 . Third-order elastic constants of Ge, MgO, and fused SiO . J. Appl. Phys. , 36 : 2504 – 13 .
  • Hughes , D S and Kelly , J L . 1953 . Second-order elastic deformations of solids . Phys. Rev. , 92 : 1145 – 9 .
  • Xhonneux , P , Courtens , E , Pelous , J and Vacher , R . 1989 . Scaling nonlinear elasticity in silica aerogels . Europhys. Lett. , 10 : 733 – 8 .
  • Page , J H , Schriemer , H P , Bailey , A E and Weitz , D A . 1995 . Experimental test of the diffusion approximation for multiply scattered sound . Phys. Rev. , E 52 : 3106 – 14 .
  • Papadakis , E P . 1981 . “ Scattering in polycrystalline media ” . In Ultrasonics, Methods of Experimental Physics , Edited by: Edmonds , P D . Vol. 19 , 237 – 98 . New York : Academic .

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