Roman Gröger

Twinning disconnections and basal–prismatic twin boundary in magnesium

Recent experiments have revealed that the twin boundaries in hexagonal materials are decorated by basal?prismatic (BP) facets. The objective of this paper is to investigate the mechanism that leads to the formation of these BP interfaces using atomistic simulations and to carry out their stability analysis under an externally applied shear. We demonstrate that the stability of the BP interface is a consequence of large capillary forces that are caused by differences of the energies of a perfect twin boundary and the BP interface. The latter is formed by the glide of twinning disconnections and therefore agrees with the theory of admissible interfacial defects. This observation implies that the glide of twinning disconnections is a primary mechanism of the twin boundary migration.

Directional versus central-force bonding in studies of the structure and glide of 1/2⟨111⟩ screw dislocations in bcc transition metals

In this paper, we address the differences between Finnis–Sinclair potentials and bond-order potentials (BOPs) when studying 1/2⟨111⟩ screw dislocations in bcc transition metals, specifically Mo and W. These two types of potentials differ in that the former is central-force, whereas the latter include angular bonding. The cores of 1/2⟨111⟩ screw dislocations have two variants, one invariant with respect to the ⟨101⟩ diad and the other not. Hence, the latter core is degenerate. The BOPs always lead to the invariant type, whereas for Finnis–Sinclair potentials both variants occur. However, the symmetry of the core does not play a decisive role in the glide of dislocations. It is the description of interatomic forces that governs both the core structure and the glide behaviour of dislocations. The general characteristics of dislocation glide, the twinning–antitwinning asymmetry and a lower Peierls stress for tension than compression are the same for both types of potentials. Whereas the results obtained with BOPs are similar for the two cases studied, Finnis–Sinclair potentials lead to a broader variety. Particularly, the slip plane at 0 K is always {110} for BOPs but it is either {110} or {112} for Finnis–Sinclair potentials. The reason is that, in the latter case, the core configuration and core transformations are less constrained than in the former case. Hence, in bcc transition metals the BOPs are a more reliable description of atomic interactions than Finnis–Sinclair potentials, but when the d band does not play any important role, the Finnis–Sinclair potentials are fully applicable.

Breakdown of the Schmid Law in BCC Molybdenum Related to the Effect of Shear Stress Perpendicular to the Slip Direction

The breakdown of the Schmid law in bcc metals has been known for a long time. The asymmetry of shearing in the slip direction 〈111〉 in the positive and negative sense, respectively, commonly identified with the twinning-antitwinning asymmetry, is undoubtedly one of the reasons. However, effect of stress components other than the shear stress in the slip direction may be important. In this paper we investigate by atomistic modeling the effect of shear stresses perpendicular to the Burgers vector on the glide of a/2〈111〉 screw dislocations. We show that these shear stresses can significantly elevate or reduce the critical resolved shear stress (CRSS) in the direction of the Burgers vector needed for the dislocation motion, i.e. the Peierls stress. This occurs owing to the changes of the core induced by these stresses. This effect may be the reason why slip systems with smaller Schmid factors may be preferred over that with the largest Schmid factor.

Deformation due to migration of faceted twin boundaries in magnesium and cobalt

Recent experimental observations show that twin boundaries in hexagonal close-packed (hcp) metals are frequently faceted. The objective of this paper is to investigate the influence of this faceting on the strain produced by twinning. We show that basal–prismatic (BP) facets are terminated by opposite disclinations and the migration of these facets along a straight twin boundary produces ordinary twinning shear. On the other hand, joining conjugate twins gives rise to BP facets terminated on the parent twin boundaries by identical disclinations. In this case, the strain produced by the migration of BP facets is an average between the strains produced by the individual conjugate twins. These theoretical studies are complemented by two EBSD measurements on cobalt that is closely related to magnesium. The misorientation profiles measured across two conjugate twin boundaries yield a misfit of approx. 7° consistent with the theoretical prediction that the corner of a twin embryo is terminated by two identical disclinations, each accommodating a misfit of 3.7°.

Effect of Eshelby twist on core structure of screw dislocations in molybdenum: atomic structure and electron microscope image simulations

This paper addresses the question as to whether the core structure of screw dislocations in Mo in the bulk can be obtained from high-resolution electron microscopy (HREM) images of such dislocations viewed end-on in a thin foil. Atomistic simulations of the core structure of screw dislocations in elastically anisotropic Mo were carried out using bond order potentials. These simulations take account automatically of the effects of the surface relaxation displacements (anisotropic Eshelby twist). They show that the differential displacements of the atoms at the surface are different with components perpendicular to the Burgers vector about five times larger than those in the middle of the foil, the latter being characteristic of the bulk. Nye tensor plots show that the surface relaxation stresses strongly affect the incompatible distortions. HREM simulations of the computed structure reflect the displacements at the exit surface, modified by interband scattering and the microscope transfer function. Nye tensor plots obtained from the HREM images show that interband scattering also affects the incompatible distortions. It is concluded that it would be very difficult to obtain information on the core structure of screw dislocations in the bulk Mo from HREM images, even under ideal experimental conditions, and that quantitative comparisons between experimental and simulated images from assumed model structures would be essential.

Temperature and strain rate dependent flow criterion for bcc transition metals based on atomistic analysis of dislocation glide

Abstract 1/2111 screw dislocations that possess non-planar cores and thus a high lattice friction (Peierls) stress control the plastic deformation of pure bcc metals. In this paper we formulate an analytical flow criterion based on the recognition that at finite temperatures the screw dislocations glide via formation and subsequent propagation of pairs of kinks. This development employs first an atomistically calculated dependence of the Peierls stress on the applied loading to construct the Peierls potential that depends on the applied stress tensor. This Peierls potential is then used to evaluate the activation enthalpy for the kink-pair formation employing mesoscopic dislocation models and its dependence on the applied stress tensor is then approximated by a relatively simple analytical form. Using the standard transition state theory to ascertain the dislocation velocity and related strain rate allows us to formulate the temperature and strain rate dependent flow criterion. Implications of this criterion are then compared with available experimental data demonstrating its excellent predictive value.

Which stresses affect the glide of screw dislocations in bcc metals

By direct application of stress in molecular statics calculations we identify the stress components that affect the glide of 1/2⟨111⟩ screw dislocations in bcc tungsten. These results prove that the hydrostatic stress and the normal stress parallel to the dislocation line do not play any role in the dislocation glide. Therefore, the Peierls stress of the dislocation cannot depend directly on the remaining two normal stresses that are perpendicular to the dislocation but, instead, on their combination that causes an equibiaxial tension-compression (and thus shear) in the plane perpendicular to the dislocation line. The Peierls stress of 1/2⟨111⟩ screw dislocations then depends only on the orientation of the plane in which the shear stress parallel to the Burgers vector is applied and on the magnitude and orientation of the shear stress perpendicular to the slip direction.By direct application of stress in molecular statics calculations we identify the stress components that affect the glide of 1/2〈111〉 screw dislocations in bcc tungsten. These results prove that the hydrostatic stress and the normal stress parallel to the dislocation line do not play any role in the dislocation glide. Therefore, the Peierls stress of the dislocation cannot depend directly on the remaining two normal stresses that are perpendicular to the dislocation, as proposed by Koester A, Ma A, Hartmaier A. Acta Mater 2012;60:3894 but, instead, on their combination that causes an equibiaxial tension-compression (and thus shear) in the plane perpendicular to the dislocation line. The Peierls stress of 1/2〈111〉 screw dislocations then depends only on the orientation of the plane in which the shear stress parallel to the Burgers vector is applied and on the magnitude and orientation of the shear stress perpendicular to the slip direction.

Incompatibility of strains and its application to mesoscopic studies of plasticity

Structural transitions are invariably affected by lattice distortions. If the body is to remain crack-free, the strain field cannot be arbitrary but has to satisfy the Saint-Venant compatibility constraint. Equivalently, an incompatibility constraint consistent with the actual dislocation network has to be satisfied in media with dislocations. This constraint can be incorporated into strain-based free energy functionals to study the influence of dislocations on phase stability. We provide a systematic analysis of this constraint in three dimensions and show how three incompatibility equations accommodate an arbitrary dislocation density. This approach allows the internal stress field to be calculated for an anisotropic material with spatially inhomogeneous microstructure and distribution of dislocations by minimizing the free energy. This is illustrated by calculating the stress field of an edge dislocation and comparing it with that of an edge dislocation in an infinite isotropic medium. We outline how this procedure can be utilized to study the interaction of plasticity with polarization and magnetization.

Atomistic studies of transformation pathways and energetics in plutonium

One of the most challenging problems in understanding the structural phase transformations in Pu is to determine the energetically favoured, continuous atomic pathways from one crystal symmetry to another. This problem involves enumerating candidate pathways and studying their energetics to garner insight into instabilities and energy barriers. The purpose of this work is to investigate the energetics of two transformation pathways for the δ → α′ transformation in Pu that were recently proposed on the basis of symmetry. These pathways require the presence of either an intermediate hexagonal closed-packed (hcp) structure or a simple hexagonal (sh) structure. A subgroup of the parent fcc and the intermediate hexagonal structure, which has trigonal symmetry, facilitates the transformation to the intermediate hcp or sh structure. Phonons then break the translational symmetry from the intermediate hcp or sh structure to the final monoclinic symmetry of the α′ structure. We perform simulations using the modified embedded atom method (MEAM) for Pu to investigate these candidate pathways. Our main conclusion is that the path via hcp is energetically favoured and the volume change for both pathways essentially occurs in the second step of the transformation, i.e. from the intermediate sh or hcp to the monoclinic structure. Our work also highlights the deficiency of the current state-of-the-art MEAM potential in capturing the anisotropy associated with the lower symmetry monoclinic structure.

Shape of Small Prismatic Dislocation Loops in Tungsten and Iron

Small prismatic dislocation loops in BCC metals have Burgers vectors either ½<111> or <100> and are usually close to circular shape. In atomistic simulations constructing prismatic dislocation loops of different shapes is straightforward, however, it is difficult to compare their formation energies, since loops of different shapes or different Burgers vectors do not necessarily have exactly the same size. Here we develop a general method to correctly compare loops of similar size but different shapes and the Burgers vectors. This method is combined with molecular statics simulations to identify the most energetically favorable shapes of prismatic dislocation loops in elastically isotropic tungsten and anisotropic α-iron.