Boundary Of Unit Cell Research Articles

Higher Order Finite Element Analysis of Finite-by-Infinite Arrays

This paper describes a finite element analysis of finite-by-infinite arrays with arbitrary composition. The analysis employs higher order tetrahedral elements for discretization and imposes appropriate boundary conditions on the unit cell boundaries. The radiation boundary condition imposed on the array aperture is derived through a spectral- and a mixed-domain formulation. The two formulations are found to produce consistent numerical results. In addition to a general code using tetrahedral elements, a special code is also developed based on brick element discretization, which utilizes the conjugate gradient fast Fourier transform (CG-FFT) method. Both computer codes are applied to the analysis of several finite-by-infinite arrays and numerical examples are presented to demonstrate their accuracy and capability.

탄소/페놀릭 8-매 주자직 복합재료의 열전도도

본 연구에서는 탄소/페놀릭 8-매 주자직 복합재료인 ACP302의 등가열전도계수를 단위구조해석을 통하여 계산하였고 또한 실험적으로 측정하였다. 먼저 8-매 주자직 복합재료의 직조섬유다발구조를 3차원 유한요소를 사용하여 미세역학적으로 상세히 모델링하였으며, 단위구조 경계면에는 주기경계조건을 가하고 해석을 수행하였다. 계산결과로부터 적층 형상 및 굴곡도, 섬유 체적비 등이 등가열전도도에 미치는 영향을 조사하였다. 또한 실험을 수행하여 열전도도를 계측하였으며 그 결과를 계산결과와 비교하였다. In this paper, thermal conductivities of carbon-phenolic 8-harness satin weave composite, ACP302, were measured and predicted. In the analysis, the satin weave unit cell was identified and modeled discretely by 3-dimensional finite elements, considering the interlaced fiber tow architecture microscopically. At the unit cell boundary, the corresponding periodic boundary conditions were applied. The results were analyzed to investigate the effect of microstructural parameters such as stacking phase shifts, waviness ratio, and fiber volume fraction. The conductivities were also obtained by experiments and compared with the numerical results.

Micro-mechanical analysis of composite materials by BEM

Applications to composites of a unit-cell model in conjunction with boundary element method (BEM) for determining their effective mechanical properties are discussed in this paper. The composite considered here consists of inclusion and matrix phases. A unit-cell model for composites with periodically distributed inhomogeneities is developed and introduced into a boundary element formulation to provide an effective means for estimating overall material constants of two-phase composites. In this model, the volume average stress and strain is calculated by the boundary tractions and displacements of the unit-cell and the periodic conditions of the composite are expressed by the periodic boundary conditions of the unit-cell. Thus BEM is suitable for performing calculations on average stress and strain fields of such composites. Numerical results for a two-phase composite with circular rigid inclusions are presented to illustrate the application of the proposed unit-cell boundary element formulation.

Ab Initio Study of the Nonequivalence of Adsorption of D- and L-Peptides on Clay Mineral Surfaces

Ab initio geometry optimizations were performed of the structures of the L and D enantiomers of the model dipeptide, N-formyl alanine amide (L-Ala and D-Ala, respectively) adsorbed on the mineral surface in the interlayer space of the 2:1 clay, nontronite. Density functional procedures were used as implemented in the ab initio program CASTEP, in fully periodic calculations in which the properties of a model unit cell are determined by including the effects of its neighboring cells in an infinite crystal. Geometry optimization included the atomic positions of the mineral and the adsorbates within the unit cell, in addition to unit cell lengths and angles, achieving full optimization of the entire crystal system. In agreement with previous studies of the adsorption of organic compounds on clay mineral surfaces, in the most stable arrangement of L-Ala and D-Ala found here, the two molecules reside flat on the mineral basal plane, forming a parallel monolayer. The resulting L-Ala/mineral cocrystal is more stable, by 6 kcal/mol, than D-Ala. A characteristic structural difference exists for the enantiomers in that, in the optimized structure of L-Ala, the C(α)–C(β) bond is directed away from one of the mineral basal planes toward the dioctahedral cavity of the other, while the side group of D-Ala is parallel to the mineral basal plane and pointing to the nearest neighbor in an adjacent unit cell. As expected, the reverse results are obtained for the adsorption of L-Ala and D-Ala on a nontronite surface that is the enantiomer of the one used above. The geometry optimizations illustrate the structural compatibility of clay mineral lattices with peptide structures. That is, balance of adsorption energies and peptide interaction energies, and mineral lattice structure and periodicity allow for adsorption structures, which involve the entire backbone of a single peptide molecule and can, at the same time, immobilize the adsorbates in such a way that stabilizing intermolecular interactions occur across unit cell boundaries. Compatibility of the repeat distances on the clay surface with repeat distances of peptides should be an important property when clay minerals serve as templates for protein synthesis.

A Picture Is Worth 1000 Words: The BLT in Teaching Crystal Structure

In explaining descriptions of crystals, many authors have emphasized the idea that Nature makes crystals, but human beings draw unit cell boundaries. The accompanying figure contains a useful classroom demonstration to drive this point home.

Thallium overlayers on Si(111): Structures of a “new” group III element

The structure and growth of Tl overlayers on Si(111)7×7 surfaces have been investigated using ultraviolet photoelectron spectroscopy, low-energy electron diffraction (LEED), Auger electron spectroscopy (AES), and scanning tunneling microscopy (STM). At low coverages Tl adsorption occurs almost exclusively on the faulted half of the (7×7) unit cell and forms small, two-dimensional clusters. With increasing Tl coverage the whole surface becomes covered while the (7×7) surface periodicity is maintained as evidenced by LEED and STM. After deposition of the first 2 monolayers (ML) the high mobility of Tl adatoms leads to the condensation of few, but large islands. At the surface of the second monolayer of Tl an interesting network of bright contrast lines is observed, which appears to be induced by the (7×7) substrate periodicity lying two layers below and which may be caused by the surface strain mediated by the (7×7) unit cell boundaries. The surface phase diagram of Tl–Si(111) at elevated temperatures contains a (1×1) structure at 1 ML coverage and an approximate (6×6) phase. The latter is due to an incommensurate structure of the second Tl layer on top of the (1×1) ML.

Computation of coarse grain structures using a homogeneous equivalent medium

This paper deals with the improvement of concentration relations when some basic hypothesis of homogenization techniques are no longer valid inducing important errors in the deduced local fields. In the first part of this work we propose a new formalism of the standard concentration rules developed in the homogenization of periodic media framework. In a second part, we insist on the fact that a homogeneous equivalent medium replacing a coarse grain material is in fact expected to be a generalized continuum. Additional stiffnesses must be attributed to the unit cell and special non-homogeneous boundary conditions and their periodic counterparts are proposed. The resulting HEM turns out to be a Cosserat continuum.

Creep strength of fiber and particulate composite materials: The effect of interface slip and diffusion

It is well known that the creep resistance of metal and intermetallic matrix composites containing fibers or particulates arises from the constraint of the matrix by the reinforcement. Experimental results indicate that, in general, at modest temperatures the creep strength of these composites is better than that of the matrix material alone. However, at temperatures higher than approximately half of the melting temperature of the matrix the composite strength is limited and in some cases the strengthening imparted by the reinforcements is completely lost. The quantitative effect of diffusional relaxation and interface slip along the matrix-reinforcement interface, on the matrix constraint and thereby on the creep resistance, is studied. The composite behavior is modeled by coupling the slip and diffusional mass transport along the interface with power law deformation of the matrix with the reinforcement considered as rigid. The transverse creep resistance of a continuous fiber composite material and the axial creep strength of a discontinuous fiber composite are investigated in plane strain and axial symmetry respectively. The relevant unit cell boundary value problems are solved by the finite element method. Results indicate that slip at the interface alone can reduce the transverse creep strength of a continuous fiber composite to levels below that of the pure matrix material. On the contrary, analysis of the axial creep resistance of discontinuous fiber composites indicates that diffusion is necessary in addition to the free slip for the same result.

Structures of atomic steps on the 7 x 7 reconstructed Si(111) surface.

We have carried out a systematic study of the structures of mono bilayer atomic steps on the 7\ifmmode\times\else\texttimes\fi{}7 reconstructed Si(111) surface whose step edges are parallel to the unit-cell boundary. Atomic steps in all possible 14 step groups have been observed; thus a complete picture of the step structure is presented. The upper step edges of ten groups terminate at unit-cell boundaries, while the remaining four groups do not. The step structure formed is the result of two factors competing to minimize the surface free energy: the structural integrity of the upper step edge and the width of the transition region at the lower terrace. There is evidence that step formation is influenced by the annealing method used. \textcopyright{} 1996 The American Physical Society.

The oestrogen receptor recognizes an imperfectly palindromic response element through an alternative side-chain conformation.

Structural studies of protein-DNA complexes have tended to give the impression that DNA recognition requires a unique molecular interface. However, many proteins recognize DNA targets that differ from what is thought to be their ideal target sequence. The steroid hormone receptors illustrate this problem in recognition rather well, since consensus DNA targets are rare. Here we describe the structure, at 2.6 A resolution, of a complex between a dimer of the DNA-binding domain from the human oestrogen receptor (ERDBD) and a non-consensus DNA target site in which there is a single base substitution in one half of the palindromic binding site. This substitution results in a 10-fold increase in the dissociation constant of the ERDBD-DNA complex. Comparison of this structure with a structure containing a consensus DNA-binding site determined previously, shows that recognition of the non-consensus sequence is achieved by the rearrangement of a lysine side chain so as to make an alternative base contact. This study suggests that proteins adapt to recognize different DNA sequences by rearranging side chains at the protein-DNA interface so as to form alternative patterns of intermolecular contacts.

Computer modelling studies of 18-crown-6 with urea and thiourea

Abstract Computer modelling studies have been carried out on the interaction of 18-crown-6 with a variety of guest molecules, including urea, thiourea and substituted ureas. The five known crystal structures of these host/guest systems were used as models. We were interested to establish whether the arrangement of guest molecules around a host molecule in the crystal was indicative of the lowest energy configuration for a host/guest fragment or was a consequence of packing effects. Two models were therefore considered for each structure and the structures minimised via molecular mechanics. In the first mode, the structure consisted of one unit cell and periodic boundary conditions were used in the calculation. Coulombic effects were calculated using the Ewald summation. In the second model, the structure consisted of an 18-crown-6 molecule surrounded by two hydrogen-bonded guest molecules. Both models were minimised using the CERIUS package using the DreidingII forcefield. The crystal structure minimisati...

Thermal conductivity of disordered harmonic solids.

As a crystal is disordered, a point may be reached where the typical mean free path of phonons is so short that the wavelength and mean free path are no longer sharp concepts, and the textbook phonon-gas model for thermal conductivity breaks down. This paper proposes an alternate theory for the disordered regime, and the subsequent paper implements the theory for a realistic model of amorphous silicon. The idea is that the dominant scattering is correctly described by a harmonic Hamiltonian, which is, in principle, transformable into a one-body problem of decoupled oscillators. From this the thermal conductivity can be exactly calculated by an analog of the Kubo-Greenwood formula for electrical conductivity of disordered metals. Anderson localization is correctly contained in this theory; localized states contribute no currents in harmonic approximation. What is required is an atomistic model with a large unit cell and periodic boundary conditions (to avoid undesired surface effects). The linear size of the model should be larger than the mean free paths of the dominant phonons. A Kubo formula and then a Kubo-Greenwood-type formula are derived for this problem. A ``mode diffusivity'' ${\mathit{D}}_{\mathit{i}}$ for the ith exact oscillator state is defined. The heat is carried by off-diagonal elements of the heat current operator, which have a nonzero contribution because the temperature gradient introduces nonzero off-diagonal elements of the density matrix 〈${\mathit{a}}_{\mathit{i}}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$${\mathit{a}}_{\mathit{j}}$〉. An effort is made to interpret these results physically. Schemes for implementing this formalism are discussed.

Analysis of three-dimensional acoustic scattering from doubly periodic structures using a source model

A novel solution is presented for the problem of three-dimensional acoustic scattering of a time-harmonic plane wave from doubly periodic structures. The general problem is first reduced to a consideration of the fields over a suitably defined unit cell. Sets of fictitious doubly periodic and properly modulated patch sources are used to simulate the fields in the homogeneous regions crossed by the unit cell boundaries. Sets of fictitious point sources are used to simulate the fields inside the regions completely enclosed within the unit cell. The complex amplitudes of the fictitious sources are adjusted to satisfy the boundary conditions at a selected set of points on the boundaries between the regions. The suggested solution procedure is simple to implement and is applicable to doubly periodic structures composed of homogeneous regions of arbitrary shape. Structures comprising acoustically rigid and soft boundaries can also be handled by the procedure. The method has been tested for accuracy by studying the cases of scattering from arrays of spherical scatterers and from doubly periodic sinusoidal surfaces.

Analysis of two-dimensional acoustic scattering from periodic structures using a hybrid source model

A method of moments solution is presented for the problem of two-dimensional acoustic scattering of a plane wave from a general piecewise homogeneous periodic structure. The reduction of the general problem to a consideration of the fields over a suitably selected period, referred to as the unit cell, is facilitated by the Floquet theorem. The solution then uses fictitious spatially periodic and properly modulated strip sources to simulate the fields in homogeneous regions crossed by the unit cell boundaries and fictitious filamentary sources to simulate the fields in homogeneous regions completely enclosed within this cell. The fields radiated by the strip sources are represented in terms of Floquet modes. Finally, the simulated fields are forced to obey the continuity conditions for the pressure and the normal component of the velocity at selected sets of points on the boundaries among the regions within the unit cell. The procedure is simple to implement, rapidly converging, and is applicable to structures of arbitrary smooth cross section. Acoustically rigid and soft regions are also treated within the general procedure. Results are given and compared with available data and with an analytic approximation.

Accurate resonance absorption calculations including 2-D effects and their representation in multigroup lattice physics codes

Recent extensions of accurate transport theory calculations of resonance absorption in reactor unit cells by finite-element techniques to a 2-D description of the cell are described. Although very time consuming, they are now a feasible alternative for benchmark calculations, in particular when applied to limited energy ranges. They have provided independent evidence for the validity of transport treatments based on a 1-D model with suitable boundary conditions at the outer unit cell boundary. The latter remain as the principal technique against which the procedures for handling resonance absorption in multigroup lattice physics codes can be checked. An improved equivalence relation between heterogeneous and homogeneous assemblies, due to Y. A. Chao, has been applied to evaluate the resonance shielding in a multigroup code in the MUFT group structure. Examples are given of the extent to which the accuracy of the calculations is improved, by comparison with benchmark calculations. Inevitable shortcomings in the treatment of resonance absorption in multigroup lattice physics codes are discussed. These are similar in nature to the problems which arise in conventional methods of fuel assembly homogenization as a preliminary to multidimensional few-group flux and power-distribution calculations in full reactor cores. In the same way, in which discontinuity factors can be defined rigorously and applied with good accuracy in practice, to overcome these difficulties, group correction factors can be used for the resonance absorption problem. Their definition involves the flux calculated by the multigroup code in the preservation of resonance reaction rates resulting from benchmark calculations, and not the flux which is obtained in the benchmark transport theory code. A description is given of a practical way for evaluating the group correction factors to be applied to the multigroup code resonance treatment, so that they can be used subsequently in rapid applications of the code. The corrections account implicitly for the approximations introduced by intermediate resonance theory and equivalence theory and, in particular, also for the neglect of interference effects between the resonances belonging to different nuclides.

A high-resolution electron microscopic study of some members of the vernier structural series Ba p(Fe 2S 4) q

BaFe 2S 4 and Ba 13(Fe 2S 4) 12 have been imaged at high resolution in an electron microscope. Agreement between observed and calculated images for BaFe 2S 4 is good. Marked heterogeneity exists in all the specimens observed and sharp unit cell boundaries are not observed. Rather, there are broad, wavy fringes suggesting that these structures should be thought of as a solid solution of moderately ordered structures.

Relaxations in Polyethylene: Orientation of the Lamellar Crystals

A torsion pendulum has been used to make mechanical measurements on linear polyethylene between −175° and +110°C at about 1 Hz. Samples in which orientation had been induced by crystallization in a temperature gradient were measured together with unoriented but otherwise comparable samples. The data are analyzed to show that the a relaxation in polyethylene is sensitive to the orientation of the deformation with respect to the structural and morphological symmetry. For shearing in the a-c face of the unit cell and lamella boundaries the relaxation average over all directions is different from the average for shearing in all possible planes in the cell and boundaries. The γ relaxation does not exhibit this difference. Various viscoelastic parameters such as the real part of the modulus and the magnitude of the relaxations do not correlate with lamella thickness in the present samples.

Collision Probabilities in Cylindrical Lattices

First-collision probabilities for a regular lattice of cylindrical fuel rods and moderator are calculated using the assumption that neutrons reaching the outer boundary of the unit cell are returne...