R.C. Pond

Atomic shearing and shuffling accompanying the motion of twinning disconnections in Zirconium

Disconnection motion along ( ) and ( ) twins in Zr is investigated using atomic-scale simulation. In particular, the high mobility of glissile disconnections is studied in terms of the atomic shears and shuffles involved. Using a quasi-static simulation procedure, the displacements of individual atoms are followed as they transit from matrix sites, through interfacial sites, and hence to twin sites by repeated passages of disconnections along the interface. It is found that the overall displacements for the cases studied are those predicted by the Bilby and Crocker (1965) theory which invokes homogeneous shear deformation. However, the present work enables atomic tracks to be followed through the cores of moving disconnections. The combinations of shears and shuffles in the two twinning systems are found to be quite distinct. In addition to tracking their coordinates, the variation of hydrostatic pressure experienced by the atoms is also quantified.

Atomic displacements accompanying deformation twinning: shears and shuffles

ABSTRACT Deformation twins grow by the motion of disconnections along their interfaces, thereby coupling shear with migration. Atomic-scale simulations of this mechanism have advanced to the point where the trajectory of each atom can be followed as it transits from a site in the shrinking grain, through the interface, and onwards to a site in the growing twin. Historically, such trajectories have been factorised into shear and shuffle components according to some defined convention. In the present article, we introduce a method of factorisation consistent with disconnection motion. This procedure is illustrated for the case of twinning in hexagonal close-packed materials, and shown to agree with simulated atomic trajectories for Zr. IMPACT STATEMENT Shear and shuffle displacements accompanying () twinning are quantified consistently with growth by the observed mechanism of disconnection motion. This advance will facilitate the understanding of twinning kinetics.

Strains and rotations in thin deposited films

Thin films deposited on misfitting substrates exhibit distortions produced by the superposition of coherency strains and the elastic fields of interfacial defects. These distortions become homogeneous strains, ϵ, and rotations, φ, beyond a characteristic distance from the interface, z, and are partitioned between the film and substrate. Residual strain arises when the density of interfacial defects is insufficient to compensate the intrinsic coherency strain, and is partitioned in a manner depending on the relative thicknesses of the two layers, d. However, rotations are not partitioned in this way. Expressions for the magnitude and partitioning of ϵ and φ are derived for the case of elastically isotropic materials. Calculated values are shown to be in excellent agreement with experimental measurements for a variety of technologically relevant cases.

Elastic and plastic aspects of martensitic transformations

Elastic and plastic aspects of martensitic transformations are discussed using the topological model. Here the interface comprises an array of transformation dislocations (disconnections) and dislocations (slip/twinning) superposed on coherently strained terraces. Plastic transformation strain arises by virtue of the conservative motion of the defect array, and is quantified directly in terms of the Burgers vectors of the defects. Superposition of the elastic fields of the defects and the coherency strain produces a short-range interfacial distortion field, but only rigid rotation, φ, of the phases at long-range. Furthermore, the treatment shows that, for elastically isotropic phases with similar moduli, elastic relaxations cause the habit plane to differ by φ/2 from the classical predictions where such relaxations are suppressed. A nonlinear analysis is presented suitable for instances of large values of φ. However, the plastic transformation strain, in combination with the relative orientation, φ, corresponds to the classically predicted shape deformation.

A comment on B. Li, H. El Kadiri and M.F. Horstemeyer ‘Extended zonal dislocations mediating twinning in titanium’

Li, Kadiri and Horstemeyer [1] recently studied twinning in titanium by atomic-scale computer simulation and proposed a new mechanism in which elementary twinning dislocations (TDs) are nucleated and glide in an extended fashion on adjacent planes. In this comment, we argue that the interpretation of the simulations is in error for several reasons. First, the Burgers vector of the TDs seen in the simulations was not determined correctly. Second, these TDs do not produce the twin mode known to occur in titanium. Third, the experimentally observed mode occurs under c-axis compression, whereas the motion of the twin boundary in [1] was in response to c-axis tension. The former mode cannot be simulated with the MD model used in [1]. Fourth, the temperature dependence of twinning found experimentally was misunderstood in [1]. We conclude that the TD responsible for this deformation mode is the one long-established by classical twinning theory and studied at the atomic level by computer simulations performed more than 20 years ago.

Identifying the multiplicity of crystallographically equivalent variants generated by iterative phase transformations in Ti

This work describes phase transformations in Ti from a purely crystallographic perspective. Iterative heating and cooling above and below 1155 K induce phase transitions between a low-temperature h.c.p. (hexagonal close packed) (6/m mm) and a high-temperature b.c.c. (body centred cubic) (m3m) structure. The crystallography of the two phases has been found to be related by the Burgers Orientation Relationship (Burgers OR). The transitions are accompanied by changes in texture, as an ever-increasing number of crystallographically equivalent variants occur with every cycle. Identifying their multiplicity is important to relate the textures before and after the transformation, in order to predict the resultant one and refine its microstructure. The four-dimensional Frank space was utilized to describe both h.c.p. and b.c.c. structures within the same orthogonal framework, and thus allow for their easy numerical manipulation through matrix algebra. Crystallographic group decomposition showed that the common symmetry maintained in both groups was that of group 2/m; therefore, the symmetry operations that generated the variants were of groups 3m and 23 for cubic and hexagonal generations, respectively. The number of all potential variants was determined for the first three variant generations, and degeneracy was indeed detected, reducing the number of variants from 72 to 57 and from 432 to 180 for the second and third generations, respectively. Degeneracy was attributed on some special alignments of symmetry operators, as a result of the Burgers OR connecting the relative orientation of the two structures.

Rejoinder to the response by B. Li [1] on our Comment [2] on the paper B. Li, H. El Kadiri and M.F. Horstemeyer ‘Extended zonal dislocations mediating twinning in titanium’

The criticisms levelled in our comment [2] against the analysis and interpretations presented in the paper by Li, El Kadiri and Horstemeyer [3] rest firmly on principles established in standard works on twinning and our own later contributions. We believe the arguments in [2] are clear, but feel that Dr Li has misconstrued them in his response [1] and that it is necessary to correct misunderstanding. We highlight a few issues in this rejoinder.

Disconnection Motion in Low- and High-Angle Symmetrical Tilt Grain Boundaries in HCP Metal

The structure of disconnections in symmetrical low- and high-angle [0001] tilt boundaries in an hcp metal are studied using atomic-scale simulation. Applied engineering strains cause such defects to move conservatively along the boundaries, producing coupled shear and migration. The Peierls stresses causing such motion are found to decrease precipitously through the transition from low- to high-angle boundaries. The reason underlying this behaviour is discussed.