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Symmetry of Crystals, Point Groups and Space Groups
Published in Dong ZhiLi, Fundamentals of Crystallography, Powder X-ray Diffraction, and Transmission Electron Microscopy for Materials Scientists, 2022
Based on the symmetry characteristics, the 32 crystallographic point groups can be classified into seven crystal systems as shown in Figure 1.5. Each crystal system has its lattice constraints due to the symmetry elements in the crystal. The order of the point group symbols for each crystal system highly reflects the symmetry characteristics of that system, and they are presented in Table 2.5.
Crystalline Structure of Metals
Published in Zainul Huda, Metallurgy for Physicists and Engineers, 2020
Crystalline solids are usually classified as belonging to one of the following seven crystal systems: (1) cubic, (2) hexagonal, (3) tetragonal, (4) trigonal, (5) orthorhombic, (6) monoclinic, and (7) triclinic; these seven systems depend on the geometry of the unit cell, as shown in Figure 2.3. It is evident in Figure 2.3 that the simplest crystal structure is the cubic system, in which all edges of the unit cell are equal to each other, and all the angles are equal to 90°. The tetragonal and orthorhombic systems refer to rectangular unit cells, but the edges are not all equal. In the remaining systems, some or all of the angles are not equal to 90°. The least symmetrical structure is the triclinic system in which no edges are equal and no angles are equal to each other or to 90° (Barret and Massalski, 1980). The hexagonal system is worth noting; here two edges of the unit cell are equal and subtend an angle of 120°. Hexagonal crystals are quite common both in metals and ceramics; examples include crystal structures of zinc, graphite, and the like.
Crystal Structure
Published in Alan Owens, Semiconductor Radiation Detectors, 2019
Crystal systems are a grouping of crystal structures according to an axial system used to describe their lattice. Each system consists of a set of three axes in a particular geometrical arrangement. There are seven unique crystal systems. The simplest and most symmetric is the cubic (or isometric) system, having the symmetry of a cube. It is defined as having four three-fold rotational axes oriented at 109.5 degrees (the tetrahedral angle) with respect to each other, forming the diagonals of the cube. The other six systems, in order of decreasing symmetry, are hexagonal, tetragonal, rhombohedral (also known as trigonal), orthorhombic, monoclinic and triclinic.
Ferroelectric, Piezoelectric Mechanism and Applications
Published in Journal of Asian Ceramic Societies, 2022
Arun Singh, Shagun Monga, Neeraj Sharma, K Sreenivas, Ram S. Katiyar
The symmetry elements are used to describe symmetry about a point in space, and employing these elements of symmetry, all crystals can be separated into 32 diverse point groups or classes [3]. These 32-point groups are subcategories of the seven basic crystal systems, the crystal system is a grouping of crystal structures that are categorized according to the axial system used to describe their “lattice”. A crystal’s lattice is a three dimensional network of atoms that are arranged in a symmetrical pattern. Each crystal system consists of a set of three axes in a particular geometrical arrangement. The seven unique crystal systems, listed in order of decreasing symmetry, are: 1. Isometric System, 2. Hexagonal System, 3. Tetragonal System, 4. Rhombohedric (Trigonal) System, 5. Orthorhombic System, 6. Monoclinic System, 7. Triclinic System. Twenty-one out of the 32-point groups lack a center of symmetry, and 20 exhibit piezoelectricity as they become polarized on the application of mechanical stress. The remaining one point group out of the 21 does not exhibit piezoelectricity, even though it lacks a center of symmetry, due to the combination of symmetry elements. Ten out of the 20 piezoelectric point groups display a polarization that has a finite and permanent value, termed as spontaneous polarization, which exists when the applied stress or field is zero, and such dielectric materials are known as polar materials or pyroelectric materials.
An unconventional approach in investigating wettability contact angle measurement in shale resources
Published in Petroleum Science and Technology, 2022
Salah Almudhhi, Mohammed Alostath, Waleed Al-Bazzaz, Hamid Sharifigaliuk, Ali Qubian
In this unconventional approach of investigating wettability in shales a fourth step classification of crystallography of mineral is included (Table 5). The crystallography setting of each mineral is interesting and confirms the complexity of the mineral contribution toward the shale rock contact angle wettability. The crystal systems available in the shale rock are all reported in (Table 6). The crystal habitat suggests that crystal lengths and angles of intersection are unique for each pure mineral crystal system. All intersect angles show angle intersections α, β and γ between 90° −120°. This result suggests that the crystallography of shale minerals is weakly-oil-wet (WOW) according to Al-Bazzaz et al. classification (2018–2019). The crystallography classification is in pure crystal habitat and the shale habitat setting has inconclusive relationship toward shale crystallography wettability.