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Physical nature of size-dependence of nano-particles properties [in Georgian]

Gerasimov, A. (2010) Physical nature of size-dependence of nano-particles properties [in Georgian]. Nano Studies, 1 . pp. 47-96. ISSN 1987-8826

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According to their sizes, nano-particles stand between small molecules and compact solids and possess properties distinguishing from both of them. Properties of solids obey certain rules, while molecules are characterized with different ones. Nano-particles, like the solids, reveal number of collective properties (phase states, heat and electric conductions etc). But, these properties were found to be size-dependent. First results obtained in fields of nano-particles formation and their investigations have shown that mankind meets with hitherto unknown form of matter. At present, properties and governing rules of solids are well studied and there exist physical conceptions allowing their interpretation. Unfortunately, at the same time there are known number of experimental facts, which cannot be explained based on these conceptions. In particular, size-dependence of the nano-particles properties is unaccountable in frames of traditional molecular-kinetic theory. Here we suggest novel conceptions argued both theoretically and experimentally those are possible to give us an explanation of any experimental fact obtained in solids. According to these conceptions, all properties of substance are determined by the states of chemical bonds between constituent atoms in given conditions. It is known that in solids, as well as in molecules, electrons contributing in chemical bonds can occupy two different kinds of quantum states, where they are strengthening or weakening the inter-atomic binding. In first case, they occupy bonding orbitals, while in second case-anti-bonding ones. In solids and their melts atomic orbitals are combined into bands. Free electron created in the anti-bonding band by the transition from bonding one or injection and corresponding unoccupied state (hole) in the bonding-band are anti-bonding quasi-particles (ABQPs). Regardless of the way of changing in their number (heating, illumination etc), ABQPs weaken chemical bonds between neighboring atoms. According to these conceptions substance energy bands structure, their hierarchy on the energy scale and population by electrons determine all properties of a substance at given temperature. Changes in these characteristics, mainly, in numbers of electrons on bonding and anti-bonding levels induced by any influence leads to changes in various properties of substance (aggregative state, conductivity, mechanical and optical properties etc). In condensed matter there is certain probability (for given ABQPs concentration) that several ABQPs due to their chaotic motion will fall in an atom vicinity, which can distinctly weaken its chemical bonds simplifying its displacement in lattice. The atomic displacements’ probability has been expressed by the formula: W_A = A*(n_ABQP/ N_a)^ß*W_ph (1), where n_ABQP is the ABQPs concentration, N_a is the concentration of atoms in substance, W_ph is probability of the excitation of phonon of certain energy near the given atom, A is a almost temperature-independent coefficient, ß is the number of ABQPs sufficient for causing an atomic displacement. One can see from stated relation that such probability mainly is determined by the concentration and not by the temperature unlike the diffused opinions that it should be an exponential function of temperature: W_A = B*exp(–U/kT) (2) (where U is the activation energy of atomic displacements, T is the absolute temperature, k is the Boltzmann constant, B is another almost temperature-independent coefficient). Novel mechanism of atomic displacements works for nano-particles too taking into account their features yielded from their electronic structure, which is a discrete spectrum with quite closely packed bonding and anti-bonding levels. In case of nano-particles, electron so ever placed on the anti-bonding level and corresponding hole on the bonding level will be freely move if energy-difference between these levels is ~ kT, what takes a place even at room temperature. ABQPs reaching nano-particles surface are reflected. This is a reason why they cannot leave nano-particle unlike to equal volume in the compact solid. Consequently, ABQSs in nano-particle have more neighboring atoms than in compact solid, which intensifies their weakening effect on bonds. Such effect can be described introducing effective concentration, ratio of which with its real value equals to the ratio of frequencies of ABQSs appearance near the given atom in nano-particle and compact solid during an atomic vibrations cycle. Because of small sizes, in nano-particles with the given ABQPs concentration ABQPs more frequently reach surface and are reflected from it. As a result, inter-atomic bonds in the surface layer are weakened if compared with those in bulk. Weakening in bonding leads to the decreasing in energy gap width and intensifies electron transitions at given temperature, which causes an excess of the ABQP concentration in the surface layer and then further decreasing in energy gap value. It yields an interesting energy structure of substance, which is characterized by the variable energy gap: lower near the surface than in bulk. Such kind of electronic structure leads to the ABQPs excess in surface layer and, consequently, to the material softness if compared with that in bulk. From it follows higher mobility of atoms in surface layer than in nano-particle’s bulk. It is clear that effective concentration increases with decreasing in nano-particles’ sizes. Consequently, in formula describing atomic displacements the real concentration should be substituted for effective concentration, which should be calculated separately for nano-particle’s given size and given process. For instance, let consider size-dependences for nano-particles melting temperature, diffusion coefficient and lattice constant values. According to novel conceptions (and it is proved experimentally), melting process in solid starts at certain critical concentration of ABQPs even below the substance melting temperature if critical concentration is achieved athermically. When nano-particles’ sizes decrease, the effective ABQPs concentration at given temperature increases and when their concentration reaches critical value the melting starts. This reasoning can be argued by the quite good fit between experimental and calculated curves for Au nano-particles melting temperature dependences on their sizes. Same reasoning gives a simple explanation why starts earlier melting process in the nano-particle’s surface region. Diffusion coefficient value is known to be determined by the probability W_A of atomic displacements (2). According to novel conceptions, mentioned probability depends on the ABQPs concentration (1). In case of nano-particles n_ABQP should be replaced by the effective concentration, which increases with decreasing nano-particles sizes. Accordingly, value of the diffusion coefficient increases as well, what is an experimentally observed fact. Novel conceptions give simple explanation why increases lattice parameter when nano-particle sizes decrease. It is known that weaker inter-atomic chemical bonding leads to the longer inter-atomic distance. At same time with decreasing in nano-particles sizes it starts increasing in ABQPs concentration. This weakens chemical bonds between atoms and, consequently, increase inter-atomic equilibrium distances, i.e. lattice parameter. In present work based on above mentioned conceptions there are explained mechanism of changes in size-dependent lattice constant, Debye and melting temperatures, mechanical properties, diffusion coefficient, heat capacity and heat conductivity of nano-particles.

Item Type:Article
Subjects:Physical Science > Nanophysics
Divisions:Faculty of Engineering, Science and Mathematics > School of Physics
ID Code:11741
Deposited By:Professor Levan Chkhartishvili
Deposited On:20 Jan 2012 16:36
Last Modified:20 Jan 2012 16:36

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