Search

Plastic deformation is a fundamentally important physical process, ultimately determining how materials can be used. Metal plasticity is governed by dislocation dynamics and lattice twinning. Although many continuum constitutive models exist, plasticity is now known to occur in discrete events arising from the self-organisation of dislocations into ‘avalanches’ under applied stress. Here we extend avalanche plasticity to high strain rates, by introducing time limitation to self-organisation. At high rates large avalanches fail to form; the system must self-organise around new constraints. Various macroscopic consequences include an increasing rate of work hardening with strain rate. We perform new measurements on high purity copper that distinguish between instantaneous and permanent strength contributions across a strength transition at 104 s−1, showing the transition to be a change in structural evolution. Strong model agreement validates our time limited self-organisation approach. Our work results in a unified, physically realistic framework for plasticity, with wide applicability. Plastic deformation in metals occurs by an avalanche of dislocations. Here, avalanche plasticity is studied experimentally as a function of strain rate in copper, showing a transition at 104 s−1 where avalanches no longer form, with a model used to explain the structural origin of the transition.

In 1957, P. Haasen and A. Kelly presented an account of experiments that showed that, in Al and Ni single crystals, the mere act of unloading during a tensile test caused a small but reproducible transient increase in flow stress, a ‘yield point’. The increase is proportional to the current work-hardened stress level. It occurs at the lowest temperatures, where diffusion is not possible, but it is enhanced at higher temperatures. The effect was interpreted as arising from dislocations that ‘anchor themselves during unloading and that this process of anchoring, which prevents reverse plastic flow, is also responsible for the yield-point effect on reloading’. Recent ideas emphasising the role of dislocation dipoles as sources for slip provide a natural explanation for these effects.

In response to a recent paper by Mughrabi and Pschenitzka (Phil. Mag. 85 3029 (2005).), an estimate is given of the saturation stress in cyclic plasticity, assuming only the bowing of screw dislocations and the simultaneous passing of them at a critical separation determined by their cross-section for mutual annihilation by cross-slip. Although, as Mughrabi and Pschenitzka show, the simple addition of the two stresses is a poor approximation, if the bowing stress is made equal to the passing stress, the equations governing the saturation stress and the associated average plastic strain in a persistent slip band are scarcely altered from earlier work (Phil. Mag. 84 2501 (2004).). A comparison between theory and experiment shows good quantitative agreement. Finally, an estimate is made of the alternating internal stress in a band, and reasons suggested for why it does not contribute to the saturation stress.

The extent to which near-edge structure depends upon long-range order is explored using polymeric systems, where one can vary the disposition of side-groups and the degree of crystallinity and compare the resulting spectra. Carbon K-edges for polystyrene in atactic and isotactic forms are compared; the former is amorphous and the latter crystalline. Differences between the spectra are very slight but observable, and are attributed to bond orientation effects and to interaction between closely-spaced hydrogens bonded to neighbouring benzene rings and to the backbone. The quality of the spectra collected at doses of less than 300 e − nm −2 from a few square microns compares favourably with previously published EXAFS data. Another example of near-edge structure is provided by segregated species. The case of iron segregated to boundaries in Zr-Nb alloys is of intense interest to the nuclear industry. An attempt has been made to interpret observed fine structure in terms of structure from reference intermetallic compounds. It seems that the fine structure displayed by the segregated iron is different from that displayed by pure metallic iron or by known compounds with Zr, but more akin to ZrNbFe

A beam of electrons, grazing the surface of a semiconductor or insulator, can cause transitions between bands of localized surface states. When the scattered beam is focused in an energy-resolving transmission electron microscope, an image of the surface is obtained. This paper uses a semiclassical model to analyse inelastic electron-surface scattering and predict the brightness and shape of the surface image. The range of validity of the semiclassical model depends on the symmetries of the initial and final surface wavefunctions in a direction perpendicular to the surface.

IV ÖZET Bu çalışma beş bölümden oluşmaktadır. Birinci bölümde, verilen bir X topolojik uzayı için C(X) ve C*(X) halkalarının cebirsel ve sıra özellikleri belirlenerek, X uzayının topolojisi ve bu halkaların ce birsel yapısı arasındaki ilişkiyi ortaya çıkaran `sıfır küme`, `ideal`, `zayıf topoloji`, `z-süzgeç` ve `C, C*-gömülme` temel kavramlarına değinilmiştir. İkinci bölümde, sabit ve serbest ideal kavramları tanımlanarak, bir X topolojik uzayı için C(X) ve C*(X) halkalarındaki tüm sabit maximal idealler karakterize edilmiştir. Ayrıca tıkız bir X uzayının C*{X) halkasının latis yapısı tarafından belirlendiğini ve böylece C* cebirinin tıkız uzayları ayırdığını gösteren Banach- Stone Teoremi verilmiştir. Bu bölümde C{X) ve C*(X) halkasında ahnan konveks ve mutlak konveks ideallere göre kalan sınıf halkaları ve bunların X uzayındaki sıfır kümeler ile ilişkili olarak kurulan kısmi sıra özelliklerine de değinilmiştir. Üçüncü bölümde, tamamen regüler bir X uzayının sıfır kümeleri ve C(X) halkasının cebirsel yapısından faydalanılarak, X uzayının, içinde C*-gömülü oldu ğu tek tıkızlama olarak karakterize edilen @X Stone- Cech tıkızlaması kurulmuştur. Bu bölümde ayrıca, ŞX uzayı için izomorfik anlamda bir model olarak, C ve C* halkalarının, Stone topolojisi ile ahnan yapı uzayları ve aralarındaki ilişkilerden söz edilmiştir. Tezin temel konusunu oluşturan gerçeltıkızlık kavramına ve C cebirinin gerçeltı- kız uzayları ayırdığını gösteren Hewitt-Izomorfizma Teoremi 'ne Dördüncü bölüm de yer verilmiştir. Bu bölümde tamamen regüler bir X uzayının, içinde C-gömülü olduğu tek gerçeltıkızlama olarak karakterize edilen v X Hewitt gerçeltıkızlaması kurularak, çeşitü karakterizasyonlarından söz edilmiştir. vX uzayı yardımı ile gerçeltıkız uzayların genel özellikleri yine bu bölümde verilmiştir. Son bölümde, gerçeltıkızlık kavramının bazı yazarlar tarafından verilen karak- terizasyonlarma değinilmiştir. Ayrıca, gerçeltıkız uzayların birleşimi ve üzerine çeşitli koşullar konulan dönüşümler altında korunmalarına ilişkin olarak bulunan bazı sonuçlar ve ters örnekler verilmiştir. Bu bölümde son olarak, Mandelker (1971) 'in, tamamen regüler ve Hausdorff olması gerekmeyen X topolojik uzay ları için gerçeltıkızlık kavramının ve vX uzayının bir genelleştirmesi üzerine olan çalışmasına yer verilmiştir. ABSTRACT This work consists of five chapters. In the first chapter several basic concepts such as `zero set`, `ideal`, `weak topology,` `z-filter` and `C, C*-embedded,` are considered. These are important in relating the topological properties of a topological space X with the order and algebraic properties of the rings C(X) and C*(X). In the. second chapter the notions of fixed and free ideal are considered and for a topological space X the fixed maximal ideals in the rings C(X) and C*(X) are characterised. For a compact space X it is noted that the lattice structure of C*(X) determines the topology of X and hence the Banach-Stone Theorem, that the ring C*(X) distinguishes between compact spaces, is obtained. In this chapter residue class rings of C(X) and C*(X) with respect to convex and absolutely convex ideals, and properties of their partial order related with the zero sets of X are also mentioned. In the third chapter the Stone-Cech compactification (3X of a completely reg ular space X is obtained, in terms of the zero sets of X and the algebraic structure of C(X), as the unique compactification of X in which X is C*-embedded. In this chapter the structure spaces of the rings C and C* under the Stone topology are also considered and used to provide a model of SX up to isomorphism. The notion of realcompactness, which forms the main topic of this work, and Hewitt's Isomorphism Theorem, which states that realcompact spaces are distin guished by the lattice structure of the ring C(X), is discussed in Chapter Four. In this chapter the space vX, known as the Hewitt realcompactification of X, is obtained as the unique realcompactification of the completely regular space X in which X is C-embedded, and various characterizations are mentioned. General properties of realcompact spaces are also given in this chapter with the help of the space vX. In the final chapter mention is made of characterizations of realcompactness given by several authors. Also, direct sums of realcompact spaces and results and counterexamples concerning the preservation of realcompactness under mappings having various properties are discussed. Finally, the generalization of the notion of realcompactness to topological spaces X which are not necessarily Hausdorff or completely regular given by Mandelker (1971) is given and properties of the generalised realcompactification vX are considered. 157