Segregation Energy Research Articles

Anomalous surface segregation behaviour of some 3d elements in ferromagnetic iron

The segregation of Cr in Fe is known to be anomalous since the barrier for surface segregation of Cr is not determined by the topmost surface layer, as one would expect, but rather by the subsurface layer where the energy of segregation is much larger and endothermic. This has been attributed to a complex interaction involving the antiferromagnetism of Cr and the ferromagnetism of Fe. We report in this paper the results of our ab initio electronic structure calculations on the segregation behaviour of all the 3d elements on the (1 0 0) surface of ferromagnetic iron in the hope of better understanding this phenomenon. We find a similar behaviour for the segregation of the next antiferromagnetic 3d element Mn in Fe, where the subsurface layer is also found to block the segregation of Mn to the surface. On the other hand, ferromagnetic Co exhibits a normal segregation behaviour. The elements Sc, Cu and Ni do not form solid solutions with ferromagnetic iron. The early elements Ti and V are non-magnetic in their metallic states, but are strongly polarized by Fe, and develop magnetic moments which are aligned antiferromagnetically to those of Fe atoms. While the subsurface layer blocks the segregation of Ti to the surface, no blocking behaviour is found for the segregation of V. The segregation behaviour of all these elements is strongly correlated with the displacement of the solute atoms on the surface of Fe. The elements showing anomalous segregation behaviour are all displaced upwards on the surface, while those showing normal segregation are pulled inwards. These results indicate that the antiferromagnetism of the segregating element plays the key role in the anomalous segregation behaviour in Fe.

Segregation of Impurities in GaAs and InAs Nanowires

Using ab initio methods based on the density functional theory, we investigate the segregation and formation energies for various dopants (Si, Be, Zn, Sn), commonly used to obtain p- or ntype conductivity in GaAs and InAs nanowires. The distribution of Au and O atoms, which may be unintentionally incorporated during the wire growth, is also studied. The calculations performed for nanowires of zinc blende and wurtzite structure show that the distribution of most of the impurities depends on the crystal structure of the wires. For example, it is shown that the same growth conditions can lead to lower energy for Si substituting Ga (donor) in the wire of wurtzite structure and substituting As (acceptor) in the wire of zinc blende structure. In contrast, we obtain that gold and oxygen atoms always tend to stay at the lateral surfaces of GaAs and InAs nanowires, in agreement with experimental findings, while for beryllium the lowest energies are found when the impurities are located in sites in the center of the wurtzite wire or along the [1; 0; 1] axis from surface to the center of the zinc blende wire, what can explain the recently observed diffusion of this impurity into the volume of GaAs wires.

First principles studies of structural, electrical and magnetic properties of semiconductor nanowires

Abstractmagnified imageThis article reviews recent advances in theoretical description of the properties of various III–V and IV–VI nanowires, which have been obtained using simple ab initio methods. The impact of crystal structure, lateral surfaces, passivation of the dangling bonds and quantum confinement on the stability of the nanowires is discussed. The second part of the paper is devoted to the analysis of III–V and IV–VI nanowires doped with various, in particular magnetic, ions. The influence of the crystal structure of the wire on the segregation and formation energies of different dopants and thus on the electric and magnetic properties of the nanowires is shown. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Cr segregation at C11b/C40 interface in MoSi2-based alloys: A first-principles study

Based on the first-principles calculation, we investigated Cr segregation behavior at the C11b/C40 lamellar interface for MoSi2-based alloys. We first elucidated the energetically stable interface structure among possible contacts between C11b and C40, where the interface energy is 1.7 meV/Å2. Without inclusion of lattice vibrational contribution to segregation energy, Cr composition at the interface was lower than that at C40 phase, which was inconsistent with the early experimental result. Inclusion of the vibrational contribution successfully resulted in strong Cr segregation at the interface over that at C11b as well as C40 phase. This indicates that Cr segregation at the most stable interface is a thermodynamically stable state, in which lattice vibration plays a significant role.

First-principles study of sulfur multi-absorption in nickel and its segregation to the Ni(100) and Ni(111) surfaces

It is of both experimental and fundamental interest to understand the sulfur (S) properties of metallic alloys. Therefore, in this work, we present the physical and chemical properties of sulfur in Ni–fcc solid solution and its chemisorption on the Ni(100) and Ni(111) surfaces using the density functional theory. It is shown that the substitutional site is more stable than the interstitial sites because of a significant “vacancy–sulfur” interaction and steric effects. The migration mechanism of S atoms in a solid solution is presented in detail, and our results are compared to the experimental data. We also discuss the interactions between sulfur and the vacancies. Adsorption of S on the Ni(100) and Ni(111) surfaces arises preferably on the most coordinated sites. A large segregation energy is calculated for the Ni(100) and Ni(111) surfaces.

The migration and formation energies of N-interstitials near [001] Fe surfaces: an ab initio study

Using density functional theory, the mechanism of surface segregation of N to the [001] Fe surface was studied. The formation and migration energies were decomposed into chemical bonding and strain energy components. While the segregation energy was determined to be −1.1 eV, the bonding and strain energy components for segregation were −0.5 and −0.6 eV, respectively. The results indicate that strain energy relaxation plays a major role in surface segregation, and that there is approximately a 7-layer transient region, which separates bulk and surface environments. The role of the strain energy on interstitial migration barriers was also critically evaluated.

Segregation of alloying atoms on the Fe(1 0 0) surface and their effects on oxygen adsorption

The segregation of 3d transition metals and their effects on oxygen adsorption on the Fe(100) surface are systematically studied using the first-principles calculations. On the one hand, Sc, Ti, Mn, Ni, Cu, and Zn have a tendency to segregate towards the surface, while V, Cr, and Co prefer to remain in the interior of Fe bulk. Furthermore, the segregation energies varies monotonically from layers 1–5 for all 3d transition metals except Ti, Cr, Mn, whose subsurface layer provides a large barrier for surface segregation. On the other hand, attractive/repulsive interaction has been observed between oxygen and alloying atom with lower/higher atomic number than that of Fe. Based on the above results, the oxidation should be expected to occur preferentially at the Sc, Ti, and Mn segregation regions on the Fe(100) surface.

Discrete particle simulation of solid separation in a jigging device

This paper presents a numerical study of solid separation in a jigging device, which is a high yield and high recovery gravity separation device widely used in ore processing. The mathematical model adopted is a combination of computational fluid dynamics (CFD) for the liquid flow and discrete element method (DEM) for particle motion. The motion of individual particles is 3 dimensional (3D) and the flow of continuous liquid is 2 dimensional (2D), considering the bed thickness is only 1/3rd of the bed width, and one CFD computational cell is used through the thickness. Periodic boundary conditions are applied on the front and rear walls to emulate a bed of larger thickness using a relatively small number of particles. Stratification is heavily dependent on fluid motion through the jig. The study explores 5 different pulsation profiles. The profiles used are — sinusoidal, triangle, sawtooth-backward, sawtooth-forward, and trapezoidal. The initial packing conditions consist of a binary-density particle system where the light particles and heavy particles, have respective densities of 2540 and 4630kg/m3. There are 1130 particles each 1cm in diameter. As an initial comparison, all simulations are conducted using a fixed peak–peak amplitude and pulsation period. Their relative performances are compared in terms of solid flow patterns, separation kinetics, energy, and mean particle position. The underlying mechanisms are explained in terms of particle–fluid interaction force. These quantitative comparisons demonstrate significant differences in the segregation rate and energy used for various pulsation profiles.

Effects of hydrogen in a vanadium grain boundary: From site occupancy to mechanical properties

We have investigated site occupancy and mechanical properties of a vanadium (V) Σ5(310)/[001] grain boundary (GB) with hydrogen (H) using a first-principles method. The segregation energy is calculated to be −0.29 eV for the energetically favorable V GB interstitial site, indicating that H energetically prefers to segregate into the V GB. We demonstrate that H can largely affect the mechanical properties of the V GB. The tensile strength and the Griffith fracture energy are reduced by approximately 13% (to 18.42 GPa) and 10% (to 1.74 J/m2) because of H segregation in comparison with that of the clean V GB, respectively. Our total energy calculations show that H acts as an embrittler to the V GB based on the Rice-Wang model. The atomic configurations and charge transfer analysis show that the segregated H weakens the surrounding interfacial V-V bonds, leading to the V GB mechanical properties degradation.

Theoretical modeling of defect segregation and space-charge formation in the BaZrO3 (210)[001] tilt grain boundary

Density-functional theory (DFT) has been used to determine the structure and interface energy of different rigid body translations (RBTs) of the (210)10011 grain boundary (GB) in BaZrO3. There exist several different stable structures with almost equally low interfacial energy. Segregation energies of protons and oxygen vacancies have been determined for the most stable (210)10011 grain boundary structure. The results suggest that both defect species favor segregation to the same site at the boundary interface with minimum segregation energies of - 1.45 eV and - 1.32 eV for vacancies and protons respectively. The segregation energies have been used in a thermodynamic space-charge model to obtain equilibrium defect concentrations and space-charge potentials at a 10% dopant concentration. Space-charge,potential barriers around 0.65 V were obtained at intermediate temperatures under hydrated conditions, where protons are the main contributor to the excess core charge. The potential is slightly lower under dry conditions. (C) 2013 Elsevier B.V. All rights reserved.

The effect of vanadium impurity on Nickel Σ5(012) grain boundary

We report first-principle density functional theory investigation on the effect of vanadium impurity in the nickel Σ5(012) symmetrical tilt grain boundary (GB) using Norm-conserving pseudopotentials. We first calculate segregation energies for interstitial and different substitutional sites in order to determine site preference and the segregation properties of V in the Ni GB. It is found that vanadium atoms prefer to segregate in the substantial sites of the GB. Furthermore, the calculations of tensile strength for different V positions in Ni Σ5(012)GB show an enhancement of the maximum tensile strength σMax up to 17%, indicating that vanadium acts as a strengthening element in Ni GB, which is in agreement with experimental observations.

The role of charge and ionic radius on fission product segregation to a model UO2 grain boundary

The segregation energies of a range of fission products in UO2 to a Σ5 symmetric tilt grain boundary have been calculated using empirical potentials and their dependency on site, charge, and ionic radius has been determined. Density functional theory calculations provide information about the detailed bonding environment around the segregates. While most of the fission products prefer to reside in sites with large free volume, there are some that form strong bonds with neighboring oxygen ions, and thus prefer sites with high oxygen coordination. This result provides insight into nuclear fuel design to enhance control of fission product retention.

Cs-Corrected STEM Observation and Atomic Modeling of Grain Boundary Impurities of Very Narrow Cu Interconnect

If we can clarify the kinds of impurities, and the role of impurities in the grain growth process during annealing, we could control grain size distributions by removal of above harmful impurities from electroplating materials leading to the realization of very low resistivity and high electro-migration resistant Cu interconnects for future high speed and low electric power consumption LSIs. Therefore, nanoscale analysis of the segregated elements at the grain boundary and understanding of the segregation mechanism are indispensable. In this study, we directly observed the segregation of impurities at the grain boundary consist of lighter elements than Cu polycrystal interconnects buried in trench using Cs-corrected STEM. We also calculated the segregation energies using ab initio method for the observed elements. Trenches in a four-point probe geometry of 80‐100 nm width, with 200 nm height and 1 mm length, and four 200 μm square pads with the same height were patterned in silicon dioxide dielectric films using electron beam lithography and reactive ion etching. Ultrathin TaN/Ta (TaN:7.5 nm; Ta:7.5 nm) and a 50 nm seed layer were sputterdeposited in that order as shown in Fig. 1. After that, an 8 in. wafer was cut into 10 mm square chips for the electroplating. The plating solution contained 0.63 mol/dm 3 nominal 3N CuSO4 ·5H2O, 0.105 mol/dm 3 H2SO4, and 3.7 × 10 −3 mol/dm 3 HCl. The required organic accelerator, organic suppressor, and leveler additives were also added to the plating solution. The anode plate used

Quantifying the energetics and length scales of carbon segregation to α-Fe symmetric tilt grain boundaries using atomistic simulations

Segregation of impurities to grain boundaries (GBs) plays an important role in both the stability and macroscopic behavior of polycrystalline materials. The research objective in this work is to better characterize the energetics and length scales involved with the process of solute and impurity segregation to GBs. Molecular statics simulations are used to calculate the segregation energies for carbon within multiple substitutional and interstitial GB sites over a database of 125 symmetric tilt GBs in Fe. The simulation results show that there are two energetically favorable GB segregation processes: (1) an octahedral C atom in the lattice segregating to an interstitial GB site and (2) an octahedral C atom and a vacancy in the lattice segregating to a grain boundary substitutional site. In both cases, lower segregation energies than appear in the bulk lattice were calculated. Moreover, based on segregation energies approaching bulk values, the length scale of interaction is larger for interstitial C than for substitutional C in the GB (≈5 Å compared to ≈3 Å from center of the GB). A subsequent data reduction and statistical representation of this dataset provides critical information about the mean segregation energy and the associated energy distributions for carbon atoms as a function of distance from the grain boundary, which quantitatively informs higher scale models with energetics and length scales necessary for capturing the segregation behavior of alloying elements and impurities in Fe. The significance of this research is the development of a methodology capable of ascertaining segregation energies over a wide range of GB character (typical of that observed in polycrystalline materials), which herein has been applied to carbon segregation to substitutional and interstitial sites in a specific class of GBs in α-Fe.

CFD–DEM investigation of particle separations using a sinusoidal jigging profile

This paper presents a numerical investigation of solid separation in jigging device. Jigging is a gravity separation method commonly used by the minerals industry to separate coal, iron ore, diamonds and other minerals on the basis of particle size and/or density. Separation is recognised as being heavily dependent on fluid motion in the jig. This study explores the effects of the inlet time dependent velocity profile in relation to a wide criterion on jigging performance. Modelling of the liquid–solid system is performed through a combination of computational fluid dynamics (CFD) to simulate liquid flow and discrete element method (DEM) to resolve particle motion. The initial packing conditions consist of a binary-density particle system of 1130 particles each 1cm in diameter. A range of jigging profiles have been implemented in mineral processing. In this study the sinusoidal pulsation profile is selected adopting variations in both amplitude and frequency. The performance of profile variants are compared in terms of solid flow patterns, separation kinetics, energy, and mean particle position. These quantitative comparisons demonstrate significant differences in the segregation rate, energy, and solid phenomena, helping find an alternative optimum operating setting for the system. In addition, boundaries of operation are found in terms of frequency and amplitude limits and the concentration mechanics are investigated in these regions.

Equilibrium and kinetic surface segregations in Cu–Sn thin films

Equilibrium and kinetic surface segregations in Cu–Sn thin films are simulated based on the modified Darken model for a finite sized system. The simulations are carried out for all compositional ranges and film thicknesses. The segregation energy and the interaction parameter for the simulation are determined respectively by the Miedema model and from the thermodynamic data used for the Cu–Sn phase diagram calculation. The strong negative interaction parameter restrains Sn surface segregation in the Cu–Sn system. The size effect on surface segregation depends on the segregation energy, interaction parameter, initial bulk concentration, temperature and film thickness.

Surface segregation measurements of In and S impurities from a dilute Cu(In,S) ternary alloy

The surface segregation of In and S from a dilute Cu(In,S) ternary alloy were measured using Auger electron spectroscopy coupled with a linear programmed heater. The alloy was linearly heated and cooled at constant rates. Segregation data of a linear heat run showed surface segregation of In that reached a maximum surface coverage of 25% followed by S, which reached a coverage of 30%. It was found that after In had reached a maximum surface coverage, it started to desegregate as soon as the S enriched the surface until In was completely replaced by S. The segregation parameters, namely, the pre‐exponential factor (D0), activation energy (Q), segregation energy (ΔG˚) and interaction energy (Ω) were extracted from the measured segregation data for both In and S segregation in Cu by simulating the measured segregation data with a theoretical segregation model (modified Darken model). The segregation parameters obtained for In segregation in Cu are D0 = 1.8 ± 0.5 × 10−5 m2 s−1, Q = 184.3 ± 1.0 kJ.mol−1, ΔG˚ = −61.4 ± 1.4 kJ.mol‐1, ΩCu−In = 3.0 ± 0.4 kJ.mol−1; for S segregation in Cu the parameters are D0 = 8.9 ± 0.5 × 10−3 m2 s−1, Q = 212.8 ± 3.0 kJ.mol−1, ΔG˚ = −120.0 ± 3.5 kJ.mol−1, ΩCu−S = 23.0 ± 2.0 kJ mol−1 and the In and S interaction parameter is ΩIn−S = −4.0 ± 0.5 kJ.mol−1. The initial parameters used for the Darken calculations were extracted from fits performed with the Fick's and Guttmann model. Copyright © 2013 John Wiley & Sons, Ltd.

New Perturbation Method for Predicting Solute Segregation Energies for Symmetric Tilt Grain Boundaries

ABSTRACTSolute atoms in dilute alloys have been shown to segregate at grain boundaries and stabilize them against grain growth. At present, most theories of the stabilization of nanostructured alloys do not account for the detailed atomic structure of the interfaces, but instead rely on averaged segregation energies. One of the reasons for this is the daunting task of determining segregation energies for a large number of possible sites in a given microstructure. We have developed a new approach to predicting and organizing interface structures in alloys that takes advantage of perturbation techniques and a disclination structural units model (DSUM) developed previously to describe grain boundary structure and properties in pure systems. The fundamental idea is to treat dilute alloys as a perturbed form of the pure metal systems whose energy can be determined by the DSUM. This paper introduces this method and gives a preliminary validation by comparing segregation energies for zirconium solute segregating to a grain boundary in copper calculated via the perturbation method and full atomistic simulations.

Phase-Field Simulation of Lamellar Structure Formation in MoSi2/NbSi2 Duplex Silicide

ABSTRACTWe conducted phase-field simulations of microstructural evolution in C11b-MoSi2 / C40-NbSi2 dual phase alloy with and without Cr-addition to examine the factors responsible for the formation and stability of the lamellar structure on the basis of thermodynamics, micromechanics and first-principles calculations. The first principles calculation was used for evaluating the interfacial energy, segregation energy of solute Cr-atoms and lattice parameters of imaginary disilicides for estimating the effects of solute distribution on the lattice misfit. When both of lattice misfit and the anisotropy of interfacial energy is taken into account, a lamellar structure similar to that observed experimentally is formed. In the absence of Cr-addition, the straightness of lamellar structure decreased slightly. When an isotropic interfacial energy is assumed, lamellar structure is not formed. Instead, a microstructure with habit planes parallel to {1 0 $\bar 1$ 1} plane of C40-phase is formed. Thus, the anisotropy of interfacial energy is crucial for the lamellar structure formation rather than the elastic energy due to lattice misfit.

Phase-Field Study on the Segregation Mechanism of Additive Elements in NbSi2/MoSi2 Duplex Silicide

ABSTRACTWe have examined segregation behavior of various alloying elements at lamellar interfaces of C40-NbSi2/C11b-MoSi2 duplex silicide by a phase-field simulation, which takes into account not only bulk chemical free energy but also segregation energy evaluated by the first principles calculation to reflect interaction between solutes and interface. The simulation suggests that segregation behaviors greatly depend on additive elements. In the case of Cr-addition, the C40-phase becomes enriched with Nb and Cr, while the C11b-phase becomes enriched with Mo, which agrees with the equilibrium phase diagram. Slight segregation of Cr atoms is observed at the interface, whereas Nb and Mo concentrations monotonically change across the diffuse interface between C11b and C40 phases. Significant segregations of Zr and Hf are formed at static interfaces, which are attributed to the chemical interaction between solute atoms and the static interface.