Instability of grain boundary grooves due to equilibrium grain boundary diffusion

All previous theoretical investigations on grain boundary grooving are based on the assumption, that the grain boundary does not participate in the material transport. In the present paper it is shown theoretically and experimentally for the first time, that by removing this restriction one obtains completely different groove profiles in comparison to those predicted by the classical grooving theory. In couples of an Al-bicrystal contacting an In-A-melt and Cu-bicrystals in contact with a BiCu-melt instabilities of the grain boundary groove are observed. Deep, channel-like grooves at the grain boundary intersection with the solid-liquid interface appear after isothermal annealing. Diffusion of In into Al and Bi into Cu grain boundaries was detected. With a mathematical model it is shown, that the observed instabilities are result of the superposition of two processes: classical grooving due to curvature dependent morphological rearrangement of the grain boundary intersecting the solid-liquid interface and grain boundary diffusion of solute (In or Bi) occurring simultaneously. Profiles of the instabilities and the kinetics of the process are calculated.     

On the chemistry of grain boundary segregation and grain boundary fracture

This paper considers the problem of impurity segregation in metals and the effect of these impurities on grain boundary cohesion. The primary goal of this paper is to provide a physical model that will allow us to think about these two processes. We describe both of them in chemical terms. Segregation is treated as a distribution of a solute between two phases. In this way, it is a typical example of heterogeneous equilibrium. We also consider the various driving forces for solute segregation and find that the correlation between decreased solubility and increased segregation, first proposed by Hondros and Seah,^[9] is still an adequate one. We introduce the discussion of grain boundary fracture by pointing out that as the impurity enters the boundary, it establishes chemical bonds with the structural units of the boundary. The segregated boundary can then be thought of as a string of molecular units with bonds of different types. Some of these bonds will be weaker than others, and they will be the ones that eventually fracture when a stress is applied. We consider the cause of these weak bonds and suggest that the primary reason for them is the transfer of electronic charge from the metal atoms to the impurity, as proposed in previous work.^[3] However, some of the ideas in the earlier models should be amended based on new results obtained from the quantum mechanical analysis of bonding in metals presented by McAdon and Goddard.^[10,11] We also suggest that intergranular brittleness of intermetallic compounds such as Ni₃Al, which occurs in the absence of impurity segregation, can be explained by the charge distribution present at the grain boundary. Finally, we provide a critique of other models that have been used to describe grain boundary fracture and segregation. This paper is based on a presentation made in the symposium “Interface Science and Engineering” presented during the 1988 World Materials Congress and the TMS Fall Meeting, Chicago, IL, September 26–29, 1988, under the auspices of the ASM-MSD Surfaces and Interfaces Committee and the TMS Electronic Device Materials Committee.     

Cavity growth on a sliding grain boundary

Cavity growth on a sliding grain boundary to which a normal stress is applied is found to be faster than that on a stationary grain boundary. The morphology of the cavity contains an asymmetric crack-like tip which prompts surface diffusion locally when the sliding is dominant, and the growth rate becomes proportional to the third power of the normal stress independent of the sliding rate. Since the sliding rates of all grain boundaries are statistically comparable, only the normal stress dependence remains important. The conditions which favor the present mechanism are examined and shown to be in good agreement with the experimental evidence in creep cavitation.     

Change in the vacancy concentration in a migrating grain boundary

The previously developed model of migration of incommensurate tilt boundaries is applied to obtain a relationship for the average fraction of grain-boundary vacancies, which is higher than the volume fraction. The concentration of vacancies near a boundary is shown to increase linearly with its migration velocity.     

Solute effects in grain boundary engineering

One of the most commonly overlooked parameters in grain boundary engineering initiatives is solute—interface interactions involving solute concentrations typically in the ppm range. In this work, experimental evidence is presented that demonstrates the significant effect of such interactions upon (1) the specific properties desired of “special” grain boundaries (e.g. resistance to corrosion) and (2) the resultant grain boundary character distribution following materials processing. Regarding the latter, it is shown how solute—grain boundary interactions impact significantly on the delicate balance of geometric (crystallographic), energetic, and kinetic influences. which ultimately dictates the grain boundary character distribution of engineered materials.     

Forces necessary to displace a defect-free grain boundary

Abstract

A systematic study was undertaken to calculate the energy associated with displacing a defect-free grain boundary from its minimum energy configuration. The energy required to slide the two crystals with respect to each other was determined by using pairwise potentials to simulate the atomic interactions. The energy required to displace the crystals was used to determine the forces necessary to displace the two crystals in the grain boundary plane. This study showed that the contours of the energy versus displacement curves were similar in the vicinity of the minimum for displacements in the boundary plane, both parallel and perpendicular to the tilt axis. Furthermore, the energy profiles were similar for both the case where the separation of the two crystals perpendicular to the boundary plane was adjusted to obtain the minimum energy, and the case where the separation was held constant

Several potentials were employed in this study, and the energy contours appeared to be relatively independent of the potential used. However, it was found that those potentials adjusted for truncation of the neighbour separation produced smoother curves and the resulting forces showed less perturbation in the vicinity of the minimum. The conclusion of this study is that for substantial grain boundary displacements to occur in real materials some sort of grain boundary defect would be required, since the forces required to displace defect-free boundaries are higher than observed.

Résumé

Une étude systematique a été entreprise afin de calculer l' énergie requise pour Ie déplacement, à partir de sa configuration d' énergie minimale, d'un joint de grain libre de défaut.

L' énergie requise pour faire glisser les deux cristaux l'un par rapport agrave; l'autre a été déterminée en utilisant des potentiels en couple dans Ie but de simuler les interactions atomiques. L' énergie requise pour Ie déplacement des cristaux a été utilisée pour déterminer les forces nécessaires à ce déplacement dans Ie plan du joint. Cette étude a révélé que les contours d'énergie en fonction des courbes de déplacement sont semblables au voisinage du minimum dans Ie cas de déplacements dans Ie plan du joint, et ce, pour des duections paralléles ou perpendiculaires à l'axe de flexion. De plus, les profils d'énergie sont semblables dans Ie cas pour lequel la séparation entre les deux cristaux, perpendiculaire au plan du joint, était ajustée pour obtenir l' énergie minimale, et également dans les cas pour lesquels la séparation était maintenue con stante.

Plusieurs potentiels furent utilisés dans cette étude et les contours d' énergie se sont révélés ètre relativement indépendants du potential employé. Cependant, il est apparu que les potentiels ajustés pour obtenir une diminution de la distance entre plus proches voisins donnaient des courbes plus lisses et les forces résultantes présentaient moins de variation au voisinage du minimum. La conclusion de cette étude est que tout déplacement important des joints de grains, dans des métaux réels, doivent impliquer certains types de défauts, car les forces requises pour déplacer des joints libres de défaut sont plus élevées que celles observées expérimentalement.     

Investigation of grain boundary diffusion in polycrystals by means of extrinsic grain boundary dislocations spreading rate

The spreading rate of extrinsic grain boundary dislocations (EGBDs) was used to study the diffusivity on grain boundaries in austenitic steel for a range of temperatures. The distribution function of the grain boundary diffusivity as well as the activation energy for grain boundary diffusion may be obtained by this method. This is an important characteristic of polycrystals. It is especially suited for investigating changes of distribution functions of grain boundary properties after various thermomechanical treatments or changes of grain boundary chemical composition as well as for studying the effect of grain boundaries on polycrystal properties. The optimal averaging methods of such distribution functions to a single diffusion coefficient were discussed. It was concluded, that EGBD spreading rate measurements provide a very sensitive method of grain boundary diffusion determination.     

Aging embrittlement and grain boundary

“Clean” 3.5NiCrMoV steels with limited contents in trace elements (P, Sn, As, Sb) are commonly provided for manufacturing big rotor shafts. The possible increase in temperature in future steam turbines has promoted the development of “superclean” steels characterized by an extra drastic decrease of manganese and silicon contents. Their higher cost in comparison to “clean” steels leads to concern above which temperature they must be considered as mandatory for resisting aging embrittlement in operation. 3.5NiCrMoV “clean” steel samples (Mn = 0.30 pct; Si = 0.10 pct) were aged at 300 °C, 350 °C, and 400 °C for 10,000 hours up to 30,000 hours. No embrittlement results from aging at 300 °C and 350 °C, but holding at 400 °C is highly detrimental. Auger spectroscopy confirms that, when aging at 400 °C, phosphorus is the main embrittling trace element. It is suggested that grain boundary embrittlement is associated with the building of a layer that contains, on the one hand, Ni and P and, on the other hand, Mo and Cr. Head of the Testing and Head of the Testing and Head of the Testing and     

On the spreading of grain boundary dislocations and its effect on grain boundary properties

The effect of dissociation of trapped lattice dislocations (TLDs) on the energy of grain boundaries (GBs) is calculated. Two possible effects are considered. The first is the change of energy of the GBs caused by the presence of TLDs cores. It was shown to be smaller than 5% of the grain boundary energy. The other, more important, is an increase of the energy of the strain fields connected with grain boundaries. Dissociation of TLDs causes an increase of incompatibility strains between plastically deformed grains. The energy of these strains is of the order the GB energy in equilibrium. The EGBDs strain fields provide a driving force for GB sliding and migration. In fact, EGBDs cannot leave the grain boundaries. Recovery of these dislocations can take place only by sliding and migration of grain boundaries.     

Diffusion driven grain boundary migration

If the grain boundary diffusion coefficient of the two species in a binary alloy differ, diffusion driven grain boundary motion should lead to predictable surface relief and shape changes. This leads to predictions and equations which would allow the determination of the separate diffusion coefficient of each species as well as the chemical diffusion coefficient for the boundary, D_b. For a thick sample the stress gradients built up by differences in the fluxes of the two species can lead to a reduced apparent D_b, especially if the solute boundary diffusion coefficient, D′₂, is appreciably greater than that of the solvent. D′₁. For Zn diffusion into Fe it appears that D′_Fe ⪢ D′_Zn. The stress built up will also slow the boundary motion.