Topological defects in crystals: A density-wave theory

A new approach for describing dislocations and other topological defects in crystals, based on the density wave theory of Ramakrishnan and Yussouff is presented. Quantitative calculations are discussed in brief for the order parameter profiles, the atomic configuration and the free energy of a screw dislocation with Burgers vector b = (a/2, a/2,a/2 ) in a bcc solid. Our results for the free energy of the dislocation in a crystal of sizeR, when expressed as (λb 2/4π) ln (αR/|b|) whereλ is the shear elastic constant, yield, for example, the valueα ⋍ 1·85 for sodium at its freezing temperature (371°K). The density distribution in the presence of the dislocation shows that the dislocation core has a columnar character. To our knowledge, this study represents the first calculation of dislocation structure, including the core, within the framework of an order parameter theory incorporating thermal effects.

Density-wave theory of dislocations in crystals

The density-wave theory of Ramakrishnan and Yussouff is extended to provide a scheme for describing dislocations and other topological defects in crystals. Quantitative calculations are presented for the order-parameter profiles, the atomic configuration, and the free energy of a screw dislocation with Burgers vector b=(a/2, a/2, a/2) in a bcc solid. These calculations are done using a simple parametrization of the direct correlation function and a gradient expansion. It is conventional to express the free energy of the dislocation in a crystal of size R as (λb2/4π)ln(αR/‖b‖), where λ is the shear elastic constant, and α is a measure of the core energy. Our results yield for Na the value α≃1.94a/(‖c1’’‖)1/2 (≃1.85) at the freezing temperature (371 K) and α≃2.48a/(‖c1’’‖)1/2 at 271 K, where c1’’ is the curvature of the first peak of the direct correlation function c(q). Detailed results for the density distribution in the dislocation, particularly the core region, are also presented. These show that the dislocation core has a columnar character. To our knowledge, this study represents the first calculation of dislocation structure, including the core, within the framework of an order-parameter theory and incorporating thermal effects.

Defects in U3+: CaF2 single crystals grown under different conditions by the temperature gradient technique

Defects in as-grown U3+ : CaF2 crystals grown with or without PbF2 as an oxygen scavenger were studied using Raman spectra, thermoluminescence glow curves, and additional absorption (AA) spectra induced by heating and gamma-irradiation. The effects of heating and irradiation on as-grown U3+: CaF2 crystals are similar, accompanied by the elimination of H-type centers and production of F-type centers. U3+ is demonstrated to act as an electron donor in the CaF2 lattice, which is oxidized to the tetravalent form by thermal activation or gamma-irradiation. In the absence of PbF(2)as an oxygen scavenger, the as-grown U3+:CaF2 crystals contain many more lattice defects in terms of both quantity and type, due to the presence of O2- impurities. Some of these defects can recombine with each other in the process of heating and gamma-irradiation. (c) 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Tentative analysis of Swirl defects in silicon crystals

Swirl defects in dislocation-free Czochralski (CZ) silicon crystals have been investigated by preferential etching, transmission electron microscopy (TER I) and electron energy loss spectroscopy (EELS) mode of a scanning transmission electron microscope (STEM). Two kinds of Swirl defects have been found with a good correspondence between striated pattern consisting of hillocks and the buried micro-defects. The Swirl defects were identified as perfect dislocation loop cluster and tetrahedral precipitate, respectively. In addition, a kind of tiny micro-defects is found to be distributed preferentially in the vicinity of the Swirl pattern although there is no detectable correspondence between hillocks and the micro-defects. The energy-filtered images have been obtained by the plasma peaks at different parts of a coherent precipitate with the Si matrix. The experimental results show some indications of the existence of oxygen and carbon in the core of the precipitate and suggest that oxygen and carbon may play important roles in the formation of Swirl defect. (C) 2000 Elsevier Science B.V. All rights reserved.

Defects in Self Assembled Colloidal Crystals

Colloidal self assembly is an efficient method for making 3-D ordered nanostructures suitable for materials such as photonic crystals and macroscopic solids for catalysis and sensor applications. Colloidal crystals grown by convective methods exhibit defects on two different scales. Macro defects such as cracks and void bands originate from the dynamics of meniscus motion during colloidal crystal growth while micro defects like vacancies, dislocation and stacking faults are indigenous to the colloidal crystalline structure. This paper analyses the crystallography and energetics of the microscopic defects from the point of view of classical thermodynamics and discusses the strategy for the control of the macroscopic defects through optimization of the liquid-vapor interface.

Toward an understanding of intermediate- and short-range defects in ZnO single crystals. A combined experimental and theoretical study

A joint use of experimental and theoretical techniques allows us to understand the key role of intermediate- and short-range defects in the structural and electronic properties of ZnO single crystals obtained by means of both conventional hydrothermal and microwave-hydrothermal synthesis methods. X-ray diffraction, Raman spectra, photoluminescence, scanning electronic and transmission electron microscopies were used to characterize the thermal properties, crystalline and optical features of the obtained nano and microwires ZnO structures. In addition, these properties were further investigated by means of two periodic models, crystalline and disordered ZnO wurtzite structure, and first principles calculations based on density functional theory at the B3LYP level. The theoretical results indicate that the key factor controlling the electronic behavior can be associated with a symmetry breaking process, creating localized electronic levels above the valence band.

Defects in thermosensitive colloidal crystals

Poly-N-Isopropylacrylamide (PNIPAM) colloidal particles form crystal phases that show a thermosensitive behaviour and can be used as atomic model systems. This polymer has both hydrophilic and hydrophobic character and has interesting stimuli-responsive properties in aqueous solution, of which the most important is the temperature response. Above a certain temperature, called Lower Critical Solution Temperature (LCST), the system undergoes a volume phase transition (VPT). Above the LCST, the water is expelled from the polymer network and the swollen state at low temperature transforms into a shrunken state at high temperature. The thermoresponsive behaviour of PNIPAM can be influenced by pH and ionic strength, as well as by the presence of copolymers, such as acrylic acid. In a system formed both by particles of PNIPAM and PNIPAM doped with acrylic acid, one can control the size ratio of the two components by changing the temperature of the mixture, while keeping particle interactions relatively the same. It is therefore possible to obtain thermoresponsive colloidal crystal in which temperature changes induce defects whose formation processes and dynamics can be analysed in an optical microscope at a convenient spatial and temporal scale. The goal of this thesis project was to find the conditions in which such a system could be formed, by using characterization techniques such as Static Light Scattering, Dynamic Light Scattering and Confocal Laser Scanning Microscopy. Two PNIPAM-AAc systems were available, and after characterization it was possible to select a suitable one, on the basis of its low polydispersity and the lack of a VPT, regardless of the external conditions (system JPN_7). The synthesis of a PNIPAM system was attempted, with particles of dimensions matching the JPN_7 system and, unlike JPN_7, displaying a VPT, and one suitable candidate for the mixed system was finally found (system CB_5). The best conditions to obtain thermoresponsive crystal were selected, and the formation and healing of defects were investigated with CLSM temperature scans. The obtained results show that the approach is the correct one and that the present report could represent a useful start for future developments in defect analysis and defect dynamics studies.

Designed functional defects in colloidal photonic crystals: switching, biomonitoring and modified photoluminescence

Es werden zwei komplementäre "bottom-up" Methoden präsentiert, die den kontrollierten Einbau von "intelligenten" planaren Defekten in selbstorganisierte kolloidale photonische Kristalle (KPKs) ermöglichen. Die Defektschicht basiert auf einem funktionellen, nanometer-skalierten dünnen Film, der entweder durch schichtweise ("layer-by-layer") Selbstorganisation und Mikrokontakttransferübertragung oder durch Aufschleudern und einer KPK-Opferfüllung hergestellt wird. Die entwickelten Techniken gestatten die Integration von maßgeschneiderten dünnen Defektfilmen bestehend aus einer enorm großen Vielfalt an Materialien; sie sind kostengünstig und können im größeren Maßstab angewendet werden. Optische Untersuchungen zeigen einen engen, durch den Defekt hervorgerufenen Transmissionszustand in der photonischen Bandlücke. Die Defektwellenlänge hängt von der optischen Dicke der Defektschicht ab. Aktives Schalten der Defektwellenlänge wird erreicht, indem Defektschichten aus Makromolekülen hergestellt werden, die über externe Erreger wie Licht, Temperatur, Redoxzyklen und mechanischen Druck adressiert werden können. Die Ergebnisse der Untersuchungen sind im Einklang mit separat durchgeführten Ellipsometrie-Messungen und theoretischen "scalar wave approximation"-Berechnungen. Darüber hinaus werden KPKs mit funktionellen biomolekularen Defekten vorgestellt. Über Verschiebungen der Defektmode können DNA-Konformationsänderungen, die enantioselektive Einlagerung eines chiralen Antitumormedikaments sowie Enzymaktivitäten optisch beobachtet werden. Die Einlagerung von fluoreszierenden Farbstoffen und Quantenpunkten in Defekt-KPKs führt zu einer eindeutigen, durch die photonische Bandlücke und den Defektzustand hervorgerufenen Modifizierung der Photolumineszenz (PL)-Spektren. Schaltbare PL-Modifizierungen werden detektiert, wenn adressierbare Defekt-KPKs verwendet werden.

X-ray Topographic Assessment of Dislocations in Crystals Grown from Solution

Crystals growing from solution, the vapour phase and from supercooled melt exhibit, as a rule, planar faces. The geometry and distribution of dislocations present within the crystals thus grown are strongly related to the growth on planar faces and to the different growth sectors rather than the physical properties of the crystals and the growth methods employed. As a result, many features of generation and geometrical arrangement of defects are common to extremely different crystal species. In this paper these commoner aspects of dislocation generation and configuration which permits one to predict their nature and distribution are discussed. For the purpose of imaging the defects a very versatile and widely applicable technique viz. x-ray diffraction topography is used. Growth dislocations in solution grown crystals follow straight path with strongly defined directions. These preferred directions which in most cases lie within an angle of ±15° to the growth normal depend on the growth direction and on the Burger's vector involved. The potential configuration of dislocations in the growing crystals can be evaluated using the theory developed by Klapper which is based on linear anisotropic elastic theory. The preferred line direction of a particular dislocation corresponds to that in which the dislocation energy per unit growth length is a minimum. The line direction analysis based on this theory enables one to characterise dislocations propagating in a growing crystal. A combined theoretical analysis and experimental investigation based on the above theory is presented.

Fe-diffusion-induced defects in InP annealed in iron phosphide ambient

Photoluminescence (PL) and photo induced current transient spectroscopy (PICTS) have been used to study deep levels in semi-insulating (SI) InP prepared by annealing undoped InP in pure phosphorus (PP) and iron phosphide (IP) ambient. Defects are much fewer in IP SI-InP than in PP SI-InP. Deep-level-related PL emission could only be detected in IP SI-InP. The results indicate that Fe diffusion inhibits the thermal formation of a number of defects in annealed InP. A complex defect has been formed in the annealing process in the presence of Fe.

Point defects in III-V compound semiconductors

Point defects in III-V compound semiconductors were analyzed systematically in this paper. The effects of substitutes, antisites, interstitials, and vacancies on lattice parameters in III-V compound semiconductors were calculated with a simple model. The formation energies of vacancies in compound semiconductors can be obtained by this calculation. A practical technique established on this model has been utilized for measuring the stoichiometry in GaAs. The relationship between stoichiometry and deep level centers in GaAs was also investigated.

Stoichiometric defects in semi-insulating GaAs

The influences of arsenic interstitials and dislocations on the lattice parameters of undoped semi-insulating (SI) GaAs single crystals were analyzed. It was shown that the dislocations in such crystals serve as effective gettering sites for arsenic interstitials due to the deformation energy of dislocations. The average excess arsenic in GaAs epilayers grown by molecular-beam epitaxy (MBE) at low temperatures (LT) is about 1%, and the lattice parameters of these epilayers are larger than those of liquid-encapsulated Czochralski-grown (LEG) SI-GaAs by about 0.1%. The atomic ratio, [As]/([Ga] + [As]), in SI-GaAs grown by low-pressure (LP) LEC is the nearest to the strict stoichiometry compared with those grown by high-pressure (HP) LEC and vertical gradient freeze (VGF). After multiple wafer annealing (MWA), the crystals grown by HPLEC become closer to be strictly stoichiometric.

Spontaneous nucleation of structural defects in inhomogeneous ion chains

Structural defects in ion crystals can be formed during a linear quench of the transverse trapping frequency across the mechanical instability from a linear chain to a zigzag structure. The density of defects after the sweep can be conveniently described by the Kibble-Zurek mechanism (KZM). In particular, the number of kinks in the zigzag ordering can be derived from a time-dependent Ginzburg-Landau equation for the order parameter, here the zigzag transverse size, under the assumption that the ions are continuously laser cooled. In a linear Paul trap, the transition becomes inhomogeneous, since the charge density is larger in the center and more rarefied at the edges. During the linear quench, the mechanical instability is first crossed in the center of the chain, and a front, at which the mechanical instability is crossed during the quench, is identified that propagates along the chain from the center to the edges. If the velocity of this front is smaller than the sound velocity, the dynamics become adiabatic even in the thermodynamic limit and no defect is produced. Otherwise, the nucleation of kinks is reduced with respect to the case in which the charges are homogeneously distributed, leading to a new scaling of the density of kinks with the quenching rate. The analytical predictions are verified numerically by integrating the Langevin equations of motion of the ions, in the presence of a time-dependent transverse confinement. We argue that the non-equilibrium dynamics of an ion chain in a Paul trap constitutes an ideal scenario to test the inhomogeneous extension of the KZM, which lacks experimental evidence to date.

X-ray and gamma irradiation effects on dipole defects in CaF2 : La, Yb, Al

Impurity-interstitial dipoles in calcium fluoride solutions with Al3+, Yb3+ and La3+ fluorides were studied using the thermally stimulated depolarization current (TSDC) technique. The dipolar complexes are formed by substitutional trivalent ions in Ca2+ sites and interstitial fluorine in nearest neighbor sites. The relaxations observed at 150 K are assigned to dipoles nnR(S)(3+)- F-i(-) (R-S = La or Yb). The purpose of this work is to study the processes of energy storage in the fluorides following X-ray and gamma irradiation. Computer modelling techniques are used to obtain the formation energy of dipole defects. (C) 2007 Elsevier Ltd. All rights reserved.