Atomic volumes

Note that for vacancies in crystalline phases, pv = 0 because My = 0. 

The mass fraction,, is the fraction of the total mass of the material associated with component v. 

The number density or concentration, c, is the number of atoms, molecules, moles, or other entities of component i per unit volume. Therefore, 

The site fraction is the number of species of a particular component that occupy a particular site divided by the total number of sites of that type. For example, in sodium chloride (NaCl) there is a distinction between cation and anion sites. Impurity species and vacancies may also be present. If there is a total of s distinct types of sites (s = 2 in NaCl) and there is a total number, ATjot, of sites of type j on which are distributed N- atoms (molecules) of component i, the fraction of sites of type j occupied by component i is 

The atomic volume of component i, fl, is the volume associated with one atom, molecule, or other entity. The total volume, Vtot, is comprised of contributions 

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A guide to tire stabilities of inter-metallic compounds can be obtained from the semi-empirical model of Miedema et al. (loc. cit.), in which the heat of interaction between two elements is determined by a contribution arising from the difference in work functions, A0, of tire elements, which leads to an exothermic contribution, and tire difference in the electron concentration at tire periphery of the atoms, A w, which leads to an endothermic contribution. The latter term is referred to in metal physics as the concentration of electrons at the periphery of the Wigner-Seitz cell which contains the nucleus and elecUonic structure of each metal atom within the atomic volume in the metallic state. This term is also closely related to tire bulk modulus of each element. The work function difference is very similar to the electronegativity difference. The equation which is used in tire Miedema treatment to... 

Element 0, electron volts nw, electron density V, atomic volume... 

The table below gives the Young s modulus, , the atomic volume, ft, and the melting temperature, T, for a number of metals. If... 

I Pontius, I Richelle, SI Wodak. Deviations from standard atomic volumes as a quality measure for protein crystal structures. I Mol Biol 264 121-136, 1996. 

L. Meyer drew up an atomic volume curve and a periodic table, but this laner was not published until 1895. 

Figure 2.1 shows a modem version of Lothar Meyer s atomic volume curve the alkali metals... 

Figure 2.1 Atomic volumes (molar volumes) of ihe elements in the solid state.

Using computers to display molecular structure is an attractive alternative to traditional line drawings for several reasons. First, the model displayed on a computer screen looks and behaves more like a real molecule than a drawing does. The computer model can be viewed from different angles, and different display formats can be used to show atomic positions, atomic volumes, and other features of interest. Second, the computer can produce a good model even when the student does not know how to make an accurate drawing. Thus, the student, working with a computer, can explore new areas of chemistry ... 

In this paper, the electronic structure of disordered Cu-Zn alloys are studied by calculations on models with Cu and Zn atoms distributed randomly on the sites of fee and bcc lattices. Concentrations of 10%, 25%, 50%, 75%, and 90% are used. The lattice spacings are the same for all the bcc models, 5.5 Bohr radii, and for all the fee models, 6.9 Bohr radii. With these lattice constants, the atomic volumes of the atoms are essentially the same in the two different crystal structures. Most of the bcc models contain 432 atoms and the fee models contain 500 atoms. These clusters are periodically reproduced to fill all space. Some of these calculations have been described previously. The test that is used to demonstrate that these clusters are large enough to be self-averaging is to repeat selected calculations with models that have the same concentration but a completely different arrangement of Cu and Zn atoms. We found differences that are quite small, and will be specified below in the discussions of specific properties. 

It has been shown by several authors that fee iron films exhibit a rich magnetic structure, depending very sensitively on the atomic volume. In particular in Fe... 

Va = molecular volume for component A, diffusing gas Vg = molecular volume for component B, diffused gas (See chapter on Packed Towers, Volume 2, 3rd Ed. for further discussion.) Compute from atomic volumes kj = diffusivity, fL/hr p/ = total pressure, atm Tg = absolute temperature, ° Kelvin Ma and Mg = molecular weights of the gases... 

Atomic number Atomic volume Atomic weight Valency... 

We picture the atoms in a liquid and in a solid as being packed rather tightly. The packing is random in the liquid and regular in the solid. With this picture, we can deduce from the volume per mole of atoms the volume to be assigned to a single atom. Consulting Table 6-111, we find that helium is distinctive in its atomic volume... 

The atomic volumes of the alkali metals increase with atomic number, as do those of the inert gases. Notice, however, that the volume occupied by an alkali atom is somewhat larger than that of the adjacent inert gas (with the exception of the lithium and helium—helium is the cause of this anomaly). The sodium atom in sodium metal occupies 30% more volume than does neon. Cesium occupies close to twice the volume of xenon. 

Here we find a continuation of the trend displayed by the inert gases and alkali metals. Compare the atomic volumes of the three adjacent elements in the solid state ... 

In each set, the atomic volumes increase going from halogen to inert gas to alkali metal, as shown graphically in Figure 6-9c. Figure 6-10 shows models constructed on the same scale to show the relative sizes of atoms indicated by the atomic volumes and by the packing of the ions in the ionic solids. 

Table 6-VI11 presents some properties of the elements we are considering. The first three, sodium, magnesium, and aluminum, are metallic. The melting points and boiling points are high and increase as we go from element to element. This trend reflects stronger and stronger bonding and it is paralleled by a decrease in the atomic volume.

Calculate the ratio of the number of electrons in a neutral xenon atom to the number in a neutral neon atom. Compare this number to the ratio of the atomic volumes of these two elements. On the basis of these two ratios, discuss the effects of electron-electron repulsions and electron-nuclear attractions on atomic size. 

How do the trends in physical properties for the halogens compare with those for the inert gases Compare boiling points, melting points, and atomic volumes. 

The volume per mole of atoms of some fourth-row elements (in the solid state) are as follows K, 45.3 Ca, 25.9 Sc, 18.0 Br, 23.5 and Kr, 32.2 ml/mole of atoms. Calculate the atomic volumes (volume per mole of atoms) for each of the fourth-row transition metals. Plot these atomic volumes and those of the elements given above against atomic numbers. 

Atomic velocity distribution, 130,131 Atomic volume, 94, 98 alkali metals, 94 halogens, 97 inert gases, 91 third-row elements, 101 Atomic weight, 33 table, inside back cover Atoms, 21 conservation of, 40 electrical nature of, 236 measuring dimensions of, 245 Avogadro, Amadeo hypothesis, 25, 52 hypothesis and kinetic theory, 58 law, 25 number, 33 Azo dyes, 344... 

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