Atomism, atomistic theories

According to E. Stroker [1], it was not the Democritean atomistic theory of matter which was the precursor of the modem Daltonian atomic theory, as generally accepted, but the Aristotelian concept of minima naturalia, developed in the Middle Age. 

Atomistic theory of nucleation — The theory applies to very small clusters, the size n of which is a discrete variable and the process of nucleus formation must be described by means of atomistic considerations. Thus, the thermodynamic barrier AG ( ) that has to be overcome in order to form an n-atomic nucleus of the new phase is given by the general formula [i-v]... 

Under the specific conditions of electrochemical metal deposition, the critically sized clusters of the new phase have been found to consist of only a few atoms, where classical thermodynamic bulk quantities cannot be applied. Therefore, the original kinetic theory of Becker and Doering was further developed to an atomistic theory of nucleation. 

The atomistic theory becomes of additional significance for the transition from 2D Me phase formation in the UPD range to 3D Me phase formation in the OPD range. Experimental results obtained using modern in situ techniques with lateral atomic resolution showed that the transition phenomena can only be interpreted on the basis of atomistic approaches. The UPD surface modification turns out to be a more general phenomenon affecting not only the nucleation processes but also the growth mode and epitaxy of 3D metal phases. 

Classical nucleation theory may be not well suited to describe the nucleation kinetics of diamond in CVD, since the critical nucleus size under the typical CVD conditions may be on the order of a few atoms. The surface energy contribution may cause a reverse effect on the phase stability and the GFobs free-energy of the formation of a critical nucleus may be negative, a case referred to as nonclassical nucleation. In such a case, atomistic theory should be employed as the starting point of theoretical analyses. 

Nernst applied the atomistic theory of electricity to chemistry, calling the unit charges positive and negative electrons, and , which combine with atoms or radicals to form ions. He had the idea that and 0 combine to form a neutral particle constituting the ether of space (Ampere had suggested this). In his last years Nernst devoted much time to cosmological speculations. 

Leukippos, Hving during the last part of the 5 century BC was the teacher of Demokritos (460-370 bc). They had a different opinion of matter and taught that the fundamental constituents of matter are the atoms. There is an infinite number of them and they are small and invisible. They exist in the unbounded void, being entirely separate from each other, and move through the void in random directions. When they collide with other atoms, suitable in shape and size, they become interlocked. In this way composite bodies are formed. The original atomistic theory was of course just a philosophy, and no more scientific than Empedokles ideas, in spite of its similarities with the science of our time. As a theory of matter it did not become reaUy important until the scientific revival in the seventeenth century. 

Electrocrystallization was certainly among Kaischev s favorite subjects, and I suppose that this is the reason why he directed to this scientific field his first Bulgarian co-workers and later also eminent scientists E. Budevski, J. Malinovski, A. Scheludko, G. Bliznakov, and B. Mutaftchiev. They all started their most successful scientific careers, namely, in the field of electrochemical science [31-33], In 1974, R. Kaischev participated also in the development of the atomistic theory of electrochemical phase formation [34, 35], which accounts for the specific properties of small clusters of atoms and molecules (see also [10,12]). 

The field variable in the PFM is a continuum quantity in the sense that atomic information is averaged out over discrete lattice points. Hence, most PFM calculations provide no direct information of the atomic confrguration both in the equilibrium and non-equilibrium states. In reality, however, microstructural evolution process is driven by configurational kinetics through atomic movements, and detailed information fed from an atomistic scale is essential for a rigorous description of the time evolution of a microstructure. It is, therefore, desirable to combine PFM with an atomistic theory in a coherent manner. 

Skeptics criticized /i as an adjustable parameter, but when Planck chose h = 6.626 x 10 " J s he was able to fit the experimental to the experimental data for essentially an exact fit One of the main critics was Wilhelm Ostwald (1853-1932), a German physical chemist, who did not accept the atomistic theory and believed energy is continuous. While Planck also was skeptical about the existence of atoms, he had to adjust his thinking when his equation produced an exact fit to experiment based on quantization. In 1909, Ostwald was awarded the Nobel Prize for his work with catalysis. From this brief discussion, you can see that even at this late date Boltzmann s 1866 KMTG prediction of tiny gas atoms was not widely accepted. The term ultraviolet catastrophe was only used later by Paul Ehrenfest in 1911 and Planck was motivated mostly by the shift in wavelength peak with temperature due to his background in thermodynamics. 

A third sort of pluralism, and one more familiar to us, is associated with Leucip)-pus and Democritus who were younger contemporaries of Anaxagoras and Empedocles. And despite the heavy influence of Aristotle vying against the atomistic theories (he also admired their clarity and consistency) forms of atomism persist after Aristotle in the school of Epicurus and still later with the Roman Lucretius. 

In Chapter 1.3.3 we have already defined the frequencies of direct attachment and detachment, W+i and W.i, of single atoms to and from the /th site of the crystal surface in the case of electrocrystaUization. In equation (2.9) the quantities co+ and fii represent the frequencies of direct attachment and detachment of single atoms to and from an n-atomic cluster and were defined by Milchev, Stoyanov and Kaischew in the framework of the atomistic theory of electrochemical nucleation [2.10-2.12], Here we shall clarify the meaning of this definition as follows. 

Since some earlier work based on anisotropic elasticity theory had not been successful in describing the observed mechanical behaviour of NiAl (for an overview see [11]), several studies have addressed dislocation processes on the atomic length scale [6, 7, 8]. Their findings are encouraging for the use of atomistic methods, since they could explain several of the experimental observations. Nevertheless, most of the quantitative data they obtained are somewhat suspicious. For example, the Peierls stresses of the (100) and (111) dislocations are rather similar [6] and far too low to explain the measured yield stresses in hard oriented crystals. 

The precursor of such atomistic studies is a description of atomic interactions or, generally, knowledge of the dependence of the total energy of the system on the positions of the atoms. In principle, this is available in ab-initio total energy calculations based on the loc density functional theory (see, for example, Pettifor and Cottrell 1992). However, for extended defects, such as dislocations and interfaces, such calculations are only feasible when the number of atoms included into the calculation is well below one hundred. Hence, only very special cases can be treated in this framework and, indeed, the bulk of the dislocation and interfacial... 

The elucidation of the factors determining the relative stability of alternative crystalline structures of a substance would be of the greatest significance in the development of the theory of the solid state. Why, for example, do some of the alkali halides crystallize with the sodium chloride structure and some with the cesium chloride structure Why does titanium dioxide under different conditions assume the different structures of rutile, brookite and anatase Why does aluminum fluosilicate, AljSiCV F2, crystallize with the structure of topaz and not with some other structure These questions are answered formally by the statement that in each case the structure with the minimum free energy is stable. This answer, however, is not satisfying what is desired in our atomistic and quantum theoretical era is the explanation of this minimum free energy in terms of atoms or ions and their properties. 

Here, we pointed to the problem of theoretical representation, in particular, in two aspects of theory (i) the existence of highly mobile atoms at the surface such as hydrogen, which are usually not considered in the atomistic models and (ii) the importance of bandgaps and relative energy levels of electronic states, which is often distorted in local density approximations. In both respects, a quick fix to the problem is not very likely. However, as both theory and experiment continue to be developed and applied in common research projects, it can be expected that the actual understanding of the processes involved in reaction on model catalysts will substantially improve over the next 10 years. After all, the ability to trace reactions and to account for the position and charge state of each reactant is already a realization of what seemed 20 years ago a fiction rather than fact. 

From these early beginnings, computer studies have developed into sophisticated tools for the understanding of defects in solids. There are two principal methods used in routine investigations atomistic simulation and quantum mechanics. In simulation, the properties of a solid are calculated using theories such as classical electrostatics, which are applied to arrays of atoms. On the other hand, the calculation of the properties of a solid via quantum mechanics essentially involves solving the Schrodinger equation for the electrons in the material. 

In contrast, the chemists Lespieau admired were Wurtz, whose La theorie atomique (1879) "converted" him to atomistic ideas, and Grimaux, whose Theories et notations (1883) left Lespieau with the impression "that a sensible man could not help but adopt atoms." 19 Grimaux merited admiration for his modern approach to chemistry after 1898, he also merited considerable sympathy when he was fired from the Ecole Polytechnique after signing the petition supporting Alfred Dreyfus.20... 

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