Article PDF
Avoid common mistakes on your manuscript.
Abbreviations
- b :
-
Burger's vector of a dislocation, taken as the distance between closest rows of atoms
- c :
-
Velocity of elastic waves;c e, ct, cl, values for extensional, transversal and longitudinal waves; also a constant
- d :
-
Logarithmic decrement
- e :
-
Logarithmic constant=2.718...
- f :
-
Vibration frequency at the temperatureT; f m, value at the temperatureT m of maximum energy dissipation;f 0, relaxed value of frequency at the temperatureT; f m,0, limiting value off m at very high temperatures
- h :
-
Planck's constant
- l :
-
Dislocation lenght
- k :
-
Boltzmann constant
- m :
-
Linear density of a dislocation
- t :
-
Time
- w :
-
Lenght of a kinked segment of a dislocation
- x :
-
Axis parallel to the dislocation line
- y :
-
Axis normal to the dislocation line
- E :
-
Energy per unit lenght which opposes the motion of a dislocation;E c constant term in the series expansion ofE(y)
- F 1 :
-
Function of the ratio (H cr/2H k) considered in Donth's theory
- H :
-
Computed value of the activation energy;H M, HW, Hs, values given by Mason, Weertman, Seeger's formulae;H k, energy of a single kink;H cr, critical energy for a couple of kinks
- M :
-
Elastic modulus;M R, MU, relaxed and unrelaxed values
- N 0 :
-
Volume density of dislocations
- Q :
-
Coefficient of resonance (quality factor) of a solid. Usually the inverse valueQ −I is taken as a measure of energy dissipation;Q −1m , value ofQ −1 at the peak
- S :
-
Total relaxation strenght;S e, Sl, values for extensional and longitudinal vibrations
- T :
-
Absolute temperature;T m, temperature of maximum energy dissipation
- U :
-
Vibration energy
- W :
-
Experimental value of the activation energy for the relaxation effect;W −I, value for the Niblett and Wilks peak; W, central value of a spectrum of activation energies
- Y :
-
Attenuation function for a single relaxation time; Yτ,YW, values computed for the centers of a time- or of an energy-spectrum
- α:
-
Attenuation coefficient of vibration amplitude with space
- β:
-
Temperature coefficient of frequency =−∂ logf/∂T
- γ:
-
Parameter characterizing the width of a Fuoss-Kirkwood spectrum
- δ(τ):
-
Density of relaxation strengt in a dislocation spectrum; δm, maximum value of δ(τ)
- Δ:
-
Increment of some physical quantity; ΔU, increment of vibration energy; ΔW, increment of activation energy
- ε:
-
Strain; ɛel,ɛap, elastic and anelastic components
- η:
-
Parameter characterizing the width of a rectangular spectrum =½logτ2/τ1
- Θ:
-
Debye's temperature
- λ:
-
Wavelenght
- μ:
-
Second Lamé's constant
- ν:
-
Computed frequency of dislocation motion;v 0, limiting value of ν at very high temperatures
- ϱ:
-
Volume density of a solid
- σ:
-
Stress; σ 0p , Feierls' stress when thermal and quantum mechanical fluctuations are disregarded
- τ:
-
Characteristic time of a relaxation effect, at the temperatureT; τ0, limiting value of τ at very high temperatures; τ central value of a relaxation spectrum; τ1,τ2, values at which the density σ(τ) is 1/√2 of its maximum value δm; limiting value of τ at very high temperatures
References
P. G. Bordoni:Journ. Acoust. Soc. Am.,26, 495 (1954).
H. E. Boemmel:Phys. Rev.,96, 220 (1954).
H. E. Boemmel, W. P. Mason, A. Warner:Phys. Rev.,99, 1894 (1955);102, 64 (1956).
D. H. Niblett andJ. Wilks:Phil. Mag.,1, 415 (1956).
T. S. Hutchison andG. J. Hutton:Can. Journ. Phys.,34, 1498 (1956).
T. S. Hutchison andA. J. Filmer:Can. Journ. Phys.,34, 159 (1956).
W. P. Mason andH. E. Boemmel:Journ. Acoust. Soc. Am.,28, 930 (1956).
D. H. Niblett andJ. Wilks:Phyl. Mag.,2, 1427 (1957).
N. G. Einspruch andR. Truell:Phys. Rev.,109, 652 (1958).
P. G. Bordoni andM. Nuovo:Effect of Crystal Dislocations upon Vibrations (Contribution to the Palais de la Science of the Exposition Universelle de Bruxelles, 1958).
H. L. Caswell:Journ. Appl. Phys.,29, 1210 (1958).
A. J. Filmer, G. J. Hutton andT. S. Hutchison:Journ. Appl. Phys.,29, 146 (1958).
V. K. Parè:Experimental and Theoretical Study of low-temperature internal Friction in Copper (Cornell University, Dept. Eng. Phys., Techn. Rep., n. 4, July 1958).
D. Thompson andF. H. Glass:Rev. Sci. Instr.,29, 1034 (1958).
P. G. Bordoni, M. Nuovo andL. Verdini:Phys. Rev. Lett.,2, 200 (1959).
P. G. Bordoni, M. Nuovo andL. Verdini:Nuovo Cimento,14, 273 (1959).
D. O. Thompson andD. K. Holmes:Journ. Appl. Phys.,30, 525 (1959).
P. G. Bordoni, M. Nuovo andL. Verdini:Relaxation of Dislocations in facecentered cubic Metals (to be published in the Proceedings of the III I.C.A. Congress Stuttgart, September 1959).
I. Barducci, M. Nuovo andL. Verdini:Bordoni Peak in Silver-gold Alloys (to be published in the Proceedings of the III I.C.A. Congress Stuttgart, September 1959);Nuovo Cimento, (to be published).
P. G. Bordoni, M. Nuovo andL. Verdini:Dislocation Relaxation in Silver, Gold, Palladium and Platinum (to be published).
References
P. G. Bordoni:Ric. Scient.,19, 851 (1949).
W. P. Mason:Phys. Rev.,98, 1136 (1955);Bell System Tech. Journ.,34, 903 (1955).
J. Weertman:Journ. Appl. Phys.,26, 202 (1955).
W. P. Mason:Journ. Acoust. Soc. Am.,27, 643 (1955).
J. Weertman:Phys. Rev.,101, 1429 (1956).
W. P. Mason:Phys. Rev.,101, 1430 (1956).
P. G. Bordoni: Proc. II I.C.A. Congress, 101 (1956).
A. Seeger:Phil. Mag.,1, 651 (1956).
H. Donth:Zeits. f. Phys.,149, 111 (1957).
A. Seeger, H. Donth andP. Pfaff:Discussions Far. Soc.,23, 19 (1957).
W. P. Mason:Physical Acoustic and the Properties of Solids (New York, 1958) p. 266–271.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bordoni, P.G. Dislocation relaxation at high frequencies. Nuovo Cim 17 (Suppl 1), 43–91 (1960). https://doi.org/10.1007/BF02911183
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02911183