On the isotropy of continuized dislocated crystals. I. The isotropic lattice distortion

The geometrical theory of continuous distributions of dislocations traditionally neglects the dependence of a distribution of dislocations on the existence of point defects created by this distribution (e.g., due to intersections of dislocation lines). In this paper the influence of such point defects on metric properties of the continuized dislocated Bravais crystalline structure is assumed to be isotropic. The influence of the point defects on the distribution of dislocations is then modeled by treating dislocations as those located in a conformally flat space. This approach leads (among others) to new results concerning the geometry of glide surfaces.     

Dislocation-related photoluminescence in silicon

Photoluminescence is studied in silicon, deformed in a well-defined and reproducible way. Usual deformation conditions (high temperature, low stress) result in sharp spectra of the D1 through D4 lines as recently described in the literature. New lines D5 and D6 emerge for predeformation as above and subsequent low-temperature, high-stress deformation. Another new sharp line, D12, is observed when both the familiar and the novel lines appear simultaneously. Annealing for 1 h atT _A 300 °C causes all new lines to disappear and the D1–D4 spectra to reappear. Quantitative annealing and TEM micrographs suggest that D5 is related to straight dislocations and D6 to stacking faults, whereas D1–D4 are due to relaxed dislocations. Photoluminescence under uniaxial stress shows that D1/D2 originate in tetragonal defects with random orientation relative to 100 directions, whereas D6 stems from triclinic centers, preferentially oriented — as are the D3/D4 centers. We conclude that the D3/D4 and the D5 and D6 defects are closely related, whereas the independent D1/D2 centers might be deformation-produced point defects in the strain region of dislocations.     

The incorporation of slip dislocations in twins

The conditions for the incorporation of slip dislocations either propagating into a twin or engulfed by a growing twin are studied from the geometrical point of view. The resulting dislocation formed in a twin is independent of the mechanism of the incorporation. Under suitable conditions no stacking faults are formed at the twin boundary. The decomposition of twinning dislocations forming the noncoherent twin boundary is described using complementary partial twinning dislocations. The theory is formulated for both type I and II twins. Compound twins are also briefly treated in the discussion. Using the tensor notation all the formulae are given in the form valid for all crystal structures.The author is greatly indebted to Mr. J. Koík for many helpful comments.     

β—SiC外延层中晶体缺陷的观察

用腐蚀法研究了β-SiC外延层中的晶体缺陷。腐蚀剂为熔融氢氧化钾。三角形尖底蚀坑对应于位错。在β-SiC中的全位错为立方晶系的73°位错和60°位错。不同堆垛方式的β-siC生长层相遇时将形成{111}交界层错,其腐蚀图象为平行于<110>方向的直线。60°位错可分解为两个1/6<112>SchockLey不全位错,并夹着一片{111}层错构成扩展位错。三个1/6<110>压杆位错与三片{111}层错可构成层错锥体。正、反堆垛的β-SiC可形成尖晶石律双晶,双晶面为(111)。腐蚀法和X射线劳厄法证实了这种双晶的存在。 关键词：     

X-ray line profile analysis of dislocations and stacking faults in deformed copper

Dislocation configurations and stacking faults in commercial copper rods after 20% and 70% cold-rolling, fatigue and unidirectional tension here studied by x-ray line profile analysis. The analysis of dislocation is based on the Stokes method, the Warren-Averbach analysis and the Wilkens theory for Gaussian or mixed type of strain broadening profiles. For the Cauchy type the range of stress field of dislocations is small, and a model of regular distribution of dislocation dipoles is proposed instead of the Wilkens model of a restrictedly random distribution of dislocations. Due to the obvious texture in all four kinds of deformed samples, the possible glide systems are obtained by using a biaxial stress system. The analysis of stacking faults is based on theories of Patterson, Warren, and Wagner by measuring profile peak shifts, asymmetry and broadening. The broadening due to perfect dislocations and stacking faults can easily be separated. The configuration parameters and density of dislocations, the probabilities of intrinsic, extrinsic and twin stacking faults were deduced in all cases.     

Investigation of V-shaped extended defects in a 4H–SiC epitaxial film

Abstract

We investigated two types of V-shaped extended defects on the basal plane in epitaxial 4H-SiC by synchrotron X-ray topography, photoluminescence imaging/spectroscopy and transmission electron microscopy (TEM). One is the (2, 5) stacking fault (in Zhdanov notation) bounded by two partial dislocations with the Burgers vector b ± 1/4[0?0?0?1]; the other is the (2, 3, 3, 5) stacking fault bounded by partial dislocations with b = ±1/4[0?0?0?1]. The core of the partial dislocations associated with the (2, 3, 3, 5) fault has an out-of-plane component (Frank component) and three in-plane components (Shockley components); the three Shockley components are cancelled out in total. The electronic structures of the (2, 5) and (2, 3, 3, 5) stacking faults were further examined by photoluminescence spectroscopy and first-principles calculations. It is suggested that the (2, 5) and (2, 3, 3, 5) stacking faults both have an interband state at a similar energy level, although they differ structurally.     

Correlation between shapes of Shockley stacking faults and structures of basal plane dislocations in 4H-SiC epilayers

Abstract

Shockley-type stacking faults expanded in 4H–SiC epilayers induced by ultraviolet illumination were investigated using a photoluminescence imaging method, a photoluminescence mapping method and X-ray topography. After ultraviolet illumination, more than 30 patterns of Shockley-type stacking faults which expanded from perfect basal plane dislocations were observed by photoluminescence imaging. The initial basal plane dislocations were crystallographically classified, and individual shapes of expanded Shockley-type stacking faults were predicted. The correspondence between the predicted shapes and observed ones was discussed.     

TEM study on relationship between stacking faults and non-basal dislocations in Mg

Recent interest in the study of stacking faults and non-basal slip in Mg alloys is partly based on the argument that these phenomena positively influence mechanical behaviour. Inspection of the published literature, however, reveals that there is a lack of fundamental information on the mechanisms that govern the formation of stacking faults, especially I1-type stacking faults (I1 faults). Moreover, controversial and sometimes contradictory mechanisms have been proposed concerning the interactions between stacking faults and dislocations. Therefore, we describe a fundamental transmission electron microscope investigation on Mg 2.5 at. % Y (Mg–2.5Y) processed via hot isostatic pressing (HIP) and extrusion at 623 K. In the as-HIPed Mg–2.5Y, many 〈c〉 and 〈a〉 dislocations, together with some 〈c + a〉 dislocations were documented, but no stacking faults were observed. In contrast, in the as-extruded Mg–2.5Y, a relatively high density of stacking faults and some non-basal dislocations were documented. Specifically, there were three different cases for the configurations of observed stacking faults. Case (I): pure I2 faults; Case (II): mixture of I1 faults and non-basal dislocations having 〈c〉 component, together with basal 〈a〉 dislocations; Case (III): mixture of predominant I2 faults and rare I1 faults, together with jog-like dislocation configuration. By comparing the differences in extended defect configurations, we propose three distinct stacking fault formation mechanisms for each case in the context of slip activity and point defect generation during extrusion. Furthermore, we discuss the role of stacking faults on deformation mechanisms in the context of dynamic interactions between stacking faults and non-basal slip.     

Photoluminescence in germanium with a quasi-equilibrium dislocation structure

The dislocation-related photoluminescence of n-Ge single crystals with a quasi-equilibrium structure of 60° dislocations is investigated at a temperature of 4.2 K. It is shown that the dislocation-related photoluminescence spectra are described by a set involving from 8 to 13 Gaussian lines with a width of less than 15 meV. With due regard for the data available in the literature, the Gaussian lines with maxima at energies in the range 0.47 < E _m ≤ 0.55 eV are assigned to the emission of 90° Shockley partial dislocations involved in quasiequilibrium segments of 60° dislocations with different values of the stacking fault width Δ (Δ = Δ₀, Δ < Δ₀, and Δ > Δ₀). It is revealed that the d8 line at the energy E _m = 0.513 eV, which corresponds to the emission of straight segments with the equilibrium stacking fault width Δ₀, dominates in the photoluminescence spectra only at dislocation densities N _D < 10⁶ cm^?2. As the dislocation density N _D increases, the intensity of the d8 line decreases with the d7 line (E _m ≈ 0.507 eV) initially and the d7 and d6 lines (E _m ≈ 0.501 eV) then becoming dominant in the photoluminescence spectrum. The d7 and d6 lines are attributed to the emission of segments with stacking fault widths Δ < Δ₀. Possible factors responsible for the formation of stacking faults with particular widths Δ ≠ Δ₀ for quasi-equilibrium dislocations are discussed.     

Equilibrium configurations of partial misfit dislocations in thin-film heterosystems

The energy characteristics of orthogonal rows of partial misfit dislocations with V-shaped stacking faults in thin-film heteroepitaxial systems are analyzed theoretically. It is shown that they should appear only in very thin epitaxial films of nanoscopic thickness and for high values of the mismatch exceeding a definite value. Under these conditions partial misfit dislocations associated with V-shaped stacking faults are typical elements of the defect structure of nanolayer heterosystems. For smaller mismatches and larger films thicknesses total misfit dislocations should form. Fiz. Tverd. Tela (St. Petersburg) 40, 2059–2064 (November 1998)     

Molecular dynamic studies of the interaction of a/6⟨112⟩ Shockley dislocations with stacking fault tetrahedra in copper. Part II: Intersection of stacking fault tetrahedra by moving twin boundaries

The interactions of moving twin boundaries with stacking fault tetrahedra (SFTs) have been studied by molecular dynamics. The results reveal a spectrum of processes occurring during these interactions. In general, they lead to damage of the parent SFT and formation of new defects in the twin lattice. The character of these defects depends on the nature of the twinning front, the size of the SFT and its orientation with respect to incoming dislocations. Typical structures that may be produced in the twin include product-SFTs, free vacancies, planar stacking faults bounded by partial dislocations, mutually linked stacking faults on non-coplanar {111} _T planes, small {111} _T tetrahedra and their partial forms. Dislocation mechanisms involved in the formation of these defects are being analyzed.     

Unconventional properties of dislocations in quasicrystals

Dislocations in quasicrystals are defined as the intersections of dislocations in a high dimensional lattice with an irrational cut which figures the physical space. This definition confers to them a number of unusual geometrical properties which can be studied either by suitable extensions of the Volterra process, or by topological approaches, which often offer complementary points of view and are presented in this paper. Amongst these unusual properties, the production of stacking faults under shear at low temperature, reshuffling processes on stacking faults, and properties of non-commutativity which could have some incidences on the interplay between dislocations in deformation processes are mentioned.Dedicated to Dr. Frantiek Kroupa in honour of his 70^th birthday.Unité de Recherche Associée 009 du CNRS, associée aux Universités de Paris VI at Paris VIIWe are very grateful to Dr. Vladimir Dmitrienko for discussions and useful remarks.     

Monazite (monoclinic LaPO4) slip systems at room temperature

Polycrystalline monazite (monoclinic LaPO₄) was deformed by spherical indentation at room temperature. Slip systems were identified using TEM of thin sections prepared parallel and close to the indented surface. Dislocation Burgers vectors (b) were identified by Burgers circuit closure in high resolution TEM images, supplemented by diffraction contrast where possible. A total of 441 b determinations were made in 97 grains. The most common slip systems were [001]/(010), [100]/(010) and [010]/(100). Slip on (001) was less common. Many other less common slip systems and Burgers vectors were also identified, including b = [101], [101], [011], [110] and [111]. b = [101] dislocations dissociate into ½[101] partials, and b = [101] dislocations are inferred to dissociate to ½[101] partials, with a low energy stacking fault of ～30 mJ/m². b = [100] dislocations may dissociate into ¼[210] + ¼[210] partials. b = [010] may sometimes dissociate to ½[010] + ½[010] partials. Other types of partial dislocations were also observed and discussed. All partial dislocations were climb dissociated. The line energies of monazite dislocations and their partials were calculated, and stacking fault structures for partial dislocations are analyzed. Satisfaction of the Von Mises criterion for full ductility most likely involves [101]/(111) and ?011?/{011} or {111} slip, but other combinations that require both b = [101] and ?011? or ?110? are possible. If deformation twinning is active, slip systems with b = ?011? or ?110? may not be necessary for full ductility.     

Strain relaxation in epitaxial GaAs/Si (0 0 1) nanostructures

Abstract

Crystal defects, present in ~100 nm GaAs nanocrystals grown by metal organic vapour phase epitaxy on top of (0 0 1)-oriented Si nanotips (with a tip opening 50–90 nm), have been studied by means of high-resolution aberration-corrected high-angle annular dark-field scanning transmission electron microscopy. The role of 60° perfect, 30° and 90° Shockley partial misfit dislocations (MDs) in the plastic strain relaxation of GaAs on Si is discussed. Formation conditions of stair-rod dislocations and coherent twin boundaries in the GaAs nanocrystals are explained. Also, although stacking faults are commonly observed, we show here that synthesis of GaAs nanocrystals with a minimum number of these defects is possible. On the other hand, from the number of MDs, we have to conclude that the GaAs nanoparticles are fully relaxed plastically, such that for the present tip sizes no substrate compliance can be observed.     

A priori probability and localized observers

A physical and mathematical framework for the analysis of probabilities in quantum theory is proposed and developed. One purpose is to surmount the problem, crucial to any reconciliation between quantum theory and space-time physics, of requiring instantaneous wave-packet collapse across the entire universe. The physical starting point is the idea of an observer as an entity, localized in space-time, for whom any physical system can be described at any moment, by a set of (not necessarily pure) quantum states compatible with his observations of the system at that moment. The mathematical starting point is the theory of local algebras from axiomatic relativistic quantum field theory. A function defining thea priori probability of mistaking one local state for another is analysed. This function is shown to possess a broad range of appropriate properties and to be uniquely defined by a selection of them. Through a general model for observations, it is argued that the probabilities defined here are as compatible with experiment as the probabilities of conventional interpretations of quantum mechanics but are more likely to be compatible, not only with modern developments in mathematical physics, but also with a complete and consistent theory of measurement.