Atoms and Void

Gradually the debate shifted to the question of what kind of atom was necessary and possible. Isaac Newton imagined something like a miniature billiard ball to serve the purposes of his mechanical universe of masses in motion It seems probable to me, he wrote in 1704, that God in the beginning formed matter in solid, massy, hard, impenetrable, movable particles, of such sizes and figures, and with such other properties, and in such proportion to space, as most conduced to the end to which he formed 

Though in the course of ages catastrophes have occurred and may yet occur in the heavens, though ancient systems may be dissolved and new systems evolved out of their ruins, the [atoms] out of which [the sun and the planets] are built—the foundation stones of the material universe—remain unbroken and unworn. They continue this day as they were created— perfect in number and measure and weight 

Max Planck thought otherwise. He doubted that atoms existed at all, as did many of his colleagues—the particulate theory of matter was an English invention more than a Continental, and its faintly Britannic odor made it repulsive to the xenophobic German nose—but if atoms did exist he was sure they could not be mechanical It is of paramount importance, he confessed in his Scient c Autobiography, that the outside world is something independent from man, something absolute, and the quest for laws which apply to this absolute appeared to me as the most sublime scientific pursuit in life. Of all the laws of physics, Planck believed that the thermodynamic laws applied most basically to the independent outside world that his need for an absolute required. He saw early that purely mechanical atoms violated the second law of thermodynamics. His choice was clear. 

The second law specifies that heat will not pass spontaneously from a colder to a hotter body without some change in the system. Or, as Planck himself generalized it in his Ph.D. dissertation at the University of Munich in 1879, that the process of heat conduction cannot be completely reversed by any means. Besides forbidding the construction of perpetual-motion machines, the second law defines what Planck s predecessor Rudolf Clausius named entropy because energy dissipates as heat whenever work is done—heat that cannot be collected back into useful organized form—the universe must slowly run down to randomness. This vision of increasing disorder means that the universe is one-way and not reversible the second law is the expression in physical form of what we call time. But the equations of mechanical physics—of what is now called classical physics— 

What the atom of each element is, whether it is a movement, or a thing, or a vortex, or a point having inertia, whether there is any limit to its divisibility, and, if so, how that limit is imposed, whether the long list of elements is final, or whether any of them have any common origin, all these questions remain surrounded by a darkness as profound as ever. 

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In the early fifteenth century (1417 CE), De Rerum Natura by Lucretius was rediscovered. It was printed fifty-six years later in 1473 CE reintroducing the Epicurian concept of the atom and void to the western world (55). 

Democritos of Abdera (bom ca. 465 b.c.) wrote, It is customary to say that there is color, sweetness, bitterness in actuality, however, there are atoms and void [60], In this sentence, the atom, as the fundamental building block of matter, was introduced into the discussion of the structure of matter. In 1807, Dalton had only to invoke this hypothesis in order to impose order on the experimental facts known at the time. For example, a crystalline structure consisting of identical particles was also in agreement with these principles. 

Figure 6.1 The icosahedron and some of its symmetry elements, (a) An icosahedron has 12 vertices and 20 triangular faces defined by 30 edges, (b) The preferred pentagonal pyramidal coordination polyhedron for 6-coordinate boron in icosahedral structures as it is not possible to generate an infinite three-dimensional lattice on the basis of fivefold symmetry, various distortions, translations and voids occur in the actual crystal structures, (c) The distortion angle 0, which varies from 0° to 25°, for various boron atoms in crystalline boron and metal borides.

The structures of boron-rich borides (e.g. MB4, MBfi, MBio, MB12, MBe6) are even more effectively dominated by inter-B bonding, and the structures comprise three-dimensional networks of B atoms and clusters in which the metal atoms occupy specific voids or otherwise vacant sites. The structures are often exceedingly complicated (for the reasons given in Section 6.2.2) for example, the cubic unit cell of YB e has ao 2344 pm and contains 1584 B and 24 Y atoms the basic structural unit is the 13-icosahedron unit of 156 B atoms found in -rhombohedral B (p. 142) there are 8 such units (1248 B) in the unit cell and the remaining 336 B atoms are statistically distributed in channels formed by the packing of the 13-icosahedron units. 

Considering the crystal imperfections that are typically found in all crystals, the crystal quality of organic pigments is a major concern. The external surface of any crystal exhibits a number of defects, which expose portions of the crystal surface to the surrounding molecules. Impurities and voids permeate the entire interior structure of the crystal. Stress, brought about by factors such as applied shear, may change the cell constants (distances between atoms, crystalline angles). It is also possible for the three dimensional order to be incomplete or limited to one or two dimensions only (dislocations, inclusions). 

In low-spin transition metal complexes, the preferential occupancy of the d orbitals in the crystal field tends to create excess density in the voids between the bonds, which means that anharmonicity tends to reinforce the electron density asphericity. We will discuss, in the following sections, to what extent the two effects can be separated by combined use of aspherical atom and anharmonic thermal motion formalisms. 

These philosophers taught that to understand nature we must get beneath the superficial qualities of things. "According to convention," said Democritus (born 460 B.C.), "there are a sweet and a bitter, a hot and a cold, and according to convention there is colour. In truth there are atoms and a void." Those investigators attempted to connect all the differences which are observed between the qualities of things with differences of size,... 

The NMR chemical shift of I29xe adsorbed on molecular sieves reflects all the interactions between the electron cloud of the xenon atoms and their environment in the intracrystalline void volume [1]. This nucleus therefore proved to be an ideal probe for investigating various zeolitic properties such as pore dimensions [2, 3], location of the countercations [4, 5], distribution of adsorbed or occluded phases [6-8] and framework polarisability [8, 9]. 

The structure of type I hydrates is repeated in melanophlogite 61), and that of hydrates of types I and II is repeated in clathrate silicides or germa-nides of Na, K, Rb, or Cs 59, 60). The alkali metal atoms are enclosed in cages of Si or Ge atoms and are thereby protected from attack by atmospheric oxygen. The limiting composition is 8G 46Si or 24G-136Si, or the same with Si replaced by Ge however, neither of these compositions is reached since some voids do not contain an alkali metal atom. The unit cells vary as follows with the bond distances between pairs of vertices in the polyhedra. 

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