Thermodynamics of Vacancies and Impurities at Grain Boundaries

The thermodynamics of vacancy and impurity adsorption at interfaces and grain boundaries (GBs) in solids is considered. Theoretical expressions are derived for the GB/interface free energy change caused by various levels of vacancy or impurity adsorption. This information is used to predict the behavior of vacancies at interfaces and GBs in a stress gradient and to forecast the effect of impurities on GB fracture strength. The latter predictions provide an interpretation of intergranular fracture behavior in terms of impurity adsorption and GB structural parameters such as GB width and value.     

Bi，Sb合金化对AZ91镁合金组织、性能影响机理研究

利用大角重位点阵模型建立了AZ91镁合金α相［0001］对称倾斜晶界原子结构模型，应用实空间的连分数方法计算了Mg合金的总结构能，合金元素引起的环境敏感镶嵌能及原子间相互作用能，讨论了主要合金元素Al及Bi，Sb在AZ91中的合金化行为.计算结果表明，Al，Bi，Sb固溶于α相内或晶界区使总结构能都降低，起到固溶强化作用；合金元素在AZ91α相内趋于均匀分布，在晶界区易占位于三角椎上部.AZ91镁合金中加入Bi或Sb时，Bi或Sb比Al容易偏聚于晶界，从而抑制了Al在晶界的偏聚，促进基体中连续的Mg₁₇Al₁₂相的析出，提高AZ91合金室温性能； AZ91合金中(α相内和晶界区)主要合金元素Al和微加元素Bi，Sb都能够形成有序相Mg₁₇Al₁₂，Mg₃Bi₂或Mg₃Sb₂，且在晶界区形成的量大.Bi，Sb加入AZ91合金中，由于Bi，Sb抑制Al在晶界的偏聚，晶界区主要析出相为Mg₃Bi₂或Mg₃Sb₂，提高镁合金高温性能. 关键词： 电子理论 合金化 晶界偏聚 镁合组织与性能     

Effect of solute atoms on fracture toughness in dilute magnesium alloys

The effect of alloying elements on the toughness and the fracture behaviour was investigated on seven kinds of Mg-0.3?at.% X (X?=?Ag, Al, Ca, Pb, Sn, Y and Zn) alloys with a grain size of 3–5?μm. The fracture toughness and fracture behaviour in magnesium alloys were closely related to the segregation energy. The Mg–Al and –Zn alloys that had small segregation energy showed high toughness and ductile fracture in most regions, while the Mg–Ca alloy with large segregation energy exhibited low toughness and intergranular fracture. These different tendencies resulted from solute segregation at grain boundaries (GBs). The change in the lattice parameter ratio was the influential material parameter regardless of whether the GB embrittlement was for enhancement or suppression.     

Interaction of Point Defects with Grain Boundaries in fcc Metals

Structures of several symmetrical tilt grain boundaries (GBs) with different tilt axes in Cu and Al and their interaction with vacancies and interstitials are studied using atomistic computer simulations with embedded-atom potentials. The lowest defect formation energy in a GB is found to correlate with the GB energy in both Cu and Al. Importantly, vacancies and self-interstitials in GBs have comparable formation energies, suggesting that both defects are equally important for GB diffusion and other properties. Vacancies in GBs can be either localized at certain sites or be delocalized over several sites. Some GB sites do not support a stable vacancy at all. Self-interstitial atoms can occupy relatively open interatomic positions, form split dumbbell configurations, or give rise to highly delocalized displacement zones. These structural forms of point defects have been observed across the whole set of twelve GBs in Cu and six GBs in Al studied in this paper as well as in our previous work [Interface Science 11, 131–148 (2003)]. It is suggested that these structural forms are general to all GBs in fcc metals. They can be explained by the existence of internal stresses and alternating tension and compression regions in the GB core.     

Effect of alloying elements and impurities on interface properties in aluminum alloys

The segregation energies of B, Si, P, Cr, Ni, Zr, and Mg on the special grain boundary (GB) Σ5 (210)[100] and on the open (210) surface of aluminum have been determined and the GB splitting energy has been calculated by the density functional theory methods. It has been shown that all elements listed above enrich the GB; for B, Si, P, Cr, Ni and Zr, Mg, interstitial and substitutional sites are preferred, respectively. The effect of alloying elements on the GB binding has been estimated using the parameter η equal to the change in the fracture work of the aluminum GB when adding alloying element atoms. From the viewpoint of strengthening the GB binding forces, Zr, Cr, Ni, and Mg are efficient, Si and B are neutral and phosphorus weakens GBs.     

Direct method for determining the segregation in silver-copper solid solutions not prone to brittle breakage of grain boundaries

A new method is proposed for measuring the chemical composition of grain boundaries (GBs) in copper-based alloys not prone to embrittlement of boundaries. This method is based on embrittlement of copper GBs by bismuth penetrating from the gas phase of bismuth telluride (Bi₂Te₃). Chemical analysis of the GB surface is performed via Auger-electron spectroscopy. The GB composition is measured in a solid solution of silver (its volume concentration is 1.4 at %) and copper. The segregation annealing temperature is 570°C. The silver concentration across the broken surface of the GB (its thickness is five to ten atomic layers) is 4.7 at %. Therefore, the ratio between silver concentrations within the GB and the grain volume (the enrichment coefficient) is approximately 3.5.     

Atomistic Modeling of Point Defects and Diffusion in Copper Grain Boundaries

The atomic structure of several symmetrical tilt grain boundaries (GBs) in Cu and their interaction with vacancies and interstitials as well as self-diffusion are studied by molecular statics, molecular dynamics, kinetic Monte Carlo (KMC), and other atomistic simulation methods. Point defect formation energy in the GBs is on average lower than in the lattice but variations from site to site within the GB core are very significant. The formation energies of vacancies and interstitials are close to one another, which makes the defects equally important for GB diffusion. Vacancies show interesting effects such as delocalization and instability at certain GB sites. They move in GBs by simple vacancy-atom exchanges or by long jumps involving several atoms. Interstitial atoms can occupy relatively open positions between atoms, form split dumbbell configurations, or form highly delocalized displacement zones. They diffuse by direct jumps or by the indirect mechanism involving a collective displacement of several atoms. Diffusion coefficients in the GBs have been calculated by KMC simulations using defect jump rates determined within the transition state theory. GB diffusion can be dominated by vacancies or interstitials, depending on the GB structure. The diffusion anisotropy also depends on the GB structure, with diffusion along the tilt axis being either faster or slower than diffusion normal to the tilt axis. In agreement with Borisov's correlation, the activation energy of GB diffusion tends to decrease with the GB energy.     

Polygonization and restoration of long-range order on heating a cold-worked iron −6.5% silicon alloy

Rearrangements taking place in the dislocation structure of single crystals of cold-worked (rolled) Fe-6.5% Si alloy (initially ordered in accordance with the DO₃ system) on subsequent annealing, accompanied by the restoration of the equilibrium degree of long-range order, are considered on the basis of an electron-microscope examination. The microscopic polygonization processes detected are analogous to those which occur in alloys with low stacking-fault energies. The processes underlying the perfection of the defect structure and the restoration of the long-range order disrupted by plastic deformation have a marked influence on one another.     

Hydrogen sorption in titanium alloys with a symmetric Σ5(310) tilt grain boundary and a (310) surface

The hydrogen sorption in intermetallic B2 TiM (M = Ni, Co, Pd) with a symmetric ??5(310) tilt grain boundary and a (310) surface is studied by density functional theory methods. The effect of hydrogen on the electronic characteristics of the alloys is analyzed as a function of a sorption position at the interfaces. The hydrogen sorption energy is shown to depend on the local environment of hydrogen; on the whole, hydrogen at the interfaces prefers titanium-rich positions. The hydrogen sorption energy in metal-rich positions decreases when the d shell of the second alloy component is filled with electrons. The grain-boundary energy, the surface energy, and the hydrogen segregation energies to the interfaces are calculated. Hydrogen sorption in titanium alloys is shown to decrease Griffith work and to favor brittle fracture along tilt grain boundaries.     

Statistical model for the formation of the alloy

The electronic structures of most semiconductor alloys are smooth functions of their composition. Binary alloys of group IV semiconductors are usually easy to prepare at any concentration, but this is not the case for the Ge_1-xSn_x alloy. Homogeneous alloys as required for nano- and optoelectronics device applications have proved difficult to form for x above a temperature-dependent critical concentration, above which Sn exhibits the tendency to segregate in the metallic cubic β phase, spoiling the semiconducting properties. The underlying mechanism for this segregation and critical concentration was not known.Through previous accurate ab initio local defect calculations we estimated the scale of energies involved in the immediate environment around a large number of Sn defects in Ge, the relaxed configurations of the defects, and the pressure directly related to the elastic field caused by the defects. This detailed information allowed us to build a simple statistical model including the defects most relevant at low x, namely substitutional α-Sn and non-substitutional β-Sn (in which a single atom occupies the centre of a Ge divacancy). Our model enables us to determine at which concentration β defects, which exhibit a tendency to segregate, can be formed in thermal equilibrium. These results coincide remarkably well with experimental findings, concerning the critical concentration above which the homogeneous alloys cannot be formed at room temperature. Our model also predicts the observed fact that at lower temperature the critical concentration increases.     

Atomic Structure and Properties of the (310) Symmetrical Tilt Grain Boundary (STGB) in SrTiO3 Part II: Comparison with Experimental Studies

The atomistic simulation results presented in Part I for SrTiO₃ (310) symmetrical tilt grain boundary (STGB, the so-called = 5 GB with 36.8° symmetrical misorientation about [001]) are analyzed in the context of available experimental studies. In particular, atomic imaging studies of SrTiO₃ GBs via high resolution TEM and incoherent Z-contrast STEM imaging; and determination of oxygen positions by combining electron energy loss spectroscopy (EELS) and bond-valence-sum rules, are compared with simulation results. The atomistic simulation data on the GB energies are compared with relative experimental estimates obtained via a novel approach of faceting of focused ion beam (FIB) induced microvoids.While there are considerable differences in details of simulation and experimental results, some basic trends seem to emerge about the core structural framework of GBs in SrTiO₃. The paper highlights the limitations of both, experimental and simulation techniques, and argues in favor of synergistic use of diverse experimental and simulation approach to determine the atomic structure and properties of GBs.     

多晶石墨烯拉伸断裂行为的分子动力学模拟

采用分子动力学模拟方法研究了不同晶界对石墨烯拉伸力学特性及断裂行为的影响. 定义了表征晶界能量特性的新参量缺陷能, 并以此为基础分析了晶界结构的能量特性. 探讨了晶界对弹性模量和强度极限等的影响以及强度对晶界能量特性的依赖关系. 结果表明: 晶界能量特性可以间接反映晶界强度; 同时, 晶界中缺陷会使实际承载碳键数量小于名义承载碳键数, 从而在较大范围内影响弹性模量. 分析了不同晶界的断裂过程, 发现了裂纹扩展方向的强度依赖性: 低强度晶界主要是以碳键直接断裂为主要方式的沿晶断裂, 而高强度晶界通常是碳键直接断裂和Stone-Wales翻转过程交替进行下的穿晶断裂. 研究结果可为石墨烯器件的设计制造提供理论指导.     

Atomic scale investigation of grain boundary structure role on intergranular deformation in aluminium

The role that grain boundary (GB) structure plays on the directional asymmetry of an intergranular crack (i.e. cleavage behaviour is favoured along one direction, while ductile behaviour along the other direction of the interface) was investigated using atomistic simulations for aluminium 〈1 1 0〉 symmetric tilt GBs. Middle-tension (M(T)) and Mode-I crack propagation specimens were used to evaluate the predictive capability of the Rice criterion. The stress–strain response of the GBs for the M(T) specimens highlighted the importance of the GB structure. The observed crack tip behaviour for certain GBs (Σ9 (2 2 1), Σ11 (3 3 2) and Σ33 (4 4 1)) with the M(T) specimen displayed an absence of directional asymmetry which is in disagreement with the Rice criterion. Moreover, in these GBs with the M(T) specimen, the dislocation emission from a GB source at a finite distance ahead of the crack tip was observed rather than from the crack tip, as suggested by the Rice criterion. In an attempt to understand discrepancy between the theoretical predictions and atomistic observations, the effect of boundary conditions (M(T), Mode-I and the edge crack) on the crack tip events was examined and it was concluded that the incipient plastic events observed were strongly influenced by the boundary conditions (i.e. activation of dislocation sources along the GB, in contrast to dislocation nucleation directly from the crack tip). In summary, these findings provide new insights into crack growth behaviour along GB interfaces and provide a physical basis for examining the role of the GB character on incipient event ahead of a crack tip and interface properties, as an input to higher scale models.     

Investigation of solid-state reaction in Ag/Sn nanostructured thin films at room temperature

Diffusion intermixing processes in nanostructured Ag/Sn thin-film system at room temperature were investigated by means of secondary neutral mass Spectrometry depth profiling technique. As it was confirmed by X-ray diffraction too, the reaction started already in the as-deposited sample. Since the bulk diffusion was frozen at room temperature, the Ag₃Sn phase was formed along the grain boundaries (GBs), gradually consuming the interior of grains, and was grown perpendicular to the GBs. At the same time, formation and growth of a small compact reaction layer near the interface were observed and the shift of the bordering parallel interfaces was controlled by GB diffusion. From the kinetics of the diffusion process in the above two mechanisms, both the interface velocity in the diffusion-induced grain boundary motion regime as well as the coefficient of parabolic growth in the planar growth regime were determined.     

Evolution of displacement cascades in Fe–Cr structures with different [001] tilt grain boundaries

Reduced-activation ferritic/martensitic steels of Cr concentration between 2.25 and 12?wt% are candidate structural materials for next-generation nuclear reactors. In this study, molecular dynamics (MD) simulation is used to generate the displacement cascades in Fe–Cr structures with different Cr concentrations by using different primary knock-on atom (PKA) energies between 2 and 10?keV. A concentration-dependent model potential has been used to describe the interactions between Fe and Cr. Single crystals (SCs) of three different coordinate bases (e.g. [310], [510], and [530]) and bi-crystal (BC) structures with three different [001] tilt grain boundaries (GBs) (e.g. Σ5, Σ13, and Σ17) have been simulated. The Wigner–Seitz cell criterion has been used to identify the produced Frenkel pairs. The results show a marked difference between collisions observed in SCs and those in BC structures. The numbers of vacancies and interstitials are found to be significantly higher in BC structures than those found in SCs. The number of point defects exhibits a power relationship with the PKA energies; however, the Cr concentration does not seem to have any influence on the number of survived point defects. In BC models, a large fraction of the total survived point defects (between 59% and 93%) tends accumulate at the GBs, which seem to trap the generated point defects. The BC structure with Σ17?GB is found to trap more defects than Σ5 and Σ13?GBs. The defect trapping is found to be dictated by the crystallographic parameters of the GBs. For all studied GBs, self-interstitial atoms (SIAs) are easily trapped within the GB region than vacancies. An analysis of defect composition reveals an enrichment of Cr in SIAs, and in BC cases, more than half of the Cr-SIAs are found to be located within the GB region.     

Molecular dynamics simulations of point defects in plutonium grain boundaries

A modified analytic embedded atom method (MAEAM) potential is constructed for fcc updelta-Pu. Molecular dynamics (MD) simulations with the potential are performed to investigate the interactions between two symmetrical tilt grain boundaries (GBs) and point defects such as He atom, vacancy and self-interstitial atom (SIA) in Pu. The calculated results show that point defect formation energies are on average lower than those in the lattice but variations from site to site along the GBs are very remarkable. Both substitutional and interstitial He atoms are trapped at GBs. Interstitial He atom is more strongly bound at the GB core than the substitutional He atom. The binding energy of SIA at GB core is higher than those of He atom and vacancy. GB core can bind many He atoms and SIAs due mainly to the fact that it contains many vacancies. Compared with He atom and SIA, the vacancy far from GB core is difficult to diffuse into the core. The GBs can act as sinks and sources of He atoms and SIAs, which may be a reason for the swelling of Pu after a period of self-irradiation because of the higher concentration of vacancy in the bulk.     

Coupled structural and magnetic properties of ferric fluoride nanostructures part I: A Metropolis atomistic study

A modified Metropolis atomistic simulation is proposed to model the structure of grain boundaries (GBs) and interfaces in ionic nanostructured systems and is applied to the magnetically interesting case of iron trifluoride (FeF₃). We chose long-range interatomic potentials adjusted on experimental results and adapted a previously established Monte Carlo scheme consisting of various modifications of the simulated annealing/Metropolis algorithm. Atomic structures of twisted and tilted GBs as a function of the relative disorientation of the grains have been achieved yielding close to experimentally measured properties. This approach takes into account the structure of the grains far from the interface in order to constrain the relative orientation of the grains, without any periodic boundary conditions. One concludes that a long-range Coulombic fall off of the interatomic potentials is necessary to obtain GB structures presenting a correct local topology but with a smooth transition from crystalline to amorphous states. The structural features are finally discussed in terms of topological aspects and local magnetic structure.     

Grain boundary segregation and relaxation in nano-grained polycrystalline alloys

The present study carries out systematic thermodynamics analysis of Grain Boundary(GB)segregation and relaxation in NanoGrained(NG)polycrystalline alloys.GB segregation and relaxation is an internal process towards thermodynamic equilibrium,which occurs naturally in NG alloys without any applied loads,causes deformation and generates internal stresses.The analysis comprehensively investigates the multiple coupling effects among chemical concentrations and mechanical stresses in GBs and grains.A hybrid approach of eigenstress and eigenstrain is developed herein to solve the multiple coupling problem.The analysis results indicate that the GB stress and grain stress induced by GB segregation and relaxation can be extremely high in NG alloys,reaching the GPa level,which play an important role in the thermal stability of NG alloys,especially via the coupling terms between stress and concentration.The present theoretic analysis proposes a novel criterion of thermal stability for NG alloys,which is determined by the difference in molar free energy between a NG alloy and its reference single crystal with the same nominal chemical composition.If the difference at a temperature is negative or zero,the NG alloy is thermal stable at that temperature,otherwise unstable.     

Grain Boundary Diffusion and Linear and Non-Linear Segregation of Ag in Cu

Ag grain boundary (GB) diffusion was measured in the Cu-0.2at%Ag alloy in a wide temperature range from 473 to 970 K. The direct measurements of Ag GB diffusivity D ^alloy _gb under conditions of the Harrison C regime revealed that D ^alloy _gb is almost identical to D ^pure _gb determined earlier for Ag diffusion in high-purity Cu (Divinski, Lohmann, and Herzig, 2001). The penetration profiles determined in the Harrison B regime showed a complex, multi-stage shape. This diffusion behavior can be rationalized assuming that besides GBs significantly covered by segregated Ag atoms, some fraction of GBs remains almost free from Ag atoms in the studied temperature interval. The total amount of pure GBs drastically decreases with decreasing temperature. This hypothesis was proven by measurements of Ag GB diffusion in Cu near 5 bicrystals, which allowed us to analyze in detail the non-linear segregation of Ag in Cu GBs.     

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.