Local similarity in organic crystals and the non-uniqueness of X-ray powder patterns

Two new concepts for molecular solids, 'local similarity' and 'boundary-preserving isometry', are defined mathematically and a theorem which relates these concepts is formulated. 'Locally similar' solids possess an identical short-range structure and a 'boundary-preserving isometry' is a new mathematical operation on a finite region of a solid that transforms mathematically a given solid to a locally similar one. It is shown further that the existence of such a 'boundary-preserving isometry' in a given solid has infinitely many 'locally similar' solids as a consequence. Chemical implications, referring to the similarity of X-ray powder patterns and patent registration, are discussed as well. These theoretical concepts, which are first introduced in a schematic manner, are proved to exist in nature by the elucidation of the crystal structure of some diketopyrrolopyrrole (DPP) derivatives with surprisingly similar powder patterns. Although the available powder patterns were not indexable, the underlying crystals could be elucidated by using the new technique of ab initio prediction of possible polymorphs and a subsequent Rietveld refinement. Further ab initio packing calculations on other molecules reveal that 'local crystal similarity' is not restricted to DPP derivatives and should also be exhibited by other molecules such as quinacridones. The 'boundary-preserving isometry' is presented as a predictive tool for crystal engineering purposes and attempts to detect it in crystals of the Cambridge Structural Database (CSD) are reported.

Molecular dynamics studies on the local disordering of σ3 and σ11 grain boundaries in aluminium bicrystal

Molecular dynamics (MD) simulations using Morse interaction potential are performed in studies of [110] symmetrical tilt grain boundary (GB) structures with mis-orientation angles 50.5 degrees(Sigma 11), 129.5 degrees(Sigma 11), 70.5 degrees(Sigma 3) and 109.5 degrees(Sigma 3) at various tempratures. The GB structures are found to start local disordering at about 0.5T(m)(T-m is the melting point of aluminium) for 50.5 degrees(Sigma 11), 0.32T(m) for 129.5 degrees(Sigma 11) and 0.38T(m) for 70.5 degrees(Sigma 3), respectively. These results agree with conclusions deduced from the anelastic measurements. But, for twin-boundary structure 109.5 degrees(Sigma 3), this disordering has not been found even when temperature increases up to 0.9T(m).

Role of interface absorption in laser-induced local heating of optical coatings

Considering the interface absorption in optical coatings, we propose a model to simulate interface absorption. Calculations are made and the temperature field of several kinds of thin film multilayers, including those of partial reflectivity, high-reflectivity, and antireflectivity coatings are analyzed. The interface absorption is found to greatly influence the temperature distribution within multilayer coatings and to weaken the laser damage resistance of the samples. The real-time results of the photothermal deflection technique for laser induced damage to samples supports the model. (C) 1997 Society of Photo-Optical Instrumentation Engineers.

Local environment of Er3+ in Er-doped Si nanoclusters embedded in SiO2 films

The local environment of Er3+ in heavily Er-doped (Er, 2.5 at. %) Si nanoclusters embedded in SiO2 films annealed at various temperatures was investigated by using the fluorescence-extended x-ray absorption fine structure spectroscopy. The results show that annealing caused a large effect on the local environment of Er3+ surrounded by O atoms and the 1.54 mu m photoluminescence intensity. The correlation between the local environment around Er3+ and the corresponding 1.54 mu m photoluminescence was discussed. (c) 2006 American Institute of Physics.

Conditions for the local manipulation of all bipartite Gaussian states

We provide a general, necessary, and sufficient condition for the possibility of transforming a mixed bipartite Gaussian state with arbitrarily many modes to another one under arbitrary local Gaussian channels, which do not include classical communication. Moreover, by means of this condition we present a necessary criterion that can be used to check the possibility of a state transformation between two mixed Gaussian states. At the same time, we prove that our criterion can be reduced to the Eisert-Plenio criterion when the mode number is chosen as 1 per side.

Conditions for the local manipulation of tripartite Gaussian states

We present the normal form of the covariance matrix for three-mode tripartite Gaussian states. By means of this result, the general form of a necessary and sufficient criterion for the possibility of a state transformation from one tripartite entangled Gaussian state to another with three modes is found. Moreover, we show that the conditions presented include not only inequalities but equalities as well.

Local transformation of mixed states of two qubits to Bell diagonal states

The optimal entanglement manipulation for a single copy of mixed states of two qubits is to transform it to a Bell diagonal state. In this paper we derive an explicit form of the local operation that can realize such a transformation. The result obtained is universal for arbitrary entangled two-qubit states and it discloses that the corresponding local filter is not unique for density matrices with rank n = 2 and can be exclusively determined for that with n = 3 and 4. As illustrations, a four-parameter family of mixed states are explored, the local filter as well as the transformation probability are given explicitly, which verify the validity of the general result.

LOCAL BENDING OF THIN FILM ON VISCOUS LAYER

Effects of deposition layer position and number/density on local bending of a thin film are systematically investigated. Because the deposition layer interacts with the thin film at the interface and there is an offset between the thin film neutral surface and the interface, the deposition layer generates not only axial stress but also bending moment. The bending moment induces an instant out-of-plane deflection of the thin film, which may or may not cause the so-called local bending. The deposition layer is modeled as a local stressor, whose location and density are demonstrated to be vital to the occurrence of local bending. The thin film rests on a viscous layer, which is governed by the Navier-Stokes equation and behaves like an elastic foundation to exert transverse forces on the thin film. The unknown feature of the axial constraint force makes the governing equation highly nonlinear even for the small deflection case. The constraint force and film transverse deflection are solved iteratively through the governing equation and the displacement constraint equation of immovable edges. This research shows that in some special cases, the deposition density increase does not necessarily reduce the local bending. By comparing the thin film deflections of different deposition numbers and positions, we also present the guideline of strengthening or suppressing the local bending.

Elasticity, stability, and ideal strength of beta-SiC in plane-wave-based ab initio calculations

On the basis of the pseudopotential plane-wave method and the local-density-functional theory, this paper studies energetics, stress-strain relation, stability, and ideal strength of beta-SiC under various loading modes, where uniform uniaxial extension and tension and biaxial proportional extension are considered along directions [001] and [111]. The lattice constant, elastic constants, and moduli of equilibrium state are calculated and the results agree well with the experimental data. As the four SI-C bonds along directions [111], [(1) over bar 11], [11(1) over bar] and [111] are not the same under the loading along [111], internal relaxation and the corresponding internal displacements must be considered. We find that, at the beginning of loading, the effect of internal displacement through the shuffle and glide plane diminishes the difference among the four Si-C bonds lengths, but will increase the difference at the subsequent loading, which will result in a crack nucleated on the {111} shuffle plane and a subsequently cleavage fracture. Thus the corresponding theoretical strength is 50.8 GPa, which agrees well with the recent experiment value, 53.4 GPa. However, with the loading along [001], internal relaxation is not important for tetragonal symmetry. Elastic constants during the uniaxial tension along [001] are calculated. Based on the stability analysis with stiffness coefficients, we find that the spinodal and Born instabilities are triggered almost at the same strain, which agrees with the previous molecular-dynamics simulation. During biaxial proportional extension, stress and strength vary proportionally with the biaxial loading ratio at the same longitudinal strain.

An analysis on overall crack-number-density of short-fatigue-cracks

The evolution of dispersed short-fatigue-cracks is analysed based on the equilibrium of crack-number-density (CND). By separating the mean value and the stochastic fluctuation of local CND, the equilibrium equation of overall CND is derived. Comparing with the mean-field equilibrium equation, the equilibrium equation of overall CND has different forms in the expression of crack-nucleation-rate or crack-growth-rate. The simulation results are compared with experimental measurements showing the stochastic analyses provide consistent tendency with experiments. The discrepancy in simulation results between overall CND and mean-field CND is discussed.

An analysis of collective damage for short fatigue cracks based on equilibrium of crack numerical density

Collective damage of short fatigue cracks was analyzed in the light of equilibrium of crack numerical density. With the estimation of crack growth rate and crack nucleation rate, the solution of the equilibrium equation was studied to reveal the distinct feature of saturation distribution for crack numerical density. The critical time that characterized the transition of short and long-crack regimes was estimated, in which the influences of grain size and grain-boundary obstacle effect were investigated. Furthermore, the total number of cracks and the first order of damage moment were discussed.

An Extension of 2D Janbu’s Generalized Procedure of Slices for 3D Slope Stability Analysis II—Numerical Method and Applications

This paper provides a numerical approach on achieving the limit equilibrium method for 3D slope stability analysis proposed in the theoretical part of the previous paper. Some programming techniques are presented to ensure the maneuverability of the method. Three examples are introduced to illustrate the use of this method. The results are given in detail such as the local factor of safety and local potential sliding direction for a slope. As the method is an extension of 2D Janbu's generalized procedure of slices (GPS), the results obtained by GPS for the longitudinal sections of a slope are also given for comparison with the 3D results. A practical landslide in Yunyang, the Three Gorges, of China, is also analyzed by the present method. Moreover, the proposed method has the advantages and disadvantages of GPS. The problem frequently encountered in calculation process is still about the convergency, especially in analyzing the stability of a cutting corner. Some advice on discretization is given to ensure convergence when the present method is used. However, the problem about convergency still needs to be further explored based on the rigorous theoretical background.

The mechanism of energy storage by shearing the solar magnetic field

In this paper, a complete set of MHD equations have been solved by numerical calculations in an attempt to study the dynamical evolutionary processes of the initial equilibrium configuration and to discuss the energy storage mechanism of the solar atmosphere by shearing the magnetic field. The initial equilibrium configuration with an arch bipolar potential field obtained from the numerical solution is similar to the configuration in the vicinity of typical solar flare before its eruption. From the magnetic induction equation in the set of MHD equations and dealing with the non-linear coupling effects between the flow field and magnetic field, the quantitative relationship has been derived for their dynamical evolution. Results show that plasma shear motion at the bottom of the solar atmosphere causes the magnetic field to shear; meanwhile the magnetic field energy is stored in local regions. With the increase of time the local magnetic energy increases and it may reach an order of 4×10^25 J during a day. Thus the local storage of magnetic energy is large enough to trigger a big solar flare and can be considered as the energy source of solar flares. The energy storage mechanism by shearing the magnetic field can well explain the slow changes in solar active regions.