Low-index Directions Research Articles

Informatics-Based Learning of Oxygen Vacancy Ordering Principles in Oxygen-Deficient Perovskites.

Ordered oxygen vacancies (OOVs) in perovskites can exhibit long-range order and may be used to direct materials properties through modifications in electronic structures and broken symmetries. Based on the various vacancy patterns observed in previously known compounds, we explore the ordering principles of oxygen-deficient perovskite oxides with ABO2.5 stoichiometry to identify other OOV variants. We performed first-principles calculations to assess the OOV stability on a data set of 50 OOV structures generated from our bespoke algorithm. The algorithm employs uniform planar vacancy patterns on (111) pseudocubic perovskite layers and the approach proves effective for generating stable OOV patterns with minimal computational loads. We find as expected that the major factors determining the stability of OOV structures include coordination preferences of transition metals and elastic penalties resulting from the assemblies of polyhedra. Cooperative rotational modes of polyhedra within the OOV structures reduce elastic instabilities by optimizing the bond valence of A- and B cations. This finding explains the observed formation of vacancy channels along low-index crystallographic directions in prototypical OOV phases. The identified ordering principles enable us to devise other stable vacancy patterns with longer periodicity for targeted property design in yet to be synthesized compounds.

Grazing incidence fast atom diffraction: general considerations, semiclassical perturbation theory and experimental implications.

Using semiclassical methods, an analytical approach to describe grazing incidence scattering of fast atoms (GIFAD) from surfaces is described. First, we consider a model with a surface corrugated in the scattering plane, which includes the surface normal and the incidence direction. The treatment uses a realistic, Morse potential, within a perturbation approach, and correctly reproduces the basic GIFAD phenomenology, whereby the scattering is directed primarily in the specular direction. Second, we treat the more general case of scattering from a surface corrugated in two-dimensions. Using time averaging along the direction of fast motion in the incidence direction, we derive a time dependent potential for the GIFAD scattering away from a low index direction. The results correctly describe the observation that diffraction is seen only when the scattering plane is aligned close to a low-index direction in the surface plane. For the case of helium scattering from LiF(001) we demonstrate that the resulting theoretical predictions agree well with experiment and show that the analysis provides new information on the scattering time and the length scale of the interaction. The analysis also gives insights into the validity of the axial surface channeling approximation (ASCA) and shows that within first order perturbation theory, along a low-index direction, the full 3-dimensional problem can be represented accurately by an equivalent 2-dimensional problem with a potential averaged along the third dimension. In contrast, away from low-index directions, the effective 2-dimensional potential in the projectile frame is time-dependent.

Self-Assembly of Nanocrystalline Structures from Freestanding Oxide Membranes.

The exploration of crystalline nanostructures enhances the understanding of quantum phenomena occurring in spatially confined quantum matter and may lead to functional materials with unforeseen applications. A novel route to fabricating nanocrystalline oxide structures of exceptional quality is presented. This is achieved by utilizing a self-assembly process of ultrathin membranes composed of the desired oxide. The thermally induced self-assembly of nanocrystalline structures is driven by dewetting the oxide membranes once they are lifted off and transferred onto sapphire surfaces. In three successive steps, the process provides nanovoids, nanowires, and nanocrystals. Regardless of substrate orientation, the nanostructures are highly anisotropic in shape due to material retraction favoring low-index crystalline lattice directions of the membranes. The orientation of the nanostructures is provided precisely by the crystal lattice of the transferred membrane. The microstructure of the nanocrystals exhibits exceptional quality, characterized by a pristine crystal structure and uniform stoichiometry, both maintained all the way down to the well-developed crystalline facets. The demonstrated self-assembly process holds the potential to improve the understanding of surface diffusion phenomena at the interface of materials, which is important for advancing epitaxial growth technology and paves the way to fabricating crystalline nanostructures by the transfer and self-assembly of membranes.

Morphology evolution and grain orientations of intermetallic compounds during the formation of full Cu3Sn joint

The morphological evolution and grain orientations of intermetallic compounds (IMCs) were investigated during the formation of full Cu3Sn joints at two soldering temperatures (310 and 430 °C). The mechanical properties of both types of full Cu3Sn joints were then analyzed. The experimental results showed that the morphology of interfacial IMCs varied significantly at two temperatures. At 310 °C, scallop-like Cu6Sn5 grains became larger but were fewer in number and the top of the scallops became rough due to the grain ripening effect. With the increase in the soldering temperature to 430 °C, Cu3Sn no longer grew uniformly as observed during soldering at 310 °C, but exhibited various growth rates. Furthermore, some η-Cu6Sn5 transformed into η′-Cu6Sn5 during cooling, and the following orientation groups between η′-Cu6Sn5 and η-Cu6Sn5, i.e., {102}η′ and {112‾0}η, {112}η′ and {101‾0}η, and {2‾01}η′ and {0001}η, were found to be near-parallel. The Cu3Sn grains were preferably oriented with [203] and [100] crystal orientations parallel to transverse direction (TD) at both temperatures. Noteworthy, the Cu3Sn grains with [203]//TD and [010]//ND grew much faster than those with other orientations at 430 °C. Moreover, molecular dynamics simulation showed that the diffusion coefficients of atoms in Cu3Sn crystals along [203] direction were significantly greater than those in other low-index crystal directions. After soldering, two types of full Cu3Sn joints obtained at different temperatures exhibited different shear strength and fracture mechanisms.

Prediction on the theoretical strength of diamond, c-BN, Cu, and CeO2

The theoretical (ideal) strength is the upper strength limit that any solid can withstand. Estimation of the theoretical strength of materials is vital for their applications. In the materials science field, the Griffith theory is the most widely used criterion for estimating the theoretical strength of materials, which sets an upper bound strength of ∼E/9. In addition, Frenkel and Orowan–Polanyi’s derivation from the force–displacement relationship using the sinusoidal correlation also gives a similar value of ∼E/10. Recently, with the improved quality of fabricated samples, people have reported the possibility of reaching or exceeding the theoretical strength. In this work, first-principles calculations based on density functional theory (DFT) are used to study the theoretical strength of four representative materials (diamond, c-BN, Cu, and CeO2) under uniaxial tensile loading along the low-index crystallographic directions. The results demonstrate that the theoretical strength of materials exhibits strong anisotropy. It is found that the ideal strength calculated by DFT is larger than the ideal strength predicted by Griffith theory or the approximate value of E/10 in all the four materials along some specific directions. This discrepancy is explained by the analysis of the fracture mechanism. In addition, based on the stability analysis of thermodynamical systems, the strength criterion based on the energy–strain relation was established, which is verified by the DFT results.

Gold-rutile interfaces with irrational crystallographic orientations

Gold-rutile interfaces have been extensively investigated particularly because of their importance to heterogeneous catalysts for many reactions such as CO oxidation and water-split reactions. Herein, we systemically study preferential orientation relationships (ORs) and atomic structures at gold-rutile interfaces using a model system of dewetted gold particles on a single-crystal rutile substrate. Four previously reported ORs are confirmed, and more importantly, a few irrational ORs (i.e., which cannot be described by low-indexed planes and directions) are newly discovered. These ORs agree with theoretical possibilities predicted according to the geometrical constraint of adjacent lattices. In addition, atomic rearrangement is observed at these interfaces, particularly in those with irrational ORs.

Understanding Shape Evolution and Phase Transition in InP Nanostructures Grown by Selective Area Epitaxy.

There is a strong demand for III-V nanostructures of different geometries and in the form of interconnected networks for quantum science applications. This can be achieved by selective area epitaxy (SAE) but the understanding of crystal growth in these complicated geometries is still insufficient to engineer the desired shape. Here, the shape evolution and crystal structure of InP nanostructures grown by SAE on InP substrates of different orientations are investigated and a unified understanding to explain these observations is established. A strong correlation between growth direction and crystal phase is revealed. Wurtzite (WZ) and zinc-blende (ZB) phases form along <111>Aand <111>Bdirections, respectively, while crystal phase remains the same along other low-index directions. The polarity induced crystal structure difference is explained by thermodynamic difference between the WZ and ZB phase nuclei on different planes. Growth from the openings is essentially determined by pattern confinement and minimization of the total surface energy, regardless of substrate orientations. A novel type-II WZ/ZB nanomembrane homojunction array is obtained by tailoring growth directions through alignment of the openings along certain crystallographic orientations. The understanding in this work lays the foundation for the design and fabrication of advanced III-V semiconductor devices based on complex geometrical nanostructures.

Analysis of InGaP(001) surface by the low energy ion scattering spectroscopy

Ion scattering spectroscopy, which is a variation of low energy ion scattering (LEIS) that employs glancing scattering angles, is performed on InGaP(001) surfaces. LEIS energy distribution are simulated by computer simulation along the <110> and <ī10> direction, and the match of the positions of the flux peaks shows that the top three atomic layers are bulk-terminated. A newly observed feature are identified as a minimum in the multiple scattering when the ion beam incidence is along a low index direction. Calculated trajectories of scattered ions. This new method for analysis of large-angle LEIS data was shown to be useful for accurately investigating complex surface structures.

The interaction of proton irradiation with Zr textured microstructure

Proton irradiation is commonly used as a surrogate for neutrons in experimental studies of structural materials for thermal reactors, such as Zr alloys. The proton beam is unidirectional which requires a choice to be made about the direction of the beam relative to the sample. The direction of the proton beam will determine what lattice orientations the protons will predominantly interact with, particularly in a sample with a strong texture. Since protons can be channelled the orientation of the crystal will affect the energy deposition and the implantation range. We have therefore investigated the degree of high energy proton channelling in crystal orientations found in a strongly textured sample of Zr. We find that the crystal orientations near low-index crystal directions like the 〈112¯0〉 zone axis encourage a higher degree of proton channelling compared with other crystal orientations commonly found in a split-basal textured sample. Channelling in these orientations can change the energy deposition of protons by 40%. Our results show that care must be taken when quantifying the damage in textured samples using a single grain orientation. To compensate for channelling effects, the damage from ion irradiation in a textured sample should be quantified by averaging the damage across many different grain orientations, especially when the irradiation temperature of the bulk is less than 300 K.

Prediction on the Theoretical Strength of Diamond, c-Bn, Cu and CeO &lt;sub&gt;2&lt;/sub&gt;

The theoretical (ideal) strength is the upper strength limit that any solid can withstand. Estimation of the theoretical strength of materials is vital for their applications. In material science field, the Griffith theory is the most widely used criterion for estimating the theoretical strength materials which sets an upper bound strength of ~ E/9. Besides, Frenkel and Orowan-Polanyi’s derivation from the force-displacement relationship using the sinusoidal correlation also gives a similar value of ~ E/10. Recently, with the improved quality of fabricated samples, people have reported the possibility of reaching or exceeding the theoretical strength. In this work, first-principles calculations based on density functional theory (DFT) is used to study the theoretical strength of four representative materials (diamond, c-BN, Cu, and CeO2) under uniaxial tensile loading along the low-index crystallographic directions. The results demonstrate that the theoretical strength of materials exhibit strong anisotropy. It is found that the ideal strength calculated by DFT is larger than the ideal strength predicted by Griffith theory or the approximate value of E/10, in all the four materials along some specific directions. This discrepancy is explained by the analysis of the fracture mechanism. In addition, based on the stability analysis of thermodynamical systems, the strength criterion based on the energy-strain relation was established which is verified by the DFT results.

Making new lamellar Al2O3/ZrO2 (Y2O3) eutectics by seeding melt-grown method

New lamellar Al2O3/ZrO2 (Y2O3) eutectics were obtained using seeding melt-grown method. The orientation relationship and interface structure of the eutectics were investigated by means of transmission Kikuchi diffraction and transmission electron microscopy. The unusual orientation relationship of the new Al2O3/ZrO2 (Y2O3) eutectics was (1 0 12¯)Al2O3 || (11¯1)ZrO2 and [0 2 2¯1]Al2O3 || [1 1 2]ZrO2 and the interface plane was (1 0 12¯)Al2O3 || (11¯1)ZrO2 with a 4.32% misfit. Furthermore, the possible preferred growth directions on the interface were predicted, which were uncommon low index directions. These results indicate that the interface structure is the leading factor of the growth behavior in binary eutectics. It can be demonstrated that the seeding melt-grown method offers a pathway to tailor the interface and growth direction of the directionally solidified eutectics.

Large-scale dislocation dynamics simulations of strain hardening of Ni microcrystals under tensile loading

The strain hardening in FCC Ni was studied along low index directions using 3-dimensional discrete dislocation dynamics. Large (20 × 20 × 50 μm) Ni microcrystals were simulated using rectangular parallelepiped-cells loaded in tension along four low-index directions ([111], [001], [110] and [112]) to shear strains of ∼0.01–0.02. Loading was at a constant strain rate of 10/sec, and all surfaces of the cell are treated as free surfaces. The FCC dislocation mobility routines were modified to include thermally activated cross-slip processes, as a function of three different stress components, using the results of previous atomistic simulations. These include bulk cross slip (cross-slip at atomic jogs), intersection cross slip (attractive and repulsive) as well as surface cross slip. One of these, repulsive intersection cross-slip, has zero activation energy and is present at all simulated deformation temperatures. The simulations were performed for three different temperatures, 5, 150 and 300 K. The strain-hardening rate is independent of temperature and of the order of μ/200 – μ/400, in agreement with experimental data for the <111> and <001> orientations of deformation. For the [001] orientation, at 5 and 150 K, the strain hardening rate decreases considerably when repulsive intersection cross-slip is removed from the simulations. The [110] and [112] orientations exhibit single-slip glide and a very low strain-hardening rate (∼μ/3000). Heterogeneity of dislocation microstructure develops spontaneously at the higher temperatures as a result of increased cross slip. Even though the strain-hardening rate is independent of temperature, the increase in dislocation density with shear strain is larger at higher temperatures. It is proposed that higher temperatures deformation produces larger dislocation-microstructure heterogeneities, providing for higher average dislocation densities and regions of low density where deformation can proceed. Also, the strain hardening rate at 300 K is controlled by the rate of increase of forest dislocation density in these lean regions.

Plane shock loading on mono- and nano-crystalline silicon carbide

The understanding of the nanoscale mechanisms of shock damage and failure in SiC is essential for its application in effective and damage tolerant coatings. We use molecular-dynamics simulations to investigate the shock properties of 3C-SiC along low-index crystallographic directions and in nanocrystalline samples with 5 nm and 10 nm grain sizes. The predicted Hugoniot in the particle velocity range of 0.1 km/s–6.0 km/s agrees well with experimental data. The shock response transitions from elastic to plastic, predominantly deformation twinning, to structural transformation to the rock-salt phase. The predicted strengths from 12.3 to 30.9 GPa, at the Hugoniot elastic limit, are in excellent agreement with experimental data.

Level-set simulation of anisotropic phase transformations via faceted growth

Level-set method is used to simulate phase transformations with anisotropic kinetics where the transforming interface is faceted. The method overcomes previous limitation of this simulation methodology in tracking dynamic evolution of a large number of growing grains. The method is then used to simulate multi-grain phase transformations where the facets are three low-index ([1 0 0], [1 1 1], [1 1 0]) planes that yield morphologies including cube, octahedron and rhombic dodecahedron. The microstructure evolves under site-saturated nucleation and constant nucleation rate. The cube morphology undergoes fastest transformation followed by octahedron, rhombic dodecahedron and sphere. It is also shown that the Johnson-Mehl-Avrami-Kolmorgorov theory can be used to describe the kinetics of the faceted phase transformation. The resulting microstructure shows non-convex grain shapes with highly corrugated surfaces. The structures are also characterized using the average grain length along certain low index crystallographic directions, the coherent length. This measurement shows that for a cubic morphology, there is a significant difference in the coherent length for low index directions, while there is no meaningful difference in the coherent length for kinetic Wulff shapes of other anisotropies examined.

Quantitative Analysis of the Crystallographic Orientation Relationship Between the Martensite and Austenite in Quenching–Partitioning–Tempering Steels

The orientation relationships (ORs) between the martensite and the retained austenite in low- and medium-carbon steels after quenching–partitioning–tempering process were studied in this work. The ORs in the studied steels are identified by selected-area electron diffraction (SAED) as either K–S or N–W ORs. Meanwhile, the ORs were also studied based on numerical fitting of electron backscatter diffraction data method suggested by Miyamoto. The simulated K–S and N–W ORs in the low-index directions generally do not well coincide with the experimental pole figure, which may be attributed to both the orientation spread from the ideal variant orientations and high symmetry of the low-index directions. However, the simulated results coincide well with experimental pole figures in the high-index directions {123}bcc. A modified method with simplicity based on Miyamoto’s work was proposed. The results indicate that the ORs determined by modified method are similar to those determined by Miyamoto’ method, that is, the OR is near K–S OR for the low-carbon Q–P–T steel, and with the increase of carbon content, the OR is closer to N–W OR in medium-carbon Q–P–T steel.

Shock-induced spall in single and nanocrystalline SiC

Shock-induced spall in SiC is investigated via high strain-rate loading molecular dynamics simulations. The dynamic response under different shock intensities is characterized along the low-index 3C-SiC crystallographic directions, [001], [110], and [111], and in a nanocrystalline sample with 5 nm average grain size. The simulation results show that all single crystal samples generate elastic, plastic, and structural phase transformation waves for increasing particle velocities in good agreement with previous investigations. However, crystal anisotropy effects affect the exact shock response and the corresponding wave structures. The Hugoniot elastic limit is significantly higher along the [111] and [110] directions while the patterns of plastic deformation, based on deformation twinning, contrast along the three crystallographic directions. The spall behavior, both for single and nanocrystalline samples vary from classical to micro-spall. The predicted spall strength is at maximum along the [111] direction, at 34 GPa, followed by the [110], and [001] directions, at 32 and 30 GPa, respectively. Nanocrystalline SiC displays a spall strength over 66.7% lower than single crystals. Spall strengths from direct and indirect methods agree well for both classical and micro-spall regimes after applying an elastic-plastic correction and considering the change in sound velocity, in particular for the case where the structural phase transformation occurs.

Non-equilibrium molecular dynamics simulations of the spallation in Ni: Effect of vacancies

The effects of defects on the fracture resistance of materials have attracted considerable attention recently. In the present work, the vacancy effects on the spallation in single-crystalline Ni are studied by nonequilibrium molecular dynamics simulations. The vacancy concentration ranges from 0% to 2.0%, and the spallation in shock wave loading along three low-index directions ([001], [110], and [111]) is investigated. We found that vacancies provide the sites of nucleation for compression-induce plasticity, and tension stress-induced plasticity plays the key role in void nucleation. Along the [001] direction, the degree of spall damage does not increase with the increase in vacancy concentration; however, along the [110] and [111] directions, it decreases with the increase in vacancy concentration when the vacancy concentration is higher than the threshold value.

A Low-Energy Ion Scattering Approach for Studying Au Nanoclusters Grown on an H2O Buffer Layer.

A novel form of alkali low-energy ion scattering is used to probe the deposition of nanoclusters onto a solid surface via buffer layer assisted growth (BLAG) in ultrahigh vacuum. A thin amorphous solid water (ASW) buffer layer is grown on a TiO2(110) single crystal cooled to 100 K. Au atoms deposited onto this layer arrange themselves into nanoclusters. The sample is then annealed to 320 K to desorb the ASW and enable the clusters to soft-land onto the substrate. Time-of-flight low-energy ion scattering, using Li+, Na+, and K+ projectiles, probes the materials during each step of the BLAG process to measure the surface composition and reveal the details of how the clusters form. The neutralization probability of Na+ ions singly scattered from the Au nanoclusters indicates that they increase in size after annealing and that the magnitude of the increase is a function of the buffer layer thickness. The adsorption of a thin, incomplete water layer prior to Au deposition forms nanoclusters that are possibly even smaller than those produced by direct deposition onto the clean substrate.

Investigation of Li/Nb-sublattices in ion implanted LiNbO3 by RBS and NRA in channelling configuration

Differently oriented LiNbO3 crystals were implanted at room temperature with 1MeV iodine ions to fluences between 2×1013 and 1×1014cm−2, which cover the transition from a low damage level up to complete amorphisation. The aim of this work was to explore the use of nuclear reaction analysis (NRA) in combination with Rutherford backscattering spectrometry (RBS) in channelling configuration for studying the damage evolution as a function of the ion fluence in both the Li and Nb sublattice. Protons with energies between 1.4 and 1.6MeV and a standard RBS setup were used. Scattering events detected at low energies result from Rutherford backscattering of protons on Nb and O atoms. At high energies alpha particles are registered, which result from the nuclear reaction between protons and Li atoms. Along different low-index crystallographic directions channelling effects within both the RBS and NRA part of the spectra are observed. However, the strength of channeling within the NRA part depends on the crystallographic direction investigated. These effects are explained by the nature of ion-channelling with respect to the small atomic number of Li and is supported by calculations of minimum yields (ratio of scattering yield in aligned and random direction) applying the computer code DICADA. The consequence is that damage studies with NRA can be only performed in Z-direction of LiNbO3. In this case, the Li and Nb sublattice were found to be similarly damaged after 1MeV iodine implantation.

Detailed analysis of impact collision ion scattering spectroscopy of bismuth selenide

Impact collision ion scattering spectroscopy (ICISS), which is a variation of low energy ion scattering (LEIS) that employs large scattering angles, is performed on Bi2Se3 surfaces prepared by ion bombardment and annealing. ICISS angular scans are collected experimentally and simulated numerically along the [120] and [1¯2¯0] azimuths, and the match of the positions of the flux peaks shows that the top three atomic layers are bulk-terminated. A newly observed feature is identified as a minimum in the multiple scattering background when the ion beam incidence is along a low index direction. Calculated scans as a function of scattering angle are employed to identify the behavior of flux peaks to show whether they originate from shadowing, blocking or both. This new method for analysis of large-angle LEIS data is shown to be useful for accurately investigating complex surface structures.