Atomic volume, definition

Chemicals exist as gases, liquids or solids. Solids have definite shapes and volume and are held together by strong intermolecular and interatomic forces. For many substances, these forces are strong enough to maintain the atoms in definite ordered arrays, called crystals. Solids with little or no crystal structure are termed amorphous. 

Partial molar (atomic) volume. Another useful and general way of discussing the actual trend in an alloy system of the average molar dimensions, as represented for instance by the molar (average) volumes, is through the definition and use of the partial molar (atomic) volume. 

Solution The ratio a/4ire0 has the units (C2 m N -1)/(C2 m-2 N-1) = m3, which are units of volume. In fact, polarizabilities of actual molecules are on the order of 10 29 m3 molecule-1 = 0.01 nm3 molecule-1, which is the magnitude of molecular volumes. For individual atoms, we expect the polarizability to increase with atomic volume since the outermost electrons are less tightly restrained by the nucleus in such cases. Extension of this principle to covalently bonded species must be done cautiously, however, since the bonding affects the overall picture. The accuracy of the proposition, then, depends on the nature of the particle under consideration. Even when the principle stated in the proposition is not literally true, it offers a convenient mnemonic for the definition of polarizability. ... 

As described above VWS and SAS are easily defined as sets of spheres centred on atoms. This definition, however, does not apply to SES in this case in fact, the pair of surfaces delimiting the boundary between the excluded volume and the solvent cannot be defined using spheres. There are several algorithms which translate the abstract definition of the SES into a complex solid composed of simple geometrical objects from which the surface can be easily tessellated. 

Integration of eqn (8.201) over an atomic volume for which the integral of V p(r) vanishes yields, term for term, the atomic virial theorem for a time-dep>endent system (eqn (8.193)) or for a stationary state (eqn (6.23)). Thus, eqn (8.201) is, in terms of its derivation and its integrated form, a local expression of the virial theorem. The atomic virial theorem provides the basis for the definition of the average energy of an atom, as discussed in Chapter 6. 

Dalton s liypothesis of the existence of atoms as definite quantities did not, however, meet with general acceptance. Davy, Wollaston, and others considered the quantities in Avhich Dalton had found the elements to unite with each other, as m oo proportional numbers or equivalents, as they expressed it, nor is it probable that Dalton s views would have received any further recognition until such time as they might have been exhumed from some musty tome, had their publication not been closely followed by that of the results of the labors of Humboldt and of Gay Lussac, concerning the volumes in which gases unite with each other. 

On atomic volume On the laws regulating the combination betwixt atoms On the forces operating on living matter On the applications of the atomic theory, and on its relation to other physical laws Speculative inquiry into the elements of matter On the knowledge of the ancients with respect the law of definite proportions etc. 

Several physical properties, including density, melting point, and boiling point, are related to the sizes of atoms, but atomic size is difficult to define. As we saw in Section 2.2, the electron density in an atom extends far beyond the nucleus, but we normally think of atonfic size as the volume containing about 90 percent of the total electron density around the nucleus. When we must be more specific, we define the size of an atom in terms of its atomic radius. Definitions for atonfic radius depend upon the identity and environment of the element in question ... 

The beauty of the above topological definition of the atom in a molecule lies in the fact that it coincides with the rigorous quantum mechanical definition of an open subsystem [27, 33, 34]. In particular, the atomic action integral, which is defined through the atomic one-particle Lagrangian density, is zero within the atomic volume ... 

The definition of N as the total length of mobile disloeation per unit volume takes us from the mieroseale (atoms in a erystal lattiee) to the meso-seale (a sealar quantity N. Equation (7.1) then takes us from the mesoseale to the maeroseale in whieh we aetually make measurement of the rate at whieh materials aeeumulate plastie strain. The quantity may also have its own evolutionary law involving yet another mesoseale variable. When the number of evolutionary equations (ealled the material eonstitutive deserip-tion) equals the number of variables, we ean perform a ealeulation of expeeted material response by eombination of the evolutionary law with equations of mass, momentum, and energy eonservation. 

How big is an atom or a molecule It should be fairly obvious that atoms and molecules do take up a definite amount of space. A gas can be compressed into a smaller volume but only so far. Liquids and solids cannot be easily compressed. While the individual molecules in a gas are widely separated and can be pushed into a much smaller volume, the molecules in a liquid or a solid are already close together and cannot be squeezed much further. The bottom line is that atoms and molecules require a certain amount of space. But how much ... 

Let us begin by looking again at the kinds of evidence we already have for the existence of atoms—the evidence from chemistry. We shall consider, in turn, the definite composition of compounds, the simple weight relations among compounds, and the reacting volumes of gases. Each behavior provides experimental support for the atomic theory. 

Here Hd is the number of atoms in a unit cell, the volume of which is V, and is the shortest interatomic distance in the arrangement. The definition contains a division by /2 so that the parameter D becomes unity for close-packing structures. Kepler s conjecture ensures that the parameter D is always less than or equal to unity. The fraction of space occupied (fi in the rigid-sphere model, which is often used in the discussion of metallic structures, is proportional to the parameter D and the relation is as follows. 

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