1. |
Łażewski J.^{♦}, Jochym P.T.^{♦}, Piekarz P.^{♦}, Sternik M.^{♦}, Parlinski K.^{♦}, Cholewiński J., Dłużewski P., Krukowski S.^{♦}, DFT modelling of the edge dislocation in 4H-SiC,
JOURNAL OF MATERIALS SCIENCE, ISSN: 0022-2461, DOI: 10.1007/s10853-019-03630-5, Vol.54, No.15, pp.10737-10745, 2019Abstract: We have presented ab initio study, based on density functional theory methods, of full-core edge dislocation impact on basic properties of 4H-SiC semiconductor. To enable calculations in periodic boundary conditions, we have proposed geometry with two dislocations with opposite Burgers vectors. For this geometry, which determines the distance between dislocations, we have estimated the creation energy per unit length of a single-edge dislocation. The radial distribution function has been used to assess the effect of the dislocations on the local crystal structure. The analysis of the electronic structure reveals mid-gap p states induced by broken atomic bonds in the dislocation core. The maps of charge distribution and electrostatic potential have been calculated, and the significant decrease in the electrostatic barriers in the vicinity of the dislocation cores has been quantified. The obtained results have been discussed in the light of previous findings and calculations based mainly on phenomenological models. Affiliations:
Łażewski J. | - | Institute of Nuclear Physics, Polish Academy of Sciences (PL) | Jochym P.T. | - | Institute of Nuclear Physics, Polish Academy of Sciences (PL) | Piekarz P. | - | Institute of Nuclear Physics, Polish Academy of Sciences (PL) | Sternik M. | - | Institute of Nuclear Physics, Polish Academy of Sciences (PL) | Parlinski K. | - | Institute of Nuclear Physics, Polish Academy of Sciences (PL) | Cholewiński J. | - | IPPT PAN | Dłużewski P. | - | IPPT PAN | Krukowski S. | - | Institute of High Pressure Physics, Polish Academy of Sciences (PL) |
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2. |
Jurczak G., Dłużewski P., Finite element modelling of threading dislocation effect on polar GaN/AlN quantum dot,
PHYSICA E-LOW-DIMENSIONAL SYSTEMS & NANOSTRUCTURES, ISSN: 1386-9477, DOI: 10.1016/j.physe.2017.08.018, Vol.95, pp.11-15, 2018Abstract: In this paper the effect of adjacent threading dislocation at the edge of the GaN/AlN quantum dot is analysed by use of the finite element analysis. Elastic as well electric effects related to dislocation core are taken into account. Two types of threading dislocations: edge- and screw-type, common for III-nitride epitaxial layers, are considered. Also, three different QD geometries are considered to estimate the impact of the threading dislocation on the quantum heterostructure. It is demonstrated that the local elastic and electric fields around dislocation affect local piezoelectric fields built-in the quantum dot. Local lattice deformation near the dislocation core reduce residual strains in the quantum dot. It is prominent in the case of edge-type dislocation. The presence of an electric charge along dislocation line provides significant shift of the total potential towards the negative values. However, estimated difference in band-to-band transition energy for edge- and screw-type dislocations are rather small, what suggest low sensitivity to the charge density along dislocation line. Unexpectedly, local strain field around the edge-type dislocation, slightly compensate the negative affect of the electrostatic potential. Keywords: Quantum dot, Threading dislocation, Piezoelectricity, Finite element modelling Affiliations:
Jurczak G. | - | IPPT PAN | Dłużewski P. | - | IPPT PAN |
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3. |
Domagała J.Z.^{♦}, Morelhão S.L.^{♦}, Sarzyński M.^{♦}, Maździarz M., Dłużewski P., Leszczyński M.^{♦}, Hybrid reciprocal lattice: application to layer stress determination in GaAlN/GaN(0001) systems with patterned substrates,
JOURNAL OF APPLIED CRYSTALLOGRAPHY, ISSN: 1600-5767, DOI: 10.1107/S1600576716004441, Vol.49, No.3, pp.798-805, 2016Abstract: Epitaxy of semiconductors is a process of tremendous importance in applied science and in the optoelectronics industry. The control of defects introduced during epitaxial growth is a key point in manufacturing devices of high efficiency and durability. In this work, it is demonstrated how useful hybrid reflections are for the study of epitaxial structures with anisotropic strain gradients due to patterned substrates. High accuracy in detecting and distinguishing elastic and plastic relaxations is one of the greatest advantages of measuring this type of reflection, as well as the fact that the method can be exploited in a symmetric reflection geometry on a commercial high-resolution diffractometer. Keywords: optoelectronics, Group III-nitride semiconductors, epitaxial growth, X-ray multiple diffraction, interface defects Affiliations:
Domagała J.Z. | - | Institute of Physics, Polish Academy of Sciences (PL) | Morelhão S.L. | - | University of Sao Paulo (BR) | Sarzyński M. | - | Military University of Technology (PL) | Maździarz M. | - | IPPT PAN | Dłużewski P. | - | IPPT PAN | Leszczyński M. | - | other affiliation |
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4. |
Jurczak G., Dłużewski P., Finite element modelling of nonlinear piezoelectricity in wurtzite GaN/AlN quantum dots,
COMPUTATIONAL MATERIALS SCIENCE, ISSN: 0927-0256, DOI: 10.1016/j.commatsci.2015.09.024, Vol.111, pp.197-202, 2016Abstract: In this paper we evaluate the effect of higher order elastic and piezoelectric coefficients on elastic and electric fields in III-nitride wurtzite crystals. To this end, finite element calculations of GaN/AlN QDs of different types are presented and compared. We show that the nonlinear elastic and piezoelectric effects modify the elastic strain field, electrostatic potential, and the build-in electric field in the QDs. These higher order effects lead to corrections of the peak values of the strain field and the electrostatic potential over 8% above the linear model. An even more significant effect, exceeding 13%, is observed for the magnitude of the electric field. Our calculations clearly show that the impact of the nonlinear correction strongly depends on the application, i.e. on the morphology and crystallographic orientation of the quantum dot. It turns out that nonlinear effects play an important role in the semipolar (View the MathML source112¯2) and nonpolar (View the MathML source112¯0) QDs. Because of the theoretical nature of physical parameters describing nonlinear material (obtained by DFT calculations) further studies and experimental verification of the nonlinear effects in nitride structures are necessary. Keywords: Piezoelectricity, Heterostructure, Nonlinearity, Quantum dot Affiliations:
Jurczak G. | - | IPPT PAN | Dłużewski P. | - | IPPT PAN |
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5. |
Young T.D., Jurczak G., Lotsari A.^{♦}, Dimitrakopulos G.P.^{♦}, Komninou Ph.^{♦}, Dłużewski P., A study of the piezoelectric properties of semipolar 11(2)over-bar2 GaN/AlN quantum dots,
PHYSICA STATUS SOLIDI B-BASIC SOLID STATE PHYSICS, ISSN: 0370-1972, DOI: 10.1002/pssb.201552156, Vol.252, No.10, pp.2296-2303, 2015Abstract: GaN quantum dots grown in (inline image)’orientated AlN are studied. The inline image-nucleated quantum dots exhibit rectangular- or trapezoid-based truncated pyramidal morphology. Another quantum dot type orientated on inline image is reported. Based on high-resolution transmission microscopy and crystal symmetry, the geometry of inline image-orientated quantum dots is proposed. A piezoelectric model is used within a finite element method to determine and compare the strain-state and electrostatic potential associated with the quantum dot morphology and an estimation of the band-edge energy is made. We report on some novel properties of the inline image-orientated quantum dot, including mixed strain-states and strain-state bowing. Keywords: III–V semiconductors, AlN, GaN, nanostructures, piezoelectric properties, quantum dots Affiliations:
Young T.D. | - | IPPT PAN | Jurczak G. | - | IPPT PAN | Lotsari A. | - | Aristotle University of Thessaloniki (GR) | Dimitrakopulos G.P. | - | Aristotle University of Thessaloniki (GR) | Komninou Ph. | - | Aristotle University of Thessaloniki (GR) | Dłużewski P. | - | IPPT PAN |
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6. |
Cholewiński J., Maździarz M., Jurczak G., Dłużewski P., Dislocation core reconstruction based on finite deformation approach and its application to 4H-SiC crystal,
INTERNATIONAL JOURNAL FOR MULTISCALE COMPUTATIONAL ENGINEERING, ISSN: 1543-1649, DOI: 10.1615/IntJMultCompEng.2014010679, Vol.12, No.5, pp.411-421, 2014Abstract: A proper reconstruction of discrete crystal structure with defects is an important problem in dislocation theory. Currently, procedures for dislocation core reconstruction presented in the literature usually neglect configuration changes. The present paper discusses a new approach, which uses an iterative algorithm to determine an atomistic configuration of the dislocation core. The mathematical background is based on finite deformation theory, in which an iterative algorithm searches for the new atomic configuration corresponding to the actual atomic configuration of the deformed crystal. Its application to the reconstruction of 4H-SiC crystal affected by the system of four threading dislocations is presented as an example. Molecular statics calculations suggest a lower potential energy, as well as dislocation core energy, per-atom energy, and per-atom stresses for the structure reconstructed by use of the iterative algorithm against the classical solution based on the Love's equations. Keywords: dislocation, dislocation core energy, finite deformation, molecular statics Affiliations:
Cholewiński J. | - | IPPT PAN | Maździarz M. | - | IPPT PAN | Jurczak G. | - | IPPT PAN | Dłużewski P. | - | IPPT PAN |
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7. |
Dłużewski P., Cholewiński J., Continuum and atomistic modelling of crystal defects,
Annual Report - Polish Academy of Sciences, ISSN: 1640-3754, pp.80-82, 2013 | |
8. |
Dimitrakopulos G.P.^{♦}, Kalesaki E.^{♦}, Kioseoglou J.^{♦}, Kehagias T.^{♦}, Lotsari A.^{♦}, Lahourcade L.^{♦}, Monroy E.^{♦}, Häusler I.^{♦}, Kirmse H.^{♦}, Neumann W.^{♦}, Jurczak G., Young T.D., Dłużewski P., Komninou Ph.^{♦}, Karakostas T.^{♦}, Morphology and strain of self-assembled semi-polar GaN quantum dots in (1112) AlN,
JOURNAL OF APPLIED PHYSICS, ISSN: 0021-8979, DOI: 10.1063/1.3506686, Vol.108, pp.104304-1-9, 2010Abstract: GaN quantum dots (QDs) grown in semipolar (11-22) AlN by plasma-assisted molecular-beam epitaxy were studied by transmission electron microscopy (TEM) and scanning transmission electron microscopy techniques. The embedded (11-2)-grown QDs exhibited pyramidal or truncated-pyramidal morphology consistent with the symmetry of the nucleating plane, and were delimited by nonpolar and semipolar nanofacets. It was also found that, in addition to the (11-22) surface, QDs nucleated at depressions comprising {10-11} facets. This was justified by ab initio density functional theory calculations showing that such GaN/AlN facets are of lower energy compared to (11-22). Based on quantitative high-resolution TEM strain measurements, the three-dimensional QD strain state was analyzed using finite-element simulations. The internal electrostatic field was then estimated, showing small potential drop along the growth direction, and limited localization at most QD interfaces. Keywords: Quantum dots, Transmission electron microscopy, III-V semiconductors, High resolution transmission electron microscopy, Epitaxy Affiliations:
Dimitrakopulos G.P. | - | Aristotle University of Thessaloniki (GR) | Kalesaki E. | - | Aristotle University of Thessaloniki (GR) | Kioseoglou J. | - | Aristotle University of Thessaloniki (GR) | Kehagias T. | - | Aristotle University of Thessaloniki (GR) | Lotsari A. | - | Aristotle University of Thessaloniki (GR) | Lahourcade L. | - | CNRS (FR) | Monroy E. | - | CNRS (FR) | Häusler I. | - | Humboldt-Universität zu Berlin (DE) | Kirmse H. | - | Humboldt-Universität zu Berlin (DE) | Neumann W. | - | Humboldt-Universität zu Berlin (DE) | Jurczak G. | - | IPPT PAN | Young T.D. | - | IPPT PAN | Dłużewski P. | - | IPPT PAN | Komninou Ph. | - | Aristotle University of Thessaloniki (GR) | Karakostas T. | - | Aristotle University of Thessaloniki (GR) |
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9. |
Dłużewski P., Young T.D., Dimitrakopulos G.^{♦}, Komninou Ph.^{♦}, Continuum and atomistic modelling of the mixed straight dislocation,
INTERNATIONAL JOURNAL FOR MULTISCALE COMPUTATIONAL ENGINEERING, ISSN: 1543-1649, DOI: 10.1615/IntJMultCompEng.v8.i3.80, Vol.8, pp.331-342, 2010Abstract: A continuum and atomistic approach to the modeling of dislocations observed by high-resolution transmission electron microscopy (HRTEM) is discussed in terms of the continuum theory of dislocations. The atomistic models are obtained by means of the use of a mathematical formula for discrete dislocations. A new analytical solution for a continuously distributed dislocation core is presented. This solution is employed in the finite element modeling of residual stresses induced by the net of dislocations visible on an HRTEM image of GaN structure. This paper terminates with some comments on the atomistic/finite-element modeling of dislocation fields. Because of some confusion concerning notations used in the literature, the mathematical foundations of the continuum theory of dislocations are revisited. Keywords: dislocations, field theory, atomistic models, finite element method, high-resolution transmission electron microscopy Affiliations:
Dłużewski P. | - | IPPT PAN | Young T.D. | - | IPPT PAN | Dimitrakopulos G. | - | Aristotle University of Thessaloniki (GR) | Komninou Ph. | - | Aristotle University of Thessaloniki (GR) |
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10. |
Maździarz M., Young T.D., Dłużewski P., Wejrzanowski T.^{♦}, Kurzydłowski K.J.^{♦}, Computer modelling of nanoindentation in the limits of a coupled molecular-statics and elastic scheme,
JOURNAL OF COMPUTATIONAL AND THEORETICAL NANOSCIENCE, ISSN: 1546-1955, DOI: 10.1166/jctn.2010.1469, Vol.7, pp.1-10, 2010Abstract: Our numerical approach to modeling elastic-plastic deformation comes back to the idea of the time-independent plasticity developed here at the molecular-statics level. We use a constitutive atomic model based on the second-moment approximation of the tight-binding potential coupled to a linear theory of elasticity solved simultaneously within the finite element method. Our model is applied to the nanoindentation problem for copper in which the indenter is represented by the equations of a sphere. For convenience the time-dependency of the nanoindentation problem is reduced to a quasi-static adiabatic scheme. A recurring theme in this paper is to determine the response of the proposed model for two differing systems: mono and polycrystalline copper. This paper discusses the force-depth response in terms of atomic bond-lengths, elastic-plastic deformations, and the instantaneous stiffness of the material. We report on an increased instantaneous stiffness of polycrystalline copper compared to that of its monocrystalline counterpart. From both a distinct and a comparative analysis of both systems, based on the relaxed positions of the atoms in the structure during the simulation, we deduce that plastic deformations at grain-boundaries are responsible for this change in the overall instantaneous stiffness of the material. Keywords: linear elasticity, material science, molecular statics, nanoindentation, quasicontinuum methods Affiliations:
Maździarz M. | - | IPPT PAN | Young T.D. | - | IPPT PAN | Dłużewski P. | - | IPPT PAN | Wejrzanowski T. | - | Warsaw University of Technology (PL) | Kurzydłowski K.J. | - | Warsaw University of Technology (PL) |
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11. |
Dłużewski P., Maździarz M., Traczykowski P.^{♦}, Jurczak G., Niihara K.^{♦}, Nowak R.^{♦}, Kurzydłowski K.^{♦}, A hybrid atomistic-continuum finite element modelling of nanoindentation and experimental verification for copper crystal,
COMPUTER ASSISTED METHODS IN ENGINEERING AND SCIENCE, ISSN: 2299-3649, Vol.15, pp.37-44, 2008Abstract: Problem of locally disordered atomic structure is solved by using a hybrid formulation in which nonlinear elastic finite elements are linked with discrete atomic interaction elements. The continuum approach uses nonlinear hyperelasticity based upon the generalized strain while the atomistic approach employs the Tight-Binding Second-Moment Approximation potential to create new type of elements. The molecular interactions yielding from constitutive models of TB-SMA were turned into interactions between nodes to solve a boundary value problem by means of finite element solver.
In this paper we present a novel way of modelling materials behaviour where both discrete (molecular dynamics) and continuum (nonlinear finite element) methods are used. As an example, the nanoindentation of a copper sample is modelled numerically by applying a hybrid formulation. Here, the central area of the sample subject to a nanoindentation operation is discretised by an atomic net where the remaining area of the sample far from indenters tip is discretised by the use of a nonlinear finite element mesh. Keywords: Nanostructure, Nanoindentation, Molecular statics, Finite element modelling Affiliations:
Dłużewski P. | - | IPPT PAN | Maździarz M. | - | IPPT PAN | Traczykowski P. | - | Institute of Plasma Physics and Laser Microfusion (PL) | Jurczak G. | - | IPPT PAN | Niihara K. | - | Nagaoka University of Technology (JP) | Nowak R. | - | Foundry Research Institute (PL) | Kurzydłowski K. | - | Warsaw University of Technology (PL) |
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12. |
Young T.D., Kioseoglou J.^{♦}, Dimitrakopulos G.P.^{♦}, Dłużewski P., Komninou Ph.^{♦}, 3D modelling of misfit networks in the interface region of heterostructures,
JOURNAL OF PHYSICS D-APPLIED PHYSICS, ISSN: 0022-3727, DOI: 10.1088/0022-3727/40/13/027, Vol.40, pp.4084-4091, 2007Abstract: We present a methodology for the stress–strain analysis of a film/substrate interface by combining crystallographic and continuum modelling. Starting from measurements of lattice parameters available from experimental observations, the heterostructure is recast initially in the form of a crystallographic model and finally as a continuum elastic model. The derived method is capable of handling dense arrays of misfit dislocations as well as large areas of the interface between two crystal structures. As an application we consider the misfit dislocation network in the GaN/Al2O3 interface region through determination of strain relaxation and associated residual stresses. Our calculated results are referred back to and found to be in good agreement with the experimental observations of misfit dislocation arrays obtained from high resolution transmission electron microscopy. Affiliations:
Young T.D. | - | IPPT PAN | Kioseoglou J. | - | Aristotle University of Thessaloniki (GR) | Dimitrakopulos G.P. | - | Aristotle University of Thessaloniki (GR) | Dłużewski P. | - | IPPT PAN | Komninou Ph. | - | Aristotle University of Thessaloniki (GR) |
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13. |
Kret S.^{♦}, Dłużewski P., Szczepańska A.^{♦}, Żak M.^{♦}, Czernecki R.^{♦}, Kryśko M.^{♦}, Leszczyński M.^{♦}, Maciejewski G., Homogenous indium distribution in InGaN/GaN laser active structure grown by LP-MOCVD on bulk GaN crystal revealed by transmission electron microscopy and X-ray diffraction,
NANOTECHNOLOGY, ISSN: 0957-4484, DOI: 10.1088/0957-4484/18/46/465707, Vol.18, No.46, pp.465707-0, 2007Abstract: We present transmission electron microscopy (TEM) and x-ray quantitative studies of the indium distribution in InxGa1−xN/GaN multiple quantum wells (MQWs) with x = 0.1 and 0.18. The quantum wells were grown by low-pressure metalorganic chemical vapour deposition (LP-MOCVD) on a bulk, dislocation-free, mono-crystalline GaN substrate. By using the quantitative TEM methodology the absolute indium concentration was determined from the 0002 lattice fringe images by the strain measurement coupled with finite element (FE) simulations of surface relaxation of the TEM sample. In the x-ray diffraction (XRD) investigation, a new simulation program was applied to monitor the indium content and lateral composition gradients. We found a very high quality of the multiple quantum wells with lateral indium fluctuations no higher than ΔxL = 0.025. The individual wells have very similar indium concentration and widths over the whole multiple quantum well (MQW) stack. We also show that the formation of 'false clusters' is not a limiting factor in indium distribution measurements. We interpreted the 'false clusters' as small In-rich islands formed on a sample surface during electron-beam exposure. Affiliations:
Kret S. | - | Institute of Physics, Polish Academy of Sciences (PL) | Dłużewski P. | - | IPPT PAN | Szczepańska A. | - | other affiliation | Żak M. | - | other affiliation | Czernecki R. | - | other affiliation | Kryśko M. | - | other affiliation | Leszczyński M. | - | other affiliation | Maciejewski G. | - | IPPT PAN |
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14. |
Dłużewski P., Nonlinear field theory of stress induced interdiffusion and mass transport,
DEFECT AND DIFFUSION FORUM, ISSN: 1662-9507, DOI: 10.4028/www.scientific.net/DDF.264.63, Vol.264, pp.63-70, 2007Abstract: Constitutive equations for interdiffusion and mass transport induced by the stress gradient in crystal lattice is presented in terms of continuum thermodynamics. Only the standard balance laws are analysed for the mass, momentum, moment of momentum, energy and entropy. In consequence the driving forces for interdiffusion of chemical constituents are determined. The forces depend not only on the stress gradient but also on the gradients of chemical components and temperature. The driving forces are used next in constitutive modelling of interdiffusion and mass transport in crystal lattice. Keywords: Chemical Strain, Driving Force, Interdiffusion, Kirkendall Effect, Mass Transport Affiliations:
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15. |
Teisseyre H.^{♦}, Suski T.^{♦}, Łepkowski S.P.^{♦}, Perlin P.^{♦}, Jurczak G., Dłużewski P., Daudin B.^{♦}, Grandjean N.^{♦}, Strong electric field and nonuniformity effects in GaN/AlN quantum dots revealed by high pressure studies,
APPLIED PHYSICS LETTERS, ISSN: 0003-6951, DOI: 10.1063/1.2219381, Vol.89, No.5, pp.51902-1-3, 2006Abstract: The photoluminescence (PL) from GaN quantum dots (QDs) embedded in AlN has been investigated under hydrostatic pressure. The measured pressure coefficient of emitted light energy [dE / dP] shows a negative value, in contrast with the positive pressure coefficient of the GaN band gap. We also observed that increasing pressure leads to a significant decrease of the light emission intensity and an asymmetric broadening of the PL band. All these effects are related to the pressure-induced increase of the built-in electric field. A comparison is made between experimental results and the proposed theoretical model which describes the pressure behavior of nitride QDs. Keywords: III-V semiconductor, Quantum dot, Piezoelectricity, Photoluminescence Affiliations:
Teisseyre H. | - | Institute of Physics, Polish Academy of Sciences (PL) | Suski T. | - | Institute of High Pressure Physics, Polish Academy of Sciences (PL) | Łepkowski S.P. | - | Institute of High Pressure Physics, Polish Academy of Sciences (PL) | Perlin P. | - | Institute of High Pressure Physics, Polish Academy of Sciences (PL) | Jurczak G. | - | IPPT PAN | Dłużewski P. | - | IPPT PAN | Daudin B. | - | CNRS (FR) | Grandjean N. | - | École Polytechnique Federale de Lausanne (CH) |
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16. |
Dłużewski P., Nonlinear field theory of stress induced diffusion in crystalline solids,
DEFECT AND DIFFUSION FORUM, ISSN: 1662-9507, DOI: 10.4028/www.scientific.net/DDF.237-240.107, Vol.237-240, pp.107-114, 2005Keywords: Chemical Strain, Dislocation Climbing, Driving Force, Interdiffusion, Kirkendall Effect, Molar Derivative, Molar Motion, Vacancy Affiliations:
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17. |
Jurczak G., Maciejewski G., Kret S.^{♦}, Dłużewski P., Ruterana P.^{♦}, Modelling of indium rich clusters in MOCVD InxGa1−xN/GaN multilayers,
JOURNAL OF ALLOYS AND COMPOUNDS, ISSN: 0925-8388, DOI: 10.1016/j.jallcom.2004.05.038, Vol.382, No.1-2, pp.10-16, 2004Abstract: Chemical composition in a ternary alloy is examined using a quantitative high resolution transmission electron microscopy, finite element modelling of the thin foil relaxation phenomena and microscopy image simulation. The measurement of local lattice distortion on transmission electron microscopy images is a powerful tool for chemical composition determination. However, for the correct interpretation of the results, one needs to take into account the inhomogeneous relaxation of the sample and the strain averaging across the sample. The 3D finite element modelling of such phenomena have been performed as a function of chemical composition and geometry of an indium rich cluster in a MOCVD InxGa1−xN/GaN quantum well. Lattice distortion field measured on: experimental transmission electron microscopy image and simulated one, obtained on the basis of finite element simulation, are compared. This procedure allows an accurate determination of chemical composition in such heterostructures. Keywords: Indium clusters, Vapour deposition, Transmissionelectron microscopy, Elasticity, Finite element method, Lattice distortion, Image simulation Affiliations:
Jurczak G. | - | IPPT PAN | Maciejewski G. | - | IPPT PAN | Kret S. | - | Institute of Physics, Polish Academy of Sciences (PL) | Dłużewski P. | - | IPPT PAN | Ruterana P. | - | CNRS (FR) |
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18. |
Dłużewski P., Maciejewski G., Jurczak G., Kret S.^{♦}, Laval J.-Y.^{♦}, Nonlinear FE analysis of residual stresses induced by dislocations in heterostructures,
COMPUTATIONAL MATERIALS SCIENCE, ISSN: 0927-0256, DOI: 10.1016/j.commatsci.2003.10.012, Vol.29, No.3, pp.379-395, 2004Abstract: In this paper the field theory of dislocations is used in the finite element analysis of residual stresses in epitaxial layers. By digital processing of the HRTEM image of a GaAs/ZnTe/CdTe system the tensor maps of dislocation distribution are extracted. Such obtained maps are used as the input data to the finite element code. The mathematical foundations of this code are based on the compatibility equations for lattice distortions. The surface tension induced by misfit dislocations is considered here in terms of a 3D boundary-value problem for stress equilibrium in the interfacial zone. The numerical results show how strongly the surface tension depends on the nonlinear elastic behaviour of the crystal structure. Keywords: Microscopy and microanalysis techniques, Nonlinear elasticity, Dislocation structure, Finite element analysis, Residual stresses, Layered structures Affiliations:
Dłużewski P. | - | IPPT PAN | Maciejewski G. | - | IPPT PAN | Jurczak G. | - | IPPT PAN | Kret S. | - | Institute of Physics, Polish Academy of Sciences (PL) | Laval J.-Y. | - | CNRS (FR) |
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19. |
Maciejewski G., Dłużewski P., Nonlinear finite element calculations of residual stresses in dislocated crystals,
COMPUTATIONAL MATERIALS SCIENCE, ISSN: 0927-0256, DOI: 10.1016/j.commatsci.2004.01.027, Vol.30, No.1-2, pp.44-49, 2004Abstract: A finite element algorithm for the determination of both residual stresses and lattice orientation in dislocated crystals is presented. The applied theoretical approach is based on the continuum theory of dislocations. Due to the compatibility condition, an initial plastic distortion field has been used to introduce an elastic incompatibility corresponding to the assumed dislocation density tensor field. The presented method gives the possibility to develop a numerical code suitable for determination of the stress field and lattice orientation. Two numerical examples are given: a low-angle dislocation wall and a subboundary structure. The method can be applied especially to dislocation sets composed of a few groups of monomial dislocations. Affiliations:
Maciejewski G. | - | IPPT PAN | Dłużewski P. | - | IPPT PAN |
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20. |
Ruterana P.^{♦}, Singh P.^{♦}, Kret S.^{♦}, Jurczak G., Maciejewski G., Dłużewski P., Cho H.K.^{♦}, Choi R.J.^{♦}, Lee H.J.^{♦}, Suh E.K.^{♦}, Quantitative evolution of the atomic structure of defects and composition fluctuations at the nanometer scale inside InGaN/GaN heterostructures,
PHYSICA STATUS SOLIDI B-BASIC SOLID STATE PHYSICS, ISSN: 0370-1972, Vol.241, No.12, pp.2643-2648, 2004Abstract: The cover picture of this issue depicts indium composition fluctuations in InGaN/GaN multi quantum wells. The coded color strain distribution (left) was derived from finite element method calculations of the strain relaxation process and high‐resolution transmission electron microscopy (HRTEM) image simulations, superimposed on the HRTEM image of the quantum wells. The possible corresponding shape and εxx strain profiles in the indium rich clusters (right) hint at a concentration close to pure InN in their core. The paper by Pierre Ruterana et al. [1] was presented at the 5th International Symposium on Blue Laser and Light Emitting Diodes (ISBLLED‐2004), held in Gyeongju, Korea, 15–19 March 2004. Keywords: HRTEM, quantum well, composition fluctuation, strain distribution Affiliations:
Ruterana P. | - | CNRS (FR) | Singh P. | - | CNRS (FR) | Kret S. | - | Institute of Physics, Polish Academy of Sciences (PL) | Jurczak G. | - | IPPT PAN | Maciejewski G. | - | IPPT PAN | Dłużewski P. | - | IPPT PAN | Cho H.K. | - | Dong-A University (KR) | Choi R.J. | - | Chonbuk National University (KR) | Lee H.J. | - | Chonbuk National University (KR) | Suh E.K. | - | Chonbuk National University (KR) |
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21. |
Dłużewski P., Jurczak G., Antúnez H.J., Logarithmic strain measure in finite element modelling of anisotropic hyperelastic materials,
Computer Assisted Mechanics and Engineering Sciences, ISSN: 1232-308X, Vol.10, No.1, pp.69-79, 2003Abstract: A new finite element to analyze problems of anisotropic hyperelasticity is presented. The constitutive equations are derived by means of the energy method, which leads to the stress measure conjugate to the logarithmic strain. Equilibrium equation are integrated in the current configuration. Multiplicative instead of additive - decomposition of the time derivative of a strain tensor function is applied as a crucial step that makes possible the formulation for anisotropic hyperelastic materials. Unlike previous known anisotropic large deformation models, the one here presented assures the energy conservation while using the anisotropic elastic constants and the logarithmic strain measure. It is underlined that for the first time a model including all these features is presented. Some numerical examples are shown to illustrate the results obtained with this model and to compare them with other known anisotropic models. Keywords: Anisotropic material, Constitutive behaviour, Elastic material, Finite element method, Logarithmic strain measure Affiliations:
Dłużewski P. | - | IPPT PAN | Jurczak G. | - | IPPT PAN | Antúnez H.J. | - | IPPT PAN |
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22. |
Dłużewski P., Jurczak G., Maciejewski G., Kret S.^{♦}, Ruterana P.^{♦}, Nouet G.^{♦}, Finite Element Simulation of Residual Stresses in Epitaxial Layers,
Materials Science Forum (MSF), ISSN: 1662-9752, DOI: 10.4028/www.scientific.net/MSF.404-407.141, Vol.404-407, pp.141-146, 2002Abstract: A nonlinear finite element approach presented here is based on the constitutive equations for anisotropic hyperelatic materials. By digital image processing the elastic incompatibilities (lattice mismatch) are extracted from the HRTEM image of GaN epilayer. Such obtained tensorial field of dislocation distribution is used next as the input data to the FE code. This approach is developed to study the stress distribution associated with lattice defects in highly mismatched heterostructures applied as buffer layers for the optically active structures. Keywords: Dislocations, Anisotropic Hyperelasticity, Residual Stresses Affiliations:
Dłużewski P. | - | IPPT PAN | Jurczak G. | - | IPPT PAN | Maciejewski G. | - | IPPT PAN | Kret S. | - | Institute of Physics, Polish Academy of Sciences (PL) | Ruterana P. | - | CNRS (FR) | Nouet G. | - | CNRS (FR) |
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23. |
Dłużewski P., Rodzik P., Elastic eigenstates in finite element modelling of large anisotropic elasticity,
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, ISSN: 0045-7825, DOI: 10.1016/S0045-7825(97)00295-8, Vol.160, No.3-4, pp.325-335, 1998Abstract: FE algorithm for large anisotropic hyper-elastic deformations is presented. This algorithm is based on the concept of the local reference configuration. The spectral decomposition of the elastic modulus tensor into eigentensors of elastic deformations has been utilized in the constitutive equations. Some numerical results are also presented. Affiliations:
Dłużewski P. | - | IPPT PAN | Rodzik P. | - | IPPT PAN |
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24. |
Dłużewski P., On geometry and continuum thermodynamics of movement of structural defects,
MECHANICS OF MATERIALS, ISSN: 0167-6636, DOI: 10.1016/0167-6636(95)00020-8, Vol.22, No.1, pp.23-41, 1996Abstract: A thermodynamic theory of the movement of point, line and surface defects is considered at finite deformations. This theory is based on the balance laws for crystal defects. The defects balance laws together with the well-known balance laws for the mass, momentum, moment of momentum, energy and entropy have been utilized to find the driving forces acting on crystal defects. Some of the derived formulae are well-known, e.g. Peach-Koehler formula, nevertheless, many new relations are obtained, e.g. for osmotic forces and for the energy flux due to the movement of crystal defects. The driving force acting on a grain boundary is found as a thermodynamic force needed to balance the jump in energy density across the moving discontinuity surface.
Using the relations derived for driving forces the problem of the constitutive modelling of the crystal defect movement is considered. The elastic behaviour of materials with structural defects is determined by a constitutive equation imposed on the free energy density. This equation takes into account the elastic strain, crystal defect densities and temperature. The crystal plasticity is described by vector constitutive equations stated between the defects velocities and the respective driving forces. Keywords: Oriented continuum, Dislocation density tensor, Driving forces, Curvature tensors Affiliations:
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25. |
Dłużewski P., Kontynualna teoria dyslokacji jako teoria konstytuwnego modelowania skończonych sprężysto-plastycznych deformacji (Praca habilitacyjna),
Prace IPPT - IFTR Reports, ISSN: 2299-3657, No.13, pp.1-112, 1996 | |
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Dłużewski P., Finite deformations of polar elastic media,
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 0020-7683, DOI: 10.1016/0020-7683(93)90087-N, Vol.30, No.16, pp.2277-2285, 1993Abstract: In many papers on oriented continua some orthonormal angular coordinates were proposed. With respect to the curvature of the orientation space, it is obvious that such coordinates could not be applied in practice. Therefore, instead of these coordinates a tensor field of rotations had to be used to define the wryness tensor.
In this paper the curvilinear coordinates in orientation space are considered. The Euler angles are an example of such coordinates. The inertia conservation law is replaced here by a constitutive relation. From the physical point of view this relation is more general and seems to be better justified than the mentioned law. Within the framework of the polar continuum theory a micromorphic structure is discussed. Some remarks on the principle of a material frame-indifference are also presented. Affiliations:
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27. |
Dłużewski P., Continuum Theory of Dislocations in Angular Coordinates,
Solid State Phenomena, ISSN: 1662-9779, DOI: 10.4028/www.scientific.net/SSP.35-36.539, Vol.35-36, pp.539-544, 1993Abstract: The dislocation density tensor is considered as a measure of angular inelastic deformation of crystal lattice. The modelling of plastic deformation of dislocated crystal is done by means of the vector constitutive relation imposed on the force-velocity dependence for dislocations. The force exerted on a dislocation is treated here as a direct reason of the dislocation movement. This force is induced by the elastic deformation of crystal lattice and by the osmotic stress due to the unbalanced concentration of vacancies. Keywords: Activation Energy of Dislocation Motion, Constitutive Equations of Dislocation Movement, Continuum Theory of Dislocations, Curvature Tensor, Dislocation Balance Law, Dislocation Density Tensor, Force on Dislocation, Internal Stress, Osmotic Pressure, Peach-Koehler Formula, Residual Stress, Thermodynamic Restrictions, Vacancy Concentration Affiliations:
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28. |
Dłużewski P., Crystal orientation spaces and remarks on the modelling of polycrystal anisotropy,
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS, ISSN: 0022-5096, DOI: 10.1016/0022-5096(91)90045-P, Vol.39, No.5, pp.651-661, 1991Abstract: recently, in many microstructural models of polycrystals the micro-macro transition is based on the averaging of crystal behaviours over all the crystal orientations. In this paper the elements of the theory of crystal orientation spaces are presented from the viewpoint of Riemannian geometry. The Euler angles are used as coordinate systems on these spaces. The angular metric tensor is introduced. It is shown that each turn of a crystal describes a geodesic line in the crystal orientation space. A simple formula to determine the finite distance between two different crystal orientations is given. It appears that the orientation region frequently used to describe the orientation distribution of f.c.c. crystals does not take into account all orientations of the crystals. Therefore a new, more suitable region has been proposed. A continuity equation for the crystal orientation distribution function (CODF) is obtained as a conservation law in this geometry. It is shown that the frequently used form of this equation is not correct. Affiliations:
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29. |
Dłużewski P., Zastosowanie teorii poślizgów do opisu procesów deformacji niesprężystych (Praca doktorska),
Prace IPPT - IFTR Reports, ISSN: 2299-3657, No.37, pp.1-91, 1985 | |