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Since it is now possible to record vibrational spectra at nanometer scales in the electron microscope, it is of interest to explore whether extended defects in crystals such as dislocations or grain boundaries will result in measurable changes of the phonon densities of states (dos) that are reflected in the spectra. Phonon densities of states were calculated for a set of high angle grain boundaries in silicon. The boundaries are modeled by supercells with up to 160 atoms, and the vibrational densities of states were calculated by taking the Fourier transform of the velocity–velocity autocorrelation function from molecular dynamics simulations with larger supercells doubled in all three directions. In selected cases, the results were checked on the original supercells by comparison with the densities of states obtained by diagonalizing the dynamical matrix calculated using density functional theory. Near the core of the grain boundary, the height of the optic phonon peak in the dos at 60 meV was suppressed relative to features due to acoustic phonons that are largely unchanged relative to their bulk values. This can be attributed to the variation in the strength of bonds in grain boundary core regions where there is a range of bond lengths.
Here nanomaterials are defined as materials with structural features of approximately 10 nm or smaller, i.e., tens of atoms across. Unique physical properties of nanomaterials originate from one or two of their essential features: (1) nanomaterials have high surface-to-volume ratios, and a large fraction of atoms located at, or near, surfaces; (2) nanomaterials confine electrons, phonons, excitons, or polarons to relatively small volumes, altering their energies. Chapter 20 focuses on the thermodynamic functions of nanostructures that determine whether a nanostructure can be synthesized, or if a nanostructure is adequately stable at a modest temperature. The internal energy of nanomaterials is increased by the surfaces, interfaces, or large composition gradients. A nanostructured material generally has a higher entropy than bulk material, however, and at finite temperature the entropy contribution to the free energy can help to offset the higher internal energy term in the free energy F = E – TS. Chapter 20 discusses the structure of nanomaterials, the thermodynamics of interfaces in nanostructures, electron states in nanostructures, and the entropy of nanostructures.
The structures and dynamics of surfaces affects the chemical reactivity and growth characteristics of materials. Chapter 11 describes atomistic structures of surfaces of crystalline materials, and describes how a crystal may grow by adding atoms to its surface. Most inorganic materials are polycrystalline aggregates, and their crystals of different orientation make contact at “grain boundaries.” Some features of atom arrangements at grain boundaries are explained, as are some aspects of the energetics and thermodynamics of grain boundaries. Grain boundaries alter both the internal energy and the entropy of materials. Surface energy varies with crystallographic orientation, and this affects the equilibrium shape of a crystal. The interaction of gas atoms with a surface, specifically the topic of gas physisorption, is presented.
A thin-walled copper (Cu)–tin (Sn) alloy cylinder was treated after spinning at 200–400°C for 0.5 h. The characteristics of the alloy microstructure under different temperatures were analyzed through electron back-scattered diffraction. The results were as follows. The grain size at 200–300°C decreases as the heat treatment temperature rises, but the grain size at 400°C increases. At 200–300°C, the microstructure primarily consists of deformed grains. It is found that the main reason for the formation of high-angle grain boundaries (HAGBs) is static recrystallization. For the grain boundary orientation differential, the low-angle sub-grain boundary gradually grows into the HAGB, and multiple annealing twin Σ9 boundaries appear. Grain orientation is generally random at any temperature range. The mechanical property test indicated that, at the upper critical recrystallization temperature of 300°C, the elongation of the Cu–Sn alloy gradually increases, and its yield strength and ultimate tensile strength rapidly decrease.
Employing atomic-scale simulations, the response of a high-angle grain boundary (GB), the soft/hard GB, against external loading was systematically investigated. Under tensile loading close to the hard orientation, strain-induced dynamic recrystallization was observed to initiate through direct soft-to-hard grain reorientation, which was triggered by stress mismatch, inhibited by surface tension from the soft-hard GB, and proceeded by interface ledges. Such grain reorientation corresponds with expansion and contraction of the hard grain along and perpendicular to the loading direction, respectively, accompanied by local atomic shuffling, providing relatively large normal strain of 8.3% with activation energy of 0.04 eV per atom. Tensile strain and residual dislocations on the hard/soft GB facilitate the initiation of dynamic recrystallization by lowering the energy barrier and the critical stress for grain reorientation, respectively.
We introduce an efficient, automated computational approach for analyzing interfaces within atom probe tomography datasets, enabling quantitative mapping of their thickness, composition, as well as the Gibbsian interfacial excess of each solute. Detailed evaluation of an experimental dataset indicates that compared with the composition map, the interfacial excess map is more robust and exhibits a relatively higher resolution to reveal compositional variations. By field evaporation simulations with a predefined emitter mimicking the experimental dataset, the impact of trajectory aberrations on the measurement of the thickness, composition, and interfacial excess of the decorated interface are systematically analyzed and discussed.
Atomistic simulations of 18 silicon 〈110〉 symmetric tilt grain boundaries are performed using Stillinger Weber, Tersoff, and the optimized Modified Embedded Atom Method potentials. We define a novel structural unit classification through dislocation core analysis to characterize the relaxed GB structures. GBs with the misorientation angle θ ranging from 13.44° to 70.53° are solely composed of Lomer dislocation cores. For GBs with θ less than but close to 70.53°, GB ‘step’ appears and the equilibrated states with lowest GB energies can be attained only when such GB ‘step’ is located in the middle of each single periodic GB structure. For the misorientation angles in the range of 93.37° ≤ θ ≤ 148.41°, GB structures become complicated since they contain multiple types of dislocation cores. This work not only facilitates the structural characterization of silicon 〈110〉 STGBs, but also may provide new insights into mirco-structure design in multicrystalline silicon.
The hydrogen embrittlement of 12Cr2Mo1R(H) steel at different strain rates were investigated after hydrogen precharging for 4 h in a 0.5 M H2SO4 solution with 2 g/L ammonium thiocyanate. Results showed that the embrittlement index increased and gradually reached a relative stable value of about 20% at the strain rate of 5 × 10−5 s−1 with the decrease of strain rates. SEM images depicted small and deep flakes at high strain rates, while flakes grew larger at slow strain rates. Most hydrogen-induced cracks (HICs) were transgranular fracture through lath grain of bainitic ferrite. High strain field surrounds the crack tips, which makes the crack tips of two close and parallel cracks deflect toward each another and even form crack coalescence. The electron backscatter diffraction technique was used to investigate the effects of grain boundaries, recrystallization fraction, kernel average misorientation map, texture component, and coincidence site lattice boundaries on the HIC propagation. High densities of dislocations and strain concentrations were found around the cracks, where grains are highly sensitive to HIC.
This research focuses on the microstructural characterization of nickel matrix composites reinforced by carbon nanotubes (CNTs). The nanocomposites were produced by a conventional powder metallurgy process and the dispersion of CNTs and mixture with nickel powders was performed in a single step by ultrasonication. Microstructural characterization of Ni–CNT nanocomposites was performed by scanning and transmission electron microscopy, electron backscattered diffraction, high-resolution transmission electron microscopy, selected area electron diffraction, and fast Fourier transform analyses. This characterization revealed CNTs embedded in the nickel grains and mainly presented as clusters at the grain boundaries. CNTs hinder recrystallization during sintering, and dislocation cells and subgrains form as a result of the recovery process.
Hydrogen embrittlement behaviors of a 22Mn–0.6C (mass%) twinning induced plasticity (TWIP) steel with the grain sizes of 21 μm (coarse grain) and 0.58 μm (ultrafine grain) were investigated by means of hydrogen precharging and subsequent slow strain rate tensile tests. The total elongation and fracture stress for both of the coarse-grained and ultrafine-grained specimens decreased by hydrogen charging. The area fraction of the brittle fracture surfaces in the ultrafine-grained specimen was much smaller than that in the coarse-grained specimen. Three-point bending test also showed that the reduction of the fracture toughness by the introduction of hydrogen was much smaller in the ultrafine-grained specimen than that in the coarse-grained specimen. It was concluded that the suppressed hydrogen embrittlement by grain refinement in the 22Mn–0.6C TWIP steel was probably due to the smaller hydrogen contents per unit grain boundary area in the finer grain-sized material.
Correlative microscopy approaches offer synergistic solutions to many research problems. One such combination, that has been studied in limited detail, is the use of atom probe tomography (APT) and transmission Kikuchi diffraction (TKD) on the same tip specimen. By combining these two powerful microscopy techniques, the microstructure of important engineering alloys can be studied in greater detail. For the first time, the accuracy of crystallographic measurements made using APT will be independently verified using TKD. Experimental data from two atom probe tips, one a nanocrystalline Al–0.5Ag alloy specimen collected on a straight flight-path atom probe and the other a high purity Mo specimen collected on a reflectron-fitted instrument, will be compared. We find that the average minimum misorientation angle, calculated from calibrated atom probe reconstructions with two different pole combinations, deviate 0.7° and 1.4°, respectively, from the TKD results. The type of atom probe and experimental conditions appear to have some impact on this accuracy and the reconstruction and measurement procedures are likely to contribute further to degradation in angular resolution. The challenges and implications of this correlative approach will also be discussed.
In the course of a thorough investigation of the performance-structure-chemistry interdependency at silicon grain boundaries, we successfully developed a method to systematically correlate aberration-corrected scanning transmission electron microscopy and atom probe tomography. The correlative approach is conducted on individual APT and TEM specimens, with the option to perform both investigations on the same specimen in the future. In the present case of a Σ9 grain boundary, joint mapping of the atomistic details of the grain boundary topology, in conjunction with chemical decoration, enables a deeper understanding of the segregation of impurities observed at such grain boundaries.
Due to gravitational self-compression, the pressure in planetary interiors can reach millions of times the atmospheric pressure. Such high pressure has a significant influence on their rheology. In the present paper, we focus on how pressure in the range of the Earth's lower mantle may influence the structure of a MgO {310}/[001] tilt boundary. The defected structure of the grain boundary (GB) will be described through its dislocation, disclination, and generalized-disclination (g-disclination) density fields. At first, the strain and rotation fields in the boundary area at different pressures are derived from the discrete atomic positions simulated by first-principles calculations. For each pressure, the discontinuities of displacement, rotation, and strain in the boundary area are continuously rendered by dislocation, disclination, and g-disclination density fields, respectively. These density fields measured at different pressures are compared to provide understanding on how pressure does influence the GB structures in Earth materials.
Scanning transmission electron microscope (STEM) through-focus imaging (TFI) has been used to determine the three-dimensional atomic structure of Bi segregation-induced brittle Cu grain boundaries (GBs). With TFI, it is possible to observe single Bi atom distributions along Cu [001] twist GBs using an aberration-corrected STEM operating at 200 kV. The depth resolution is ~5 nm. Specimens with GBs intentionally inclined with respect to the microscope’s optic axis were used to investigate Bi segregant atom distributions along and through the Cu GB. It was found that Bi atoms exist at most once per Cu unit cell along the GB, meaning that no continuous GB film is present. Therefore, the reduced fracture toughness of this particular Bi-doped Cu boundary would not be caused by fracture of Bi–Bi bonds.
Lead-free positive temperature coefficient of resistance (PTC) thermistors were synthesized from (1 − x/100)BaTiO3–(x/100)(Bi1/2K1/2)TiO3-based solid solutions, using a conventional mixed-oxide fabrication route, and sintered in N2 followed by air annealing. A maximum TC of 205 °C was achieved for x = 20. An increase in x from 0 to 20 decreased the grain size by more than 92% and increased room temperature resistivity (ρRT) by 7 orders of magnitude. For x ≤ 10, PTC ratio (ρmax/ρmin) ≈ 104.5 and temperature coefficient of resistivity (α) > 10.3%/°C were achieved using Mn and Al2O3:SiO2:TiO2 (AST) additions. For x > 10, ρmax/ρmin > 103 and α > 8%/°C were only obtained in samples sintered in N2 without subsequent air annealing. Complex impedance analysis revealed three relaxation processes, attributed to a semiconducting grain core, a PTC active grain boundary interface, and a grain boundary insulating layer. Local electrical activity was investigated by hot-stage conductive mode microscopy. The existence of symmetrical grain boundary electron beam-induced current and β-conductivity contrast at the grain boundaries, consistent with the presence of an electron trapping two-dimensional grain boundary plane, compensated by positive space charge layers and a low conductivity vacancy-rich layer, was revealed for the first time within this system.
The irradiation damage behaviors of single crystal (SC), coarse-grained (CG), and nanograined (NG) copper (Cu) films were investigated under Helium (He) ion implantation at 450 °C with different ion fluences. In irradiated SC films, plenty of cavities are nucleated, and some of them preferentially formed on growth defects or dislocation lines. In the irradiated CG Cu, cavities formed both in grain interior and along grain boundaries; obvious void-denuded zones can be identified near grain boundaries. In contrast, irradiation-induced cavities in NG Cu were observed mainly gathering along grain boundaries with much less cavities in the grain interiors. The grains in irradiated NG Cu are significantly coarsened. The number density and average radius of cavities in NG Cu was smaller than that in irradiated SC Cu and CG Cu. These experiments indicate that grain boundaries are efficient sinks for irradiation-induced vacancies and highlight the important role of reducing grain size in suppressing radiation-induced void swelling.
The dislocation distribution of high-quality single-crystal gallium nitride (GaN) films grown by the hybrid vapor phase epitaxy was analyzed. This study examined the domain structure of GaN from the dislocation distribution on the macroscale by optical microscopy. The surface structure of GaN consisted of domains with microcolumns as the substructure. The inner domains contained a lower density of dislocations but a large number of these dislocations were observed along the domain boundaries. The existence of a domain boundary structure doubly increased the total dislocation density.
We study the existence of grain boundaries in the Swift–Hohenberg equation. The analysis relies on a spatial dynamics formulation of the existence problem and a centre-manifold reduction. In this setting, the grain boundaries are found as heteroclinic orbits of a reduced system of ordinary differential equations in normal form. We show persistence of the leading-order approximation using transversality induced by wavenumber selection.
The present study was carried out to evaluate the microstructures and mechanical properties of severely deformed Ni-30Cr alloy. Cross-roll rolling (CRR) as severe plastic deformation (SPD) process was introduced and Ni-30Cr alloy sheets were cold rolled to a 90% thickness reduction and subsequently annealed at 700 °C for 30 min so as to obtain the recrystallized microstructure. For the analysis of grain boundary character distributions (GBCDs), electron back-scattered diffraction (EBSD) technique was introduced. CRR on Ni-30Cr alloy was effective to enhance the grain refinement through heat treatment; consequently, average grain size was significantly reduced from 33 μm in initial material to 0.6 μm in CRR processed material. This grain refinement directly affected the mechanical properties improvement, in which yield and tensile strengths were significantly increased than those of initial material. In this study, we systematically discussed the grain refinement, accompanying with increase in mechanical properties, in terms of the effective strain imposed by CRR, comparing with conventional rolling (CR).
Over the last few years there have been significant developments in the field of three-dimensional atom probe (3DAP) analysis. This article reviews some of the technical compromises that have led to different instrument designs and the recent improvements in performance. An instrument has now been developed, based around a novel reflectron configuration combining both energy compensation and focusing elements, that yields a large field of view and very high mass resolution. The use of laser pulsing in the 3DAP, together with developments in specimen preparation methods using a focused ion-beam instrument, have led to a significant widening in the range of materials science problems that can be addressed with the 3DAP. Recent studies of semiconductor materials and devices are described.