Peierls Stress and Creep of a Linear Chain

J. H. Weiner; W. T. Sanders

doi:10.1103/PhysRev.134.A1007

Access by Xinjiang University

Peierls Stress and Creep of a Linear Chain

J. H. Weiner and W. T. Sanders

Department of Mechanical Engineering, Columbia University, New York, New York

PDF

Phys. Rev. 134, A1007 – Published 18 May, 1964

DOI: https://doi.org/10.1103/PhysRev.134.A1007

Abstract

The Frenkel-Kontorova dislocation model is modified by replacing the sinusoidal substrate force by one which is piecewise linear. Exact solutions are found for the static configuration and for the Peierls stress, $σ_{P}$ . Good agreement is found between these values of $σ_{P}$ and those obtained previously for a two-dimensional Rosenstock-Newell model. The atoms of the linear chain are then considered in random motion corresponding to thermal equilibrium and under an applied stress $σ < σ_{P}$ . The time required for motion of the dislocation from one position of stable equilibrium to an adjacent one is computed by means of a rate-theory formulation adapted to the present type of problem in which the positions of all the atoms in the chain are required to vary in passing over the potential barrier. The theoretical transition times for an infinite chain are compared with analog computer results for a six-atom chain and reasonably good agreement is found.

References (14)

J. Lothe and J. P. Hirth, Phys. Rev. 115, 543 (1959)
A. Seeger, H. Donth, and F. Pfaff, Discussions Faraday Soc. 23, 19 (1957)
J. Frenkel and T. Kontorova, Phys. Z. Sowjetunion 13, 1 (1938) J. Phys. (U.S.S.R.) 1, 137 (1939) [J. Kratochvil and V. L. Indenbom, Czech. J. Phys. 13, 814 (1963)]
W. T. Sanders, Phys. Rev. 128, 1540 (1962)
H. Eyring, J. Chem. Phys. 3, 107 (1935) C. Wert and C. Zener, Phys. Rev. 76, 1169 (1949) C. Wert, ibid. 79, 601 (1950) G. H. Vineyard, Phys. Chem. Solids 3, 121 (1957)
Omitted endnote
F. R. Gantmacher and M. G. Krein, Oszillationsmatrizen, Oszillationskerne und Kleine Schwingungen Mechanischer Systeme (Akademie-Verlag, Berlin, 1960), p. 80
Lord Rayleigh, The Theory of Sound (Dover Publications, New York, 1945), Vol. 1, p. 111
R. Hobart and V. Celli, J. Appl. Phys. 33, 60 (1962)
Omitted endnote
Omitted endnote
S. O. Rice, Bell Syst. Tech. J. 24, 58 (1945) Selected Papers on Noise and Stochastic Processes, edited by N. Wax (Dover Publications, New York, 1954), p. 190
A. Seeger, Phil. Mag. 1, 651 (1956)
J. Weertman, J. Appl. Phys. 28, 1185 (1957)

[c1] J. Lothe and J. P. Hirth, Phys. Rev. 115, 543 (1959)

[c2] A. Seeger, H. Donth, and F. Pfaff, Discussions Faraday Soc. 23, 19 (1957)

[c3] J. Frenkel and T. Kontorova, Phys. Z. Sowjetunion 13, 1 (1938) J. Phys. (U.S.S.R.) 1, 137 (1939) [J. Kratochvil and V. L. Indenbom, Czech. J. Phys. 13, 814 (1963)]

[c4] W. T. Sanders, Phys. Rev. 128, 1540 (1962)

[c5] H. Eyring, J. Chem. Phys. 3, 107 (1935) C. Wert and C. Zener, Phys. Rev. 76, 1169 (1949) C. Wert, ibid. 79, 601 (1950) G. H. Vineyard, Phys. Chem. Solids 3, 121 (1957)

[c6] Omitted endnote

[c7] F. R. Gantmacher and M. G. Krein, Oszillationsmatrizen, Oszillationskerne und Kleine Schwingungen Mechanischer Systeme (Akademie-Verlag, Berlin, 1960), p. 80

[c8] Lord Rayleigh, The Theory of Sound (Dover Publications, New York, 1945), Vol. 1, p. 111

[c9] R. Hobart and V. Celli, J. Appl. Phys. 33, 60 (1962)

[c10] Omitted endnote

[c11] Omitted endnote

[c12] S. O. Rice, Bell Syst. Tech. J. 24, 58 (1945) Selected Papers on Noise and Stochastic Processes, edited by N. Wax (Dover Publications, New York, 1954), p. 190

[c13] A. Seeger, Phil. Mag. 1, 651 (1956)

[c14] J. Weertman, J. Appl. Phys. 28, 1185 (1957)

Physical Review Journals Archive

Export citation

Export citation

Peierls Stress and Creep of a Linear Chain

Abstract

References (14)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation