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

Waves Random Media

Volumn 6, Issue 4, 1996, Pages 361-386

  Schriemer, H P ^a   Pachet, N G ^a   Page, J H ^a  

^a UNIVERSITY OF MANITOBA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0642295072     PISSN: 09597174     EISSN: None     Source Type: Journal    
DOI: 10.1088/0959-7174/6/4/004     Document Type: Article

References (45)

1. Deptuck D, Harrison J D and Zawadzki P 1985 Measurement of elasticity and conductivity of a threedimensional percolation system Phys. Rev. Lett. 54 913-6
2. Kantor Y and Webman I 1984 Elastic properties of random percolating systems Phys. Rev. Lett. 52 1891-4
3. 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
4. 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
5. 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
6. Vacher R, Woignier T, Pelous J and Courtens E 1988 Structure and self-similarity of silica aerogels Phys. Rev. B 37 6500-3
7. 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
8. Courtens E, Vacher R, Pelous J and Woignier T 1988 Observation of fractons in silica aerogels Europhys. Lett. 6 245-50
9. Courtens E and Vacher R 1992 Structure and dynamics of silica aerogels Phil. Mag. B 65 347-55
10. Stoll E and Courtens E 1990 Connectivity and the fractal dimension of percolation clusters Z. Phys. B 81 1-2
11. Pachet N and Page J H 1989 Ultrasonic velocity and attenuation in a glass-bead percolation system Phonons 89 ed S Hunklinger et al (Singapore: World Scientific) pp 679-81
12. Schriemer H P and Page J H 1992 Ultrasonic investigation of acoustic phonons at megaHertz frequencies in sintered glass-bead networks Phonon Scattering in Condensed Matter VII (Springer Series in Solid State Sciences) ed M Meisser and R O Pohl (Berlin: Springer) pp 281-2
13. Stauffer D 1985 Introduction to Percolation Theory (London: Taylor and Francis)
14. Roux S and Guyon E 1986 Transport exponents in percolation On Growth and Form ed E Stanley and N Ostrowsky (Dordrecht: Nijhoff) pp 273-7
15. Alexander A and Orbach R 1982 Density of states on fractals: 'fractons' J. Physique 43 625-31
16. Rammal R and Toulouse G 1983 Random walks on fractal structures and percolation clusters J. Physique Lett. 44 L13-22
17. Aharony A, Alexander S, Entin-Wohlman O and Orbach R 1986 Scattering of fractons, the loffe-Regel criterion, and the 4/3 conjecture Phys. Rev. Lett. 58 132-5
18. Stauffer D 1986 Percolation and cluster size distribution On Growth and Form ed E Stanley and N Ostrowsky (Dordrecht: Nijhoff) pp 79-100
19. Webman I and Grest G S 1984 Dynamic behaviour of fractal structures Phys. Rev. B 31 1689-92
20. Born M and Huang K 1954 Dynamical Theory of Crystal Lattices (New York: Oxford University Press)
21. 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
22. 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
23. Feng S and Sahimi M 1985 Position-space renormalization for elastic percolation networks with bond-bending forces Phys. Rev. B 31 1671-3
24. Bergman D J 1985 Elastic moduli near percolation: universal ratio and critical exponent Phys. Rev. B 31 1696-8
25. Roux S 1986 Relation between elastic and scalar transport exponent in percolation J. Phys. A: Math. Gen. 19 L351-6
26. 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
27. Zabolitsky J G, Bergman D J and Stauffer D 1986 Precision calculation of elasticity for percolation J. Stat. Phys. 44 211-23
28. 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
29. Ioffe A F and Regel A R 1960 Prog. Semicond. 4 237
30. 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
31. Page J H and McCulloch R D 1986 Phase-insensitive measurements of ultrasonic attenuation near the phonon-fracton crossover in sintered powder Phonon Scattering in Condensed Matter V (Springer Series in Solid-State Sciences) ed A C Anderson and J P Wolfe (Berlin: Springer) pp 221-3
32. Cohen M H, Jortner J and Webman I 1977 Electrical Transport and Optical Properties of Inhomogeneous Media ed J C Garland and D B Tanner (New York: AIP)
33. Liebovitch L S and Toth T 1989 A fast algorithm to determine fractal dimensions by box counting Phys. Lett. 141A 386-90
34. Huang Q, Lorch J R and Dubes R C 1994 Can the fractal dimension of images be measured? Pattern Recog. 27 339-49
35. Pachet N G 1990 Ultrasonic velocity and attenuation in a glass-bead percolation system MSc Thesis University of Manitoba, Winnipeg
36. Paul A 1982 Chemistry of Glasses (London: Chapman and Hall)
37. Alexander A 1984 Is the elastic energy of amorphous materials rotationally invariant? J. Physique 45 1939-45
38. Halperin B I, Feng S and Sen P N 1985 Differences between lattice and continuum percolation transport exponents Phys. Rev. Lett. 54 2391-4
39. 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
40. Bergman D J and Kantor Y 1984 Critical properties of an elastic fractal Phys. Rev. Lett. 53 511-4
41. Bogardus E H 1965 Third-order elastic constants of Ge, MgO, and fused SiO J. Appl. Phys. 36 2504-13
42. Hughes D S and Kelly J L 1953 Second-order elastic deformations of solids Phys. Rev. 92 1145-9
43. Xhonneux P, Courtens E, Pelous J and Vacher R 1989 Scaling nonlinear elasticity in silica aerogels Europhys. Lett. 10 733-8
44. Page J H, Schriemer H P, Bailey A E and Weitz DA 1995 Experimental test of the diffusion approximation for multiply scattered sound Phys. Rev. E 52 3106-14
45. Papadakis E P 1981 Scattering in polycrystalline media Ultrasonics, Methods of Experimentat Physics 19 ed P D Edmonds (New York: Academic) pp 237-98