Electrostatic energy in ionic crystals

1981 ◽  
Vol 375 (1763) ◽  
pp. 475-505 ◽  
Keyword(s):  
Dipole Moment ◽  
Ionic Crystal ◽  
Unit Cell ◽  
Electrostatic Energy ◽  
Cubic Crystal ◽  
Simple Cubic ◽  
Dependent Part ◽  
Unit Cells ◽  
Cell Energy

The problem of calculating electrostatic energies in large, finite and arbitrarily shaped pieces of ionic crystal is analysed. The electrostatic energy of a unit cell of the crystal deep within the interior of the piece of crystal is shown to be composed of a shape-independent part depending on the structure of the crystal lattice concerned and the distribution of ions within a unit cell, and a shape-dependent part which depends on the shape of the piece of crystal and the dipole moment of a unit cell. The shape-dependent part is zero if this dipole moment is zero. The electrostatic energy of the whole piece of crystal is shown to be the unit cell energy multiplied by the number of unit cells in the piece of crystal, plus corrections proportional to the surface area of the piece of crystal. These surface corrections are calculated explicitly for a finite cube of simple cubic crystal. Different descriptions of the same crystal structure are shown to lead to different bulk energies. This disagreement is discussed for the CsCl lattice, and is shown to arise from the way the different descriptions of the lattice imply different surface structures on the surface of a cube of crystal. The energy of a test charge at the surface of a cube of simple cubic crystal, and then the energy of layers of charges on the surfaces of a cube of simple cubic crystal, are analysed. The analyses confirm the origin of the disagreement in bulk energies for the two descriptions of the CsCl lattice. The role of the energies of surface layers in the bulk electrostatic energy of a piece of ionic crystal, and the relation of this bulk energy to a shape-independent Madelung constant are discussed. Some conjectures on the role of bulk energies in surface reconstruction are also discussed.

Importance of Unit Cells in Accurate Evaluation of the Characteristics of Graphene

2016 ◽  
Vol 71 (4) ◽  
pp. 315-320 ◽  
Author(s):  
Hassan Sabzyan ◽  
Narges Sadeghpour
Keyword(s):  
Electric Field ◽  
Density Functional ◽  
Unit Cell ◽  
Atomic Charges ◽  
Dft Methods ◽  
Functional Theory ◽  
Accurate Evaluation ◽  
Unit Cell Size ◽  
Unit Cells ◽  
Cell Energy

AbstractEffects of the size of the unit cell on energy, atomic charges, and phonon frequencies of graphene at the Γ point of the Brillouin zone are studied in the absence and presence of an electric field using density functional theory (DFT) methods (LDA and DFT-PBE functionals with Goedecker–Teter–Hutter (GTH) and Troullier–Martins (TM) norm-conserving pseudopotentials). Two types of unit cells containing nC=4–28 carbon atoms are considered. Results show that stability of graphene increases with increasing size of the unit cell. Energy, atomic charges, and phonon frequencies all converge above nC=24 for all functional-pseudopotentials used. Except for the LDA-GTH calculations, application of an electric field of 0.4 and 0.9 V/nm strengths does not change the trends with the size of the unit cell but instead slightly decreases the binding energy of graphene. Results of this study show that the choice of unit cell size and type is critical for calculation of reliable characteristics of graphene.

scholarly journals Effect of unit cell shape and strut size on flexural properties of ordered Copper foam

2019 ◽  
Vol 12 (3) ◽  
Author(s):  
Pulak M Pandey ◽  
Gurminder Singh
Keyword(s):  
Cell Shape ◽  
Flexural Modulus ◽  
Unit Cell ◽  
The Body ◽  
Flexural Properties ◽  
Copper Foam ◽  
Simple Cubic ◽  
Unit Cells ◽  
Cell Shapes ◽  
Different Shapes

The effect of unit cell shape and strut size variation was studied on the flexural properties of the ordered copper foam in the present study. The developed rapid manufacturing method using 3D printing and ultrasonic vibrationassisted pressureless sintering was employed to fabricate samples. Two different shapes such as simple cubic (SC) and body-centred cubic (BCC) were used as the unit cells for the samples with three different strut sizes 1, 1.3 and 1.6 mm. Three-point bend test was performed to obtain the flexural properties such as flexural modulus and ultimate flexural strength. Different shapes of failure curves were noticed during the test, which was owing to the different unit cell shapes. The fracture was obtained to be brittle in nature due to the micro-pores of the struts. The fractured surfaces of the two different unit cells were also studied. The samples with the simple cubic unit cell shapes possessed better flexural properties as compared to the body-centred cubic unit cell samples.

The orientation of sickle hemoglobin fibers within fascicles

1988 ◽  
Vol 46 ◽  
pp. 400-401
Author(s):  
Christopher A. Miller ◽  
Bridget Carragher ◽  
William A. McDade ◽  
Robert Josephs
Keyword(s):  
Sickle Cell ◽  
Sickle Cell Anemia ◽  
Relative Orientation ◽  
Unit Cell ◽  
Red Cell ◽  
High Ph ◽  
Sickle Hemoglobin ◽  
Polar Crystal ◽  
Helical Configuration

Highly ordered bundles of deoxyhemoglobin S (HbS) fibers, termed fascicles, are intermediates in the high pH crystallization pathway of HbS. These fibers consist of 7 Wishner-Love double strands in a helical configuration. Since each double strand has a polarity, the odd number of double strands in the fiber imparts a net polarity to the structure. HbS crystals have a unit cell containing two double strands, one of each polarity, resulting in a net polarity of zero. Therefore a rearrangement of the double strands must occur to form a non-polar crystal from the polar fibers. To determine the role of fascicles as an intermediate in the crystallization pathway it is important to understand the relative orientation of fibers within fascicles. Furthermore, an understanding of fascicle structure may have implications for the design of potential sickling inhibitors, since it is bundles of fibers which cause the red cell distortion responsible for the vaso-occlusive complications characteristic of sickle cell anemia.

Bayesian removal of noise for increased sensitivity in vector pattern recognition lattice imaging of interfaces

1993 ◽  
Vol 51 ◽  
pp. 994-995
Author(s):  
L. Fei ◽  
P. Fraundorf
Keyword(s):  
Pattern Recognition ◽  
Perfect Crystal ◽  
Unit Cell ◽  
Ion Milling ◽  
Beam Radiation ◽  
Major Interest ◽  
Unit Cells ◽  
Mapping Process ◽  
Increased Sensitivity ◽  
Electron Microscopes

Interface structure is of major interest in microscopy. With high resolution transmission electron microscopes (TEMs) and scanning probe microscopes, it is possible to reveal structure of interfaces in unit cells, in some cases with atomic resolution. A. Ourmazd et al. proposed quantifying such observations by using vector pattern recognition to map chemical composition changes across the interface in TEM images with unit cell resolution. The sensitivity of the mapping process, however, is limited by the repeatability of unit cell images of perfect crystal, and hence by the amount of delocalized noise, e.g. due to ion milling or beam radiation damage. Bayesian removal of noise, based on statistical inference, can be used to reduce the amount of non-periodic noise in images after acquisition. The basic principle of Bayesian phase-model background subtraction, according to our previous study, is that the optimum (rms error minimizing strategy) Fourier phases of the noise can be obtained provided the amplitudes of the noise is given, while the noise amplitude can often be estimated from the image itself.

scholarly journals Prediction of Effective Thermal Conductivities of Four-Directional Carbon/Carbon Composites by Unit Cells with Different Sizes

2021 ◽  
Vol 11 (3) ◽  
pp. 1171
Author(s):  
Chang Xu ◽  
Zhihong Sun ◽  
Guowei Shao
Keyword(s):  
Carbon Fiber ◽  
Longitudinal Direction ◽  
Unit Cell ◽  
Carbon Composites ◽  
Temperature Boundary ◽  
The Matrix ◽  
Unit Cells ◽  
Experimental Values ◽  
Different Diameters ◽  
Thermal Conductivities

Two-unit cells developed to predict the effective thermal conductivities of four-directional carbon/carbon composites with the finite element method are proposed in this paper. The smaller-size unit cell is formulated from the larger-size unit cell by two 180° rotational transformations. The temperature boundary conditions corresponding to the two-unit cells are derived, and the validity is verified by the temperature and heat flux distributions at specific positions of the larger-size unit cell and the smaller-size unit cell. The thermal conductivities of the carbon fiber bundles and carbon fiber rods are measured firstly. Then, combined with the properties of the matrix, the effective thermal conductivities of the four-directional carbon/carbon composites are numerically predicted. The results in transverse direction predicted by the larger-size unit cell and the smaller-size unit cell are both higher than experimental values, which are 5.8 to 6.2% and 7.3 to 8.2%, respectively. In longitudinal direction, the calculated thermal conductivities of the larger-size unit cell and the smaller-size unit cell are 6.8% and 6.2% higher than the experimental results, respectively. In addition, carbon fiber rods with different diameters are set to clarify the influence on the effective thermal conductivities of the four-directional carbon/carbon composites.

scholarly journals A Multiband Antenna Stacked with Novel Metamaterial SCSRR and CSSRR for WiMAX/WLAN Applications

Micromachines ◽  
2021 ◽  
Vol 12 (2) ◽  
pp. 113
Author(s):  
Rajiv Mohan David ◽  
Mohammad Saadh AW ◽  
Tanweer Ali ◽  
Pradeep Kumar
Keyword(s):  
Split Ring Resonator ◽  
Unit Cell ◽  
Ring Resonators ◽  
Split Ring ◽  
Medium Theory ◽  
High Frequency Structure Simulator ◽  
Dimension Analysis ◽  
Unit Cells ◽  
Coaxial Feed ◽  
Triple Band

This paper presents an innovative method for the design of a triple band meta-mode antenna. This unique design of antenna finds application in a particular frequency band of WLAN and WiMAX. This antenna comprises of a square complimentary split ring resonator (SCSRR), a coaxial feed, and two symmetrical comb shaped split ring resonators (CSSRR). The metamaterial unit cell SCSRR independently gains control in the band range 3.15–3.25 GHz (WiMAX), whereas two symmetrical CSSRR unit cell controls the band in the ranges 3.91–4.01 GHz and 5.79–5.94 GHz (WLAN). This design methodology and the study of the suggested unit cells structure are reviewed in classical waveguide medium theory. The antenna has a miniaturized size of only 0.213λ0 × 0.192λ0 × 0.0271λ0 (20 × 18 × 2.54 mm3, where λ0 is the free space wavelength at 3.2 GHz). The detailed dimension analysis of the proposed antenna and its radiation efficiency are also presented in this paper. All the necessary simulations are carried out in High Frequency Structure Simulator (HFSS) 13.0 tool.

scholarly journals Dynamic crushing behavior of closed-cell aluminum foams based on different space-filling unit cells

2021 ◽  
Vol 21 (3) ◽  
Author(s):  
S. Talebi ◽  
R. Hedayati ◽  
M. Sadighi
Keyword(s):  
Surface Area ◽  
Dynamic Behavior ◽  
Energy Absorption ◽  
Peak Stress ◽  
Absorption Capacity ◽  
Unit Cell ◽  
Lattice Structures ◽  
Energy Absorption Capacity ◽  
Closed Cell ◽  
Unit Cells

AbstractClosed-cell metal foams are cellular solids that show unique properties such as high strength to weight ratio, high energy absorption capacity, and low thermal conductivity. Due to being computation and cost effective, modeling the behavior of closed-cell foams using regular unit cells has attracted a lot of attention in this regard. Recent developments in additive manufacturing techniques which have made the production of rationally designed porous structures feasible has also contributed to recent increasing interest in studying the mechanical behavior of regular lattice structures. In this study, five different topologies namely Kelvin, Weaire–Phelan, rhombicuboctahedron, octahedral, and truncated cube are considered for constructing lattice structures. The effects of foam density and impact velocity on the stress–strain curves, first peak stress, and energy absorption capacity are investigated. The results showed that unit cell topology has a very significant effect on the stiffness, first peak stress, failure mode, and energy absorption capacity. Among all the unit cell types, the Kelvin unit cell demonstrated the most similar behavior to experimental test results. The Weaire–Phelan unit cell, while showing promising results in low and medium densities, demonstrated unstable behavior at high impact velocity. The lattice structures with high fractions of vertical walls (truncated cube and rhombicuboctahedron) showed higher stiffness and first peak stress values as compared to lattice structures with high ratio of oblique walls (Weaire–Phelan and Kelvin). However, as for the energy absorption capacity, other factors were important. The lattice structures with high cell wall surface area had higher energy absorption capacities as compared to lattice structures with low surface area. The results of this study are not only beneficial in determining the proper unit cell type in numerical modeling of dynamic behavior of closed-cell foams, but they are also advantageous in studying the dynamic behavior of additively manufactured lattice structures with different topologies.

The Role of Topology and Tissue Mechanics in Remora Attachment

2014 ◽  
Vol 1648 ◽  
Author(s):  
Michael Culler ◽  
Keri A. Ledford ◽  
Jason H. Nadler
Keyword(s):  
Finite Element ◽  
Material Properties ◽  
Tissue Mechanics ◽  
Unit Cell ◽  
Surface Topology ◽  
Finite Element Models ◽  
Cell Geometry ◽  
Critical Step ◽  
Tissue Material

ABSTRACTRemora fish are capable of fast, reversible and reliable adhesion to a wide variety of both natural and artificial marine hosts through a uniquely evolved dorsal pad. This adhesion is partially attributed to suction, which requires a robust seal between the pad interior and the ambient environment. Understanding the behavior of remora adhesion based on measurable surface parameters and material properties is a critical step when creating artificial, bio-inspired devices. In this work, structural and fluid finite element models (FEM) based on a simplified “unit cell” geometry were developed to predict the behavior of the seal with respect to host/remora surface topology and tissue material properties.

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