On the structure of vacancies in grain boundaries

The atomic structure of vacancies in high angle grain boundaries was investigated by means of computer simulations. The results obtained suggest that vacancies in short-periodic grain boundaries (boundaries of good atomic fit) are localized similarly to vacancies in crystal lattices. In non-random boundaries (poor atomic fit), a vacancy entering the boundary triggers the rearrangement of many boundary atoms. These rearrangements redistribute and partly remove the free-volume associated with the vacancy.     

Coincidence lattice model for the structure and energy of grain boundaries

The Coincidence Site Lattice (CSL) model of grain boundaries is developed on a simple physical basis. We propose 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 0-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 ∑ 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 ∑ boundaries and to approach a larger constant value for all large ∑ 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 ∑ boundaries. The model appears to be consistent with our present knowledge of boundary structure and energy, and its general applicability is discussed.     

Some comments on the structure of high angle grain boundaries

Abstract

Fluxing trials were conducted at Brunswick Smelting over a four-month period to determine the effect of slag composition on slag lead losses, blast furnace coke consumption and smelting rate. A computer program was developed to analyse the blast furnace operating data so that relationships between slag variables and lead loss could be examined. Microscopic studies were carried out on granulated slag samples obtained from the smelter to identify the forms of lead in slag and to relate these forms to the flux composition of the slag.

The results of this investigation indicate that low lead losses in slag can be achieved with good blast furnace throughput by maintaining a slag composition of 40–42 wt % iron and 0.85–0.90 lime-silica ratio. The benefits expected from operating at these levels are reduced fluxing costs, lower coke consumption and increased savings in lead recovery.     

Structure,chemistry, and stress corrosion cracking of grain boundaries in alloys 600 and 690

The microstructure in six commercial batches of alloys 600 and 690 has been investigated using scanning electron microscopy (SEM), analytical transmission electron microscopy (ATEM), atom probe field ion microscopy (APFIM), and secondary ion mass spectroscopy (SIMS). The materials were also tested with respect to their resistance to intergranular stress corrosion cracking (IGSCC) in high-purity water at 365 °. Applied microanalytical techniques allowed direct measurement of carbon concentration in the matrix together with determination of grain boundary micro structure and microchemistry in all material conditions. The distribution of oxygen near a crack in material tested with respect to IGSCC was also investigated. The role of carbon and chromium and intergranular precipitates on IGSCC is discussed.     

Low energy grain boundaries in silver and copper close to the melting point

Crystallographic parameters of low energy grain boundaries in silver and copper in the temperature range 0.8-0.996 T_m have been studied. The investigations have been carried out by sintering single crystalline spheres to single crystalline plates having surfaces parallel to low index planes. In the above temperature range the most important energy cusps were found to be associated with [110] tilt boundaries. This result indicates that the parallelity of close packed rows of atoms from both grains surfaces leads to low energy grain boundary structures. The distribution of misorientation angles for low energy [1 1 0] tilt boundaries is almost continuous at 0.8 T_m. At higher temperatures the spheres select some orientations as more preferred than others. This set of orientations is smaller than predicted according to recent geometrical criteria for low energy boundaries. It can be interpreted in terms of grain boundary faceting in such a way that it contains compact structural units of low energy. There seems to be no connection between the type of structural units in the grain boundary and the present crystallographic criteria. This is the reason why these criteria fail to select between nonsymmetrical boundaries of higher and lower energy.     

Dissociation of grain boundaries induced by changes of composition,the ejection of dislocations from grain boundaries,and the nucleation of diffusion induced grain boundary migration

We present various observations of the dissociation of large and small angle grain boundaries in copper during the alloying of the specimens with zinc. In all large angle cases, this dissociation takes the form of the large angle boundary reacting to form another large angle boundary and a small angle boundary. This process may be of great importance in understanding the nucleation of diffusion induced grain boundary migration. Small angle boundaries can undergo complete disintegration upon the addition of zinc, and the magnitude of the stress involved in such a disintegration is estimated.     

Relationships between grain boundary structure and energy

The Read-Shockley equation describing the dependence of the grain boundary energy on misorientation of the grains, has been reformulated using the recently developed structural unit model of the atomic structure of grain boundaries, so that it is applicable to general high angle boundaries. The boundary energy then consists of the energy of a reference structure, and of the core and elastic energies of the corresponding DSC dislocations. While the latter part of the boundary energy is determined using the elastic theory of dislocations the former two parts are determined on the basis of atomistics of grain boundaries employing the structural unit model. In the framework of this analysis the minimum number of reference structures in a given misorientation range as well as the extent of misorientations related to a given reference structure are determined unambiguously. Hence, the positions of cusps in the energy vs misorientation dependence and their relative depths and extents are also determined uniquely. The validity of this model is demonstrated for the [001] and [111̄] symmetrical tilt boundaries which have been studied by atomistic computer simulations.     

The effect of grain boundaries on the athermal stress of tantalum and tantalum-tungsten alloys

The temperature dependence of the yield stress of polycrystalline Ta, Ta-2.47 wt pct W (Ta-2.5W), and Ta-9.80 wt pct W (Ta-10W) was measured to study the effect of grain boundaries and tungsten concentration on athermal strength components. Compression tests were performed over a temperature range from 77 to 1223 K at strain rates of 10⁻⁴ and 10⁻¹ s⁻¹. The test results show that the yield stress of Ta becomes independent of temperature above about 400 K, indicating an “athermal” regime. In contrast, the temperature dependence of yield stress was still significant for Ta-10W up to the maximum test temperature. An analysis of the test data using single-crystal data in conjunction with Taylor factors was performed to assess the effect of grain boundaries on the athermal component of flow stress at 600 K. The results indicated that the long-range athermal stress at the yield point due to grain boundaries is approximately 13 to 41 MPa for the study materials and decreases with an increase in tungsten concentration. These results are discussed with regard to constitutive modeling of flow stress.     

Dislocations,vacancies and solutes in grain boundaries

Abstract

Three types of dislocation have been observed in grain boundaries. The experimental evidence, which is circumstantial but quite strong, picks out only one type – the lattice dislocation – as the influence controlling grain boundary sliding of very small and very large amounts. The evidence also indicates that lattice dislocations in grain boundaries are the main sources and sinks of vacancies there. The degree to which solute atoms segregate to grain, boundaries is an inverse function of their solubility in the crystaL The theory of segregation contains a difficulty involving the expression for entropy of the segregated atoms, and a way of dealing with this is indicated.

Résumé

Trois types de dislocations ont été observés aux joints de grains. Les preuves expérimentales, qui sont circonstantielles et suffisamment fortes, révèlent que seulement un, type, les dislocations du réseau, contrôle le glissement des joints de grains soit à très faible soit à très forte amplitude. Ces preuves indiquent aussi que les dislocations du réseau situées dans les joints de grains agissent principalement comme source et puits de lacunes. Le degré de ségrégation des, atomes de soluté aux joints de grains est une fonction inverse de leur solubilité dans le cristal Dans la théorie de la ségrégation une difficulté se présente pour exprimer l'entropie des atomes ségrégés et l'auteur propose une methode pour résoudre cette difficulté.     

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.     

The structure and energy of antiphase boundaries in Ll2 alloys

A detailed analysis of the antiphase boundary atomic structure and energy for a general boundary plane is reported. It has been shown that Flinn's expression for the antiphase boundary energy is essentially correct for most of the boundary planes, but does not hold for some low indices planes. Those planes are exceptional by the occurence of so called dual antiphase boundary structure. Theoretical results are discussed in relation to the dependence of the flow stress on temperature in Ll₂ ordered alloys. The presented model may serve as a basis for elucidation of climb type dislocation dissociation which has been recently observed by electron microscope using weak beam technique.     

The influence of thermal treatment on the chemistry and structure of grain boundaries in inconel 600

Although it is widely accepted that certain heat treatments result in carbide precipitation accompanied by chromium depletion at the grain boundaries, no direct evidence of this phenomenon exists for Inconel 600. Using the Scanning Transmission Electron Microscope (STEM), the extent of grain boundary chromium depletion is quantitatively determined as a function of thermal treatment time at 700 °C following a 30 min solution anneal at 1100 °C. Results confirm the presence of grain boundary chromium depletion that varies in extent with time at temperature, the chromium concentration falling to values as low as 3 wt pct. The chromium depletion volume is characterized by a depletion parameter which is correlated with intergranular corrosion test results to determine a self-healing (desensitization) chromium concentration of 9 wt pct. Trace element segregation at grain boundaries is measured by Auger Electron Spectroscopy (AES) as a function of aging treatment. Results show that after thermally treating samples for various times at 700 °C, phosphorus is always present at the grain boundaries. Intergranular corrosion behavior as a function of thermal treatment appears to be governed more strongly by chromium depletion than trace element segregation. G. S. WAS, formerly Research Assistant, Nuclear Engineering Dept., Massachusetts Institute of Technology H. H. TISCHNER, formerly Postdoctoral Associate, Department of Materials Science and Engineering, Massachusetts Institute of Technology     

Atomic structure and energy of ∑ = 5 tilt boundaries in gold

The atomic structure of 2 = 5(θ = 36.9 deg) [001] tilt boundaries in gold has been investigated by high-resolution electron microscopy (HREM). Image simulations and experimental conditions for observing grain boundary atomic structure in gold are presented. Two preferred orientations corresponding to symmetric {310} and asymmetric {430}//{100} inclinations have been observed frequently. A single symmetric {210} inclination has also been observed. The atomic structures of these three boundaries are presented. An average ratio of grain boundary to surface energy, γ_gb/γ_s, of 0.62 has been measured at 200 °C. Unique atomic structures are observed for {310}, {430}//{100}, and {210} inclinations, and multiplicities in atomic structures have not been detected. Interfacial volume expansion of these interfaces is presented and compared to computational models. 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.     

The wetting transition in high and low energy grain boundaries in the Cu(In) system

Wetting of two symmetrical tilt grain boundaries, 77° 〈110〉 and 141° 〈110〉, in synthetic copper bicrystals with a Cu(In) melt was studied in the temperature range 690°990°C. The contact angle at the site of GB intersection with the solid-melt interface was measured. A wetting transition occurred at T_w = 960 ± 6°C for the 77° 〈110〉 grain boundary and at T_w = 930 ± 5°C for the 141° 〈110〉 grain boundary. The contact angle approached zero for this transition. The relative surface energies of the two boundaries were measured using the thermal grooving technique. The energy of the 77° 〈110〉 grain boundary is about 40% lower than that of the 141° 〈110〉 grain boundary. Therefore, it has been shown experimentally that the lower the grain boundary energy, the higher the wetting transition temperature. This is in agreement with the thermodynamic model of wetting transitions on grain boundaries.