Solute-atom segregation at symmetric twist and tilt boundaries in binary metallic alloys on an atomic-scale

Monte Carlo and overlapping distributions Monte Carlo (ODMC) techniques are employed to simulate grain boundary (GB) segregation in a number of single-phase binary metallic alloys—the Au-Pt, Cu-Ni, Ni-Pd, and Ni-Pt systems. For a series of symmetric [001] twist and [001] tilt boundaries, with coincident site lattice (CSL) structures, we demonstrate that the Gibbsian interfacial excess of solute is a systematic function of the misorientation angle. We also explore in detail whether the GB solid solution behavior is ideal or nonideal by comparing the results of Monte Carlo and ODMC simulations. The range of binding free energies of specific atomic sites at GBs for solute atoms is also studied. The simulational results obtained demonstrate that the thermodynamic and statistical thermodynamic models commonly used to explain GB segregation are too simple to account for the microscopic segregation patterns observed, and that it is extremely difficult. If not impossible, to extract the observed microscopic information employing macroscopic models.     

Atomistic simulations of interactions between the 1 / 2⟨111⟩ edge dislocation and symmetric tilt grain boundaries in tungsten

The strength of polycrystals is largely controlled by the interaction between lattice dislocations and grain boundaries. The atomistic details of these interactions are difficult to discern even by advanced high-resolution microscopy methods. In this paper we present results of atomistic simulations of interactions between an edge dislocation and three symmetric tilt grain boundaries in body-centred cubic tungsten. Our simulations reveal that the outcome of the dislocation–grain-boundary interaction depends sensitively on the grain boundary structure, the geometry of the slip systems in neighbouring grains, and the precise location of the interaction within the grain boundary. A detailed analysis of the evolution of the grain boundary structures and local stress fields during dislocation absorption and transmission is provided.     

Cation Segregation in an Oxide Ceramic with Low Solubility: Yttrium Doped α-Alumina

The segregation behaviour of a cation (yttrium) with a low solubility in the polycrystalline oxide host (a-Al₂O₃) has been investigated at temperatures between 1450 and 1650°C using analytical scanning transmission electron microscopy. Three distinct segregation regimes were identified. In the first, the yttrium adsorbs to all grain boundaries with a high partitioning coefficient, and this can be modelled using a simple McLean-Langmuir type absorption isotherm. In the second, a noticeable deviation from this isotherm is observed and the grain boundary excess reaches a maximum of 9 Y-cat/nm² and precipitates of a second phase (yttrium aluminate garnet, YAG) start to form. In the third regime, the grain boundary excess of the cation settles down to a value of 6–7 Y-cat/nm² that is in equilibrium with the YAG precipitates. In a material (accidentally) co-doped with Zr, the Zr seems to behave in a similar way to the Y and the Y + Zr grain boundary excess behaves in the same way as the Y grain boundary excess in the pure Y-doped system. In this latter system, Y-stabilised cubic zirconia is precipitated in addition to YAG at higher Y + Zr concentrations.     

Creating and destroying vacancies in solids and non-equilibrium grain-boundary segregation

Determining how the vacancies in excess of equilibrium concentration are created and destroyed in solids is crucial for understanding many of their physical characteristics and processes. Grain boundaries are known to be sources and sinks for bulk vacancies, but the exchange that will occur between the grain boundary and the bulk under a stress is still obscure. In the present paper, we show that grain boundaries will work as sources to emit vacancies when a compressive stress is exerted on them and as sinks to absorb vacancies when a tensile stress is exerted. At the same time, this physical process will produce solute non-equilibrium grain-boundary segregation and dilution. A set of kinetic equations is established to describe this physical process. Additionally an attempt has been made to simulate the experimental data with the kinetic equations to justify the physical process.     

Solute distribution in nanocrystalline Ni–W alloys examined through atom probe tomography

Atom probe tomography is used to observe the solute distribution in electrodeposited nanocrystalline Ni–W alloys with three different grain sizes (3, 10 and 20?nm) and the results are compared with atomistic computer simulations. The presence of grain boundary segregation is confirmed by detailed analysis of composition fluctuations in both experimental and simulated structures, and its extent quantified by a frequency distribution analysis. In contrast to other nanocrystalline alloys previously examined by atom probe tomography, such as Ni–P, the present nanocrystalline Ni–W alloys exhibit only a subtle amount of solute segregation to the intergranular regions.     

Thermodynamic stability of binary nanocrystalline alloys: analysis of solute and excess vacancy

Regarding that the excess volume in grain boundaries (GBs) is released as the vacancies which are accommodated by the crystal bulk during grain growth, a free-energy function for binary nanocrystalline solid solution is proposed, based on the pairwise nearest-neighbor interactions. The model, for the given composition and temperature, predicts an equilibrium grain size, subjected to a mixed effect due to solute segregation and due to excess vacancies. Furthermore, excess-vacancy-inhibited grain coarsening can be attained, which plays a minor role in holding the thermal stability of nanocrystalline alloys, as compared to the effect of solute segregation.     

Diffusion, Solute Segregations and Interfacial Energies in Some Material: An Overview

We have shown a connection among the three important properties of interfaces, namely, the free energy, diffusion and solute segregation through the conjecture that the interface free energy is the difference between those responsible for diffusion in the lattice and the interface itself. The interface energy is known to decrease upon solute additions. We discuss the methodology and the thermodynamical analysis of the diffusion parameters which enable extraction of the interfacial energies and illustrate them by results obtained in a wide variety of materials. Investigations carried out in pure polycrystalline metals have yielded grain boundary energies comparable to those directly measured. Furthermore, we discuss the role of solute segregation at grain boundaries in alloys in altering diffusion. From the perturbations caused, the solute segregation parameters—the enthalpy and the entropy of binding—have been extracted and levels of solute concentrations estimated. It is shown that similar analyses when applied to complex materials, e.g. the Pb–Sn eutectic alloy, several intermetallic compounds, and oxide systems, also result in acceptable values of interface energies and segregation factors. Finally, some ad-hoc guidelines are provided to alter diffusion in interfaces through solute additions in order to achieve some end use engineering objectives.     

Solute-atom segregation/structure relations at high-angle (002) twist boundaries in dilute Ni−Pt alloys

Monte Carlo simulations, utilizing embedded atom method (EAM) potentials, are employed to investigate in detail solute-atom segregation behavior at high-angle symmetrical (002) twist boundaries, at T=850 K, in Pt-3 at.% Ni and Ni-3 at.% Pt alloys. Solute enhancement in those alloys occurs on both sides of the phase diagram, although it is considerably higher on the Ni-rich side. The distributions of solute concentrations within the first and the second planes are very inhomogeneous, with the sites highly enhanced in solute being in the minority. The remaining sites exhibit little or no enhancement. The highest level of solute concentrations at individual sites continues to increase with the value of the rotations angle, , until saturation occurs at about the =5 misorientation. The large differences in concentrations between different types of sites suggest the possibility of an ordered grain-boundary phase. The correlation between the structure and solute species concentrations in most cases follows the trends observed for low-angle boundaries: Pt as a solute prefers the structural units of the perfect crystal type, while Ni as a solute tends to segregate at the filler units associated with the cores of the primary grain boundary dislocations. A strong correlation is observed between the position of a site in the first or second (002) plane and the plane of the interface. Rigid-body translations are detected for two boundaries on the Pt-rich side of the phase diagram. Roughening and possible structural multiplicity occur in the =5 boundary on the Ni-rich side. The same boundary on the Pt-rich side of the phase diagram exhibits a considerable amount of structural and chemical disorder.     

Theoretical aspects of solute segregation to high-angle grain boundaries

A high-angle grain boundary is modeled as a planar defect characterized by its thickness and atomic density. We successively examine the elastic and electronic contributions to the solute/grain boundary binding energy. We deduce the effect of the grain boundary physical parameters on its propensity for segregation. The thickness of high-angle grain boundaries is not a fundamental parameter for segregation. The atomic density in the grain boundary controls the electronic binding energy. The rate of change of elastic constants with the density is the important factor in the elastic contribution to segregation. We conclude that segregation to boundaries with small excess volumes is not precluded.     

Grain-boundary anelastic relaxation and non-equilibrium dilution induced by compressive stress and its kinetic simulation

Grain boundaries are known to be sources and sinks for bulk vacancies, but the exchange that occurs between the grain boundary and the bulk under a low stress is still obscure. In the present paper, it is shown that grain boundaries may act as sources to emit vacancies when an anelastic deformation occurs under a compressive stress. These emitted supersaturated vacancies are combined with solute atoms to form complexes. Solute non-equilibrium grain-boundary dilution may be induced by the diffusion of complexes away from the boundary. An equation of solute concentration at grain boundary is derived under stress equilibrium during its anelastic relaxation. Furthermore, kinetic equations are also established to describe the non-equilibrium grain-boundary dilution. Additionally, an attempt is made to simulate experimental data to justify the present model.     

Yttrium segregation and surface phases of yttria-stabilized zirconia (1 1 1) surface

Surface segregation of yttria-stabilized zirconia (YSZ) was studied via first-principles computations and thermodynamics. For the cubic YSZ (1 1 1) surface, yttrium can segregate only to a subsurface layer, and these segregation phases are terminated at the surface by defective oxygen layers with honeycomb structure. The segregation is independent of the bulk yttrium concentration at high oxygen partial pressures or low temperatures. At very low oxygen partial pressures and high temperatures there is no surface yttrium segregation and the surface is terminated by O–Zr. Our results provide a reasonable explanation for previous experimental work, and also a framework for extending our understanding of cation segregation in oxide surfaces.     

Computer simulation of solute segregation to a Σ = 5 tilt boundary in Au,Cu and Ni

A Lattice Energy Function that combines a Mie type interatomic potential and a free electron gas volume dependence has been applied to the study of grain boundary energy and structure of a Σ = 5 tilt boundary in Au, Cu and Ni and of solute segregation to the same. Interatomic potentials and volume dependencies of the solvent and solute were adjusted to fit the relative partial molar enthalpy and volume at infinite dilution order to construct a AB type potential and volume dependence. This AB interaction is then applied to calculate the binding energies of solute to various grain boundary sites and the resulting change in grain boundary energy. A relationship between the binding energy and change in grain boundary is derived. The relative values of the grain boundary energy are in agreement with experimental values of the average grain boundary energies. The relative binding energies of the tested solvent-solute systems are in agreemnet with expectations that certain systems should have larger binding energies than others. The behavior of solute binding energies and local relaxations are in agreement with other studies of grain boundary segregation which use different Lattice Energy Functions and relaxation algorithms. The change in grain boundary energy is shown to be directly proportional to the binding energy.     

Theoretical study of the initial stage of InN growth on cubic zirconia (111) substrates

An initial stage of InN growth on cubic zirconia (111) substrates has been investigated using first‐principles calculations based on density functional theory (DFT). We have evaluated adsorption energies of indium and nitrogen atoms on cubic zirconia (111) surfaces, and have found that the differences in the adsorption energies of the indium atoms at various adsorption sites were small, indicating that the migration of the indium atoms on zirconia (111) surfaces occurs readily. On the other hand, we have found that the differences in the adsorption energies of the nitrogen atoms at various adsorption sites were large, implying that the nitrogen atoms tend to stay at the stable site with the largest adsorption energy, which was identified as the O–Zr bridge site. These results suggest that the first layer of InN films is the nitrogen layer. In addition, we have found that the energetically favorable arrangement is comprised of InN(0001)//cubic zirconia (111) and InN $ [11\bar 20] $ //cubic zirconia $ [1 \bar 10], $ which is quite consistent with previously obtained experimental data. Furthermore, the hybridization effect between N 2p and O 2p plays a crucial role in determining the interface structure for the growth of InN on cubic zirconia (111) surfaces. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The relationship between grain-boundary structure and segregation in a rapidly solidified Fe-P alloy

It is well known that the amount of solute segregation can vary from one grain boundary to another. Though it is accepted that this variation is due to differences in boundary structure and crystallography, direct correlation between the degree of segregation and specific boundary structural characteristics is not well documented. In the present paper, P grain-boundary segregation in rapidly solidified Fe was studied by X-ray mapping (XRM) in a scanning transmission electron microscope (STEM). The boundary structure was characterized by convergent beam electron diffraction (CBED). To explore the relationship between the degree of segregation and boundary structure, a parameter?β?is introduced, which describes how well the two crystal planes on either side of a grain boundary match each other in a manner similar to the long-established plane matching theory. The introduction of this parameter enables us to relate the degree of segregation to boundary structure in a consistent way, e.g., both small-angle and low?Σ?symmetric boundaries correspond to low angle of β, leads to a low degree of segregation.     

Stability of cubic zirconia and of stoichiometric zirconia nanoparticles

Using the electron density functional method, it is shown that the oxygen sublattice of cubic zirconia is unstable with respect to random displacements of oxygen atoms, which results in general instability of bulk cubic zirconia at low temperatures. A comparison of the equilibrium atomic structures and total energies of stoichiometric ZrO₂ nanoparticles about 1 nm in size shows that particles with cubic symmetry are more stable than those with rhombic (close-to-tetragonal) symmetry. The electronic structure of nanoparticles exhibits an energy gap at the Fermi level; however, this gap (depending on the symmetry and size of the particle) can be much narrower than the energy gap of the bulk material.     

Grain boundary compositions in stoichiometric and off-stoichiometric Y1Ba2Cu3O7−x

The grain boundary segregation behavior of stoichiometric and off-stoichiometric YBa₂Cu₃O_7−x has been studied with analytical electron microscopy (AEM) to complement previous results obtained with Auger electron spectroscopy (AES). It was observed that the grain boundary segregation levels varied from boundary to boundary. In stoichiometry material, excess copper and deficient oxygen were observed at the grain boundaries. In materials containing excess barium, excess yttrium and deficient copper levels were observed at the grain boundaries. The grain boundary segregation levels in the materials containing excess barium can be related to the resistivity and critical current density results. Preferential segregation to specific sites in grain boundaries was observed by AEM. The effect of grain boundary segregation on the superconducting properties of these materials is discussed in terms of the weak link behavior and a possible percolative mechanism in order to maintain a continuous current path.     

Point defect interactions with crystal interfaces

The structures of a small closed system of grain boundaries and the interactions of vacancies with these boundaries has been investigated using computer simulation techniques based on empirical interatomic potentials. The boundaries chosen are the {;111}; and {;112}; twins in both body centred cubic and face centred cubic metals, the potentials used being matched to the physical properties of iron and copper. Two stable structures arise for the {;112};_bcc twin so that effectively five boundaries have been studied. The structures and energies of these are extremely varied, the {;112};_fcc twin in particular being very broad. This influences the binding of vacancies to the boundaries and the migration of vacancies along the boundaries. Near the {;111};_bcc twin a split-vacancy consisting of a divacancy and an interstitial is the most stable configuration. This has a very high binding energy and an exceptionally high migration energy. Near the other boundaries the vacancy migration energies are less than in the bulk. The implications of the results are discussed.     

Free energies of interfaces from quasi-harmonic theory: A critical appraisal

A critical assessment is given of the quasi-harmonic approximation, and various approximations to the quasi-harmonic approximation, with regard to predicting the free energy and atomic structure of grain boundaries in silicon at elevated temperatures. The quasi-harmonic results are compared with those obtained by molecular dynamics and thermodynamic integration. It is found that the quasi-harmonic approximation yields accurate excess free energies and atomic structures of grain boundaries at 1,000 K. The anharmonic contribution to the free energy that is absent in the quasi-harmonic contribution is virtually the same at a grain boundary in Si and in the perfect crystal. The second-moment and Einstein approximations to the full quasi-harmonic theory yield unreliable free energies, but reasonably accurate atomic structures. However, excess free energies are quite well described by the Einstein model. It is concluded that the quasi-harmonic approximation works remarkably well in silicon. The simplest approximations to the phonon density of states lead to unreliable results for the free energy, but cancellation of errors occurs to a large extent when excess free energies are computed.     

Application of automated crystallography for transmission electron microscopy in the study of grain-boundary segregation

Analytical Electron Microscopy (AEM) has brought significant progress in the study of grain-boundary segregation. Using X-ray energy-dispersive spectrometry (XEDS) in the AEM, elemental segregation information can be related to the crystallographic character of the same boundary via conventional Transmission Electron Microscope (TEM) diffraction techniques. While significant efforts have been made to improve XEDS analysis of sub-nanometer segregation layers, the methods for crystallographic characterization of grain boundaries have remained the same for several decades and labor-intensive processes. Recently, a method termed Automated Crystallography for TEM (ACT) was developed, which automates crystallographic characterization of grains under TEM observation. In the present work, we combine ACT and X-ray mapping via EDS in AEM for the study of Sb grain-boundary segregation in a rapidly solidified Cu-0.08 wt % Sb alloy. In contrast with previous reports, a large degree of anisotropy in Sb segregation level between different boundaries is found. ACT results suggest that one of the several grain boundaries observed with no detectable Sb segregation is very close to a Sigma 3 coincidence-site lattice structure. The reason for the observed anisotropy in the present alloy is discussed, based upon McLean's theory of segregation.