The American Mineralogist Crystal Structure Database
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
Crystal Structures
Crystal Structures Academic Resource Center Crystallinity: Repeating or periodic array over large atomic distances. 3-D pattern in which each atom is bonded to its nearest neighbors Crystal structure: the manner in which atoms, ions, or molecules are spatially arranged. Unit cell: small repeating entity of the atomic structure. The basic building block of the crystal structure. It defines the entire crystal structure with the atom positions within. Lattice: 3D array of points coinciding with atom positions (center of spheres) Metallic Crystal Structures FCC (face centered cubic): Atoms are arranged at the corners and center of each cube face of the cell. FCC continued Close packed Plane: On each face of the cube Atoms are assumed to touch along face diagonals. 4 atoms in one unit cell. a 2R 2 BCC: Body Centered Cubic • Atoms are arranged at the corners of the cube with another atom at the cube center. BCC continued • Close Packed Plane cuts the unit cube in half diagonally • 2 atoms in one unit cell 4R a 3 Hexagonal Close Packed (HCP) • Cell of an HCP lattice is visualized as a top and bottom plane of 7 atoms, forming a regular hexagon around a central atom. In between these planes is a half- hexagon of 3 atoms. • There are two lattice parameters in HCP, a and c, representing the basal and height parameters Volume respectively. 6 atoms per unit cell Coordination number – the number of nearest neighbor atoms or ions surrounding an atom or ion. For FCC and HCP systems, the coordination number is 12. For BCC it’s 8. -
Crystal Structure of a Material Is Way in Which Atoms, Ions, Molecules Are Spatially Arranged in 3-D Space
Crystalline Structures – The Basics •Crystal structure of a material is way in which atoms, ions, molecules are spatially arranged in 3-D space. •Crystal structure = lattice (unit cell geometry) + basis (atom, ion, or molecule positions placed on lattice points within the unit cell). •A lattice is used in context when describing crystalline structures, means a 3-D array of points in space. Every lattice point must have identical surroundings. •Unit cell: smallest repetitive volume •Each crystal structure is built by stacking which contains the complete lattice unit cells and placing objects (motifs, pattern of a crystal. A unit cell is chosen basis) on the lattice points: to represent the highest level of geometric symmetry of the crystal structure. It’s the basic structural unit or building block of crystal structure. 7 crystal systems in 3-D 14 crystal lattices in 3-D a, b, and c are the lattice constants 1 a, b, g are the interaxial angles Metallic Crystal Structures (the simplest) •Recall, that a) coulombic attraction between delocalized valence electrons and positively charged cores is isotropic (non-directional), b) typically, only one element is present, so all atomic radii are the same, c) nearest neighbor distances tend to be small, and d) electron cloud shields cores from each other. •For these reasons, metallic bonding leads to close packed, dense crystal structures that maximize space filling and coordination number (number of nearest neighbors). •Most elemental metals crystallize in the FCC (face-centered cubic), BCC (body-centered cubic, or HCP (hexagonal close packed) structures: Room temperature crystal structure Crystal structure just before it melts 2 Recall: Simple Cubic (SC) Structure • Rare due to low packing density (only a-Po has this structure) • Close-packed directions are cube edges. -
Multidisciplinary Design Project Engineering Dictionary Version 0.0.2
Multidisciplinary Design Project Engineering Dictionary Version 0.0.2 February 15, 2006 . DRAFT Cambridge-MIT Institute Multidisciplinary Design Project This Dictionary/Glossary of Engineering terms has been compiled to compliment the work developed as part of the Multi-disciplinary Design Project (MDP), which is a programme to develop teaching material and kits to aid the running of mechtronics projects in Universities and Schools. The project is being carried out with support from the Cambridge-MIT Institute undergraduate teaching programe. For more information about the project please visit the MDP website at http://www-mdp.eng.cam.ac.uk or contact Dr. Peter Long Prof. Alex Slocum Cambridge University Engineering Department Massachusetts Institute of Technology Trumpington Street, 77 Massachusetts Ave. Cambridge. Cambridge MA 02139-4307 CB2 1PZ. USA e-mail: [email protected] e-mail: [email protected] tel: +44 (0) 1223 332779 tel: +1 617 253 0012 For information about the CMI initiative please see Cambridge-MIT Institute website :- http://www.cambridge-mit.org CMI CMI, University of Cambridge Massachusetts Institute of Technology 10 Miller’s Yard, 77 Massachusetts Ave. Mill Lane, Cambridge MA 02139-4307 Cambridge. CB2 1RQ. USA tel: +44 (0) 1223 327207 tel. +1 617 253 7732 fax: +44 (0) 1223 765891 fax. +1 617 258 8539 . DRAFT 2 CMI-MDP Programme 1 Introduction This dictionary/glossary has not been developed as a definative work but as a useful reference book for engi- neering students to search when looking for the meaning of a word/phrase. It has been compiled from a number of existing glossaries together with a number of local additions. -
Crystal Structure
Physics 927 E.Y.Tsymbal Section 1: Crystal Structure A solid is said to be a crystal if atoms are arranged in such a way that their positions are exactly periodic. This concept is illustrated in Fig.1 using a two-dimensional (2D) structure. y T C Fig.1 A B a x 1 A perfect crystal maintains this periodicity in both the x and y directions from -∞ to +∞. As follows from this periodicity, the atoms A, B, C, etc. are equivalent. In other words, for an observer located at any of these atomic sites, the crystal appears exactly the same. The same idea can be expressed by saying that a crystal possesses a translational symmetry. The translational symmetry means that if the crystal is translated by any vector joining two atoms, say T in Fig.1, the crystal appears exactly the same as it did before the translation. In other words the crystal remains invariant under any such translation. The structure of all crystals can be described in terms of a lattice, with a group of atoms attached to every lattice point. For example, in the case of structure shown in Fig.1, if we replace each atom by a geometrical point located at the equilibrium position of that atom, we obtain a crystal lattice. The crystal lattice has the same geometrical properties as the crystal, but it is devoid of any physical contents. There are two classes of lattices: the Bravais and the non-Bravais. In a Bravais lattice all lattice points are equivalent and hence by necessity all atoms in the crystal are of the same kind. -
Crystal Structures and Symmetries
Crystal Structures and Symmetries G. Roth This document has been published in Manuel Angst, Thomas Brückel, Dieter Richter, Reiner Zorn (Eds.): Scattering Methods for Condensed Matter Research: Towards Novel Applications at Future Sources Lecture Notes of the 43rd IFF Spring School 2012 Schriften des Forschungszentrums Jülich / Reihe Schlüsseltechnologien / Key Tech- nologies, Vol. 33 JCNS, PGI, ICS, IAS Forschungszentrum Jülich GmbH, JCNS, PGI, ICS, IAS, 2012 ISBN: 978-3-89336-759-7 All rights reserved. B 1 Crystal Structures and Symmetries G. Roth Institute of Crystallography RWTH Aachen University Contents B 1 Crystal Structures and Symmetries ................................................1 1.1 Crystal lattices ...................................................................................2 1.2 Crystallographic coordinate systems ..............................................4 1.3 Symmetry-operations and -elements...............................................7 1.4 Crystallographic point groups and space groups ........................10 1.5 Quasicrystals....................................................................................13 1.6 Application: Structure description of YBa2Cu3O7-δ ....................14 ________________________ Lecture Notes of the 43rd IFF Spring School "Scattering Methods for Condensed Matter Research: Towards Novel Applications at Future Sources" (Forschungszentrum Jülich, 2012). All rights reserved. B1.2 G. Roth Introduction The term “crystal” derives from the Greek κρύσταλλος , which was first -
Crystal Structure and Mechanical Properties of Thbc2
crystals Article Crystal Structure and Mechanical Properties of ThBC2 Xinchun Zhou and Baobing Zheng * College of Physics and Optoelectronic Technology & Advanced Titanium Alloys and Functional Coatings Cooperative Innovation Center, Baoji University of Arts and Sciences, Baoji 721016, China * Correspondence: [email protected]; Tel.: +86-917-3364-258 Received: 6 July 2019; Accepted: 27 July 2019; Published: 29 July 2019 Abstract: Thorium borocarbide compounds have fascinating physical properties and diverse structures, and hence have stimulated great interest. In this work, we determine the ground state structure of ThBC2 by the unbiased structure prediction method based on first-principles calculations. The dynamical and elastic stabilities of our proposed ThBC2 are verified by the calculations of phonon spectrum and elastic constants. To study the mechanical properties fundamentally, we estimated the elastic anisotropy of ThBC2. The results show that the Young’s and shear moduli possess high degree of anisotropy. The ideal strength calculations reveal that ThBC2 readily collapses upon applied stress due to small ideal strengths. The cleavage fracture probably occurs along the [111] direction while slip may easily appear along the [110] direction on the (111) plane for ThBC2. In addition, we provide an atomic explanation for the different characteristics of the strain–stress curves under different strains. Keywords: ThBC2; crystal structure; anisotropic mechanical properties; ideal strength; first-principles calculations 1. Introduction Due to the potential application in fission fuel, actinoid-metal borocarbides are of great interest, especially thorium borocarbide compounds [1–7]. Thorium borocarbide compounds have diversified stoichiometric proportions with different crystal structures due to the flexible B–C framework. -
1.1 Silicon Crystal Structure
EECS143 Microfabrication Technology Professor Ali Javey Introduction to Materials Lecture 1 Evolution of Devices Yesterday’s Transistor (1947) Today’s Transistor (2006) Why “Semiconductors”? • Conductors – e.g Metals • Insulators – e.g. Sand (SiO2 ) • Semiconductors – conductivity between conductors and insulators – Generally crystalline in structure • In recent years, non-crystalline semiconductors have become commercially very important Polycrystalline amorphous crystalline What are semiconductors Elements: Si, Ge, C Binary: GaAs, InSb, SiC, CdSe, etc. Ternary+: AlGaAs, InGaAs, etc. Electrons and Holes in Semiconductors Silicon Crystal Structure • Unit cell of silicon crystal is cubic. • Each Si atom has 4 nearest neighbors. 5.43 Å Silicon Wafers and Crystal Planes z z z • The standard notation for crystal planes is y y y based on the cubic unit cell. x x (100) x (011) (111) • Silicon wafers are usually cut along the (100) plane (100) plane with a flat (011) or notch to help orient flat Si (111) plane the wafer during IC fabrication. Bond Model of Electrons and Holes (Intrinsic Si) Si Si Si • Silicon crystal in a two-dimensional Si Si Si representation. Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si Si • When an electron breaks loose and becomes a conduction electron, a hole is also created. Dopants in Silicon Si Si Si Si Si Si Si As Si Si B Si Si Si Si Si Si Si N-type Si P-type Si • As (Arsenic), a Group V element, introduces conduction electrons and creates N-type silicon, and is called a donor. -
Preparation, Crystal Structure, Properties, and Electronic Band Structure of Tltase3 Christoph L
Preparation, Crystal Structure, Properties, and Electronic Band Structure of TlTaSe3 Christoph L. Teskea, Wolfgang Benscha, Diana Beneab, Jan Min´arb, Alexander Perlovb, and Hubert Ebertb a Institut f¨ur Anorganische Chemie, Christian-Albrechts-Universit¨at, Otto-Hahn-Platz 6/7, D-24098 Kiel, Germany b M¨unchen, Department Chemie – Physikalische Chemie, Ludwigs-Maximilians-Universit¨at, Butenandtstraße 11, D-81377 M¨unchen Reprint requests to Dr. C. Teske. Fax: +49 431 880 1520. E-mail: [email protected] Z. Naturforsch. 60b, 858 – 866 (2005); received June 10, 2005 TlTaSe3 was prepared from a fused mixture of Tl4Ta2Se11, Ta and Se in the molar ratio 1:2:1. The compound shows dimorphism with H-TlTaSe3, hexagonal, space group P63/mmc, a = 7.2436(6), c = 5.9736(6) A,˚ c/a = 1.213 and O-TlTaSe3, orthorhombic, space group Pnma, a = 9.554(13), b = 3.6244(6), c = 14.7271(17) A.˚ The crystal structure of H-TlTaSe3 is isotypic to BaVSe3 whereas that of O-TlTaSe3 is closely related to the NH4CdCl3-type. Characteristic features of the structures are: 1 2− ∞[TaSe3 ] chains of regular octahedra sharing faces along [001] for the hexagonal form and columns 1 2− of double edge-sharing octahedra ∞[Ta2Se6 ] running along [010] for O-TlTaSe3. The columns are each separated by Tl+ ions with the coordination number CN = 12 and CN = 8 respectively. The structures are compared and discussed in context with other isotypic structures of chalcogenides. The orthorhombic modification O-TlTaSe3 is a semiconductor while H-TlTaSe3 shows conventional metallic behaviour. The electronic structures of both modifications are discussed on the base of band structure calculations performed within the framework of density functional theory. -
Crystal Structures of Minerals in the Lower Mantle
6 Crystal Structures of Minerals in the Lower Mantle June K. Wicks and Thomas S. Duffy ABSTRACT The crystal structures of lower mantle minerals are vital components for interpreting geophysical observations of Earth’s deep interior and in understanding the history and composition of this complex and remote region. The expected minerals in the lower mantle have been inferred from high pressure‐temperature experiments on mantle‐relevant compositions augmented by theoretical studies and observations of inclusions in natural diamonds of deep origin. While bridgmanite, ferropericlase, and CaSiO3 perovskite are expected to make up the bulk of the mineralogy in most of the lower mantle, other phases such as SiO2 polymorphs or hydrous silicates and oxides may play an important subsidiary role or may be regionally important. Here we describe the crystal structure of the key minerals expected to be found in the deep mantle and discuss some examples of the relationship between structure and chemical and physical properties of these phases. 6.1. IntrODUCTION properties of lower mantle minerals [Duffy, 2005; Mao and Mao, 2007; Shen and Wang, 2014; Ito, 2015]. Earth’s lower mantle, which spans from 660 km depth The crystal structure is the most fundamental property to the core‐mantle boundary (CMB), encompasses nearly of a mineral and is intimately related to its major physical three quarters of the mass of the bulk silicate Earth (crust and chemical characteristics, including compressibility, and mantle). Our understanding of the mineralogy and density, -
Engineering Materials and Processes Lecture 4 – Crystal Structure of Metals
Engineering Materials and Processes Lecture 4 – Crystal Structure of Metals Grains after acid etching: Wikipedia Crystal Structure of Metals Reference Text Section Higgins RA & Bolton, 2010. Materials for Engineers and Technicians, Ch 4 5th ed, Butterworth Heinemann Additional Readings Section Sheedy, P. A, 1994. Materials : Their properties, testing and selection Ch 1 Callister, W. Jr. and Rethwisch, D., 2010, Materials Science and Ch 3 Engineering: An Introduction, 8th Ed, Wiley, New York. Engineering Materials and Processes Crystal Structure of Metals Crystals are the lattice structure that metal atoms form when they become solid. In engineering, crystals of metal are called grains. Grains in cast aluminium www.spaceflight.esa.int Engineering Materials and Processes Solid, Liquid, Gas Everything can exist as either solid, liquid or gas. (state). This depends on temperature and pressure. Mercury freezes at -9°C and boils (to form a gas or vapour) at 357°C at 1 atm. Liquid Mercury: Wikipedia At the other end of the scale, tungsten melts at 3410°C and ° Mercury vapour streetlights: theage.com.au boils at 5930 C. Engineering Materials and Processes Classification of Materials by State • Solid: Rigid structure of atoms (or molecules). A regular pattern of atoms is called a crystal (ceramics) or a grain (metals). Random is called amorphous (some plastics). Low temperature all materials freeze (become solid). • Liquid: A liquid is a substance that flows (fluid) but does not compress easily. Solids become liquid when heated to their melting point (fusion) • Gas: A gas is a compressible fluid, that expands to fill its container. At high temperature all materials vapourise to a gas. -
Crystal Structure CRYSTAL STRUCTURES
Crystal Structure CRYSTAL STRUCTURES Lecture 2 A.H. Harker Physics and Astronomy UCL Lattice and Basis Version: June 6, 2002; Typeset on October 30, 2003,15:28 2 1.4.8 Fourteen Lattices in Three Dimensions Version: June 6, 2002; Typeset on October 30, 2003,15:28 3 System Type Restrictions Triclinic P a =6 b =6 c, α =6 β =6 γ Monoclinic P,C a =6 b =6 c, α = γ = 90◦ =6 β Orthorhmobic P,C,I,F a =6 b =6 c, α = β = γ = 90◦ Tetragonal P,I a = b =6 c, α = β = γ = 90◦ Cubic P,I,F1 a = b = c, α = β = γ = 90◦ Trigonal P a = b = c, α = β = γ < 120◦, =6 90◦ Hexagonal P a = b =6 c, α = β = 90◦, γ = 120◦ No need to learn details except for cubic, basic ideas of hexagonal. Version: June 6, 2002; Typeset on October 30, 2003,15:28 4 1.4.9 Cubic Unit Cells Primitive Unit Cells of cubic system Simple cubic: cube containing one lattice point (or 8 corner points each shared among 8 cubes: 8 × 1 8 = 1). Body centred cubic: 2 points in cubic cell Version: June 6, 2002; Typeset on October 30, 2003,15:28 5 Rhombohedral primitive cell of body centred cubic system. Face centred cubic: 4 points in cubic cell (8 corner points shared 8 1 1 ways, 6 face points shared 2 ways: 8 × 8 + 6 × 2 = 4. Version: June 6, 2002; Typeset on October 30, 2003,15:28 6 Rhombohedral primitive cell of face centred cubic system. -
Diamond Unit Cell
Diamond Crystal Structure Diamond is a metastable allotrope of carbon where the each carbon atom is bonded covalently with other surrounding four carbon atoms and are arranged in a variation of the face centered cubic crystal structure called a diamond lattice Diamond Unit Cell Figure shows four atoms (dark) bonded to four others within the volume of the cell. Six atoms fall on the middle of each of the six cube faces, showing two bonds. Out of eight cube corners, four atoms bond to an atom within the cube. The other four bond to adjacent cubes of the crystal Lattice Vector and Basis Atoms So the structure consists of two basis atoms and may be thought of as two inter-penetrating face centered cubic lattices, with a basis of two identical carbon atoms associated with each lattice point one displaced from the other by a translation of ao(1/4,1/4,1/4) along a body diagonal so we can say the diamond cubic structure is a combination of two interpenetrating FCC sub lattices displaced along the body diagonal of the cubic cell by 1/4th length of that diagonal. Thus the origins of two FCC sub lattices lie at (0, 0, 0) and (1/4, 1/4,1/4) (a) (b) (aa) Crystallographic unit cell (unit cube) of the diamond structure (bb) The primitive basis vectors of the face centered cubic lattice and the two atoms forming the basis are highlighted. The primitive basis vectors and the two atoms at (0,0,0) and ao(1/4,1/4,1/4) are highlighted in Figure(b)and the basis vectors of the direct Bravais lattice are Where ao denotes the lattice constant of the relaxed lattice.