wells - structural inorganic chemistry 4e (clarendon, 1975)

wells - structural inorganic chemistry 4e (clarendon, 1975)

Inorganic

Chemistry

A.F WELLS

CLARENDON PRESS - OXFORD

Oxford University Press

Ely House, London W1

1975

4th Edition

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Oxford University Press, Ely House, London W.1

GLASGOW NEW YORK TORONTO MELBOURNE WELLINGTON

CAPE TOWN IBADAN NAIROBI DAR ES SALAAM LUSAKA ADDIS ABABA DELHl BOMBAY CALCUTTA MADRAS KARACHI LAHORE DACCA

KUALA LUMPUR SINGAPORE HONG KONG TOKYO

I S B N 0 1 9 8 5 5 3 5 4 4

0 O X F O R D U N I V E R S I T Y P R E S S 1 9 7 5

All rights reserved No part of this publication may be reproduced, storedin a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of' Oxford University Press

PRINTED IN GREAT BRITAIN BY

WILLIAM C L O W E S & S O N S L I M I T E D

L O N D O N , C O L C H E S T E R A N D B E C C L E S

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Preface

This book has been almosl entirely rewritten, but its purpose and general organization remain the same las those of previous editions The Introduction t o the first (1945) edition included dhe following paragraph: 'The reasons for writing this book were, firstly, the conviqtion that the structural side of inorganic chemistry cannot be put on a sound basls until the knowledge gained from the study of the solid state has been incorporated into chemistry as an integral part of that subject, and secondly, the equally strolng conviction that it is unsatisfactory merely to add information about the structures of solids to the descriptions of the elements and compounds as usually presented in a systematic treatment of inorganic chemistry.' Now, after a period of thirty years during which considerable advances have been made in solid state chemistry, it is still true to say that the structures and properties

of solids receive very little atte~ntion in most treatments of inorganic chemistry, and this in spite of the fact that most elements and most inorganic compounds are solids at ordinary temperaturw This state of affairs would seem to be sufficient justification for the appearance of yet another edition of this book

Since the results of structurkl studies of crystals are described in crystallographic language the first requirement is that these results be made available in a form intelligible to chemists It was this challenge that first attracted the author, and it is hoped that this book will continue to provide teachers of chemistry with facts and ideas which can be incorporated into their teaching However, while any addition of structural information to the donventional teaching of inorganic chemistry is to be welcomed the real need is a radical change of outlook and the recognition that not only is the structure of a substance in all states of aggregation an essential part of its full description (or characterization) but also that the structures and properties of solids form an integral part, pedhaps the major part, of the subject

The general plan of the boqk is as follows Part I deals with a number of general topics and is intended as an introduction to the more detailed Part 11, which forms the larger part of the book In Part I1 the structural chemistry of the elements is described systematically, and the arrangement of material is based on the groups of the Periodic Table The advanlces made during the past decade have necessitated considerable changes in these latter chapters, but the major structural changes have been made in the content of Part I

Since a concise treatment of certain geometrical and topological topics is not readily available elsewhere mode space has been devoted to these than in previous editions at the expense of subjects such as the experimental methods of structural chemistry, which at best can receive only a sketchy treatment in a volume such as

Preface

this Many students find difficulty in appreciating the three-dimensional geometry

of crystal structures from two-dimensional illustrations (even stereoscopic photo- graphs) In order to acquire some facility in visualising the three-dimensional arrangements of atoms in crystals some acquaintance is necessary with symmetry, repeating patterns, sphere-packings, and related topics Some of this material could

be, and sometimes is, introduced into teaching at an early age However, there is a tendency in some quarters to regard solid geometry as old-fashioned and to replace

it in school curricula by more fashionable aspects of mathematics This adds to the difficulties of those teachers of chemistry who wish to modernize their teaching by including information about the structures of solids Unless the student has an adequate grounding in the topics noted above little is gained by adding diagrams of unit cells of crystal structures to conventional chemistry texts

The educational value of building models representing the arrangements of atoms in crystals cannot be over-emphasized; and by this we mean that the student actually assembles the model and does not simply look at a ready-made model, however much more elegant the latter may be Some very tentative suggestions for model building have been offered in the author's Models in Structural Inorganic Chemistry, to which the abbreviation MSIC in the present volume refers

References The present volume has never been intended as a reference work, though it may serve as a useful starting-point when information is required on a particular topic As an essential part of the educational process the advanced student should be encouraged to adopt a critical attitude towards the written word (including the present text); he must learn where to find the original literature and

to begin to form his own judgment of the validity of conclusions drawn from experimental data It is becoming increasingly difficult to locate the original source

of a particular item of information, and for this reason numerous references to the scientific literature are included in the systematic part of this book These generally refer to the latest work, in which references to earlier work are usually included To save space (and expense) the names of scientific journals have been abbreviated to the forms listed on pp mi-xxiii

Indexes There are two indexes The arrangement of entries in the formula index is not entirely systematic for there is no wholly satisfactory way of indexing inorganic compounds which retains chemically acceptable groupings of atoms The formulae have been arranged so as to emphasize the feature most likely to be of interest t o the chemist The subject index is largely restricted to names of minerals and organic compounds and to topics which are not readily located in the list of contents

Acknowledgments During the writing of this book, which of necessity owes much to the work and ideas of other workers in this and related fields, I have had the benefit of helpful discussions with a number of colleagues, of whom I would particularly mention Dr B C Chamberland I wish to thank Dr B G Bagley and the editor of Nature (London) for permission to use Fig 4.3, Dr H T Evans and

Preface

John Wiley and Sons for Figs Sc, 7, 10, 11, and 12b in Chapter 11, and Drs G T Kokotailo and W M Meier for Fig 23.27 It gives me great pleasure to acknowledge the debt that I owe to my wife for her support and encouragement over a period of many years

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Contents

PART I

1 INTRODUCTION

The importance of the solid state

Structural formulae of inorganic compounds

Geometrical and topological limitations o n

the structures of molecules and crystals

The complete structural chemistry of an

element or compound

Structure in the solid state

Structural changes o n melting

Structural changes in the liquid state

Structural changes o n boiling or sub-

Crystals containing finite complexes

Relations between crystal structures

2 SYMMETRY

Symmetry elements

Repeating patterns, unit cells, and lattices

One- and two-dimensional lattices;

point groups

Three-dimensional lattices; space groups

Point groups; crystal systems

Equivalent positions in space groups

Examples of 'anomalous' symmetry

Plane nets Derivation of plane nets Configurations of plane nets Three-dimensional nets

Derivation of 3D nets Further characterization of 3 D nets Nets with polyhedral cavities Interpenetrating nets Polyhedral molecules and ions Tetrahedral complexes Octahedral molecules and ions Cubic molecules and ions Miscellaneous polyhedral complexes Cyclic molecules and ions

Infinite linear molecules and ions Crystal structures based o n 3-connected nets Types of structural unit

The plane hexagon net Structures based on other plane 3-con- nected nets

Structures based o n 3D 3-connected nets

Contents

Crystal structures based o n 4-connected nets 99

Structures based o n the plane 4-gon net 100

Layers of type A Layers of type

AX Layers of type A X 2 Layers

Structures based o n the diamond net 102

AX2 structures Structures based o n 5

systems of interpenetrating

Structures based o n more complex 4-

More complex tetrahedral nets Nets

with planar and tetrahedral co-

ordination Nets with polyhedral

Space-filling arrangements of polyhedra

Space-fillings of regular and Archi-

medean solids

Space-fillings of dodecahedra and

related polyhedra

4 SPHERE PACKINGS

Periodic packings of equal spheres

Simple cubic packing

The body-centred cubic packing

The closest packing of equal spheres

Icosahedral sphere packings

Sphere packings based o n closest-packed

layers

Interstices between close-packed layers

Structures with some pairs of adjacent

layers of type A

Hexagonal and cubic closest packing of

equal spheres

More complex types of closest packing

Close-packed arrangements of atoms of

Close-packed structures with atoms in tetra-

hedral and octahedral interstices

An alternative representation of close-packed structures

Structures built from close-packed AX3 layers ABX3 structures

A3 B2 X9 structures A2 BX6 structures TETRAHEDRAL AND OCTAHEDRAL STRUCTURES

Structures as assemblies of coordination poly- hedra

Limitations o n bond angles at shared X atoms

The maximum number of polyhedra with a common vertex

Tetrahedral structures Tetrahedra sharing vertices only Tetrahedra sharing edges only Tetrahedra sharing edges and vertices Octahedral structures

Some finite groups of octahedra Infinite systems of linked octahedra Octahedra sharing only vertices Octahedra sharing only edges Octahedra sharing edges and vertices Octahedra sharing faces only Octahedra sharing faces and vertices Octahedra sharing faces and edges Octahedra sharing faces, edges, and vertices

Structures built from tetrahedra and octa- hedra

6 SOME SIMPLE AX, STRUCTURES

l 3 The caesium chloride structure

Compounds ABX4, A2 BX6, etc, with

Thefluorite(AX;)andantifluorite(A2 X)structures 204

structure: t h e Fe,Al structure 206

Contents

Anions or cations of more than one

Replacement of cations t o form charged

Replacement of some OH in M(OH)2

Attachment of additional metal atoms

Structures with similar analytical descriptions 2 18

The LiNiOz, NaHF2, and CsIC12 struc-

The CrB, yellow T1I ( B 33), and related

The PdS2, A g F z , and P-Hg02 structures 223

Relations between the structures of some

Superstructures and other related structures 227

7 BONDS IN MOLECULES AND CRYSTALS 230

The shapes of simple molecules and ions of

Linear 16-electron molecules and ions 239

Triangular arrangement of 3 electron

The 20electrc:! group The 26-

electron group The 32electron

Trigonal bipyramidal arrangement of 5

The 22electron group The 28-

electron group The 34electron

Octahedral arrangement of 6 electron

The 36electron group The 42-

electron group The 48-electron

I Molecules (ions) containing directly bonded metal atoms without

11 Molec,ules (ions) containing directly bonded metal atoms and bridging

111 Crystals containing finite, 1-, or

The lattice energy of a simple ionic

Monohalides Dihalides and tri-

The 'anti-layer' and 'anti-chain' struc-

Preference for tetrahedral or octa- hedral coordination Distorted

Ternary hydrides

Contents

Hydrido complexes of transition metals

The hydrogen bond

The properties of hydrogen bonds

Bond energies and lengths

Position of the H atom

The hydrogen bond in crystals

Oxides and oxy-ions

Oxyfluorides and KXe03 F

THE HALOGENS-SIMPLE HALIDES

The properties of bromine trifluoride

The structures of interhalogen com-

Metal hydrogen halides

Oxy-compounds of the halogens

Oxides and oxyfluorides

Oxy-cations

Oxy-acids and oxy-anions

Acids HXO and their salts Acids HXOz and their salts Acids

H X 0 3 and their salts Acids

H X 0 4 and their salts Periodates containing octahedrally coordi-

of alkaline-earths, etc B subgroup

Trinuclear halide complexes of Re 366

Halide complexes of Nb, Ta, Mo, W, Pd, and Pt-containing metal 'clusters' 367

Metal halides in the fused and vapour states 372

xii

Contents

Complex fluorides of A1 and Fe(r11) 394

Ions of Mo and W

molybdate ion The paratungstate

Oxides M3 0 OXYGEN

The stereochemistry of oxygen

Differences between oxygen and sulphur 4 15

The oxygen molecule and dioxygenyl

Peroxides, superoxides, and sesquiox-

Oxides M2 0, Oxides M3 0 4

The oxides of iron The oxides of aluminium The oxides of manganese Framework structures

xiii

Contents

Layer structures

The oxides of lead

Lead monoxide, PbO

Red lead, Pb3 0 4

Lead sesquioxide, Pb2 O3

Lead dioxide, PbOz

The oxygen chemistry of some transition

Lower oxides Vanadium pentoxide

and vanadates Vanadium oxy-

The scheelite and fergusonite structures 489

The pseudobrookite structure, Az BO5 498

The pyrochlore structure, A2 B2 0, 499

Complex oxides containing Ti, V, Nb, Mo, or W 502

The structures of hydroxides M(OH), 5 17 Hydroxides MOH, M(OH)2, and M(OH)3 with n o hydrogen bond- ing Hydroxides M(OH)? and M(OH)3 with hydrogen bonds 518-522

The crystal structures of basic salts 530

Proton positions in ice polymorphs 539

Aqueous solutions Hydrates

Clathrate hydrates xiv

The location of H atoms of hydrogen

16 SULPHUR, SELENIUM, AND TELLURIUM

The stereochemistry of sulphur

Elementary sulphur, selenium, and tellurium

Sulphur

Selenium

Tellurium

Cyclic S, Se, and Te cations

Molecules S R z , SeR2, and TeRz

The halides of sulphur, selenium, and tel-

Oxyhalides of S, Se, and Te

The oxides of S, Se, and Te

Pyramidal ions and molecules

Tetrahedral ions and molecules

The pyrosulphate and related ions

Introduction Sulphides Mz S Monosulphides Monosulphides of transition metals The nickel arsenide structure The PtS (cooperite) structure 608-1 1

The sulphides of vanadium, niobium,

Sulphides structurally related to zinc-

Contents

18 NITROGEN

Introduction

The stereochemistry of nitrogen

Nitrogen forming four tetrahedral bonds

Ammonium and related ions

Nitrogen forming three pyramidal bonds

Ammonia and related compounds

Amides and imides

Nitrogen forming two bonds =N'

Di-imide and difluorodiazine

Compounds containing the system

[ N N

Nl Azides

The oxygen chemistry of nitrogen

Oxides

Nitrous oxide, N2 0 Nitric oxide,

NO Nitrogen dioxide, NOz

Dinitrogen trioxide, N2 03 Di-

nitrogen tetroxide, N2 0 4 Di-

nitrogen pentoxide, Nz 05 6 5 0-2

Nitryl halides and nitronium com-

Nitrous acid Metal nitrites and nitri-

t o compounds Organic nitro

compounds Hyponitrous acid

Oxyhyponitrite ion Peroxynitrite

ion Nitric acid and nitrate ion

Metal nitrates and nitrato com-

plexes Covalent nitrates 657-65

The sulphides of nitrogen and related com-

Phosphides of metals The structures of simple molecules Molecules PX3

HCP and the PH; ion Hydrides and molecules P2X4 and p3 x5

Phosphoryl and thiophosphoryl halides Other tetrahedral molecules and ions Phosphorus pentahalides, PX4* and P&- ions

Molecules PR5 , PR5-,X,, and mixed halides

The oxides and oxysulphide Phosphorus trioxide Phosphorus pentoxide Phosphorus oxysulphide Molecules of the same geometrical type

as P 4 0 1 0

The oxy-acids of phosphorus and their salts Orthophosphorous acid

Hypophosphorous acid Hypophosphoric acid Diphosphorous acid Isohypophosphoric acid Phosphoric acid and phosphates Orthophosphoric acid and orthophos- phates

Pyrophosphates Linear polyphosphates Metaphosphates Mono- and di-fluorophosphoric acids Phosphoramidates

Phosphorothioates Other substituted phosphoric acids etc Phosphorus sulphides

Phosphorus thiohalides Cyclic phosphorus compounds Compounds containing P, rings Compounds containing (PN), rings

Contents

Elementary arsenic, antimony, and bismuth 70 1

The structural chemistry of As, Sb, and Bi 701

Molecules MX3 : valence group (2, 6) 703

Tetrahedral ions MX; : valence group

Ions M X i : valence group (2, 8) 704

Pentahalides and molecules MX5 :

Formation of octahedral bonds by

As(v), S b ( v ) , and Bi(v): valence

Formation of octahedral bonds by

Formation o f square pyramidal bonds

by Sb(111) and Bi(r11): valence group

The crystalline trihalides of As, Sb, and

Complex halides of trivalent Sb and Bi 707

The oxygen chemistry of trivalent As, Sb, and

Complex oxides of trivalent As and Sb 712

The systems Ca(Sr, Ba, Cd, Pb)O-

Complex oxyhalides of Bi with Li, Na,

The oxygen chemistry of pentavalent arsenic

The oxy-compounds of pentavalent As 717

The oxy-compounds of pentavalent Sb 718

Salts containing Sb(0H); ions Com-

plex oxides based o n SbOd co-

The stereochemistry of carbon

The tetrahedral carbon atom Diamond: saturated organic compounds Carbon fluorides (fluorocarbons) Carbon forming three bonds

Bond arrangement =c(

Carbonyl halides and thiocarbonyl halides Carboxylic acids and related compounds

Derivatives of graphite Graphitic oxide Graphitic 'salts'

C a r b o n monofluoride Com- pounds o f graphite with alkali metals and bromine Graphite complexes with metal halides

The oxides and sulphides of carbon Carbon monoxide

Carbon dioxide and disulphide: car- bony1 sulphide

Carbon suboxide Acetylene and derivatives Cyanogen and related compounds Cyanogen

HCN: cyanides and isocyanides of non- metals

Cyanogen halides Cyanamide Dicyandiamide Cyanuric compounds Isocyanic acid and isocyanates Isothiocyanic acid, thiocyanates, and isothiocyanates

Metal thiocyanates and isothiocyanates Ionic thiocyanates Covalent thio- cyanates and isothiocyanates Thiocyanates containing bridging

Contents

22 METAL CYANIDES, CARBIDES, CAR-

BONYLS, AND ALKYLS

Metal cyanides

Simple ionic cyanides

Covalent cyanides containing -CN

Covalent cyanides containing -CN-

Prussian blue and related compounds

Miscellaneous cyanide and isocyanide

complexes

Metal carbides

Metal carbonyls

Preparation and properties

The structures of carbonyls and related

compounds

Carbonyl hydrides

Carbonyl halides

Nitrosyl carbonyls

Mixed metal carbonyls

Miscellaneous carbonyl derivatives of

Alkyls of B subgroup metals

Alkyls of groups I and I1 metals and A1

Organo-silicon compounds and silicon poly-

Hydroxyborates and anhydrous poly-

Other borates containing tetrahedrally

xviii

The lengths of B - 0 bonds 8 6 1

Cyclic Hz Bz 0 3 , boroxine, H3 B3O3,

The molecular structures of the boranes 8 6 6

Diborane, Bz H6 Tetraborane (1 o),

The BHi ion The B 3 H i ion Poly-

hedral ions Metal derivatives of

The structural chemistry of CU(I), Ag(r), and

The formation of 2 collinear bonds by

CU(I), A ~ ( I ) , and Au(1) 8 7 9

The formation of 4 tetrahedral bonds

The formation of 3 bonds by Cu(r) and

The structural chemistry of cupric com-

Structures of chelate cupric compounds 8 9 2

The formation of trigonal bipyramidal

bonds by CU(II)

Octahedral complexes

Cupric halides-simple and complex

Cupric hydroxy-salts

The sulphides of copper

The structural chemistry of Au(111)

26 THE ELEMENTS O F SUBGROUPS IIB, IIIB,

The structural chemistry of gallium and

The structural chemistry of tin and lead 9 3 1

Tetrahedral coordination Trigonal bipyramidal coordination Octa- hedral coordination 7- and 8-co-

ordinated Sn(1v); 8-coordinated

METALS Introduction The stereochemistry of Ti(1v) in some finite complexes

The stereochemistry of V(IV) in some finite complexes

The structural chemistry of C ~ ( I V ) , Cr(v), and C ~ ( V I )

Compounds of C r ( r v ) Compounds of C r ( v ) Compounds of Cr(v1) Compounds containing Cr in two oxida-

Higher coordination numbers of metals in

xix

Contents

Co(11) forming 4 bonds Co(11) form-

ing 5 bonds CO(II) forming 6

Introductory The isomerism of

cobaltammines The structures of

The stereochemistry of N ~ ( I I ) - ~ ' 964

Ni(11) forming 4 coplanar bonds

Ni(11) forming 4 tetrahedral

bonds Ni(11) forming 5 bonds

Ni(11) forming 6 octahedral

The structural chemistry of Pd and Pt 9 7 4

Planar complexes of Pd(11) and Pt(11) 974

Some highly-coloured compounds of Pt 9 8 0

Pd(11) and Pt(11) forming 6 octahedral

Trimethyl platinum chloride and related

The crystal chemistry of the lanthanides

The crystal chemistry of thorium 99 1

The crystal chemistry of protoactinium 992

fluorides of the 5 f elements

Oxides of uranium Uranyl com-

pounds Uranates and complex

Non-metals and the later B subgroup

Boron, aluminium, the elements of sub-

The transition elements and those o f

Interatomic distances in metals: metallic radii 1020

Crystal structure and physical properties 1026

The XYS , XYI ,, XY 3 and related

Acta Chemica Scandinavica

Acta Chimica Sinica

Australian Journal of Chemistry

Australian Journal of Scientific Research

Arkiv for Kemi

Arkiv for Kemi, Mineralogi och Geologi

Analytical Chemistry

American Mineralogist

Angewandte Chemie

Annalen der Physik

Acta Physicochimica URSS

Annual Review of Physical Chemistry

Applied Scientific Research

Berichte

Berichte der Bunsengesellschaft fiir physikalische Chemie

Bulletin of the Chemical Society of Japan

Bulletin des SociBtbs chimiques Belges

Bulletin de la SociktB chimique de France

Bulletin de la SociBtb franqaise de minbralogie et de cristallographie

Chimia (Switzerland)

Chemische Berichte

Chemical Communications (Journal of The Chemical Society, Chemical

Communications)

Canadian Journal of Physics

Comptes rendus hebdomadaires des SBances de 1'AcadCmie des Sciences

(Paris)

Comptes rendus de 1'Acadbmie des Sciences de 1'URSS

Doklady Akademii Nauk SSSR

Experientia

Fortschritte der Mineralogie

Gazzetta chimica italiana

Helvetica Chimica Acta

Inorganic Chemistry

Inorganica Chimica Acta

Industrial and Engineering Chemistry

Journal of the American Chemical Society

Journal of the American Ceramic Society

Journal of Applied Physics

xxi

Journal of Crystal Growth

Journal of Chemical Physics

Journal of the Chemical Society (London)

Journal of the Electrochemical Society

Journal of Inorganic and Nuclear Chemistry

Journal of t h e Less-common Metals

Journal of Metals

Journal of Molecular Spectroscopy

Journal of Nuclear Materials

Journal of Organometallic Chemistry

Journal of Physical Chemistry

Journal of the Physics and Chemistry of Solids

Journal de Physique (Paris)

Journal of the Physical Society of Japan

Kristallografiya

Kongelige Danske Videnskabernes Selkab Matematisk-fysiske Meddeleser Monatshefte fiir Chemie u n d verwandte Teile anderer Wissenschaften Mineralogical Journal of Japan

Mineralogical Magazine (and Journal of the Mineralogical Society) Mineralogical Magazine (Japan)

Materials Research Bulletin

M6morial des Services chimiques de 1'6tat (Paris)

Nature

Journal of Research of the National Bureau of Standards

Naturforschung

Neues Jahrbuch fur Mineralogie

Nature (Physical Sciences)

Naturwissenschaften

Proceedings of the Chemical Society

Proceedings koninklijke nederlandse Akademic van Wetenschappen Philosophical Magazine

Proceedings of the National Academy of Sciences of the U.S.A

Physical Review

Physical Review Letters

Philips Research Reports

Physica Status Solidi

Quarterly Reviews of The Chemical Society

Russian Journal of Inorganic Chemistry

Reviews of Modem Physics

Reviews of Pure and Applied Chemistry (Royal Australian Chemical Institute)

Solid State Communications

Transactions of the American Institute o f Mining and Metallurgical Engineers

Transactions of the Faraday Society

Tidsskrift for Kjemi, Bergvesen og Metallurgi

Zeitschrift fur anorganische (und allgemeine) Chemie

Abbreviations

ZK Zeitschrift fiir Kristallographie

ZPC Zeitschrift fur physikalische Chemie

x x iii

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Part I

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Introduction

In this introductory chapter we discuss in a general way a number of topics which are intended to indicate the scope of our subject and the reasons for the choice of topics which receive more detailed attention in subsequent chapters

The number of elements known exceeds one hundred, so that if each one combined with each of the others to form a single binary compound there would be approximately five thousand such compounds In fact not all elements combine with all the others, but on the other hand some combine to form more than one compound This is true of many pairs of metals, and other examples, chosen at random, include:

YB2, YB4, YB6, YB12, and YBb6;

CrF2, CrF3, CrF4, CrF5, CrF6, and Cr2FS;

CrS, Cr&, Cr5S6, Cr3S4, and Cr2S3

The number of binary compounds alone is evidently considerable, and there is an indefinitely large number of compounds built of atoms of three or more elements

It seems logical to concentrate our attention first on the simplest compounds such

as binary halides, chalconides, etc., for it would appear unlikely that we could understand the structures of more complex compounds unless the structures of the simpler ones are known and understood However, it should be noted that simplicity of chemical formula may be deceptive, for the structures of many compounds with simple chemical formulae present considerable problems in bonding, and indeed the structures of some elements are incomprehensibly complex (for example, B and red P) On the other hand, there are compounds with complex formulae which have structures based on an essentially simple pattern, as are the numerous structures described in Chapter 3 which are based on the diamond net, one of the simplest 3-dimensional frameworks We shall make a point of looking for the simple underlying structural themes in the belief that Nature prefers simplicity to complexity and also because structures are most easily understood if reduced to their simplest terms

The importance of the solid state

"

Since we shall devote most of the first part of this book to matters directly concerned with the solid state it is appropriate to note a few general points, to some of which we return later in this chapter

up on the surface of the solid reactant In all cases where a crystalline material is formed or broken down, the process involves the lattice energy of the crystal The familiar Born-Haber cycle for the reaction between solid sodium and gaseous chlorine to form solid NaCl provides a simple example of the interrelation of heats

of dissociation, ionization energy and affinity, lattice energy, and heat of reaction (ii) Organic compounds (other than polymers) exist as finite molecules in all states of aggregation This means, first, that the structural problem consists only in discovering the structure of the finite molecule, and second, that this could in principle be determined by studying its structure in the solid, liquid, or vapour state Apart from possible geometrical changes such as rotation about single bonds and small dimensional changes due to temperature differences, the basic topology and geometry could be studied in any state of aggregation Some inorganic compounds also exist as finite molecules in the solid, liquid, and gaseous states, for example, many simple molecules formed by non-metals (HC1, C 0 2 ) and also some compounds of metals (Sn14, Cr(C0)6) Accurate information about the structures

of simple molecules, both organic and inorganic, comes from spectroscopic and electron diffraction studies of the vapours, but these methods are not applicable to very complex molecules Because crystalline solids are periodic structures they act

as diffraction gratings for X-rays and neutrons, and in principle the structure of any molecule, however complex, can be determined by diffraction studies of the solid

In contrast to organic compounds and the minority of inorganic compounds mentioned above, the great majority of solid inorganic compounds have structures

in which there is linking of atoms into systems which extend indefinitely in one, two, or three dimensions Such structures are characteristic only of the solid state and must necessarily break down when the crystal is dissolved, melted, or vaporized The study of crystal structures has therefore extended the scope of structural chemistry far beyond that of the finite groups of atoms to which classical stereochemistry was restricted to include all the periodic arrangements of atoms found in crystalline solids

Because the great majority of inorganic compounds are compounds of one or more metals with non-metals, and because most of them are solids under ordinary conditions, the greater part of structural inorganic chemistry is concerned with the structures of solids The only compounds of metals which have any structural chemistry, apart from that of the crystalline compound, are those molecules or ions that can be studied in solution or the molecules of compounds that can be melted

or vaporized without decomposition It is unlikely that very much accurate

4

Introduction

structural information will ever be obtained from liquids, whereas electron diffraction or spectroscopic studies can be made of molecules in the gas phase provided they are not too complex It is important therefore to distinguish between solid compounds which can be vaporized without decomposition and those which

can exist on& as solids By this we mean that their existence depends on types of

bonding which are possible only in the solid state Some simple halides and a few oxides of metals have been studied as vapours, and if the vapour species is not present in the crystal the information so obtained is complementary to that obtained by studying the solid On the other hand, many simple compounds M,X, are unlikely to exist in the vapour state because the particular ratio of metal to non-metal atoms is only realizable in an infinite array of atoms between which certain types of bonding can operate Crystalline Cs20 consists of infinite layers, but nevertheless we can envisage molecules of Cs20 in the vapour However, oxides such as Cs30 and Cs,O depend for their existence on extended systems of metal-metal bonds which would not be possible in a finite molecule

Comparatively little is yet known about the high temperature chemistry of metal halides, oxides, etc.; for example, the structures of molecules such as FeC13 or of oxides M203, M 0 2 , M2O5, or indeed whether these species are formed or are unstable (like S O 2 ) Certainly complex halides and oxides, can exist only in the crystalline state, and this is true also of other large and important groups of compounds such as salts containing oxy ions, 'acid' and 'basic' salts, and hydrates One particularly important result of the study of crystal structures has been the

recognition that non-stoichiometric compounds are not the rarities they were once

thought to be A non-stoichiometric compound may be very broadly defined as a

solid phase which is stable over a range of composition This definition covers at one extreme all cases of 'isomophous replacement' and all kinds of solid solution, the composition of which may cover the whole range from one pure component to the other At the other extreme there are phosphors (luminescent ZnS or ZnS-Cu), which owe their properties to misplaced and/or impurity atoms which act as 'electron traps', and coloured halides (alkali or alkaline-earth) in which some of the halide-ion-sites are occupied by electrons (F-centres); these defects are present in very small concentration, often in the range 1 0 - ~ - 1 0 ~ Of more interest to the inorganic chemist is the fact that many simple binary compounds exhibit ranges of composition, the range depending on the temperature and mode of preparation The non-stoichiometry implies disorder in the structure and usually the presence of

an element in more than one valence state, and can give rise to semiconductivity and catalytic activity Examples of non-stoichiometric binary compounds include many oxides and sulphides, some hydrides, and interstitial solid solutions of C and

N in metals More complex examples include various complex oxides with layer and framework structures, such as the bronzes (p 505) The existence of green and black NiO, with very different physical properties, the recent preparation for the first time of stoichiometric FeO, and the fact that Fe6S7 is not FeS containing excess S but FeS deficient in Fe (that is, Fel-,S) are matters of obvious importance to the inorganic chemist

The compositions and properties and indeed the very existence of non-

5

Introduction

stoichiometric compounds can be understood only in terms of their structures This

is particularly evident in cases where the non-stoichiometry arises from the inclusion of foreign atoms or molecules in a crystalline structure It can occur in crystals built of finite molecules or crystals containing large finite ions For example, if Pd2Br4[As(CH3)312 (p 28) is crystallized from dioxane the crystals can retain non-stoichiometric amounts of the solvent in the tunnels between the molecules, and these molecules can be removed without disruption of the structure (Fig 1.9(a)) In the mineral beryl (p 815) the large cyclic (Si6oI8)l 2 - ions are stacked in columns, and helium can be occluded in the tunnels Some crystals with layer structures can take up material between the layers Examples include the lamellar compounds of graphite (p 734) and of clay minerals (p 823) An unusual type of layer structure is that of Ni(CN), NH3 which can take up molecules of H20, C6H6, C6H5NH2, etc between the layers (Fig 1.9(b)) Structures of this kind are called 'clathrates', and examples are noted on p 28

(iii) The great wealth of information about atomic arrangement in crystals and

in particular the detailed information about bond lengths and interbond angles provided by studies of crystal structures is the raw material for the theoretician interested in bonding and its relation to physical properties

All elements and compounds can be solidified under appropriate conditions of temperature and pressure, and the properties and structures of solids show that we must recognize four extreme types of bonding:

(a) the polar (ionic) bond in crystalline salts such as NaCl or CaF,,

(b) the dovalent bond in non-ionizable molecules such as C12, S8, etc., which exist in both the crystalline elements and also in their vapours, and in crystals such

as diamond in which the length of the C-C bond is the same as in molecules such as H3C-CH3,

(c) the metallic bond in metals and intermetallic compounds (alloys), which

is responsible for their characteristic optical and electrical properties, and

(d) the much weaker van der Waals bond between chemically saturated molecules such as those just mentioned-witness the much larger distances between atoms of different molecules as compared with those within such molecules In crystalline C12 the bond length is 1.99 A, but the shortest distance between C1 atoms of different molecules is 3.34 A The van der Waals bond is responsible for the cohesive forces in liquid or solid argon or chlorine and more generally between neutral molecules chains, and layers in numerous crystals whose structures will be described later

Although it is convenient and customary to recognize these four extreme types

of bonding it should be realized that bonds of these 'pure' types-if indeed the term 'pure' has any clear physical or chemical meaning-are probably rather rare, particularly in the case of the first two types Bonds of an essentially ionic type occur in salts formed from the most electropositive combined with the most electronegative elements and between, for example, the cations and the 0 atoms of the complex ion in oxy-salts such as NaN03 Covalent bonds occur in the non-metallic elements and in compounds containing non-metals which do not differ

Introduction

greatly in 'electronegativity' (see p 236) However, it would seem that the great majority of bonds in inorganic compounds must be regarded as intermediate in character between these extreme types For example, most bonds between metals and nonmetals have some ionic and some covalent character, and at present there is

no entirely satisfactory way of describing such bonds

Evidently many crystals contain bonds of two or more quite distinct types In molecular crystals consisting of non-polar molecules the bonds within the molecule may be essentially covalent (e.g S6 or S8) or of some intermediate ionic-covalent nature (e.g SiF4), and those between the molecules are van der Waals bonds In a crystal containing complex ions the bonds within the complex ion may approxi- mate to covalent bonds while those between the complex ion and the cations (or anions) are essentially ionic in character, as in the case of NaN03 already quoted

In other crystals there are additional interactions between certain of the atoms which are not so obviously essential as in these cases to the cohesion of the crystal

An example is the metal-metal bonding in dioxides with the rutile structure, a structure which in many cases is stable in the absence of such bonding

It is also necessary to recognize certain other types of interactions which, although weaker than ionic or covalent bonds, are important in determining or influencing the structures of particular groups of crystalline compounds-for example, hydrogen bonds (bridges) and charge-transfer bonds Hydrogen bonds are

of rather widespread occurrence and are discussed in more detail in later chapters (iv) It is perhaps unnecessary to emphasize here that there is in general no direct relation between the chemical formula of a solid and its structure For example, only the first member of the series

HI AuI CuI NaI CsI AX

1 2 4 6 8 (C.N o f A by X)t consists of discrete molecules A-X under ordinary conditions All the other compounds are solids at ordinary temperatures and consist of infinite arrays of A and X atoms in which the metal atoms are bonded to, respectively, two, four, six, and eight X atoms Figure 1.1 shows some simple examples of systems with the composition AX Two are finite groups, (a) the dirner and (b) the tetramer; the remainder are infinite arrangements (c) 1-dimensional, (d) and (e) 2-dimensional, and (0 3-dimensional The number of ways of realizing a particular ratio of atoms may be large; Fig 1.2 shows some systems with the composition AX3

Examples of all the systems shown in Figs 1.1 and 1.2 will be found in later chapters In the upper part of Table 1.1 we list seven different ways in which an

F : M ratio of 5 : 1 is attained in crystalline pentahalides; the list could be extended

if anions (MXS)"- are included, as will be seen from the structures of complex halides in Chapter 10 Conversely, we may consider how different formulae MX,

arise with the same coordination number o f M For tetrahedral and octahedral coordination this problem is considered in some detail in Chapter 5; the examples

of Table 1.1 may be of interest as examples of the less usual coordination number

t C.N = Coordination number

(a) c.n 2

(d) c.n 3

FIG 1.1 Arrangements of equal numbers of atoms of two kinds

nine In order to gain a real understanding of the meaning of the formulae of inorganic compounds it is evidently necessary to think in three rather than two dimensions and in terms of infinite as well as finite groups of atoms

(v) The chemist is familiar with isomerism (p 47), which refers to differences

in the structures of finite molecules or complex ions having a particular chemical composition If infinite arrangements of atoms are permitted, in addition to finite groups, the probability of alternative atomic arrangements is greatly increased, as is evident from Figs 1.1 and 1.2

An element or compound is described as polymorphic if it forms two or more

crystalline phases differing in atomic arrangement (The earlier term allotropy is

still used to refer to different 'forms' of elements, but except for the special case of

O2 and O3 allotropes are simply polymorphs.) Polymorphism of both elements and compounds is the rule rather than the exception, and the structural chemistry of any element or compound includes the structures of all its polymorphs just as that

of a molecule includes the structures of its isomers The differences between the structures of polymorphs range from minor difference such as the change from fixed to random orientation (or complete rotation) of a molecule or complex ion in the high temperature form of a substance (for example, crystalline YCI, salts containing NH:, NO;, CN-, and other complex ions), or the a-P changes of the

forms of Si0.2, to major differences involving reconstruction of the whole crystal (the polymorphs of C,P, SiOz, etc.)

Originally the only variable in studies of polymorphism was the temperature, and substances are described as enantiotropic if the polymorphic change takes place

8

Introduction

FIG 1.2 Some ways of realizing a ratio of 3X:A in finite or infinite groupings of atoms: (a)-(d), finite groups AX3, AX2 and AX4, A2X6 and A3X9, (e)-(g), infinite linear systems,

(h) infinite two-dimensional system, (i) infinite three-dimensional complex

at a definite transition temperature or monotropic if one form is stable at all temperatures under atmospheric pressure Extensive work by Bridgman showed that many elements (and compounds such as ice) undergo structural changes when subjected to pressure, the changes being detected as discontinuities in physical properties such as resistivity or compressibility In some cases the high pressure structure can be retained by quenching in liquid nitrogen and studied under atmospheric pressure by normal X-ray techniques During the last decade the study

of high pressure polymorphs has been greatly extended by the introduction of new apparatus (such as the tetrahedral anvil) which not only increase the range of

pressures attainable but also permit the X-ray (and neutron) diffraction study of the phase while under pressure Studies of halides and oxides, in addition to

Introduction

TABLE 1 1

Structures o f crystalline pen tahalides

Examples of tricapped trigonal prism coordination

Members of families of closely related structures, the formation of which i:

dependent on the growth mechanism of the crystals, are termed polytypes The)

are not normal polymorphs, and are formed only by compounds with certain type

of structure The best-known examples are Sic, Cd12, ZnS, and certain comple: oxides, notably ferrites, to which reference should be made for further details

(vi) When atoms are bonded together to form either finite or infinite grouping

complications can occur owing to the conflicting requirements of the various atom due to their relative sizes or preferred interbond angles It is well known that thi problem arises in finite groups of atoms, as may be seen from scale models o

molecules and complex ions It is, however, less generally appreciated tha geometrical and topological restrictions enter in much more subtle ways in 31 structures and may be directly relevant to problems which seem at first sight to b

Introduction

purely chemical in nature As examples we may instance the relative stabilities of series of oxy-salts (for example, alkali-metal orthoborates and orthosilicates), the crystallization of salts from aqueous solution in the anhydrous state or as hydrates, and the behaviour of the nitrate ion as a bidentate or monodentate ligand We return briefly to the subject later in this chapter and consider it in more detail in Chapter 7

Structural formulae of inorganic compounds

Elemental analysis gives the relative numbers of atoms of different elements in a compound; it yields an 'empirical' formula The simplest type of structural formula indicates how the atoms are linked together, and to this simple topological picture may be added information describing the geometry of the system The nature of a structural formula depends on the extent of the linking of the atoms If the compound consists of finite molecules it is necessary to know the molecular weight and then to determine the topology and geometry of the molecule:

HNO . t H2N202 - ,N=N /OH - bond lengths and

elemental molecular infrared and Raman angles

analysis weight spectroscopy

indicate

trans configuration

If the atoms (in a solid) are linked to form a 1-, 2-, or 3-dimensional system the term molecular weight has no meaning, and the structural formula must describe some characteristic set of atoms which on repetition reproduces the arrangement found in the crystal The repeat unit in an infinite 1-dimensional system is readily found by noting the points at which the pattern repeats itself:

repeat unit

0

The complete description of the chain requires metrical information as in the case

of a finite group It should be noted that if the geometry of the chain is taken into account, that is, the actual spatial arrangement of the atoms in the crystal, then the (crystallographic) repeat unit may be larger than the simplest 'chemical' repeat unit The crystallographic repeat unit is that set of atoms which reproduces the observed

11

Introduction

structure when repeated in the same orientation, that is, by simple translations in one, two, or three directions The chemical repeat unit is not concerned with orientation This distinction is illustrated in Fig 1.3(a) for the HgO chain The chemical repeat unit consists of one Hg and one 0 atom whereas if we have regard

to the geometrical configuration of the (planar) chain we must recognize a repeat unit containing 2 Hg + 2 0 atoms The various forms of AX3 chains formed from

tetrahedral AX4 groups sharing two vertices (X atoms) provide further examples (p

8 16); one is included in Fig 1.3(b)

FIG 1.3 Repeat units in chains

Similar considerations apply to structures extending in two or three dimensions The repeat unit of a 2D pattern is a unit cell which by translation in the directions

of two (non-parallel) axes reproduces the infinite pattern One crystalline form of

h 2 O 3 is built of infinite layers of the kind shown in Fig 1.4(a), the unit cell being indicated by the broken lines The pattern arises from As03 groups sharing their 0 atoms with three similar groups, or alternatively, the repeat unit is A S ( O ~ / ~ ) ~ These units are oriented in two ways to form the infinite layer, with the result that the crystallographic repeat unit-which must reproduce the pattern merely by translations in two directions-contains two of these AS(^^/^)^ units, or As2O3

The crystallographic repeat unit of a 3D pattern is a parallelepiped containing a representative collection of atoms which on repetition in the directions of its edges forms the (potentially infinite) crystal As in the case of a 1- or 2-dimensional pattern this unit cell may, and usually does, contain more than one basic 'chemical' unit (corresponding to the simplest chemical formula)

The following remarks may be helpful at this point; they are amplified in later chapters There is no unique unit cell in a crystal structure, but if there are

12

Introduction

FIG 1.4 (a) Alternative unit cells of layer structure of Asz03 @) Projection of unit cell of a

structure containing four atoms

symmetry elements certain conventions are adopted about the choice of axes (directions of the edges of the unit cell) For example, crystalline NaCl has cubic symmetry (see Chapter 2) and the structure is therefore referred to a cubic unit cell This cell contains 4 NaCl, but the structure may be described in terms of cells containing 2 NaCl or 1 NaCl; these alternative unit cells for the NaCl structure are illustrated in Fig 6.3 (p 197) It is sometimes convenient to choose a different origin, that is, to translate the cell in the directions of one or more of the axes, and the origin is not necessarily taken at an atom in the structure For example, the unit cell of the projection of Fig 1.4(a) does not have an atom at the origin but it is a more convenient cell than the one indicated by the dotted lines because it gives the coordinates + ($ $)rather than (00) and (3 5) for the two equivalent As atoms

If there are atoms at the corners or on the edges or faces of a unit cell it may be difficult to reconcile the number of atoms shown in a diagram with the chemical formula-see, for example, the cell outlined by the broken lines in Fig 1.4(a) It is only necessary to remember that the cell content includes all atoms whose centres lie within the cell and that atoms lying at the corner or on an edge or face count as follows:

unit cell of 2D pattern:

atom at corner belongs to four cells,

atom on edge belongs to two cells

unit cell of 3D pattern:

atom at corner belongs to eight cells,

atom on edge belongs to four cells

atom in face belongs to two cells

The cell content in each case could alternatively be shown by shading that portion

of each atom which lies wholly within the cell (Fig 14(b))

Each atom shown in a projection repeats at a distance c above and below the

13

Introduction

FIG 1.5 Projection of body-

centred structure showing 8-co-

ordination of atoms

FIG 1.7 Projection of 4-fold

helix along its axis The atom at

height f is connected to the atom

vertically above the one shown at

height 0

plane of the paper, where c is the repeat distance in the structure along the direction of projection Figure 1 S represents the projection on its base of a cube containing an atom at its centre (body-centred cubic structure) The atom A has eight equidistant neighbours at the vertices of a cube, since the atoms at height 0

(i.e in the plane of the paper) repeat at height 1 (in units of the distance c) Similarly the atom B has the same arrangement of eight nearest neighbours (For some exercises on this topic see MSIC, p 52.)

In order to simplify an illustration of a structure it is common practice to show a set of nearest neighbours (coordination group) as a polyhedral group Thus the projection of the rutile structure of one of the forms of TiOz may be shown as either (a) or (b) in Fig 1.6 In (a) the heavy lines indicate Ti-0 bonds, and it may

be deduced from the coordinates of the atoms that there is an octahedral

FIG 1.6 Projections of the structure of rutile (TiOz): (a) showing atoms and their heights,

(b) showing the octahedral Ti06 coordination groups

coordination group of six 0 atoms around each Ti atom In (b) the lines represent the edges of the octahedral coordination groups Since it is important that at least the two commonest coordination polyhedra should be recognized when viewed in a number of directions we illustrate several projections of the tetrahedron and octahedron at the beginning of Chapter 5

Atoms arranged around 3-, 4-, or 6-fold helices project along the helical axis as

triangle, square, or hexagon respectively A pair of lines may be used to indicate

that a number of atoms do not form a closed circuit but are arranged on a helix perpendicular to the plane of the paper (Fig 1.7)

It is perhaps unnecessary to stress that a formula should correspond as closely as possible to the structure of the compound, that is, to the molecule or other grouping present, as, for example, Na3B3O6 for sodium metaborate, which contains cyclic ~ ~ 0 : - ions Compounds containing metal atoms in two oxidation states are of interest in this connection If the oxidation numbers differ by unity the formula does not reduce to a simpler form (for example, Fe304, Cr,F,), but if

Studies of crystal structures have led to the revision of many chemical formulae by regrouping the atoms to correspond to the actual groups present in the crystal This

is particularly true of compounds originally formulated as hydrates; some examples follow

Hydrate Structural formula

NaB02 2 H 2 0 Na [B(OH)41

Na2B40, 10 H 2 0 Na2 [B405(OH)41 8 H2O

FeCl, 6 H 2 0 [FeC12(H20)4] C1 2 H 2 0

ZrOC12 8 H20 [Zr4(OH)8@2 0 ) 1 1 Cis 12 Hz 0

The formulae of many inorganic compounds do not at first sight appear compatible with the normal valences of the atoms but are in fact readily interpretable in the light of the structure of the molecule or crystal In organic chemistry we are familiar with the fact that the H : C ratios in saturated

hydrocarbons, in all of which carbon is tetravalent, range from the maximum value four in CH4 to two in (CH2), owing to the presence of C-C bonds Similarly the unexpected formula, P4S3, of one of the sulphides of phosphorus arises from the presence of P-P bonds; the formation by P(III) of three and by S(II) of two bonds

would give the formula P4S6 if all bonds were P-S bonds

Bonding between atoms of the same element also occurs in many crystalline binary compounds and leads to formulae such as CdP4, PdP2, and PdS2 which are not reconcilable with the normal oxidation numbers of Cd and Pd until their crystal structures are known The structures of PdP2 and PdSz are described shortly; for CdP4 see p 677

Our final point relating to the structural formulae of solids is that in general crystallographers have not greatly concerned themselves with interpreting the structures of solids to chemists As a result much of the structural chemistry of solids became segregated in yet another subdivision of chemistry (crystal chemistry,

or more recently, solid-state chemistry), and many chemists still tend to make a mental distinction between the structures of solids and of the finite molecules and complex ions that can be studied in solution or in the gaseous state The infinite layer structures of black and red phosphorus are manifestly only more complex examples of P forming three bonds as in the finite (tetrahedral) P4 molecule of

Many compounds of Pd(11) may be formulated in a consistent way so that the metal atom acquires a share in six additional electrons and forms planar dsp2 bonds Of the two simple possibilities (a) and (b) the former enables us to

formulate the infinite chain of PdC1, and the pd2c12- ion (since a bridging C1 is represented as at (c)), while (b) represent the situation in ~ d ~ l z - , though the actual state of the ion (e) is presumably intermediate between the 'ionic' picture (d) and the 'covalent' one ( 0 :

In crystalline PdO (and similarly for PdS and PtS) 0 forms four tetrahedral bonds and the metal forms four coplanar bonds, and we have the bond pictures

\ and , ~ d <

k/ L

The compounds PdS2 and PdP2, which might not appear to be compounds of

P ~ ( I I ) , can be formulated in the following way The disulphide consists of layers