Large Cross‐Free Sets in Steiner Triple Systems

A cross‐free set of size m in a Steiner triple system is three pairwise disjoint m‐element subsets such that no intersects all the three ‐s. We conjecture that for every admissible n there is an STS(n) with a cross‐free set of size which if true, is best possible. We prove this conjecture for the case , constructing an STS containing a cross‐free set of size 6k. We note that some of the 3‐bichromatic STSs, constructed by Colbourn, Dinitz, and Rosa, have cross‐free sets of size close to 6k (but cannot have size exactly 6k). The constructed STS shows that equality is possible for in the following result: in every 3‐coloring of the blocks of any Steiner triple system STS(n) there is a monochromatic connected component of size at least (we conjecture that equality holds for every admissible n). The analog problem can be asked for r‐colorings as well, if and is a prime power, we show that the answer is the same as in case of complete graphs: in every r‐coloring of the blocks of any STS(n), there is a monochromatic connected component with at least points, and this is sharp for infinitely many n.     

Closed and open-ended stacking fault tetrahedra formation along the interfaces of Cu–Al nanolayered metals

Stacking fault tetrahedra (SFTs) are volume defects that typically form by the clustering of vacancies in face-centred cubic (FCC) metals. Here, we report a dislocation-based mechanism of SFT formation initiated from the semi-coherent interfaces of Cu–Al nanoscale multilayered metals subjected to out-of-plane tension. Our molecular dynamics simulations show that Shockley partials are first emitted into the Cu interlayers from the dissociated misfit dislocations along the Cu–Al interface and interact to form SFTs above the triangular intrinsic stacking faults along the interface. Under further deformation, Shockley partials are also emitted into the Al interlayers and interact to form SFTs above the triangular FCC planes along the interface. The resulting dislocation structure comprises closed SFTs within the Cu interlayers which are tied across the Cu–Al interfaces to open-ended SFTs within the Al interlayers. This unique plastic deformation mechanism results in considerable strain hardening of the Cu–Al nanolayered metal, which achieves its highest tensile strength at a critical interlayer thickness of ~4 nm corresponding to the highest possible density of complete SFTs within the nanolayer structure.     

One-dimensional migration of interstitial clusters in SUS316L and its model alloys at elevated temperatures

For self-interstitial atom (SIA) clusters in various concentrated alloys, one-dimensional (1D) migration is induced by electron irradiation around 300 K. But at elevated temperatures, the 1D migration frequency decreases to less than one-tenth of that around 300 K in iron-based bcc alloys. In this study, we examined mechanisms of 1D migration at elevated temperatures using in situ observation of SUS316L and its model alloys with high-voltage electron microscopy. First, for elevated temperatures, we examined the effects of annealing and short-term electron irradiation of SIA clusters on their subsequent 1D migration. In annealed SUS316L, 1D migration was suppressed and then recovered by prolonged irradiation at 300 K. In high-purity model alloy Fe-18Cr-13Ni, annealing or irradiation had no effect. Addition of carbon or oxygen to the model alloy suppressed 1D migration after annealing. Manganese and silicon did not suppress 1D migration after annealing but after short-term electron irradiation. The suppression was attributable to the pinning of SIA clusters by segregated solute elements, and the recovery was to the dissolution of the segregation by interatomic mixing under electron irradiation. Next, we examined 1D migration of SIA clusters in SUS316L under continuous electron irradiation at elevated temperatures. The 1D migration frequency at 673 K was proportional to the irradiation intensity. It was as high as half of that at 300 K. We proposed that 1D migration is controlled by the competition of two effects: induction of 1D migration by interatomic mixing and suppression by solute segregation.     

Low-Energy Dislocation Structure (LEDS) character of dislocation boundaries aligned with slip planes in rolled aluminium

For the specific slip geometry of two sets of coplanar systems (a total of four systems) in fcc metals, the range of dislocation networks in boundaries aligned with one of the two active slip planes is predicted from the Frank equation for boundaries free of long-range elastic stresses. Detailed comparison with experimental data for eight dislocation boundaries in cold-rolled aluminium grains of the 45° ND rotated Cube orientation is conducted. It is concluded that the boundaries are Low-Energy Dislocation Structures, which are in good agreement with the Frank equation while also lowering the energy by dislocation reactions. Cross slip plays a role in the boundary formation process.     

Effect of source strength on dislocation pileups in the presence of stress gradients

The behaviour of a dislocation pileup with a finite-strength source is investigated in the presence of various stress gradients within a continuum model where a free-dislocation region exists around the source. Expressions for dislocation density and stress field within the pileup are derived for the situation where there are first and second spatial gradients in applied stress. For a pileup configuration under an applied stress, yielding occurs when the force acting on the leading dislocations at the pileup tips reaches the obstacle strength, and at the same time, it is required that the source be at the threshold stress for dislocation production. A numerical methodology is presented to solve the underlying equations that represent the yielding conditions. The yield stress calculated for a pileup configuration is found to depend on stress gradients, obstacle spacing and source/obstacle strengths. It increases with increasing the first stress gradient, yet dependent on the second stress gradient. Furthermore, while the dependency of yield stress on the obstacle spacing intensifies with increasing the first stress gradient, it diminishes with an increase of second stress gradient. Therefore, the second stress gradient, as a newly introduced parameter, can provide a new physical insight into the size-dependent plasticity phenomena at small length scales.     

The dislocation equation as a generalization of Peierls equation

A fundamental equation is derived for the structure of dislocations in solids. With the interaction potential that can be obtained properly from the first principle, the equation provides a complete basis for a comprehensive study of the dislocation structure. In particular, the full structural feature and related properties of dislocation can be predicted theoretically, which makes it possible to compare precisely the theoretical results and what is produced by experiments or numerical simulations.     

Effect of pH value on the growth morphology of KH2PO4 crystal grown in defined crystallographic direction

KH₂PO₄ single crystals were grown in aqueous solution at different pH values by using “point seeds” with a defined crystallographic direction at 59 degree to the Z axis. Atomic Force Microscope (AFM) was applied to observe the surface morphology of (100) face. It was found that at the same supersaturation, the larger steps appeared at the lower pH value before appearance of 2D nucleus. We found that 2D nucleus was occurred at σ ≤ 0.04 when pH value is <2.8. The occurrence of 2D nucleus was caused by the decreasing step‐edge free energy with the decreasing of pH value in the growth solution. In this paper, we observed the morphologies of (100) faces of KDP crystals which grew in solutions with different pH values. 2D nucleuses appeared on the terrace of growth steps when pH value down to 2.8 and 3.2 at supersaturation of 0.04, while pH value down to 2.4, only 2D nucleation control the growth. Therefore, the pH value can change the growth mechanism of KDP crystals.     

PbTiO3/SrTiO3(010)异质界面上的周期性失配位错及电子富集

It is important to determine the effects of misfit dislocations and other defects on the domain structure, ferroelectricity, conductivity, and other physical properties of ferroelectric thin films to understand their ferroelectric and piezoelectric behaviors. Much attention has been given to ferroelectric PbTiO₃/SrTiO₃ or PbZr_0.2Ti_0.8O₃/SrTiO₃ heterointerfaces, at which improper ferroelectricity, a spin-polarized two-dimensional electron gas, and other physical phenomena have been found. However, those heterointerfaces were all (001) planes, and there has been no experimental studies on the growth of (010) PbTiO₃/SrTiO₃ heterointerface due to the 6.4% misfit between two materials. In this study, we selected an atomically flat (010) PbTiO₃/SrTiO₃ heterointerface grown using a two-step hydrothermal method as the research subject, and this is the first experimental report on that interface. Interfacial dislocations can play a significant role in causing dramatic changes in the Curie temperature and polarization distribution near the dislocation cores, especially when the size of a ferroelectric thin film is scaled down to the nanoscale. The results of previous studies on the effects of interfacial dislocations on the physical properties of ferroelectric thin films have been contradictory. Thus, this issue needs to be explored more deeply in the future. This study used aberration corrected scanning transmission electron microscopy (STEM) to study the atomic structure of a (010) PbTiO₃/SrTiO₃ heterointerface and found periodic misfit dislocations with a Burgers vector of a[001]. The extra planes at the dislocation cores could relieve the misfit strain between the two materials in the [001] direction and thus allowed the growth of such an atomically sharp heterointerface. Moreover, monochromated electron energy-loss spectroscopy with an atomic scale spatial resolution and high energy resolution was used to explore the charge distribution near the periodic misfit dislocation cores. The fine structure of the Ti L edge was quantitatively analyzed by linearly fitting the experimental spectra recorded at various locations near and at the misfit dislocation cores with the Ti³⁺ and Ti⁴⁺ reference spectra. Therefore, the accurate valence change of Ti could be determined, which corresponded to the charge distribution. The probable existence of an aggregation of electrons was found near the a[001] dislocation cores, and the density of the electrons calculated from the valence change was 0.26 electrons per unit cell. Based on an analysis of the fine structure of the oxygen K edge, it could be argued that the electrons aggregating at the dislocation cores came from the oxygen vacancies in the interior regions of the PbTiO₃. This aggregation of electrons will probably increase the electron conductivity along the dislocation line. The physics of two-dimensional charge distributions at oxide interfaces have been intensively studied, however, little attention had been given to the one-dimensional charge distribution. Therefore, the results of this study can stimulate research interest in exploring the influence of the interfacial dislocations on the physics of ferroelectric heterointerfaces.     

Assessment of Hydrocarbon Electron‐Impact Ionization Cross Section Measurements for Magnetic Fusion

Partial ionization cross section experiments have been carried out recently at the University of Innsbruck for three types of hydrocarbons, i.e. acetylene, ethylene and propene. Cross section data fits are generated and compared to the compilation of earlier experimental data summarized in the online database HYDKIN [www.hydkin.de]. New data fits are brought into a suitable form to be incorporated into the database. In order to illuminate underlying dissociation mechanisms the energy dependence of branching ratios above energies of 20 –30 eV is reviewed in light of the present results (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On some colorings of a double graph

In this note, we present some results concerning the chromatic index, the total chromatic index, the adjacent vertex distinguishing chromatic index and the adjacent vertex distinguishing total chromatic index for double graphs. In particular, we study the double graphs of class 1 and of type 1.