First-principles calculation of grain boundary energy and grain boundary excess free volume in aluminum: role of grain boundary elastic energy

We examined the grain boundary energy (GBE) and grain boundary excess free volume (BFV) by applying the first-principles calculation for six [110] symmetric tilt grain boundaries in aluminum to clarify the origin of GBE. The GBE increased linearly as BFV increased. The elastic energy associated with BFV, namely the grain boundary elastic energy, was estimated as a function of BFV and the shear modulus. The grain boundary elastic energies were close in value to the GBEs. The charge density distributions indicated that the bonding in the grain boundary region is significantly different from the bonding in the bulk. The grain boundary elastic energies were 15–32% higher than the GBEs. This overestimation of the grain boundary elastic energy is caused by the characteristics of the electronic bonding at the grain boundary, which is different from bonding in the bulk. We have concluded that GBE results mainly from the grain boundary elastic energy.     

Grain boundary excess free volume—direct thermodynamic measurement

The grain boundary excess free volume (BFV) along with the surface tension determines the major thermodynamic properties of grain boundaries. The BFV controls to a large extent the evolution and stability of polycrystals. Unfortunately, our knowledge about the BFV is completely restricted to data generated by computer simulations, which, in turn, are strictly limited to grain boundaries in the vicinity of special misorientations. We developed a special technique that makes it possible to measure the BFV for practically any grain boundary and provides a way of estimating the BFV for grain boundaries of different classes with high accuracy. A knowledge of the BFV is especially important for fine grained and nanocrystalline systems where it opens new possibilities to design the physical properties and microstructure of such polycrystals.     

Influence of alloying on the free energy of austenitic grain boundaries in steel

We compute the free energy of austenitic grain boundaries for steels whose carbon content is equal to 0.2%, for chrome-manganese steels with various concentrations of molybdenum and phosphorus, and for chrome-manganese-molybdenum steel. On the basis of regression analysis, we develop an interpolational model which enables one to estimate (both qualitatively and quantitatively) not only the effects of each element on the free energy of grain boundaries but also changes in these effects caused by the presence of other elements with different surface activities. It is shown that changes in the influence of alloying elements on the boundary energy of multicomponent systems can be explained by the interaction of different elements. Philadelphia, USA. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 32, No. 3, pp. 55–62, May–June, 1996.     

Influence of alloying on the free energy of austenitic grain boundaries in steel

We compute the conditional energy σ, of austenitic grain boundaries and analyze changes in boundary energy at elevated temperatures for low-carbon, chrome-manganese and chrome-manganese-molybdcnum steels. It is established that σ, varies within the range 1.0–1.3 J/m² and that, in almost all cases of alloying, the effect caused by a decrease in the surface energy of iron is so strong that even in the presence of chorophobic elements σ, decreases at elevated temperatures. For multicomponent steels, we analyze variations of the temperature coefficients of boundary energy. Philadelphia, United States of America. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 32, No. 4, pp. 63–68, July–August, 1996     

Influence of alloying on the free energy of austenitic grain boundaries in steel

We compute the free energy of boundaries of austenitic grains and analyze the effect of alloying elements (Mo, Ni, V, W, Nb, Ce, Cr, Ti, Al, Si, B, and Cu) on the boundary energy of low-carbon, chromemanganese, and chrome-manganese-molybdenum steels. By using regression analysis, we develop interpolational models for the qualitative and quantitative evaluation of the effect of each element on the free energy of grain boundaries. Philadelphia, USA. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 32, No. 2, pp. 24–34, March–April, 1996.     

How to best measure atomic segregation to grain boundaries by analytical transmission electron microscopy

This study provides an overview of the recent experiments employing methods that analyse, systematically, series of analytical spectra acquired either in nanobeam mode in a transmission electron microscope or using elemental mapping in a scanning transmission electron microscope. A general framework is presented that describes how best to analyse series of such spectra to quantify the areal density of atoms contained within a very thin layer of a matrix material, as, for example, appropriate to measure grain boundary segregation. We show that a systematic quantification of spectra as a function of area size illuminated by the electron beam eliminates the large systematic errors inherent in simpler approaches based on spatial difference methods, integration of compositional profiles acquired with highly focused nanoprobes or simple repeats of such measurements. Our method has been successfully applied to study dopant segregation to inversion domain boundaries in ZnO, to quantify the thicknesses of sub-nm thin layers during epitaxial growth by molecular beam epitaxy of (In)GaAs and to prove the absence of gettering of dopants at Σ = 3{111} grain boundaries in Si, with a precision <1 atom/nm² in all these cases.     

Electromigration of grain boundaries in aluminum

The electromigration of grain boundaries has been investigated with aluminum wires (99.999% purity, 1 mm in diameter) in the temperature range 340°–540°C under a current stress of 6×10³ A cm^-2. Grain boundary migration in aluminum is found to be reduced or enhanced by the currents stress when the grain boundary migrates in or against the current direction, respectively. The effects of additions of copper, silicon and zirconium to aluminum on the electromigration of the grain boundaries have also been examined. The contribution of electromigration to normal grain boundary migration is found to be increased by the addition of solutes. The results are discussed on the basis of the impurity drag mechanism of grain boundary migration.     

Electron microscopy: probing the atomic structure and chemistry of grain boundaries, interfaces and defects

At the heart of ‘ dynamic embrittlement’ phenomena is the stress-induced segregation of microscopic quantities of embrittling impurities to fracture surfaces. Grain boundaries and interfaces are often the natural weak links in a material. The structural and chemical information of such internal interfaces can be probed on an atomic scale using transmission electron microscopy. High-resolution electron microscopy can be used to determine the atomic coordinates of crystalline interfaces. Electron-energy-loss spectroscopy (EELS) and energy-dispersive X-ray spectroscopy can be performed on any boundary or defect and can provide chemical information such as composition and bonding. The spatial resolution of EDS is limited by low collection efficiency to around 10 Å. The more efficient signal collection for EELS allows almost atomic resolution for light elements. EELS fine structure offers a fingerprint of the local boundary arrangements, and also insight into the bonding (and possible reactivity) of boundaries and other defects. Overall, electron microscopy can be used to identify the atomistic characteristics of those interfaces susceptible to dynamic embrittlement. The structural and electronic information obtained can be used as a starting point for semi-empirical and ab initio simulations.     

Strengths of grain boundaries in pure metals

Abstract

The relative surface energies for brittle fracture along grain boundaries or along crystal planes, at low temperatures, are estimated and used in a criterion for the relative strengths of boundaries and cleavages. It is concluded that the boundary is weaker than the crystal in a wide range of metals; that it becomes weaker as the ratio of shear modulus to bulk modulus increases; and that brittle pure metals, such as iridium and molybdenum, fracture preferentially on grain boundaries. The critical modulus ratio is in all cases lower than that for the ductile–brittle cleavage transition.

MST/1154     

The role of recalcitrant grain boundaries in cleavage cracking in polycrystals

Recalcitrant grain boundaries offer an important resistance to cleavage crack advance through crack trapping. In this article, this effect is studied based on an energy analysis. It is found that the critical energy release rate is dominated by a single parameter, Q, that collects together factors such as work of separation, grain size, and crack length. For short cracks, the crack trapping effect leads to an increase in fracture resistance by 20–30%. For long cracks, the crack trapping effect is negligible.     

Influence of chemical composition and excess free volume on surface crystallization of amorphous alloys

Small-angle x-ray scattering and electron Auger spectroscopy were used to study the distribution of the excess free volume and the chemical composition of the surface layers of amorphous alloy ribbons. The relationship between these structure parameters and the surface crystallization characteristics of amorphous alloys is analyzed. Pis’ma Zh. Tekh. Fiz. 24, 58–64 (December 12, 1998)     

Bismuth-induced embrittlement of copper grain boundaries

Catastrophic brittle fracture of crystalline materials is one of the best documented but most poorly understood fundamental phenomena in materials science. Embrittlement of copper by bismuth is a classic example of this phenomenon. Because brittle fracture in any structural material can involve human tragedy, a better understanding of the mechanisms behind it is of the highest interest. In this study, we use a combination of two state-of-the-art atomic characterization techniques and ab initio theoretical materials simulations to investigate the geometric and electronic structure of a copper grain boundary with and without bismuth. Only with this unique combination of methods are we able to observe the actual distribution of bismuth in the boundary and detect changes in the electronic structure caused by the bismuth impurity. We find that the copper atoms that surround the segregated bismuth in the grain boundary become embrittled by taking on a more zinc-like electronic structure.