Nanostructured Materials: Basic Concept and Microstructure

Abstract

Nanostructured Materials (NsM) are materials with a microstructure the characteristic length scale of which is on the order of a few (typically 1–10) nanometers. NsM may be in or far away from thermodynamic equilibrium. NsM synthesized by supramolecular chemistry are examples of NsM in thermodynamic equilibrium. NsM consisting of nanometer-sized crystallites (e.g. of Au or NaCl) with different crystallographic orientations and/or chemical compositions are far away from thermodynamic equilibrium. The properties of NsM deviate from those of single crystals (or coarse-grained polycrystals) and/or glasses with the same average chemical composition. This deviation results from the reduced size and/or dimensionality of the nanometer-sized crystallites as well as from the numerous interfaces between adjacent crystallites. An attempt is made to summarize the basic physical concepts and the microstructural features of equilibrium and non-equilibrium NsM.

Full text

NANOSTRUCTURED MATERIALS: BASIC CONCEPTS AND
MICROSTRUCTURE p
H. GLEITER
Forschungszentrum Karlsruhe, Institute of Nanotechnology, D-76021 Karlsruhe, Germany
(Received 1 June 1999; accepted 15 July 1999)
AbstractÐNanostructured Materials (NsM) are materials with a microstructure the characteristic length
scale of which is on the order of a few (typically 1±10) nanometers. NsM may be in or far away from ther-
modynamic equilibrium. NsM synthesized by supramolecular chemistry are examples of NsM in thermo-
dynamic equilibrium. NsM consisting of nanometer-sized crystallites (e.g. of Au or NaCl) with dierent
crystallographic orientations and/or chemical compositions are far away from thermodynamic equilibrium.
The properties of NsM deviate from those of single crystals (or coarse-grained polycrystals) and/or glasses
with the same average chemical composition. This deviation results from the reduced size and/or dimen-
sionality of the nanometer-sized crystallites as well as from the numerous interfaces between adjacent crys-
tallites. An attempt is made to summarize the basic physical concepts and the microstructural features of
equilibrium and non-equilibrium NsM. #2000 Acta Metallurgica Inc. Published by Elsevier Science Ltd.
All rights reserved.
Keywords: Nanostructured materials; Chemical stability; Thermodynamics; Mechanical properties; Micro-
structure
1. BASIC CONCEPTS
1.1. Categories of nanostructured materials
One of the very basic results of the physics and
chemistry of solids is the insight that most proper-
ties of solids depend on the microstructure, i.e. the
chemical composition, the arrangement of the
atoms (the atomic structure) and the size of a solid
in one, two or three dimensions. In other words, if
one changes one or several of these parameters, the
properties of a solid vary. The most well-known
example of the correlation between the atomic
structure and the properties of a bulk material is
probably the spectacular variation in the hardness
of carbon when it transforms from diamond to
graphite. Comparable variations have been noted if
the atomic structure of a solid deviates far from
equilibrium or if its size is reduced to a few intera-
tomic spacings in one, two or three dimensions. An
example of the latter case is the change in color of
CdS crystals if their size is reduced to a few nano-
meters [1].
The synthesis of materials and/or devices with
new properties by means of the controlled manipu-
lation of their microstructure on the atomic level
has become an emerging interdisciplinary ®eld
based on solid state physics, chemistry, biology and
materials science. The materials and/or devices
involved may be divided into the following three
categories [2].
The ®rst category comprises materials and/or
devices with reduced dimensions and/or dimension-
ality in the form of (isolated, substrate-supported or
embedded) nanometer-sized particles, thin wires or
thin ®lms. CVD, PVD, inert gas condensation, var-
ious aerosol techniques, precipitation from the
vapor, from supersaturated liquids or solids (both
crystalline and amorphous) appear to be the tech-
niques most frequently used to generate this type of
microstructure. Well-known examples of technologi-
cal applications of materials the properties of which
depend on this type of microstructure are catalysts
and semiconductor devices utilizing single or multi-
layer quantum well structures.
The second category comprises materials and/or
devices in which the nanometer-sized microstructure
is limited to a thin (nanometer-sized) surface region
of a bulk material. PVD, CVD, ion implantation
and laser beam treatments are the most widely
applied procedures to modify the chemical compo-
sition and/or atomic structure of solid surfaces on a
nanometer scale. Surfaces with enhanced corrosion
resistance, hardness, wear resistance or protective
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coatings (e.g. by diamond) are examples taken from
today's technology in which the properties of a thin
surface layer are improved by means of creating a
nanometer-sized microstructure in a thin surface
region. An important subgroup of this category are
materials, the surface region of which are structured
laterally on a nanometer scale by ``writing'' a nano-
meter-sized structural pattern on the free surface.
For example, patterns in the form of an array of
nanometer-sized islands (e.g. quantum dots) con-
nected by thin (nanometer scale) wires. Patterns of
this type may be synthesized by lithography, by
means of local probes (e.g. the tip of a tunneling
microscope, near-®eld methods, focussed electron or
ion beams) and/or surface precipitation processes.
Processes and devices of this sort are expected to
play a key role in the production of the next gener-
ation of electronic devices such as highly integrated
circuits, terrabit memories, single electron transis-
tors, quantum computers, etc.
In this paper we shall focus attention on the third
category of bulk solids with a nanometer-scale
microstructure. In fact, we shall focus on bulk
solids in which the chemical composition, the
atomic arrangement and/or the size of the building
blocks (e.g. crystallites or atomic/molecular groups)
forming the solid vary on a length scale of a few
nanometers throughout the bulk.
Two classes of such solids may be distinguished.
In the ®rst class, the atomic structure and/or the
chemical composition varies in space continuously
throughout the solid on an atomic scale. Glasses,
gels, supersaturated solid solutions or implanted
materials are examples of this type (cf. Fig. 1). In
many cases these types of solids are produced by
quenching a high-temperature (equilibrium) struc-
ture, e.g. a melt or a solid solution to low tempera-
tures at which the structure is far away from
equilibrium.
In the last two decades a second class of ma-
terials with a nanometer-sized microstructure has
been synthesized and studied. These materials are
assembled of nanometer-sized building blocksÐ
mostly crystallitesÐas displayed in Fig. 2. These
building blocks may dier in their atomic structure,
their crystallographic orientation and/or their
chemical composition. If the building blocks are
crystallites, incoherent or coherent interfaces may
be formed between them, depending on the atomic
structure, the crystallographic orientation and/or
the chemical composition of adjacent crystallites. In
other words, materials assembled of nanometer-
sized building blocks are microstructurally hetero-
geneous consisting of the building blocks (e.g. crys-
tallites) and the regions between adjacent building
blocks (e.g. grain boundaries). It is this inherently
heterogeneous structure on a nanometer scale that
is crucial for many of their properties and dis-
tinguishes them from glasses, gels, etc. that are
microstructurally homogeneous (cf. Figs 1 and 2).
Materials with a nanometer-sized microstructure
are called ``Nanostructured Materials'' (NsM) orÐ
synonymouslyÐnanophase materials, nanocrystal-
line materials or supramolecular solids. In this
paper we shall focus on these ``Nanostructured
Materials'' and use this term exclusively.
The synthesis, characterization and processing of
such NsM are part of an emerging and rapidly
growing ®eld referred to as nanotechnology. R&D
in this ®eld emphasizes scienti®c discoveries in gen-
eration of materials with controlled microstructural
characteristics, research on their processing into
bulk materials with engineered properties and tech-
nological functions, and introduction of new device
concepts and manufacturing methods.
1.2. Eects controlling the properties of
nanostructured materials
As the properties of solids depend on size, atomic
structure and chemical composition, NsM exhibit
new properties due to one or several of the follow-
ing eects.
Fig. 1. Two-dimensional model of an Al
2
O
3
glass [3].
Fig. 2. Two-dimensional model of a nanostructured ma-
terial. The atoms in the centers of the crystals are indi-
cated in black. The ones in the boundary core regions are
represented as open circles [13].
2 GLEITER: NANOSTRUCTURED MATERIALS

1.2.1. Size eects. Size eects result if the charac-
teristic size of the building blocks of the microstruc-
ture (e.g. the crystallite size, Fig. 2) is reduced to
the point where critical length scales of physical
phenomena (e.g. the mean free paths of electrons or
phonons, a coherency length, a screening length,
etc.) become comparable with the characteristic size
of the building blocks of the microstructure. An
example is shown in Fig. 3. If the thickness of the
layers of a superlattice is comparable with the
wavelength of the electrons at the Fermi edge, dis-
crete energy levels for electrons and holes are
formed in the quantum wells. Such size eects mod-
ifying the mechanical and optical properties are dis-
played in Figs 7(a) and (b).
1.2.2. Change of the dimensionality of the system.
If a NsM consists of thin needle-shaped or ¯at,
two-dimensional crystallites (cf. Fig. 6), only two or
one dimension of the building blocks becomes com-
parable with the length scale of a physical phenom-
enon. In other words, in these cases the NsM
becomes a two- or one-dimensional system with
respect to this phenomenon.
1.2.3. Changes of the atomic structure. Changes in
the atomic structure result if a high density of inco-
herent interfaces (Fig. 2)Ðor other lattice defects
such as dislocations, vacancies, etc.Ðis incorpor-
ated. The cores of lattice defects represent a con-
strained state of solid matter diering structurally
from (unconstrained) crystals and/or glasses. As a
consequence, a solid containing a high density of
defect cores diers structurally from a defect-free
solid with the same (average) chemical composition.
The boundaries in Fig. 2 represent an example of
this eect: the mis®t between adjacent crystallites
changes the atomic structure (e.g. the average
atomic density, the nearest-neighbor coordination,
etc.) in the boundary regions relative to the perfect
crystal (cf. Section 2.1.3). At high defect densities
the volume fraction of defect cores becomes com-
parable with the volume fraction of the crystalline
regions. In fact, this is the case if the crystal diam-
eter becomes comparable with the thickness of the
interfaces, i.e. for crystal sizes on the order of one
or a few nanometers as is the case in NsM.
1.2.4. Alloying of components (e.g. elements) that
are immiscible in the solid and/or the molten state.
The following cases of this type of immiscible com-
ponents in NsM may be distinguished: solute atoms
Fig. 3. Energy-band diagrams for undoped GaAs±Al
x
Ga
1ÿx
As superlattices showing conduction and
valence-band edges with heterostructure potential wells at x0:3, DEc'300 meV:The horizontal lines
represent quantum-well discrete energy levels for electrons and holes con®ned in the GaAs layers [5].
Fig. 4. Schematic model of the structure of nanostructured
Cu±Bi and W±Ga alloys. The open circles represent the
Cu or W atoms, respectively, forming the nanometer-sized
crystals. The black circles are the Bi or Ga atoms, respect-
ively, incorporated in the boundaries at sites of enhanced
local free volume. The atomic structure shown was
deduced from EXAFS and X-ray diraction measurements
[6].
GLEITER: NANOSTRUCTURED MATERIALS 3

(Fig. 4) with little solubility in the lattice of the
crystallites frequently segregate to the boundary
cores (e.g. the free energy of the system in several
alloys is reduced if large solute atoms segregate to
the boundary core). The second case of nanostruc-
tured alloys results if the crystallites of a NsM have
dierent chemical compositions. Even if the con-
stituents are immiscible in the crystalline and/or
molten state (e.g. Fe and Ag), the formation of
solid solutions in the boundary regions of the NsM
has been noticed (Fig. 5) [7].
Finally, it may be pointed out that NsM are by
no means limited to polycrystalline materials con-
sisting of the type displayed in Fig. 2. In semicrys-
talline polymers, nanometer-sized microstructures
are formed that consist of crystalline and non-crys-
talline regions diering in molecular structure and/
or chemical composition (Figs 19 and 20).
Polymeric NsM will be discussed in Sections 2.1.8
and 2.1.9. NsM synthesized by supramolecular
chemistry result if dierent types of molecular
building blocks are self-assembled into a large var-
iety of one-, two- or three-dimensional arrays (Figs
23±27). NsM of this type will be considered in
Section 2.2.
The remarkable potential the ®eld of NsM oers
in the form of bulk materials, composites or coating
materials to optoelectronic engineering, magnetic
recording technologies, micro-manufacturing, bioen-
gineering, etc. is recognized by industry. Large-scale
programs, institutes and research networks have
been initiated recently on these and other topics in
the United States, Japan, EC, China and other
countries.
In order to keep this article within the length
required, it will be limited to considering the micro-
structure of equilibrium and non-equilibrium NsM.
In other words, nanostructured devices, carbon-
based nanostructures (e.g. fullerenes, nanotubes),
high surface area (nanometer-sized) materials, sus-
pensions of nanometer-sized crystals, thin ®lms and
materials with nanostructured surface regions will
not be discussed. Concerning recent review articles
on NsM we refer to Refs [2, 4, 8±13].
2. MICROSTRUCTURES
Materials with nanometer-sized microstructures
may be classi®ed according to their free energy into
equilibrium NsM and NsM far away from thermo-
dynamic equilibrium which will be called ``non-
equilibrium NsM''.
2.1. Non-equilibrium Nanostructured Materials
Non-equilibrium NsM are materials composed of
structural elementsÐmostly crystallitesÐwith a
characteristic size (at least in one direction) of a few
nanometers (Fig. 2). In other words, non-equili-
brium NsM are inherently heterogeneous on a nano-
meter scale consisting of nanometer-sized building
blocks separated by boundary regions. The various
types of non-equilibrium NsM dier by the charac-
teristic features of their building blocks (e.g. crystal-
lites with dierent or identical chemical
composition, dierent or identical atomic structure,
dierent or identical shape, size, etc.). However, the
size, structure, etc. of the building blocks are not
the only microstructural features distinguishing
dierent NsM. In fact, the boundary regions
between them play a similar role. The chemical
composition, atomic structure, thickness, etc. of the
boundary regions are equally crucial for the proper-
ties of NsM (e.g. Figs 2, 4 and 5). In other words,
even if the building blocks, e.g. the crystallites of
two NsM, have comparable size, chemical compo-
sition, etc., the properties of both NsM may deviate
signi®cantly if their interfacial structures dier.
Dierent interfacial structures may result if the two
NsM have been synthesized by dierent procedures.
For example, nanocrystalline Ni (crystal size about
10 nm, density about 94%) prepared by consolida-
tion of Ni powder exhibited little (<3%) ductility
whereas nanocrystalline Ni (similar grain size and
chemical composition) obtained by means of an
electro-deposition process could be deformed exten-
sively (>100%). The major dierence noticed
between both materials was the energy stored in the
interfacial regions suggesting dierent interfacial
structures (cf. also Section 2.1.7). Numerous other
examples emphasizing the signi®cance of the micro-
structure for the properties of NsM may be found
in the literature [4±13].
One of the technologically attractive features of
non-equilibrium NsM is the fact that their micro-
Fig. 5. Schematic model of nanocrystalline Ag±Fe alloys
according to the data of Mo
Èssbauer spectroscopy. The
alloys consist of a mixture of nanometer-sized Ag and Fe
crystals (represented by open and full circles, respectively).
In the (strained) interfacial regions between Ag and Fe
crystals, solid solutions of Fe atoms in Ag crystallites, and
Ag atoms in the Fe crystallites are formed although both
components are immiscible in the liquid as well as in the
solid state. Similar eects may occur in the grain bound-
aries between adjacent Fe and Ag crystals [7].
4 GLEITER: NANOSTRUCTURED MATERIALS

structure (and properties) can be manipulatedÐas
in all non-equilibrium systemsÐby the mode of
preparation. This allows a wide variety of micro-
structures (and hence properties) to be generated.
Naturally, the other side of the coin is that any
technological application of NsM is only possible if
one is able to fully characterize and control their
microstructure, and if the correlation between their
properties and their microstructure is well under-
stood so that NsM with controlled properties can
be produced reproducibly. This is one of the
reasons for focussing a large portion of this article
on the microstructure of NsM.
2.1.1. Classi®cation of Nanostructured Materials.
Let us ®rst consider non-polymeric NsM. Non-poly-
meric NsM consisting of nanometer-sized crystal-
lites and interfaces may be classi®ed [2] according
to their chemical composition and the shape (dimen-
sionality) of their microstructural constituents
(boundary regions and crystallites; Fig. 6).
According to the shape of the crystallites, three cat-
egories of NsM may be distinguished: layer-shaped
crystallites, rod-shaped crystallites (with layer thick-
ness or rod diameters in the order of a few nano-
meters), and NsM composed of equiaxed
nanometer-sized crystallites. Depending on the
chemical composition of the crystallites, the three
categories of NsM may be grouped into four
families. In the most simple case (®rst family, Fig.
6), all crystallites and interfacial regions have the
same chemical composition. Examples of this family
of NsM are semicrystalline polymers (consisting of
stacked crystalline lamellae separated by non-crys-
talline regions; ®rst category in Fig. 6) or NsM
made up of equiaxed nanometer-sized crystals, e.g.
of Cu (third category). NsM belonging to the sec-
ond family consist of crystallites with dierent
chemical compositions (indicated in Fig. 6 by dier-
ent thickness of the lines used for hatching).
Quantum well (multilayer) structures are probably
the most well-known examples of this type (®rst
category). If the compositional variation occurs pri-
marily between crystallites and the interfacial
regions, the third family of NsM is obtained. In
this case one type of atoms (molecules) segregates
preferentially to the interfacial regions so that the
structural modulation (crystals/interfaces) is coupled
to the local chemical modulation. NsM consisting
of nanometer-sized W crystals with Ga atoms segre-
Fig. 6. Classi®cation schema for NsM according to their chemical composition and the dimensionality
(shape) of the crystallites (structural elements) forming the NsM. The boundary regions of the ®rst and
second family of NsM are indicated in black to emphasize the dierent atomic arrangements in the
crystallites and in the boundaries. The chemical composition of the (black) boundary regions and the
crystallites is identical in the ®rst family. In the second family, the (black) boundaries are the regions
where two crystals of dierent chemical composition are joined together causing a steep concentration
gradient [2].
GLEITER: NANOSTRUCTURED MATERIALS 5

gated to the grain boundaries (Fig. 4) are an
example of this type (third category). An interesting
new type of such materials was recently produced
by co-milling Al
2
O
3
and Ga. It turned out that this
procedure resulted in nanometer-sized Al
2
O
3
crys-
tals separated by a network of non-crystalline layers
of Ga [14]. Depending on the Ga content, the thick-
ness of the Ga boundaries between the Al
2
O
3
crys-
tals varies between less than a monolayer and up to
about seven layers of Ga. The fourth family of
NsM is formed by nanometer-sized crystallites
(layers, rods or equiaxed crystallites) dispersed in a
matrix of dierent chemical composition.
Precipitation-hardened alloys belong in this group
of NsM. Nanometer-sized Ni
3
Al precipitates dis-
persed in a Ni matrixÐgenerated by annealing a
supersaturated Ni±Al solid solutionÐare an
example of such alloys. Most high-temperature ma-
terials used in jet engines of modern aircraft are
based on precipitation-hardened Ni
3
Al/Ni alloys [cf.
Fig. 7(a)].
The NsM considered so far consisted mostly of
crystalline components. However, in addition, NsM
are known in which one or all constituents are non-
crystalline. For example, semicrystalline polymers
consist of alternating (nanometer thick) crystalline
and non-crystalline layers (cf. Figs 19 and 20). The
various types of microstructures that may be
formed in polymeric NsM will be discussed in
Section 2.1.8. Other NsM consisting of a crystalline
and a non-crystalline structural component are par-
tially crystallized glasses and nanocrystalline metal
nitrides, carbides of the type M
n
N, M
n
C
metal Ti, Zr, Nb, W, V) embedded in an amor-
phous matrix, e.g. a Si
3
N
4
matrix. Metal nitrides
embedded in amorphous Si
3
N
4
have been prepared
by high-frequency discharge, direct current dis-
charge or plasma-induced chemical vapor depo-
sition [15]. The remarkable feature of these
materials is their hardness which seems to be com-
parable with or higher than that of diamond.
Elastic image forces are argued to require a very
high stress to force dislocations to cut through the
nanometer-sized nitride crystallites. This high stress
may, however, not lead to fracture because any
crack formed in one of the crystallites is suggested
to be stopped by the ductile amorphous Si
3
N
4
matrix surrounding the cracked crystallite. Another
family of technologically interesting NsM consisting
of nanometer-sized crystallites embedded in an
amorphous matrix is nanocrystalline magnetic ma-
terials. They are derived from crystallizing amor-
phous ribbons of (Fe, B)-based metallic glasses.
Their microstructure is characterized by 10±25 nm-
sized grains of a b.c.c.-a-FeX phase consuming
about 70±80% of the total volume. This phase is
homogeneously dispersed in an amorphous matrix.
The two families of alloys showing the best per-
formance characteristics are Fe±Cu±Nb±B±Si
(FINEMET) and Fe±Zr±Cu±B±Si (NANOPERM).
``Finemet'' alloys have a saturation induction of
about 1.2 T and their properties at high frequencies
are comparable with the best Co-based amorphous
metals. The outstanding features of ``Nanoperm''
alloys are the very low losses exhibited at low fre-
quencies <100 Hzoering potential for appli-
cations in electrical power distribution
transformers.
Spinodally decomposed glasses represent NsM in
which all constituents are non-crystalline. Finally,
crystalline or non-crystalline materials containing a
high density of nanometer-sized voids (e.g. due to
the a-particle irradiation) are NsM, one component
of which is a gas or vacuum. A well-known example
of a NsM with a void-type structure is porous Si.
Porous Si has attracted considerable attention
because of its strong photoluminescence in visible
light. Two fundamental features of bulk Si limit its
use in optoelectronic devices: the centrosymmetric
crystal structure prevents a linear electro-optical
Fig. 7. (a) Flow stress of Ni±13 at.% Ni alloys as a function of the size of the Ni
3
Al precipitates. (b)
Photoluminescence spectra of nanocrystalline ZnO with dierent crystal sizes in comparison with the
bulk material. The detection wavelength was 550 nm [2].
6 GLEITER: NANOSTRUCTURED MATERIALS

eect. Hence, Si cannot be used for light modu-
lation. Secondly, the band gap of Si is indirect and
lies in the infrared region Eg01:170 eV). As a con-
sequence, Si was considered unsuitable for light-
emitting technologies. In 1990 it was reported that
porous Si could luminesce. Two lines of thought
were put forward to explain the eect: quantum
con®nement and luminescence of chemical com-
plexes attached to the free surface of the silicon
crystallites. The quantum con®nement model pro-
poses the carriers in porous Si to be con®ned to
microcrystallites with a size of 1±4 nm formed due
to the porosity of the Si. The chemical complexes
capable of luminescing in the observed spectral
range were proposed to be siloxene compounds, a
complex of Si, H and O. Recently, ``hybrid models''
were discussed where both, the interior and the sur-
face of the porous Si are involved in the photolumi-
nescence.
Obviously, the model of a non-equilibrium NsM
considered so far (Fig. 2) is highly simpli®ed in the
sense that it is based on a hard-sphere approach.
Nonetheless, two characteristic features of a NsM
are already borne out by this approach: the nano-
meter-sized crystallites are expected to exhibit size
and/or dimensionality eects for the reasons given
in the previous paragraph (Section 1.2). Moreover,
several properties (e.g. diusion, internal friction,
etc.) of a NsM should be controlled by the presence
of a high density of grain and/or interphase bound-
aries. Indeed, these kinds of eects have been
revealed by a large number of experimental studies
in recent years (see, e.g. [52]). For the sake of brev-
ity, this paper will be limited to discussing only one
or very few experiments as a representative example
for each case.
2.1.2. Size eects. Figure 7(a) shows the depen-
dence of the ¯ow stress of a nanocomposite consist-
ing of nanometer-sized Ni
3
Al crystallites dispersed
in a matrix made up of a NiAl solid solution. The
total volume fraction of Ni
3
Al crystallites is the
same for all Ni
3
Al crystal sizes shown in Fig. 7(a);
the only parameter varied is the size of the Ni
3
Al
crystallites. Figure 7(b) displays the blue shift in the
luminescence spectra as a function of the crystal
size for nanocrystalline ZnO (consisting of consoli-
dated ZnO crystals separated by grain boundaries).
The blue shift is a quantum size eect. If the crys-
tallite size becomes comparable or smaller than the
de Broglie wavelength of the charge carriers gener-
ated by the absorbed light, the con®nement
increases the energy required for absorption. This
energy increase shifts the absorption/luminescence
spectra towards shorter wavelengths (blue).
Another eect related to the reduced size of the
crystallites in NsM concerns the atomic structure of
the interfaces. More precisely, the question: is the
atomic structure of the interfaces between nano-
meter-sized crystallites dierent from the structure
of the interfaces between crystals of in®nite size
(same chemical composition, orientation, relation-
ship, etc.)? So far, only a few speci®c cases have
been studied experimentally and theoretically by
means of molecular dynamics computations. The
results of these studies may be summarized as fol-
lows: in metallic NsM, the low-temperature atomic
structure of the boundaries of a NsM diers from
the structure of the boundaries in a coarse polycrys-
tal primarily by the rigid body translation. The
deviating rigid body relaxation of both types of
boundaries results from the dierent constraints in
both materials: in coarse-grained polycrystals adja-
cent crystallites are free to minimize the boundary
energy by a translational motion relative to one
another (called rigid body relaxation). In a NsM
the constraints exerted by the neighboring nano-
meter-sized crystallites limit the rigid body relax-
Fig. 8. Comparison of the vibrational density of states
g(n) for nanocrystalline Cu (crystal size 8.2 A
Ê, solid line)
with those for a Lennard±Jones glass (molecular-dynamics
simulation, dash±dotted line) and for the perfect f.c.c.
crystal (dashed line); nis the phonon frequency [29].
Fig. 9. Comparison of the temperature dependence of the
total free energy of nanocrystalline Cu (for dierent grain
sizes as indicated in the ®gure) with a Lennard±Jones glass
[29] and the perfect crystal.
GLEITER: NANOSTRUCTURED MATERIALS 7

ation more the smaller the crystallites are. Another
crystallite size eect concerns the structural stability
of NsM [28, 29]. The vibrational densities of state
of a NsM and of the related glass, determined from
lattice-dynamics simulations, exhibit low- and high-
frequency modes not seen in the perfect crystal
(Fig. 8). The low-frequency modes give rise to a
low-temperature peak in the excess speci®c heat in
both types of metastable microstructures. Free-
energy simulations of NsM and the related glass
suggest that a phase transition from the nanocrys-
talline state to the glass should occur below a criti-
cal grain size. Figure 9 displays the dependence of
the free energy of various NsM with dierent grain
sizes. Obviously, below a crystal size of about
1.4 nm, NsM are unstable relative to the glass as
they exhibit a higher free energy. A structural trans-
formation consistent with these results was, in fact,
reported for nanocrystalline Si prepared by glow
discharge decomposition of silane: nanostructured
Si was noticed by Raman spectroscopy to transform
into amorphous Si if the crystal size was reduced
below a critical value of a few nanometers [26, 27].
2.1.3. Reduced density and coordination in the
boundaries. In the core of incoherent interfaces, the
mis®t between crystallites joined together (Fig. 2)
locally modi®es the atomic structure by reducing
the atomic density and by altering the coordination
between nearest-neighbor atoms relative to the per-
fect crystal. The reduced density (or enhanced free
volume) in the boundaries is directly visible in high-
resolution electron micrographs [16] and has also
been evidenced by Mo
Èssbauer spectroscopy. The
Mo
Èssbauer spectra of the interfacial component of
nanocrystalline Fe exhibit a pressure-induced re-
versible change in the isomer shift that is about one
order of magnitude larger than that of the a-Fe
crystals and of glassy iron alloys [17]. The enhanced
isomer shift indicates an enhanced compressibility
of the boundary regions and thus a reduced inter-
facial density.
The modi®ed nearest-neighbor coordination in
the boundary regions relative to a perfect crystal
(with the same chemical composition) has been
revealed (Fig. 10) by measuring (X-ray diraction)
the pair correlation functions of nanostructured Pd
and of a Pd single crystal [18]. The same result was
obtained by Mo
Èssbauer studies of FeF
2
,a-Fe
2
O
3
and g-Fe
2
O
3
. The grain boundary structure of these
materials was found to consist of structural units
the coordinations of which dier from the ones in
the crystalline state [19, 20].
2.1.4. Chemical binding eects. The atomic struc-
tures of the boundary regions in NsM are expected
to depend on the type of chemical binding forces.
The following picture seems to emerge from the
presently available experimental and theoretical stu-
dies on the correlation between chemical binding
and the nature of the boundaries in NsM.
In materials with directional bonds (e.g. Si, C),
the boundary structure depends signi®cantly [21, 22]
on the competition between local structural disorder
in the boundary and localized variation in the hy-
bridization of the bonds in the region of the inter-
faces. Silicon and carbon provide relatively simple
cases for the physical understanding of the coupling
between structural disorder and bonding modi®-
cations. Silicon is a purely sp
3
bonded material.
Diamond exhibits greater bond stiness combined
with the ability to change hybridization in a disor-
dered environment from sp
3
to sp
2
. The interplay
between these two factors may be elucidated by
comparing the dierent ways in which the two ma-
terials respond to structural disorder. Figures 11(a)
and (b) compare the atomic structures of two grain
boundaries in diamond and Si. In both materials,
the (111) boundary [Fig. 11(b)] is clearly more
ordered than the (100) boundary shown in Fig.
11(a). The dierent degrees of disorder in both
types of boundaries are evidenced by the much
lower energy of the (111) grain boundary relative to
the (100) interface (130% in diamond and 147%
in Si) [22].
The average nearest-neighbor coordination, hCi,
of the atoms in the two center planes of the dia-
mond (100) and (111) grain boundaries are 3.16
and 3.50, respectively. These low values are indica-
tive of a signi®cant fraction of grain boundary
atoms being only threefold-coordinated (i.e. by sp
2
bonded). Eighty percent of all (100) grain boundary
atoms are threefold-coordinated compared to
``only'' 50% in the (111) grain boundary [22],
whereas practically all other atoms are tetrahedrally
coordinated. By contrast, in Si these two grain
boundaries have hCi14:02 and 4.06, respectivelyÐ
that is, close to the perfect tetrahedral coordination
Fig. 10. Coordination number (measured by X-ray scatter-
ing) for nanocrystalline Pd (12 nm crystal size) relative to
a Pd single crystal as a function of the interatomic spa-
cings [18]. N
NSM
and N
SC
are the measured coordination
numbers of the nanocrystalline Pd and of a Pd single crys-
tal.
8 GLEITER: NANOSTRUCTURED MATERIALS

with only a few three- and ®vefold-coordinated Si
atoms in the grain boundary unit cell [22].
These dierences are strikingly apparent in the
related bond-angle distribution functions shown in
Fig. 11(c). For example, the presence of equal frac-
tions of three- and fourfold-coordinated C atoms
and the high degree of structural ordering in the
diamond (111) grain boundary give rise to two dis-
tinct peaks, one near the sp
3
bond angle of 109.478
and the other near the sp
2
bond angle of 1208.By
comparison, in Si the sp
2
peak is completely absent.
In contrast to the (111) grain boundary, the bond-
angle distribution function of the high-energy (100)
grain boundary in both diamond and Si is similar
to that of the corresponding bulk amorphous ma-
terial. However, whereasÐin diamondÐthe peak is
centered near the sp
2
bond angle, indicating the pre-
sence of mostly threefold-coordinated C atoms and
signi®cant structural disordering, in Si the peak is
centered at the tetrahedral bond angle.
This comparison reveals that because in Si sp
2
-
type bonding is not allowed, a large driving force
exists for the initially threefold-coordinated atoms
in the unrelaxed grain boundary to recover as much
as possible their full fourfold coordinationÐeven
at the cost of severe grain boundary disordering
[Fig. 11(a)]. In contrast, diamond has only a small
driving force for structural disordering [see also
Fig. 11(a)], at the cost of signi®cant bond dis-
ordering.
Fig. 11. Projected structures of the high-temperature relaxed (a) (100) S29 and (b) (111) S30 twist
boundaries in diamond and Si [22]. All the nearest-neighbor bonds between grain boundary atoms are
shown. (c) Distribution of bond angles (in arbitrary units) for the atoms in the two center planes of the
above grain boundaries. For comparison the distributions for bulk amorphous carbon and silicon are
also shown [21].
GLEITER: NANOSTRUCTURED MATERIALS 9

Based on these results, the number of threefold-
coordinated C atoms was estimated and was found
to agree with recent Raman scattering experiments
on nanocrystalline diamond grown from fullerene
precursors [23]. The physical signi®cance of the
similarity of the bond-angle distribution of the
amorphous Si and the (100) S29 boundary [Figs
11(a) and (c)] was investigated further [24, 25] com-
paring the atomic arrangement in nanocrystalline Si
averaged over many boundaries between nano-
meter-sized Si grains with dierent orientation re-
lationships. The fully dense nanostructured Si was
synthesized (molecular dynamics) by inserting small
crystalline seeds with randomly preselected crystal-
lographic orientations into a Si melt (Fig. 12).
Subsequent cooling below the melting point of Si
resulted in the growth of the inserted seed crystals
to form equilibrated grain boundaries in a fully
dense polycrystalline Si. The boundary structure
(Fig. 13) may be compared with the structure of
amorphous Si by comparing the radial and angular
distribution functions of the various interfacial
structural components (boundaries, triple lines, etc.)
of the nanometer-sized Si with the radial and angu-
lar distribution functions of amorphous Si [Figs
14(a) and (b)]. The results obtained indicate that
the atomic arrangement in the interfaces of Si is
Fig. 12. Cubic, three-dimensional periodic simulation cell
containing four randomly oriented seed grains arranged
on a f.c.c. lattice and embedded in the melt (schematic)
[25].
Fig. 13. Positions of the atoms within a slice of thickness
0.5a
0
cut out (parallel to the X±Yplane, Fig. 12) of a
nanocrystalline material [25]. The nanocrystalline material
was generated by the procedure described in Fig. 12. The
solid circles represent atoms with excess energies larger
than 0.1 eV.
Fig. 14. (a) Typical local radial distribution functions,
G(r), for the nanocrystalline Si (cf. Fig. 13) with a grain
size of 5.4 nm. Shown is a comparison of these local radial
distribution functions for the atoms in the grain boundary
regions, the triple lines, the fourfold and sixfold point
grain junctions, with the overall radial distribution func-
tion of bulk amorphous silicon [25]. (b) Angular distri-
bution functions, P(cos y), for the same defected regions
as in (a).
10 GLEITER: NANOSTRUCTURED MATERIALS

similar to the atomic arrangement of amorphous Si.
In fact, these results suggest that nanometer-sized Si
may be treated as a two-phase system consisting of
an ordered crystalline phase (in the crystal interiors)
connected by an amorphous-like intergranular
phase.
2.1.5. Temperature eects. Elevated temperatures
seem to aect the microstructure of NsM by one or
both of the following two types of processes:
.grain growth;
.temperature-induced variations of the atomic
structure.
2.1.5.1.Grain growth. Grain growth in NsM is pri-
marily driven by the excess energy stored in the
grain or interphase boundaries. Analogous to the
growth of cells in soap froths, the boundaries move
toward their centers of curvature and the rate of
movement varies with the amount of curvature. The
earliest theoretical considerations of the kinetics of
normal grain growth assume a linear relationship
between the rate of grain growth and the inverse
grain size, which in turn is proportional to the
radius of curvature of the grain boundaries [30, 31].
This assumption yields, under ideal conditions, the
following equation for grain growth:
D2ÿD2
0kt 1
where D
0
and Dare the grain sizes at the beginning
of the experiment and at time, t, respectively. Kis a
constant that depends on temperature [cf. equation
(3)]. A number of more recent theoretical treat-
ments came to the same conclusion that normal
grain growth should ideally occur in a parabolic
manner [32]. However, this is rarely observed except
for high-purity metals at high homologous tempera-
tures. For practical purposes, the most widely used
relationship [equation (2)] incorporates the empiri-
cal time exponent nR0:5 which allows the descrip-
tion of isothermal grain growth that often does not
®t the ideal relationship modeled by equation (1):
D1=nÿD1=n
0k0tor Dk0tD1=n
0n:2
The rate constant k(or k') can be expressed in an
Arrhenius-type equation:
kk0expfÿQ=RT g3
where Qis the activation enthalpy for isothermal
grain growth, Rthe molar gas constant and k
0
a
constant that is independent of the absolute tem-
perature T. The activation enthalpy, Q, is often
used to determine the microscopic mechanism
which dominates the grain growth.
Grain growth studies have been carried out for
various NsM using TEM [33±37], DSC [38], X-ray
diraction [37, 39] and Raman spectroscopy. The
materials studied were prepared by crystallizing
glasses [39±43, 50], sliding wear [35], inert gas con-
densation [33, 44, 45], electrodeposition [49], elec-
tron gun evaporation, mechanical milling [37, 46±
48, 53] and CVD. For recent reviews about grain
growth in NsM we refer to Refs [9, 37, 45, 48].
Studies of the grain growth process in NsM pro-
duced by the crystallization of glasses have the
attractive feature that pore-free nanocrystalline ma-
terials are obtained. Obviously, the synthesis of
NsM by crystallization of glasses is limited to the
speci®c chemical compositions that permit the prep-
aration of the glassy state, e.g. by rapidly cooling,
by a sol±gel process, etc. Moreover, only those
glasses are suitable for grain growth studies in NsM
that convert the glassy phase directly into a crystal-
line phase of the same chemical composition [51].
For example, a stable tetragonal (Fe, Co)Zr
2
phase
forms directly from the ternary Fe±Co±Zr amor-
phous phase, while in the binary Fe±Zr alloys, the
amorphous phase ®rst results in a metastable f.c.c.
FeZr
2
phase which later transforms to the equili-
brium tetragonal FeZr
2
phase. Grain growth studies
were performed for both the stable and metastable
phases and it was found that the grain size increases
with annealing time [43]. It has also been noted that
grain growth starts at a lower temperature in the
nanocrystalline sample with smaller grains [42] and
that grain growth is rapid above a certain tempera-
ture and becomes negligible for longer annealing
times.
As grain growth involves the transport of atoms
across and presumably also along the boundaries,
the activation energy of the process is frequently
compared with that of grain boundary diusion. As
may be seen from Table I in Ref. [48], the two acti-
vation energies agree reasonably well in most sys-
tems studied so far.
Ganapathi et al. [35] tried to ®t their grain
growth data on nanocrystalline Cu produced by
sliding wear and observed an excellent ®t for values
of nof 1/2, 1/3 or 1/4. Thus, they concluded that it
is dicult to identify the grain growth mechanism
on the basis of the exponent nalone, and that grain
growth in nanocrystalline materials probably occurs
in a manner similar to that in conventional poly-
crystalline materials.
In most of the studies involving nanocrystalline
materials, the value of nis dierent from the value
of 0.5, deduced from the parabolic relationship for
grain growth [equations (1) and (2)]. Thus, in ad-
dition to Zener drag (where a particle interacts with
the grain boundary to reduce the energy of the
boundary±particle system and restrains the bound-
ary movement [73]), other mechanisms such as pin-
ning of grain boundaries by pores, solute atoms or
inclusions may also be operative. The fact that
pores [33, 54] and impurity doping [55] have con-
siderable eect on the grain growth characteristics
was demonstrated in TiO
2
. For an initial grain size
GLEITER: NANOSTRUCTURED MATERIALS 11

of 14 nm, when the porosity was about 25%, the
grain size (after annealing for 20 h at 7008C) was
30 nm [54]. When the porosity was reduced to
about 10%, the grain size for a similar annealing
treatment was dramatically increased to 500 nm.
The same authors have also demonstrated that sin-
tering the same nanocrystalline material under
pressure (1 GPa), or with appropriate dopants such
as Y, can suppress the grain growth [56].
In general, nseems to change during grain
growth and tends toward the ideal value of 0.5 as is
found in high-purity materials or at high annealing
temperatures (Fig. 15). The values obtained for n
from grain growth measurements seem to dependÐ
at least in some systemsÐon the evaluation of the
experimental data. For example, Krill and co-
workers [53] re-evaluated Marlow and Koch's
results [48]. The data ®t used by Marlow and Koch
yielded n0:32:Krill and co-workers showed that
the same measurements can be equally well matched
by an impurity drag model with a growth exponent
of n0:5:Another problem associated with grain
growth in nanocrystalline samples containing impu-
rities has recently been re-emphasized [70] although
it is known to exist in principle in coarse-grained
polycrystals as well [71]. During grain growth, the
area available to the segregant is reduced. Thus, if
all impurity atoms remain in (or close to) the
boundaries, their concentration must increase which
should manifest itself in an enhanced drag force
(rather than being independent of grain size as is
commonly assumed). Recent measurements using
Pd±Zr solute solutions seem to con®rm the expected
impurity drag enhancement [70]. Naturally, in NsM
this eect will be enhanced relative to a coarse-
grained polycrystal due to the large reduction of the
boundary area during grain growth.
Abnormal grain growth in NsM has been
observed at room temperature or slightly above in
some instances, e.g. in Cu, Ag, Pd [44, 72] and crys-
tallized metallic glasses of the FINEMET type [50].
Similar to the observation of Hahn et al., Gertsman
and Birringer [72] also noted that grain growth
occurs preferentially in the denser materials.
Anomalous grain growth has been suggested to be
due to: (a) a certain non-uniformity of the grain
size distribution in the as-prepared samples (so that
the larger grains act as nuclei); and (b) impurity
segregation. If the impurity distribution is spatially
non-uniform, enhanced grain growth may occur in
regions of lowest impurity content. The reason why
such abnormal grain growth does not occur in
many coarse-grained polycrystalline materials has
been attributed to the enhanced grain boundary
enthalpy (leading to high driving forces) and/or
non-equilibrium grain boundary structures (leading
to increased mobility of grain boundaries) in the
nanocrystalline materials.
2.1.5.2.Stability against grain growth. Several
approaches for preventing grain growth have been
proposed. On the one hand are those that aim to
slow down the growth kinetics by reducing the driv-
ing force (the grain boundary free energy) or the
grain boundary mobility. In these cases the material
remains in an unstable state where small local re-
arrangements of the grain boundary planes can
reduce the material's free energy, but the time inter-
val and temperature required for signi®cant grain
growth to take place are increased. The second type
of stabilization aims at achieving a truly metastable
Fig. 15. Time exponent for isothermal grain growth of various nanocrystalline materials as a function
of the reduced annealing temperature [48].
12 GLEITER: NANOSTRUCTURED MATERIALS

state where each small variation of the total grain
boundary area increases the free energy of the ma-
terial. In this case a large energy barrier has to be
overcome, e.g. by thermal activation, in order to
start the evolution towards the equilibrium state,
the single crystal.
Inclusions of a second phase act as pinning sites
for grain boundaries in essentially the same way as
do pores during sintering: the total free energy of a
segment of boundary intersecting an inclusion is
reduced by the product of the cross-section of the
inclusion and the speci®c boundary free energy.
Zener (quoted by Smith [73]) derived a relation
between the stable grain radius Rand the radius r
and volume fraction fof the inclusions: R=r13=4f:
This relationship implies that when a ®ne dispersion
of small inclusions can be generated, then small
volume fractions of inclusions can stabilize a micro-
structure with a very ®ne grain size. In the stable
microstructure the location of each boundary corre-
sponds to a local energy minimum, and the material
is therefore in a metastable state. When the tem-
perature is increased, grain growth will remain sup-
pressed until the inclusions dissolve in the matrix or
until they become mobile. A number of experimen-
tal investigations of this eect are reviewed in Refs
[9, 74]. Retarded grain growth will also result from
solute drag eects. In many solid solutions, solute
atoms are known to segregate to the boundaries
forming a solute cloud in the vicinity of the bound-
ary.
If the boundary migrates, three modes of motion
may occur depending on the relative rates of
boundary and solute-cloud mobility.
.If the boundary migrates slowly{, it drags its
solute cloud along with it, thus reducing the
boundary mobility and, hence, grain growth.
.If the boundary migrates very fast, it breaks
away from the solute atoms and moves freely.
.At intermediate migration rates, the boundary
breaks loose locally from its cloud and this
impurity-free segment bulges out. The resulting
increase of the boundary area reduces the rate of
motion of the impurity-free boundary segment
and permits the impurity cloud to be formed
again (``jerky motion'').
All three modes of boundary motion have been
observed experimentally in coarse-grained polycrys-
tals [75]. The ®rst two cases are likely to occur in
NsM as well. In fact, pinning of the grain bound-
aries in nanocrystalline Ni solid by the Ni
3
P pre-
cipitates in a crystallized Ni±P amorphous alloy
[36] and segregation of Si to grain boundaries in a
Ni±Si solid solution [76] have been found to be re-
sponsible for preventing grain growth in nanocrys-
talline phases. In addition to the kinetic factors
discussed so far, energetic eects may also aect the
growth rate of the crystallites in NsM. For example,
Lu [42] studied the thermal stability of 7±48 nm
grains in a Ni±P alloy and concluded that samples
with smaller grain sizes have enhanced thermal
stabilities, suggesting that the grain growth tem-
peratures and the activation energy for growth in a
nanocrystalline solid are higher in comparison with
coarser grains. This is attributed to the con®gur-
ation and the energetic state of the interfaces in the
nanocrystalline materials.
In general, the solute solubility in the core of
grain boundaries diers considerably from the solu-
bility in the interior of the crystals. Therefore, in
thermodynamic equilibrium, the grain boundaries
are enriched or depleted in solute. This can have
two bene®cial eects on the stability of the micro-
structure. The ®rst eect is solute drag and was dis-
cussed in the previous paragraph. The second eect
is a reduction of the driving force for grain growth.
According to the Gibbs adsorption equation [77],
the grain boundary free energy decreases when
solute segregates to the boundary. Experimental evi-
dence shows that the decrease can be substantial
[78], and the theory indicates that in alloy systems
with a large atomic size mismatch, the grain bound-
ary free energy may even be reduced to zero [79±
81].
As a consequence of the solute enrichment at the
grain boundaries and of the large speci®c grain
boundary area, theory and experiment [82, 83] show
that nanocrystalline materials also have an
enhanced overall solubility for solute with a large
heat of segregation.
The potential existence of alloy systems with a
vanishing grain boundary free energy has led to
speculations on the existence of a metastable nano-
crystalline state in which grain growth requires that
the nucleation barrier for the formation of a second
phase be overcome by thermal activation [79±81].
While there is as yet no de®nite experimental proof
of the existence of a metastable nanocrystalline
state, there are a number of experimental obser-
vations that favor its existence. Y±Fe is an alloy
system with a large atomic size dierence,
suggesting a large enthalpy of grain boundary segre-
gation. In Y±Fe alloys (prepared by inert gas con-
densation) Fe segregates to the grain boundaries
[82]. In agreement with the theoretical predictions,
the grain size of the alloy samples decreases as the
alloy concentration is enhanced, and reaches values
as small as 2 nm. Although alloys with a low Fe
molar fraction, x
Fe
, undergo grain growth upon
annealing, alloys with higher x
Fe
show little grain
growth before the equilibrium phase YFe
2
nucle-
ates, indicating that energetic rather than kinetic
factors are responsible for the suppression of
growth. A similar correlation between the onset of
{The terms ``slow'' and ``fast'' refer to the mobility of
the boundary relative to the (diusive) mobility of the
solute cloud.
GLEITER: NANOSTRUCTURED MATERIALS 13

grain growth and the nucleation of the stable inter-
metallic phase has also been observed in Nb±Cu
alloy prepared by high-energy ball milling [84]. The
grain size of mechanically alloyed Pd±Zr solid sol-
utions has also been found to decrease with increas-
ing solute concentration, and the heat release upon
annealing indicates that solute (Zr) segregates to the
grain boundaries, thereby reducing the speci®c
grain boundary energy and impeding grain growth
[81]. It has also been demonstrated that alloying
solute to ceramic nanometer-sized particles results
in a drastic change in the grain-size density trajec-
tory, with a substantially lower grain size in the
densely sintered body [85]. Finally, the existence of
stable liquid microstructures with a nanometer-scale
structure and a large number of internal interfaces,
the microemulsions, lends support to the expec-
tation that solid microstructures can also be stabil-
ized against growth at very ®ne grain sizes and
elevated temperatures.
In NsM consisting of nanometer-sized crystallites
(TiN) embedded in an amorphous matrix (of amor-
phous Si
3
N
4
), the rate of crystal growth was
observed to decrease with crystal size [96]. In fact,
if the crystal size was about 1 nm no measurable
crystal growth occurred at temperatures below
12008C (which is about 80% of the decomposition
temperature). If the crystal size was about 10 nm,
the grain growth started at 8008C. The physical
reasons for this ``inverse'' grain growth kinetics are
not yet fully understood [96]. An attempt to ration-
alize the surprising stability in terms of the high
cohesive energy of the amorphous/crystalline inter-
face has been proposed.
2.1.5.3.Temperature induced variation in the atomic
structure of the boundaries. A variation in the
atomic structure of the boundaries of NsM as a
function of temperature was recently reported for
nanocrystalline Si. As was discussed in Section
2.1.4, the boundaries in nanocrystalline Si exhibit
an amorphous-like structure (cf. Figs 13 and 14).
This structure was found [24] to represent an equili-
brium structure by contrast with bulk amorphous
Si. If the nanometer-sized Si is heated to elevated
temperatures, the amorphous structure seems to
undergo (above a glass transition temperature T
g
)a
reversible and dynamical structural transformation
from the structure of amorphous Si to liquid Si. By
contrast with the bulk glass transition, however,
this transition is continuous, fully reversible and
thermally activated, starting at T
g
and being com-
plete at the equilibrium melting point T
m
of Si, at
which the entire nanometer-sized Si sample is
liquid. Figure 16(b) shows the reversibility of the
structural transition. A reversible temperature vari-
ation from 1600 to 900 K and back to 1600 K
Fig. 16. (a) Temperature dependence of the volume expansion, dV(in units of the zero-temperature lat-
tice parameter) per unit grain boundary area for the high-energy (100), S29 grain boundary in sili-
con. The bulk glass transition temperature T
g
and melting point T
m
are indicated on the top axis. (b)
Response to thermal cycling of the volume expansion dVfor the (100), S29 twist grain boundary, il-
lustrating the reversibility of the transition between the con®ned amorphous and liquid grain boundary
phases; tis the simulation time [86].
Fig. 17. Comparison of the bond-angle distribution func-
tions, P(y), for the con®ned amorphous and con®ned
grain boundary phases with those for bulk amorphous
and supercooled liquid silicon, respectively. In perfect-crys-
tal silicon at T0K,P(y) exhibits a single d-function
peak at the tetrahedral angle yt109:478[86].
14 GLEITER: NANOSTRUCTURED MATERIALS

results in a reversible variation of the free volume
(dV) of the boundary [86]. The temperature-depen-
dent variation of dVis summarized in Fig. 16(a).
Between T
g
and the melting point of Si (T
m
), dV
varies continuously and reversibly between the
amorphous and the molten state of Si. In other
words, a continuous, reversible phase transition
exists between the amorphous Si and the liquid Si
(continuous melting and solidi®cation). Figure 17
compares the angular correlation functions, P(y),
of the boundaries in Si with the ones of bulk amor-
phous and liquid Si: at and below T
g
[i.e. below
900 K, cf. Fig. 16(a)] the angular distribution func-
tion of the boundaries is similar to that of bulk
amorphous Si. The same applies at 1600 K for
liquid Si and the structure of the boundaries (Fig.
17).
2.1.6. Formation of non-equilibrium alloys. In sev-
eral nanostructured alloys, the solute solubility in
the boundary regions was noticed to deviate from
the solute solubility in the crystal lattice. The dier-
ent solubilities (and presumably other eects as
well) lead to the formation of alloys in nanocrystal-
line materials which do not exist in coarse-grained
polycrystals, as was pointed out in Section 1.2.4.
Fig. 18. Sequential STM images of a nanostructured Pd surface, imaged with a tunneling voltage of
ÿ40 mV (tip negative) and a tunneling current of 6 nA. The area of 400 400 nm2is scanned at
2.5 min/image. Typical roughness data for the as-prepared samples as shown here are: peak to
valley 400 nm, r.m.s. roughness 80 nm, average roughness 65 nm:(a) Image obtained from the ®rst
scan. (b) Image from the ®fth scan (taken 10 min after the ®rst scan), indicating the initial movements
of some randomly distributed grains around the voids. (c) Image from the seventh scan, taken 15 min
after the ®rst scan. Grains were pictured to be moving dynamically in a worm-like fashion to yield
channel-like grain boundaries [89].
GLEITER: NANOSTRUCTURED MATERIALS 15

2.1.7. Time±temperature history and preparation
eects. The NsM discussed so far are a non-equili-
brium state of condensed matter. Hence, their struc-
ture and properties depend not only on the
chemical composition and the size/shape of the
crystallites but also on the mode of preparation and
the previous time±temperature history of the ma-
terial. For example, the enthalpy stored in nano-
crystalline Pt may be reduced during annealing [87]
up to 50% without grain growth (i.e. at constant
crystal size and chemical composition). The re-
duction is presumably caused by atomic rearrange-
ments in the boundary regions. Measurements of
other properties of NsM (e.g. thermal expansion,
speci®c heat, compressibility) and spectroscopic stu-
dies (e.g. by Mo
Èssbauer or positron lifetime spec-
troscopy) indicate structural dierences between
chemically identical NsM with comparable crystal-
lite sizes if these materials were prepared by dier-
ent methods and/or if their previous time±
temperature history was dierent (e.g. [88]). In fact,
similar eects have been reported for other non-
equilibrium states of condensed matter (e.g. glasses).
The non-equilibrium character of NsM implies that
any comparison of experimental observations is
meaningful only if the specimens used have compar-
able crystal size, chemical composition, preparation
mode and time±temperature history. Moreover, the
non-equilibrium character of NsM renders them
susceptible to structural modi®cations by the
methods applied to study their structure [89]. An
example is shown in Fig. 18.
2.1.8. Polymeric Nanostructured Materials. So far,
the considerations have been limited to elemental or
low molecular weight NsM, i.e. NsM formed by
atoms/molecules that are more or less spherical in
shape. A dierent situation arises if NsM are syn-
thesized from high molecular weight polymers, i.e.
long, ¯exible molecular chains.
It is one of the remarkable features of semicrys-
talline polymers that a nanostructured morphology
is always formed if these polymers are crystallized
from the melt or from solution, unless crystalliza-
tion occurs under high pressure or if high pressure
annealing is applied subsequent to crystallization.
However, if a polymer is crystallized from solution
or from the melt under ambient pressure, multilayer
structures consisting of stacks of polymer single
crystals result (Fig. 19). Inside the crystals, the
atoms forming the polymer chains arrange in a per-
iodic three-dimensional (crystalline) fashion. The
disordered interfacial regions between neighboring
crystals (Fig. 19) consist of macromolecules folding
Fig. 19. Molecular folding in semicrystalline polymers
resulting in stacks of lamellar crystals with a thickness of
about 10±20 nm separated by ``amorphous'' regions.
Fig. 20. (a) Stacked lamellar morphology in polyethylene
(TEM bright ®eld). (b) Needle-like morphology in polybu-
tene-1 (TEM bright ®eld). (c) Oriented micellar mor-
phology in polyethylene terephthalate (TEM dark ®eld
micrograph). (d) Shish-kebab morphology in isotactic
polystyrene (TEM dark ®eld micrograph) [90].
16 GLEITER: NANOSTRUCTURED MATERIALS

back into the same crystal and of tie molecules that
meander between neighboring crystals. The typical
thicknesses of the crystal lamellae are of the order
of 10±20 nm. These relatively small crystal thick-
nesses have been interpreted in terms of a higher
nucleation rate of chain-folded crystals relative to
extended chain crystals or in terms of a frozen-in
equilibrium structure: at the crystallization tempera-
ture, the excess entropy associated with the chain
folds may reduce the Gibbs free energy of the
chain-folded crystal below that of the extended-
chain crystal. Hence, at the crystallization tempera-
ture, crystallization will result in chain-folded crys-
tals rather than in extended-chain crystals.
Estimates of the excess entropy associated with the
chain folds lead to a thickness of the nucleating
crystals of about 10±20 nm. It may be pointed out
that the nucleation of imperfect crystals during
crystallization is not limited to polymeric materials.
The excess entropy associated with vacancies, e.g.
in elemental crystals, results in an equilibrium
vacancy concentration at the melting temperature,
i.e. in the nucleation of imperfect crystals. In
metals, this equilibrium vacancy concentration at
the melting temperature is typically about 10
ÿ4
.
Chain folding may lead to rather complex nano-
meter-sized microstructures, depending on the
crystallization conditions. Spherulites consisting of
radially arranged twisted lamellae are preferred in
unstrained melts. However, if the melt is strained
during solidi®cation, dierent morphologies may
result, depending on the strain rate and the crystal-
lization temperature (i.e. the undercooling). High
crystallization temperatures and small strain rates
favor a stacked lamellar morphology [Fig. 20(a)],
high temperatures combined with high strain rates
result in needle-like arrangements [Fig. 20(b)]. Low
temperatures and high strain rates lead to oriented
micellar structures [Fig. 20(c)]. The transition
between these morphologies is continuous and mix-
tures of them may also be obtained under suitable
conditions [Fig. 20(d)]. The way to an additional
variety of nanostructured morphologies was opened
when multicomponent polymer systems, so-called
polymer blends, were prepared. Polymer blends
usually do not form spacially homogeneous solid
solutions but separate on length scales ranging from
a few nanometers to many micrometers. The fol-
lowing types of nanostructured morphologies of
polymer blends are formed in blends made up of
one crystallizable and one amorphous (non-crystal-
lizable) component: (I) The spherulites of the crys-
tallizable component grow in a matrix consisting
mainly of the non-crystallizable polymer. (II) The
non-crystallizable component may be incorporated
into the interlamellar regions of the spherulites of
the crystallizable polymer. The spherulites are
space-®lling. (III) The non-crystallizable component
may be included within the spherulites of the crys-
tallizable polymer forming domains having dimen-
sions larger than the interlamellar spacing. For
blends of two crystallizable components, the four
most common morphologies are: (I) Crystals of the
two components are dispersed in an amorphous
matrix. (II) One component crystallizes in a spheru-
litic morphology while the other crystallizes in a
simpler mode, e.g. in the form of stacked crystals.
(III) Both components exhibit a separate spherulitic
structure. (IV) The two components crystallize sim-
ultaneously resulting in so-called mixed spherulites,
which contain lamellae of both polymers.
2.1.9. Self-organized{nanostructured arrays
2.1.9.1.Non-polymeric NsM. A modi®ed Stranski±
Krastanov growth mechanism has been noticed to
result in self-organized (periodic) arrays of nano-
meter-sized crystallites. If a thin InGaAs layer is
grown on a AlGaAs substrate, the InGaAs layer
disintegrates into small islands once it is thicker
than a critical value [91]. These islands are spon-
taneously overgrown by a AlGaAs layer so that
Fig. 21. (a) Growth model of buried quantum dots of
InGaAs in AlGaAs [91]. (b) STM of the surface of a
AlGaAs crystal. Underneath the surface small quantum
dot crystals of In
0.2
Ga
0.4
As are buried (a). The crystallites
are periodically arranged [91].
{In this paper the term self-organization is used for
dynamic multistable systems generating, spontaneously, a
well-de®ned functional microstructure. It covers systems
exhibiting spontaneous emergence of order in either space
and/or time and also includes dissipative structures such
as non-linear chemical processes, energy ¯ow, etc. Systems
are called self-assembled if the spontaneously created
structure is in equilibrium [92±95].
GLEITER: NANOSTRUCTURED MATERIALS 17

nanometer-sized InGaAs crystals buried in AlGaAs
result (Fig. 21). The observations reported indicate
that the size, morphology and the periodic arrange-
ment of the buried islands are driven by a reduction
in the total free energy of the system. The driving
force for the periodic arrangement of the crystallites
seems to be the reduction in the strain energy of the
system (cf. Ref. [174]).
2.1.9.2.Polymeric NsM. Block copolymers consti-
tute a class of self-organized nanostructured ma-
terials. The macromolecules of a block copolymer
consist of two or more chemically dierent sections
that may be periodically or randomly arranged
along the central backbone of the macromolecules
and/or in the form of side branches. An example of
a block copolymer is atactic polystyrene blocks
alternating with blocks of polybutadiene or polyiso-
prene. The blocks are usually non-compatible and
aggregate in separate phases on a nanometer scale
if the copolymer is crystallized.
As an example of the various self-organized
nanostructured morphologies possible in such sys-
tems, Fig. 22 displays the morphologies formed in
the system polystyrene/polybutadiene as a function
of the relative polystyrene fraction. The large var-
iety of nanostructured morphologies that may be
obtained in polymers depending on the crystalliza-
tion conditions (cf. Section 2.1.8) and the chemical
structure of the macromolecules causes the proper-
ties of polymers to vary dramatically depending on
the processing conditions.
NsM formed by block copolymers seem to rep-
resent (metastable) equilibrium structures despite
the high excess energy stored in the interfaces
between the structural constituents, e.g. the poly-
styrene and the polybutadiene regions. The for-
mation of these interfaces results from the local
accumulation of the compatible segments of the
macromolecules. Hence, the only way to remove
these interfaces would be to generate a solid sol-
ution of the dierent segments forming the block
copolymer, e.g. a solid solution of polystyrene and
polybutadiene. However, the solid solution has a
higher free energy than the nanometer-scaled micro-
structure. Hence, due to the block structure of the
macromolecule, the microstructure of lowest free
energy that the system can form during crystalliza-
tion, is a nanometer-sized arrangement of regions
formed by chemically identical block segments.
These regions are separated by interfaces. In other
words, the nanometer-sized microstructure is
already ``implanted'' into the system by way of the
block copolymer synthesis of the macromolecules.
The only way to avoid the high density of interfaces
between the constituents would be to break the (co-
valent) bonds of the backbone of the polymer at
the points where the polystyrene and polybutadiene
blocks are joined together and by joining the seg-
ments of the same chemical structure into new
macromolecules of pure polystyrene or polybuta-
diene.
2.2. Equilibrium Nanostructured Materials
2.2.1. Supramolecular self-assembled structures.
Fig. 22. Electron micrographs of the morphologies of a copolymer consisting of polystyrene and poly-
butadiene blocks, as a function of the fraction of polystyrene blocks. The spacial arrangements of the
polystyrene and polybutadiene in the solidi®ed polymer are indicated in the drawings above the micro-
graphs [90].
18 GLEITER: NANOSTRUCTURED MATERIALS

Fig. 23. (a) Oligopyridine ligands with the ability to form helical structures. The ligands shown consist
of two, three, four or ®ve 2,2-bipyridine units [98]. (b) Formation of enantiomeric double-stranded heli-
cates from two to ®ve tetrahedrally coordinated metal ions [Cu(I), Ag(I), dotted circles]. (c) Structural
model deduced from X-ray diraction studies.
GLEITER: NANOSTRUCTURED MATERIALS 19

Supramolecules are oligomolecular species that
result from the intermolecular association of a few
components (receptors and substrates) following an
inherent assembling pattern based on the principles
of molecular recognition. Supramolecular self-
assembly{concerns the spontaneous association of
either a few or a large number of components
resulting in the generation of either discrete oligo-
molecular supermolecules or of extended polymole-
cular assemblies such as molecular layers, ®lms,
membranes, etc. In other words, speci®c phases
having well-de®ned microscopic molecular arrange-
ments and related macroscopic characteristics [97].
Fig. 24. Self-organized triple-helical structure. The structure comprises three ligand molecules each of
which contains three 2,2'-bipyridine units and three octahedrally coordinated Ni(II) ions [98, 100, 101].
Bottom: Structure of a trihelicate deduced by X-ray diraction.
{Self-assembly should be distinguished from templating.
Templating involves the use of a suitable substrate that
causes the stepwise assembly of molecular or supramolecu-
lar structures. These structures would not assemble in the
same way without the template.
20 GLEITER: NANOSTRUCTURED MATERIALS

Fig. 25. Top: Schematic diagram of the self-assembly of an inorganic lattice. The lattice consists of six
linear molecules each of which contains three bonding sites. The molecules are held together by nine
metal atoms attached to the bonding sites. Middle: Spontaneous formation of a 3 3 lattice comprising
six molecules each of which consists of two pyridine and two pyridazine groups. The bonding sites con-
tain two nitrogen atoms. The molecules are held together by nine tetrahedrally binding Ag(I) ions [98].
Bottom: Structure of a lattice of this type deduced from X-ray diraction data [98].
GLEITER: NANOSTRUCTURED MATERIALS 21

Self-assembly seems to open the way to nanos-
tructures, organized and functional species of nano-
meter-sized dimensions that bridge the gap between
molecular events and macroscopic features of bulk
materials. For a detailed discussion of this develop-
ment and of future perspectives, we refer to Ref.
[97]. The present review will be limited to outline
only those aspects of the ®eld [97, 98] that are
directly related to the synthesis of NsM.
2.2.2. Self-assembled inorganic architectures
2.2.2.1.Multiple helical metal complexes. Self-
assembled supramolecular structures may be gener-
ated if linear oligobipyridine ligands formed by two
or up to ®ve 2,2 '-bipyridine units are brought
together with Cu(I) ions. In the presence of Cu(I)
ions, the ligands spontaneously assemble into
double-stranded di- to pentahelicates [99] consisting
of two ligand strands wrapped around one another,
Cu(I) holding them together (Fig. 23). An import-
ant feature of this nanometer-sized structure is that
it allows the attachment of substituents to the bipy
units arranged in a helical fashion. If the Cu(I) ions
are replaced by Ni(II) ions, a triple helix results
consisting of three strands held together by three
Ni(II) ions (Fig. 24).
2.2.3. Multicomponent self-assembly of nanometer-
sized structures: racks, ladders, grids.
Multicomponent self-assembly allows the spon-
taneous generation of well-de®ned three-dimen-
sional molecular architectures in the form of racks,
ladders or grids. They are formed by the complexa-
tion of linear ligands or extended units with metal
ions in tetrahedral or octahedral sites. Figure 25
displays (as an example) a 3 3nm-sized grid made
up of two pyridine groups and one bipyridazine
unit connected by Ag(I) ions [102±104].
2.2.4. Self-assembled organic architectures. Self-
assembly of organic architectures utilizes the follow-
ing types of interaction between the components
involved: electrostatic interaction, hydrogen bond-
ing, van de Waals or donor±acceptor eects. If the
self-assembling molecules incorporate speci®c opti-
cal, electrical, magnetic, etc. properties, their order-
ing on a nanometer scale induces a range of novel
features.
Self-assembly by hydrogen bonding leads to two-
or three-dimensional molecular architectures which
often have a typical length scale of a few nano-
meters. The self-assembly of structures of this type
requires the presence of hydrogen-bonding subunits
Fig. 26. Self-assembly of a supramolecular ribbon from barbituric acid and 2,4,6-triaminopyrimidine
units [97, 105].
Fig. 27. Schematic diagram indicating some of the (many) possible nanometer-sized molecular struc-
tures to be synthesized by supramolecular polymer chemistry [107].
22 GLEITER: NANOSTRUCTURED MATERIALS

the disposition of which determines the topology of
the architecture. Ribbon, tape, rosette, cage-like
and tubular morphologies have been synthesized.
For example, Fig. 26 displays a supramolecular rib-
bon structure [105, 106]; with increasing control
being achieved over the molecular design of the
building subunits, a large variety of new two- and
three-dimensional architectures will be realized.
Supramolecular interactions play a crucial role in
the formation of liquid crystals and in supramolecu-
lar polymer chemistry. The latter involves the
designed manipulation of molecular interactions
(e.g. hydrogen bonding, etc.) and recognition pro-
cesses (receptor±substrate interaction) to generate
main-chain or side-chain supramolecular polymers
by self-assembly of complementary monomeric
components.
Figure 27 displays some of the dierent types of
polymeric superstructures that represent supramole-
cular versions of various species and procedures of
supramolecular polymer chemistry leading to ma-
terials with nanometer-sized microstructures.
Recognition eects are expected to play a major
role in the assembly and self-organization processes.
In the case of macromolecules, the supramolecular
association may be either intermolecular occurring
between the large molecules, or intramolecular
involving recognition sites located either in the
main chain or in side-chain appendages. The con-
trolled manipulation of the intermolecular inter-
action opens the way to the supramolecular
engineering of NsM.
2.2.5. Supramolecular materials and nanochemis-
try. The ability to control the way in which mol-
ecules associate allows the design of nanometer-
sized molecular architectures. Some implications for
nanotechnology appear to be obvious. For example,
surfaces with molecular recognition units will dis-
play selective surface binding leading to recog-
nition-controlled adhesion. Components derived
from biological structures are likely to yield bioma-
terials such as biomesogens, biominerals obtained
by using supramolecular assemblies as support for
inorganic particles in protein cages. Solid-state inor-
ganic self-assembled structures present tunnels,
cages and micropores where size, shape and spacing
may be tailored to serve as selective hosts for nano-
meter-sized crystals, nano-wires or related entities.
Self-assembly of inorganic architectures based on
organometallic building blocks yield various types
of frameworks such as Sb or Te chains, chains of
metal complexes, honeycomb or diamond arrays,
frameworks of metal chalcogenides with helical
structures, networks of interlocked rings of inor-
ganic and organic nature.
By increasing the size of the entities, nanochemis-
try approaches the length scale of lithography and
may thus turn out to be an important tool in pro-
ducing the next generation of devices.
2.2.6. DNA self-assembled nanostructures. As was
pointed out in the previous section, it is one of the
basic results of organic chemistry that intermolecu-
lar interaction is based on ®xation, molecular recog-
nition and coordination. In other words, molecular
binding is highly selective implying a complemen-
tary geometry that lays the basis for molecular rec-
ognition. The control of newly synthesized
molecular structures relies on this speci®city and
geometric constraints between the partners held
together by intermolecular interactions. With this
criterion in mind, DNA is an extremely favorable
``construction material'' for nanoscale structures. It
permits the informational character of macromol-
ecules of biological systems to be utilized. In fact,
the construction of sticky ®gures using branched
DNA molecules as building blocks has been demon-
Fig. 28. (a) Stable branched DNA molecule. (b) Sticky ends of the DNA molecules. (c) Assembly of
four sticky-ended DNA molecules into a square-shaped pattern [108, 109].
GLEITER: NANOSTRUCTURED MATERIALS 23

strated to open the way to the synthesis of a large
variety of DNA arrangements [108, 109]. The edges
of these arrangements consist of double-helical
DNA and the vertices correspond to the branch
points of stable DNA branched junctions. This
strategy is illustrated in Fig. 28. On the left-hand
side the stable branched DNA molecule is dis-
played. The ®gure in the middle indicates the sticky
ends. Four of these sticky-ended molecules are
assembled into a quadrilateral (right-hand side of
Fig. 28). The same technique has been applied to
synthesize two- and three-dimensional periodic nano-
meter-sized DNA structures [110, 111] with prede-
®ned topologies, e.g. cubes, truncated octahedrons,
etc. (Fig. 29). In order to synthesize macroscopic
periodic arrays made up of cubes, truncated octa-
hedrons, etc. DNA motifs that are more rigid than
branched junctions are required [112, 113]. Suitable
structures of this type seem to be double crossover
molecules. By attaching such molecules to the sides
of DNA triangles and deltahedra, two- and three-
dimensional nanometer-sized structures may be syn-
thesized.
2.2.7. Template-assisted nanostructured materials
and self-replication. The basic idea of templating is
to position the components into predetermined con-
®gurations so that subsequent reactions, deliberately
performed on the pre-assembled species or occur-
ring spontaneously within them, will lead to the
generation of the desired nanoscale structure. The
templating process may become self-replication if
Fig. 29. Cube and truncated octahedron assembled of DNA molecules [110, 111].
Fig. 30. Transmission electron micrograph images of (a) the lamellar morphology, (b) the cubic phase
with Ia3d symmetry viewed along its (111) zone axis, and (c) the hexagonal phase viewed along its
(001) zone axis of the silica/surfactant nanostructured composites by co-assembly bars 30 nm[121].
24 GLEITER: NANOSTRUCTURED MATERIALS

spontaneous reproduction of one of the initial
species takes place by binding, positioning and con-
densation [114±116].
Inorganic and organic templating has been used
for the generation of nanometer-sized polymer
arrangements displaying molecular recognition
through imprinting, i.e. a speci®c shape and size-
selective mark on the surface or in the bulk of the
polymer. Imprinting into polymeric materials has
been achieved by either a covalent or a noncovalent
approach. The former uses the reversible covalent
binding of the substrate to the monomer [117, 118].
In the latter, suitable functionalized monomers are
left to prearrange around the substrate. Removal of
the imprint molecule from the polymer leaves recog-
nition sites that are complementary in geometry
and functionality.
Mesophase templating represents a special case
that appears to be of considerable signi®cance for
the development of this area. Silica precursors when
mixed with surfactants result in polymerized silica
``casts'' or ``templates'' of commonly observed sur-
factant±water liquid crystals. Three dierent meso-
porous geometries have been reported [119±122],
each mirroring an underlying surfactant±water
mesophase (Fig. 30). These mesoporous materials
are constructed of walls of amorphous silica, only
about 1 nm thick, organized about a repetitive
arrangement of pores up to 10 nm in diameter. The
resulting materials are locally amorphous (on
atomic length scales) and periodic on larger length
scales.
The availability of highly controlled pores on the
1±10 nm scale oers opportunities for creating unu-
sual composites, with structures and properties
unlike any that have been made to date. However,
the eective use of mesoporous silicates requires
two critical achievements: (i) controlling the meso-
phase pore structure; and (ii) synthesizing large
monolithic and mesoporous ``building blocks'' for
the construction of larger, viable composite ma-
terials. Although important information exists on
some aspects of controlling the mesoporous struc-
ture [119, 123], large-scale structures have not yet
been constructed.
The synthesis scheme of silica-based mesostruc-
tured materials [119, 122, 123] using assemblies of
surfactant molecules to template the condensation
of inorganic species has been extended to include a
wide variety of transition metal oxides [124] and,
recently, cadmium sul®de and selenide semiconduc-
tors [125]. Although the exact mechanism for this
type of mineralization is still controversial [122],
this technique holds great promise as a synthetic
scheme to produce nanostructured materials with
novel thermal, electronic, optical, mechanical and
selective molecular transport properties. Continuous
mesoporous silicate ®lms can be grown on a variety
of substrates [126], e.g. mica, graphite or block
copolymers. In fact, nanostructured BaTiO
3
®lms
have been grown on a polybutadiene±polystyrene
triblock copolymer [127].
A special case is the reproduction of the template
itself by self-replication. Reactions occurring in
organized media (molecular layers, mesophases, ves-
icles) [128±142] oer an entry into the ®eld.
Molecular imprinting processes represent a way of
copying the information required for recognition of
the template. Self-replication takes place when a
molecule catalyses its own formation by acting as a
template for the constituents, which react to gener-
ate a copy of the template. Such systems display
autocatalysis and may be termed informational or
non-informational depending on whether or not
replication involves the conservation of a sequence
of information [143]. Several self-replicating systems
have been developed in which the template is gener-
ated from two components. The ®rst one consists of
the replication of a self-complementary or palindro-
mic hexanucleotide CCGCGG from two trinucleo-
tides CCG and CGG in the presence of a
condensing agent [144±150]. The more recent ones
involve: (i) the formation of an amide bond
between two building blocks undergoing selective
hydrogen bonding with the template [151±154]; and
(ii) an amine and aldehyde to imine condensation
between components interacting with the template
via ion-pairing between an amidinium cation and a
carboxylate anion [155, 156]. Self-replication of oli-
gonucleotides in reverse micelles has also been
reported [157].
Supramolecular templating processes seem to
provide an ecient route for the synthesis of nano-
porous materials used as molecular sieves, catalysts,
sensors, etc. In fact, mesoporous bulk [119, 120,
158, 159] and thin-®lm [160±162] silicates with pore
sizes of 2±10 nm have been synthesized by using
micellar aggregates of long-chain organic surfactant
molecules as templates to direct the structure of the
silicate network. Potential applications of these mol-
ecular-sieve materials are catalysts, separation mem-
branes and components of sensors. Mesoporous
oxides have been synthesized by similar means. In
these mesoporous oxides, transition metals partially
[163] and/or fully [164±168] substitute silicon.
Templating with organic molecules has also been
long used for the synthesis of microporous ma-
terialsÐsynthetic zeolitesÐwith pore sizes as small
as 0.4±1.5 nm. In this case, the organic molecules
are shorter-chain amphiphiles which act as discrete
entities around which the framework crystallizes
[169±171]. It was recently shown [172] that such
short-chain molecules can aggregate into supramo-
lecular templates when they form bonds with tran-
sition-metal (niobium) alkoxides, and that in this
way they can direct the formation of transition-
metal oxides with pore sizes of less than 2 nm.
These pore sizes, which result from the smaller di-
ameter of micellar structures of the short-chain
amines relative to the longer-chain surfactants used
GLEITER: NANOSTRUCTURED MATERIALS 25

for the synthesis of mesoporous materials, qualify
the resulting molecular sieves as microporous, even
though the supramolecular templating mechanism is
similar to that used to make the mesoporous ma-
terials. This approach extends the supramolecular
templating method to aord microporous tran-
sition-metal oxides.
Figure 31 illustrates schematically the synthesis of
hexagonally packed transition-metal oxide mesopor-
ous molecular sieves for Nb [172]. It involves the
following ®ve steps: (1) partial hydrolysis of nio-
bium ethoxide at low temperatures; (2) introduction
of hexylamine; (3) self-assembly of hexylamines as
supramolecular templates; (4) condensation and
crystallization of the inorganic framework at high
temperatures; and (5) amine removal by acidic
washes. Figure 32 illustrates the surfactant removal
process and the ®nal mesoporous structure for a Ta
metal oxide mesoporous material [173]. The N±Ta
bonds are cleaved by protolysis at ÿ788C in the
®rst step. The protonated surfactant is then
removed by washing the material in dry 2-propanol
(IPA) at ambient temperature for 24 h. Washing
with water gives the ®nal hydrated product.
Fig. 31. Schematic illustration of the synthesis of microporous transition-metal (Nb) oxide molecular
sieves by supramolecular templating: (1) partial hydrolysis of niobium ethoxide at low temperatures; (2)
introduction of hexylamine; (3) self-assembly of hexylamines as supramolecular templates at ambient
temperature (RT); (4) condensation and crystallization of inorganic framework at 1808C; and (5) amine
removal by acidic washes [172].
Fig. 32. Illustration of the surfactant removal process from hexagonally packed mesoporous Ta oxide
molecular sieves by a treatment with tri¯ic acid [173]. The N±Ta bond is cleaved by protolysis at
ÿ788C in the ®rst step. The protonated surfactant is then removed by washing the material in dry 2-
propanol (IPA) at ambient temperature for 24 h. Washing with water gives the ®nal hydrated product.
26 GLEITER: NANOSTRUCTURED MATERIALS

AcknowledgementsÐI am indebted to Drs D. Wolf, S.
Phillpot and P. Keblinski for numerous contributions and
a most stimulating cooperation over may years. The ®nan-
cial support by the Alexander von Humboldt Foundation,
the Max Planck Society and the Forschungszentrum
Karlsruhe is gratefully acknowledged.
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