Observation of structural units at symmetric [001] tilt boundaries in SrTiO3

Incoherent Z-contrast imaging in the scanning transmission electron microscope allows atom column positions to be deduced directly from the experimental image, including locations where the column separation is less than the resolution limit. Maximum entropy analysis applied to the incoherent image locates the high-Z columns to an accuracy of ±0.2 Å. Oxygen coordination at the boundary plane can be deduced by high spatial resolution electron energy loss spectroscopy, and approximate column positions determined by simple bond-valence sum calculations. Observations of 25° (=85), 36° (=5) and 67° (=13) [001] symmetric tilt grain boundaries in SrTiO₃ bicrystals show that half columns are a ubiquitous feature of grain boundary structural units. The observed structural units can be combined to produce structural models for symmetric tilt boundaries over a 0–90° range. The =17 (410), =5 (310), and =5 (210) are found to be favored boundaries and the structures of all the other tilt boundaries are comprised of these units combined with =1 (100) and =1 (110) structural units. All the proposed boundary models show continuity of grain boundary structure over the entire misorientation range. The =17 (410) structural unit is asymmetric which induces microfacetting on all boundaries less than the =5, 36.87° misorientation.Work Supported by the U.S. Department of Energy under contract DE-Ac05-84OR21400.     

Faceting of Σ3 and Σ9 Grain Boundaries in Copper

Faceting is a well documented phenomenon known both for surfaces and interfaces, particularly, grain boundaries (GBs). Faceting can be considered as a phase transition when the original surface or GB dissociates onto flat segments whose energy is less than that of the original surface or GB. For the investigation of GB faceting a cylindrical Cu bicrystal with an island grain was grown by the Bridgman technique. Grain 1 in this bicrystal is completely surrounded by grain 2. The dissociation 9 3 + 3 proceeds during the growth of the bicrystal. The twins appear instead of {111}₁/{115}₂ or (110)_9CSL facet. GB faceting was studied at 1293 K, 1073 K, and 873 K. The profiles of the GB thermal groove were analysed by atomic force microscopy. Wulff-Herring plots and GB phase diagrams have been constructed for the 3, 9 and 9 + 3 GBs. With increasing temperature the facets with low-density CSL-planes disappear in the GB shape. GB roughening phase transition can be responsible for this phenomenon.     

Geometry of Σ9 and Σ11 asymmetrical grain boundaries

It is shown how the decomposition scheme into structural units can be developed for rational asymmetrical tilt grain boundaries without computer simulations. The method is illustrated on the 9 and 11 grain boundaries in the f.c.c. lattice for which experimental observations of the boundary structures are available. Besides short-period boundaries, which may serve as elementary structural units, the irrational aperiodic asymmetrical boundaries are also considered. There are clear experimental indications that some of them, namely those composed of dense-packed atomic planes, and called special asymmetrical boundaries, behave differently from the other more general boundaries.     

Properties of Quantum Languages

The class of quantum languages Q() over an alphabet is the class of languages accepted by quantum automata. We study properties of Q() and compare Q() with the class of regular languages R(). It is shown that Q() is closed under union, intersection, and reversal but is not closed under complementation, concatenation, or Kleene star. It is also shown that Q() and R() are incomparable. Finally, we prove that L Q() if and only if L admits a transition amplitude function satisfying a certain property and a similar characterization is given for R().     

Sigma-Boundary Statistics by Length and Number

This paper presents a rationale for comparative use of length fraction and number fraction statistics in grain boundary analysis from orientation maps generated by electron back-scatter diffraction (EBSD). The length and number fraction statistics for 3 ⁿ coincidence site lattice (CSL) boundaries were measured and compared. The length fraction of 3 boundaries was 0.48 whereas the number fraction was significantly less, 0.36. A simple model was generated to estimate both the length fraction and number fraction of annealing twins (a subset of 3). The model showed that the number fraction of twins is 0.68, 0.75, 0.79 and 0.82 of the length fraction for 1, 2, 3 and 4 twins-per-grain respectively. For the experimental data the number fraction was 0.76 of the length fraction, implying that there were on average two twins-per-grain. In contrast to the 3 case, the length fraction for 9 and 27 boundaries was less than the number fraction. There are more inaccuracies involved in obtaining the number fraction than in obtaining the length fraction from EBSD maps, therefore the length fraction should be recommended as the standard reporting method. However a knowledge of the distribution in the microstructure of 3 ⁿ segments is often crucial to the inquiry in addition to the length fraction.     

Light Σ hypernuclei and Σ− atoms

The structures of ⁴ He and ⁷ Li are investigated within the frame of the [³H + ⁺] + + [³He + ^o] model and the microscopic cluster model +2N+, respectively. The different binding mechanism between ⁴ He and ⁷ Li is emphasized together with a brief discussion on the ⁴ Be hypernucleus. It is clarified that the ⁴ He hypernucleus is bound due to the cooperative contribution from the and terms of -N interaction, while the ⁷ Li hypernucleus is bound mainly due to the term of -N interaction. The combined analysis of ^– atoms and ⁴ He hypernucleus is shown to be useful to reveal the characteristic differences among the model D, model F and soft core versions of the Nijmegen OBE potentials.The authors would like to express their sincere thanks to J. ofka, O. Richter, M. Sotona, L. Majling, A. Cieply and other colleagues in Nuclear Physics Institute (e/Prague), and H. Band, Y. Yamamoto and T. Motoba, for collaboration and useful discussions. We dedicate this article to the memory of the excellent activities of the late Prof. Jan ofka.     

Microstructure Observations for Diffusion Induced Recrystallization and Diffusion Induced Grain Boundary Migration on Surfaces of Zincified Cu Bicrystals With [1 1 0] Twist Boundaries

The formation behavior of the fine-grain region alloyed with Zn due to diffusion induced recrystallization (DIR) in the Cu(Zn) system was experimentally examined for the surfaces polished in different manners using a Cu bicrystal containing a [1 1 0] twist boundary with a misorientation angle of = 46° zincified at 673 K for 2.88 × 10⁴ s with Cu-15 wt% Zn and Cu-30 wt% Zn alloys by a capsule zincification technique. The extent and morphology of the fine-grain DIR region vary depending on the surface conditions and the composition of the Zn-source Cu-Zn alloy. For the specimen with the surface electrolytically polished in an etchant consisting of 20 vol% of nitric acid and 80 vol% of methanol, no DIR region was formed on the whole surface when the Cu-15 wt% Zn alloy was used as a Zn source.In order to observe the morphology of the moving grain boundary owing to diffusion induced grain boundary migration (DIGM) without influences of DIR, Cu bicrystals with [1 1 0] twist boundaries of = 32 ( 27), 39 ( 9), 46, 51 ( 11) and 55° were electrolytically polished in the etchant mentioned above. The polished Cu bicrystals were zincified at 673 K for 2.88 × 10⁴ s using the Cu-15 wt% Zn alloy as a Zn source. Remarkable surface relief and clear slip bands were recognized on the surfaces due to DIGM for the specimens with the 32 ( 27) and 46° boundaries. The moving boundary became zigzag owing to the slip bands parallel to the moving direction. On the other hand, such surface relief and slip bands were not observed for the specimens with the 39 ( 9), 51 ( 11) and 55° boundaries. The moving boundary was considerably irregular for = 39° whereas rather smooth for = 51 ( 11) and 55°. The migration behavior of the grain boundary was not affected by the interruption of the zincification.     

Deviation from Reference Planes and Reference Misorientation for Σ3 Boundaries

The purpose of the present work is to study the crystallography of a particular family of interfaces, 3 boundaries in copper, in the context of the relationships between 3 plane indices, their deviation from reference planes, and the deviation from exact 3 matching, v/v_m. The relatively high values of v/v_m recorded were considered to be the result of texture development during annealing and various back twinning and 3ⁿ impingement interactions. The results show that there is a reasonable correlation between the deviation from a reference misorientation (v/v_m) and the deviation from reference interface plane (R). Measurement of v/v_m alone provides an indirect estimate of the plane type and hence energy of the boundary, at least for 3 boundaries, and moreover is more germane to the experimental mode of data collection. The effect of intragrain orientation variations on the interface parameters was also studied, and it was shown that there is a 20% difference between misorientations calculated near the interface compared with displaced from the interface.     

Sewing Polyakov amplitudes I: Sewing at a fixed conformal structure

We consider the problem of reconstructing the correlation functions of a conformal field theory on a surface from the correlation functions on a surface obtained from by cutting along a closed curve. We show that under quite general conditions, the correlation functions on the cut surface can be sewn by integrating over appropriate boundary valuess of the field.Supported in part by DOE grant DE-AC02-76ERO2220Supported in part by DOE grant DE-AS06-88ER40423     

ИЗУЧЕНИЕ ИНТЕГРАЛЬН ОЙ И ЛОКАЛЬНОЙ ЧУВСТВИТЕЛЬНОСТИ ФО ТОКАТОДОВ И ИХ ВЛИЯНИ Е НА ГОРИЗОНТАЛЬНЫЙ УЧ АСТОК ХАРАКТЕРИСТИК И СЦИНТИЛЛЯЦИОННОГО Д ЕТЕКТОРА

, RCA 5819, 19 41PK411 ( ). - , .     

Strain Induced Grain Boundary Premelting along Twin Boundaries in Copper Polycrystals

A polycrystalline copper sample was compressed at room temperature, then the temperature was raised to 873 K in a vacuum and annealed without unloading. Grain boundary cracks were found at 3 coherent twin boundaries. The formation of these cracks can be interpreted based on the idea of strain induced grain boundary premelting (SIGBPM). It is emphasized that 3 twin boundaries can be one of the most dangerous boundaries for crack formation when certain experimental conditions are satisfied.     

Four-wave mixing in CO via the C 1Σ+ (υ′=0) state

Coherent vacuum ultraviolet (VUV) radiation was generated by four-wave difference frequency mixing (_VUV=2₁–₂) of pulsed dye laser radiation in carbon monoxide (CO). The frequency ₁ was tuned to the C ¹⁺(=0)X ¹⁺(=0) two-photon transition, while the dye laser frequency ₂ was scaned around 17650 cm^–1 which corresponds to the A ¹(=7)«C ¹⁺(=0) transition energy. The VUV intensity was found to be strongly wavelength dependent. The analysis of the spectrum revealed (i) that the VUV intensity was enhanced by the rotational levels of the A ¹(=7) state and (ii) that the off-resonance excitation in the C ¹⁺(=0)X ¹⁺(=0) two-photon transition greatly contributed to the present four-wave mixing process. The effects of pumping laser detuning, saturation and foreign gases are briefly discussed.     

Measurement of the reaction γp → K0Σat photon energies up to 2.6 GeV⋆

The reaction p K⁰⁺ was measured in the photon energy range from threshold up to 2.6 GeV with the SAPHIR detector at the electron stretcher facility, ELSA, in Bonn. Results are presented on the reaction cross-section and the polarization of the ⁺ as a function of the kaon production angle in the centre-of-mass system, cos^c.m._K, and the photon energy. The cross-section is lower and varies less with photon energy and kaon production angle than that of p K⁺⁰. The ⁺ is polarized predominantly at cos^c.m._K 0. The data presented here are more precise than previous ones obtained with SAPHIR and extend the photon energy range to higher values. They are compared to isobar model calculations.     

Mathematical properties of the vacuum polarization function

This paper is an investigation of certain mathematical properties of the vacuum polarization function (s). We show that (s) is a Herglotz function, has no complex zeroes, and belongs to the class of functions called typically real. In addition, we obtain upper bounds on the higher derivatives of (s), at s=0, given that we know the value of the first derivative at that point.Research supported in part by NASA Grant NSG-8035     

Symplectic Structures on Moduli Spaces of Parabolic Higgs Bundles and Hilbert Scheme

Parabolic triples of the form (E_*,,) are considered, where (E_*,) is a parabolic Higgs bundle on a given compact Riemann surface X with parabolic structure on a fixed divisor S, and is a nonzero section of the underlying vector bundle. Sending such a triple to the Higgs bundle (E_*,) a map from the moduli space of stable parabolic triples to the moduli space of stable parabolic Higgs bundles is obtained. The pull back, by this map, of the symplectic form on the moduli space of stable parabolic Higgs bundles will be denoted by d. On the other hand, there is a map from the moduli space of stable parabolic triples to a Hilbert scheme Hilb(Z), where Z denotes the total space of the line bundle K_{X X}(S), that sends a triple (E_*,,) to the divisor defined by the section on the spectral curve corresponding to the parabolic Higgs bundle (E_*,). Using this map and a meromorphic one–form on Hilb(Z), a natural two–form on the moduli space of stable parabolic triples is constructed. It is shown here that this form coincides with the above mentioned form d.     

On the Brownian motion of a massive sphere suspended in a hard-sphere fluid. II. Molecular dynamics estimates of the friction coefficient

The friction coefficient exerted by a hard-sphere fluid on an infinitely massive Brownian sphere is calculated for several size ratios , where and are the diameters of the Brownian and fluid spheres, respectively. The exact microscopic expression derived in part I of this work from kinetic theory is transformed and shown to be proportional to the time integral of the autocorrelation function of the momentum transferred from the fluid to the Brownian sphere during instantaneous collisions. Three different methods are described to extract the friction coefficient from molecular dynamics simulations carried out onfinite systems. The three independent methods lead to estimates of which agree within statisticalerrors (typically 5%). The results are compared to the predictions of Enskog theory and of the hydrodynamic Stokes law. The former breaks down as the size ratio and/or the packing fraction of the fluid increase. Somewhat surprisingly, Stokes' law is found to hold withstick boundary conditions, in the range 1/4.5 explored in the present simulations, with a hydrodynamic diameterd=. The analysis of the moleuclar dynamics data on the basis of Stokes' law withslip boundary conditions is less conclusive, although the right trend is found as / increases.     

C*-algebras and Mackey's axioms

A non-commutative version of probability theory is outlined, based on the concept of a*-algebra of operators (sequentially weakly closedC*-algebra of operators). Using the theory of*-algebras, we relate theC*-algebra approach to quantum mechanics as developed byKadison with the probabilistic approach to quantum mechanics as axiomatized byMackey. The*-algebra approach to quantum mechanics includes the case of classical statistical mechanics; this important case is excluded by theW*-algebra approach. By considering the*-algebra, rather than the von Neumann algebra, generated by the givenC*-algebraA in its reduced atomic representation, we show that a difficulty encountered byGuenin concerning the domain of a state can be resolved.     

Metastable states and T=0 hysteresis in the random-field Ising model on random graphs

We study the ferromagnetic random-field Ising model on random graphs of fixed connectivity z (Bethe lattice) in the presence of an external magnetic field H. We compute the number of single-spin-flip stable configurations with a given magnetization m and study the connection between the distribution of these metastable states in the H-m plane (focusing on the region where the number is exponentially large) and the shape of the saturation hysteresis loop obtained by cycling the field between - and + at T=0. The annealed complexity A(m,H) is calculated for z=2,3,4 and the quenched complexity Q(m,H) for z=2. We prove explicitly for z=2 that the contour Q(m,H)=0 coincides with the saturation loop. On the other hand, we show that A(m,H) is irrelevant for describing, even qualitatively, the observable hysteresis properties of the system.     

On the structure of Σ-hypernuclei

We investigate the-nucleus potential in the framework of a relativistic mean field approximation. As input for the elementaryN interaction we supplement the-repulsion by the exchange of an effective, complex-meson to account for theN N conversion. As the main result we find that the strength of ths absorptive central potential is smaller than the corresponding real part, whereas in the spin-orbit interaction, which is expected to be much weaker than for a nucleon, the imaginary component dominates.This work was partially supported by CNPq, FINEP (Brazil) and by the Bilateral Cooperation W. Germany — Brazil (KFA — CNPq).     

The C1 Σ +-B1-Σ + amplified spontaneous emission in CO

The first observation of the amplified spontaneous emission (ASE) from the RydbergC ^{1 +}( = 0) state of CO is reported. When theC ^{1 +}( = 0) state was populated through the two-photon excitation, infrared radiation near 2.0 m was ejected in forward as well as backward directions along the laser propagation. The assignment as theC ^{1 +}( = 0) B ^{1 +}( = 0) transition was confirmed. Several characteristics of ASE from theC ^{1 +}( = 0) state are presented.This work was supported by the Morino Foundation, a Grant-in-Aid (No. 07640697) and that on Priority-Area-Research Photoreaction Dynamics (No. 07228268) from the Ministry of Education, Science, Sports and Culture, Japan.