Group representation of bicrystal invariant translations with an application to the topology of secondary grain boundary dislocations

All DSC-Lattice translations of one lattice with respect to the second lattice of a bicrystal are described as a group. It is shown that the matrix representation of this group can be used to solve topological problems connected with secondary grain boundary dislocations (SGBDs) such as finding the step in the boundary associated with the SGBD. We have formulated this problem by establishing the step vector S associated with the Burgers vector b of the SGBD in a cubic bicrystal. The problem is then solved in 2D, and the way to generalize to 3D is indicated

Coincidence lattice model for the structure and energy of grain boundaries

It is proposed that, to a good approximation, the construction of a boundary can be described in terms of three basic steps: (1) a rigid body joining of two perfect crystals along the boundary plane (Step I); (2) a primary relaxation (Step II) consisting of relaxations in the boundary centered on O-Lattice elements which act to improve lattice matching in these regions; and (3) a possible secondary relaxation (Step III) which produces the final structure composed of patches of a low ..sigma.. boundary and secondary grain boundary dislocations. The energy after Step I is obtained by summing pairwise interactions across the boundary and is found to be relatively low for a number of low ..sigma.. boundaries and to approach a larger constant value for all large ..sigma.. boundaries. The energy decrease due to Step II varies monotonically with crystal misorientation according to a Read-Shockley function, and the energy decrease associated with Step III produces cusps in the energy versus misorientation curve at misorientations corresponding to low ..sigma.. boundaries. The model appears to be consistent with the present knowledge of boundary structure and energy, and its general applicability is discussed

Volume dependence of computed grain boundary energy

Over the past five years there have been numerous studies of grain boundary structure using the method of computer molecular statics which assume pairwise central potentials for the interatomic interaction. Emphasis is usually placed on relative grain boundary energies but these may be inaccurate due to various, but related, approximations and constraints implicity imposed on the calculation-namely central forces, finite model size, fixed border conditions and volume dependent contributions to the energy of the system. It is the purpose of this work to clarify how these particular properties of the model can affect the computed grain boundary energy and demonstrate instances in which the quoted energy has strictly been inaccurate. The implication of these results, especially on how they affect the method of relaxation and the resulting grain boundary structure is discussed

SOLUTE-ATOM SEGREGATION AND TWO-DIMENSIONAL PHASE TRANSITIONS IN STACKING FAULTS : AN ATOM-PROBE FIELD-ION MICROSCOPE STUDY

Nous avons étudié, à l'aide d'un microscope à émissions d'ions avec sonde atomique, des effets de ségrégation pour des fautes d'empilement individuelles dans les alliages Co-0.96 at.% Nb et Co-0.98 at.% Fe. La composition des fautes d'empilement a été mesurée dans ces alliages dans la gamme de température 450 à 575°C. La concentration moyenne de soluté dans les fautes d'empilement décroit avec l'augmentation de température. Des petites fluctuations (~5 to 20 A de diamètre) riches en soluté, dépendant de la température, dont la composition diffère de façon significative de la composition moyenne d'une faute, ont été observées dans le plan des fautes d'empilement. Le fait que ces fluctuations sont dépendantes de la température suggère qu'en plus de ségrégation solutée nous avons observé une phase de transition à deux dimensions dans les fautes d'empilement. Une ségrégation isotherme de type Fowler-Guggenheim a été dérivée ce qui explique de façon semiquantitative la dépendance de la température de la composition moyenne d'une faute.The atom-probe field-ion microscope has been employed to study solute-atom segregation effects to individual stacking faults in Co-0.96 at.% Nb and Co-0.98 at.% Fe alloys. The compositions of stacking faults have been measured in these alloys in the temperature range 450 to 575°C. The mean solute concentration in the stacking faults decreases with increasing temperature. Small temperature-dependent solute-rich fluctuations (~5 to 20 A diameter), whose compositions differ significantly from the average fault compositions, have been observed in the plane of the stacking fault. The temperature dependence of these fluctuations suggests that in addition to solute-atom segregation we have observed a two-dimensional phase transition in the stacking fault. A Fowler-Guggenheim type segregation isotherm has been derived, which semi-quantitatively explains the temperature dependence of the mean composition of a fault

Computer simulation study of the structure of vacancies in grain boundaries

The structure of vacancies in grain boundaries has been investigated by computer molecular statics employing pairwise potentials. In order to gain an impression of the vacancy structures which may occur generally, a number of variables was investigated including: metal type, boundary type, degree of lattice coincidence and choice of boundary site. In all cases the vacancies remained as distinguishable point defects in the relatively irregular boundary structures. However, it was found that the vacancy often induced relatively large atomic displacements in the core of the boundary. These displacements often occurred only in the direct vicinity of the vacancy, but in certain cases they were widely distributed in the boundary, sometimes at surprisingly large distances

Determination of vacancy mechanism for grain boundary self-diffusion by computer simulation

It is currently well established that the fast self-diffusion which occurs along grain boundaries (GBs) in metals must occur by a point defect exchange mechanism. For example, it is known that rapid GB diffusion can transport a net current of atoms along GBs during both sintering and diffusional creep, and that the two species in a binary substitutional alloy diffuse at different rates in GBs. However, it has not been possible to establish firmly whether the defect mechanism involves the exchange of atoms with vacancy or interstitial point defects. It has been suspected that the vacancy exchange mechanism must apply but it has been difficult to prove this hypothesis because of a lack of detailed information at the atomistic level. The results are presented of an effort to establish the GB self-diffusion mechanism in a bcc iron ..sigma.. = 5 (36.9/sup 0/) (001) (310) tilt boundary using the combined methods of computer molecular statics and molecular dynamics simulation