Accuracy in EM Fields Calculations Using a Combined FE-IE Approach
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FE-IE hybrid finite element-integral equation EM f↗
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Analytical evaluation of a surface integral expressing the coupling between interior and exterior volumes in a FE-IE approach
Recently an approach which combines the finite element technique and an integral equation to determine the fields scattered by inhomogeneous bodies of complicated shape has been proposed. Basically, a mathematical surface which encloses the scatterers is introduced, thus dividing the space into an interior and an exterior volume, in which the finite element technique and an integral equation for EM scattering, respectively, are applied. The integral equation is set up for the tangential components of the fields at the surface, while the interior volume the unknowns are the total fields. Continuity of the tangential fields at the boundary, as required by Maxwell's equations, is imposed, thus coupling the two methods to obtain a consistent solution. The coupling term is expressed by a surface integral formed by the dot product of a FE basis function and an IE testing function, or viceversa. By choosing the boundary to be a surface of revolution and by making a convenient selection of IE basis (testing) functions, it is possible to evaluate the integrals analytically on surfaces such as curved triangles, curved quadrilaterals and curved pentagons. We will illustrate the salient steps involved in setting up and carrying out these integrals and discuss what class of basis (testing) functions and analytic surfaces of revolution they are applicable to. Analytic calculations offer the advantage of better accuracy than purely numerical ones, and, when combined with them, often shed light on issues of numerical convergence and limiting values. Furthermore, they may reduce computation time and storage requirements.
Zuffada, C.↗
Irradiation-induced amorphization of Fe-Y-based second phase particles in accident-tolerant FeCrAl alloys
Here, second phase intermetallic particles in an advanced accident-tolerant FeCrAl (Fe-13Cr-5Al-2Mo) alloy are formed in the α-Fe matrix during processing. These particles are prominently related to the added Y. Neutron irradiation to ~7 displacements per atom (dpa) with a dose rate of ~8.16 × 10 -7 dpa/s at 282 °C resulted in the amorphization of these precipitates which could degrade the mechanical properties of the FeCrAl alloys. Analytical electron microscopy and diffraction analysis combined with structural freedom analysis have been used to investigate the radiation resistance of the second phase particles. Radiation tolerance is closely linked to the particle Fe-Y content and can be tailored using the structure freedom value.
36 MATERIALS SCIENCE↗
Performing spectroscopic and specific heat studies of improper ferroelectrics
The results of infrared measurements on Ni-Br, Cu-Cl, and Fe-I boracite improper ferroelectrics and far infrared measurements of Ni-Br boracite are presented. The boracites have the general formula X3B7O3Y, where X = divalent metal and Y = halogen. They undergo a first order phase transition from a high temperature paraelectric phase with cubic symmetry to a ferroelectric phase with orthorhombic symmetry. The boracites are "improper ferroelectrics" since the spontaneous polarization is not the primary order parameter in the cubic-orthorhombic phase transition. Current understanding of these materials is that the primary order parameter is associated with a doubly degenerate zone-boundary phonon in the cubic phase. The degenerate critical modes become homogeneous and split into the A sub 1 and A sub 2 modes in the orthorhombic phase, doubling the volume of the primitive cell. An harmonic coupling between the softing A sub 1 and a low frequency A sub 1 optic mode induces a spontaneous polarization as a secondary effect in the ferroelectric phase. This secondary non-critical nature of the ferroelectric mode earns these materials the "improper" title and is responsible for their unique properties and high figure of merit in detector use.
Coleman, L. B.↗
Recalibration of Mount Wilson Doppler measurements (Research note)
The dispersion calibration of spectroscopic velocity measurements made with the 150-ft tower telescope at Mt. Wilson Observatory is revised upward by 0.55 percent on the basis of observations of the six lines of comparable shape and equivalent width nearest the 5250.2-A line of Fe-I used in the solar Doppler rate measurements. The dispersion results are presented in a graph, and the superiority of the Kitt Peak wavelength tables (Pierce and Breckenridge, 1973) over those of Moore et al. (1966) is demonstrated. As a result of the recalibration, all recent spectroscopic velocities from this telescope must be revised downward by 0.55 percent.
Snodgrass, H. B.↗
An efficient formulation of the coupled finite element-integral equation technique for solving large 3D scattering problems
It is often desirable to calculate the electromagnetic fields inside and about a complicated system of scattering bodies, as well as in their far-field region. The finite element method (FE) is well suited to solving the interior problem, but the domain has to be limited to a manageable size. At the truncation of the FE mesh one can either impose approximate (absorbing) boundary conditions or set up an integral equation (IE) for the fields scattered from the bodies. The latter approach is preferable since it results in higher accuracy. Hence, the two techniques can be successfully combined by introducing a surface that encloses the scatterers, applying a FE model to the inner volume and setting up an IE for the tangential fields components on the surface. Here the continuity of the tangential fields is used bo obtain a consistent solution. A few coupled FE-IE methods have recently appeared in the literature. The approach presented here has the advantage of using edge-based finite elements, a type of finite elements with degrees of freedom associated with edges of the mesh. Because of their properties, they are better suited than the conventional node based elements to represent electromagnetic fields, particularly when inhomogeneous regions are modeled, since the node based elements impose an unnatural continuity of all field components across boundaries of mesh elements. Additionally, our approach is well suited to handle large size problems and lends itself to code parallelization. We will discuss the salient features that make our approach very efficient from the standpoint of numerical computation, and the fields and RCS of a few objects are illustrated as examples.
Cwik, T.↗
Materials Data on YFe5 by Materials Project
YFe5 crystallizes in the hexagonal P6/mmm space group. The structure is three-dimensional. Y is bonded in a 6-coordinate geometry to eighteen Fe atoms. There are six shorter (2.93 Å) and twelve longer (3.21 Å) Y–Fe bond lengths. There are two inequivalent Fe sites. In the first Fe site, Fe is bonded to four equivalent Y and eight Fe atoms to form a mixture of corner, edge, and face-sharing FeY4Fe8 cuboctahedra. There are four shorter (2.45 Å) and four longer (2.54 Å) Fe–Fe bond lengths. In the second Fe site, Fe is bonded in a 12-coordinate geometry to three equivalent Y and six equivalent Fe atoms.
36 MATERIALS SCIENCE↗
Materials Data on Y3Fe29 by Materials Project
Y3Fe29 crystallizes in the monoclinic C2/m space group. The structure is three-dimensional. there are two inequivalent Y sites. In the first Y site, Y is bonded in a 12-coordinate geometry to twenty Fe atoms. There are a spread of Y–Fe bond distances ranging from 2.99–3.23 Å. In the second Y site, Y is bonded in a 11-coordinate geometry to nineteen Fe atoms. There are a spread of Y–Fe bond distances ranging from 2.99–3.29 Å. There are eleven inequivalent Fe sites. In the first Fe site, Fe is bonded to two equivalent Y and ten Fe atoms to form FeY2Fe10 cuboctahedra that share corners with eighteen FeY2Fe10 cuboctahedra, edges with eight FeY3Fe9 cuboctahedra, and faces with fourteen FeY2Fe10 cuboctahedra. There are a spread of Fe–Fe bond distances ranging from 2.36–2.58 Å. In the second Fe site, Fe is bonded to two equivalent Y and ten Fe atoms to form a mixture of corner, edge, and face-sharing FeY2Fe10 cuboctahedra. There are eight shorter (2.44 Å) and two longer (2.60 Å) Fe–Fe bond lengths. In the third Fe site, Fe is bonded in a 2-coordinate geometry to one Y and thirteen Fe atoms. There are a spread of Fe–Fe bond distances ranging from 2.39–2.89 Å. In the fourth Fe site, Fe is bonded in a 2-coordinate geometry to one Y and thirteen Fe atoms. There are a spread of Fe–Fe bond distances ranging from 2.57–2.91 Å. In the fifth Fe site, Fe is bonded to two Y and ten Fe atoms to form a mixture of distorted corner, edge, and face-sharing FeY2Fe10 cuboctahedra. There are a spread of Fe–Fe bond distances ranging from 2.39–2.68 Å. In the sixth Fe site, Fe is bonded in a 12-coordinate geometry to two equivalent Y and ten Fe atoms. There are a spread of Fe–Fe bond distances ranging from 2.45–2.60 Å. In the seventh Fe site, Fe is bonded in a 2-coordinate geometry to one Y and thirteen Fe atoms. There are a spread of Fe–Fe bond distances ranging from 2.40–2.60 Å. In the eighth Fe site, Fe is bonded to two Y and ten Fe atoms to form a mixture of distorted corner, edge, and face-sharing FeY2Fe10 cuboctahedra. Both Fe–Fe bond lengths are 2.42 Å. In the ninth Fe site, Fe is bonded to two Y and ten Fe atoms to form a mixture of corner, edge, and face-sharing FeY2Fe10 cuboctahedra. There are one shorter (2.43 Å) and one longer (2.46 Å) Fe–Fe bond lengths. In the tenth Fe site, Fe is bonded to three Y and nine Fe atoms to form a mixture of corner, edge, and face-sharing FeY3Fe9 cuboctahedra. Both Fe–Fe bond lengths are 2.46 Å. In the eleventh Fe site, Fe is bonded to three equivalent Y and nine Fe atoms to form a mixture of corner, edge, and face-sharing FeY3Fe9 cuboctahedra. The Fe–Fe bond length is 2.45 Å.
36 MATERIALS SCIENCE↗
Materials Data on YFe2 by Materials Project
YFe2 is Cubic Laves structured and crystallizes in the cubic Fd-3m space group. The structure is three-dimensional. Y is bonded in a 12-coordinate geometry to twelve equivalent Fe atoms. All Y–Fe bond lengths are 3.02 Å. Fe is bonded to six equivalent Y and six equivalent Fe atoms to form a mixture of corner, edge, and face-sharing FeY6Fe6 cuboctahedra. All Fe–Fe bond lengths are 2.58 Å.
36 MATERIALS SCIENCE↗
Materials Data on FeI2 by Materials Project
FeI2 is trigonal omega structured and crystallizes in the trigonal P-3m1 space group. The structure is two-dimensional and consists of one FeI2 sheet oriented in the (0, 0, 1) direction. Fe2+ is bonded to six equivalent I1- atoms to form edge-sharing FeI6 octahedra. All Fe–I bond lengths are 2.83 Å. I1- is bonded in a distorted T-shaped geometry to three equivalent Fe2+ atoms.
36 MATERIALS SCIENCE↗
Materials Data on Y2Fe17 by Materials Project
Y2Fe17 crystallizes in the hexagonal P6_3/mmc space group. The structure is three-dimensional. there are two inequivalent Y sites. In the first Y site, Y is bonded in a 12-coordinate geometry to eighteen Fe atoms. There are a spread of Y–Fe bond distances ranging from 2.99–3.29 Å. In the second Y site, Y is bonded in a 8-coordinate geometry to twenty Fe atoms. There are a spread of Y–Fe bond distances ranging from 2.93–3.20 Å. There are four inequivalent Fe sites. In the first Fe site, Fe is bonded in a 2-coordinate geometry to one Y and thirteen Fe atoms. There are a spread of Fe–Fe bond distances ranging from 2.36–2.78 Å. In the second Fe site, Fe is bonded to two equivalent Y and ten Fe atoms to form FeY2Fe10 cuboctahedra that share corners with fourteen FeY2Fe10 cuboctahedra, edges with six equivalent FeY3Fe9 cuboctahedra, and faces with ten FeY2Fe10 cuboctahedra. There are four shorter (2.44 Å) and four longer (2.47 Å) Fe–Fe bond lengths. In the third Fe site, Fe is bonded in a 12-coordinate geometry to two Y and ten Fe atoms. There are a spread of Fe–Fe bond distances ranging from 2.46–2.59 Å. In the fourth Fe site, Fe is bonded to three Y and nine Fe atoms to form a mixture of distorted face, edge, and corner-sharing FeY3Fe9 cuboctahedra. Both Fe–Fe bond lengths are 2.47 Å.
36 MATERIALS SCIENCE↗
Materials Data on YFe2 by Materials Project
YFe2 is Cubic Laves structured and crystallizes in the cubic I-43m space group. The structure is three-dimensional. there are five inequivalent Y sites. In the first Y site, Y is bonded in a 12-coordinate geometry to twelve equivalent Fe atoms. All Y–Fe bond lengths are 3.00 Å. In the second Y site, Y is bonded in a 12-coordinate geometry to twelve Fe atoms. There are eight shorter (3.01 Å) and four longer (3.02 Å) Y–Fe bond lengths. In the third Y site, Y is bonded in a 12-coordinate geometry to twelve Fe atoms. There are a spread of Y–Fe bond distances ranging from 3.00–3.04 Å. In the fourth Y site, Y is bonded in a 12-coordinate geometry to twelve Fe atoms. There are a spread of Y–Fe bond distances ranging from 2.99–3.05 Å. In the fifth Y site, Y is bonded in a 12-coordinate geometry to twelve Fe atoms. There are a spread of Y–Fe bond distances ranging from 2.97–3.03 Å. There are five inequivalent Fe sites. In the first Fe site, Fe is bonded to six Y and six Fe atoms to form a mixture of face, edge, and corner-sharing FeY6Fe6 cuboctahedra. There are three shorter (2.54 Å) and three longer (2.56 Å) Fe–Fe bond lengths. In the second Fe site, Fe is bonded to six Y and six Fe atoms to form a mixture of face, edge, and corner-sharing FeY6Fe6 cuboctahedra. There are a spread of Fe–Fe bond distances ranging from 2.56–2.58 Å. In the third Fe site, Fe is bonded to six Y and six Fe atoms to form a mixture of face, edge, and corner-sharing FeY6Fe6 cuboctahedra. There are two shorter (2.55 Å) and three longer (2.56 Å) Fe–Fe bond lengths. In the fourth Fe site, Fe is bonded to six Y and six Fe atoms to form a mixture of face, edge, and corner-sharing FeY6Fe6 cuboctahedra. There are one shorter (2.53 Å) and four longer (2.58 Å) Fe–Fe bond lengths. In the fifth Fe site, Fe is bonded to six Y and six Fe atoms to form a mixture of face, edge, and corner-sharing FeY6Fe6 cuboctahedra. The Fe–Fe bond length is 2.63 Å.
36 MATERIALS SCIENCE↗
Materials Data on YFe3 by Materials Project
YFe3 crystallizes in the hexagonal P6_3/mmc space group. The structure is three-dimensional. there are two inequivalent Y sites. In the first Y site, Y is bonded in a 12-coordinate geometry to twelve Fe atoms. There are a spread of Y–Fe bond distances ranging from 2.95–3.05 Å. In the second Y site, Y is bonded in a 6-coordinate geometry to eighteen Fe atoms. There are six shorter (2.95 Å) and twelve longer (3.22 Å) Y–Fe bond lengths. There are four inequivalent Fe sites. In the first Fe site, Fe is bonded to five Y and seven Fe atoms to form a mixture of edge, face, and corner-sharing FeY5Fe7 cuboctahedra. There are a spread of Fe–Fe bond distances ranging from 2.45–2.56 Å. In the second Fe site, Fe is bonded in a 12-coordinate geometry to three equivalent Y and six equivalent Fe atoms. In the third Fe site, Fe is bonded in a 12-coordinate geometry to three equivalent Y and six equivalent Fe atoms. In the fourth Fe site, Fe is bonded to six equivalent Y and six equivalent Fe atoms to form FeY6Fe6 cuboctahedra that share corners with twelve equivalent FeY5Fe7 cuboctahedra, edges with six equivalent FeY6Fe6 cuboctahedra, and faces with eighteen equivalent FeY5Fe7 cuboctahedra.
36 MATERIALS SCIENCE↗
Materials Data on Y2Fe17 by Materials Project
Y2Fe17 crystallizes in the trigonal R-3m space group. The structure is three-dimensional. Y is bonded in a 10-coordinate geometry to nineteen Fe atoms. There are a spread of Y–Fe bond distances ranging from 3.02–3.26 Å. There are four inequivalent Fe sites. In the first Fe site, Fe is bonded to two equivalent Y and ten Fe atoms to form FeY2Fe10 cuboctahedra that share corners with fourteen FeY2Fe10 cuboctahedra, edges with six equivalent FeY3Fe9 cuboctahedra, and faces with ten FeY2Fe10 cuboctahedra. There are a spread of Fe–Fe bond distances ranging from 2.42–2.60 Å. In the second Fe site, Fe is bonded in a 12-coordinate geometry to two equivalent Y and ten Fe atoms. There are a spread of Fe–Fe bond distances ranging from 2.49–2.76 Å. In the third Fe site, Fe is bonded to three equivalent Y and nine Fe atoms to form a mixture of face, edge, and corner-sharing FeY3Fe9 cuboctahedra. There are two shorter (2.48 Å) and one longer (2.64 Å) Fe–Fe bond lengths. In the fourth Fe site, Fe is bonded in a 2-coordinate geometry to one Y and thirteen Fe atoms. The Fe–Fe bond length is 2.38 Å.
36 MATERIALS SCIENCE↗
Materials Data on YFe2 by Materials Project
YFe2 is Cubic Laves-like structured and crystallizes in the tetragonal I-4 space group. The structure is three-dimensional. there are four inequivalent Y sites. In the first Y site, Y is bonded in a 12-coordinate geometry to twelve Fe atoms. There are a spread of Y–Fe bond distances ranging from 3.01–3.03 Å. In the second Y site, Y is bonded in a 12-coordinate geometry to twelve Fe atoms. There are four shorter (3.01 Å) and eight longer (3.02 Å) Y–Fe bond lengths. In the third Y site, Y is bonded in a 12-coordinate geometry to twelve Fe atoms. There are a spread of Y–Fe bond distances ranging from 2.99–3.04 Å. In the fourth Y site, Y is bonded in a 12-coordinate geometry to twelve Fe atoms. There are a spread of Y–Fe bond distances ranging from 2.98–3.06 Å. There are five inequivalent Fe sites. In the first Fe site, Fe is bonded to six Y and six Fe atoms to form a mixture of face, edge, and corner-sharing FeY6Fe6 cuboctahedra. There are a spread of Fe–Fe bond distances ranging from 2.54–2.62 Å. In the second Fe site, Fe is bonded to six Y and six Fe atoms to form a mixture of face, edge, and corner-sharing FeY6Fe6 cuboctahedra. There are a spread of Fe–Fe bond distances ranging from 2.56–2.61 Å. In the third Fe site, Fe is bonded to six Y and six Fe atoms to form a mixture of face, edge, and corner-sharing FeY6Fe6 cuboctahedra. There are a spread of Fe–Fe bond distances ranging from 2.55–2.60 Å. In the fourth Fe site, Fe is bonded to six Y and six Fe atoms to form a mixture of face, edge, and corner-sharing FeY6Fe6 cuboctahedra. There are one shorter (2.54 Å) and three longer (2.56 Å) Fe–Fe bond lengths. In the fifth Fe site, Fe is bonded to six Y and six Fe atoms to form a mixture of face, edge, and corner-sharing FeY6Fe6 cuboctahedra.
36 MATERIALS SCIENCE↗