Atomic and molecular volumes

There are also important classes of metallic compounds in which one component is not metallic in its elemental forms. The transition metal borides and carbides are such compounds, and TiC, which has a simple structure, has been selected for discussion in some detail. Indeed AuSn as well would be such a case if a—Sn were the only form of that element. In TiC X-ray absorption and emission and photoelectron results have been obtained for the core levels of both Ti and C. Ramqvist and co-workers have analyzed these data by comparing the shifts of different core levels in the same atom (22). This approach avoids difficulties caused by uncertainties both in the dep terms and in Fiatt, but it requires dealing with the small differences between already small individual level shifts. The relevant atomic and molecular volumes are tabulated in Table 4. If diamond, the carbon analog of a—Sn, is used as the volume characteristic of C, one has... 

The atomic and molecular volumes of inorganic liquids were considered from the point of view of the Lewis-Langmuir theory of atomic structure by Pease.2 Tasiro gave the formula log v=[ml /(p+k)]+log Voo, where Vao=sp. vol. at infinite pressure, iw=tangent of the angle between the isotherm and the abscissa axis, fc=an arbitrary constant 2 5651 Voo=b (van der Waals s constant). 

By ideal gas we mean a gas whose atomic and molecular volumes and attraction entities exert no significant influence upon the bulk volume or pressure. All real gases deviate from ideality at very low temperatures and very high pressures. In many cases (and especially so for combustion) the ideal gas law is sufficiently accurate for engineering purposes. Remarkably, the universal gas constant and heat capacities are related ... 

For the hydrogen atom, for example, the electron density is negligible at a distance beyond about 1.2 x 10" m (1.2 A or 0.12 nm) from the nucleus. The atom can therefore be regarded as a sphere with this radius. This radius is referred to as the van der Waals radius, after the Dutch physicist J. D. van der Waals (1837-1923) who related such radii and the corresponding atomic and molecular volumes to the pressure-volume behavior of gases. 

Increasingly, values for atomic and molecular volume are available from theoretical calculations. The calculated values vary somewhat, depending on... 

Here is in units of cm /s, T is the absolute temperature (K), Pj the total pressure in atmospheres, and V are the atomic and molecular volume contributions. These are empirical constants that correspond very approximately to the molar volume of the substances in cm /mol. They have been tabulated and a partial list for use with organic molecules appears in Table 3.2. 

Atomic and Molecular Volume Contributions for Diffusivity Calculations... 

All the aforesaid on the adsorption of acceptor atom and molecular particles lends support to the general conclusion of suitability of the designed sintered semiconductor oxide films (mainly ZnO) as highly sensitive semiconductor sensors meant to quantitatively detect extremely low concentrations of atom and molecular acceptor and donor particles in a concentration range of 10 -10 atoms per cubic centimetre in the volume adjacent to a semiconductor sensor. 

The bond modulus is a quite simple parameter. It is the ratio of an atomic (or molecular) energy, and an atomic (or molecular) volume. Essentially all of the volumes of interest are known from crystallography, and the energies are... 

Silver and gold form a simple alloy system because they have nearly the same atomic diameters 2.89 and 2.88 Angstroms, respectively. Both have f.c.c. crystal structures, and both come from the same column of the Periodic Table so they are isoelectronic. The two metals are mutually soluble with a heat of mixing, AUm = -48meV/atom. The molecular volume, Vm = 8.5 x 10 24cm3, so the heat of mixing density, AUm/Vm is 90.4 x 108ergs/cm3. 

A connection between ys and the melting point Tm °K was repeatedly suggested. Thus ys is said32) to be proportional to Tm/V2/3, V being the atomic or molecular volume. An almost identical rule has been advocated for metals more recently 34 namely... 

Since a does correlate with V (equation 10) and molecular volumes can be treated as summations over atomic and/or group contributions , it might be inferred that an analogous approximation (equation 12) could be applied for a ... 

Part of a three-volume set covering applications of group theory to physics. The articles by McIntosh and by Wulfman are well worth reading. They contain relatively short and self-contained presentations of material about symmetries of atomic and molecular systems that is difficult to find elsewhere in comparably accessible form. 

I. P. Grant and H. M. Quiney, Progress with BERTHA A relativistic atomic and molecular structure package, this Volume. 

This book has evolved from the author s previous attempts to give a general description of the ideas which are used to describe atomic and molecular structure, and fulsome thanks go to Ellis Horwood, the publisher of some of my books, for his generous permission to use some of the material in the present volume. 

The dimensions of the polarizability a are those of volume. The polarizability of a metallic Bphere is equal to the volume of the sphere, and we may anticipate that the polarizabilities of atoms and ions will be roughly equal to the atomic or molecular volumes. The polarizability of the normal hydrogen atom is found by an accurate quantum-mechanical calculation to be 4.5 ao that is, very nearly the volume of a sphere with radius equal to the Bohr-orbit radius a0 (4.19 a ). 

This text is a much-revised version of the book previously published as Volume II of my book Quantum Chemistry. The first chapter of the present book reviews quantum mechanics and atomic and molecular electronic structure, so that this book can be used completely independently of any other book. 

So far we have looked at molecular orbitals in a simplified way as electron pairs that try to seek locations of minimum potential energy. Now that double bonds are under consideration, it will pay us to examine in greater detail the characteristics of both atomic and molecular orbitals. You recall that an atomic orbital is a volume element oriented with respect to the nucleus of the atom where there is a high probability of finding (at the most) two electrons that are identical in quantum numbers except for direction of spin. The orbital of each type of electron (5, p, [Pg.134]

The radial distance distribution in simple atomic and molecular fluids is determined essentially by the exclusion volume of the particles. Zemike and Prins [12] have used this fact to construct a one-dimensional fluid model and calculated its radial distance correlation function and its scattering function. The only interaction between the particles is given by their exclusion volume (which is, of course, an exclusion length in the one-dimensional case) making the particles impenetrable. The statistical properties of these one-dimensional fluids are completely determined by their free volume fraction which facilitates the configurational fluctuations. 

A wavefunction ip and its eigenvalue E define an orbital. The orbital is therefore an energy level available for electrons and it implies the relevant electron distribution. In mathematical models, these distributions extend to infinity, but in a pictorial representation it is sufficient to draw the volume in which the probability of presence of the electron is rather arbitrarily around 90%. The spatial distribution of atomic and molecular orbitals have implications for processes of electron tunneling (section 4.2.1). 

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