The Size Effect of Thin Films on the Peierls Stress of Edge Dislocations

Abstract

In this paper, we have developed a half-space Peierls—Nabarro (HSPN) model to evaluate dislocation mobility on material surface. The free-surface induced size effect on the mobility of an edge dislocation in thin films is investigated by using the model. The thickness of the thin layer between the dislocation and the free surface significantly influences the mobility of the dislocation. The Peierls stress of the edge dislocation in a thin film may be expressed as a function of the thickness of the thin film. A closed-form solution is obtained for the scaling factor, defined as the ratio of the modified Peierls stress to the conventional one in bulk materials, which allows for the characterization of the size (depth) effect on the Peierls stress of the edge dislocation in the half-space. Depending on the core size of the dislocation, the Peierls stress of a surface edge dislocation is about 5% to 25% less than that found in bulk materials.

Keywords

Dislocations lattice friction Peierls—Nabarro model scaling law size effects

Get full access to this article

View all access options for this article.

References

Vendik, O.G. , Zubko, S.P. and Ter-martirosayn , L.T. Experimental evidence of the size effect in thin ferroelectric films. Applied Physics Letters, 73, 37-39 (1998).

Espinosa, H. and Prorok, B. Size effects on the mechanical behavior of gold thin films. Journal of Materials Science, 38, 4125-4128 (2003 ).

Bazant, Z. , Guo, Z. , Espinosa, H. , Zhu, Y. and Peng, B. Epitaxially influenced boundary layer model for size effect in thin metallic films. Journal of Applied Physics, 97, 073506 (2005 ).

Han, C.-S. , Hartmaiera, A. , Gao , H. and Huang, Y. Discrete dislocation dynamics simulations of surface induced size effects in plasticity. Materials Science and Engineering: A, 415, 225-233 (2005).

Peierls, R. The size of a dislocation. Proceedings of the Physical Society of London, 52, 34-37 (1940).

Nabarro, F.R.N. Dislocations in a simple cubic lattice. Proceedings of the Physical Society of London, 59, 256-272 (1947).

Lee, C.-L. and Li, S. A half-space Peierls-Nabarro model and the mobility of screw dislocations in a thin film. Acta Materialia , 55, 2149-2157 (2007).

Joos, B. and Duesbery, M.S. The Peierls stress of dislocations: An analytic formula. Physical Review Letters, 78, 266-269 (1997).

Vitek, V. Intrinsic stacking faults in body-centred cubic crystals. Philosophical Magazine, 18, 773-786 (1968).

10.

Joos, B. , Ren, Q. and Duesbery, M.S. Peierls-Nabarro model of dislocations in silicon with generalized stacking-fault restoring forces. Physical Review B, 50, 5890-5898 (1994).

11.

Schoeck, G. The generalized Peierls-Nabarro model. Philosophical Magazine A-Physics of Condensed Matter Structure Defects and Mechanical Properties, 69, 1085-1095 (1994 ).

12.

Juan, Y.M. and Kaxiras, E. Generalized stacking fault energy surfaces and dislocation properties of silicon: A first-principles theoretical study . Philosophical Magazine A-Physics of Condensed Matter Structure Defects and Mechanical Properties, 74, 1367-1384 (1996 ).

13.

Bulatov, V.V. and Kaxiras, E. Semidiscrete variational Peierls framework for dislocation core properties. Physical Review Letters, 78, 4221-4224 (1997).

14.

Hartford, J. , von Sydow, B. , Wahnstrom , G. and Lundqvist, B.I. Peierls barriers and stresses for edge dislocations in Pd and Al calculated from first principles. Physical Review B, 58, 2487-2496 (1998).

15.

G. Schoeck , The Peierls energy revisited. Philosophical Magazine a-Physics of Condensed Matter Structure Defects and Mechanical Properties, 79 (11) (1999) 2629-2636.

16.

Schoeck, G. Peierls energy of dislocations: A critical assessment. Physical Review Letters, 82, 2310-2313 (1999).

17.

Wang, J.N. A new modification of the formulation of Peierls stress, Acta Materialia, 44, 1541-1546 (1996 ).

18.

Wang, J.N. Prediction of Peierls stresses for different crystals. Materials Science and Engineering A-Structural Materials Properties Microstructure and Processing, 206, 259-269 (1996).

19.

Lu, G. , Kioussis, N. , Bulatov , V. and Kaxiras, E. The Peierls-Nabarro model revisited. Philosophical Magazine Letters, 80, 675-682 (2000).

20.

Nabarro, F.R.N. Fifty-year study of the Peierls-Nabarro stress. Materials Science and Engineering A-Structural Materials Properties Microstructure and Processing, 234, 67-76 (1997).

21.

Schoeck, G. The Peierls model: Progress and limitations . Materials Science and Engineering A-Structural Materials Properties Microstructure and Processing, 400, 7-17 (2005).

22.

Hirth, J.P. and Lothe, J. Theory of Dislocations, 2nd Edition, Krieger, Malabar, FL, 1992.

23.

Freund, L.B. and Suresh, S. Thin Film Materials: Stress, Defect Formation, and Surface Evolution, Cambridge University Press, New York, 2003.

24.

Kreyszig, E. Advanced Engineering Mathematics, Wiley, New York, 8th edition, 1998.

25.

Hansen, E.R. A Table of Series and Products, Prentice-Hall Series in Automatic Computation , Prentice-Hall, Englewood Cliffs, NJ, 1975.