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• Redox potential Redox systems
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One of the widespread methods for obtaining metal nanoparticles is laser evaporation of atoms from the surface (Fig. 33).

Rice. 33. Installation for obtaining metal nanoparticles by laser evaporation of atoms from the surface.

The study of the mass spectra of the flow of the resulting lead nanoparticles showed that clusters of 7 and 10 atoms are more likely than others. This means that they are more stable than clusters of other sizes. These numbers (for other elements they may have different meanings) are called electronic magic numbers. Their presence makes it possible to consider clusters as superatoms, which led to the appearance of the "jelly model" for the description of metal clusters.

In the jelly model, a cluster of atoms is treated as one large atom. The positive charge of the nucleus of each cluster atom is considered to be uniformly distributed over the ball with a volume equal to that of the cluster. Such a spherically symmetric potential well models the interaction potential of electrons with nuclei. Thus, the energy levels of the cluster can be obtained by solving the Schrödinger equation for the described system, similarly to how it is done for the hydrogen atom. On fig. 33 shows energy level diagrams of the hydrogen atom and a system with a spherically symmetric positive charge distribution. Superscripts refer to the number of electrons filling a given energy level. Electronic magic numbers correspond to the total number of superatom electrons at which the upper energy level is completely filled. Note that the order of the levels in the jelly model differs from that in the hydrogen atom. In this model, magic numbers correspond to clusters with sizes such that all levels containing electrons are completely filled.

Rice. 34. Comparison of the energy levels of a hydrogen atom and a small-atom cluster in the jelly model. The electronic magic numbers of He, Ne, Ar, Kr atoms are 2, 10, 18, 36, respectively (Kr levels are not shown in the figure), and 2, 18, 40 for clusters

An alternative model used to calculate the properties of clusters treats them as molecules and applies existing molecular orbital theories, such as density functional theory, to the calculations.

The crystal structure of a nanoparticle is usually the same as that of the bulk material, but with a slightly different lattice parameter (Fig. 35).

X-ray diffraction for an aluminum particle with a size of 80 nm shows the unit cell of the fcc lattice shown in Fig. 35 a, the same as for bulk aluminum. However, in some cases, small particles with sizes< 5 нм могут иметь другую структуру. Интересно рассмотреть алюминиевый кластер из 13 атомов, так как это - магическое число. На рис. 35 б показаны три возможных расположения атомов в кластере. На основе критерия максимизации количества связей при минимизации объема, а также того факта, что в объеме структурой алюминия является ГЦК, можно ожидать, что структура такой наночастицы также будет ГЦК. Однако вычисления молекулярных орбиталей по методу функционалов плотности предсказывают, что наименьшую энергию имеет икосаэдрическая форма, то есть вероятно изменение структуры.

Rice. 35. Geometric structure. (a) - Unit cell of bulk aluminum, (b) - Three possible structures of the Al13 cluster

It should be noted that the structure of an isolated nanoparticle may differ from a ligand-stabilized structure.

Clusters of different sizes have different electronic structures and, accordingly, different distances between levels. The average energy will be determined not so much by the chemical nature of the atoms as by the particle size.

Due to the fact that the electronic structure of a nanoparticle depends on its size, the ability to react with other substances should also depend on its size. This fact is of great importance for the design of catalysts.

Nanoclusters and nanocrystals are nanosized complexes of atoms or molecules. The main difference between them lies in the nature of the arrangement of the atoms or molecules that form them, as well as the chemical bonds between them.

According to the degree of structure ordering, nanoclusters are divided into ordered, otherwise called magic, and disordered.

In magic nanoclusters, atoms or molecules are arranged in a certain order and are quite strongly interconnected. This ensures a relatively high stability of magical nanoclusters, their immunity to external influences. Magic nanoclusters are similar to nanoclusters in their stability. At the same time, in magic nanoclusters, atoms or molecules in their arrangement do not form a crystal lattice typical of nanocrystals.

Disordered nanoclusters are characterized by a lack of order in the arrangement of atoms or molecules and weak chemical bonds. In this they differ significantly from both magical nanoclusters and nanocrystals. At the same time, disordered nanoclusters play a special role in the formation of nanocrystals.

4.1. nanoclusters

4.1.1. Ordered nanoclusters

The peculiarity of ordered, or magic, nanoclusters is that they are characterized not by arbitrary, but by strictly defined, energetically most favorable - the so-called magic numbers of atoms or molecules. As a consequence, they are characterized by a nonmonotonic dependence of their properties on dimensions, i.e. on the number of atoms or molecules that form them.

The increased stability inherent in magic clusters is due to the rigidity of their atomic or molecular configuration, which

satisfies tight packing requirements and conforms to certain types of complete geometries.

Calculations show that, in principle, the existence of various configurations of densely packed atoms is possible, and all these configurations are various combinations of groups of three atoms, in which the atoms are located at equal distances from each other and form an equilateral triangle (Fig. 4.1).

Rice. 4.1. Configurations of nanoclusters of N close-packed atoms

a – tetrahedron (N = 4); b – trigonal bipyramid (N = 5) as a combination of two tetrahedra;

in – square pyramid ( N = 5); (d) tripyramid (N = 6) formed by three tetrahedra; (e) octahedron (N = 6); (f) pentagonal bipyramid (N = 7); (g) a star-shaped tetrahedron (N = 8) is formed by five tetrahedra – one more tetrahedron is attached to each of the 4 faces of the central tetrahedron; h - icosahedron (N = 13) contains a central atom surrounded by 12 atoms united in 20 equilateral triangles, and has six

axes of symmetry of the 5th order.

The simplest of these configurations, corresponding to the smallest nanocluster consisting of four atoms, is the tetrahedron (Fig. 6.1, a), which is included as an integral part in other, more complex configurations. As seen in fig. 6.1, nanoclusters can have crystallographic symmetry, which is characterized by fivefold symmetry axes. This fundamentally distinguishes them from crystals, the structure of which is characterized by the presence of a crystal lattice and can only have symmetry axes of the 1st, 2nd, 3rd, 4th and 6th orders. In particular, the smallest stable nanocluster with one axis of symmetry of the 5th order contains seven atoms and has the shape of a pentagonal bipyramid (Fig. 4.1, f), the next stable configuration with six axes of symmetry of the 5th order is a nanocluster in the form of an icosahedron of 13 atoms ( Fig. 4.1, h).

Close-packed metal configurations can occur in the so-called ligand metal nanoclusters, which are based on a metal core surrounded by a shell of ligands, i.e. units of molecular compounds. In such nanoclusters, the properties of the surface layers of the metal core can change under the influence of the surrounding ligand shell. Such influence of the external environment does not take place in ligandless nanoclusters. Ligand-free metal and carbon nanoclusters are the most common among them, which can also be characterized by a close packing of their constituent atoms.

In ligand metal nanoclusters, the nuclei consist of a strictly defined magic number of atoms, which is determined by the formula

				(10n 3	15n2	11n3) ,

where n is the number of layers around the central atom. According to (6.1), the set of magic numbers corresponding to the most stable nuclei of the nanoclast

ditch, can be as follows: N = 13, 55, 147, 309, 561, 923, 561, 1415, 2057,

2869 etc. The minimum size nucleus contains 13 atoms: one atom in the center and 12 in the first layer. Known, for example, are 13-atom (single-layer) nanoclusters (NO3 )4 , 55-atom (two-layer) nanoclusters Rh55 (PPh3 )12 Cl6 , 561-atom (five-layer) nanoclusters Pd561 phen60 (OAc)180 (phen - phenatrolin), 1415 -atomic (seven-layer) nanoclusters Pd1415 phen 60 O1100 and others. As seen in fig. 6.1h, the configuration of the smallest stable ligand metal nanocluster with N = 13 has the shape of a 12-vertex polyhedron - an icosahedron.

The stability of ligand-free metal nanoclusters is generally determined by two series of magic numbers, one of which is related to the geometric factor, i.e., dense packing of atoms (as in ligand nanoclusters), and the other one with a special electronic structure of nanoclusters, consisting of two subsystems: positively charged ions united into a nucleus and electrons surrounding them, which form electron shells similar to electron shells in an atom. The most stable electronic configurations of nanoclusters are formed when the electron shells are completely filled, which corresponds to certain numbers of electrons, the so-called “electronic magic” numbers.

Rice. 4.2. An array of Si nanoislands,

obtained by sputtering five monatomic Si layers onto a Si (100) surface coated with a thin layer of SiO 2

STM image

The stability of carbon nanoclusters is due to the magic numbers of carbon atoms. There are small carbon nanoclusters (with N< 24) и большие (с N ≥ 24) . Малые нанокластеры проявляют устойчивость при нечетных магических числах (N = 3, 7, 11, 19, 23), среди них наиболее стабильными являются нанокластеры с N = 7, 11, 19, 23. В свою очередь, большие нанокластеры проявляют устойчивость при четных магических числах (N = 24, 28, 32, 36, 50, 60, 70, …), среди них наиболее стабильными являются нанокластеры с N = 60 и 70. Углеродные нанокластеры с N ≥ 24 иначе называют фуллеренами, которые принято обозначать символом СN . Таким образом, наиболее стабильными являются фуллерены С60 и С70 . Следует заметить, что фуллерены также рассматриваются как полиморфные модификации углерода (наряду с графитом и алмазом). Это означает, что они представляют собой особые по структуре нанокристаллы. Итак, можно сказать, что на сегодняшний день имеется двойственный подход к определению фуллеренов – как нанокластеров, с одной стороны, и как нанокристаллов, с другой. Более того, довольно часто фуллерены рассматривают как гигантские молекулы углерода, что может быть обусловлено наличием аналогии в структуре фуллеренов и сложных молекул ряда органических соединений, характеризующихся пространственной конфигурацией, а также в характере проявления химических свойств тех и других.

Magic nanoclusters can form under various conditions, both in the bulk of the condensing medium and on the substrate surface, which can have a certain effect on the nature of nanocluster formation.

Let us consider, as an example, the features of the formation of nanosized islands during the deposition of foreign atoms on the surface of a solid body. The deposited atoms migrate over the surface and, connecting with each other, form islands. This process is stochastic (random) in nature. Therefore, the islands differ in size and are unevenly distributed over the surface.

measured (Fig. 4.2). However, under certain conditions, it is possible to achieve a very desirable effect in practical terms, when all the islands are of the same size and form a homogeneous array, and ideally, an ordered periodic structure. In particular, if about 1/3 of a monoatomic aluminum layer is deposited on an atomically clean Si (111) silicon surface at a temperature of about 550°C under conditions of ultrahigh vacuum (~10–10 Torr), then an ordered array of nanoclusters is formed on the surface - islands of atomic size (Fig. 4.3). All nanoclusters turn out to be identical: each of them includes a strictly defined number of Al atoms equal to 6, which is magic for nanoclusters. In addition, Al atoms interact with Si atoms. As a result, a configuration consisting of six Al atoms and three Si atoms is formed. Thus, special nanoclusters of the Al6 Si3 type are formed.

Rice. 4.3. An ordered array of magic clusters obtained on the surface

Si (111) as a result of self-organization of deposited Al atoms

on the left – STM image illustrating the general view of the array; on the right is a diagram of the atomic structure of magic clusters: each cluster consists of six

three Al atoms (outer circles) and three Si atoms (inner circles).

The formation of magic nanoclusters in this case is explained by two important factors. The first factor is due to the special properties of the configuration of Al and Si atoms, in which all chemical bonds are closed, due to which it has a high stability. When one or more atoms are added or removed, such a stable configuration of atoms does not arise. The second factor is due to the special properties of the Si (111) surface, which has an ordering effect on the nucleation and growth of nanoislands. In this case, the size of the magic nanocluster

Al6 Si3 successfully coincides with the size of the unit cell of the surface, due to which exactly one nanocluster is placed in each half of the cell. As a result, an almost perfect ordered array of magic nanoclusters is formed.

4.1.2. Disordered nanoclusters and the lower limit of nanocrystallinity

Disordered nanoclusters are unstable formations similar in structure to the so-called van der Waals molecules - clusters of a small number of molecules (atoms) that arise due to weak interaction due to van der Waals forces. They behave like liquids and are prone to spontaneous decay.

Disordered nanoclusters play a key role in the formation of nanocrystals, actually being prototypes of nanocrystals, otherwise called crystalline nanoparticles, which are characterized by an ordered arrangement of atoms or molecules and strong chemical bonds - like massive crystals (macrocrystals).

Nanocrystals can be up to 10 nm or more in size and, accordingly, contain a fairly large number of atoms or molecules (from several thousand to several hundred thousand or more). As for the lower limit of the size of nanocrystals, this issue requires special discussion. In this regard, the analysis of cluster mechanisms of crystallization is of particular interest.

Consider, as an example, the crystallization of a supersaturated solution. There are three main models of nucleation: fluctuation (FMN), cluster (CMN) and fluctuation-cluster (FCMZ)

- in accordance with what is accepted in each of them as the primary source of the formation of nuclei.

According to the FMZ, nuclei arise as a result of fluctuations in the solution density, i.e. The immediate source of nuclei are fluctuation clusters of atoms of the dissolved substance – local areas of the solution with a volume V f with an increased density ρ f > ρ m , where ρ m is the density in the main volume of the solution that is not subject to fluctuations – the matrix. In the general case, fluctuations lead to the formation of nanoclusters of various volumes V c . Nanoclusters with V c< V c(cr) , где V c(cr) – некоторый критический

volume, immediately decay into the original atoms. Nanoclusters with V c > V c(cr) become stable nuclei capable of continuing their growth. Nanoclusters with V c = V c(cr) are critical nuclei that are in a state of unstable equilibrium: they decay or turn into stable nuclei.

According to CMH, nuclei are formed from nanoclusters, which, in turn, arise from fluctuation clusters. A special feature of QMS is that it allows for clusters with V c< V c(cr) возможность некоторого времени жизни, в течение которого нанокластеры способны изменяться в своем объеме, уменьшаясь вплоть до полного распада либо увеличиваясь вплоть до перехода в устойчивые зародыши. Считается, что нанокластеры изменяются в объеме либо за счет присоединения к ним отдельных атомов из матрицы или же отрыва от них атомов и их перехода в матрицу либо за счет объединения нанокластеров в ходе взаимных столкновений.

According to the FKMZ, the nucleation of crystals occurs through the interaction of previously formed nanoclusters with V c< V c(cr) и флуктуационных скоплений. Возможность такого взаимодействия обусловлена непрерывной миграцией нанокластеров в объеме среды и неоднородностью пространст- венно-временного распределения флуктуаций, в результате чего местоположение флуктуаций, возникающих в период миграции нанокластеров, может случайным образом совпадать с местоположением нанокластеров. Как следствие, нанокластеры способны существенно укрупняться за счет присоединения к ним атомов из флуктуационных скоплений.

Thus, an obligatory condition for the formation of a crystalline phase is the appearance of critical nuclei, i.e. disordered nanoclusters of a certain size, at which they become potential crystallization centers. Hence it follows that the size of critical nuclei can be considered, on the one hand, as the lower limit of the nanocrystalline state, i.e. as the minimum possible size of nanocrystals that can form as a result of crystallization, and, on the other hand, as the upper limit of the nanocluster state, i.e. as the maximum possible size of disordered nanoclusters, upon reaching which they pass into a stable state and turn into nanocrystals. According to estimates, critical nuclei have dimensions of the order of 1 nm. It should be noted that for any substance there is no strictly fixed size of critical nuclei, since this size depends on the properties of the crystallizing medium, in particular, on the degree of its deviation.

dependence on the state of thermodynamic equilibrium (in the case of solutions, on the degree of their supersaturation).

In the ideal case, nanocrystals formed during crystallization have a perfect single-crystal structure, which is possible when they are formed as a result of the growth of clusters by successively attaching individual atoms or molecules of the crystallizing substance to them. In reality, the structure of nanocrystals can be characterized by various defects: vacancies, dislocations, etc. It should be noted, however, that the probability of the occurrence of these defects is extremely low and decreases significantly with decreasing nanoparticle size. In particular, the estimated calculation shows that nanoparticles with a size of less than 10 nm contain practically no vacancies. The high perfection of the structure of small crystals is a well-known fact: a typical example of this is whiskers (the so-called “whiskers”), which have the form of rods with a diameter of about 1 μm or less and practically do not contain defects.

The formation of nanocrystals by the cluster mechanism, namely, by combining a number of nanoclusters, can cause the formation of an inhomogeneous block structure. The possibility of the existence of such a structure of nanocrystals is confirmed by the results of their study by diffraction analysis and electron microscopy, indicating that their structure can correspond to both single crystals and polycrystals. In particular, studies of ceramic nanoparticles based on ZrO2 show that they can consist of several structural fragments that differ from each other.

There is another approach to estimating the minimum possible size of nanocrystals based on an analysis of the features of their crystal structure. In nanocrystals, as well as in macrocrystals, atoms in their spatial arrangement form a crystal lattice. One of the most important characteristics of the crystal lattice is the coordination number, i.e. the number of neighboring atoms closest to a given atom. The set of nearest neighboring atoms forms the so-called 1st coordination sphere. Similarly, we can talk about the 2nd, 3rd, 4th, etc. coordination areas. As the size of the nanocrystal decreases, a situation may arise that the symmetry elements inherent in this type of crystals will disappear, i.e. long-range order in the arrangement of atoms will be violated and, accordingly, the number of coordination spheres will be

shrink. Conventionally, it is considered that the lower limit of the nanocrystalline state occurs when the size of nanocrystals becomes commensurate with three coordination spheres (for example, for Ni this corresponds to 0.6 nm). With a further decrease in size, nanocrystals pass into nanoclusters, the most important distinguishing feature of which, compared with nanocrystals, is the loss of symmetry inherent in the crystal structure.

4.2. Nanocrystals

4.2.1. Inorganic nanocrystals

Nanocrystals of inorganic composition are very widespread both in nature and in technology. Existing methods make it possible to obtain inorganic nanocrystals of the most diverse composition:

metals and alloys (most often based on Fe);

ceramics based on simple oxides (Al2 O3, Cr2 O3, etc.), double oxides (spinels CoO Al2 O3, etc.), triple oxides (cordierite 2MgO 2Al2 O3 5Al2 O3 ), nitrides (AlN, TiN, etc. ), oxynitrides (Si3 N4 -Al2 O3 -AlN and

others), carbides (TiC, ZrC, etc.); carbon (diamond, graphite);

semiconductors (CdS, CdSe, InP, etc.).

It is also possible to obtain composite inorganic nanocrystals, for example, composition WC-Co.

The sizes of the obtained nanocrystals can vary within a fairly wide range: from 1 to 100 nm or more, depending on the type of nanocrystals and methods for their preparation. In most cases, they do not exceed 100 nm for metals and ceramics, 50 nm for diamond and graphite, and 10 nm for semiconductors.

Most often, inorganic nanocrystals are obtained in the form of nanopowders. Individual crystalline nanoparticles can be formed during the preparation of nanosuspensions, where they play the role of a dispersed phase. In addition, they can be part of the matrix of nanocomposites. Such nanocrystals are called matrix.

Crystalline nanoparticles of inorganic substances are quite widespread in nature. Most often, they are distributed in the atmosphere, forming nanoaerosols. Significant amounts of nanoparticles are contained in hydrothermal solutions, usually having a temperature of about 400°C. However, when the solutions are cooled (as a result of the combination with cold water), the nanoparticles grow larger, becoming visually observable. They also exist in rocks and magma. In rocks, nanoparticles are formed as a result of chemical weathering of silica, aluminosilicates, magnetites, and other types of minerals. The magma pouring onto the surface of the Earth, being in its depth, participated in high-temperature geological processes and passed through the formation of nanoparticles, which then became the embryo for the growth of large crystals of minerals and just silicates that form the earth's crust.

In addition, crystalline nanoparticles exist in space, where they are formed by physical processes, including the impact (explosive) mechanism, as well as electrical discharges and condensation reactions that occur in the solar nebula. Back in the late 1980s, the Americans collected protoplanetary dust on their spacecraft. Analysis performed in terrestrial laboratories showed that this dust has a size of 10 to about 150 nm and belongs to carbonaceous chondrites. Minerals contained in the Earth's mantle have a similar composition. From this we can conclude that, at least, the terrestrial planets of the Solar System originated from nanoparticles, the composition of which corresponds to carbonaceous chondrites.

Nanocrystals have a number of unusual properties, the most important feature of which is the manifestation of size effects.

Nanocrystals have a significant specific surface, which significantly increases their reactivity. For a spherical nanoparticle with diameter d and surface layer thickness δ, the fraction of the surface layer in its total volume V is determined by the expression

		d 3 / 6	(d2)3 / 6
			d 3 / 6

At d = 10–20 nm and δ = 0.5–1.5 nm (which corresponds to 3–4 atomic monolayers), the surface layer accounts for up to 50% of the total substance of the nanoparticle. It is believed that traditional ideas about the surface

macroparticle energies are quite acceptable for nanoparticles larger than 10 nm. At a size of less than 1 nm, almost the entire nanoparticle can acquire the properties of a surface layer, i.e. to pass into a special state, different from the state of macroparticles. The nature of the state of nanoparticles in the intermediate size range of 1–10 nm can manifest itself in different ways for nanoparticles of different types.

In terms of energy, it is advantageous for nanocrystals to assume states in which their surface energy decreases. The surface energy is minimal for crystal structures characterized by the closest packings; therefore, for nanocrystals, face-centered cubic (fcc) and hexagonal sweat-packed (hcp) structures are most preferable (Fig. 4.4).

So, for example, electron diffraction studies show that nanocrystals of a number of metals (Nb, Ta, Mo, W) with a size of 5-10 nm have an fcc or hcp lattice, while in the normal state these metals have a body-centered (bcc) lattice.

AT In the densest packings (Fig. 4.4), each ball (atom) is surrounded by twelve balls (atoms), therefore, these packings have a coordination number of 12. For a cubic packing, the coordination polyhedron is a cuboctahedron, for a hexagonal packing, a hexagonal cuboctahedron.

The transition from massive crystals to nanocrystals is accompanied by a change in interatomic distances and periods of the crystal lattice

. For example, it has been established by electron diffraction that a decrease in the size of Al nanocrystals from 20 to 6 nm leads to a decrease in the lattice period by 1.5%. A similar decrease in the lattice period by 0.1% was observed with a decrease in the particle size of Ag and Au from 40 to 10 nm (Fig. 4.5). The size effect of the lattice period is noted not only for metals, but also for compounds, in particular, titanium, zirconium, and niobium nitrides.

AT Possible reasons for this effect are considered to be

the influence of excess Laplace pressure p = 2 /r , created by surface tension, the value of which increases with decreasing particle size r ; as well as the lack of compensation for relatively small nanoparticles of interatomic bonds of surface atoms, in contrast to atoms located inside nanoparticles, and, as a result, a reduction in the distances between atomic planes near the surface of nanoparticles.

When analyzing the change in the lattice period of nanoparticles, one should take into account the above-mentioned possibility of transition from less dense

structures to denser ones with a decrease in the size of nanoparticles. For example, according to electron diffraction data, when the diameter d of Gd, Tb, Dy, Er, Eu, and Yb nanoparticles decreases from 8 to 5 nm, the hcp structure and lattice parameters characteristic of bulk metals are preserved, and with a further decrease in the size of nanoparticles, a noticeable decrease in lattice parameters is observed; however, at the same time, the shape of the electron diffraction patterns changed, which indicated a structural transformation - the transition from hcp to a denser fcc structure, and not a decrease in the parameters of the hcp lattice. Thus, in order to reliably reveal the size effect on the lattice period of nanoparticles, it is also necessary to take into account the possibility of structural transformations.

Rice. 4.4. Crystal structures with the densest

packs of atoms

a - three-layer cubic packaging, ... ABSASAVS…,

b – two-layer hexagonal packing, … ABABAV…

The size dependence of the surface energy of nanocrystals determines the corresponding dependence of the melting temperature, which in the case of isometric nanocrystals can be approximately described by the formula

T m (1

where Tmr

is the melting temperature of the nanocrystal, depending on its size r,

T m is the melting temperature of a massive crystal,

is a constant, depending on

density

melting

material

) 10-4

surface energy.

dimensional

temperature

melting

takes place for nanocrystals

less than 10 nm in size. For

nanocrystals larger than

d, nm

10 nm this effect is almost non-existent

Rice. 4.5. Relative change

nanoparticles also appear when

grating period

depending on

melting

behave

on the diameter d of the se-

ribs Ag and gold Au

bulk samples.

Peculiarities

dimensional

The temperature effects of nanocrystals were studied mainly in the course of melting of island films of a number of metals using the electron diffraction method. Island films were obtained by evaporation of the metal and its subsequent deposition on the substrate. In this case, nanocrystals were formed on the substrate in the form of islands about 5 nm in size. A decrease in the melting temperature was observed experimentally for nanocrystals of various substances: Ag, Al, Au, Bi, Cu, Ga, In, Pb, Sn, etc. . On fig. 4.6 shows a typical T mr dependence for gold nanocrystals.

The reasons for the size effect of the melting temperature have not yet been fully elucidated. According to the so-called surface melting mechanism, nanocrystals begin to melt from the surface with the formation of a liquid shell, after which the melting front propagates deep into the volume. In this case, the equilibrium temperature between the crystalline core and the surrounding liquid shell is taken as the melting temperature of a nanocrystal. According to the so-called oscillatory mechanism of nanocrystal melting, as the temperature rises, the amplitude of thermal vibrations of atoms around their equilibrium position in the crystal lattice increases and, when it reaches a certain

critical fraction of the distance between the equilibrium positions of neighboring atoms, the vibrations begin to interfere mutually in such a way that the nanocrystal becomes mechanically unstable. In this case, the melting temperature is random, and its most probable values ​​are determined by the value associated with the characteristic time of fluctuation overcoming of the melting energy barrier.

	In nanocrystals, in comparison with bulk crystals,
	T m , K									change in thermal properties, which is related to
										zano with changes in the parameters of
										non-linear spectrum, i.e. nature of heat
										out vibrations of atoms or molecules. In particular, it is assumed that
										reduction in the size of nanocrystals
										causes a shift in the phonon spectrum
								r , nm
										tra to the region of high frequencies. Oso-
	Rice. 4.6. Temperature dependence									features of the phonon spectrum of nano-
	melting T m on the radius r of nanoparticles									crystals are reflected, first of all,
										on their heat capacity - the ratio of ele-
	solid line – calculation by formula (1);
										mental amount of heat, co-
	dotted line -				melting point macro-
										communicated by him in any process,
	scoping sample Au

to a corresponding change in their temperature. The heat capacity of nanocrystals depends not only on their size, but also on their composition. For example, in non-metallic materials, the greatest contribution to the heat capacity is made by the energy of thermal vibrations of atoms or molecules located at the nodes of the crystal lattice (lattice heat capacity), while in metals, in addition, a relatively small contribution to the heat capacity is made by conduction electrons (electronic heat capacity).

Studies of the heat capacity of nanocrystals were carried out mainly on the example of metals. It has been established that the heat capacity of Ni nanoparticles with a size of ~20 nm is almost 2 times greater than the heat capacity of bulk nickel at a temperature of 300-800K. Similarly, the heat capacity of Cu nanoparticles ~50 nm in size is almost 2 times greater than the heat capacity of bulk copper at temperatures below 450K. The results of measuring the heat capacity of Ag nanoparticles with a size of 10 nm in the region of very low temperatures of 0.05-10.0 K in a magnetic field with a magnetic flux density of up to 6 T show that at T > 1K the heat capacity of Ag nanoparticles is 3-10 times greater than the heat capacity of bulk silver. On fig.

T 2, K 2

Rice. 4.7. Temperature dependence

heat capacity С of Pd nanoparticles

1, 2 - nanoparticles with sizes of 3 nm and 6.6 nm, 3 - bulk palladium

C / T, J mol -1 K -2

4.7 shows the temperature dependence of the heat capacity of Pd nanoparticles of different sizes.

Nanocrystals are characterized by special electronic, magnetic and optical properties, which are due to various quantum mechanical phenomena.

Features of the electronic properties of nanocrystals begin to manifest themselves under the condition that the size of the region of localization of free charge carriers (electrons) becomes commensurate with the de Broglie wavelength

B h / 2 m * E ,

where m * is the effective mass of electrons, the value of which is determined by the features of the movement of electrons in the crystal, E is the energy of electrons, h is Planck's constant. In this case, the effect of size on the electronic properties can be different for nanocrystals of different compositions. For example, for metals λВ = 0.1-1.0 nm, i.e. size effect becomes noticeable only for very small nanocrystals, while

while for semimetals (Bi) and semiconductors (especially narrow-gap ones - InSb) λВ ≈ 100 nm, i.e. the effect of size can be noticeable for nanocrystals with quite

but a wide range of sizes.

A characteristic example of a special manifestation of the magnetic properties of nanocrystals is the change in the magnetic susceptibility and coercive force with a decrease in the size of nanocrystals.

The magnetic susceptibility χ establishes the relationship between the magnetization M characterizing the magnetic state of matter in a magnetic field and representing the vector sum of the magnetic moments of the elementary carriers of magnetism per unit volume, and the strength of the magnetizing field H (M = χH ). The value of χ and the nature of its dependence on the magnetic field strength and temperature serve as a critical

arias for separating substances according to their magnetic properties into dia-, para-, ferro- and antiferromagnets, as well as ferrimagnets. Taking this circumstance into account, the effect of size on the magnetic susceptibility can be different for nanocrystals of different types of magnetic substances. For example, a decrease in the size of nanocrystals from 1000 to 1 nm leads to an increase in diamagnetism in the case of Se and a decrease in paramagnetism in the case of Te.

The coercive force is an important characteristic of the magnetization curve, numerically equal to the field strength H c , which must be applied in the direction opposite to the direction of the magnetizing field in order to remove the residual magnetization. The value of H c determines the width of the magnetic hysteresis loop formed during the passage of the full cycle of magnetization - demagnetization, taking into account which magnetic materials are divided into magnetically hard (with a wide hysteresis loop, it is difficult to remagnetize) and magnetically soft (with a narrow hysteresis loop, easily remagnetize ). The results of studies of ferromagnetic nanocrystals of a number of substances show that the coercive force increases as the nanocrystals decrease to a certain critical size. In particular, the maximum values ​​of Hc are achieved for Fe, Ni, and Cu nanocrystals with average diameters of 20–25, 50–70, and 20 cm, respectively.

The optical properties of nanocrystals, in particular, such as the scattering and absorption of light, quite significantly manifest their features, consisting in the presence of a size dependence, provided that the sizes of nanocrystals are noticeably smaller than the radiation wavelength and do not exceed

In most cases, the properties of nanocrystals due to quantum mechanical phenomena are most pronounced in ensembles of nanoparticles, in particular, in nanocrystalline materials or in matrix nanocomposites.

Technologies for obtaining crystalline nanoparticles are very diverse. Usually they are synthesized in the form of nanopowders.

Most often, the synthesis of nanoparticles is carried out from the vapor-gas phase or plasma, using the technologies of evaporation-condensation and plasma-chemical synthesis, respectively.

According to the evaporation-condensation technology, nanoparticles are formed by crystallization from a vapor-gas mixture, which is formed by the evaporation of the source material at a controlled temperature in an inert gas atmosphere (Ar, He, H2) of low pressure and then condenses near

or on a cold surface. In addition, evaporation and condensation can take place in a vacuum. In this case, nanoparticles crystallize from pure vapor.

Evaporation-condensation technology is widely used to obtain nanoparticles of metals (Al, Ag, Au, Cd, Cu, Zn) and alloys (Au-Cu, Fe-Cu),

frames (metal carbides, oxides and nitrides), as well as semiconductors

Various methods of heating are used to evaporate the material. So, for example, metals can be heated in a crucible placed in an electric furnace. It is also possible to heat a metal wire by passing an electric current through it. The energy supply to the evaporated material can be carried out by an electric arc discharge in a plasma, by induction heating by high and microwave frequency currents, by a laser or electron beam. Nanoparticles of oxides, carbides, and nitrides are obtained by heating metals in a rarefied atmosphere of the reagent gas, oxygen O2 (in the case of oxides), methane CH4 (in the case of carbides), nitrogen N2, or ammonia NH3 (in the case of nitrides). In this case, it is efficient to use pulsed laser radiation for heating.

The vapor-gas phase can also be formed as a result of thermal decomposition of organometallic compounds used as precursors (raw materials). On fig. 4.8. shows a diagram of a plant operating with the use of such precursors, which, together with a neutral carrier gas, are fed into a heated tubular reactor. The nanoparticles formed in the reactor are deposited on a rotating cooled cylinder, from where they are scraped off by a scraper into a collector. This plant is used for the industrial production of oxide nanopowders.

(Al2 O3 , CeO3 , Fe2 O3 , In2 O3 , TiO2 , ZnO, ZrO2 , Y2 O3 ), as well as carbides and nitrile

A high-temperature gas-vapor mixture can condense when it enters a large-volume chamber filled with a cold inert gas. In this case, the gas-vapor mixture will be cooled both due to expansion and due to contact with a cold inert atmosphere. A condensation method is also possible, based on the supply of two coaxial jets into the chamber: the vapor-gas mixture is supplied along the axis, and an annular jet of cold inert gas enters along its periphery.

Condensation from the vapor-gas phase can produce particles ranging in size from 2 to several hundred nanometers. Size as well as composition of nanoparticles

can be varied by changing the pressure and composition of the atmosphere (inert gas and reagent gas), the intensity and duration of heating, the temperature gradient between the evaporated material and the surface on which the vapor condenses. If the sizes of nanoparticles are very small, then they can remain suspended in the gas without settling on the surface. In this case, special filters are used to collect the obtained powders, centrifugal precipitation or liquid film trapping is carried out.

Rice. 4.8. Installation scheme for obtaining ceramic nanopowders

1 - carrier gas supply, 2 - precursor source, 3 - control valves, 4 - working chamber, heated tubular reactor, 6 - cooled rotating

cylinder, 7 - collector, 8 - scraper

According to the technology of plasma-chemical synthesis, nanoparticles are formed in low-temperature (4000-8000 K) nitrogen, ammonia, hydrocarbon or argon plasma of arc, high-frequency (HF) or microwave (MW) discharges. The nature of the synthesis process essentially depends on the type of plasma torch - the device in which plasma is generated. Arc plasmatrons are more productive, however, RF and, especially, microwave plasmatrons provide finer and cleaner powders (Fig. 4.9).

TiN). Synthesis of oxides is carried out in the plasma of an electric arc discharge by evaporation of the metal, followed by the oxidation of vapors or the oxidation of metal particles in oxygen. Carbides of metals, boron and silicon are usually obtained by the interaction of chlorides of the corresponding elements with hydrogen and methane or other hydrocarbons in an argon arc or HF plasma, nitrides - by the interaction of chlorides with ammonia or a mixture of nitrogen and hydrogen in a microwave plasma. Metal nanopowders are also obtained by plasma-chemical synthesis. For example, copper nanopowders are obtained by reducing copper chloride with hydrogen in an argon arc plasma. The plasma-chemical synthesis of refractory metals is especially promising.

(W, Mo, etc.). Synthesized nanoparticles usually have sizes from 10 to 100-200 nm or more.

Technologies for obtaining crystalline nanoparticles based on the use of high-energy mechanical effects are distinguished by high efficiency. These include mechanochemical, detonation and electroexplosive synthesis.

Mechanochemical synthesis is based on the processing of solid mixtures, which results in grinding and plastic deformation of materials, intensification of mass transfer and mixing of mixture components at the atomic level, and activation of the chemical interaction of solid reagents.

As a result of mechanical action, a stress field is created in the contact areas of a solid, the relaxation of which can occur by heat release, the formation of a new surface, the formation of various defects in crystals, and the excitation of chemical reactions in the solid phase.

The mechanical action during the grinding of materials is impulsive; therefore, the appearance of a stress field and its subsequent relaxation occur only at the moment of particle collision and in a short time after it. In addition, the mechanical action is local, since it does not occur in the entire mass of the solid, but only where the stress field arises and then relaxes.

Mechanical abrasion is a high-performance method for the mass production of nanopowders of various materials: metals, alloys, intermetallic compounds, ceramics, and composites. As a result of mechanical abrasion and mechanical alloying, complete solubility in the solid state of such elements can be achieved, the mutual solubility of which is negligible under equilibrium conditions.

For mechanochemical synthesis, planetary, ball and vibration mills are used, which provide an average size of the obtained powders from 200 to 5-10 nm.

Detonation synthesis is based on the use of shock wave energy. It is widely used to obtain diamond powders with an average particle size of 4 nm by shock-wave treatment of mixtures of graphite with metals at a shock wave pressure of up to several tens of GPa. It is also possible to obtain diamond powders by the explosion of organic substances with a high carbon content and a relatively low oxygen content.

Detonation synthesis is used to obtain nanopowders of oxides of Al, Mg, Ti, Zr, Zn and other metals. In this case, metals are used as the starting material, which are processed in an active oxygen-containing medium (for example, O2 + N2). In this case, at the stage of metal expansion, its combustion occurs with the formation of a nanodispersed oxide. Detonation synthesis technology also makes it possible to obtain MgO whiskers with an average diameter of 60 nm and a length-to-diameter ratio of up to 100. In addition, using a carbon-containing CO2 atmosphere, nanotubes can be synthesized.

Electroexplosive synthesis, used to obtain nanopowders of metals and alloys, is a process of electric explosion of a thin metal wire with a diameter of 0.1-1.0 mm with a short-term passage of a powerful current pulse through it. An electric explosion is accompanied by the generation of shock waves and causes rapid heating of metals at a rate of more than 1,107 K/s to temperatures exceeding 104 K. The metal overheats above the melting point and evaporates. As a result of condensation in a stream of rapidly expanding vapor, particles with a size of up to 50 nm or less are formed.

Crystalline nanoparticles can be synthesized in heat-stimulated reactions. During thermal decomposition, complex elemental and organometallic compounds, hydroxides, carbonyls, formates, nitrates, oxalates, amides and amides of metals are usually used as the starting material, which decompose at a certain temperature with the formation of a synthesized substance and the release of a gas phase. By pyrolysis of formates of iron, cobalt, nickel, copper in vacuum or in an inert gas at a temperature of 470-530 K, metal powders are obtained with an average particle size of 100-300 nm.

In practical terms, the thermal decomposition of organometallic compounds by shock heating of the gas, which occurs in a shock tube, is of interest. At the shock wave front, the temperature can reach 1000–2000 K. The resulting highly supersaturated metal vapor rapidly condenses. In this way, nanopowders of iron, bismuth, lead and other metals are obtained. Similarly, during pyrolysis, a supersonic outflow of the resulting vapors from the chamber through a nozzle into a vacuum is created. During expansion, the vapors cool down and pass into a supersaturated state, as a result of which nanopowders are formed, which flow out of the nozzle in the form of an aerosol.

Thermal decomposition produces silicon carbide and silicon nitride nanopowders from polycarbosilanes, polycarbosilokeanes, and polysilazanes; boron carbide aluminum nitride from aluminum polyamideimide (in ammonia); boron carbide polyvinyl pentaborane boron carbide, etc.

An effective method for obtaining metal nanopowders is the reduction of metal compounds (hydroxides, chlorides, nitrates, carbonates) in a hydrogen flow at a temperature of less than 500 K.

Technologies for obtaining nanopowders using colloidal solutions are widely used, which consist in the synthesis of nanopowders.

particles from the initial reagents of the solution and interrupting the reaction at a certain point in time, after which the dispersed system is transferred from the liquid colloidal state to the dispersed solid. For example, cadmium sulfide nanopowder is obtained by precipitation from a solution of cadmium perchlorate and sodium sulfide. In this case, the growth of the nanoparticle sizes is interrupted by an abrupt increase in the pH of the solution.

The process of precipitation from colloidal solutions is highly selective and makes it possible to obtain nanoparticles with a very narrow size distribution. The disadvantage of the process is the danger of coalescence of the resulting nanoparticles, to prevent which various polymeric additives are used. Metal clusters of gold, platinum, and palladium obtained in this way usually contain from 300 to 2000 atoms. In addition, to obtain highly dispersed powders, precipitates of colloidal solutions consisting of agglomerated nanoparticles are calcined. For example, silicon carbide nanopowder (particle size 40 nm) is obtained by hydrolysis of organic silicon salts followed by calcination in argon at

In some cases, the hydrolysis of metal salts is used to synthesize colloidal oxide particles. For example, titanium, zirconium, aluminum, and yttrium oxide nanopowders can be obtained by hydrolysis of the corresponding chlorides or hypochlorites.

To obtain highly dispersed powders from colloidal solutions, cryogenic drying is also used, during which the solution is sprayed into a chamber with a cryogenic medium, where solution droplets freeze in the form of small particles. Then the pressure of the gaseous medium is lowered so that it is less than the equilibrium pressure over the frozen solvent, and the material is heated under continuous pumping to sublimate the solvent. As a result, porous granules of the same composition are formed, by calcination of which nanopowders are obtained.

Of particular interest is the synthesis of crystalline nanoparticles in matrices. One of the possible methods for obtaining matrix nanocrystals is based on the partial crystallization of rapidly solidifying amorphous alloys. In this case, a structure is formed containing an amorphous phase and crystalline nanoparticles precipitated in the amorphous phase. On fig. 4.10 shows a micrograph of a rapidly solidified amorphous alloy Al 94,5

rials with solutions, followed by precipitation of the substances contained in the solutions into the pores. In this way, for example, metal nanoparticles are synthesized in zeolites - alkaline or alkaline earth aluminosilicates.

ny metals with a regular porous structure. In this case, the sizes of the resulting nanoparticles are determined by the pore sizes of the zeolites (1–2 nm). Usually, matrix nanoparticles act as structural elements of specially prepared bulk nanocomposites.

4.2.2. Organic nanocrystals

Organic nanocrystals are much less common than inorganic ones. Among them, polymeric nanocrystals are the best known. They are matrix-type nanocrystals that form as a result of partial crystallization of polymers from melts or solutions. In this case, the formed structure of polymers consists of an amorphous matrix and crystalline nanoinclusions distributed in its volume. The volume fraction of the crystalline phase determines the degree of crystallinity of polymers, which can vary within fairly wide limits, depending on the type of polymer and the conditions of solidification. For example, in polyamide, the degree of crystallinity can vary from 0 to

ly, folding like a gar-

midges (Fig. 4.11). The thickness of the lamellas

Rice. 4.11. Folded model

is about 10 nm, while

polymer nanocrystal

length can be up to several

H ≈ 10 nm

hundreds of nanometers. Depending on me-

crystallization mechanism, the shape of nanocrystals can be diamond-shaped (polyethylene), hexagonal (polyformaldehyde), tetragonal (polyethylene oxide), in the form of a parallelogram (polyacrylonitrile), etc.

		In practice, during processing
		polymer materials crystallization
		tion usually occurs under the action
		stresses. This leads to
		lamellae are oriented along some
		ryh certain directions. On the-
		example, in the case of processing polymer-
		material by extrusion they
	Rice. 4.12. Packet structure model	oriented perpendicular to
		extrusion board. It leads to
	polymer nanocrystal
		the formation of the so-called bundle
	1 - the center of the bundle structure,
	2 - lamellar crystal	structures of nanocrystals (Fig. 4.12).
		The central part of the stack structure,

which plays the role of a crystallization nucleus, is located in the direction of extrusion and perpendicular to the planes of the lamellas.

The gold standard is 20 years old

Russian scientists found deposits under their feet

The economic nightmare from the novel “Engineer Garin’s Hyperboloid” may come true. The gold standard, which currency market experts are talking about returning to, may die without being revived. And all thanks to the discovery of Russian scientists

Simply put, Russian scientists from the Far Eastern Geological Institute, the Institute of Chemistry, the Institute of Tectonics and Geophysics, and the Institute of Mining of the Far Eastern Branch of the Russian Academy of Sciences, under the leadership of Academician Alexander Khanchuk, managed to discover a new type of precious metal deposits: “organometallic nanoclusters of gold and platinoids in the composition of graphite.” Such deposits are widely distributed in the world and, more importantly, are located in habitable, well-developed infrastructure areas.

And the weights are golden!

Graphite deposits have long been known and, as previously thought, well studied. "Caught" in them, geologists and traces of gold and other precious metals - in small quantities. But traces of gold in different rocks are not as rare as it is commonly thought - the question is what is the concentration and ease of extraction.

• Native gold deposits (for example, black shale) are valuable because the whole process of gold mining consists, in essence, in the purification of available gold from associated rocks. The chemical method of extracting gold is already more costly and laborious; industrial gold mining is justified here only at a high concentration of gold. So far only minor traces of gold and platinoids have been found in graphite deposits. At the same time, they are in a state associated with graphite, that is, chemical extraction technologies are required. Unprofitable.

Everything changed when Khanchuk's group checked graphite deposits not in the traditional chemical way, “test tube”, but with the help of ion mass spectrometry and neutron activation analysis. The ion mass spectrometer, in particular, helped to see nanoforms of gold and platinoids "hidden" in graphite. In the traditional chemical analysis, they were not determined, since gold was not separated from the graphite “adhesion”.

• What did it give? A complete change in the idea of ​​the concentration of precious metals in graphite deposits. So, Khanchuk's group studied rock samples from long-known graphite deposits in Primorye, the Khabarovsk Territory and the Jewish Autonomous Region. Moreover, in Primorye, the deposit has been known since the 50s, it can be developed by an open method - that is, without expensive mining operations.

The usual chemical analysis of the samples examined by the group of scientists gave a gold concentration of 3.7 g per ton, and a spectrographic analysis - up to 17.8 g / t. For platinum: 0.04-3.56 g/t "in vitro" and up to 18.55 g/t - on the spectrometer. Palladium, the most valuable catalyst and additive that improves the properties of metal alloys, was found in concentrations up to 18.55 g/t instead of 0.02-0.55 g/t using the traditional method of analysis. That is, noble metals turned out to be many times more than previously thought.

• However, is such a concentration of gold and platinoids sufficient for the deposit to be of practical interest? Academician Vitaly Filonyuk, a specialist in gold deposits, professor at the Irkutsk State Technical University and the Institute of Subsoil Use, makes such comparisons. The minimum concentration of gold in Russia is at the Kuranakh group of deposits (Aldan region of South Yakutia): 1.5 g/t. The exploitation of the deposit began 30 years ago with 5-7 g/t, a total of 130 tons of gold was mined. The maximum concentration of gold - at the new deposit "Kupol" (Chukotka), the depleted deposit "Kubaka" (Magadan region) - up to 20 g/t and more. That is, the studied deposits are in the group with a concentration above the average.

Alexander Khanchuk

Eldorado underfoot

Practically gold is lying under our feet: explored graphite deposits are widespread all over the world - there are large deposits, for example, in the Leningrad region, in the USA, in Europe ... Until now, it simply never occurred to anyone to check them for gold using innovative methods, admits Khanchuk. Now that a virtually new form of precious metal ores has been discovered, one must think that such studies will take place everywhere. And Far Eastern scientists have no doubt that gold and platinoids will be found in comparable concentrations: the type of deposits is the same.

• True, technologies for extracting such nanoinclusions of noble metals from graphite are only being developed. According to Alexander Khanchuk, before the start of industrial development will take about twenty years. And the technologies will most likely be more expensive than traditional ones - moreover, platinoids are extracted from graphite harder than gold.

But, Khanchuk notes, the reduction in price will come due to the fact that the deposits themselves are accessible, located in areas with developed infrastructure, and extraction is possible by surface methods. Vitaly Filonyuk is skeptical about the results of the work of Far Eastern scientists, he believes that there is not enough data for far-reaching conclusions, but he agrees that industrial production is possible in 20 years.

“Load the gold in barrels”

However, what is an interesting scientific fact and a reason for discussion for scientists is just a knife in the back for the world economy. Judge for yourself. Today, when the weakness of the dollar has become obvious to the whole world, everyone has started talking about the need for a new world currency - from economists to currency speculators like George Soros, from the World Bank to the governments of different countries. And more and more often the scales are leaning towards the need to return to the gold standard. After all, the idea of ​​a flexible mutual change in the exchange rates of world currencies was undermined by the issuing policy of the United States: who will now guarantee that the new world currency will not be depreciated by the policy of the government issuing it?

• Gold in this sense is much more sustainable - the total gold reserves in the central banks of the world as of July 2008 were estimated at 29,822.6 tons (20% of all assets). True, there is much more gold in private ownership - for example, India imports 700-800 tons of gold annually, and the total private reserves in this country, where gold jewelry is a traditional wedding gift, are estimated at 15-20 thousand tons. But still there is not much gold in the world. And most importantly, its production volumes have so far been stable.

.

In total, over the past 6,000 years, mankind has mined approximately 145,000 tons of gold. Moreover, before 1848, less than 10,000 tons were extracted from the bowels - more than 90% of the mined gold falls on the last century and a half. It was the increase in gold mining due to new technologies that contributed to the fall in the popularity of gold. However, everything, even advanced methods of gold mining, could not overcome the limitations of proven gold reserves. According to the US Office of Geology and Mineral Resources, the volume of proven world gold reserves, the extraction of which is possible and economically viable, is only 47 thousand tons. At the same time, for several decades, world gold mining has been about 2.5 thousand tons of gold per year. This figure is corrected only downward: old gold deposits dry up, and new ones hardly appear.

One of the oldest examples of the use of nanotechnology is the colored stained glass of medieval cathedrals, which is a transparent body with inclusions in the form of nanosized metal particles. Glasses containing a small amount of dispersed nanoclusters demonstrate a variety of unusual optical properties with wide application possibilities. The wavelength of maximum optical absorption, which largely determines the color of glass, depends on the size and type of metal particles. On fig. 8.17 shows an example of the influence of the size of gold nanoparticles on the optical absorption spectrum of SiO 2 glass in the visible range. These data confirm the shift of the optical absorption peak to shorter wavelengths as the nanoparticle size decreases from 80 to 20 nm. Such a spectrum is caused by plasma absorption in metal nanoparticles. At very high frequencies, conduction electrons in a metal behave like a plasma, that is, an electrically neutral ionized gas in which mobile electrons are negative charges, and a positive charge remains on the fixed atoms of the lattice. If the clusters are smaller than the wavelength of the incident light and are well scattered, so that they can be considered as non-interacting with each other, then the electromagnetic wave causes the electron plasma to oscillate, leading to its absorption. To calculate the dependence of the absorption coefficient on the wavelength, you can use the theory developed by Mie (Mie). The absorption coefficient α of a small spherical metal particle in a non-absorbing medium is given as

where Ns- concentration of spheres of volume V , ε 1 and ε 2 - real and imaginary parts of the permittivity of spheres, n 0 - the refractive index of the non-absorbing medium; and λ is the wavelength of the incident light.

Another property of composite metallized glasses that is important for technology is optical nonlinearity, that is, the dependence of the refractive indices on the intensity of the incident light. Such glasses have a significant third-order susceptibility, which leads to the following form of the dependence of the refractive index P on the intensity of the incident light I:

n=n 0 +n 2 I (8.9)

When the particle size is reduced to 10 nm, the effects of quantum localization begin to play an important role, changing the optical characteristics of the material.

The oldest method for producing composite metallized glasses is to add metal particles to the melt. However, it is difficult to control the properties of glass, which depend on the degree of particle aggregation. Therefore, more controlled processes such as ion implantation have been developed. Glass is treated with an ion beam consisting of implanted metal atoms with energies from 10 keV to 10 MeV. Ion exchange is also used to introduce metal particles into glass. On fig. 8.18 shows an experimental setup for introducing silver particles into glass by ion exchange. Univalent near-surface atoms, such as sodium, present in the near-surface layers in all glasses, are replaced by other ions, such as silver. To do this, the glass base is placed in a salt melt located between the electrodes, to which the voltage indicated in Fig. 8.18 polarities. The sodium ions in the glass diffuse towards the negative electrode, and the silver diffuses from the silver-containing electrolyte onto the glass surface.

porous silicon

During electrochemical etching of a silicon wafer, pores are formed. On fig. 8.19 shows an image of the (100) plane of silicon, obtained on a scanning tunneling microscope after etching. Pores (dark areas) of micron sizes are visible. This material is called porous silicon (PoSi). By changing the processing conditions, nanometer sizes of such pores can be achieved. Interest in the study of porous silicon increased in 1990, when its fluorescence was discovered at room temperature. Luminescence is the absorption of energy by a substance with its subsequent re-emission in the visible or close to visible range. If the emission occurs in less than 10 -8 s, the process is called fluorescence, and if there is a delay in re-emission, then it is called phosphorescence. Ordinary (non-porous) silicon has a weak fluorescence between 0.96 and 1.20 eV, that is, at energies close to the band gap of 1.125 eV at room temperature. Such fluorescence in silicon is a consequence of electron transitions through the band gap. However, as can be seen in Fig. 8.20, porous silicon exhibits strong light-induced luminescence with energies noticeably greater than 1.4 eV at a temperature of 300 K. The position of the peak in the emission spectrum is determined by the etching time of the sample. This discovery received a lot of attention due to the possibility of using photoactive silicon in well-established technologies to create new displays or optoelectronic pairs. Silicon is the most common base for transistors, which are switches in computers.

On fig. 8.21 shows one of the ways to etch silicon. The sample is placed on a metal, for example, aluminum bottom of a container, the walls of which are made of polyethylene or Teflon, which do not react with hydrofluoric acid (HF), which is used as an etchant.

A voltage is applied between the platinum electrode and the silicon wafer, with the silicon acting as the positive electrode. The parameters that affect the characteristics of the pores are the concentration of HF in the electrolyte, the current strength, the presence of surfactants, and the polarity of the applied voltage. Silicon atoms have four valence electrons and form bonds in the crystal with four nearest neighbors. If one of them is replaced by a phosphorus atom with five valence electrons, then four of its electrons will participate in the formation of bonds with the four nearest silicon atoms, leaving one electron unbound and able to participate in charge transfer, contributing to conductivity. This creates levels in the band gap that lie close to the bottom of the conduction band. Silicon with this kind of dopant is called an n-type semiconductor. If the impurity atom is aluminum, which has three valence electrons, then one electron is not enough to form four bonds with the nearest atoms. The structure that appears in this case is called a hole. Holes can also participate in charge transfer and increase conductivity. Silicon doped in this way is called a p-type semiconductor. It turns out that the size of the pores formed in silicon depends on what type it is, n- or p-. When p-type silicon is etched, a very fine network of pores with sizes less than 10 nm is formed.

To explain the origin of the luminescence of porous silicon, many theories have been proposed based on various hypotheses, which take into account the following factors: the presence of oxides on the pore surface; influence of the state of surface defects; the formation of quantum wires, quantum dots and the resulting quantum localization; surface states of quantum dots. Porous silicon also exhibits electroluminescence, in which the glow is caused by a small voltage applied to the sample, and cathodoluminescence, caused by electrons bombarding the sample.

LECTURE #

Classification of nanoclusters. Nanoparticles

Material from Introduction to Nanotechnology.

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Nanoparticles are particles whose size is less than 100 nm. Nanoparticles are composed of 106 or fewer atoms, and their properties differ from those of a bulk substance composed of the same atoms (see figure).

Nanoparticles smaller than 10 nm are called nanoclusters. The word cluster comes from the English "cluster" - a cluster, a bunch. Usually, a nanocluster contains up to 1000 atoms.

Many physical laws valid in macroscopic physics (macroscopic physics "deals" with objects whose dimensions are much larger than 100 nm) are violated for nanoparticles. For example, the well-known formulas for adding the resistances of conductors when they are connected in parallel and in series are unfair. Water in rock nanopores does not freeze down to –20…–30оС, and the melting temperature of gold nanoparticles is significantly lower compared to a massive sample.

In recent years, many publications have given spectacular examples of the influence of particle sizes of a particular substance on its properties - electrical, magnetic, optical. Thus, the color of ruby ​​glass depends on the content and size of colloidal (microscopic) gold particles. Colloidal solutions of gold can give a whole gamut of colors - from orange (particle size less than 10 nm) and ruby ​​(10-20 nm) to blue (about 40 nm). The London Museum of the Royal Institute stores colloidal solutions of gold, which were obtained by Michael Faraday in the middle of the 19th century, who was the first to associate their color variations with particle size.

The fraction of surface atoms becomes larger as the particle size decreases. For nanoparticles, almost all atoms are "surface", so their chemical activity is very high. For this reason, metal nanoparticles tend to combine. At the same time, in living organisms (plants, bacteria, microscopic fungi), metals, as it turned out, often exist in the form of clusters consisting of a combination of a relatively small number of atoms.

Wave-particle duality allows you to assign a specific wavelength to each particle. In particular, this applies to waves that characterize an electron in a crystal, to waves associated with the motion of elementary atomic magnets, etc. Unusual properties of nanostructures hinder their trivial technical use and at the same time open up completely unexpected technical prospects.

Consider a cluster of spherical geometry consisting of i atoms. The volume of such a cluster can be written as:

https://pandia.ru/text/80/170/images/image006_17.gif" alt="(!LANG:Image:image016.gif" width="84" height="54 src=">, (2.2)!}

where a is the average radius of one particle.

Then you can write:

https://pandia.ru/text/80/170/images/image008_13.gif" alt="(!LANG:Image:image020.gif" width="205" height="36 src=">. (2.4)!}

Number of atoms on the surface iS is related to the surface area through the ratio:

https://pandia.ru/text/80/170/images/image010_12.gif" alt="(!LANG:Image:image026.gif" width="205" height="54 src=">. (2.6)!}

As can be seen from formula (2.6), the fraction of atoms on the cluster surface rapidly decreases with increasing cluster size. A noticeable effect of the surface is manifested at cluster sizes smaller than 100 nm.

An example is silver nanoparticles, which have unique antibacterial properties. The fact that silver ions are able to neutralize harmful bacteria and microorganisms has been known for a long time. It has been established that silver nanoparticles are thousands of times more effective in fighting bacteria and viruses than many other substances.

Classification of nanoobjects

There are many different ways to classify nanoobjects. According to the simplest of them, all nanoobjects are divided into two large classes - solid (“external”) and porous (“internal”) (scheme).

Classification of nanoobjects
Solid objects are classified by dimension: 1) three-dimensional (3D) structures, they are called nanoclusters ( cluster- accumulation, bunch); 2) flat two-dimensional (2D) objects - nanofilms; 3) linear one-dimensional (1D) structures - nanowires, or nanowires (nanowires); 4) zero-dimensional (0D) objects - nanodots, or quantum dots. Porous structures include nanotubes and nanoporous materials, such as amorphous silicates.

Some of the most actively studied structures are nanoclusters- consist of metal atoms or relatively simple molecules. Since the properties of clusters depend very strongly on their size (size effect), their own classification has been developed for them - according to size (table).

Table

Classification of metal nanoclusters by size (from a lecture by prof.)

In chemistry, the term "cluster" is used to denote a group of closely spaced and closely related atoms, molecules, ions, and sometimes even ultrafine particles.

This concept was first introduced in 1964, when Professor F. Cotton proposed to call clusters chemical compounds in which metal atoms form a chemical bond with each other. As a rule, in such compounds, metal metal clusters are bound to ligands that have a stabilizing effect and surround the metal core of the cluster like a shell. Cluster compounds of metals with the general formula MmLn are classified into small (m/n< 1), средние (m/n ~ 1), большие (m/n >1) and giant (m >> n) clusters. Small clusters usually contain up to 12 metal atoms, medium and large - up to 150, and giant (their diameter reaches 2-10 nm) - more than 150 atoms.

Although the term "cluster" has been widely used relatively recently, the very concept of a small group of atoms, ions, or molecules is natural for chemistry, since it is associated with the formation of nuclei during crystallization or associates in a liquid. Clusters also include nanoparticles with an ordered structure, having a given packing of atoms and a regular geometric shape.

It turned out that the shape of nanoclusters significantly depends on their size, especially for a small number of atoms. The results of experimental studies, combined with theoretical calculations, showed that gold nanoclusters containing 13 and 14 atoms have a planar structure, in the case of 16 atoms they have a three-dimensional structure, and in the case of 20 they form a face-centered cubic cell resembling the structure of ordinary gold. It would seem that with a further increase in the number of atoms, this structure should be preserved. However, it is not. A particle consisting of 24 gold atoms in the gas phase has an unusual elongated shape (Fig.). Using chemical methods, it is possible to attach other molecules to clusters from the surface, which are able to organize them into more complex structures. Gold Nanoparticles Combined with Fragments of Polystyrene Molecules [–CH2–CH(C6H5)–] n or polyethylene oxide (–CH2CH2O–) n, when they enter water, they are combined by their polystyrene fragments into cylindrical aggregates resembling colloidal particles - micelles, and some of them reach a length of 1000 nm.

Natural polymers such as gelatin or agar-agar are also used as substances that transfer gold nanoparticles into solution. By treating them with chloroauric acid or its salt, and then with a reducing agent, nanopowders are obtained that are soluble in water with the formation of bright red solutions containing colloidal gold particles.

Interestingly, nanoclusters are present even in ordinary water. They are agglomerates of individual water molecules connected to each other by hydrogen bonds. It has been calculated that in saturated water vapor at room temperature and atmospheric pressure, there are 10,000 dimers (H2O)2, 10 cyclic trimers (H2O)3, and one tetramer (H2O)4 per 10 million single water molecules. In liquid water, particles of a much larger molecular weight, formed from several tens and even hundreds of water molecules, have also been found. Some of them exist in several isomeric modifications that differ in the form and order of connection of individual molecules. Especially many clusters are found in water at low temperatures, near the melting point. Such water is characterized by special properties - it has a higher density compared to ice and is better absorbed by plants. This is another example of the fact that the properties of a substance are determined not only by its qualitative or quantitative composition, i.e., by its chemical formula, but also by its structure, including at the nanolevel.

Recently, scientists have been able to synthesize nanotubes of boron nitride, as well as some metals, such as gold. In terms of strength, they are significantly inferior to carbon ones, but, due to their much larger diameter, they are able to include even relatively large molecules. To obtain gold nanotubes, heating is not required - all operations are carried out at room temperature. A colloidal solution of gold with a particle size of 14 nm is passed through a column filled with porous alumina. In this case, gold clusters get stuck in the pores present in the aluminum oxide structure, uniting with each other into nanotubes. To free the formed nanotubes from aluminum oxide, the powder is treated with acid - aluminum oxide dissolves, and gold nanotubes settle at the bottom of the vessel, resembling algae in a micrograph.

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Types of metal particles (1Å=10-10 m)

As the transition from a single atom in a zero-valent state (M) to a metal particle that has all the properties of a compact metal, the system goes through a number of intermediate stages:

Morphology" href="/text/category/morfologiya/" rel="bookmark">morphological elements. Then stable large particles of the new phase are formed.

https://pandia.ru/text/80/170/images/image018_11.gif" width="623" height="104 src="> For a chemically more complex system, the interaction of dissimilar atoms leads to the formation of molecules with a predominantly covalent or a mixed covalent-ionic bond, the degree of ionicity of which increases as the difference in the electronegativity of the elements that form the molecules increases.

There are two types of nanoparticles: particles of an ordered structure with a size of 1–5 nm, containing up to 1000 atoms (nanoclusters or nanocrystals), and actually nanoparticles with a diameter of 5 to 100 nm, consisting of 103–106 atoms. Such a classification is correct only for isotropic (spherical) particles. filiform and

lamellar particles can contain many more atoms and have one or even two linear dimensions that exceed the threshold value, but their properties remain characteristic of a substance in a nanocrystalline state. The ratio of the linear sizes of nanoparticles makes it possible to consider them as one-, two-, or three-dimensional nanoparticles. If a nanoparticle has a complex shape and structure, then not the linear size as a whole, but the size of its structural element is considered as a characteristic one. Such particles are called nanostructures.

CLUSTERS AND QUANTUM-SIZE EFFECTS

The term "cluster" comes from the English word cluster - bunch, swarm, accumulation. Clusters occupy an intermediate position between individual molecules and macrobodies. The presence of unique properties in nanoclusters is associated with a limited number of their constituent atoms, since the scale effects are the stronger, the closer the particle size is to the atomic one. Therefore, the properties of a single isolated cluster can be compared both with the properties of individual atoms and molecules, and with the properties of a massive solid. The concept of "isolated cluster" is very abstract, since it is practically impossible to obtain a cluster that does not interact with the environment.

The existence of energetically more favorable “magic” clusters can explain the nonmonotonic dependence of the properties of nanoclusters on their sizes. The formation of the core of a molecular cluster occurs in accordance with the concept of dense packing of metal atoms, similar to the formation of a massive metal. The number of metal atoms in a close-packed nucleus constructed as a regular 12-vertex polyhedron (cuboctahedron, icosahedron, or anticuboctahedron) is calculated by the formula:

N=1/3 (10n3 + 15n2 + 11n + 3) (1),

where n is the number of layers around the central atom. Thus, the minimum close-packed nucleus contains 13 atoms: one central atom and 12 atoms from the first layer. The result is a set of "magic" numbers N=13, 55, 147, 309, 561, 923, 1415, 2057, etc., corresponding to the most stable nuclei of metal clusters.

The electrons of the metal atoms constituting the core of the cluster are not delocalized, in contrast to the generalized electrons of the same metal atoms in a massive sample, but form discrete energy levels that are different from molecular orbitals. On passing from a bulk metal to a cluster, and then to a molecule, a transition from delocalized s- and d-electrons, which form the conduction band of a massive metal, to non-delocalized electrons, which form discrete energy levels in a cluster, and then to molecular orbitals. The appearance of discrete electronic bands in metal clusters, the size of which lies in the region of 1-4 nm, should be accompanied by the appearance of one-electron transitions.

An effective way to observe such effects is tunneling microscopy, which makes it possible to obtain current-voltage characteristics by fixing the microscope tip on a molecular cluster. When passing from the cluster to the tip of the tunneling microscope, the electron overcomes the Coulomb barrier, the value of which is equal to the electrostatic energy ΔE = e2/2C (C is the capacitance of the nanocluster, proportional to its size).

For small clusters, the electrostatic energy of an electron becomes greater than its kinetic energy kT , therefore, steps appear on the current-voltage curve U=f(I) corresponding to one electronic transition. Thus, with a decrease in the size of the cluster and the temperature of the one-electron transition, the linear dependence U=f(I), which is characteristic of a bulk metal, is violated.

Quantum size effects have been observed in the study of the magnetic susceptibility and heat capacity of molecular clusters of palladium at ultralow temperatures. It is shown that an increase in the cluster size leads to an increase in the specific magnetic susceptibility, which, at a particle size of ~30 nm, becomes equal to the value for the bulk metal. Bulk Pd has Pauli paramagnetism, which is provided by electrons with energy EF near the Fermi energy, so its magnetic susceptibility is practically independent of temperature up to liquid helium temperatures. Calculations show that upon going from Pd2057 to Pd561, i.e., upon decreasing the size of the Pd cluster, the density of states decreases at EF , which causes a change in magnetic susceptibility. The calculation predicts that as the temperature decreases (T → 0), only the susceptibility drops to zero or increases to infinity for an even and odd number of electrons, respectively, should occur. Since we studied clusters containing an odd number of electrons, we actually observed an increase in the magnetic susceptibility: significant for Pd561 (with a maximum at T<2 К), слабый для Pd1415 и почти полное отсутствие температурной зависимости для что характерно для массивного Pd.

No less interesting regularities were observed when measuring the heat capacity of giant Pd molecular clusters. Massive solids are characterized by a linear temperature dependence of the electronic heat capacity С~Т . The transition from a massive solid to nanoclusters is accompanied by the appearance of quantum size effects, which manifest themselves in the deviation of the C=f(T) dependence from linear as the cluster size decreases. Thus, the greatest deviation from the linear dependence is observed for Pd561. Taking into account the correction for the ligand dependence (С~ТЗ) for nanoclusters at ultralow temperatures Т<1К была получена зависимость С~Т2.

It is known that the heat capacity of a cluster is C=kT/δ (δ - average distance between energy levels, δ = EF/N, where N is the number of electrons in the cluster). Calculations of the δ/k values ​​carried out for the Pd561, Pd1415, and Pd2057 clusters, as well as for a colloidal Pd cluster with a size of -15 nm, gave values ​​of 12; 4.5; 3.0; and 0.06K

respectively. Thus, the unusual dependence C ~ T2 in the region T<1К свидетельствует о влиянии квантоворазмерных эффектов. Таким образом, рассматривая те или иные явления, необходимо учитывать, что крупные частицы сходны по своему строению с соответствующей макрофазой, тогда как нанообъекты имеют иную структуру. Некоторые масштабные эффекты обнаруживаются уже при d<10 мкм.

The organization of a nanostructure from nanoclusters occurs according to the same laws as the formation of clusters from atoms.

On fig. presents a colloidal gold particle of almost spherical shape, obtained as a result of spontaneous aggregation of nanocrystals with an average size of 35 ± 5 nm. However, clusters have a significant difference from atoms - they have a real surface and real intercluster boundaries. Due to the large surface of nanoclusters, and, consequently, the excess surface energy, aggregation processes are inevitable, directed towards a decrease in the Gibbs energy. Moreover, inter-cluster interactions create stresses, excess energy and excess pressure at the boundaries of clusters. Therefore, the formation of nanosystems from nanoclusters is accompanied by the appearance of a large number of defects and stresses, which leads to a fundamental change in the properties of the nanosystem.

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