Aluminum interatomic distance

Fig. 4.9 Energies of free cations and of ionic compounds as a function of the oxidation state of the cation. Top Lines represent the ionization energy necessary to form the +1. +2, +3, and + 4 cations of sodium, magnesium, and aluminum. Note that although the ionization energy increases most sharply when a noble gas configuration is broken, isolated cations are always less stable in Itiifher oxidation states. Bottom Lines represent the sum of ionization energy and ionic bonding energy for hypothetical molecules MX, MXj, MXj, and MX in which the interatomic distance, r, has been arbitrarily set at 200 pm. Note that the most stable compounds (identified by arrows) arc NaX, MgXj, and AlXj. (All of the.se molecules will be stabilized additionally to a small extent by the electron affinity of X.)...

Scotford DM (1975) A test of aluminum in quartz as a geothermometer. Am Mineral 60 139-142 Scott HG (1975) Phase relationship in the zirconia-yttria system. J Mater Sci 10 1827-1835 Seifert F, Czank M, Simons B, Schmahl W (1987) A conunensurate-inconunensurate phase transition in iron-bearing ermanites. Phys Chem Minerals 14 26-35 Shannon RD (1976) Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides. Acta Crystallogr A32 751-767... 

For crystalline solids, the equilibrium interatomic distance, r0, can be estimated from knowledge of lattice site separation distances and is typically expressed as some fraction of the lattice parameter ac. Aluminum forms a face-centered-cubic (fee) lattice, with lattice parameter ac = 0.405 nm. Since the densest packing direction is along the face diagonal, i.e., along the (110) direction, the equilibrium interatomic distance in Al is 4la /2 = 0 29nm. We can also calculate the distance... 

Another description considers corundum crystal as built up from groups (Fig.4, p.33). In fact, the interatomic distances A -0 in 2 3 are larger (1.97 A) than those between one aluminum... 

In dimeric [Me(I)A10CH2CH20Me]2, 39, three different values were observed for the aluminum-oxygen interatomic distances (AI-O 1.826, 1.875, and 2.026 A) [88]. 

The sum of the covalent radii for the aluminum-sulfur pair is 2.23 A and the observed interatomic distances in the cited compounds fall in the range 2.35-2.40 A (see the review [113]). In monomeric Al[S(2,4,6-Bu 3QH2)]3, in which bulky organic groups prevent self-assembly, the Al-S interatomic distances are in the range 2.177-2.191 A [114], suggesting a small amount of r-delocalization. Supra-molecular self-assembly persists in solution, and the dimer-trimer equilibria have been investigated by NMR spectroscopy. 

Table 3.3. Aluminum-nitrogen interatomic distances in Al-N cage supermolecules.

Group 13 Metals - Aluminum, Gallium, Indium, Thallium 133 Table 3.7. Interatomic distances in gallium-arsenic supermolecules. 

Figure 2.8 A correlation diagram approximating how the MOs of the 2p levels of two Aluminum atoms form and are modified in energy as the respective Aluminum nuclei approach each other. This is extrapolated to zero interatomic distance such that they form the nuclei of Iron. Of note is the fact that aU but the 2p r MOs cross into the conduction band.

An example of a correlation diagram constructed from the collision of two Aluminum atoms is shown in Figure 2.8. This shows the modification in the core level MOs formed from the 2p levels as the two Aluminum atoms approach each other to zero interatomic distance (for the sake of clarity, the other levels are not shown). Zero distance is used as this allows for the extrapolation of the MO energies to those of Iron (the nucleus that would be formed). The understanding of how the MOs are modified allows for the prediction of which core holes are most likely formed during such collisions, as well as the minimum energy and distance required (Figure 2.8). 

As an example, the fact that the 4fo- level (one of the levels that arises from the 2p core level on MO formation) crosses the conduction band when the two Aluminum nuclei are within 0.7 A of each other (this is almost half the equilibrium interatomic distance) suggests that a 2p electron can be left behind in the conduction band as the two atoms recede from the collision. This would then leave a 2p core hole (see Joyes 1969a, 1969b), which would then de-excite through either Auger electron emission or fluorescence. 

These are not very oommon minerals, and the only example included here is vesuvianite. This is a complex structure with both isolated silica tetrahedra and sorosilicate groups. The ideal formula is Cai9AltFe(Al,Mg,Fe)8Sii807o (0H)8- The calcium is eight coordinated, aluminum is six coordinated, the disordered site is six coordinated and iron is both six and five coordinated. There are disordered sites in the structure which complicates the minerals. The interatomic distances are shown in Table 4.10 and the structure is shown in Figure 4.15. 

Table 2. Interatomic Distances and Bond Lengths of Aluminum Octahedra (from TAKtoCHi [1966])...

A calculation based on the decrease of the electron density at the surface and on the relaxation of the top lattice plane resulted22 in values such as 190 and 1234 erg/cm2 for the 100 faces of sodium and aluminum, respectively. The above relaxation, that is, the ratio of the interplanar distance in bulk to that in the external region was calculated23, assuming a Morse type interatomic potential. The above ratio appeared to be, e.g., 1.13 for the 100 face of calcium, and 1.016 for the 111 face of lead. The relaxation lowered the energy 7 by 0.5 to 7% for different metals and crystal faces. 

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