nanomaterials and nanochemistry, 2007, p.748

Part I Basic Principles and Fundamental Properties 1 Size Effects on Structure and Morphology of Free or Supported Nanoparticles C.. Size Effects on Structure and Morphology of Free or Sup

Nanomaterials and Nanochemistry

C Br´echignac P Houdy M Lahmani (Eds.)

Catherine Br´echignac, PhD

Member of l’Acad´emie des sciences (French Academy of Sciences)

President of the CNRS

Centre universitaire Paris-Sud, Laboratoire Aim´e Cotton

Bˆatiment 505, 91405 Orsay Cedex, France

Club Nano-Micro-Technologie de Paris

Boulevard François Mitterrand, 91025 ´ Evry C´edex, France

E-mail: marcel.lahmani@univ-evry.fr

Translation from the French language edition of

“Les nanosciences – Nanomat´eriaux et nanochimie"

© 2006 Editions Belin, France

ISBN 978-3-540-72992-1 Springer Berlin Heidelberg New York

This work is subject to copyright All rights are reserved, whether the whole or part of the material

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Foreword to the French Edition

Nanomaterials constitute an important branch in the burgeoning field ofnanoscience Size reduction can lead to a whole range of new physicochemi-cal properties and a wealth of potential applications However, access to thesenanostructured entities requires the development of suitable methods for theirelaboration

This book, aimed at MSc or PhD students and young engineers, researchscientists and teachers, provides a complete review of all relevant aspects fromthe fabrication of nanomaterials able to carry out new functions to the self-assembly of complex structures

Part I provides a theoretical description of the basic principles and damental properties of nanomaterials, whilst Part II treats the physical andchemical properties of nanoscale structures Methods for designing and fabri-cating such structures are then discussed in Parts III and IV

fun-In Part V, a great many industrial applications, some still under ment, are used to demonstrate the significant economic potential of these newstructures and their consequences in various areas of everyday life

develop-Supramolecular chemistry can provide novel ways of moving forward inthis domain Indeed, molecular recognition phenomena, based on molecularinformation, can be used to form supramolecular materials in a spontaneousbut controlled manner, by self-organisation starting from their components.Self-organisation processes thus represent a powerful method for building func-tional nanomaterials, which may provide a way of avoiding ever more delicateand costly nanofabrication and nanomanipulation processes

It seems fair to hope that the meeting of supramolecular chemistry withmaterials science will soon open up new lines of development in nanoscienceand nanotechnology The present work lays the foundations on which theseprospects may be pursued

Preface to the French Edition

The present book Nanoscience II – Nanomaterials and Nanochemistry has been designed as the natural continuation of Nanoscience I – Nanotechnology and Nanophysics It seemed to us to provide an essential complement, consid-

ering the significant developments and economic potential of nanomaterials.Many applications of nanomaterials will undoubtedly use current technology,with a few modifications However, as work proceeds in this area, there isevery reason to think that the new properties they give rise to will also lead

to major industrial developments

The chapters of the book are grouped into five main parts:

• The fundamental physicochemical principles and the basic features of

mat-ter on the nanoscale

• The basic properties relevant to this state of matter.

• Methods for designing nanomaterials and nanoparticles.

• Fabrication processes for nanostructured bulk materials and nanoporous

materials

• A selection of current and future industrial applications.

As a guide to the layout of the book, let us recall a few general ideas.First of all, what is meant by the term ‘nanomaterial’ ? From an etymo-logical standpoint, it would not appear to be very explicit Indeed, the prefix

‘nano’ used in scales of physical units means one billionth, or 10−9, of the

rel-evant unit In the present case it refers to the nanometer, or one billionth of ameter When we use the term nanomaterial, we are thus specifying an order

of magnitude of a geometric dimension But then what is it in nanomaterialsthat is of nanometric dimensions?

To answer this question, we must now consider the second part of the term,viz., ‘material’ A material is matter that has been transformed or adapted

to be able to fulfill some particular function One can say that this matterhas been functionalised Many materials we use and which appear to thenaked eye to be of a perfectly continuous constitution are in fact made up ofgrains of crystallised matter with dimensions often of the order of the micron

VIII Preface to the French Edition

(one millionth of a meter, or 10−6m) This is true in particular for most

metals and ceramics in common use, but it is not the case for glasses andso-called plastics, which are amorphous, or can be considered as such for thepurposes of the present discussion These micrometric grains are of coursevery small compared with the dimensions of the objects generally made withsuch materials However, they are very large compared with the dimensions

of the atoms that make them up Indeed, atoms have diameters ten thousandtimes smaller than these grains Consequently, there are some (104)3= 1012

or a thousand billion iron atoms in a grain of steel of diameter 1 micron.Forty years ago, it was realised that the properties of certain materialscould be modified, improved or adapted in specific ways if, during the fabri-cation process, the grains making them up could be made much smaller Thefirst ‘nanomaterials’ were born They can be found today in many and variedfields of application, from cosmetics, through magnetic and electronic record-ing devices to precision cutting tools Further research and new developmentsare under way to invent or improve novel nanomaterials, exploiting the waytheir properties depend on grain sizes

More recently, over the past twenty years or so, the term ‘nanomaterials’has also sometimes been used to refer to matter in which the atoms make

up assemblages with dimensions of the order of a few nanometers A priori,these assemblages, known as clusters, have nothing in common with nano-materials as they were previously defined By their very nature, these newmaterials, unlike their predecessors, can only be conceived on the nanometricscale However, they too can exhibit quite exceptional properties and are cur-rently the subject of much scientific interest both on the level of fundamentalresearch and for their prospective applications The elaboration of memorycells on a quasi-molecular scale can be cited as one of the most exciting ofthese prospects

To get a clearer idea of the distinction between these two families of materials, let us take the example of solid architectures made from carbonatoms:

nano-• In the solid state, carbon is known to occur in two crystal forms: graphite

and diamond Both can be produced in the form of very small grains, afew nanometers in size Carbon can therefore be produced at least in theform of a powder, comprising nanograins of graphite or diamond One thusseeks to establish how the properties of graphite or diamond will vary withthe grain dimensions

• Furthermore, it has now been known for around twenty years how to make

a type of molecule known as a fullerene, the most familiar being C60, whichcomprises 60 carbon atoms We have also discovered, even more recently,how to create another special kind of architecture from carbon atoms,namely carbon nanotubes C60like the nanotubes is neither graphite nordiamond reduced to the nanometric length scale They are both entirelynovel entities, totally different from the traditional forms of solid carbon

Preface to the French Edition IX

Conceptually, therefore, there seem to be two large families of nanomaterialsand hence two communities of research scientists which have evolved inde-pendently of one another These two communities can be distinguished in thefollowing ways:

• by the nature and spirit of the fundamental research they carry out,

• by the applications, which are conventional for the first community because

they generally seek to improve or optimise the performance of a materialthat is already known and used in the same field, e.g., greater data orenergy storage capacity, increased hardness or greater aptitude for plasticdeformation, etc In contrast, the prospective applications are completelynovel in the second family of nanomaterials, e.g., carbon nanotube mem-ories, implying basic computer processing units on the molecular scale!However, this distinction cannot be so clearly made in the case of metals Afterall, is there a fundamental distinction between a cluster of silver atoms and

a nanometric silver grain? Can we not consider a silver nanograin containing

10× 10 × 10 = 103 atoms as a rather large silver cluster? Is this not anartificial distinction between the two communities and the two concepts ofwhat constitutes a nanomaterial?

From a historical perspective, the distinction between these two nities and the two concepts would appear to be justified One community,using the so-called bottom-up approach, started with the atom and built upnano-objects from there, while the other, adopting a top-down approach setout from standard bulk materials to design and produce the same materialsbut made up from nanometric grains

commu-Likewise, the development of processes and products based on advancedknowledge of the chemistry of molecular or particle synthesis, or supramole-cular chemistry, will lead to a wide range of objects with novel properties asregards strength, optics, electronics, magnetism, biology, and so on

In the end we should therefore arrive at a single physicochemistry of objects, a multiscale physicochemistry that will take into account the organ-isational state and properties of nanograins as a function of their size or thenumber of atoms making them up

X Preface to the French Edition

Acknowledgements

We would like to thank all members of the French nanoscience nity (CNRS, CEA, universities, Grandes Ecoles, industry) who gave a veryfavourable welcome to the writing of these pedagogical introductions to nan-otechnology and nanophysics, nanomaterials and nanochemistry (presentedhere), and nanobiotechnology and nanobiology (to be published soon), andwithout which they would have been impossible Special thanks go, of course,

commu-to all those who contributed commu-to these books

We would also like to thank the late Hubert Curien of the Academy ofSciences (Paris) and Jean-Marie Lehn (Nobel Prize for Chemistry) for con-tributing the forewords to volumes I and II of this series, and also PatriceHesto who gave invaluable advice when the project first began

We warmly acknowledge the material and financial support of the FrenchMinistry of Research, orchestrated by Jean-Louis Robert of the Department

of Physics, Chemistry, and Engineering Sciences, and Michel Lanoo, Director

of the Department of Physical Sciences and Mathematics at the CNRS.Likewise, our warmest thanks go to Claude Puech, President of theClub NanoMicroTechnologie, everyone at the LMN (Laboratoire d’´etude desMilieux Nanom´etriques at the University of Evry, France) and the GIFO(Groupement des Industries Fran¸caises de l’Optique) for their administrativeand logistical support

Finally, we would like to thank Henri Van Damme and Dominique Givordfor their continued scientific support, especially during copy-editing sessions,and Paul Siffert of the European Materials Research Society for supportingthe English edition of the book

Marcel Lahmani, Catherine Br´ echignac and Philippe Houdy

Part I Basic Principles and Fundamental Properties

1 Size Effects on Structure and Morphology

of Free or Supported Nanoparticles

C Henry 3

1.1 Size and Confinement Effects 3

1.1.1 Introduction 3

1.1.2 Fraction of Surface Atoms 3

1.1.3 Specific Surface Energy and Surface Stress 4

1.1.4 Effect on the Lattice Parameter 5

1.1.5 Effect on the Phonon Density of States 8

1.2 Nanoparticle Morphology 8

1.2.1 Equilibrium Shape of a Macroscopic Crystal 8

1.2.2 Equilibrium Shape of Nanometric Crystals 10

1.2.3 Morphology of Supported Particles 17

References 32

2 Structure and Phase Transitions in Nanocrystals J.-C Ni` epce, L Pizzagalli 35

2.1 Introduction 35

2.2 Crystalline Phase Transitions in Nanocrystals 39

2.2.1 Phase Transitions and Grain Size Dependence 39

2.2.2 Elementary Thermodynamics of the Grain Size Dependence of Phase Transitions 40

2.2.3 Influence of the Surface or Interface on Nanocrystals 42

2.2.4 Modification of Transition Barriers 44

2.3 Geometric Evolution of the Lattice in Nanocrystals 46

2.3.1 Grain Size Dependence 46

2.3.2 Theory 47

2.3.3 Influence of the Nanocrystal Surface or Interface on the Lattice Parameter 50

XII Contents

2.3.4 Is There a Continuous Variation of the Crystal State

Within Nanocrystals? 51

References 53

3 Thermodynamics and Solid–Liquid Transitions P Labastie, F Calvo 55

3.1 Size Dependence of the Solid–Liquid Transition 56

3.1.1 From the Macroscopic to the Nanometric 56

3.1.2 From Nanoparticles to Molecules 64

3.2 Thermodynamics of Very Small Systems 67

3.2.1 General Considerations 67

3.2.2 Non-Equivalence of the Gibbs Ensembles 68

3.2.3 Dynamically Coexisting Phases 69

3.2.4 Stability of an Isolated Particle Thermodynamic Equilibrium 73

3.3 Evaporation: Consequences and Observations 74

3.3.1 Statistical Theories of Evaporation 74

3.3.2 Link with the Solid–Liquid Transition Numerical Results 79 3.3.3 Experimental Investigation of Evaporation 80

3.3.4 Beyond Unimolecular Evaporation 81

3.3.5 Toward the Liquid–Gas Transition 82

References 86

4 Modelling and Simulating the Dynamics of Nano-Objects A Pimpinelli 89

4.1 Introduction 89

4.2 Free Clusters of Atoms Molecular Dynamics Simulations 90

4.3 Evolution of Free and Supported Nanoclusters Toward Equilibrium Kinetic Monte Carlo Simulations 93

References 97

Part II Physical and Chemical Properties on the Nanoscale 5 Magnetism in Nanomaterials D Givord 101

5.1 Introduction 101

5.2 Magnetism in Matter 102

5.2.1 Magnetic Moment 102

5.2.2 Magnetic Order 105

5.2.3 Magnetocrystalline Anisotropy 108

5.3 Magnetisation Process and Magnetic Materials 110

5.3.1 Energy of the Demagnetising Field Domains and Walls 111

5.3.2 The Magnetisation Process 112

5.3.3 Magnetic Materials 115

Contents XIII

5.4 Magnetism in Small Systems 116

5.4.1 Magnetic Moments in Clusters 116

5.4.2 Magnetic Order in Nanoparticles 119

5.4.3 Magnetic Anisotropy in Clusters and Nanoparticles 120

5.5 Magnetostatics and Magnetisation Processes in Nanoparticles 121

5.5.1 Single-Domain Magnetic Particles 121

5.5.2 Thermal Activation and Superparamagnetism 122

5.5.3 Coherent Rotation in Nanoparticles 123

5.5.4 From Thermal Activation to the Macroscopic Tunnel Effect 124 5.6 Magnetism in Coupled Nanosystems 126

5.6.1 Exchange-Coupled Nanocrystals Ultrasoft Materials and Enhanced Remanence 126

5.6.2 Coercivity in Nanocomposites 128

5.6.3 Exchange Bias in Systems of Ferromagnetic Nanoparticles Coupled with an Antiferromagnetic Matrix 130

References 132

6 Electronic Structure in Clusters and Nanoparticles F Spiegelman 135

6.1 Introduction 135

6.2 Liquid-Drop Model 139

6.3 Methods for Calculating Electronic Structure 141

6.3.1 Born–Oppenheimer Approximation Surface Potential 142

6.3.2 Ab Initio Calculation of Electronic Structure 144

6.3.3 Density Functional Theory 147

6.3.4 Charge Analysis 149

6.3.5 Approximate and Semi-Empirical Descriptions 150

6.3.6 Energy Bands and Densities of States 152

6.4 Applications to Some Typical Examples 154

6.4.1 Metallic Nanoparticles 154

6.4.2 Molecular Clusters 162

6.4.3 Ionic and Ionocovalent Clusters 170

6.4.4 Covalent Systems 175

6.5 Valence Changes 178

6.5.1 Transitions with Size 178

6.5.2 Transitions with Stoichiometry 179

6.6 Nanotubes 182

6.7 Prospects 185

References 188

7 Optical Properties of Metallic Nanoparticles F Vall´ ee 197

7.1 Optical Response for Free Clusters and Composite Materials 198

XIV Contents

in the Quasi-Static Approximation: Nanospheres 199

7.3 Dielectric Constant of a Metal: Nanometric Size Effect 203

7.4 Surface Plasmon Resonance in the Quasi-Static Approximation: Nanospheres 207

7.5 Surface Plasmon Resonance: Quantum Effects for Small Sizes (D < 5 nm) 211

7.6 General Case for Nanospheres: The Mie Model 213

7.7 Non-Spherical or Inhomogeneous Nanoparticles in the Quasi-Static Model 216

7.7.1 Shape Effects: Ellipsoids 216

7.7.2 Structure Effects: Core–Shell System 217

7.8 Optical Response of a Single Metal Nanoparticle 219

7.9 Electromagnetic Field Enhancement: Applications 221

7.9.1 Nonlinear Optical Response 221

7.9.2 Time-Resolved Spectroscopy 222

7.9.3 Local Enhancement of Raman Scattering: SERS 223

7.10 Conclusion 224

References 226

8 Mechanical and Nanomechanical Properties C Tromas, M Verdier, M Fivel, P Aubert, S Labdi, Z.-Q Feng, M Zei, P Joli 229

8.1 Macroscopic Mechanical Properties 229

8.1.1 Introduction 229

8.1.2 Elastic Properties 229

8.1.3 Hardness 231

8.1.4 Ductility 234

8.1.5 Numerical Modelling 236

8.2 Nanomechanical Properties 238

8.2.1 Experimentation 238

8.2.2 Computer Modelling 254

References 265

9 Superplasticity T Rouxel 269

9.1 Introduction 269

9.2 Mechanism 270

9.3 Superplastic Nanostructured Materials 276

9.4 Industrial Applications 277

References 280

Contents XV

10 Reactivity of Metal Nanoparticles

J.-C Bertolini, J.-L Rousset 281

10.1 Size Effects 282

10.1.1 Structural Properties 282

10.1.2 Electronic Properties 286

10.1.3 Reactivity in Chemisorption and Catalysis of Monometallic Nanoparticles 288

10.2 Support Effects 293

10.3 Alloying Effects 295

10.3.1 Effect of Surface Segregation 296

10.3.2 Geometric Effects 297

10.3.3 Electronic Effects 298

10.4 Preparation and Implementation in the Laboratory and in Industry 299

References 302

11 Inverse Systems – Nanoporous Solids J Patarin, O Spalla, F Di Renzo 305

11.1 Introduction 305

11.2 Nomenclature: The Main Families of Porous Materials 305

11.3 Zeolites and Related Microporous Solids Definition and Structure 307

11.4 Ordered Mesoporous Solids 309

11.5 Disordered Nanoporous Solids 311

References 314

12 Inverse Systems – Confined Fluids: Phase Diagram and Metastability E Charlaix, R Denoyel 315

12.1 Displacement of First Order Transitions: Evaporation and Condensation 315

12.1.1 Adsorption Isotherms 315

12.1.2 Capillary Condensation 317

12.1.3 Capillary Pressure and the Kelvin Radius 319

12.1.4 Non-Wetting Fluid 320

12.1.5 Perfectly Wetting Fluid 320

12.1.6 Hysteresis, Metastability and Nucleation 322

12.2 Melting–Solidification 325

12.3 Modification of the Critical Temperature 329

12.4 Ultraconfinement: Microporous Materials 331

References 334

XVI Contents

13 Supramolecular Chemistry: Applications and Prospects

N Solladi´ e, J.-F Nierengarten 335

13.1 From Molecular to Supramolecular Chemistry 335

13.2 Molecular Recognition 335

13.3 Anionic Coordination Chemistry and Recognition of Anionic Substrates 338

13.4 Multiple Recognition 338

13.5 Applications 341

13.6 Prospects 343

References 344

14 Nanocomposites: The End of Compromise H Van Damme 347

14.1 Composites and Nanocomposites 347

14.2 Introduction to Polymers 351

14.2.1 Ideal Chains 352

14.2.2 The Glass Transition 354

14.2.3 Entropic Elasticity 357

14.3 Nanofillers 359

14.3.1 Clays 359

14.3.2 Carbon Nanotubes 363

14.4 Strengthening and Permeability Control: Models 364

14.4.1 Strengthening: Increasing the Modulus 364

14.4.2 Impermeability: Reducing the Diffusivity 367

14.5 Strengthening and Permeability of Nanocomposites: Facts and Explanations 369

14.5.1 Strengthening: Successes and Failures 369

14.5.2 Impermeability 376

14.5.3 Dimensional Stability 377

14.5.4 Fire Resistance 379

14.6 Conclusion 379

References 380

Part III Synthesis of Nanomaterials and Nanoparticles 15 Specific Features of Nanoscale Growth J Livage, D Roux 383

15.1 Introduction 383

15.2 Thermodynamics of Phase Transitions 383

15.3 Dynamics of Phase Transitions 385

15.3.1 Thermodynamics of Spinodal Decomposition 386

15.3.2 Thermodynamics of Nucleation–Growth 388

15.4 Size Control 389

15.5 Triggering the Phase Transition 391

Contents XVII

15.6 Application to Solid Nanoparticles 392

15.6.1 Controlling Nucleation 392

15.6.2 Controlling Growth 393

15.6.3 Controlling Aggregation Stability of Colloidal Dispersions 393 15.7 Breaking Matter into Pieces 393

References 394

16 Gas Phase Synthesis of Nanopowders Y Champion 395

16.1 Introduction 395

16.2 The Need for Gas State Processing 397

16.3 Main Stages of Gas Phase Synthesis 400

16.4 Spontaneous Condensation of Nanoparticles: Homogeneous Nucleation 401

16.5 Undesirable Post-Condensation Effects and Control of the Nanometric State 408

16.5.1 Why Do These Effects Occur? 409

16.5.2 Particle Growth by Gas Condensation 410

16.5.3 Coalescent Coagulation 411

16.6 Vapour Formation and the Production of Nanopowders 416

16.6.1 Physical Processes 416

16.6.2 Chemical Processing: Laser Pyrolysis 424

16.7 Conclusion 426

References 426

17 Synthesis of Nanocomposite Powders by Gas–Solid Reaction and by Precipitation C Laurent 429

17.1 Introduction 429

17.2 Synthesis of Nanocomposite Powders by Gas–Solid Reactions 430

17.2.1 Synthesis of Intergranular Nanocomposite and Nano–Nano Composite Powders 430

17.2.2 Synthesis of Intragranular and Hybrid Nanocomposite Powders 433

17.3 Conclusion 438

References 438

18 Colloidal Methods and Shape Anisotropy D Ingert 441

18.1 Introduction 441

18.2 Surfactants 442

18.3 Reverse Micelles: Spherical Nanoreactors 445

18.4 Factors Affecting Shape Control 448

18.4.1 Effect of the Colloidal Template on Shape Control 448

XVIII Contents

18.4.2 Effect of Anions on Nanocrystal Growth 449

18.4.3 Effect of Molecular Adsorption on Nanocrystalline Growth 451 18.5 Conclusion 452

References 453

19 Mechanical Milling E Gaffet, G Le Ca¨ er 455

19.1 Introduction 455

19.1.1 Mechanosynthesis 455

19.1.2 Mechanical Activation 455

19.2 Ball Mills 456

19.3 Mechanisms 458

19.3.1 Reducing Cristallite Sizes 458

19.3.2 Parameters Relevant to Mechanical Alloying and Activation 459

19.3.3 Mechanics of Mechanical Alloying 461

19.4 Materials and Their Applications 462

19.4.1 Mechanical Alloying 462

19.4.2 Mechanical Activation 462

19.5 Shaping and Densifying Nanomaterials 464

19.5.1 Standard Processes 464

19.5.2 Mechanically-Activated Field-Activated Pressure-Assisted Synthesis (MAFAPAS) 464

19.6 Severe Plastic Deformation (SPD) 466

19.6.1 High-Pressure Torsion (HPT) 467

19.6.2 Equal Channel Angular Pressing (ECAP) 468

19.7 Bulk Mechanical Alloying 468

19.8 Synthesis of Nanocomposites by Extrusion, Drawing, and Embossing 468

References 469

20 Supercritical Fluids A Taleb 473

20.1 Definition 473

20.2 Physicochemical Properties 475

20.2.1 Solubility 475

20.2.2 Viscosity 477

20.2.3 Diffusion 477

20.2.4 Thermal Conductivity 479

20.3 Applications 479

20.3.1 Purification and Extraction 479

20.3.2 Synthesis 480

References 484

Contents XIX

Part IV Fabrication of Nanostructured Bulk Materials

and Nanoporous Materials

21 Bulk Nanostructured Materials

Obtained by Powder Sintering

F Bernard, J.-C Ni` epce 489

21.1 Sintering 489

21.1.1 Definition 489

21.1.2 The Physical Phenomena of Sintering 489

21.1.3 Different Sintering Conditions 489

21.1.4 Preserving Nanostructure During Sintering 491

21.2 Spark Plasma Sintering (SPS) 491

21.2.1 Basic Principle 491

21.2.2 Advantages of the SPS Process 493

21.2.3 Illustrations in the Field of Nanomaterials 493

References 495

22 Self-Assembly of Nanomaterials at Macroscopic Scales A Courty 497

22.1 Fabrication of Nanomaterials 498

22.2 2D and 3D Nanomaterial Structures 500

22.2.1 Depositing Nanomaterials on a Solid Substrate 500

22.2.2 Forces Inducing Self-Organisation 502

22.2.3 Crystal Structure of 2D and 3D Nanomaterials 508

22.3 Conclusion 513

References 513

23 Assemblies of Magnetic Nanoparticles J Richardi 515

23.1 Magnetic Properties of Nanoparticle Assemblies 515

23.2 Structure of Magnetic Nanoparticle Assemblies Deposited Without Field 519

23.3 Structure of Magnetic Nanoparticle Assemblies Deposited with Field 523

23.3.1 Perpendicular Field 523

23.3.2 Parallel Field 526

References 527

24 Nanostructured Coatings J.-P Rivi` ere 529

24.1 Methodology for Making Superhard Nanostructured Coatings 530

24.1.1 Multilayers with Nanometric Period 530

24.1.2 Nanocomposites 532

24.2 Methods of Synthesis 536

24.2.1 General Principles 536

XX Contents

24.2.2 Plasma-Activated Chemical Vapour Deposition (PACVD) 539 24.2.3 Physical Vapour Deposition

by Sputtering and Cathodic Arc 540

24.2.4 PVD by Ion Beam Sputtering 544

References 546

25 Dispersion in Solids D Babonneau 549

25.1 Chemical Methods 550

25.1.1 Synthesis of Doped Glasses 550

25.1.2 Sol–Gel Method 551

25.2 Physical Methods 554

25.2.1 Ion Implantation 555

25.2.2 Vapour Deposition and Sputtering Methods 559

25.2.3 Pulsed Laser Deposition 562

25.2.4 Low Energy Cluster Beam Deposition (LECBD) 563

References 565

26 Nanoporous Media J Patarin, O Spalla, F Di Renzo 569

26.1 Introduction 569

26.2 Synthesis of Crystalline Microporous Solids 569

26.2.1 Methods of Synthesis 569

26.2.2 The Crystallisation Process Exemplified by Zeolites 571

26.2.3 Main Organic Structure-Directing Agents Used to Synthesise Crystalline Microporous Solids 573

26.2.4 Role of Inorganic Cations and Organic Species 573

26.2.5 Organic Species and the Template Effect 574

26.2.6 Porosity of Zeolites and Related Solids 576

26.2.7 Applications of Zeolitic Materials 577

26.3 Synthesis of Ordered Mesoporous Solids 579

26.3.1 Methods of Synthesis 579

26.3.2 Definition and Role of the Surfactant 581

26.3.3 Mechanisms for the Formation of MCM-41 Phase 582

26.3.4 Characteristics of Mesoporous Silicas Obtained in the Presence of Amphiphilic Molecules 588

26.3.5 Structural Characterisation of Nanoporous Solids by X-Ray and Neutron Scattering 589

26.4 Conclusion 593

References 593

27 Molecular Imprinting V Dufaud, L Bonneviot 597

27.1 Introduction 597

27.2 Fundamental Considerations 598

27.2.1 General Principles 598

Contents XXI

27.2.2 Role of Complexation Sites During the Imprinting Process 599

27.2.3 Structure and Properties of the Polymer Matrix 602

27.3 Procedures and Methods for Molecular Imprinting 603

27.3.1 Imprinted Organic Polymers 603

27.3.2 Imprinted Inorganic Matrices 604

27.4 Applications 608

27.4.1 Separating a Mixture of Herbicides 609

27.4.2 Synthesis of α-Aspartame 609

27.4.3 Chiral Separation of Amino Acids by Ligand Exchange at a Metal Site 610

27.4.4 Specific Elimination of Lanthanides and Actinides in a Highly Radioactive Effluent 610

27.5 Recent Challenges and Progress 612

References 613

Part V Applications of Nanomaterials 28 Electronics and Electromagnetism J.-C Ni` epce, D Givord 617

28.1 Multilayer Ceramic Capacitors 617

28.1.1 What Is a Multilayer Ceramic Capacitor? 617

28.1.2 Market Requirements 619

28.1.3 Constraints Laid Down by these Requirements 620

28.1.4 BaTiO3 Ceramic Dielectrics with Nanograins: The Favoured Solution 621

28.2 Magnetic Recording 626

28.2.1 General Operation 626

28.2.2 Recording Materials Longitudinal and Perpendicular Recording 627

28.2.3 Write Heads 629

28.2.4 Read Heads 629

28.2.5 Disk Drive Motor 630

References 631

29 Optics P Maestro, M Chagny, P.-P Jobert, H Van Damme, S Berthier 633

29.1 Cosmetics 633

29.1.1 Introduction 633

29.1.2 Nano-Titanium Oxides in Cosmetics: Solar Skin Protection 633 29.1.3 Conclusion 635

29.2 Nanophosphors 635

29.2.1 Introduction 635

29.2.2 Phosphors: General Considerations 636

29.2.3 Operating Principle 638

XXII Contents

29.2.4 Industrial Applications 638

29.2.5 Conclusion 640

29.3 Surface Nanoengineering 640

29.3.1 What Is the Surface Area of a Town? 640

29.3.2 Superhydrophobic Surfaces 641

29.3.3 Self-Cleaning and Superhydrophilic Surfaces 644

29.3.4 When Concrete Cleans the Air We Breathe 648

29.4 Photonic Crystals 649

29.4.1 The Colourful World of Birds and Insects 649

29.4.2 Photonic Crystals and Photonic Band Gaps 650

29.4.3 Guides and Cavities 653

29.4.4 From Colloidal Crystals to Photonic Crystals 654

References 658

30 Mechanics P Maestro, E Gaffet, G Le Ca¨ er, A Mocellin, E Reynaud, T Rouxel, M Soulard, J Patarin, L Thilly, F Lecouturier 661

30.1 Silica Precipitates for High-Performance Tyres 661

30.1.1 Fabrication of Silica Precipitates 661

30.1.2 Tyres and Other Applications 662

30.2 Ceramic–Metal Composite Welding Supports 663

30.2.1 Ceramics 664

30.2.2 Reactive Mechanical Alloying and High-Energy Ball Milling 665

30.2.3 Improving Properties 667

30.3 Reinforced Amorphous Matrices 668

30.3.1 Not All Materials Are Ordered 668

30.3.2 Incorporating Nanoparticles into Amorphous Matrices 669

30.3.3 Prospects 673

30.3.4 The Long Road 675

30.4 Nanoporous Solids as Molecular Springs, Shock Absorbers and Bumpers 676

30.4.1 Introduction 676

30.4.2 Basic Idea 676

30.4.3 Pressure–Volume Diagram 677

30.4.4 Stored Energy and Restored Energy 678

30.4.5 Causes of Irreversibility 679

30.4.6 Behaviour of the Solid and Liquid 680

30.4.7 Practical Applications 683

30.5 High Field Coils 685

30.5.1 Specifications for Generating High Pulsed Magnetic Fields 685 30.5.2 Synthesis of Reinforced Copper Matrix Conductors 687

30.5.3 Geometry and Microstructure of Cu/Nb Nanofilamentary Conductors 688

Contents XXIII

30.5.4 Physical Properties

of Cu/Nb Nanofilamentary Conductors 69030.5.5 Conclusion 693References 693

31 Biology and the Environment

P Maestro, P Couvreur, D Roux, D Givord, J.-A Dalmon,

J.-C Bertolini, F.J Cadete Santos Aires 695

31.1 Inorganic Catalysts for Diesel Engines 69531.2 Nanotechnology and New Medicines 69731.2.1 Introduction 69731.2.2 Artificial Carriers: Liposomes and Nanoparticles 69731.2.3 Conclusion 70131.3 Magnetic Nanoparticles

and Biomedical Applications 70131.3.1 Magnetotactic Bacteria 70231.3.2 Homing Pigeons 70231.3.3 Magnetic Separation 70331.3.4 Magnetic Nanoparticles as MRI Contrast Agents 70431.3.5 Magnetic Nanoparticles and Treatment of Tumours 70531.4 Zeolitic Membranes for Separation Processes

and Catalytic Reactors 70631.4.1 Introduction 70631.4.2 Microporous Membranes 70731.4.3 Zeolitic Membranes: Synthesis and Characterisation 70731.4.4 Application to Gas Separation 70831.4.5 Application to a Catalytic Reactor 70931.5 Metal Nanoparticles and Catalysis 71031.5.1 Synthesis and Characterisation of Pd/Si3N4Catalysts 71131.5.2 Total Oxidation of Methane:

Implementation in the Laboratory 71331.5.3 Application to Radiant Panels (Infrared Energy Emission) 713References 715

Index 717

Laboratoire de M´etallurgie Physique

Universit´e de Poitiers SP2MI

Fr´ ed´ eric Bernard

Institut Carnot de Bourgogne

Universit´e Denis Diderot

Institut des Nanosciences

de Paris, France

berthier@ccr.jussieu.fr

Jean-Claude Bertolini

Institut de Recherchessur la CatalyseUniversit´e Claude Bernard Lyon I

2 avenue Albert Einstein

69626 Villeurbanne Cedex, Francejean-claude.bertolini@

catalyse.cnrs.fr

Laurent Bonneviot

Laboratoire de chimieEcole Normale Sup´erieure de Lyon

Francisco Jos´ e Cadete Santos Aires

Institut de Recherchessur la CatalyseUniversit´e Claude Bernard Lyon I

2 avenue Albert Einstein

69626 Villeurbanne Cedex, Francefrancisco.aires@catalyse.cnrs.fr

XXVI List of Contributors

Florent Calvo

Laboratoire de Physique Quantique

Institut de Recherche

sur les Syst`emes Atomiques

et Mol´eculaire Complexes

Universit´e Paul Sabatier

Laboratoire des mat´eriaux

m´esoscopiques et nanom´etriques

Universit´e Pierre et Marie Curie

Jean-Alain Dalmon

Institut de Recherchessur la CatalyseUniversit´e Claude Bernard Lyon I

2 avenue Albert Einstein

69626 Villeurbanne Cedexjean-alain.dalmon@catalyse.cnrs.fr

Renaud Denoyel

MADIRELCentre de J´erˆomeUniversit´e de Provence,

13397 Marseille Cedex 20, Francerenaud.denoyel@up.univ-mrs.fr

V´ eronique Dufaud

Laboratoire de chimieEcole Normale Sup´erieure de Lyon

List of Contributors XXVII

Marc Fivel

G´enie physique et m´ecanique

des mat´eriaux

Laboratoire des mat´eriaux

m´esoscopiques et nanom´etriques

Universit´e Pierre et Marie Curie

et Mol´eculaire ComplexesUniversit´e Paul Sabatier

118 route de Narbonne

31062 Toulouse, Francepierre.labastie@irsamc

ups-tlse.fr

Sid Labdi

Laboratoire d’´etudedes milieux nanom´etriquesUniversit´e d’Evry

118 route de Narbonne

31062 Toulouse Cedex 09, Francelaurent@chimie.ups-tlse.fr

XXVIII List of Contributors

Laboratoire National des Champs

Magn´etiques Puls´es

Universit´e Paul Sabatier

143, avenue de Rangueil BP 14245

31432 Toulouse Cedex 4, France

lecouturier@lncmp.org

Jacques Livage

Coll`ege de France

Laboratoire de la Mati`ere

Jean-Claude Ni` epce

Institut Carnot de Bourgogne

Jean-Fran¸ cois Nierengarten

Groupe de Chimie des Full`erenes

et des Syst`emes Conjugu´esLaboratoire de Chimie

24, avenue des Landais

63177 Aubi`eres Cedex, FranceVisiting professor

University of Maryland, USAalpimpin@univ-bpclermont.fr

Emmanuelle Reynaud

LARMAURUniversit´e de Rennes I

35042 Rennes, Franceemmanuelle.reynaud@univ-rennes1.fr

List of Contributors XXIX

Johannes Richardi

Laboratoire des mat´eriaux

m´esoscopiques et nanom´etriques

Universit´e Pierre et Marie Curie

4, place Jussieu

75005 Paris, France

richardi@ccr.jussieu.fr

Jean-Paul Rivi` ere

Laboratoire de M´etallurgie Physique

Universit´e de Poitiers SP2MI

Universit´e Claude Bernard Lyon I

2 avenue Albert Einstein

Groupe de Synth`ese

de Syst`emes Porphyriniques

91191 Gif-sur-Yvette CedexFrance

spalla@drecam.saclay.cea.fr

Fernand Spiegelman

Laboratoire de Physique QuantiqueInstitut de Recherche

sur les Syst`emes Atomiques

et Mol´eculaire ComplexesUniversit´e Paul Sabatier

118 route de Narbonne

31062 Toulouse, Francefernand.spiegelman@irsamc.ups-tlse.fr

Abdelhafed Taleb

Laboratoire d’´electrochimie

et de chimie analytiqueUniversit´e Pierre et Marie Curie

4, place Jussieu

75005 Paris, Franceataleb@ccr.jussieu.fr

XXX List of Contributors

Christophe Tromas

Laboratoire de M´etallurgie Physique

Universit´e de Poitiers SP2MI

1130, rue de la Piscine B.P 75

38402 Saint-Martin d’H`eresFrance

m.verdier@ltpcm.inpg.fr

Maria Zei

Laboratoire d’´etudedes milieux nanom´etriquesUniversit´e d’Evry

Bld F Mitterrand

91025 EVRY Cedex, Francemzei@univ-evry.fr

Size Effects on Structure and Morphology

of Free or Supported Nanoparticles

in the object

In the second case, one considers the evolution of the properties of a sample

as its size is whittled down from macroscopic toward nanometric lengths It isthis approach that we shall examine here, whilst mentioning zones of overlapand exclusion between the two approaches

1.1.2 Fraction of Surface Atoms

Consider a homogeneous solid material of compact shape (let us say spherical)and macroscopic dimensions (let us say millimetric) Most of its properties will

be related to its chemical composition and crystal structure This is what istraditionally studied in the physics and chemistry of solids For an object

of this size, the surface atoms comprise a negligible proportion of the totalnumber of atoms and will therefore play a negligible role in the bulk properties

of the material Note, however, that surface atoms will nevertheless play apredominant role in properties involving exchanges at the interface betweenthe object and the surrounding medium This is the case, for example, when

we consider chemical reactivity (and catalysis) and crystal growth, which arediscussed later in the book

It can be seen from Fig 1.1 that, when the size of the object is reduced

to the nanometric range, i.e., < 10 nm, the proportion of surface atoms is

Fig 1.1.Proportion of surface atoms for a spherical particles comprising Nvatoms

with Nsat the surface

no longer negligible Hence, at 5 nm (around 8,000 atoms), this proportion

is about 20%, whilst at 2 nm (around 500 atoms), it stands at 50% Thisproportion can be estimated for the transition metals by the relation

Ns

Nv ≈ 1

where R is the radius in nm This empirical law gives a proportion of surface

atoms of 100% for a size of 1 nm Of course, (1.1) is no longer valid for smallerdimensions We shall see that the fact that a large fraction of the atoms arelocated at the surface of the object will modify its properties To tackle thisquestion, we shall need to review certain physical quantities associated withsurfaces, namely the specific surface energy and the surface stress

1.1.3 Specific Surface Energy and Surface Stress

The specific surface energy γ (J/m2) can be represented as the energy duced by cleaving a crystal divided by the surface area thereby created Moregenerally, the specific surface energy can be defined as follows In order to

pro-increase the surface area of an object by an amount dA, e.g., by changing the

shape of the object, the work required to do this will be

γ is the specific surface energy In this case, the area of the object has increased

by displacing atoms from the bulk to the surface However, one could alsoincrease the area by stretching it, i.e., keeping the number of surface atomsconstant The work required to do this will then be

1 Size Effects on Structure and Morphology of Nanoparticles 5

where g ij is the surface stress in J/m2 This is a tensorial quantity because

it depends on the crystallographic axes The surface stress is related to theelastic stresses resulting from deformation of the surface (strain) It is related

to the specific surface energy by

g ij = δ ij γ + ∂γ

where u ij is the strain tensor and δ ij the Kronecker symbol Note that for a

liquid there is no strain tensor and g ij = γ Indeed, if one tries to increase the

surface area of a liquid, the bulk atoms will move to the surface to keep thedensity constant The surface stress reduces to the specific surface energy

1.1.4 Effect on the Lattice Parameter

Let us now consider the effects of the increase in the surface-to-volume ratio asthe object size decreases To do this, we consider first the very simple case of

a liquid sphere of diameter 2R Due to the curvature of the surface, a pressure

is generated toward the inside of the sphere The excess pressure ∆P inside

the sphere, in the purely hydrostatic case, is given by the Laplace equation

where dV is the volume change corresponding to a change dA in the area of

the droplet In the case of a sphere, (1.5) takes the form

For a spherical solid, the specific surface energy must be replaced by the

surface stress tensor g ij To simplify the problem, consider the case of a solid

with simple cubic structure In this case, γ is isotropic and we have

where v is the atomic volume of the solid, which can also be defined as a3,

where a is the lattice parameter Combining (1.5) and (1.8), We obtain the

relative variation of the lattice parameter:

Fig 1.2.Contraction of the lattice parameter of copper clusters as a function of the

reciprocal of their diameter Circles correspond to measurements of electron energy

loss near an ionisation threshold (SEELFS) Taken from De Crescenzi et al [1] The

straight line shows measurements of X-ray absorption (EXAFS) Taken from Apai

et al [2]

We thus find that there is a contraction of the crystal lattice due to thepressure exerted toward the interior of the particle This contraction is pro-portional to the surface stress and inversely proportional to the particle size.The lattice contraction in nanometric particles has been observed on manyoccasions Figure 1.2 shows the change in lattice parameter for copper clus-ters, measured by the electron energy loss technique known as SEELFS andalso by X-ray absorption near an ionisation threshold (see below)

Determination of Local Order in a Material EXAFS and SEELFS

These two techniques exploit the absorption of energy by an atom under the impact

of a beam of X-ray photons or high-energy electrons

The first of these, also the oldest, goes by the name of extended X-ray absorptionfine structure (EXAFS) It refers to fine structure spectroscopy in the vicinity of

an X-ray absorption threshold An X-ray photon is absorbed by a given atom inthe material, exciting an electron from an inner electron shell to an unoccupiedstate above the Fermi level, which corresponds to a well-defined energy for eachtype of atom, whence the chemical sensitivity of the method The excited atomrelaxes by emitting an electron whose wave function interacts with neighbouringatoms If the atoms are in a crystal lattice, interference will occur between the wavefunction of the photoelectron and the wave functions of neighbouring atoms Thiswill cause a change in the absorption of X rays by the target atom (and neighbouringatoms), which will be detected in the form of low amplitude oscillations in the X-rayabsorption spectrum near the chosen atomic absorption threshold A full analysis ofthis technique can be found in [3]

In practice, carrying out a Fourier transform of these oscillations, one obtainsthe radial distribution of atoms in the vicinity of the target atom (up to a phasefactor) For example, if we consider a solid with NaCl-type structure and examine

a sodium threshold, we find a first peak in the radial distribution corresponding

to the Na–Cl separation, followed by a second peak corresponding to the Na–Naseparation, and a third peak corresponding to the second Na–Cl separation Theintensities of the various peaks are proportional to the number of atoms in the

1 Size Effects on Structure and Morphology of Nanoparticles 7

considered coordination sphere This technique can thus be used to measure thelocal order in monatomic or multiatomic materials In contrast to X-ray diffraction,

it can be used on objects with no long-range order or on small clusters In the lattercase, it is extremely useful for determining the lattice parameter (see Fig 1.2).The technique known as surface extended electron energy loss fine structure(SEELFS) is analogous to EXAFS, except that the atom is excited by an electron ofwell-defined energy (usually in the range 3–10 keV) and the energy loss spectrum ismeasured near an ionisation threshold of the relevant target atom Since the electrons

do not penetrate very far into the material, this technique can only be used to studysurfaces or thin films Spectra are analysed in an analogous way to those produced

by EXAFS, but for a quantitative analysis, one must take into account the fact thatthe excitation is obtained by electrons The reader is referred to [4] for more details

As can be seen from Fig 1.2, the contraction varies linearly with the reciprocal

of the particle size For a diameter of 2 nm, it is 2% According to (1.9), thegradient of the straight line yields the value of the surface stress as 3.35 J/m2.The pressure exerted on the crystal lattice is then 6.7 GPa, which is extremelyhigh

It is reasonable to ask how far (1.9) remains valid Put another way, canone still appeal to quantities like the specific surface energy and the surfacestress, quantities defined in the context of macroscopic thermodynamics, whendealing with nanoscale systems? To address these questions, one may turn tonumerical simulation Indeed, good (semi-empirical) interatomic potentials

are available for describing metals, i.e., n-body potentials in which each bond

depends on the local atomic environment, in contrast to the so-called pairwisepotentials [5–7]

Figure 1.3 shows the change in the lattice parameter as a function of thereciprocal of the radius of spherical particles, obtained by numerical simulationusing EAM-type (embedded atom method) semi-empirical potentials [8] The

relationship is linear down to a size of about 4a0, where a0 is the latticeparameter This corresponds to a diameter of 2.5–3 nm One might expect tofind that at smaller sizes the relationship expressed by (1.9) would no longer

be valid However, it seems that this discrepancy is rather due to the fact thatthe specific surface energy and surface stress are no longer constant Indeed,with the same kind of simulation, these two quantities have been calculated fordifferent (spherical) particle sizes and the results do indeed show that they are

no longer constant below a diameter of about 2–3 nm In fact, they increase asthe size continues to decrease One might think that these deviations are due

to the constraint, imposed in the calculation, of a spherical particle shapewhich, as we shall see below, does not correspond to the equilibrium shape ofthe crystal particles In fact, this is not the case for, as we shall show inSect 1.2.2, even for nanoparticles having their equilibrium shape, the surfaceenergy and surface stress nevertheless increase as the size decreases

Fig 1.3.Change in lattice parameter, relative to the bulk solid, as a function of the

reciprocal of the radius for spherical clusters (with fcc structure) of Ag (stars), Au (triangles), Cu (diamonds), and Pt (circles) Numerical simulations at 0 K Taken

from Swaminarayan et al [8]

1.1.5 Effect on the Phonon Density of States

Another effect of size reduction can be seen in the lattice dynamics of metric particles When the surface-to-volume ratio reaches a certain value,the phonon spectrum broadens [9, 10] Phonons are quasi-particles represent-ing the vibrational modes of atoms in the lattice On the low frequency side,the broadening is due to the contribution of surface atoms which have softermodes The broadening toward higher frequencies is due to the lattice con-traction which corresponds to increased rigidity in the system, itself the con-sequence of increased interatomic forces These changes in the distribution ofthe phonon spectrum also affect the thermodynamic properties of the system.Note in particular that there is an increase in the vibrational entropy and that

nano-the specific heat deviates from a T3dependence at low temperatures.The increase in the surface-to-volume ratio when the size decreases alsohas a significant effect on the melting temperature of nano-objects This pointwill be dealt with in the chapter on phase transitions

1.2 Nanoparticle Morphology

1.2.1 Equilibrium Shape of a Macroscopic Crystal

The shape of a crystal generally depends on growth conditions, which areusually very far from equilibrium, and for this reason it is not unique However,

1 Size Effects on Structure and Morphology of Nanoparticles 9

of the equilibrium shape of the crystal (Wulff polyhedron) From [11]

under conditions of thermodynamic equilibrium, the shape of a crystal isunique This last result was first obtained by Wulff over a century ago [12].The solution to this problem consists in minimising the total surface energy

Es For a liquid the result is immediate: one obtains a sphere For a crystal,

the specific surface energy γ depends on the orientation of the crystal face.

One must therefore minimise

Es=

i

where the index i represents the different facets with areas A i and specific

surface energy γ i Wulff showed that the minimal energy is obtained for a

polyhedron in which the central distances h i to the faces are proportional to

their surface energies γ i This is the well-known Wulff theorem:

Wulff Construction for the Equilibrium Shape of a Crystal

The Wulff construction provides an easy way of determining the equilibrium shape

of a crystal if one knows the dependence of the specific surface energy on the crystal

10 C Henry

orientation (γ-graph) Consider a projection of the γ-graph along an axis of metry of the crystal, as shown in Fig 1.4 Starting from the center of symmetry O, draw the radial vectors out to each point of the γ-graph and then draw straight

sym-lines normal to the radial vectors at these points The inner envelope obtained fromthe set of all these normals represents the projection of the equilibrium shape of thecrystal along the chosen crystal axis (a hexagon in the case illustrated) It is clearfrom the figure that the facets of the equilibrium shape correspond to the cusps

of the γ-graph at the minima of the surface energy When the temperature of the

crystal comes close to the melting temperature, the cusps will be less and less deep(the anisotropy of the surface energy decreases) and the equilibrium shape tends tospherical

At 0 K, the equilibrium shape contains only a few different faces with thelowest surface energies For metals with face centered cubic (fcc) structure,the equilibrium shape is a truncated octahedron exposing the faces (111) and(100) (see Fig 1.5) For a metal with body centered cubic (bcc) structure,the shape is a dodecahedron For ionic crystals which have a high degree ofsurface energy anisotropy, a single face shows up and the equilibrium shape

of crystals like NaCl or MgO is a cube

1.2.2 Equilibrium Shape of Nanometric Crystals

The Wulff theorem can be rigorously proven for a macroscopic crystal Butwhat happens for a nanometric crystal? From the theoretical point of view,this problem can be handled using numerical simulation As we have seen,

we now possess realistic interatomic potentials for most metals Moleculardynamics can then be used to seek the shape corresponding to minimal energyfor constructions of different sizes Many calculations of this kind have beencarried out over the past few years (see for example [13]) Figure 1.5 shows thefour main shapes that arise for fcc metals, namely, the truncated octahedron,the cubo-octahedron, the icosahedron, and the truncated decahedron (alsoknown as the Marks decahedron)

These calculations show that for very small sizes the icosahedron is themost stable shape This result is easy to understand, because it is the mostcompact shape: it maximises the binding energy by having a shape very close

to spherical and it exposes only (111) facets which have the lowest surfaceenergy However, this structure is not a crystal structure It cannot there-fore extend to macroscopic crystals In an icosahedron, the central atoms aresubject to a very high degree of compression, whilst the surface atoms are re-laxed If an icosahedron is made to grow, the energy related to these stressesbecomes too large compared with the gain in compactness and the structuretends to the normal one, i.e., fcc in this case Figure 1.6 shows the stabilitydiagrams of copper, silver, gold, nickel, palladium and platinum clusters up

to 50,000 atoms [13]

It can be seen that, beyond a certain size, the equilibrium shape changesfrom an icosahedron to a truncated octahedron The cubo-octahedron (not

1 Size Effects on Structure and Morphology of Nanoparticles 11

Fig 1.5 Morphology of nanoparticles (a) Truncated octahedron with 201 atoms (b) Cubo-octahedron with 147 atoms (c) Icosahedron with 147 atoms (d) Trun-

cated decahedron with 146 atoms

Table 1.1. Magic numbers for different clusters: icosahedron, cubo-octahedron,truncated (Marks) decahedron, and truncated octahedron (Wulff polyhedron for anfcc crystal)

200 atoms for gold and around 30,000 atoms for copper Note also that thecalculated sizes correspond to closed shell polyhedra, i.e., with no vacancies

or adatoms at the surface These closed shells are obtained for very precisenumbers of atoms called magic numbers (see Table 1.1) The magic numberscorrespond to clusters with higher stability than clusters with a neighbouringnumber of atoms

12 C Henry

Ag

Au Pd

1,42 1,40 1,38 1,36 1,34 1,32

1,97 1,95 1,93 1,91 1,89 1,87

∆

∆

∆

Fig 1.6. Stability of different structures of Cu, Ag, Au, Ni, Pd and Pt clusters as

a function of the number of atoms N Black circle: icosahedron Black diamond : truncated decahedron White square: truncated octahedron Calculations made us- ing molecular dynamics simulations with an N -body potential Taken from Mottet

et al [13]

For clusters with a number of atoms intermediate between two tive closed shells, the shape can be different and it may even oscillate betweenshapes with fivefold symmetry (icosahedron, decahedron) and shapes corre-sponding to an fcc structure [14] In any case, it should be noted that the en-ergy difference between the various structures for very small clusters is actuallyvery low, so that in practice, at finite temperatures, a range of shapes is ob-served In situ electron microscope observations show that the shape of smallmetallic particles fluctuates incessantly between different structures, passingthrough disordered structures Figure 1.7 shows a series of high-resolutionelectron microscope images of the same gold particle containing about 450atoms With the electron microscope, we visualise the projections of columns

consecu-of atoms It can be seen that the particle alternates between an fcc structureand a structure with fivefold symmetry

This phenomenon of shape and structure fluctations, known as ing, has been widely studied It was first thought that it was an artifact of elec-tron microscopy due to the large amount of energy transferred to the sample

quasimelt-by the electron beam (100–300 keV) However, with the development of newmicroscopes operating with very low currents, it was shown that, although

1 Size Effects on Structure and Morphology of Nanoparticles 13

Fig 1.7.High-resolution electron microscope images of a 2-nm gold cluster ing 459 atoms The structure fluctuates during the observation period The particle

compris-changes between an fcc truncated octahedral shape [(e), (f ), and (j)], a polyhedron with fcc structure and a twinned structure [(a), (d), and (i)], and a multitwinned icosahedral structure [(b) and (h)] Taken from Iijima and Ichihashi [15] with kind

permission of the American Physical Society c
1986

in some cases the electron beam can accelerate the process, the ing phenomenon is an intrinsic feature of the very small size of the particles.Ajayan et Marks [16] calculated the free energy of metal particles with differentstructures and morphologies using a continuous model based on macroscopicthermodynamic quantities (surface energy, surface and bulk elastic energy,entropy) Using their results, the authors were able to plot the phase diagramshown in Fig 1.8

quasimelt-This shows once again that at small sizes the icosahedron is the moststable, followed by the decahedron and finally the Wulff polyhedron (crystalstructure) At the smallest sizes, there is a new phase known as quasimelt-ing This corresponds to objects in which the energy difference between thevarious structures is low enough to allow them, at finite temperatures, to fluc-tuate between these structures (see Fig 1.7) Doraiswamy and Marks tried tocheck these theoretical predictions by making quantitative measurements ofthe appearance of the different structures, observing gold particles with high-resolution electron microscopy [17] They showed that, for sizes in the range2–8 nm, observation frequencies agree with theoretical predictions Icosahe-dral particles are more frequently observed at very small sizes, whilst above

a size of 3–4 nm, monocrystalline particles predominate The frequency of currence of decahedral particles increases with the size up to about 7 nm,exceeding the frequency of icosahedra at about 4 nm

oc-We have seen that for very small clusters the crystal structure is not themost stable For larger particles, the thermodynamically most stable struc-ture is the Wulff polyhedron, e.g., the truncated octahedron for a metal with

I=0,98 1400

dif-n (100)

(111)

m

E2

E1

Fig 1.9. Wulff polyhedron for an fcc crystal (truncated octahedron) The edges

between (100) and (111) faces and between pairs of (111) faces have lengths m and

fcc structure which is the equilibrium shape of a macroscopic crystal Theproportions of the different facets making up the polyhedron is defined bythe Wulff theorem and the associated construction (see p 9) However, it isinteresting to ask for what sizes these results are valid In fact, there are tworeasons for raising this question:

• The values obtained for the surface energy of macroscopic surfaces may

no longer be valid

• The edges separating the different facets are composed of atoms with lower

coordination than the atoms in the facets themselves, and the specific