A. G. Crocker

The structure of high-angle (001) CSL twist boundaries in f.c.c. metals

Abstract The discrete lattice approach using computer simulation techniques and empirical interatomic potentials representing copper and nickel is used to calculate the structure and energy of four coincidence lattice (001) twist boundaries. These have singular misorientations of 36·9°, 22·6°, 28·1° and 16·3°, corresponding to ∊ = 5, 13, 17 and 25 respectively. It is found that for each of these boundaries three distinct symmetric structures may arise, two of which involve translations parallel to the interface. For a given ∊ and potential the energies of the three relaxed structures are found to be similar, and for each potential the energy increases with the angle of misorientation. Volume increases occurring at the boundaries are found to correspond to displacements of about 0·07 [001] for copper and 0·13 [001] for nickel and to be insensitive to ∊. Relaxations parallel to the interfaces are always compatible with the symmetry of the boundaries and tend to increase in magnitude with ∊. The implications...

A computer simulation study of the structures of twin boundaries in body-centred cubic crystals

Abstract The structures of {112} twin boundaries in body-centred cubic crystals have been studied using computer simulation methods and interatomic potentials representing iron, molybdenum and tungsten. Two distinct structures were found to be stable or metastable in the models used. These were the conventional twin boundary defined by a reflection orientation relation and a twin in which the boundary consisted of a layer of cells which project on the {110} plane as interlocking isosceles triangles. In the case of iron the two boundaries, when fully relaxed, are found to have almost identical energies but for molybdenum and tungsten the reflection boundary is preferred. The twin boundary energies for these two metals are three or four times as large as those for iron. Volume increases are predicted for the reflection twins in all throe metals but for molybdenum a surprising volume decrease arises for the isosceles twin. The results suggest that in some b.c.c. metals both types of boundary may arise in whi...

The structure of small vacancy clusters in face-centred-cubic metals

Abstract In face-centred-cubic metals it is possible to form four distinct types of close-packed trivacancy and 20 types of tetravacancy. The structures and energies of these clusters have been investigated using computer-simulation methods and an interatomic potential representing copper. One of the trivacancies and six of the tetravacancies are found to relax to collapsed forms and it is these clusters that have the lowest epergies.

A computer simulation study of the interaction of vacancies with twin boundaries in body-centred cubic crystals

Abstract The interaction of vacancies and divacancies with (112) twin boundaries in body-centred cubic crystals has been investigated using computer simulation methods and interatomic potentials representing iron, molybdenum and tungsten. Two distinct twin boundary structures, known as the reflection and isosceles types, may arise in practice and both were considered. Interaction energies were obtained as a function of vacancy- or divacancy-boundary separation and as a function of strain perpendicular to the interface. For the single vacancy the maximum binding energies for the two boundaries are similar in magnitude and occur when the vacancy lies adjacent to but not in the interface. For the reflection, but not the isosceles, boundary the binding energy is sensitive to strain. First and second nearest-neighbour divacancies in all possible orientations relative to the twin boundaries were examined together with three imperfect divacancies, which may occur at the interfaces. The most stable types were fou...

Migration of vacancies near twin boundaries and stacking faults in face-centred-cubic metals

Abstract Computer-simulation studies have shown that the migration energies of vacancies along twin boundaries and stacking faults in a model of a face-centred-cubic crystal representing copper ere up to 10% less then in a perfect crystal. The implications of this result are discussed.

The crystallography of deformation kinking

Abstract Kinking is a secondary deformation mode of crystalline materials being controlled by slip and often occurring as an accommodation mechanism for twins. However, it can also be considered to be a deformation mode in its own right. The composition plane and shear direction of a kink band can then be defined using the familiar K 1, η1 notation normally used to describe the crystallography of deformation twins. Equations for these elements, which for kinks are a function of the shear strain, are presented. Following the analogy with twinning, observed deformation kinking modes can be classified as type I, type II or compound. Results of detailed experimental studies of kinking in crystalline mercury and niobium have played an important role in developing this classification scheme which is based on the symmetry of the associated slip plane and direction. The need for further experimental studies on kinking is stressed and links with analyses of other intercrystalline boundaries discussed.

Migration of vacancies near twin boundaries in body-centred-cubic metals

Computer simulation methods have been used to demonstrate that the migration energy of a single vacancy in or-iron can be changed dramatically by the presence of a neighbouring { 112) twin boundary. In particular, vacancy migration parallel to a twin boundary is enhanced, which suggests that the presence of twins may have important consequences for diffusional creep. The results can be interpreted satisfactorily in terms of the atomic structure of the twin boundary and are therefore considered to be typical of all body-centred-cubic met.&. Possible effects of other boundaries on vacancy migration are also discussed briefly. In a recent computer simulation study (Ingle, Bristowe and Crocker 1976) it was shown that significant attractive interactions exist between vacancies and coherent twin boundaries in b.c.c. metals. Both single and divacancies were considered and several important differences in behaviour were noted for the two distinct types of (112) twin boundary which may arise. These two boundaries, referred to as reflection and isosceles types, are illustrated schematically in fig. 1. The orientation relationship for the conventional reflection twin (fig. 1 (a)) is a mirror image across the interface, whereas that for the alternative isosceles twin (fig. 1 (b)) is reflection in the interface plus an additional displacement in the anti-twinning sense of &[1 IT]. The vacancy and divacancy interactions with these boundaries were examined as a function of both inter-defect separation and uniaxial stress applied along the [112] direction. Prompted by this work, computer simulation experiments have been carried out to determine whether, in addition to there being significant interaction energies, any effects of twin boundaries on the migration energies of vacancies could be detected. Indeed some preliminary results (Ingle and Crocker 1976) indicated that marked changes in these energies could occur. The purpose of the present paper is to describe fully the results of this investigation. Thus the migration energies of single vacancies for all the important jumps in the vicinity of reflection and isosceles twin boundaries are examined in computer models of a-iron. In each case the boundaries studied were the fully-relaxed structures discussed by Bristowe and Crocker (1 975). The migration of single vacancies in b.c.c. metals proceeds via nearestneighbour Q(111) atomic jumps and a number of studies have been carried out to determine the migration energies in unstressed perfect crystals. Johnson (1964) and Johnson and Wilson (1972) have examined these energies in crystals simulated using empirical potentials and Wynblatt ( 1968) and Neumann, Tolle and Hirschwald (1 972) have examined the corresponding energies obtained using Morse potentials. For a-iron, the results of Johnson (1964) took the

Zonal twinning dislocations in body centred cubic crystals

Abstract A computer simulation study of steps in b.c.c. twin boundaries has resulted in the discovery of an unexpected type of twinning dislocation. The defect has the same Burgers vector as the conventional perfect twinning dislocation but is associated with a double interfacial step in the opposite sense. It therefore has a low self energy but zonal character. Its structure is examined and the operation of the corresponding twinning mode discussed. It is suggested that this defect may play a significant role in the interaction of slip and twin boundaries in b.c.c. metals.

Configurations of close-packed clusters of substitutional point defects in crystals

Abstract A theoretical study is described of the possible crystallographic configurations of small groups of either vacancies or solutes in which each point defect has at least one other point defect in a nearest-neighbour position. The number of cluster configurations that may arise for a given number of point defects depends critically on the crystal structure and in some cases a large number of types is possible each with a group of crystallographically equivalent variants. General procedures for describing and classifying these configurations are discussed. Clusters of three and four defects in all possible single lattice structures and in some important double lattice structures are enumerated. The relationships which exist between configurations in different lattices are emphasized and possible extensions and applications of the analysis are discussed. In particular the results provide a basis for a study of the nucleation of extended crystal defects using computer simulation techniques.

Elastic self-energies of undissociated dislocation jogs

Abstract Analytic expressions are derived for the elastic energy of an undissociated jog lying perpendicular to an undissociated straight dislocation line of arbitrary Burgers vector in an otherwise perfect infinite isotropic elastic medium. These expressions are the most accurate which can presently be obtained, but the analysis still involves minor approximations. In particular, those associated with the contribution to the energy arising from the work done by core surface tractions at the corners in the dislocation are important for short jogs and are discussed in detail. Numerical results are presented and these and the analytic expressions are compared with those of previous workers, which involve major approximations. It is concluded that even the new expressions are not reliable for short jogs.