Table Of ContentIngenta Select: Electronic Publishing Solutions file:///C:/EncyclopediaNN03/03/03.files/m_cp1-1.htm
Encyclopedia of Nanoscience and Nanotechnology
Volume 3 Number 1 2004
Electromagnetism in Nanogranular Metal Oxides 1
Christian Brosseau
Electron Beam Writing in Nanoparticle Films 17
Y. Chen; R. E. Palmer
Electron Dynamics in Metallic Nanoparticles 29
M. Aeschlimann
Electron Holography of Nanostructured Materials 41
Rafal E. Dunin-Borkowski; Martha R. McCartney; David J. Smith
Electron Raman Scattering in Nanostructures 101
R. Betancourt-Riera; R. Riera; J. L. Marín; R. Rosas
Electronic Properties and Applications of Carbon Nanotubes 139
Markus Ahlskog; Christophe Laurent; Mark Baxendale; Maria Huhtala
Electronic Properties of Carbon Nanotubes 163
J. González
Electronic Structure of Semiconductor Nanoparticles 181
Sameer Sapra; J. Nanda; D. D. Sarma
Electronic Tunnelling Time in Nanostructures 193
V. Gasparian; M. Ortuño; O. del Barco
Embedded Metal and Alloy Nanoparticles 217
K. Chattopadhyay; V. Bhattacharya
Epitaxy of Ion-Irradiated Quartz 233
Klaus-Peter Lieb
Epoxy/Clay Nanocomposites 253
Nandika Anne D'Souza
Equilibrium Properties of Mesoscopic Quantum Conductors 267
L. Saminadayar; C. Bäuerle; D. Mailly
Evanescent Wave Spectroscopy 287
V. G. Bordo; H.-G. Rubahn
Extreme Ultraviolet Nanolithography 297
Paul B. Mirkarimi
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Fast Atomic Force Microscopy 307
Fredy R. Zypman
Fe-Cu Nanoalloying 321
J. Z. Jiang; X. J. Liu
Ferroelectric Nanocrystal Dispersed Oxide Glasses 335
B. K. Chaudhuri; H. Sakata; S. Mollah; H. D. Yang
Ferroelectric Nanodomains 359
A. Gruverman
Ferroelectric Nanomaterials 377
Pushan Ayyub
Field Emission of Carbon Nanotubes 401
Z. P. Huang; Y. Tu; D. L. Carnahan; Z. F. Ren
Filling of Carbon Nanotubes 417
Pawan K. Tyagi; Manoj K. Singh; D. S. Misra
Fivefold Twinned Nanoparticles 431
H. Hofmeister
Fluoride-Based Magnetic Heterostructures 453
D. H. Mosca; N. Mattoso; W. H. Schreiner; M. Eddrief; V. H. Etgens
Focused Ion Beam Nanofabrication 469
Andrei V. Stanishevsky
Formation of Bulk Nanostructured Alloys 485
H. W. Kui
Formation of Nanostructured Polymers 497
Beinn V. O. Muir; Christine K. Luscombe; Wilhelm T. S. Huck
Friction of Model Self-Assembled Monolayers 511
J. A. Harrison; G. T. Gao; R. J. Harrison; G. M. Chateauneuf; P. T. Mikulski
Fullerene Dimers 529
Hidekazu Shimotani; Nita Dragoe; Koichi Kitazawa
Fullerene Lipid Films 545
Naotoshi Nakashima
Fullerene Mechanochemistry 557
Guan-Wu Wang
Fullerene Nanomaterials 567
Shashadhar Samal
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Fullerenes for Photovoltaics 661
E. A. Katz
Functionalities of Dendrimers 685
Toyoko Imae; Katsuya Funayama; Yuko Nakanishi; Kenkichi Yoshii
GaAs-Based Nanodevices 703
Eric Donkor
GaInNAs Quantum Well Lasers 719
W. Li; M. Pessa; T. Jouhti; C. S. Peng; E.-M. Pavelescu
γ-Irradiation Preparation of Nanomaterials 731
Yi Xie; Yujie Xiong
Gas Adsorption on Carbon Nanotubes 749
A. D. Migone; S. Talapatra
Gas Sensors from Nanostructured Metal Oxides 769
Simonetta Capone; Pietro Siciliano
Germanium Nanocrystals 805
Shinji Nozaki; Hiroshi Morisaki; Seiichi Sato
Germanium Nanocrystals Structure 821
A. V. Kolobov
Germanium-on-Silicon Infrared Detectors 829
G. Masini; L. Colace; G. Assanto
Giant Magnetoresistance in Cobalt-Based Multilayers 843
D. H. Mosca; D. K. Lottis
Growth Simulations of Nanoclusters 865
F. Baletto; R. Ferrando; A. C. Levi
High-Field Conduction in Nanostructures 891
R. D. Gould
HiPco Process for Single-Wall Carbon Nanotube Production 917
Pavel Nikolaev
Hybrid Solar Cells 929
Elif Arici; N. Serdar Sariciftci; Dieter Meissner
Copyright © 2004 American Scientific Publishers
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Encyclopedia of
Nanoscience and
Nanotechnology
www.aspbs.com/enn
Electromagnetism in Nanogranular
Metal Oxides
Christian Brosseau
Université de Bretagne Occidentale, Brest, France
CONTENTS both for transport properties and optics are only begin-
ning to be explored. Interest in nanophases has expanded
1. Introduction
asinvestigatorshaverecognizedthatmanyoftheproperties
2. Nanogranular Metal Oxides of finely divided matter strongly depend on the interfacial
3. Physical Properties properties of the constituents by virtue of the high fraction
of the overall material that is in the vicinity of an inter-
4. Conclusions
face as well as of the confinement of electrons, excitons,
Glossary and photons in small volumes. This allows the exploration
References of a vast range of experimental regimens, from noninter-
acting to strongly correlated. Their highly specific surface
areacombinedwiththeirsmallnessledtotheobservationof
1. INTRODUCTION many unique behaviors, such as superparamagnetism in Fe
clusters embedded in a nonmagnetic medium [14]. Observe
The science of manipulating matter on the nanometer scale
that usual microwave materials, such as the ferrites, are
hasprovidedscientistsandengineersattheforefrontofthis
often heavy, and may not have very desirable mechanical
research with a remarkable diverse set of tools for probing
properties. In contrast, micro- and nanostructured compos-
the behavior of nanophases. One of the strengths of this
ite materials can be designed with considerable magnetic
sector is the concomitance of the scientific interests in the
activity and can be made extremely light. One of the inter-
universities with the economic interests of the markets for
esting and important issues in predicting and understand-
new nanotechnologies. In that respect, the electromagnetic
ingnanostructuresandtheirfunctionalbehaviorsiswhether
characterizationofdrygranularmaterialscanbeconsidered
the properties of matter evolve gradually from bulk, as sys-
amajorpartoftheemergingfieldofadvancedmaterialsrel-
tem size is reduced, and what determines this evolutionary
evant to the fields of electronics, photonics, or information
behavior. Because electronic properties of interfaces affect
technology. Powder metallurgy in particular offers oppor-
the carrier mobility and scattering in a material, plasmon
tunities for engineering and ultimately trying to control
excitations at planar interfaces and at nanoparticle inter-
novelfeatures,functions,andpropertiesofgranularmateri-
faces have also been studied [15–17]. Recently, it has been
alsondifferentscalesbyusingappropriateprocedures,with
arguedthattheelectronicbandstructureofnanocrystalscan
promising commercial applications. Over the past decade
or so, a substantial amount of research and development be different from the band structure of the bulk semicon-
across the scientific community has been conducted in the ductor, that is, the opening of the semiconductor band gap
areas of nanotechnology for materials and device structures due to electron confinement [2, 13]. From the technologi-
whose characteristic feature sizes are at or near the nano- calpointofview,theobservationofgiantmagnetoresistance
meterscaleandsignificantfundamentaladvanceshavebeen [18, 19] or large coercivities [20, 21] in various nanophase
made; see, for example, [1–12] and references therein. In materials has attracted much attention. Despite a number
addition, the increasing demand for new materials that sat- of notable contributions, theory has often been outpaced
isfy multiple roles, for example, electrical and mechanical by these rapid experimental advances. From an applications
functions, has provided the impetus for an important new standpoint, powder metallurgy is a particularly attractive
area of research of nanomaterials science. An elaborate technique for preparation of nanophase materials in that it
overview of the most recent advances and emerging new offers a rapid, cost-effective, and controllable route to yield
aspects of nanoscience and nanotechnology has been given materials with specific properties. To improve performance
by Nalwa et al. [13]. The potentially profound implications and reliability of powder metallurgy, experimenters have
ISBN:1-58883-059-4/$35.00 EncyclopediaofNanoscienceandNanotechnology
Copyright©2004byAmericanScientificPublishers EditedbyH.S.Nalwa
Allrightsofreproductioninanyformreserved. Volume3: Pages(1–16)
2 ElectromagnetisminNanogranularMetalOxides
developed a range of techniques for performing characteri- size of the grains that may couple to form larger mag-
zationofpropertiesofnanophasessuchasstructural,dielec- netic switching units. Moreover, there is a fair amount of
tric, magnetic, and/or coupling between of these properties. experimental evidence that shows an enhanced coercivity
The practical importance and industrial interest in these for nanoparticles [32]. In the sintering process, compaction
materials demand optimization of several types of proper- occurs due to the enhanced diffusion between neighboring
tiesinthesematerials.Thesepropertiesincludepolarization, particles. The advantage of the hot isostatic pressing pro-
magnetization, and stability of the materials to mechanical, cess is that the porosity of the final product is negligible,
electrical,andmagneticfieldsappliedduringprocessingand andthereforethebasicpropertiesoftheproductarebetter.
operation.Oneofthefundamentalgoalsofthisfieldshould The technique of mechanical alloying typically involves the
betheunderstandingoftherelationshipsoftheseproperties high-energyballmillingofelementalpowdermixtures.Dur-
on the composition, particle size and boundaries variations, ing the milling process, large powder particles may undergo
defectstructure,andseparationoftheresidualpores,butin plasticdeformationand/orfragmentation,andsmallpowder
most cases they are not well understood. particles may coalesce by cold welding. The repeated frag-
mentation and coalescence of powder particles causes the
intimate mixing of particles on the nanoscale. Meanwhile,
1.1. Powder Metallurgy Composites
the exchange coupling between neighboring magnetic parti-
and Magnetic Properties cles can overcome the anisotropy and demagnetizing effect
of individual particles [33]. From the theoretical point of
Although extensive literature exists on the properties of
view, Stoner and Wohlfarth (SW) were pioneers in studying
nanophase materials, only a limited number of systematic
thehystereticbehaviorofarandomdistributionofnoninter-
studieshavebeenreportedontheelectromagneticandmag-
actingmagneticparticles[34,35].Thisearly,insightful,work
netic properties of granular systems. It is useful to succintly
(in1948)haspointedtowardinterestingeffectsthatarespe-
summarizeexistingstudies.Shaikhandco-workers[22]were
cific to single-domain particles, for example, the reduced
among the first to report on the dielectric properties of
uinltcrraefianseewgirtahindeedcrBeaasTiniOg3g:rathinespizeer,mrietaticvhitiyngwaaspeoabksevravleudetaot raenmdatnheenccoeerrcaitvioityMMisrs His e=qu0a(cid:16)4l8t(cid:1)o2K01.(cid:2)5, wfohrerueniKaxiaisl tphaertmiclaegs-,
1(cid:1)manddecreasingsubsequentlywithanyfurtherdecrease netocrystalline anisotrocpy constaMnst. Since its 1introduction,
of the grain size. Panina and co-workers [23] found that the SW model was expanded by others [36] for multiax-
the effective permeability of composite materials contain- ial cubic or competing types of magnetic anisotropy. How-
ing micrometer-sized, Fe particles tends to zero near the ever, the SW model is static theory and does not take into
percolationthreshold.NewnhamandTrolier-McKinstry[24] account thermal fluctuations in the magnetization process:
examined ferroelectric nanocomposites consisting of parti- therefore, its range of validity is restricted to low temper-
cles in the nanometer scale dispersed in a matrix to get atures or very strong anisotropies [37]. Still in use in the
higherfrequenciesaswellasotheradvantagessuchasminia- currentliteraturetoexplorethecaseofhighertemperatures
turization. Also noteworthy is the observation of Xiao and and/or if anisotropies are small is the superparamagnetic
Chien [25] that the coercivity changes in a dramatic varia- Néel–Brownapproacheventuallymodifiedtoinclude(mag-
tion in granular Fe/silica mixtures, which was interpretated netostatic)dipolarinteractionsamongmagneticnanograins,
by invoking percolation effects. In recent years a number of whichprovidesanimportantframeworkfortheunderstand-
studies [7, 19, 26–30] have focused on the behavior of fine ing and interpretation of experimental data [38–40]. Within
magnetic particles in a nonmagnetic metallic matrix. Until this framework, magnetization reversal takes place by ther-
now,thevastmajorityofthesepublicationssuggestthatthe mal activation over finite energy barriers, leading to tem-
magnetic state of the particles is influenced by the effect of perature and time dependences of the magnetic behavior.
the surface whose contribution becomes predominant. On However, it is worth noting that the effect of interparticle
anotherfront,questionsconcerningthecoercivityandrever- interactions cannot be easily included in this model, except
salmagnetizationinnanophaseshavealsocometothefore. as a mean-field approximation. Some authors argued that
Particles of ferromagnetic metals with dimension typically the enhanced remanence ratio (>0(cid:16)5) observed experimen-
below100nmaretoosmalltoshowwell-developeddomain tally in nanoscale isotropic magnetic materials may be due
structures [31] because the exchange correlation length is to the exchange coupling between neighboring nanograins
much greater than the particle size. For ultrafine magneti- [41, 42]. It should, perhaps, be emphasized in this context
callyorderedparticles,thereexistsacriticalsizebelowwhich that one important, and as yet not completely answered,
the grains can acquire only single magnetic domains even question concerns the understanding and the control of the
in zero applied magnetic field. The critical size of a sin- dynamicmagnetizationprocessesinthesegranularmaterials
gle domain particle can be evaluated D∗ (cid:2) 36(cid:4)AK (cid:5)1/2M−2, onnanosecondtimescales.Ageneralframeworkforunder-
2(cid:3) 1 S
where A is the exchange constant and K is the magne- standing the damping mechanism in nanostructures is prov-
J
tocrystalline anisotropy constant. For Fe, Ni, and Co, D∗ ing elusive. Finally, we observe that these basic and applied
is on the order of a few tens of nanometers, depending considerations have stimulated much research concerning
on the shape of the particle. As areal recording density in the effect of both dipolar and exchange interactions on the
magnetic storage devices approaches a few 102 Gbits/in2, magnetic and transport properties of interacting nanoscale
themediumshouldpossessmagneticallyisolatedfinegrains particles [27, 29, 35, 43]. However, it is worth noting that
(less than 10 nm in gram size) exhibiting a narrow-size dis- some of the results are controversial, and several studies
tribution. The areal density remains limited by the random reaching contradictory conclusions exist.
ElectromagnetisminNanogranularMetalOxides 3
1.2. Electromagnetic Transport Inrecentyears,anewracefortheunderstandingofmagne-
in Heterostructures toelectric properties in condensed matter systems was initi-
atedbytherecentdiscoveryofnewtypesofunconventional
Theoreticians pointed out that the theoretical framework
materials, that is, bianisotropic media in which the electric
usedinmanyinstancestoexplaintheelectromagnetictrans- displacementandthemagneticfieldvectorsdependonboth
port in granular materials is a modelization in terms of a the electric field and the magnetic induction vectors [51].
continuum media. As previously observed elsewhere [44], However, the problem remains unsolved due to its intrin-
the basic assumption used is that there exist length scales sic many-body complexity from intergranular magnetostatic
above which fluctuations at the microscopic level may be and exchange interactions. The interplay between collective
ignored. In this way, useful predictions of a granular mate- magnetic properties and transport properties in these sys-
rial’s bulk properties can be made with no references to its temspresentsarichphenomenologyandofferstheprospect
discrete nature. At issue is the manner in which these local of new functionality for specific applications [35, 51]. This
fluctuations influence the dynamics of ensemble-averaged chapter is intended to introduce the reader to the field by
quantities such as the effective permittivity (cid:18) and the effec- providing some insights into some of the theoretical and
tive permeability (cid:1). A related basic question is to examine experimental approaches that have been employed thus far
the links with coarse-graining models based on the effec- tounderstandtherelationshipsbetweenparticlesizeandthe
tive medium approximation (EMA). This major simplifying dynamical and hysteretic properties of granular solids con-
approximation is based on a self-consistent procedure in sisting of heterogeneous dispersions of magnetic particles
which a grain of one component is assumed to have a con- withdimensionsrangingfromnanometerstomicrometersin
venient shape and to be embedded in an effective medium anonmagnetichost.Theintriguingprospectiveofextending
whose properties are determined self-consistently. In par- magnetic and electromagnetic studies of heterostructures
ticular, it is natural to ask if this long-wavelength physics into the domain of nanophases may be hindered by the col-
approach is still relevant to describe (and, if so, how) the lective transport properties of strongly correlated spins sys-
response of the material at microwave frequencies by the tems.Therefore,magneticandelectromagneticbehaviorsin
materialsparameters(cid:18)and(cid:1)andwhathappensingranular nanosystems are challenging in terms of both experimental
media, such as those made up of very fine grains. Particu- observation and development of theoretical analyses.
larly related to the current work are earlier model calcula-
tions which showed that the macroscopic character of the
2. NANOGRANULAR METAL OXIDES
materialsparameters(cid:18)and(cid:1)oftwo-phasesystemsdepends
sensitively on the microstructural properties such as grain To our knowledge, to date few experimental studies have
size, particle shape, and grain boundaries type [45]. Early addressed the physical mechanisms involved in the electro-
conceptualizationsofEMAapproachesarcgivenin[44–47]. magnetic wave transport in nanogranular metal oxides, with
Anotherclassicreviewwefoundusefulforgeneralinforma- only a few systems having received significant attention; see
tion is that of Bergman and Stroud [48]. Historically, one Table 1 for a summary. It should be emphasized parenthet-
fruitful venue for studying the electromagnetic properties ically that the oxidation mechanisms of metal nanoparticles
of random heterostructures has been the concept of per- have considerable fundamental and technical importance
colation, which may shine light on the importance of the andhavebeenthefocusofmanyexperimentalandtheoret-
three-dimensional (3D) metal-insulator transition [49]. The icalstudiesduringthepastdecade.Duetothehighfraction
fundamentalpreceptofthepercolationmodelisthepredic- of the overall material in the vicinity of the surface, nano-
tion of a percolation threshold above which particles form particlescanbeextremelysusceptibletooxidation.Oneway
a connecting network. Additionally, advances in ab initio toensurethechemicalstabilityofnanoparticlesistoencap-
computational techniques along with constantly growing sulate the reactive particles in a protective matrix. In clini-
computational resources now provide opportunities for the calapplications,thecoatingprotectsthenanoparticlesfrom
development of a much more profound understanding of leaching in an acidic environment. In the current work, we
thebulkmagneticandtransportpropertiesofgranularmag- willexaminethelinksbetweenthepropertiesoftheindivid-
neticsolids[45,46].Thepowerofthesecomputationaltech- ual particles with those of the bulk materials. The study of
these materials offered the opportunity to explore the use
niques, as a viable alternative to expensive or complicated
laboratory experiments, provides theoreticians with a tool
for exploring and predicting the electromagnetic properties
Table1. Compositematerialsstudied.
fornanostructuredmaterials.Inthepastithasbeendemon-
strated that there are numerous questions or unresolved Compositematerials Ref.
issues on the effective materials properties of heterostruc-
Fe/SiO [42]
tures. One such issue is the effect of size on the materials 2
Fe/Al O [42]
parameters (cid:18) and (cid:1). There are also interesting microwave 2 3
(cid:20)-Fe O/ZnO [29,66,thiswork]
(cid:1)measurementsonsubmicrometer-sizedispersedCo ,Ni 2 3
x 1−x MgO/Ba Sr TiO [99]
particles, where it was shown that losses are associated with LaAlO3/Bxa1S−rx T3iO [100]
x 1−x 3
domain structure or surface effects [50]. Additionally, there SrTiO3/Ba Sr TiO [101]
x 1−x 3
are few quantitative data on the effect of the distribution
Note:Inrecentyears,understandingoftheelectromagneticpropertiesofnano-
of the magnetostatic interaction fields between the parti-
granularmetaloxideshasadvancedsteadily.Thematerialsstudiedalongwiththe
cles. There is another good motivation to study this issue. correspondingreferencearelistedinthetable.
4 ElectromagnetisminNanogranularMetalOxides
of powder metallurgy as a route to tunable magnetoelec- and nanostructures and will eventually shed light into other
tric materials, with properties tailored to the demands of unsolved problems.
various applications. In writing this chapter, we have cho- Because there is no review that covers electromagnetism
sen naturally to draw on our expertise, which is electro- of nanophases, our emphasis has been on producing a
magnetism of nanostructures. We consider the ZnO–Fe O self-contained account of the basic physical pictures, while
2 3
system as a prototype system to illustrate the magnetic and referring the reader to the original literature for details.
electromagnetic transport properties of particulate compos- Computerized literature searches citing “electromagnetism
ite materials for at least four main reasons. First, these of nanogranular metal oxides” as key words find very few
metal oxides are commonly found in technological applica- articles. As a result, it is impossible to give a comprehen-
tions; for example, ZnO is a remarkable II–VI semiconduc- sive review of the electromagnetic properties of many of
torwithwideapplicationsforvariousdevicessuchasoptical these materials. We shall therefore limit ourselves to dis-
waveguides [52], piezoelectric transducers [53], and varis- cussing an overview of some of the electromagnetic and
tors [54–56], and maghemite ((cid:20)-Fe O ) is the most popu- magnetic properties of heterostructures composed of metal
2 3
largeneral-purposemagnetictapematerial[57–59].Second, oxide nanoparticulate powders, Samples consist of grains of
characterization of the crystal oxides has been carried out the magnetic phase ((cid:20)-Fe O ) homogeneously dispersed in
2 3
by a variety of experimental techniques. For example, the a nonmagnetic insulating background (ZnO). In this review
magnetic behavior of (cid:20)-Fe O has been studied extensively: the starting powders had different origins. The micro oxide
2 3
it is a ferrimagnetic spinel with a bulk saturation magneti- powders were purchased from Aldrich Chemical Co. and
zationof390kAm−1 [60–62].Muchworkhasbeendevoted marked as ≥99% pure, whereas the nano oxide powders
to the magnetic properties of (cid:20)-Fe O nanoparticles; for were supplied from Nanophase Technologies Corp. (Burr
2 3
example, Dai et al. [62] found that the long-range mag- Ridge, II). The manufacturer’s specifications are listed in
netostatic interactions between surfactant coated (cid:20)-Fe O Table 2. Control over the average particle size and shape
2 3
nanoparticles and the blocking temperature (below which was achieved by transmission electron microscopy (TEM).
the moments are blocked) can be increased by decreasing Epoxy resin (Scotchcast 265) purchased from 3M and was
theaverageinterparticledistancethroughanincreaseofthe used as binder phase. Composite materials for this inves-
applied pressure on the bulk samples. (cid:20)-Fe O is of partic- tigation were prepared by a four-step procedure. (1) The
2 3
ular interest because of its applications in devices such as appropriate amounts of metal oxide powders were first pre-
magneticrecordingmedia.(cid:20)-Fe O isametastablephaseat heated at 200 (cid:5)C for dehydratation, and then, after cooling
2 3
ambiantconditionsandtendstotransformtoastable-phase, toroomtemperature,thepowdersweresubsequentlymixed
antiferromagnetic hematite ((cid:20)-Fe O ), when heated up to with acetone and a certain amount of epoxy resin in a bath
2 3
400(cid:5)C.Ferrimagneticoxidesofironcombinetheproperties sonicator for 1 h; the mixture was then cast into a culture
of a magnetic material with that of an insulator. Commer- dish and the acetone was allowed to evaporate slowly at
cially available pure ZnO and (cid:20)-Fe O , powders were used room temperature. (2) The mold was filled by the resulting
2 3
as basic components of the composite materials and had mixturer. (3) The powder was compacted to a specified size
different origins. Third, the low cost and ease of fabrica- andshape.(4)Thedensepowdercompactwasejectedfrom
tion of these materials make study of the electromagnetic the mold. Room temperature-pressed ZnO/Fe O compacts
2 3
and magnetic properties of their small clusters, where the were made under a pressure of 107 N m−2 for 2 min. As a
size and composition can be varied, extremely interesting. result of this procedure, test samples with a toroidal shape
Fourth, nanostructures of these materials exhibit materials of 7 mm outside diameter were used for electromagnetic
properties that can differ strongly from those of the bulk spectroscopy experiments. In the following we refer to the
phases[62–66].Weareconvincedthatthecomprehensionof samples containing micrometer-sized particles and those
complex problems posed by nanogranular metal oxides has containing nanometer-sized particles as M-type and N-type
the potential to produce a substantial advance in electro- samples, respectively. We studied three sets of samples that
magnetismandmagnetismofcondensedmatternanophases nominally had volume fractions of 0.10, 0.15, and 0.25 of
Table2. Selectedphysicalpropertiesofthepowdersinvestigatedinthisstudy.
Powder ZnO ZnO (cid:20)-Fe O (cid:20)-Fe O
2 3 2 3
Averageparticlesizea(cid:21)b 1(cid:1)m 49nm 5(cid:1)m 23nm
Powdercolor White White Purple Brown
Specificsurfacearea 22 51
BET(m2 g−1)
Morphology Elongated Elongated Nearly Nearly
spherical, spherical,
faceted faceted
Crystalphase Wurtzite Wurtzite Maghemite Maghemite
(cubicspinel) (cubicspinel)
Densitya (gcm−3) 5.61 5.6 5.24 5.2
aFrommanufacturerproductliterature.
bDeterminedfromspecificsurfacearea.
ElectromagnetisminNanogranularMetalOxides 5
epoxy. The fractional volume of voids (porosity) is deduced (cubic spinel). The average grain sizes were obtained in the
knowing the volume fractions of ZnO, Fe O , and epoxy XRD analysis from the line broadening of the diffraction
2 3
and was controlled by density measurements. Throughout peak and by using the Scherrer formula and are consistent
thetext,f denotesthevolumefractionofFe O and(cid:23)indi- with the estimates obtained from TEM.
2 3
cates the volume fraction of the epoxy resin.
3.1. Dielectric Properties
3. PHYSICAL PROPERTIES
Representativefrequencydependencecurvesoftherealand
imaginary parts of the relative effective permittivity (cid:18) for
In this chapter we focus on the present understanding of
N and M composite. samples (f = 0(cid:16)53 and (cid:23) = 0(cid:16)25) are
what we think are the most remarkable electromagnetic
plotted in Figure 2a and b. Upon inspection of these fig-
properties of nanogranular metal oxides, observed by state
ures we observe that (cid:18)(cid:7) is a slowly decreasing function for
oftheartexperimentsandinterpretedwithmodemtheories.
N samples and constant for M samples in the range of fre-
We have organized the discussion into three main modules:
quencies explored. The larger conductivity for N composite
(1) zero-field (ZF) permittivity and permeability of a set of
samples, shown in Figure 2b, can probably be attributed to
mixtures having different compositions and grain sizes (see
theincreaseofthedensityofinterfacesassurface-to-volume
AppendixAforthemeasurementdetails),(2)gyromagnetic
ratio increases in magnetic nanostructures. Figure 2c and d
resonance, and (3) magnetic hysteresis loop data for these
show the corresponding plots for the real and imaginary
samples.Weendthechapterwithsomeconcludingremarks
parts of the relative permeability (cid:1). From Figure 2c and d,
and a brief look at some open questions that remain in the
one can see the differences between the permeability of M
electromagnetic properties of particulate nanophases.
samples and that of N samples. Perhaps the most intriguing
TEMbrightfieldusingaJEOLmicroscopeatanacceler-
fact is that whatever the volume fraction of Fe O investi-
atingvoltageof100kVwasusedtorevealthegrainsizeand 2 3
gated (from 0 to 58 vol%), M samples do not show absorb-
shapeoftheas-receivedZnOandFe O particles.Thepar-
2 3 ing properties in the microwave range. To gain a better
ticles in solution were brought onto holey carbon films sus-
understandingofhowthecompositionaffectsthepermittiv-
pendedovercoppergridsforTEMobservations.FromTEM
ity and permeability, a set of experiments was conducted in
micrographsofthepowders,wehaveobservedthattheindi-
which the volume fraction of Fe O is varied, as illustrated
vidualZnOparticleiselongatedwithanaverageaspectratio 2 3
inFigure3aandd.ItisnoticeablethatthedatainFigure3a
ofabout3:1whereas(cid:20)-Fe O particlesarenearlyspherically
2 3 and b, corresponding to M and N samples at F = (cid:26) =
shaped. To obtain information on the morphology of the 2(cid:3)
1 GHz, are almost coincident. Another important observa-
mixtures, scanning electron microscopy (SEM) data were
tion is that there is no evidence for a percolation threshold
collected using JEOL 6400 scanning electron microscopy
overthewholevolumefractionofFe O rangeinvestigated.
operatingatanacceleratingvoltageof25kVandmagnifica- 2 3
Figure 3c and d indicate that the (cid:1)(cid:7)(cid:4)f(cid:5) and (cid:1)(cid:7)(cid:7)(cid:4)f(cid:5) curves
tionof60,000.Samplesweremountedonanaluminiumstub
show substantial changes from M and N samples; for exam-
usinganadhesivecarbontabandweregold-coated.Arepre-
ple, (cid:1)(cid:7) is enhanced by a factor of 3 and (cid:1)(cid:7)(cid:7) is enhanced by
sentative SEM image of a cross-sectional view of a compos-
a factor of 20 for f ≈0(cid:16)5
ite sample is displayed in Figure 1. A visual examination of
Theexperimentalplotsof(cid:18)(cid:7)(cid:4)f(cid:5)and(cid:18)(cid:7)(cid:7)(cid:4)f(cid:5)werecompared
Figure1revealsafinelydispersedstructureandalargevoid
with the results of simple calculations in Figure 3a and b
distribution. The identification of the crystalline phases was
using the Bruggeman symmetric medium equation; that is,
carriedoutbypowderX-raydiffraction(XRD)withCuK , (cid:3)
(cid:24) f(cid:4)(cid:4)(cid:18)−(cid:18)(cid:5)/(cid:4)2(cid:18)+(cid:18)(cid:5)(cid:5) = 0, where f and (cid:18) denote the
radiation. ZnO crystallizes in the hexagonal wurtzite struc- i i i i i i
volume fraction and permittivity of the constituent i (cid:4)i =
ture whereas the crystal structure of Fe O is maghemite
2 3 Fe O ,ZnO,epoxyresinorair).SeeAppendixBfordetails.
2 3
The inputs Bruggeman’s equation were obtained from our
measurements and the literature [66–70]. The permittivities
predicted by this model are inconsistent with experiment in
magnitude and in composition trend.
We believe that the discrepancies originate from two
assumptions. First, the theory of Bruggeman assumes that
the electric dipole–dipole interactions between the inclu-
sions is taken into account in an average way. Unlike the
dilute limit case, for which dipolar interactions provide a
good description of the electrostatic interactions between
the inclusions provided that the composite has the assumed
geometry(inwhichamaterialofonetypeisembeddedinan
identifiablehostmaterial),suchanapproachfailstoaccount
for high concentrations of inclusions. Moreover, it does not
500nm
depend explicitly on the size of the grains. This is because
onlythedipoleterm,whichisproportionaltograinvolume,
is retained in the series expansion of the amplitude of the
Figure1. SEMmicrographsoffracturecross-sectionviewofacompos-
itesample(f =0(cid:16)53and(cid:23)=0(cid:16)25)showingthedistributionofparticle magneticfieldscatteredbyasinglegrain.Thus,onlyvolume
sizes.Theblackbarinthelowerrightcorneris500nm. fractions appear in this approach. A second source of this
6 ElectromagnetisminNanogranularMetalOxides
(a) 4
N
(a) 10 3
M
7,5 µ′ 2
M
N
ε′ 5 1
0
2.5
0 0.2 0.4 0.6 0.8
f
0
0.1 1 10 (b) 2
F(GHz)
1.5
(b) 2
N
µ′′ 1
1.5
0.5
ε′′ 1 M
N 0
0.5 0 0.2 0.4 0.6 0.8
M f
0
(c) 20
0.1 1 10
F(GHz)
15
(c) 4
N ε′ 10
3
5
µ′ 2
0
0 0.2 0.4 0.6 0.8
1
M f
0 (d) 10
0.1 1 10
F(GHz)
7.5
(d) 3
ε′′ 5
N
2.5
2
µ′′ 0
0 0.2 0.4 0.6 0.8
1
f
M
Figure3. Variation of the relative permittivity as a function of the
0 volume fraction Fe O, for M-type (triangles) and N-type (circles)
2 3
0.1 1 10 ZnO/Fe O composite samples at a given value of frequency, F =
2 3
F(GHz) 1GHz.Roomtemperature.Squaresin(a)and(b)indicatethevalues
of(cid:18)(cid:7)and(cid:18)(cid:7)(cid:7)calculatedusingthemean-fieldBruggemanmodelandtak-
Figure2. Thefrequencydependenceoftherelativepermittivity(cid:18)and ingasinputs(cid:18) (1GHz)=38(cid:16)2−j0(cid:16)3,(cid:18) (1GHz)=14(cid:16)2−j0(cid:16)3,
ZnO Fe2O3
the relative permeability (cid:1) for micrometer-sized (M, red curve) and (cid:18) (1GHz)=5−j0(cid:16)01,and(cid:18) (1GHz)=1−j0.Observethatthe
cpoxy air
nanometer-sized (N, thick red curve) ZnO/Fe O composite samples caluculated values take into account the porosity of the samples. Red
2 3
and a given value of the volume fraction of Fe O, f =0(cid:16)53. Room symbolscorrespondto(cid:23)=0(cid:16)25,greensymbolscorrespondto(cid:23)=0(cid:16)15,
2 3
temperature.(cid:23)=0(cid:16)25(a)Realpart(cid:18)(cid:7),(b)imaginarypart(cid:18)(cid:7)(cid:7),(c)real and light blue symbols correspond to (cid:23)=0(cid:16)10. (a) real part (cid:18)(cid:7) of the
part(cid:1)(cid:7),and(d)imaginarypart(cid:1)(cid:7)(cid:7). relative permittivity, (b) imaginary part (cid:18)(cid:7)(cid:7) of the relative permittivity,
(c)realpart(cid:1)(cid:7) oftherelativepermeability,and(d)imaginarypart(cid:1)(cid:7)(cid:7)
oftherelativepermeability.
ElectromagnetisminNanogranularMetalOxides 7
discrepancy is that the parameters for the material are not
uniform, but rather they are influenced by the presence of
(a)
defects such as impurities and grain boundaries. It is usu-
ally argued that EMA approaches have the disadvantages 4
typical of all mean-field theories because they Ignore the
3
fluctuations in the system. It assumes that the local elec-
tric field is the same in the volume occupied by each con- µ′ 2
sntfihteeietaludrbesunthfltrkeoinmrientgthbeieoornfuhasnecdetbesaerrcomiaesustarsyue[7cdo1tiu]ff.rfeteWhr.eTecoehcxneaisslmitldeieancrtrcatoeebsnlcoytofiopftnrihcoemtloosccttaahhltoetfieserefialndicngst 100.530.440.3f30.240.13 0 7.02 2.59 F0.(96GHz)0.35 0.13
thatthestandardeffective(continuous)mediumapproxima-
(b)
tions underlying the present calculations were done under
the simplifying assumption of spherical particles, even if 3
there is a significant departure from perfect sphericity for
the ZnO particles. However, the use of depolarizing factors 2
to account for shape anisotropy of the ZnO particles still µ′′
loerayOdasbnstdeorevaexpsieagrlnsimoifiectnahnta.ttdneoviactoionndubcettiwoneen(ptehrecomlaetiaonn-)fietlhdrethshe-- 10 0.96 0.35 0.13
old is evidenced, indicating a disconnected Fe2O3 particles 0.530.440.f330.240.13 0 7.02 2.59F (GHz)
network. In these powder compact composites, the pres-
ence of insulating grains and of the amorphous epoxy resin (c) 2
increases the conduction barrier height and therefore is
expectedtodecreasetheoverallconductivityofthesamples.
z)
However, even if the volume fraction of Fe O —and hence H
2 3 G 1.5
the intergrain spacing—and grain size were independently (
0
adjustable, we have not yet studied the local charge trans- F
port mechanisms. A difficulty is that transport through such
systemsofteninvolvesprocessesthatarestronglyinfluenced 1
0 0.2 0.4 0.6
bylocalfluctuations,includingvariationsinmorphologyand f
particle sizes.
(d) 8
3.2. Gyromagnetic Resonance 6
z)
H
An interesting observation can be made in the results of (G 4
F
Figure 3. In addition, a 3D rendering of the (cid:1)(cid:7)(cid:4)f(cid:21)F(cid:5) ∆
2
and (cid:1)(cid:7)(cid:7)(cid:4)f(cid:21)F(cid:5) surfaces over the f–F plane is exhibited in
Figure 4a and b. It is apparent from Figure 4c that the res- 0
0 0.2 0.4 0.6
onance frequency F is slightly increased the percentage of f
0
Fe O isincreased.OnecanseefromFigure4dthattheres-
2 3 (e) 1
onancewidthathalf-height(cid:29)F decreasessignificantlyasthe
percentageofFe O isincreased.Forcompleteness,wealso
2 3
showthethreesetsofdatacorrespondingtof =25vol%for
(cid:18)(cid:7)(cid:21)(cid:18)(cid:7)(cid:7)(cid:21)(cid:1)(cid:7), and (cid:1)(cid:7)(cid:7) in Figure 5a through d, where the epoxy α 0.5
concentrationisincreasedfrom(cid:23)=10vol%to(cid:23)=15and
25 vol%. Careful inspection of the (cid:1)(cid:7)(cid:7) curves with different
epoxy volume fractions reveals a fine structure of the broad 0
0 0.2 0.4 0.6
resonanceline.Thiseffectismostpronouncedforthecurve
f
corresponding to (cid:23)=25 vol% in Figure 5d.
We now turn our attention to a phenomenological analy- Figure4. (a)Realpart(cid:1)(cid:7) ofthepermeabilityona(f(cid:21)F)surface.f =
sis of the gyromagnetic resonance observed in N-type sam- 0(cid:16)53and(cid:23)=0(cid:16)25.(b)SameasinFigure4afortheimaginarypart(cid:1)(cid:7)(cid:7).
ples. To go further one must fit the gyromagnetic reso- f =0(cid:16)53and(cid:23)=0(cid:16)25.(c)TheresonancefrequencyF0asafunctionof
nance to an appropriate functional form for the dynam- the volume fraction of Fe2O3. The blue line shows the calculated val-
ues using our modeling approach (see text). Red symbols correspond
ics of magnetization. We now give technical information
to (cid:23)=0(cid:16)25 and green symbols correspond to (cid:23)=0(cid:16)15. (d) The res-
about the calculations and analyze the results in detail.
onance width (cid:29)F as a function of the volume fraction of Fe O. The
The dynamics of an individual magnetic moment can 2 3
bluelineshowsthecalculatedvaluesusingourmodelingapproach(see
be described by a magnetization vector M(cid:10). In theoreti- text).SamenotationforthesymbolsasinFigure4c.(e)Thedamping
cal aspect, the response of this magnetization vector to constant (cid:24), obtained from the fit of the gyromagnetic resonance, as a
the effective field is commonly described by the Landau– functionofthevolumefractionofFe O.
2 3
Lifshitz–Gilbert (LLG) equation of motion, which has the
