Close Packings of Spheres I.

Similar documents
These metal centres interact through metallic bonding

1.10 Close packed structures cubic and hexagonal close packing

Chem 253, UC, Berkeley. Chem 253, UC, Berkeley

Ceramic Science 4RO3. Lecture 2. Tannaz Javadi. September 16, 2013

Unit-1 THE SOLID STATE QUESTIONS VSA QUESTIONS (1 - MARK QUESTIONS)

Stacking Oranges. Packing atoms together Long Range Order. What controls the nearest number of atoms? Hard Sphere Model. Hard Sphere Model.

Chemistry/Materials Science and Engineering C150 Introduction to Materials Chemistry

CHAPTER 2: ATOMIC ARRANGEMENTS AND MINERALOGICAL STRUCTURES. Sarah Lambart

SOLID-STATE STRUCTURE.. FUNDAMENTALS

(C) Na 2. (B) NaWO 3 WO 3

Chapter 16. Liquids and Solids. Chapter 16 Slide 1 of 87

SECOND MIDTERM EXAM Chemistry April 2011 Professor Buhro

Fundamental concepts and language Unit cells Crystal structures! Face-centered cubic! Body-centered cubic! Hexagonal close-packed Close packed

Unit 1 The Solid State

Chapter Outline. How do atoms arrange themselves to form solids?

TOPIC 2. STRUCTURE OF MATERIALS III

Crystal Structure. Andrew R. Barron Carissa Smith. 1 Introduction. 2 Crystallography

Crystal Structures of Interest

Chapter Outline How do atoms arrange themselves to form solids?

Metallic crystal structures The atomic bonding is metallic and thus non-directional in nature

FINAL EXAM KEY. Professor Buhro. ID Number:

Part 1. References: Gray: Chapter 6 OGN: Chapter 19 and (24.1)

CRYSTAL LATTICE. Defining lattice: Mathematical construct; ideally infinite arrangement of points in space.

Two marks questions and answers. 1. what is a Crystal? (or) What are crystalline materials? Give examples

CH445/545 Winter 2008

ENGINEERING MATERIALS LECTURE #4

Symmetry in crystalline solids.

Basic Solid State Chemistry, 2 nd ed. West, A. R.

CHAPTER 3. Crystal Structures and Crystal Geometry 3-1

The structures of pure metals are crystalline (crystal lattice) with regular arrangement of metal atoms that are identical perfect spheres.

Review key concepts from last lecture (lattice + basis = unit cell) Bravais lattices Important crystal structures Intro to miller indices

Analytical Methods for Materials

Chapter 12: Structures & Properties of Ceramics

Energy and Packing. Materials and Packing

Structure of silica glasses (Chapter 12)

Point Defects in Metals

Ionic Conductivity and Solid Electrolytes II: Materials and Applications

Carbon nanostructures. (

Chem 241. Lecture 19. UMass Amherst Biochemistry... Teaching Initiative

Chapter 3. The structures of simple solids Structures of Solids Crystalline solids Amorphous solids

UNIT V -CRYSTAL STRUCTURE

Packing of atoms in solids

Lecture # 11 References:

Chapter 8: Molecules and Materials

Chapter 3: Structures of Metals & Ceramics

What is a crystal? Historic definition before the advent of crystallography. - A material with a regularly repeating structural motif

Planar Defects in Materials. Planar Defects in Materials

CHAPTER 3: CRYSTAL STRUCTURES & PROPERTIES

Introduction to Engineering Materials ENGR2000 Chapter 3: The Structure of Crystalline Solids. Dr. Coates

CRYSTAL STRUCTURE, MECHANICAL BEHAVIOUR & FAILURE OF MATERIALS

Density Computations

Materials and their structures

STATE OF SOLIDIFICATION & CRYSTAL STRUCTURE

CHAPTER 5 IMPERFECTIONS IN SOLIDS PROBLEM SOLUTIONS

Oxides and Hydroxides


Donald Neamen 물리전자 / 김삼동 1-1

Mat E 272 Lectures 22-23: Introduction to Ceramic Materials

Ceramics are inorganic, non-metallic. Ceramics. Ceramics exhibit ionic, covalent bonding or a combination of the two (like in Al 2 O 3 )

Why Study Minerals? blocks of Earth materials. to understanding rock formation

How to Make Micro/Nano Devices?

C h a p t e r 4 : D e f e c t s i n C r y s t a l s

Problem 1: (a) Describe the ß-ZnS structure and show how it is related to the FCC structure.

Chapter 3 Structure of Crystalline Solids

Imperfections: Good or Bad? Structural imperfections (defects) Compositional imperfections (impurities)

Fine Structure and Magnetism of the Cubic Oxide Compound Ni 0.3 Zn 0.7 O

Introduction to Materials Science and Engineering

CHAPTER 5 IMPERFECTIONS IN SOLIDS PROBLEM SOLUTIONS ev /atom = exp. kt ( =

Free Electron Model What kind of interactions hold metal atoms together? How does this explain high electrical and thermal conductivity?

Semiconductors. Types of Solids. Figure 10.30: Energy-level diagrams for (a) an n-type semiconductor and (b) a ptype semiconductor.

It is instructive however for you to do a simple structure by hand. Rocksalt Structure. Quite common in nature. KCl, NaCl, MgO

Free Electron Model What kind of interactions hold metal atoms together? How does this explain high electrical and thermal conductivity?

7.3 Bonding in Metals > Chapter 7 Ionic and Metallic Bonding. 7.3 Bonding in Metals. 7.1 Ions 7.2 Ionic Bonds and Ionic Compounds

Study of crystalline structure and physical constants in solids: NaCl, CsCI, ZnS

Impurities in Solids. Crystal Electro- Element R% Structure negativity Valence

Non-crystalline Materials

Experiment 3 * Thermochromism in the Ionic Conductor, Cu 2 HgI 4

Excess Volume at Grain Boundaries in hcp Metals

Synthesis and characterization of Aln 2 O 4 indates, A ˆ Mg, Ca, Sr, Ba

Greenwood & Earnshaw. Chapter 7. Aluminium, Gallium, Indium and Thallium. Observations. The Trihalides of Aluminum

Übungsaufgaben zur Kristallographie Serie 4

Twins & Dislocations in HCP Textbook & Paper Reviews. Cindy Smith

Steric Effects on the. Transition in YH x

Chapter 20 CHEMISTRY. Metallurgy and the Chemistry of Metals. Dr. Ibrahim Suleiman

Review of Metallic Structure

ENERGY AND PACKING. Chapter 3 CRYSTAL STRUCTURE & PROPERTIES MATERIALS AND PACKING METALLIC CRYSTALS ISSUES TO ADDRESS...

Fundamentals of Crystalline State p. 1 Introduction p. 1 Crystalline state p. 2 Crystal lattice and crystal structure p. 4 Shape of the unit cell p.

GY 302: Crystallography & Mineralogy

Point Defects. Vacancies are the most important form. Vacancies Self-interstitials

CHAPTER 2. Structural Issues of Semiconductors

Fundamentals of Crystalline State and Crystal Lattice p. 1 Crystalline State p. 2 Crystal Lattice and Unit Cell p. 4 Shape of the Unit Cell p.

3.40 Sketch within a cubic unit cell the following planes: (a) (01 1 ) (b) (112 ) (c) (102 ) (d) (13 1) Solution

Diffraction Basics. The qualitative basics:

Structure of a new Al-rich phase, [K, Na] 0.9 [Mg, Fe] 2 [Mg, Fe, Al, Si] 6 O 12, synthesized at 24 GPa

Engineering 45: Properties of Materials Final Exam May 9, 2012 Name: Student ID number:

Primitive cells, Wigner-Seitz cells, and 2D lattices. 4P70, Solid State Physics Chris Wiebe

An Introduction to X-Ray Powder Diffraction. credits to: Scott A Speakman, Patrick McArdle Edited by Di Cicco 2014

9/28/2013 9:26 PM. Chapter 3. The structure of crystalline solids. Dr. Mohammad Abuhaiba, PE

NON-CRYSTALLINE MATERIALS

Greenwood & Earnshaw. Chapter 7. Aluminium, Gallium, Indium and Thallium

Transcription:

Close Packings of Spheres I. close packed layer a non-close packed layer stacking of 2 close packed layers 3rd layer at position S: h.c.p. 3rd layer at position T: c.c.p. h.c.p.: hexagonal close packing c.c.p.: cubic close packing (or f.c.c.: face-centered cubic) space filling: 74.05% A. R. West, Solid State Chemistry and ist Applications, Wiley & Sons, 1984.

Close Packings of Spheres II. hexagonal close packing h.c.p. stacking sequence:... A B A B A B... Z = 2; 2 octahedral voids; 4 tetrahedral voids unit cell http://za0510pc5.chemie.uni-bonn.de/akglhome Graphics: ATOMS V5.1, E. Dowty, Shape Software 1999.

Close Packings of Spheres III. cubic close packing c.c.p. or f.c.c. stacking sequence:... A B C A B C A B C... Z = 4; 4 octahedral voids; 8 tetrahedral voids http://za0510pc5.chemie.uni-bonn.de/akglhome Graphics: ATOMS V5.1, E.Dowty, Shape Software 1999.

Symmetry of a Cubic Close Packing Spacegroup: F 4/m 3 2/m (short: F m 3 m) F: lattice centering 4/m: C 4 rotation axis // a m mirror plane a 3: C 3i rotation-inversion axis // [1 1 1] 2/m: C 2 rotation axis // [1 1 0] m mirror plane [1 1 0] A. R. West, Solid State Chemistry and ist Applications, Wiley & Sons, 1984.

Symmetry of a Hexagonal Close Packing Spacegroup: P 6 3 /m 2/m 2/c (short: P 6 3 /m m c) P: lattice centeringc 6 3 /m: 6 3 screw axis // c m mirror plane c 2/m: C 2 rotation axis // [2 1 0] m mirror plane [2 1 0] 2/c: C 2 rotation axis // [1 0 0] c glide plane [1 0 0] A. R. West, Solid State Chemistry and ist Applications, Wiley & Sons, 1984.c

Body-centered Cubic Arrangement Spacegroup: I m 3 m 2 Atoms / unit cell 68% space filling Coordination of an atom: 8 + 6 (8x2.48Å, 6x2,86Å in iron) C.N. = 12 for h.c.p. and f.c.c Caveat! Spacegroup P m 3 m for CsCl U. Müller, Anorganische Strukturchemie, Teubner Studienbücher Chemie, 1991.

Metal Structures I. h c i hexagonal close packed cubic close packed body-centered cubic (68% space filling) others U. Müller, Anorganische Strukturchemie, Teubner Studienbücher Chemie, 1991.

Some More Close Packed Structures topological concept! The h.c.p. oxide layers in rutile and γ- Li 3 PO 4 are not planar but are buckled. The oxide ion arrangement in these may alternatively be described as tetragonal packed (t.p.). A. R. West, Solid State Chemistry and its Applications, Wiley & Sons, 1984.

Rocksalt Structure Type I. NaCl, f.c.c. array of Na + all octahedral voids are occupied by Cl Or vice versa! Stacking sequence for cations and anions is identical Space group: F m 3 m U. Müller, Anorganische Strukturchemie, Teubner Studienbücher Chemie, 1991. M. Almon, Seminar, University of Gießen, 1999.

Kristallstrukturen - Gittermodelle Steinsalz (Halit), NaCl, kubisch, a = 5,62 Å Cl Na + Röntgenstrukturanalyse http://za0510pc5.chemie.uni-bonn.de/akglhome

Rock Salt Structure Type II. Members of the rock salt structure family Again! Chemically different compounds adopt the same crystal structure. U. Müller, Anorganische Strukturchemie, Teubner Studienbücher Chemie, 1991.

Wurtzite (ZnS) Structure Type ZnS, h.c.p. array of Zn 2+ ½ of tetrahedral voids occupied by S 2 Or vice versa! Stacking sequence for cations and anions is identical Zn 2+ -Ion Space group: P 6 3 m c S 2- -Ion U. Müller, Anorganische Strukturchemie, Teubner Studienbücher Chemie, 1991. M. Almon, Seminar, University of Gießen, 1999.

Structures Related to ZnO (Wurtzite type) β-ligao 2, Pbn2 1 β-li 2 BeGeO 4, Pn β II -Li 3 PO 4, Pmn2 1 β II -Li 2 ZnSiO 4, Pmn2 1 ZnO, P6 3 mc A. R. West, Solid State Chemistry and its Applications, Wiley & Sons, 1984.

Wurtzite and NiAs-Type I. Wurtzite NiAs for both types h.c.p. of anions A. R. West, Solid State Chemistry and its Applications, Wiley & Sons, 1984.

Wurtzite and NiAs-Type II. No cation-cation interaction! A. R. West, Solid State Chemistry and its Applications, Wiley & Sons, 1984.

Wurtzite and NiAs-Type III. Cation-cation interaction! A. R. West, Solid State Chemistry and its Applications, Wiley & Sons, 1984.

Zinc Blende (Sphalerite) and Fluorite ZnS, f.c.c. array of Zn 2+ ½ of tetrahedral voids occupied by S 2 CaF 2, f.c.c. array of Ca 2+ all tetrahedral voids occupied by F alternative representation of the fluorite structure pronouncing the cubic [CaF 8 ] coordination units A. R. West, Solid State Chemistry and its Applications, Wiley & Sons, 1984.

NiAs-Type Structure Family c/a ratio for members of the NiAs family: 1.39 to 1.68 (ideal: 1.633 for h.c.p.) P 3 metal-metal interaction along c-axis valence electron concentration v.e.c. determines distortion (P ) P 2 4 sophisticated balance between M-M and P-P interactions U. Müller, Anorganische Strukturchemie, Teubner Studienbücher Chemie, 1991. R. Hoffmann, Solids and Surfaces, VCH Verlagsgesellschaft, Weinheim, 1988.

Diamond - Sphalerite Diamond C Sphalerite, Zinc Blende ZnS F 4 1 /d 3 2/m F 4 3 m U. Müller, Anorganische Strukturchemie, Teubner Studienbücher Chemie, 1991.

Various AB 2 -Structure Types Major AB 2 -structure types: SiO 2 (Quartz, Cristobalite, 4 : 2); TiO 2 (Rutile, 6 : 3); CaF 2 (Fluorite, 8 : 4) Specialities: CdCl 2 and CdI 2 : layer type structures, various stacking sequences A. R. West, Solid State Chemistry and its Applications, Wiley & Sons, 1984.

Some More Close Packed Structures topological concept! The h.c.p. oxide layers in rutile and γ- Li 3 PO 4 are not planar but are buckled. The oxide ion arrangement in these may alternatively be described as tetragonal packed (t.p.). A. R. West, Solid State Chemistry and its Applications, Wiley & Sons, 1984.

TiO 2 Rutile Structure Type I. O 2- - Ionen Ti 4+ - Ionen Space group: P 42/m n m Lattice [0 0 1], c-axis [1 0 0] [1 1 0] eacho 2- -ion is square-planar coordinated by 3 Ti 4+ (C.N. = 3) eachti 4+ -ion is octahedrally coordinated by 6 O 2- (C.N. = 6) A. R. West, Solid State Chemistry and its Applications, Wiley & Sons, 1984. M. Almon, Seminar, University of Gießen, 1999.

TiO 2 Rutile Structure Type II. representations of the crystal structure: from the unit cell to a 3-dimensional arrangement characteristic: chains of the edge-sharing octahedra [TiO 6 ] A. R. West, Solid State Chemistry and its Applications, Wiley & Sons, 1984. M. Almon, Seminar, University of Gießen, 1999.

Rutile Type Structures Oxides as well as fluorides adopt the structure type Many derivatives of the rutile structure type are known A. R. West, Solid State Chemistry and its Applications, Wiley & Sons, 1984.

Cristobalite SiO 2 b a Space group: F d 3 m Lattice [1 0 0], a-axis [1 1 1] [1 1 0] Diamond SiO 2 f. c. c. arrangement of C and Si with C (Si) in ½ of the tetrahedral voids Elektrides Oxides 2e O 2 topological relation! U. Müller, Anorganische Strukturchemie, Teubner Studienbücher Chemie, 1991.

Carnegieite An Alumosilicate Na[AlSiO 4 ] [ ][Si 2 O 4 ] U. Müller, Anorganische Strukturchemie, Teubner Studienbücher Chemie, 1991.

α-quartz SiO 2 I. Space group: P 3 2 2 1 chiral and polar piezoelectric material http://za0510pc5.chemie.uni-bonn.de/akglhome U. Müller, Anorganische Strukturchemie, Teubner Studienbücher Chemie, 1991.

α-quartz SiO 2 II. 3 2 - and 3 1 -screw axis, respectively screw axis: combined rotation & translation chiral (enantiomeric) crystals http://za0510pc5.chemie.uni-bonn.de/akglhome U. Müller, Anorganische Strukturchemie, Teubner Studienbücher Chemie, 1991.

Spinell Mg II Al III 2 O 4 kubisch, a = 8,081 Å; Baueinheiten: [Mg II O 4 ] und [Al III O 6 ] O 2 Al/Cr 3+ Mg 2+ Chromophor [CrO 6 ] http://za0510pc5.chemie.uni-bonn.de/akglhome

Rinmans Grün und Thénards Blau Zn II Co III 2O 4 Co II Al III 2O 4 Chromophor: [Co III O 6 ] Chromophor: [Co II O 4 ] Farbpigmente http://za0510pc5.chemie.uni-bonn.de/akglhome

ReO 3 and derived Structures I. ReO 3 Structure Type P m 3 m, a = 3,734 Å corner-sharing octahedra ReO 6/2 http://za0510pc5.chemie.uni-bonn.de/akglhome

ReO 3 and derived Structures II. Introduction of a crystallograpic shear plane CS Reduction [ReO 6/2 ] [ReO 6/2 ] + [ReO 3/2 O 3/3 ] ReO 3 a ReO 3 + b ReO 2.5 http://za0510pc5.chemie.uni-bonn.de/akglhome

ReO 3 and derived Structures III. Tungsten tri-oxide WO 3-x O. T. Sørensen Ed., Nonstoichiometric Oxides, Academic Press, 1981.

2024 © businessdocbox.com Privacy Policy | Terms of Service | Feedback