Theory and simulation of coupled grain boundary migration and grain rotation in low angle grain boundaries

Abstract

Microstructure evolution due to coupled grain boundary migration and grain rotation in low angle grain boundaries is studied through a combination of molecular dynamics and phase field modeling. We have performed two dimensional molecular dynamics simulations on a bicrystal with a circular grain embedded in a larger grain. Both size and orientation of the embedded grain are observed to evolve with time. The shrinking embedded grain is observed to have two regimes: constant dislocation density on the grain boundary followed by constant rate of increase in dislocation density. Based on these observations from the molecular dynamics simulations, a theoretical formulation of the kinetics of coupled grain rotation is developed. The grain rotation rate is derived for the two regimes of constant dislocation density and constant rate of change of dislocation density on the grain boundary during evolution. The theoretical calculation of the grain rotation rate shows strong dependence on the grain size and compares very well with the molecular dynamics simulations. A multi-order parameter based phase field model with coupled grain rotation is developed using the theoretical formulation to model polycrystalline microstructure evolution.     

Current transport along grain boundaries in d-wave superconductors

The use of a classic phase retrieval algorithm has been previously used to determine the local critical current J_c(x) along the length of grain boundary Josephson junctions that can be characterized using a standard s-wave model. The phase retrieval approach has been modified for use with d-wave dominated superconductors to allow for negative local currents along the boundary. In general solutions to the 1-D phase problem are not unique, however in the present work special constraints are employed experimentally to ensure uniqueness. The various current distribution solutions and their possible uniqueness are explored. The solutions are consistent with most existing d-wave Josephson junction boundary models and can be used to understand the basic current distribution along 45° YaBa₂Cu₃O_7−x grain boundary junctions as well as providing a means for mapping the location of self-generated flux cores.     

Modeling the optical constants of CuGaSe2 and CuInSe2

The dielectric function data for CuGaSe₂ and CuInSe₂ have been modeled for both perpendicular (E⊥c) and parallel (E∥c) polarizations. We employ the modified Adachi’s model dielectric function model with variable broadening. Variable broadening is accomplished by replacing the damping constant Γ with the energy-dependent expression Γ(E), where the shape of the broadening function is determined by two adjustable model parameters. In spite of one additional parameter per transition, this model requires fewer parameters than the conventional Adachi’s model to achieve equal or better agreement with the experimental data. Our calculations give the relative rms errors for the real and imaginary parts of the index of refraction, δ_n and δ_k, equal to 0.9% and 9.5% for CuGaSe₂ (E⊥c), 0.8% and 7.3% for CuGaSe₂ (E∥c), 1.1% and 3.0% for CuInSe₂ (E⊥c), and 2.5% and 3.7% for CuInSe₂ (E∥c), respectively. Received: 10 July 2000 / Accepted: 10 July 2000 / Published online: 9 November 2000     

Electrically benign behavior of grain boundaries in polycrystalline CuInSe2 films

The classic grain-boundary (GB) model concludes that GBs in polycrystalline semiconductors create deep levels that are extremely harmful to optoelectronic applications. However, our first-principles density-functional theory calculations reveal that, surprisingly, GBs in CuInSe2 (CIS) do not follow the classic GB model: GBs in CIS do not create deep levels due to the large atomic relaxation in GB regions. Thus, unlike the classic GB model, GBs in CIS are electrically benign, which explains the long-standing puzzling fact that polycrystalline CIS solar cells with remarkable efficiency can be achieved without deliberate GB passivation. This benign electrical character of GBs in CIS is confirmed by our scanning Kelvin probe microscopy measurements on Cu(In,Ga)Se2 chalcopyrite films.     

Dislocation nucleation from symmetric tilt grain boundaries in body-centered cubic vanadium

We perform molecular dynamics (MD) simulations with two interatomic potentials to study dislocation nucleation from six symmetric tilt grain boundaries (GB) using bicrystal models in body-centered cubic vanadium. The influences of the misorientation angle are explored in the context of activated slip systems, critical resolved shear stress (CRSS), and GB energy. It is found that for four GBs, the activated slip systems are not those with the highest Schmid factor, i.e., the Schmid law breaks down. For all misorientation angles, the bicrystal is associated with a lower CRSS than their single crystalline counterparts. Moreover, the GB energy decreases in compressive loading at the yield point with respect to the undeformed configuration, in contrast to tensile loading.     

Schottky-type grain boundaries in CCTO ceramics

In this work we studied electrical barriers existing at CaCu₃Ti₄O₁₂ (CCTO) ceramics using dc electrical measurements. CCTO pellets were produced by solid state reaction method and X-ray diffractograms showed which single phase polycrystalline samples were obtained. The samples were electrically characterized by dc and ac measurements as a function of temperature, and semiconductor theory was applied to analyze the barrier at grain boundaries. The ac results showed the sample’s permittivity is almost constant (10⁴) as function of temperature at low frequencies and it changes from 100 to 10⁴ as the temperature increases at high frequencies. Using dc measurements as a function of temperature, the behavior of barriers was studied in detail. Comparison between Schottky and Poole-Frenkel models was performed, and results prove that CCTO barriers are more influenced by temperature than by electric field (Schottky barriers). Besides, the behavior of barrier width as function of temperature was also studied and experimental results confirm the theoretical assumptions.     

Ab initio modelling of the interaction of H interstitials with grain boundaries in bcc Fe

Hydrogen that is accumulated within the grain boundaries can lead to a decrease of the critical strain required to fracture the material. The paper presents results of ab initio modelling of hydrogen–grain boundary interaction in ferromagnetic bcc iron. Modelling was performed using density functional theory with generalised gradient approximation (GGA’96), as implemented in WIEN2k package. Three fully relaxed tilt grain boundaries, Σ5(310), Σ5(210) and Σ3(111), were studied. The supercells contained 40–48 atoms, i.e. 20–24 atoms in each of the two ‘grains’. Calculated formation energies of grain boundaries is 1.44, 1.83 and 1.46 J/m² and the maximum binding (trapping) energies of hydrogen to the boundaries are 0.43, 0.83 and 0.39 eV, respectively. These values are close to other researchers’ data. The higher value of trapping energy of the Σ5(210) boundary is probably due to the asymmetrical atom configurations resulting from mutual rigid shift of the two grains that was necessary to be introduced to provide optimal distances between Fe atoms, unlike the other two boundary types.     

Defect chemistry of grain boundaries in proton-conducting solid oxides

The defect chemistry of charged grain boundaries in an acceptor-doped oxide in equilibrium with water vapour is examined theoretically. The basis of the theoretical approach is that the formation of charged grain boundaries and attendant space-charge zones is governed by differences in the standard chemical potentials of oxygen vacancies and hydroxide ions between bulk and grain-boundary core, that is, by the thermodynamic driving energies for defect redistribution. A one-dimensional continuum treatment is used to predict the space-charge potential and defect concentrations in the grain-boundary core as a function of water partial pressure, temperature and acceptor dopant concentration for various values of the two thermodynamic driving energies. The results are discussed with respect to experimental data in the literature for acceptor-doped perovskite oxides (e.g. BaZrO₃) and fluorite oxides (e.g. CeO₂).     

Effects of severe-strain-induced defects on the mechanical response of two kinds of high-angle grain boundaries

ABSTRACT

Grain boundaries of metallic materials subjected to severe plastic deformation exhibit significantly enhanced diffusivity and excess energy compared with their relaxed poly- or bi-crystalline counterparts even when the macroscopic degrees of freedom are the same in both types of grain boundaries. Boundaries of excess energy are/can be relaxed by annealing. As a first step in accounting for this experimentally observed high-energy state of general high-angle grain boundaries subjected to severe plastic deformation, a concept of localised basic shear units and the presence of localised extra free volume in these units situated in different locations in the grain boundaries, which was originally proposed to explain steady-state structural superplastic flow, is made use of. Using MD simulation, the mechanical response of these modified grain boundaries is compared with that of their relaxed state. The results are also compared with a case of a homogeneous distribution of extra free volume within the grain boundary. The localised shear units containing extra free volume introduced in the grain boundaries are found to alter their physical and mechanical features strongly, which, in turn, drastically affect, consistent with experimental results, the mechanical response of the heavily deformed material.     

Effect of manganese on grain boundary segregation of sulfur in iron

The ASED-MO theory was used to study the electronic effects of S and the S-Mn couple upon the chemical embrittlement of Fe grain boundaries. The results obtained for S alone in a model of grain boundary (GB) are consistent with its observed behavior as a chemical embrittling agent. It was found that the total energy of the cluster decreases when the S atom is located at the GB. When S segregate at the Fe GB containing Mn, the embrittlement process was modified. The crystal orbital overlap population (COOP) curves gives a measure of Fe-Fe bond weakening due to the segregated atoms at the GB. Our calculations show that Mn behaves as a weak embrittler on the Fe GB. The Fe-Mn bonds were strengthened, while Fe-Fe bonds of the capped trigonal prism of the GB (CTP) were weakened. On the other hand, when S segregate at the Mn/Fe cluster, some metallic bonds were resistant to chemical embrittlement.     

Mechanical properties of twist grain boundaries in Cu

In a previous paper we studied the Young's and shear modulus of a high-angle twist grain boundary (5) in Cu, using the EAM, and related it to the uniaxial strain derivatives of single crystals. In this paper, we discuss elastic properties of ten additional twist grain boundaries, from 8.8–43.6°. The monolayer Young's modulus at each boundary was calculated and found to be 20–50% higher than the bulk value for all eleven boundaries for both csl and type1 structures. The monolayer shear modulus at each boundary was calculated and found to be 93–98% lower than the bulk value for six grain boundaries with csl structure and found to decrease with increasing twist angle. The critical shear stress was also calculated for eleven boundaries with csl structure and found to roughly decrease with increasing twist angle.     

Mobility of low-angle grain boundaries in pure metals

The mobility of low-angle grain boundaries in pure metals is reviewed and several theoretical treatments are provided. The approach that provides the best agreement with the available experimental data is one in which the mobility is controlled by vacancy diffusion through the bulk to (and from) the dislocations that comprise the boundary that are bowing out between pinning points. The pinning points are presumed to be extrinsic dislocations swept into the boundaries or grown in during the prior processing of the material. This approach yields a mobility that is constant with respect to misorientation angle, up to the transition to the high-angle regime. For small misorientations of the order 1°, however, the mobility appears to increase with decreasing misorientation angle.     

Electronic properties of grains and grain boundaries in graphene grown by chemical vapor deposition

We synthesize hexagonal shaped single-crystal graphene, with edges parallel to the zig-zag orientations, by ambient pressure CVD on polycrystalline Cu foils. We measure the electronic properties of such grains as well as of individual graphene grain boundaries, formed when two grains merged during the growth. The grain boundaries are visualized using Raman mapping of the D band intensity, and we show that individual boundaries between coalesced grains impede electrical transport in graphene and induce prominent weak localization, indicative of intervalley scattering in graphene.     

The influence of tilt grain boundaries on the mechanical properties of bicrystalline graphene nanoribbons

The mechanical properties of bicrystalline graphene nanoribbons with various tilt grain boundaries (GBs) which typically consist of repeating pentagon–heptagon ring defects are investigated based on the method of molecular structural mechanics. The GB models are constructed via the theory of disclinations in crystals, and the elastic properties and ultimate strength of bicrystalline graphene nanoribbons are calculated under uniaxial tensile loads in perpendicular and parallel directions to grain boundaries. The dependence of mechanical properties is analyzed on the chirality and misorientation angles of graphene nanoribbons, and the experimental phenomena that Young's modulus and ultimate strength of bicrystalline graphene nanoribbons can either increase or decrease with the grain boundary angles are further verified and discussed. In addition, the influence of GB on the size effects of graphene Young's modulus is also analyzed.     

Co-energy of surface and grain boundary in Ag film

A model is proposed for calculating the co-energy of surface and grain boundary (GB) by the modified analytical embedded atom method (MAEAM). As example, the energy densities E_d of the two adjacent grains are obtained when their (0 0 1) twist GB meets the free surface (h₁ k₁ 0)/(h₂ k₂ 0) of Ag film. The period along the boundary line on the surface is found and the energy density is calculated for the situations either with or without periodicity. The results show that, the energy value achieved via this model can be stable even for most grains with boundary line smaller than 100 nm. Among the grains with (h k 0) surface, (1 0 0) grains should be favored and grow fastest when they meet (1 1 0) grains.     

团簇LaO的理论研究

采用密度泛函理论研究LaO团簇体系。中性分子LaO的基态是两重态(2Σ),阴离子LaO-和阳离子LaO 的基态都是单重态(1Σ)。使用不同的方法计算团簇LaO的电子亲和能和电离能。计算结果表明用BLYP方法和弥散极化基组计算结果和实验数据吻合较好。用含时密度泛函理论计算团簇LaO的低能激发态,从理论上归属LaO-的光电子能谱的谱峰和LaO的吸收光谱的谱峰。计算得到与实验一致的结果。     

丙烯腈双自由基终止过程态密度变化的研究

本文采用密度泛函理论对丙烯腈单体自由基(CH3)2(CN)C-CH2-(CN)CH两种终止反应过程中各原子态密度变化进行研究.用B3LYP/6-31G(d)基组对反应物、偶合中间体、过渡态和产物的结构进行优化,计算了各物种的红外频率和各原子的态密度.研究结果表明,偶合中间体a和歧化产物P的化学稳定性较好,丙烯腈单体自由基R和过渡态TS的化学稳定性比较差;各驻点物种的HOMO、LUMO轨道基本是相同原子贡献,且C、N原子贡献程度基本在95%左右;丙烯腈单体自由基R、过渡态TS的HOMO、LUMO相对比较独立,与前线轨道附近的其他能级（HOMO-2、HOMO-1、LUMO+1、LUMO+2）的能量差比较大.