Nanostructured State

The essential defects of both nanostructured and micro-crystalline materials are the intergrain boundaries, which are the junctions between monocrystalline regions in one-phase materials and interphase boundaries in multiphase materials. Side by side with stacking faults and twin boundaries, the intergrain/interphase boundaries are classified as two-dimensional (or planar) defects of the crystal structure. The density of the boundaries in nanocomposites can reach 1019 cm-3 [176]. The high density of the boundaries transforms a microcrystalline structure, which has grain sizes on the micrometer scale, into a new type of structure, the so-called nanostructured materials [177-182], which represent a certain "symbiosis" of the crystal structure and the

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Encyclopedia of Nanoscience and Nanotechnology Edited by H. S. Nalwa Volume 10: Pages (191-236)

planar defects in the form of intergrain/interphase boundaries. Such coexistence of a crystal structure and its planar defects usually results in phenomenal properties, which are radically different from microcrystalline and amorphous materials of the same composition.

The properties of nanocomposites can be changed into either their strengthening such as diffusivity, toughness, and hardness [183] or their slackening such as density and ther-moconductivity [183, 184] in comparison with coarse-grained materials of the same composition. Modeling and prediction of the functional properties of nanocomposites is a very important issue as well [185-190]. For example, tantalum carbide and hafnium nitride of NaCl-type structure with stoi-chiometry of TaC0 85 and HfN0 75 have a hardness of 12 GPa and 16 GPa, respectively. However, close-packed phases of the same stoichiometry, that is, £-Ta4C3 and £-Hf4N3, have a hardness of approximately 1 GPa and 8 GPa, respectively [191]. The point is that stacking faults are inherent elements of the £-Ta4C3 and £-Hf4N3 crystal lattices [192-195], that is, three stacking faults per unit cell [192]. The well-ordered stacking faults drastically change the physical properties of such materials [196].

To obtain the nanostructured state, the dimensions of the morphological elements (i.e., the average diameter of grains, thickness of layers, etc.), which form the nanostruc-tured state [176, 179, 180, 197-202], should be within the nanoscale range. The nanoscale sizes of the morphological elements usually cover the range between 2 and 100 nm (1 nm = 10-9 m).

As is well known [197, 203-209], when the sizes of the morphological elements become comparable with the characteristic distances related to appropriate physical phenomena (e.g., short-circuit diffusion paths, size of magnetic domains, the effective carrier de Broglie wavelength, Bohr radii of the excitonic states, the electron/photon mean free path, dimensions of defects, a wavelength of light, the superconducting coherence length, etc.), the physical phenomena manifest themselves in nanoscale sizes and the corresponding anomalous features of the nanocomposites may be revealed, for example, diffusion processes [210-216], electrical resistivity [217-219], specific heat [220, 221], thermal expansion [222], optical transparency [197], magnetic properties [177, 223-232], superconductivity [233-235], the group velocities of acoustic phonons [236], laser middle-infrared emission [237, 238], resonant tunneling [239], critical fields/currents in superconductors [240], change in color [241], a solid solubility [242, 243], thermal conductivity [244-246], optical absorption spectra [247, 248], nanosize-dependent luminescence [249, 250], metastable phase formation [251, 252], corrosion resistance [253-255], mechanical properties [256-263] increasing in hardness particularly, and so on. As to coatings with high hardness, when the grain/layer sizes, core of dislocation, sizes of dislocation sources, and boundary thickness become comparable with each other on a nanometer scale, some nanostructured coatings exhibit intriguing high hardness [1]. This brief enumeration demonstrates the variety of properties that depend on morphological elements when they reach nanoscale sizes.

In nature, some living organisms reveal the ability to reproduce hybrid organic-inorganic nanocomposites in the form of shells containing inorganic nanocrystals and some percentage of organic binders [264-268]. The shells of the living organisms represent nanocomposite materials possessing high toughness. A few examples of such nanocomposites are demonstrated below. Strombus gigas shells consist of aragonite (i.e., the metastable orthorhombic polymorph of CaCO3) in the form of nanolamellae having a length of 1-20 nm and an average width of 5 nm [264]. Red abalone shells consist of a hybrid ceramic-polymer nanocomposite having CaCO3 crystal sizes in the range of 200-300 nm and a superplastic organic binder 20-30 nm thick [265]. Cristaria plicata shells are built from three layers [266]; one of them, the pearl layer, is constructed with many ultrathin hard slices, which have thickness of about 100 nm. The shells of the bivalve mollusk Cristaria plicata are ceramic nanocomposite consisting of a polygonal-shaped aragonite (CaCO3) platelet approximately 500 nm thick. The platelets are connected by a thin (~30 nm) organic layer of protein-polysaccharide binder [269]. The fine and properly organized nanostructure of the shells has been adapted as an example to develop similar synthetic nanomaterials [270, 271]. For example, the hardness of TiC/Fe nanolay-ered composite coatings constructed similarly to the shells can reach a hardness of 42 GPa [272].

Here the nanostructured composite (or nanocomposite) coatings in question are generally classified into two groups according to the dimensions of the morphological elements. If the morphological element consists of alternating layers of two different materials within a nanoscale thickness, these coatings are termed nanolayered composite coatings. If the morphological element consists of nanograins, the coatings are termed nanocrystalline composite coatings. In general, the term nanostructured composite coatings includes both types of coatings. Ramified classifications of nanostructured materials can be found elsewhere [273-276].

The first group unites nanolayered composite coatings, or so-called heterostructures or superlattices [277]. Super-lattices, which are defined as epitaxial structures inheriting the crystallographic orientation of the prelayer [278], provide a more narrow definition than nanolayered composite coatings. The term nanolayered composite coatings is chosen here because it is the most coincident terminology for nanoscience.

As a rule, nanolayered composite coatings are two-phase nanocomposites consisting of alternating nanolayers of two functionally different materials denoted A and B (Fig. 1). The total thickness (hA + hB) of the two alternating nanolay-ers, called the bilayer repeat period (A) [277], amounts to a few dozen nanometers (practically up to 40 nm). Important parameters for the description of nanolayered composites include [279]:

• Thickness of bilayer repeat period

• Thickness ratio of nanolayers within the bilayer repeat period

• Degree of interdiffusion and roughness at interfaces

Two other dimensions (length and width) of the nanolay-ers are unlimited and significantly larger as compared with their thickness. A few hundreds of such alternating nanolay-ers of different materials create a nanolayered composite coating. The hardness of this nanolayered "sandwich" is considerably enhanced when the bilayer repeat period has

Figure 1. Draft of two-dimensional representation of nanolayered composite coatings: (a) nanolayered composite coatings with monocrys-talline structure (monocrystalline type) and (b) nanolayered composite coatings with nanocrystalline structure (nanocrystalline type). Reprinted with permission from [175], G. M. Demyashev et al., in "Handbook of Organic-Inorganic Hybrid Materials and Nanocomposites" (H. S. Nalwa, Ed.), Vol. 2, Chap. 13. American Scientific Publishers, Stevenson Ranch, CA, 2003. © 2003, American Scientific Publishers.

Figure 1. Draft of two-dimensional representation of nanolayered composite coatings: (a) nanolayered composite coatings with monocrys-talline structure (monocrystalline type) and (b) nanolayered composite coatings with nanocrystalline structure (nanocrystalline type). Reprinted with permission from [175], G. M. Demyashev et al., in "Handbook of Organic-Inorganic Hybrid Materials and Nanocomposites" (H. S. Nalwa, Ed.), Vol. 2, Chap. 13. American Scientific Publishers, Stevenson Ranch, CA, 2003. © 2003, American Scientific Publishers.

an optimal value for each coupled material forming the nanolayered coating.

It is necessary to distinguish nanolayered composite coatings from both monocrystalline and nanocrystalline types of nanolayered composites (Fig. 1). The discrepancy is similar to the difference between monocrystalline and polycrys-talline states. The monocrystalline type (1) has a monocrystalline structure of nanolayers and (2) exhibits an epitaxial crystalline relationship between joined nanolayers [280]. In the case of polycrystalline-type nanocomposites, every nanolayer has, first, a nanoscrystalline structure with a number of nanograin boundaries and, second, interfaces between jointed nanolayers, which represent an incoherent interphase boundary.

The second group of nanocomposites unites nanocrys-talline composite coatings (Fig. 2), which are usually a composition of two or more phases. The term nanocrys-talline composite coatings refers to coatings that consist of nanocrystals/nanograins (nc-A) embedded predominantly in an amorphous or low-dimensional matrix (a-B) of another

Figure 2. Cross-sectional sketch of as-deposited nanocrystalline composite coatings, where nc-A is nanocrystalline phase A and a-B is amorphous phase B. Reprinted with permission from [281], C. Mitterer et al., Surf. Coat. Technol. 120-121, 405 (1999). © 1999, Elsevier Science.

material. Interphase boundaries are inherent elements of nanostructures in multiphase nanocomposites.

On an atomic scale, if atoms are represented by circles (Fig. 3), a two-dimensional representation of nanocrystalline structures can be considered as a mixture of two structural components [176, 283, 284]: nanograins with a crystal lattice of ordered atoms, denoted by black circles, and intercrystal-lite boundaries, depicted with white circles in Figure 3. The average grain sizes of the nanocrystalline coatings vary from 2 to 100 nm and can contain from 102 to 108 atoms [285].

Intergrain boundaries are inherent elements of the structure of one-phase coatings. A lot of research has been devoted to intergrain boundaries in nanocomposites [182, 286-297]. The intergrain boundary width of nanocrystalline materials is usually between 0.5 and 1.2 nm [178, 282, 298, 299]. The average atomic density of the boundaries is relatively lower than that in a crystal lattice of nanograins. Atoms in the boundaries, which vary from special close-packed boundaries to widely spaced ones [300, 301], display a wide range of interatomic spacings. The average density of the boundaries can vary from 70% to 85% of the perfect crystal lattice [176], which is from 15% to 30% less than the

Figure 3. Schematic representation of a nanocrystalline structure on atomic scale: individual nanograins (black circles represent bulk atoms) and nanograin boundaries (white circles represent grain atoms). Reprinted with permission from [282], H. Gleiter, Prog. Mater. Sci. 33, 223 (1989). © 1989, Elsevier Science.

Figure 3. Schematic representation of a nanocrystalline structure on atomic scale: individual nanograins (black circles represent bulk atoms) and nanograin boundaries (white circles represent grain atoms). Reprinted with permission from [282], H. Gleiter, Prog. Mater. Sci. 33, 223 (1989). © 1989, Elsevier Science.

atomic density in the perfect crystal structure, depending on the type of bonds encountered in the crystal lattice [197]. The properties of the grains, such as transport, thermody-namic, and mechanical properties, differ from the properties of the boundaries. Therefore, nanocrystalline coatings can be treated as two-component structures, that is, a mixture of nanograins and grain boundaries [284, 302], even in the case of single-phase nanocomposites.

A reduction in grain size leads to an increasing volumetric portion of atoms located in the boundaries. It was found [303] that the volumetric fraction of atoms in the boundaries is 87.5% for 2-nm grain materials, approximately 44% for 3-nm grain materials, about 50% for 5-nm grain materials, approximately 30% for 10-nm grain materials, and only 3% for 100-nm grain materials.

The portion of boundaries (C) in a bulk material can be estimated from [298]:

where A is the grain boundary thickness and d is the average grain size. Considering the grains as regular 14-sided tetrakaidecahedrons with the hexagonal faces of the grain boundaries, it was calculated [303] that the intercrystalline (ic) volumetric fraction is

Vk = 1 - l(d - A)/df the volumetric portion of the grain boundaries (gb) is

and the volumetric part of the triple junctions (tj) is

Vtj = V ic V gb where d is the average grain diameter and A is the average size of the grain boundaries. Note that d > A.

Figure 4 displays the dependence of Vic, Vgb, and Vtj on the average grain diameter. The volumetric fraction of the triple junctions, which are defined as intersections of three (or more) adjoining grain boundaries [198, 304, 305], becomes an important element of the nanostructure [256, 306]. Triple junctions are considered [307-311] as disclina-tions depending on the specific crystallographic arrangement of adjoining nanograins. The atomic structure of the boundaries in nanocrystalline materials differs from the atomic structure of the boundaries in coarse-grained microcrys-talline materials by rigid-body relaxation [273]. It is clear from Figure 4 why nanostructured materials have been defined as having grain sizes (at least in one dimension) between 2 and 100 nm.

With decreasing grain size, the interatomic distances in the crystal lattice of the nanograins increase, and, as consequence, the density of the nanograins decreases [312, 313]. It was experimentally demonstrated [314, 315] that the crystal lattice expansion mainly exists near the grain boundaries. The crystal lattice expansion of the nanocomposites could be conditional upon nonlinear effects caused by the existence of stress fields [316]. The "x-3 law" for the stress field and a model of the crystal lattice expansion of nanostruc-tured materials caused by vacancies and vacancy clusters

Figure 4. Influence of nanograin size on the calculated volumetric portion of intercrystalline regions, grain boundaries, and triple junctions, assuming an average grain boundary thickness of 1 nm. Reprinted with permission from [198], C. Suryanarayana et al., J. Mater. Res. 7, 2114 (1992). © 1992, Materials Research Society.

Figure 4. Influence of nanograin size on the calculated volumetric portion of intercrystalline regions, grain boundaries, and triple junctions, assuming an average grain boundary thickness of 1 nm. Reprinted with permission from [198], C. Suryanarayana et al., J. Mater. Res. 7, 2114 (1992). © 1992, Materials Research Society.

have been proposed [317]. The calculated deviation of lattice parameters for nanograins [317] in nanocrystalline Ni coatings was found to be in good agreement with the experimental data [312]. The maximum elastic modulus due to lattice distortion was estimated for an optimal nanograin size of 15-20 nm [318].

Nanocomposites belong to nonequilibrium (metastable) structures [211, 319, 320] formed during extreme conditions of synthesis. It was evaluated for Ni-P [321] that the release of heat energy was 339 mJ for 5-nm grain materials, whereas, for 5-^m grain materials, the heat energy released was only about 0.7 mJ. Similar dependence was obtained for the SiC fiber nanocomposite with an average grain size of approximately 3 nm [322].

Therefore, nanocomposites share the following fundamental features [323]:

• Grains/layers confined to less than 100 nm in at least one dimension.

• Significant atomic fraction associated with interfaces and triple junctions.

• Interaction between the constituent domains.

The nanostructured state was considered [282] a new state of solids equally with

• Coarse-grained microcrystallines

• Monocrystals

In particular, the important characteristics of nanocompos-ites that influence hardness include [198]:

• Grains (size, distribution, and morphology)

• Nature and morphology of grain/interphase boundaries

• Structure of intercrystalline regions

• Local composition of nanogains and interfaces

• Porosity of nanostructured composites

• Impurities trapped due to the processing medium

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