1. |
Jurczak G., Variation of second-order piezoelectric coefficients with respect to a finite strain measure,
Acta Crystallographica Section A FOUNDATIONS AND ADVANCES, ISSN: 2053-2733, DOI: 10.1107/S2053273318008628, Vol.A74, pp.518-523, 2018Abstract: In this article the consequence of a change of finite strain measure is theoretically considered for nonlinear piezoelectric crystals. Analytical predictions show that second-order piezoelectric coefficients are finite strain measure dependent. Therefore, the use of any finite strain measure in constitutive modelling of piezoelectric materials requires an adequate choice of higher-order piezoelectric coefficients. This allows one to avoid unwanted corrections to the elastic and electric fields in the case of nonlinear modelling of piezoelectric materials, e.g. for piezoelectric heterostructures such as quantum wells or dots. A general transformation formula for second-order piezoelectric coefficients (elastostriction) is derived. As an example, specific transformation formulae for two common crystallographic classes, namely 43m and 6mm, are presented. The piezoelectric coefficients for GaN and GaAs crystals, as representative cases of these crystal classes, are recalculated and their dependence on the strain measure is demonstrated. A further implication of that effect is that a complete set of second-order piezoelectric coefficients should contain additional information about the strain measure applied during calculations or measurements. Keywords: piezoelectricity, nonlinear piezoelectricity, elastostriction, finite strain measure Affiliations:
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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. |
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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4. |
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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5. |
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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6. |
Jurczak G., Young T.D., Finite element modelling of semi and nonpolar GaN/AlN quantum dots,
APPLIED SURFACE SCIENCE, ISSN: 0169-4332, Vol.260, pp.59-64, 2012Abstract: This paper describes results of a finite element analysis of the elastic and electric field distribution in a semipolar and a nonpolar isolated quantum dot based on previously obtained measurements from transmission electron microscopy. The two quantum dot orientations are each investigated and compared in terms of the resultant piezoelectric fields and their redistribution due to growth orientation and quantum dot geometry/surface effects. Alongside that, a standard polar quantum dot is investigated as a reference-state system. It is found that the geometry of quantum dots grown in alternative orientations affect the elastic strain and, along with orientation dependent spontaneous polarisation, modify the electrostatic potential and the built-in electric fields. A theoretical verification of a reduction in the quantum confined Stark effect by determining the band edge splitting energies for electron and hole states is given. Keywords: Piezoelectricity, Continuum mechanics, Finite element method, Quantum dots Affiliations:
Jurczak G. | - | IPPT PAN | Young T.D. | - | IPPT PAN |
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7. |
Maździarz M., Young T.D., Jurczak G., A study of the effect of prerelaxation on the nanoindentation process of crystalline copper,
ARCHIVES OF MECHANICS, ISSN: 0373-2029, Vol.63, No.5-6, pp.533-548, 2011Abstract: This paper examines how prerelaxation effects the development of the mechanics of a nanoindentation simulation. In particular, the force-depth relation, indentation stress-strain curves, hardness and elastic modulus, are investigated through molecular statics simulations of a nanoindentation process, starting from initial relaxation by: (i) molecular dynamics and (ii) molecular statics. It is found that initial relaxation conditions change the quantitative response of the system, but not the qualitative response of the system. This has a significant impact on the computational time and quality of the residual mechanical behaviour of the system. Additionally, the method of determining of the elastic modulus is examined for the spherical and planar indenter; and the numerical results are compared. An overview of the relationship between the grain size and hardness of polycrystalline copper is examined and conclusions are drawn. Keywords: molecular statics, molecular dynamics, nanoindentation, copper Affiliations:
Maździarz M. | - | IPPT PAN | Young T.D. | - | IPPT PAN | Jurczak G. | - | IPPT PAN |
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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. |
Alfonso C.^{♦}, Alexandre L.^{♦}, Leroux Ch.^{♦}, Jurczak G., Saikaly W.^{♦}, Charai A.^{♦}, Thibault-Penisson J.^{♦}, HOLZ lines splitting on SiGe/Si relaxed samples: Analytical solutions for the kinematical equation,
ULTRAMICROSCOPY, ISSN: 0304-3991, Vol.110, No.4, pp.285-296, 2010Abstract: Sample thinning for TEM observation introduces large changes with respect to the initial strain state of the bulk sample and particularly relaxation via the free surfaces which leads to HOLZ lines splitting in the CBED pattern. This phenomenon has been simulated owing to extensive calculations either in the kinematical or the dynamical framework of electron diffraction mainly using displacement fields resulting from finite element modelling of the sample relaxation. HOLZ line splitting is well reproduced and numerical fits can be used to compare experimental and calculated curves. This paper proposes new analytical solutions for the kinematical equation of electron diffraction. Simple mathematical functions are used to approximate the deformation profiles. We showed that, under certain conditions, the rocking curve profile can be analytically calculated, thus providing some clue to separate different contributions to the rocking curves against deformation profile. These simplified analytical expressions are used to extract the maximum amplitude displacement within the sample with about 10% accuracy. This accuracy can even be improved to 1% with a short adjustement routine. The influence of the shape of the displacement profile on the rocking curves is demonstrated. Keywords: Convergent beam electron diffraction, Kinematical theory of electron diffraction, Analytical expressions, Strain measurement Affiliations:
Alfonso C. | - | CNRS (FR) | Alexandre L. | - | CNRS (FR) | Leroux Ch. | - | CNRS (FR) | Jurczak G. | - | IPPT PAN | Saikaly W. | - | CNRS (FR) | Charai A. | - | CNRS (FR) | Thibault-Penisson J. | - | CNRS (FR) |
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10. |
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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11. |
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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12. |
Łepkowski S.P.^{♦}, Majewski J.A.^{♦}, Jurczak G., Nonlinear elasticity in III-N compounds: ab-initio calculations,
PHYSICAL REVIEW B, ISSN: 1098-0121, Vol.72, pp.245201-0, 2005Abstract: We have studied the nonlinear elasticity effects in zinc-blende and wurtzite crystallographic phases of III-N compounds. Particularly, we have determined the pressure dependences of elastic constants in InN, GaN, and AlN by performing ab initio calculations in the framework of plane-wave pseudopotential implementation of the density-functional theory. The calculations have been performed employing two exchange-correlation functionals, one within the local density approximation and the other within the generalized gradient approximation. We have found that C11, C12 in zinc-blende nitrides and C11, C12, C13, C33 in wurtzite nitrides depend significantly on hydrostatic pressure. Much weaker dependence on pressure has been observed for C44 elastic constant in both zinc-blende and wurtzite phases. Further, we have examined the influence of pressure dependence of elastic constants on the pressure coefficient of light emission, dE / dP, in wurtzite InGaN / GaN and GaN / AlGaN quantum wells. We have shown that the pressure dependence of elastic constants leads to a significant reduction of dE / dP in nitride quantum wells. Finally, we have considered the influence of nonlinear elasticity of III-N compounds on the properties of hexagonal nitride quantum dots (QDs). For typical wurtzite GaN / AlN QDs, we have shown that taking into account pressure dependence of elastic constants results in the decrease of volumetric strain in the QD region by about 7%. Simultaneously, the average z component of the piezoelectric polarization in the QDs increases by 0.1 MV/ cm compared to the case when linear elastic theory is used. Both effects, i.e., decrease of volumetric strain as well as increase of piezoelectric field, decrease the band-to-band transition energies in the QDs. Keywords: III-V semiconductor, ab-initio calculation, nonlinear elasticity, third order elastic coefficient Affiliations:
Łepkowski S.P. | - | Institute of High Pressure Physics, Polish Academy of Sciences (PL) | Majewski J.A. | - | other affiliation | Jurczak G. | - | IPPT PAN |
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13. |
Łepkowski S.P.^{♦}, Majewski J.A.^{♦}, Jurczak G., Nonlinear elasticity in wurtzite GaN/AlN planar superlattices and quantum dots,
ACTA PHYSICA POLONICA A, ISSN: 0587-4246, Vol.108, No.5, pp.749-754, 2005Abstract: The elastic stiffness tensors for wurtzite GaN and AlN show a significant hydrostatic pressure dependence, which is the evidence of nonlinear elasticity of these compounds. We have examined how pressure dependence of elastic constants for wurtzite nitrides influences elastic and piezoelectric properties of GaN/AlN planar superlattices and quantum dots. Particularly, we show that built-in hydrostatic pressure, present in both quantum wells of the GaN/AlN superlattices and GaN/AlN quantum dots, increases significantly by 0.3–0.7 GPa when nonlinear elasticity is used. Consequently, the compressive volumetric strain in quantum wells and quantum dots decreases in comparison to the case of the linear elastic theory. However, the z-component of the built-in electric field in the quantum wells and quantum dots increases considerably when nonlinear elasticity is taken into account. Both effects, i.e., a decrease in the compressive volumetric strain as well as an increase in the built-in electric field, decrease the band-to-band transition energies in the quantum wells and quantum dots. Keywords: III-V semiconductor, nonlinear elasticity, third order elasic coefficient Affiliations:
Łepkowski S.P. | - | Institute of High Pressure Physics, Polish Academy of Sciences (PL) | Majewski J.A. | - | other affiliation | Jurczak G. | - | IPPT PAN |
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14. |
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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15. |
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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16. |
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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17. |
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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18. |
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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