Three-dimensional pentamode acoustic metamaterials with hexagonal unit cells

2019 ◽  
Vol 145 (3) ◽  
pp. 1372-1377 ◽  
Author(s):  
Qi Li ◽  
Jeffrey S. Vipperman
Keyword(s):  
Three Dimensional ◽  
Acoustic Metamaterials ◽  
Unit Cells

Crystal Structure Analysis of Cu-Zr Alloys by Convergent Beam Diffraction

1981 ◽  
Vol 39 ◽  
pp. 354-355
Author(s):  
A. F. Marshall ◽  
J. W. Steeds ◽  
D. Bouchet ◽  
S. L. Shinde ◽  
R. G. Walmsley
Keyword(s):  
Crystal Structure ◽  
Point Group ◽  
Intermetallic Phase ◽  
Three Dimensional ◽  
Crystal Structure Analysis ◽  
Ion Milling ◽  
Composition And Structure ◽  
Unit Cells ◽  
Sputter Deposited ◽  
Convergent Beam

Convergent beam electron diffraction is a powerful technique for determining the crystal structure of a material in TEM. In this paper we have applied it to the study of the intermetallic phases in the Cu-rich end of the Cu-Zr system. These phases are highly ordered. Their composition and structure has been previously studied by microprobe and x-ray diffraction with sometimes conflicting results.The crystalline phases were obtained by annealing amorphous sputter-deposited Cu-Zr. Specimens were thinned for TEM by ion milling and observed in a Philips EM 400. Due to the large unit cells involved, a small convergence angle of diffraction was used; however, the three-dimensional lattice and symmetry information of convergent beam microdiffraction patterns is still present. The results are as follows:1) 21 at% Zr in Cu: annealed at 500°C for 5 hours. An intermetallic phase, Cu3.6Zr (21.7% Zr), space group P6/m has been proposed near this composition (2). The major phase of our annealed material was hexagonal with a point group determined as 6/m.

Prediction of internal geometry and tensile behavior of 3D woven solid structures by mathematical coding

2021 ◽  
pp. 152808372110013
Author(s):  
Vivek R Jayan ◽  
Lekhani Tripathi ◽  
Promoda Kumar Behera ◽  
Michal Petru ◽  
BK Behera
Keyword(s):  
Volume Fraction ◽  
Three Dimensional ◽  
Areal Density ◽  
Woven Fabrics ◽  
Tensile Behavior ◽  
Geometrical Parameters ◽  
Fiber Volume ◽  
Acceptable Error ◽  
Internal Geometry ◽  
Unit Cells

The internal geometry of composite material is one of the most important factors that influence its performance and service life. A new approach is proposed for the prediction of internal geometry and tensile behavior of the 3 D (three dimensional) woven fabrics by creating the unit cell using mathematical coding. In many technical applications, textile materials are subjected to rates of loading or straining that may be much greater in magnitude than the regular household applications of these materials. The main aim of this study is to provide a generalized method for all the structures. By mathematical coding, unit cells of 3 D woven orthogonal, warp interlock and angle interlock structures have been created. The study then focuses on developing code to analyze the geometrical parameters of the fabric like fabric thickness, areal density, and fiber volume fraction. Then, the tensile behavior of the coded 3 D structures is studied in Ansys platform and the results are compared with experimental values for authentication of geometrical parameters as well as for tensile behavior. The results show that the mathematical coding approach is a more efficient modeling technique with an acceptable error percentage.

The crystal structure of myoglobin. VI. Seal myoglobin

1960 ◽  
Vol 258 (1293) ◽  
pp. 181-201 ◽  
Keyword(s):  
Tertiary Structure ◽  
Heavy Atom ◽  
Three Dimensional ◽  
Sperm Whale ◽  
Fourier Synthesis ◽  
Heavy Atoms ◽  
Isomorphous Replacement ◽  
Unit Cells ◽  
The Common ◽  
Sperm Whale Myoglobin

Myoglobin from the common seal ( Phoca vitulina ) when crystallized from ammonium sulphate forms monoclinic crystals with space group the unit cell, a = 57·9Å, b = 29·6Å, c = 106·4Å, β = 102°15', contains four molecules. The method of isomorphous replacement has been used in an investigation of the centrosymmetric b -axis projection in which it has been possible to determine signs for nearly all the h0l reflexions having spacings greater than 4Å. Three independent heavy-atom derivatives were employed and the signs so determined have been used to compute a map of the electron density projected on the (010) plane. This projection has been interpreted in terms of the molecule of sperm-whale myoglobin, as deduced by Bodo, Dintzis, Kendrew & Wyckoff (1959) from a three-dimensional Fourier synthesis to 6Å resolution. The results of the interpretation show that the two myoglobin molecules are very similar in form (tertiary structure) in spite of the differences in their amino-acid composition. The relative orientation of the two unit cells with respect to the myoglobin molecule is given and a comparison is made of the positions of the heavy atoms in each molecule.

scholarly journals Development of PLA Fibers as an Antimicrobial Agent with Enhanced Infection Resistance using Electrospinning/Plasma Technology

2020 ◽  
Author(s):  
Abdelrahman Mahmoud ◽  
Mohammed Naser ◽  
Mahmoud Abdelrasool ◽  
Khalid Jama ◽  
Mohamed Hussein ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Three Dimensional ◽  
Plasma Technology ◽  
Energy Increase ◽  
The Past ◽  
Unit Cells ◽  
Infection Resistance ◽  
Dimensional Shape ◽  
Fiber Dimensions ◽  
Three Dimensional Shape

Humans are vulnerable and easily prone to all kind of injuries, diseases, and traumas that can be damaging to their tissues (including its building unit, cells), bones, or even organs. Therefore, they would need assistance in healing or re-growing once again. Medical scaffolds have emerged over the past decades as one of the most important concepts in the tissue-engineering field as they enable and aide the re-growth of tissues and their successors. An optimal medical scaffold should be addressing the following factors: biocompatibility, biodegradability, mechanical properties, scaffold architecture/porosity, precise three-dimensional shape and manufacturing technology. There are several materials utilized in the fabrication of medical scaffolds, but one of the most extensively studied polymers is polylactic acid (PLA). PLA is biodegradable thermoplastic aliphatic polyester that is derived from naturally produced lactic acid. PLA is characterized with its excellent mechanical properties, biodegradability, promising eco-friendly, and excellent biocompatibility. PLA can be fabricated into nanofibers for medical scaffolds used through many techniques; electrospinning is one of the widely used methods for such fabrication. Electrospinning is a favorable technique because in the preparation of scaffolds, some parameters such as fiber dimensions, morphology, and porosity are easily controlled. A problem that is associated with medical scaffolds, such as inflammation and infection, was reported in many cases resulting in a degradation of tissues. Therefore, a surface modification was thought of as a needed solution which mostly focuses on an incorporation of extra functionalities responsible for the surface free energy increase (wettability). Therefore, plasma technique was a favorable solution for the surface treatment and modification. Plasma treatment enables the formation of free radicals. These radicals can be easily utilized for grafting process. Subsequently, ascorbic acid (ASA) could be incorporated as anti-inflammatory and anti-infection agent on the plasma pretreated surface of scaffolds.

Development of Scaffold Building Units and Assembly for Tissue Engineering Using Fused Deposition Modelling

2009 ◽  
Vol 83-86 ◽  
pp. 269-274 ◽  
Author(s):  
Syed H. Masood ◽  
Kadhim Alamara
Keyword(s):  
Tissue Engineering ◽  
Pore Size ◽  
Fused Deposition Modeling ◽  
Porous Scaffold ◽  
Cell Structure ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Fused Deposition Modelling ◽  
Fused Deposition ◽  
Unit Cells

In tissue engineering (TE), a porous scaffold structure of biodegradable material is required as a template to guide the proliferation, growth and development of cells appropriately in three dimensions. The scaffold must meet design requirements of appropriate porosity, pore size and interconnected structure to allow cell proliferation and adhesion. This paper presents a methodology for design and manufacture of TE scaffolds with varying porosity by employing open structure building units and Fused Deposition Modeling (FDM) rapid prototyping technique. A computer modeling approach for constructing and assembly of three-dimensional unit cell structure is presented to provide a solution of scaffolds design that can potentially meet the diverse requirements of TE applications. A parametric set of open polyhedral unit cells is used to assist the user in designing the required micro-architecture of the scaffold with required porosity and pore size and then the Boolean operation is used to create the scaffold of a given CAD model from the designed microstructure. The procedure is verified by fabrication of physical scaffolds using the commercial FDM system.

Design of Three-Dimensional, Triply Periodic Unit Cell Scaffold Structures for Additive Manufacturing

2018 ◽  
Vol 140 (7) ◽  
Author(s):  
Mazher Iqbal Mohammed ◽  
Ian Gibson
Keyword(s):  
Additive Manufacturing ◽  
Periodic Structures ◽  
Three Dimensional ◽  
Unit Cell ◽  
Final Size ◽  
Fused Filament Fabrication ◽  
Cell Structures ◽  
Triply Periodic ◽  
Unit Cells ◽  
Scaffold Structure

Highly organized, porous architectures leverage the true potential of additive manufacturing (AM) as they can simply not be manufactured by any other means. However, their mainstream usage is being hindered by the traditional methodologies of design which are heavily mathematically orientated and do not allow ease of controlling geometrical attributes. In this study, we aim to address these limitations through a more design-driven approach and demonstrate how complex mathematical surfaces, such as triply periodic structures, can be used to generate unit cells and be applied to design scaffold structures in both regular and irregular volumes in addition to hybrid formats. We examine the conversion of several triply periodic mathematical surfaces into unit cell structures and use these to design scaffolds, which are subsequently manufactured using fused filament fabrication (FFF) additive manufacturing. We present techniques to convert these functions from a two-dimensional surface to three-dimensional (3D) unit cell, fine tune the porosity and surface area, and examine the nuances behind conversion into a scaffold structure suitable for 3D printing. It was found that there are constraints in the final size of unit cell that can be suitably translated through a wider structure while still allowing for repeatable printing, which ultimately restricts the attainable porosities and smallest printed feature size. We found this limit to be approximately three times the stated precision of the 3D printer used this study. Ultimately, this work provides guidance to designers/engineers creating porous structures, and findings could be useful in applications such as tissue engineering and product light-weighting.

scholarly journals Divergent Design of Mechanical Metamaterials Clan Deducted from Arc-serpentine Curve

2021 ◽  
Author(s):  
Shengli Mi ◽  
Hongyi Yao ◽  
Xiaoyu Zhao ◽  
Wei Sun
Keyword(s):  
Thick Plate ◽  
Three Dimensional ◽  
Spatial Arrangement ◽  
Design Strategies ◽  
Shape Morphing ◽  
Mechanical Metamaterials ◽  
Unit Cells ◽  
Combinatorial Principles ◽  
Composite Curve ◽  
Typical Design

Abstract The exotic properties of mechanical metamaterials are determined by their unit-cells' structure and spatial arrangement, in analogy with the atoms of conventional materials. Companioned with the mechanism of structural or cellular materials1–5, the ancient wisdom of origami6–11 and kirigami12–16 and the involvement of multiphysics interaction2,17,18 enrich the programable mechanical behaviors of metamaterials, including shape-morphing8,12,14,16,19, compliance4,5,8,17,20, texture2,18,21, and topology11,18,22−25. However, typical design strategies are mainly convergent, which transfers various structures into one family of metamaterials that are relatively incompatible with the others and do not fully bring combinatorial principles3,10,26 into play. Here, we report a divergent strategy that designs a clan of mechanical metamaterials with diverse properties derived from a symmetric curve consisting of serpentines and arcs. We derived this composite curve into planar and cubic unit-cells and modularized them by attaching magnetics. Moreover, stacking each of them yields two- and three-dimensional auxetic metamaterials, respectively. Assembling with both modules, we achieved three thick plate-like metamaterials separately with flexibility, in-plane buckling, and foldability. Furthermore, we demonstrated that the hybrid of paradox properties is possible by combining two of the above assembles. We anticipate that this divergent strategy paves the path of building a hierarchical library of diverse combinable mechanical metamaterials and making conventional convergent strategies more efficient to various requests. Main

An Executable Notation, With Illustrations From Elementary Crystallography

1994 ◽  
Author(s):  
Donald B. Mclntyre
Keyword(s):  
Plate Tectonics ◽  
Periodic Structures ◽  
Dimensional Space ◽  
Reciprocal Lattice ◽  
Three Dimensional ◽  
Cubic Symmetry ◽  
Multiple Data ◽  
Special Cases ◽  
Unit Cells ◽  
Crystallographic Axes

Elementary crystallography is an ideal context for introducing students to mathematical geology. Students meet crystallography early because rocks are made of crystalline minerals. Moreover, morphological crystallography is largely the study of lines and planes in real three-dimensional space, and visualizing the relationships is excellent training for other aspects of geology; many algorithms learned in crystallography (e.g., rotation of arrays) apply also to structural geology and plate tectonics. Sets of lines and planes should be treated as entities, and crystallography is an ideal environment for introducing what Sylvester (1884) called "Universal Algebra or the Algebra of multiple quantity." In modern terminology, we need SIMD (Single Instruction, Multiple Data) or even MIMD. This approach, initiated by W.H. Bond in 1946, dispels the mysticism unnecessarily associated with Miller indices and the reciprocal lattice; edges and face-normals are vectors in the same space. The growth of mathematical notation has been haphazard, new symbols often being introduced before the full significance of the functions they represent had been understood (Cajori, 1951; Mclntyre, 1991b). Iverson introduced a consistent notation in 1960 (e.g., Iverson 1960, 1962, 1980). His language, greatly extended in the executable form called J (Iverson, 1993), is used here. For information on its availability as shareware, see the Appendix. Publications suitable as tutorials in , J are available (e.g., Iverson. 1991; Mclntyre, 1991 a, b; 1992a,b,c; 1993). Crystals are periodic structures consisting of unit cells (parallelepipeds) repeated by translation along axes parallel to the cell edges. These edges define the crystallographic axes. In a crystal of cubic symmetry they are orthogonal and equal in length (Cartesian). Those of a triclinic crystal, on the other hand, are unequal in length and not at right angles. The triclinic system is the general case; others are special cases. The formal description of a crystal gives prominent place to the lengths of the axes (a, b, and c) and the interaxial angles ( α, β, and γ). A canonical form groups these values into a 2 x 3 table (matrix), the first row being the lengths and the second the angles.

The phase problem and electron-density maps

2010 ◽  
Author(s):  
Jenny Pickworth Glusker ◽  
Kenneth N. Trueblood
Keyword(s):  
Crystal Structure ◽  
Fourier Series ◽  
Diffraction Pattern ◽  
Electron Density ◽  
Bragg Reflection ◽  
Three Dimensional ◽  
Density Maps ◽  
Structure Factors ◽  
Unit Cells ◽  
Phase Angles

In order to obtain an image of the material that has scattered X rays and given a diffraction pattern, which is the aim of these studies, one must perform a three-dimensional Fourier summation. The theorem of Jean Baptiste Joseph Fourier, a French mathematician and physicist, states that a continuous, periodic function can be represented by the summation of cosine and sine terms (Fourier, 1822). Such a set of terms, described as a Fourier series, can be used in diffraction analysis because the electron density in a crystal is a periodic distribution of scattering matter formed by the regular packing of approximately identical unit cells. The Fourier series that is used provides an equation that describes the electron density in the crystal under study. Each atom contains electrons; the higher its atomic number the greater the number of electrons in its nucleus, and therefore the higher its peak in an electrondensity map.We showed in Chapter 5 how a structure factor amplitude, |F (hkl)|, the measurable quantity in the X-ray diffraction pattern, can be determined if the arrangement of atoms in the crystal structure is known (Sommerfeld, 1921). Now we will show how we can calculate the electron density in a crystal structure if data on the structure factors, including their relative phase angles, are available. The Fourier series is described as a “synthesis” when it involves structure amplitudes and relative phases and builds up a picture of the electron density in the crystal. By contrast, a “Fourier analysis” leads to the components that make up this series. The term “relative” is used here because the phase of a Bragg reflection is described relative to that of an imaginary wave diffracted in the same direction at a chosen origin of the unit cell.

scholarly journals Direct-tuning methods for semiconductor metamaterials

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Li Min ◽  
Wenjin Wang ◽  
Lirong Huang ◽  
Yonghong Ling ◽  
Tongjun Liu ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Spatial Light Modulators ◽  
Efficient Manner ◽  
Resonance Strength ◽  
Tuning Method ◽  
Resonance Modes ◽  
Resonance Frequencies ◽  
Unit Cells ◽  
Low Efficiency ◽  
Semiconductor Metamaterials

AbstractAmong various tunable optical devices, tunable metamaterials have exhibited their excellent ability to dynamically manipulate lights in an efficient manner. However, for unchangeable optical properties of metals, electromagnetic resonances of popular metallic metamaterials are usually tuned indirectly by varying the properties or structures of substrates around the resonant unit cells, and the tuning of metallic metamaterials has significantly low efficiency. In this paper, a direct-tuning method for semiconductor metamaterials is proposed. The resonance strength and resonance frequencies of the metamaterials can be significantly tuned by controlling free carriers’ distributions in unit cells under an applied voltage. This direct-tuning method has been verified in both two-dimensional and three-dimensional semiconductor metamaterials. In principle, the method allows for simplifying the structure of tunable metamaterials and opens the path to applications in ultrathin, linearly-tunable, and on-chip integrated optical components (e.g., tunable ultrathin lenses, nanoscale spatial light modulators and optical cavities with resonance modes switchable).

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