A study of grain boundaries between molybdenum trioxide smoke particles

Pairs of dislocation-free molybdenum trioxide smoke crystals have been examined by transmission electron microscopy. Crystals joined on their b-faces tend to be either parallel or to have the c-axis of one perpendicular to the c-axis of the other. The preference for perpendicularity is evidence that the near-coincidence boundary that exists between perpendicular crystals has low energy.In addition to a preference for the perpendicular orientation there was a small but significant preference for the orientation obtained by rotating one member of a pair of perpendicular crystals about the normal to the contact plane until the (101) planes of one crystal are precisely parallel to the (101̄) planes of the other. The rotation (in radians) needed to do this is equal to the misfit between the a and c axes of MoO₃.     

A statistical analysis of cavity nucleation at particles in grain boundaries

Cavity nucleation on grain boundary particles during creep has been examined using a classical thermodynamic method. The particle sizes and spacings are assumed to obey a log-normal distribution. It is found that a threshold shear stress is needed for cavity nucleation to occur. When the resolved shear stress on a grain boundary segment reaches the threshold stress, a critical normal stress for cavity nucleation is produced on the panicle-matrix interface by grain boundary sliding and cavity nucleation occurs. The threshold stress is determined mainly by the concentration and distribution of grain boundary particles and falls in the stress range of engineering applications. A program has been developed to calculate the fraction of particles which can serve as nucleation sites. The model is used to predict the onset of cavitation in the oxide dispersion strengthened alloy Inconel MA 754. Implications for avoiding the nucleation of cavities in engineering alloys are discussed.     

Superplastic deformation carried by grain boundaries

A model of plastic deformation based on grain rolling is proposed for the interpretation of large superplastic strains that may be reached in some metallic as well as ceramic materials in certain ranges of high temperatures and strain rates. The deformation process is modelled by the motion of grain boundary dislocations that glide on the grain facets when sliding takes place and climb on the facets with normal stresses. A constitutive equation for the strain rate is derived for steady state deformation when the emission rate of climbing dislocations is a constant determined by the dislocations climb velocity.     

Precipitation of austenite particles at grain boundaries during aging of Fe-Mn-Ni steel

Precipitation of austenite particles at grain and lath boundaries after aging treatment of a Fe-8Mn-7Ni alloy was investigated by selected area electron diffraction (SAD), X-ray energy dispersive spectrometry (EDS) in a scanning transmission electron microscope (STEM), and high-resolution (HRTEM) analysis. High spatial-resolution (2 to 5 nm) EDS analysis revealed no significant segregation of alloying elements at grain boundaries but the precipitation of very fine particles of Mn- and Ni-rich phase. Detailed EDS, SAD, and HRTEM analyses all confirmed that these particles are austenite phase, which have a Kurdjumov-Sachs (K-S) orientation relationship with one of the adjacent grain. The concentration of Mn and Ni in austenite, measured by EDS, varied from ∼15 pct to a maximum of ∼30 pct. Low-voltage scanning electron microscopy (SEM) fractographs also revealed the presence of very fine, second-phase precipitates on the fracture surface of the embrittled alloys.     

Dissolution of precipitates by migrating grain boundaries

We discuss a new effect observed in a TiYO alloy. During recrystallisation, migrating grain boundaries dissolve small yttria precipitates. We present a theoretical model which describes this phenomenon. The interaction between the moving interface and the precipitates is due to the attraction of solid solution atoms by the wall. We argue that in the case of our experiment, this attractive force must be long ranged.     

Structure of grain boundaries

The present discussion is concerned with the more relevant experimental studies, performed since about 1952, that provide evidence on the structure of large angle boundaries. These experiments include diffusion, mobility, energy, and field ion studies of grain boundaries. It is shown that the results of these experiments provide support for a model that can be described quite accurately in terms of coincidence in the boundary plane, a dislocation array, and a ledge structure.     

Geometry of grain boundaries

The first part of this paper deals with the problem of describing and measuring microstructure in exact terms. The Euclidean parameters: volume, area, length, and angle can be measured and expressed only in terms of the total of each in unit volume. Average properties, such as average grain diameter, are accessible only through the topological parameters, specifically number in unit volume, which can be measured only by serial sectioning. The parameters which have been used to represent the concept of grain size are analyzed and shown in most cases to represent a function of grain boundary area. In a second section of this paper the geometric problem of plastic slip through a grain boundary is analyzed. A method is proposed by which all of the components of the deformation, as well as the crystallographic directions, can be manipulated simultaneously through the use of a stereographic projection. The third section of this paper is concerned with the geometry of grain growth. The polycrystalline state is described as a grain boundary network, which must respond to the requirements of surface tension. The several topological changes in a network which can contribute to grain growth are described.     

Thermotransport in grain boundaries

Thermotransport effects in grain boundaries in lead were studied by means of a temperature gradient (≤60 K cm⁻¹) lying parallel to the planes of the boundaries. The temperature gradient was observed to result in grain boundary sliding, migration and enhanced boundary diffusion. These effects are interpreted in terms of climb and/or glide motion of grain boundary dislocations induced by the gradient. The behaviour of boundaries in temperature gradients seems to differ from the behaviour reported in concentration gradients (diffusion induced boundary migration) suggesting different mechanisms to operate in both cases.     

Selective segregation at grain boundaries

Abstract

Experimental observations provide support for two different types of solute enhancement at interfaces, namely equilibrium and non-equilibrium segregation. It is shown that these segregation processes are dependent upon the structures of different large-angle grain boundaries. Experimental data clearly indicate that this selective grain boundary segregation influences the mobility and energy of grain boundaries.

A fundamental relationship is found to exist between the energy of coincidence boundaries and the density of shared atom sites (or the size of the periodic unit) in the boundary. The energy and mobility results provide strong support for the boundary coincidence and “relaxed” coincidence models of grain boundary structure.

A selective solute segregation to grain boundaries can lead to the formation of preferred orientations in annealed materials and enhanced corrosion at grain boundaries.

Résumé

Les études expérimentales apportent des arguments aux deux types differents d'enrichissement en soluté aux interfaces, c'est-à-dire la ségrégation d'équilibre et la ségrégation de non-équilibre. Ces deux modes de ségrégation dépendent de la structure des différents joints de grains à forte désorientation. Les résultats expérimentaux indiquent clairement que cette ségrégation sélective aux joints de grains influence la mobilité et l'énergie des joints de grains.

Une relation fondamentale existe entre L'energie des joints en coincidence et la densité des sites atomiques partagés (ou la taille des unités périodiques) dans le joint. Les résultats relatifs à l'énergie et à la mobilité amènent de fortes preuves au modèle de joints de grains basé sur la coincidence ou la coincidence «relaxée».

Une ségrégation sélective du soluté aux joints de grains peut conduire à la formation d'orientations préférentielles dans les matériaux recuits et favoriser la corrosion aux joints de grains.     

Plane coalescence at grain boundaries

The atomic structures of four symmetric tilt or twin boundaries in face centred cubic crystals have been investigated using an empirical inter-atomic potential representing copper. In each case the boundary energy corresponding to the relaxed structure and the associated volume increase have been determined. As anticipated the (111) boundary exhibits little relaxation but the predicted structures for the (113), (120) and (112) boundaries all involve translations away from the conventional mirror image orientation relation. In addition one pair of planes at the (120) boundary coalesce completely and four pairs of planes at the (112) boundary coalesce partially. The resulting structure in the latter case is broad and asymmetric. The (111) boundary has by far the lowest energy followed by (113), (112) and (012). Some aspects of the results, particularly the phenomenon of coalescence, the relative energies, and the breadth of the (112) boundary are very different from earlier computer simulation results on these interfaces, obtained using an aluminium potential. The reasons for this and the implications of the results are discussed.     

Cavity nucleation at particles on sliding grain boundaries. A shear crack model for grain boundary sliding in creeping polycrystals

The paper summarizes the results of classical nucleation theory applied to the nucleation of creep cavities at hard second-phase particles. Stress concentrations at particles in sliding grain boundaries are analysed for the cases that the particles can be circumvented by diffusion and power-law creep and for purely elastic material response. The shear stress which is effectively transmitted through a sliding grain boundary in a polycrystal is calculated using a shear crack model. Comparison of the results with finite element calculations for a planar, hexagonal array of grains shows that the accuracy of the model is satisfactory. The duration of elastic transients is estimated and it is found that, in the numerical examples considered, stress relaxation times are shorter than the incubation time for cavity nucleation. From the calculated stress concentration factors it is concluded that cavities cannot be nucleated by the considered mechanism of vacancy condensation unless the nuclei have a narrow, rather than spherical, shape.     

The thermal expansion of grain boundaries

The thermal expansion öf grain boundaries in copper was measured by a newly developed method comparing the thermal expansion of copper polycrystals (same chemical composition) with small (17 μm) and large (19 mm) grain sizes. From these measurements, the thermal expansion coefficient of a grain boundary in copper was deduced to be 40 to 80·10⁻⁶K⁻¹ which is about 2.5 to 5 times the expansion coefficient of a copper crystal suggesting large anharmonic atomic vibrations in grain boundaries. The thermal expansion of grain boundaries (which was not measurable so far) may be used to test structural models of interfaces.