The Structure of Ionic Compounds: Closest Packing

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The Structure of Ionic Compounds: Closest Packing Ionic Compounds Applications of Chemistry to Mineralogy Claude H. Yoder Franklin and Marshall College A John Wiley & Sons, Inc., Publication Ionic Compounds Ionic Compounds Applications of Chemistry to Mineralogy Claude H. Yoder Franklin and Marshall College A John Wiley & Sons, Inc., Publication Copyright © 2006 by John Wiley & Sons, Inc. All rights reserved Published by John Wiley & Sons, Inc., Hoboken, New Jersey Published simultaneously in Canada No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4470, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at http://www.wiley.com/go/permission. Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at (800) 762-2974, outside the United States at (317) 572-3993 or fax (317) 572-4002. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic formats. For more information about Wiley products, visit our web site at www.wiley.com. Library of Congress Cataloging-in-Publication Data: Yoder, Claude H. Ionic compounds : applications of chemistry to mineralogy / Claude H. Yoder. p. cm. Includes bibliographical references and index. ISBN-13: 978-0-471-74046-9 (pbk.) ISBN-10: 0-471-74046-2 (pbk.) 1. Ionic crystals. 2. Ionic structure. 3. Crystallography. I. Title. QD921.Y63 2007 549′.18—dc22 2006012524 Printed in the United States of America 10987654321 Contents Preface vii 3.3 Crystal Systems 53 3.3.1 Crystallographic Axes 54 1. Bonding and Composition 1 4. The Structure of Some Simple 1.1 Types of Bonding 3 Closest-packed Compounds 59 1.2 Ionic Compounds 5 1.2.1 Types of Ions 5 4.1 Symmetry of the AB and ABC 1.2.2 Names of Ions 8 Closest-packed Arrangements 59 1.3 Percent Composition and Empirical 4.2 The Unit Cell 60 Formula 11 4.3 The NaCl Structure 65 1.3.1 The Mole 13 4.4 The Sphalerite Structure 68 Molar Mass (Formula 4.5 Axial Relationships 72 Weight) 15 4.6 Wurtzite, a Polymorph of 1.3.2 Calculation of Empirical Formula Sphalerite 74 from Percent Composition 15 1.3.3 Use of Oxide Data 17 4.7 The Fluorite Structure 76 1.3.4 Formulas for Solid 4.8 The Rutile Structure, Polyhedral Solutions 18 Coordination Models 80 1.4 Covalent Character in Ionic Compounds 19 5. Factors that Affect the Symmetry 1.5 Interactions Between Ions 22 of the Unit Cell 87 1.5.1 Some Laws of 5.1 Effect of Cation 87 Electrostatics 22 5.1.1 The Chalcopyrite Structure and Potential Energy of Charged Solid Solution 88 Particles 23 90 1.5.2 Lattice Energy and Its Effect on 5.2 Effect of the Anion 5.2.1 Some Oxy Anions 90 Properties 27 5.2.2 The Pyrite Structure 92 2. The Structure of Ionic Compounds: 5.2.3 The Calcite Structure 95 5.2.4 Aragonite, A Polymorph of Closest Packing 29 Calcite 97 2.1 Closest Packing of Ions 30 5.2.5 Several Sulfates, Anhydrite and 2.1.1 The Holes Between the Barite 100 Layers 31 5.2.6 Several Silicates, Zircon, and 2.1.2 Stacking Sequences 33 Beryl 106 2.1.3 Closest Packing for Ionic The Silicates 108 Compounds 36 5.3 Effect of Temperature and 2.1.4 Relationship of Formula to Pressure 113 Occupation of Voids 39 6. Physical Properties: Morphology 115 3. The Symmetry of Crystals 41 6.1 Crystal Morphology 115 3.1 Symmetry Elements 41 6.2 Miller Indices 115 3.2 Hermann-Mauguin Notation (Point 6.3 Forms 118 Groups) 49 6.3.1 Habit 127 v vi Ionic Compounds Table of Contents 6.4 Deviations in Crystal 8.2 Reaction with Acids 157 Growth 129 8.2.1 Types of Chemical 6.4.1 Parallel Growth 129 Reactions 157 6.4.2 Twinning 129 8.2.2 Water as Both Acid and 6.4.3 Epitaxis and Base 159 Pseudomorphism 131 8.2.3 Strong and Weak Acids 160 8.2.4 Conjugate Bases 160 8.3 Use of Chemical Reactions for 7. Physical Properties: Color 135 Identification 162 7.1 Light and the Electromagnetic Spectrum 135 Appendices 165 7.2 The Nature of Electrons 136 1. The Periodic Chart 165 7.3 Electron Configurations 142 2. The Elements: Symbols, Melting Points, 7.4 The Crystal Field Model 143 Boiling Points, Densities, and 7.5 Colored Cations 147 Electronegativities 169 7.6 Ion Impurities 148 3. Metallic, Covalent, and Ionic Radii 171 7.7 Crystal Defects 148 4. Quartz 173 5. Crystal System Identification 8. Chemical Properties 149 Practice 177 8.1 Solubility 149 6. Crystal Systems and Classes 179 8.1.1 Energetics of Dissolution 151 7. Additional Reading and Resources 181 8.1.2 Solubility Rules 155 8.1.3 Double Salts 156 Index 183 Preface This introduction to ionic compounds is designed for the reader who wants a better under- standing of the concepts that are used by the chemist and mineralogist in their attempts to unravel the mysteries of nature. The emphasis on the relationship of structure at the atomic level to the symmetry and properties of crystals will be of particular interest to those inter- ested in mineralogy. The book requires no knowledge of chemistry or mineralogy beyond that obtained in a typical secondary school curriculum. It is designed to appeal to the min- eralogy student who wants to delve more deeply into the relationships between structure and bonding at the atomic level and the macroscopic properties of minerals. It should also appeal to the serious mineral collector who wants to learn more about the chemical and crystallographic properties of his collection. Finally, the author hopes that the book will be of value to those students of geology who want to bolster their understanding of chemistry. The author believes that learning is enhanced by the reader’s active participation in the material. Consequently, brief segments of information are followed by a question that the reader should grapple with before looking at the answer. In most cases, the questions are not difficult and can be answered with minimal effort. However, even this amount of reflection, in the author’s experience, increases understanding of the subject material. The author has made considerable use of the excellent computer program Crystal- Maker3 (written by David Palmer), for illustrations throughout this book. Information about this program can be obtained from the web site http://www.crystalmaker.co.uk. The program Kristall2000 (written by Klaus Schilling), was used for drawings of crystal forms. The author is grateful for reviews of portions of the manuscript by Dr. Peter Leavens (University of Delaware), Joe Dague (Chambersburg, PA), John S. White (Stewartstown, PA), Amy Hoffman (California Institute of Technology), Dr. Stanley Mertzman (Franklin and Marshall College), and Dr. Robert Wiebe (Franklin and Marshall College), for the technical assistance of Sarah Correll, Carol Strausser, Peter Weed, Jonie Young, Kate Seeds, Ben Williams, Erin Roschel, and for the loan of specimens or photos by Lee Tori and George Godas. vii Chapter 1 Bonding and Composition The way in which atoms in compounds are held together is one of the major concerns of the chemist. Atoms differ in the number of protons and neutrons in their nuclei, the very tiny center of the atom that contains all of the positive charge contributed by the protons. For example, atoms of carbon contain 6 protons, while atoms of silicon contain 14 protons. Although every atom of carbon must contain 6 protons, the number of neutrons, which have no charge, can vary. Two atoms of the same element that have different numbers of neutrons are called isotopes. The predominant isotope of carbon, carbon-12, contains 6 protons and 6 neutrons. The mass number, the sum of the number of protons and neutrons, is used to designate the isotope. About 1% of naturally occurring carbon is carbon-13, which has 6 protons and 7 neutrons in the nucleus. Each neutral atom must also have elec- trons equal in number to the number of protons. If the atom gains electrons to become a negative ion, the number of electrons exceeds the number of protons. Thus, a neutral sodium atom contains 11 negatively charged electrons, but a sodium atom with a single negative charge, Na−, contains 12 electrons, and the common Na+ ion contains only 10 electrons.
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