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Crystal Clear
Published in Sharon Ann Holgate, Understanding Solid State Physics, 2021
The unit cells labelled A and B each contain a total of one lattice point, since there is only actually one quarter of each of the four points at the corners of the cell within the area of the cell. Any unit cell that contains just one lattice point is known as a primitive unit cell (sometimes shortened to “primitive cell”). This is the minimum volume (in 3-D) or area (in 2-D) that any unit cell can have and still be able to build up the entire crystal structure if it is repeated over and over again by translating it along one of its edges.
An Introduction to Metals
Published in Bankim Chandra Ray, Rajesh Kumar Prusty, Deepak Nayak, Phase Transformations and Heat Treatments of Steels, 2020
Bankim Chandra Ray, Rajesh Kumar Prusty, Deepak Nayak
In a crystalline material, atoms occupy some specific points in the space. An example of atomic arrangement is shown in Figure 1.4a. Atomic positions (center of the atom) can be thought of the points of intersection of an array of infinite length lines. This array of straight lines is termed as space lattice (Figure 1.4b). These atomic positions are identical to each other, or in other words, all the atoms are having the same surroundings. A basis or motif can be defined as a group of atoms that are located at a particular order with respect to each other. Combination of both the lattice and motif gives rise to the complete crystal structure of the atoms. A unit cell in a crystal is further defined as the smallest representative volume element (Figure 1.4c), which upon repetition in all three dimensions yields the complete crystal structure. A unit cell is a fundamental entity of all the crystalline materials. A unit cell is constituted by its six parameters, three intersecting axial lengths (sides), and correspondingly three angles between each pair of axes. The unit cell dimensions in the X, Y, and Z (not necessarily perpendicular to each other) directions are normally represented by a, b, and c, respectively. α, β, and γ represent the angles between Y and Z, Z and X, and X and Y, respectively, as shown in Figure 1.4d.
Crystalline Structure of Metals
Published in Zainul Huda, Metallurgy for Physicists and Engineers, 2020
Ideally, a crystal is a repetition of identical structural units in a three dimensional space. A unit cell is the smallest repeating pattern of atomic arrangement in a crystal structure. A lattice refers to the periodicity in the crystal. The terms “crystal lattice” and “crystal structure” may be used interchangeably. A unit cell can be described in terms of the lengths of three adjacent edges (a, b, and c) and the angles between them (α, β, and γ) (see Figure 2.2).
Low-frequency property and vibration reduction design of chiral star-shaped compositive mechanical metamaterials
Published in Mechanics of Advanced Materials and Structures, 2023
Ying Zhang, Liang Wang, Qian Ding, Hongge Han, Jinxin Xu, Hao Yan, Yongtao Sun, Qun Yan, Haoqiang Gao
The smallest periodic unit of a crystal lattice is called the unit cell. The whole lattice can be obtained by translation of the primitive cell according to two non-collinear vectors, which are denoted the basis vectors [43]. The basis vectors are given by ei (i = 1,2). The coordinates of each lattice point are the positive lattice of the lattice. Where rj represents the position of the reference cell in the crystal, and q(rj) represents the position of any lattice point in the crystal, then where, qjis the amplitude, ω is the frequency in rad/s, and k is the wave vector of the plane wave.
Effective elastic, thermoelastic, and piezoelectric properties of braided composites using equivalent laminate modeling
Published in Advanced Composite Materials, 2021
Genio Odi Putra, Dae-Hyun Hwang, Jae-Hung Han
A unit cell is defined as the smallest part of a specified material that contains sufficient information of its homogenized macroscopic characteristics. The unit cell size is determined by the yarn dimension, the yarn distribution, and the braiding angle configuration. In this work, the length of the unit cell was selected as the axial spacing between center lines of twoneighboring braider yarns, while the width of the unit cell was selected as the axial yarn spacing. Figure 5 exhibits a unit cell representation for triaxial configuration.
Influence of tin precursor concentration on physical properties of nebulized spray deposited tin disulfide thin films
Published in Journal of Asian Ceramic Societies, 2018
N. Anitha, M. Anitha, J. Raj Mohamed, S. Valanarasu, L. Amalraj
The dislocation is an irregularity in the crystal structure. It can strongly affect many properties of the materials. Crystalline materials contain a periodic structure with the molecules or atoms placed in repeating fixed positions and this periodicity can be determined by the unit cell parameters. The dislocation or the crystallographic defects interrupt the regular periodic lattice structure. The dislocation density (δ) can be evaluated using relation [27].