Metals atomic volume

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... 

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

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

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.

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... 

Increasing atomic mass accounts for both these trends. The volume occupied by an individual atom in the metallic lattice varies slowly within the d block, so the more massive the nucleus, the greater the density of the metal. Toward the end of each row, density decreases for the same reason that melting point decreases. The added electrons occupy antibonding orbitals, and this leads to a looser array of atoms, larger atomic volume, and decreased density. 

The increasing volume of chemical production, insufficient capacity and high price of olefins stimulate the rising trend in the innovation of current processes. High attention has been devoted to the direct ammoxidation of propane to acrylonitrile. A number of mixed oxide catalysts were investigated in propane ammoxidation [1]. However, up to now no catalytic system achieved reaction parameters suitable for commercial application. Nowadays the attention in the field of activation and conversion of paraffins is turned to catalytic systems where atomically dispersed metal ions are responsible for the activity of the catalysts. Ones of appropriate candidates are Fe-zeolites. Very recently, an activity of Fe-silicalite in the ammoxidation of propane was reported [2, 3]. This catalytic system exhibited relatively low yield (maximally 10% for propane to acrylonitrile). Despite the low performance, Fe-silicalites are one of the few zeolitic systems, which reveal some catalytic activity in propane ammoxidation, and therefore, we believe that it has a potential to be improved. Up to this day, investigation of Fe-silicalite and Fe-MFI catalysts in the propane ammoxidation were only reported in the literature. In this study, we compare the catalytic activity of Fe-silicalite and Fe-MTW zeolites in direct ammoxidation of propane to acrylonitrile. 

Element 114 will be a metal in the same group as Pb, element 82 (18 cm3/mol) Sn, element 50 (18 cm3 /mol) and Ge, element 32(14 cm3 /mol). We note that the atomic volume of Pb and Sn are essentially equal, probably due to the lanthanide contraction. If there is also an actinide contraction, element 114 will have an atomic volume of 18 cm3 / mol. If there is no actinide contraction, we would predict a molar volume of 22 cm3 / mol. This need to estimate atomic volume is what makes the value for density inaccurate. 

Since contraction in the direction of the bulk metal actually takes place during disproportionation [99, 100], as shown in the discussion of the Al69 and Al77 clusters 61 and 63 (cf. Section 2.3.4.1.3), the intermediate existence of a fl-A modification with a larger atom volume cannot be excluded. 

As an example for the specific case of vanadium alloys with palladium, the trend of the average atomic volume of the alloys is shown in Fig. 4.20 and compared with the phase diagram. These data were obtained by Ellner (2004) who studied the solid solutions of several metals (Ti, V, Cr, Mn, Fe, Co and Ni) in palladium. The alloys were heat treated at 800°C and water-quenched. From the unit cell parameters measured by X-ray diffraction methods, the average atomic volume was obtained Vat = c 14 (see Table 4.3). These data together with those of the literature were reported in a graph, and the partial molar (atomic) value of the vanadium volume in Pd solid solution (Fv)... 

Figure 4.20. Palladium-vanadium system. In (a) the phase diagram is shown the phase sequence at 800°C is indicated. The corresponding trend of the average atomic volume is shown in (b). For pure vanadium the value of the partial atomic volume in Pd solution is indicated (Vv, as obtained by extrapolation from the Pd-rich alloys) and, as a reference, the elemental atomic volume (FatV) of the pure metal.

Figure 4.21. Solid solutions of transition metals (Me) in palladium. The elemental atomic volumes of the pure metals (f Mc, open circles) and their partial atomic volumes in Pd solid solution (FMe, filled circles) are shown (adapted from Ellner (2004)).

The methodology for obtaining the partial atomic volume and its application as a realistic measure of atomic size in metals and alloys has been discussed by Bhatia and Cahn (2005) they illustrated its use as a powerful tool in understanding the behaviour of solid solutions in both ordered and disordered states. 

The metals are comparatively soft and ductile impurities generally have hardening and embrittling effects. Notice, as a result of the lanthanide contraction, the nearly equal atomic volumes of Nb and Ta, and the consequent very different values of the densities. 

Table XI gives the room-temperature, atmospheric pressure crystal structures, densities, and atomic volumes, along with the melting points and standard enthalpies of vaporization (cohesive energies), for the actinide metals. These particular physical properties have been chosen as those of concern to the preparative chemist who wishes to prepare an actinide metal and then characterize it via X-ray powder diffraction. The numerical values have been selected from the literature by the authors.

Actinide metal Crystal structure Density (g/cm ) Atomic volume (A ) Melting point (K) Enthalpy of vaporization AH, g (kJ/mol)... 

Steel-gray crystalline brittle metal hexagonal crystal system atomic volume 13.09 cc/g atom three allotropes are known namely, the a-metaUic form, a black amorphous vitreous solid known as P-arsenic, and also a yellow aUotrope. A few other allotropes may also exist but are not confirmed. Sublimes at 613°C when heated at normal atmospheric pressure melts at 817°C at 28 atm density 5.72 g/cc (P-metallic form) and 4.70 g/cm (p-amor-phous form) hardness 3.5 Mohs electrical resistivity (ohm-cm at 20°C) 33.3xlCh (B—metallic polycrystalline form) and 107 (p—amorphous form) insoluble in water. 

Symbol Ce atomic number 58 atomic weight 140.115 a rare-earth metal a lanthanide series inner-transition /-block element metaUic radius (alpha form) 1.8247A(CN=12) atomic volume 20.696 cm /mol electronic configuration [Xe]4fi5di6s2 common valence states -i-3 and +4 four stable isotopes Ce-140 and Ce-142 are the two major ones, their percent abundances 88.48% and 11.07%, respectively. Ce—138 (0.25%) and Ce—136(0.193%) are minor isotopes several artificial radioactive isotopes including Ce-144, a major fission product (ti 284.5 days), are known. 

Silvery metal density 13.51 g/cm (calculated) atomic volume IScm /mole melts in the range 1,300 to 1,380°C magnetic susceptibihty 12.2xl0-8cgs units/mole at 25°C dissolves in mineral acids. 

Symbol Dy atomic number 66 atomic weight 162.50 a lanthanide series, inner transition, rare earth metal electron configuration [Xe]4 5di6s2 atomic volume 19.032 cm /g. atom atomic radius 1.773A ionic radius 0.908A most common valence state +3. 

Symbol Ho atomic number 67 atomic weight 164.93 a lanthanide series rare earth element electron configuration [Xe]4/ii6s2 valence state +3 metallic radius (coordination number 12) 1.767A atomic volume 18.78 cc/mol ionic radius Ho3+ 0.894A one naturally occurring isotope. Ho-165. 

Symbol Mg atomic number 12 atomic weight 24.305 a Group II A (Group 2) alkaline-earth metal atomic radius 1.60A ionic radius (Mg2+) 0.72A atomic volume 14.0 cm /mol electron configuration [Ne]3s2 valence +2 ionization potential 7.646 and 15.035eV for Mg+ and Mg2+, respectively three natural isotopes Mg-24(78.99%), Mg-25(10.00%), Mg-26(11.01%). 

---