An elastoplastic theory of dislocations as a physical field theory with torsion

We consider a static theory of dislocations with moment stress in an anisotropic or isotropic elastoplastical material as a T(3)-gauge theory. We obtain Yang-Mills type field equations which express the force and the moment equilibrium. Additionally, we discuss several constitutive laws between the dislocation density and the moment stress. For a straight screw dislocation, we find the stress field which is modified near the dislocation core due to the appearance of moment stress. For the first time, we calculate the localized moment stress, the Nye tensor, the elastoplastic energy and the modified Peach-Koehler force of a screw dislocation in this framework. Moreover, we discuss the straightforward analogy between a screw dislocation and a magnetic vortex. The dislocation theory in solids is also considered as a three-dimensional effective theory of gravity.Comment: 38 pages, 6 figures, RevTe

Stress-free states of continuum dislocation fields: Rotations, grain boundaries, and the Nye dislocation density tensor

We derive general relations between grain boundaries, rotational deformations, and stress-free states for the mesoscale continuum Nye dislocation density tensor. Dislocations generally are associated with long-range stress fields. We provide the general form for dislocation density fields whose stress fields vanish. We explain that a grain boundary (a dislocation wall satisfying Frank's formula) has vanishing stress in the continuum limit. We show that the general stress-free state can be written explicitly as a (perhaps continuous) superposition of flat Frank walls. We show that the stress-free states are also naturally interpreted as configurations generated by a general spatially-dependent rotational deformation. Finally, we propose a least-squares definition for the spatially-dependent rotation field of a general (stressful) dislocation density field.Comment: 9 pages, 3 figure

A gauge theoretic approach to elasticity with microrotations

We formulate elasticity theory with microrotations using the framework of gauge theories, which has been developed and successfully applied in various areas of gravitation and cosmology. Following this approach, we demonstrate the existence of particle-like solutions. Mathematically this is due to the fact that our equations of motion are of Sine-Gordon type and thus have soliton type solutions. Similar to Skyrmions and Kinks in classical field theory, we can show explicitly that these solutions have a topological origin.Comment: 15 pages, 1 figure; revised and extended version, one extra page; revised and extended versio

Volterra Distortions, Spinning Strings, and Cosmic Defects

Cosmic strings, as topological spacetime defects, show striking resemblance to defects in solid continua: distortions, which can be classified into disclinations and dislocations, are line-like defects characterized by a delta function-valued curvature and torsion distribution giving rise to rotational and translational holonomy. We exploit this analogy and investigate how distortions can be adapted in a systematic manner from solid state systems to Einstein-Cartan gravity. As distortions are efficiently described within the framework of a SO(3) {\rlap{\supset}\times}} T(3) gauge theory of solid continua with line defects, we are led in a straightforward way to a Poincar\'e gauge approach to gravity which is a natural framework for introducing the notion of distorted spacetimes. Constructing all ten possible distorted spacetimes, we recover, inter alia, the well-known exterior spacetime of a spin-polarized cosmic string as a special case of such a geometry. In a second step, we search for matter distributions which, in Einstein-Cartan gravity, act as sources of distorted spacetimes. The resulting solutions, appropriately matched to the distorted vacua, are cylindrically symmetric and are interpreted as spin-polarized cosmic strings and cosmic dislocations.Comment: 24 pages, LaTeX, 9 eps figures; remarks on energy conditions added, discussion extended, version to be published in Class. Quantum Gra

First-principles calculation of intrinsic defect formation volumes in silicon

We present an extensive first-principles study of the pressure dependence of the formation enthalpies of all the know vacancy and self-interstitial configurations in silicon, in each charge state from -2 through +2. The neutral vacancy is found to have a formation volume that varies markedly with pressure, leading to a remarkably large negative value (-0.68 atomic volumes) for the zero-pressure formation volume of a Frenkel pair (V + I). The interaction of volume and charge was examined, leading to pressure--Fermi level stability diagrams of the defects. Finally, we quantify the anisotropic nature of the lattice relaxation around the neutral defects.Comment: 9 pages, 9 figure

Geometric Measure of Indistinguishability for Groups of Identical Particles

The concept of p-orthogonality (1=< p =< n) between n-particle states is introduced. It generalizes common orthogonality, which is equivalent to n-orthogonality, and strong orthogonality between fermionic states, which is equivalent to 1-orthogonality. Within the class of non p-orthogonal states a finer measure of non p-orthogonality is provided by Araki's angles between p-internal spaces. The p-orthogonality concept is a geometric measure of indistinguishability that is independent of the representation chosen for the quantum states. It induces a new hierarchy of approximations for group function methods. The simplifications that occur in the calculation of matrix elements between p-orthogonal group functions are presented

Aharonov-Bohm Effect and Disclinations in an Elastic Medium

In this work we investigate quasiparticles in the background of defects in solids using the geometric theory of defects. We use the parallel transport matrix to study the Aharonov-Bohm effect in this background. For quasiparticles moving in this effective medium we demonstrate an effect similar to the gravitational Aharonov- Bohm effect. We analyze this effect in an elastic medium with one and $N$ defects.Comment: 6 pages, Revtex

Lithotectonic elements and geological events in the Hengshan-Wutai-Fuping belt: A synthesis and implications for the evolution of the Trans-North China Orogen

The Hengshan-Wutai-Fuping belt is located in the middle segment of the Trans-North China Orogen, a Palaeoproterozoic continental collisional belt along which the Eastern and Western blocks amalgamated to form the North China Craton. The belt consists of the medium- to high-grade Hengshan and Fuping gneiss complexes and the intervening low- to medium-grade Wutai granite-greenstone terrane, and most igneous rocks in the belt are calc-alkaline and have affinities to magmatic arcs. Previous tectonic models assumed that the Hengshan and Fuping gneiss assemblages were an older basement to the Wutai supracrustal rocks, but recent studies indicate that the three complexes constitute a single, long-lived Neoarchaean to Palaeoproterozoic magmatic arc where the Wutai Complex represents an upper crustal domain, whereas the Hengshan and Fuping gneisses represent the lower crustal components forming the root of the arc. The earliest arc-related magmatism in the belt occurred at 2560-2520 Ma, marked by the emplacement of the Wutai granitoids, which was followed by arc volcanism at 2530-2515 Ma, forming the Wutai greenstones. Extension driven by widespread arc volcanism led to the development of a back-arc basin or a marginal sea, which divided the belt into the Hengshan-Wutai island arc (Japan-type) and the Fuping relict arc. At 2520-2480 Ma, subduction beneath the Hengshan-Wutai island arc caused partial melting of the lower crust to form the Hengshan tonalitic-trondhjemitic-granodioritic (TTG) suites, whereas eastward-directed subduction of the marginal sea led to the reactivation of the Fuping relict arc, where the Fuping tonalitic-trondhjemitic-granodioritic suite was emplaced. In the period 2360-2000 Ma, sporadic phases of isolated granitoid magmatism occurred in the Hengshan-Wutai-Fuping region, forming 2360 Ma, c. 2250 Ma and 2000-2100 Ma granitoids in the Hengshan Complex, the c. 2100 Ma Wangjiahui and Dawaliang granites in the Wutai Complex, and the 2100-2000 Ma Nanying granitoids in the Fuping Complex. At c. 1920 Ma, the Hengshan-Wutai island arc underwent an extensional event, possibly due to the subduction of an oceanic ridge, leading to the emplacement of pre-tectonic gabbroic dykes that were subsequently metamorphosed, together with their host rocks, to form medium- to high-pressure granulites. At 1880-1820 Ma, the Hengshan-Wutai-Fuping arc system was juxtaposed, intensely deformed and metamorphosed during a major and regionally extensive orogenic event, the Lüliang Orogeny, which generated the Trans-North China Orogen through collision of the Eastern and Western blocks. The Hengshan-Wutai-Fuping belt was finally stabilized after emplacement of a mafic dyke swarm at 1780-1750 Ma. © 2007 Cambridge University Press.published_or_final_versio

Disclinations, dislocations and continuous defects: a reappraisal

Disclinations, first observed in mesomorphic phases, are relevant to a number of ill-ordered condensed matter media, with continuous symmetries or frustrated order. They also appear in polycrystals at the edges of grain boundaries. They are of limited interest in solid single crystals, where, owing to their large elastic stresses, they mostly appear in close pairs of opposite signs. The relaxation mechanisms associated with a disclination in its creation, motion, change of shape, involve an interplay with continuous or quantized dislocations and/or continuous disclinations. These are attached to the disclinations or are akin to Nye's dislocation densities, well suited here. The notion of 'extended Volterra process' takes these relaxation processes into account and covers different situations where this interplay takes place. These concepts are illustrated by applications in amorphous solids, mesomorphic phases and frustrated media in their curved habit space. The powerful topological theory of line defects only considers defects stable against relaxation processes compatible with the structure considered. It can be seen as a simplified case of the approach considered here, well suited for media of high plasticity or/and complex structures. Topological stability cannot guarantee energetic stability and sometimes cannot distinguish finer details of structure of defects.Comment: 72 pages, 36 figure

Lithotectonic elements and geological events in the Hengshan-Wutai-Fuping belt: A synthesis and implications for the evolution of the Trans-North China Orogen

The Hengshan-Wutai-Fuping belt is located in the middle segment of the Trans-North China Orogen, a Palaeoproterozoic continental collisional belt along which the Eastern and Western blocks amalgamated to form the North China Craton. The belt consists of the medium- to high-grade Hengshan and Fuping gneiss complexes and the intervening low- to medium-grade Wutai granite-greenstone terrane, and most igneous rocks in the belt are calc-alkaline and have affinities to magmatic arcs. Previous tectonic models assumed that the Hengshan and Fuping gneiss assemblages were an older basement to the Wutai supracrustal rocks, but recent studies indicate that the three complexes constitute a single, long-lived Neoarchaean to Palaeoproterozoic magmatic arc where the Wutai Complex represents an upper crustal domain, whereas the Hengshan and Fuping gneisses represent the lower crustal components forming the root of the arc. The earliest arc-related magmatism in the belt occurred at 2560-2520 Ma, marked by the emplacement of the Wutai granitoids, which was followed by arc volcanism at 2530-2515 Ma, forming the Wutai greenstones. Extension driven by widespread arc volcanism led to the development of a back-arc basin or a marginal sea, which divided the belt into the Hengshan-Wutai island arc (Japan-type) and the Fuping relict arc. At 2520-2480 Ma, subduction beneath the Hengshan-Wutai island arc caused partial melting of the lower crust to form the Hengshan tonalitic-trondhjemitic-granodioritic (TTG) suites, whereas eastward-directed subduction of the marginal sea led to the reactivation of the Fuping relict arc, where the Fuping tonalitic-trondhjemitic-granodioritic suite was emplaced. In the period 2360-2000 Ma, sporadic phases of isolated granitoid magmatism occurred in the Hengshan-Wutai-Fuping region, forming 2360 Ma, c. 2250 Ma and 2000-2100 Ma granitoids in the Hengshan Complex, the c. 2100 Ma Wangjiahui and Dawaliang granites in the Wutai Complex, and the 2100-2000 Ma Nanying granitoids in the Fuping Complex. At c. 1920 Ma, the Hengshan-Wutai island arc underwent an extensional event, possibly due to the subduction of an oceanic ridge, leading to the emplacement of pre-tectonic gabbroic dykes that were subsequently metamorphosed, together with their host rocks, to form medium- to high-pressure granulites. At 1880-1820 Ma, the Hengshan-Wutai-Fuping arc system was juxtaposed, intensely deformed and metamorphosed during a major and regionally extensive orogenic event, the Lüliang Orogeny, which generated the Trans-North China Orogen through collision of the Eastern and Western blocks. The Hengshan-Wutai-Fuping belt was finally stabilized after emplacement of a mafic dyke swarm at 1780-1750 Ma. © 2007 Cambridge University Press.published_or_final_versio