Dislocation Core Effects on Mobility

Dislocation Core Effects on Mobility Wei Cai1,∗ Vasily V. Bulatov1,† Jinpeng Chang2, Ju Li2‡ and Sidney Yip2§ 1 Lawrence Livermore National Laboratory, University of California, Livermore, CA 94551 2 Department of Nuclear Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139 Chapter 64 in Dislocations in Solids, F.R.N. Nabarro and J.P. Hirth, ed., volume 12, p. 1 (2004) Imprint: North-Holland ISBN: 0-444-51483-X http://www.elsevier.com/wps/find/bookvolume.cws home/503920/vol11 ∗Present Address: Durand 259, 496 Lomita Mall, Department of Mechanical Engineer- ing, Stanford University, Stanford, CA 94305-4040 Phone: (650)736-1671 Fax: (650)723- 1778 Email: [email protected] †Phone: (925)-423-0124 Email: [email protected] ‡Present address: Department of Materials Science and Engineering, Ohio State Uni- versity, Columbus, OH 43210. §To whom correspondence should be addressed. Mailing address: M.I.T. Room 24-208, 77 Mass Ave, Cambridge, MA 02139. Phone: (617)253-3809 Fax: (617) 258-8863 Email: [email protected] 1 Contents 1 Introduction 3 2 FCC Metals 8 2.1 Core Structure . 8 2.2 Mobility . 11 2.3 Junctions . 15 2.4 Cross-slip . 20 2.5 Interaction with point defects . 23 2.6 Outstanding issues . 28 3 Diamond-Cubic Semiconductors 29 3.1 Introduction . 29 3.2 Core structure and lattice resistance . 34 3.3 Secondary core defects . 43 3.4 Dislocation mobility . 57 3.5 Outstanding issues . 71 4 BCC Metals 73 4.1 Introduction . 73 4.2 Core structure and lattice resistance . 76 4.3 Secondary core defects . 84 4.4 Dislocation mobility . 93 4.5 Outstanding issues . 102 5 Concluding Remarks 105 2 1 Introduction The purpose of this chapter is to discuss the atomic structure and interactions in the dislocation core and their effects on dislocation mobility from the standpoint of theoretical concepts, physical models and simulation stud- ies, with due consideration of relevant experimental results. Several previous chapters in this series provide the necessary background and more extensive exposition into several topics to be discussed here: Bullough and Tewary, “Lattice Theories of Dislocations” (vol. 2, 1979), Weertman and Weertman, “Moving Dislocations” (vol. 3, 1980), Schoeck, “Thermodynam- ics and Thermal Activation of Dislocations” (vol. 3, 1980), and M. Duesbery, “The Dislocation Core and Plasticity” (vol. 8, 1989). Rather than being comprehensive, our intent in this new chapter is to highlight some of the recent developments in understanding dislocation core structure and mobility. These include the driving forces and activation barriers for dislocation motion, the models which relate mobility to core properties, and the results of atomistic simulations at the levels of first-principles calculations and empirical and semi-empirical interatomic potentials. In our discussions, the major emphasis is placed on physical ideas and observations. In fact, technical details of modelling and experiments are only briefly mentioned and only where required for clarification of physics issues or for interpretation of results. In this introductory section we provide general background and introduce several basic concepts in order to frame the discussion given in three subse- quent sections dealing with particular crystal structures and material types: FCC metals, diamond-cubic semiconductors, and BCC metals. The reason for treating FCC materials first is that historically the understanding of core effects on dislocation mobility developed mostly in conjunction with this crystallography class. FCC systems give us a good chance to discuss some of the better established views and approaches and set the stage for contrasting these with more recent observations of core effects in other materials. Dis- location cores in FCC materials tend to be planar and spread out in extent; they dissociate into partials that interact with each other and move by glid- ing on a slip plane. Dislocation response to stress in these systems generally obeys the Schmid law established for macroscopic crystal plasticity. A well- known model, due to Peierls and Nabarro, provides a simple framework that captures dislocation core and mobility behaviour in FCC metals reasonably well. In contrast, dislocation cores and dislocation mobility in semiconductors are affected by strong directional bonding that is responsible for the 3 appearance of a rich family of secondary core defects. The existence of glide and shuffle sets of dislocation positions in diamond cubic semiconductors in- troduces still more complexity with regard to the role of core mechanisms in dislocation motion. Plasticity behaviour of BCC metals is controlled, to a large extent, by the motion of screw dislocations. The core of screw dislocations is relatively compact but in some BCC metals exhibits a tendency to three-way non-planar dissociation or polarization. Dislocation mobility exhibits large deviation from the canonical Schmid behaviour as a function of stress. The connection between details of core structure and mobility of screw dislocations in BCC metals has been a topic of intense research but remains somewhat controversial. Of all known material systems, the most pronounced and intricate core effects arguably are observed in ordered inter- metallic alloys, such as nickel-based superalloys or TiAl composites. These however are discussed in great detail in a recent volume (vol. 10) of this series and will not be considered here. Since the most recent chapter by M.S. Duesbery (vol. 8) that was ded- icated to dislocation core and crystal plasticity, several important developments have come to fore that brought about significant progress towards quantitative analysis of the dislocation core structure and its effects on mobility. A major factor in these recent developments is the emergence of new capabilities for accurate first-principles electronic structure calculations of dislocation core structure, energy and mobility. Over the same period, the models based on the empirical potentials have been used to explore realistic complexity of fully three-dimensional dynamics of individual dislocations and dislocation groups. These recent simulations revealed a rich sub-structure of secondary core defects and multiple mechanisms of dislocation motion in 3D. Yet another principal development of the past decade is the emergence of the fully three-dimensional mesoscale simulation methodology of Dislocation Dy- namics (DD) that can be used, in principle, for computational prediction of overall crystal plasticity behaviour from the underlying physics of dislocation motion. For this impressive development to deliver on its ultimate promise, understanding of the core mechanisms of dislocation mobility is crucial. Fi- delity of DD simulations places high demands on the accuracy of dislocation mobility functions that can be derived and parameterised from direct atomistic simulations, dislocation theory and experimental observations. On the experimental side, new capabilities for HREM allow for direct observations of the secondary structure of dislocations and approach the limits of resolution required to resolve the relevant details of the dislocation core structure [1]. 4 However, reading through this chapter one is likely to observe that the progress towards understanding dislocation core effects has not been always steady. A few seemingly well established ideas and concepts now appear to be in conflict with the more recent data, while other previous inconsistencies no longer exist in light of the new results. Even if it is disturbing that a number of key issues in dislocation mobility remain controversial, we consider this as an indication to critically revisit, given the new capabilities, some of the existing concepts in dislocation physics. We believe the situation presents an opportunity to develop new knowledge of dislocation mobility that is more coherent and quantitative than previously existed. Basic concepts Plastic strain produced in response to shear stress is a cumulative result of multiple displacements along the crystallographic slip planes in quanta of the Burgers vector. Conservative dislocation motion or glide involves local atomic displacements that proceed through switching one or few interatomic bonds at a time. In comparison, homogeneous shear along the crystallographic slip plane requires switching all interatomic bonds across the plane at once and, as such, must be prohibitively expensive energetically unless the stress reaches rather high values near the theoretical shear strength (typically of the order of µ/10, with µ the shear modulus of the material). Experimen- tally observed values of the yield stress are typically much lower than this ideal shear resistance, with notable exceptions of deformation response of whiskers [2] and single crystals under nano-indentation [3, 4]. Exactly how a dislocation moves is defined by the energetics of bond- switching rearrangements required for its translation by a unit atomic dis- tance in the glide plane. Somewhat loosely, one can define the core as a region of crystal lattice around the dislocation line in which the relative displacements of the neighbouring atoms exceed the elastic limit (say 2% in terms of the local shear strain). Given the highly non-linear character of interatomic interactions in the core, it is clearly the relative motion of the core atoms that contributes most to the energetics of dislocation translation. Conversely, the relative displacements of the atoms outside the core will not contribute as much to the

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