Atomic mixing

Quantum chemical methods, exemplified by CASSCF and other MCSCF methods, have now evolved to an extent where it is possible to routinely treat accurately the excited electronic states of molecules containing a number of atoms. Mixed nuclear dynamics, such as swarm of trajectory based surface hopping or Ehrenfest dynamics, or the Gaussian wavepacket based multiple spawning method, use an approximate representation of the nuclear wavepacket based on classical trajectories. They are thus able to use the infoiination from quantum chemistry calculations required for the propagation of the nuclei in the form of forces. These methods seem able to reproduce, at least qualitatively, the dynamics of non-adiabatic systems. Test calculations have now been run using duect dynamics, and these show that even a small number of trajectories is able to produce useful mechanistic infomiation about the photochemistry of a system. In some cases it is even possible to extract some quantitative information. 

Atomic Mixing. Depending on their mass, energy and impact angle the primary ions reach a mean depth until they are finally stopped by many collisions with sample atoms. Sample atoms are moved from their initial locations (see Sect. 3.1.1). This re-... 

MC-SCF treatments written in terms of coupled Fock equations [44], The simplest examples are the two-configuration SCF theory [45] used in and pi+2 atomic mixing [46], or bonding-antibonding molecular problems [47], and more generally the Clementi-Veillard electron-pair MC-SCF theory [48],... 

Figure 4.12 Secondary neutral and ion mass spectra of a 1 1 Fe-Ni alloy in the mass regions of monomers lop) and dimers (bottom). The dimer distribution indicates that iron and nickel are atomically mixed, as expected in an Fe-Ni alloy. Note the higher sensitivity of SIMS for iron and the manganese impurity (from ter Veen [36]).

Transposing the mixing equation (1.3.4) derived for 87Sr/86Sr and using the subscripts sa, sp, and mix for sample, spike, and mixture, we write the atomic mixing equation as... 

First, consider a binary liquid A-B in which A and B atoms mix substitutionally on a quasi-lattice with coordination number Z. There is the possibility that A-B pairs will be formed from A-A and B-B pairs by the following relation... 

Most metals of practical importance are actually mixtures of two or more metals. Recall from Section 1.1.3 that these intimate mixtures of metals are called alloys, and when the bond between the metals is partially ionic, they are termed intermetallics. For the purposes of this chapter, and especially this section, we will not need to distinguish between an intermetallic and an alloy, except to note that when a compound is indicated on a phase diagram (e.g., CuAb), it indicates an intermetallic compound. We are concerned only with the thermodynamics that describe the intimate mixing of two species under equilibrium conditions. The factors affecting how two metal atoms mix has already been described in Section 1.1.3. Recall that the solubility of one element in another depends on the relative atomic radii, the electronegativity difference between the two elements, the similarity in crystal structures, and the valencies of the two elements. Thermodynamics does not yet allow us to translate these properties of atoms directly into free energies, but these factors are what contribute to the free energy of... 

In pyridine the energetically high-lying 2s and 2px AO s of the N atom mix to form the n MO. In X -phosphorin a similar situation arises if one mixes the high-lying 3s and 3px orbitals of phosphorus. Since the s orbital component is greater... 

Ion sputtering induces lattice defects and atomic mixing among surface layers. Sputtering yield is different for different chemical species. Thus the composition of a sputtered surface is not necessarily the true composition of that layer. 

Prepare with heating a saturated ammonium sulphate solution in an amount such that there is one molecule of this salt per iron atom. Mix the prepared hot solutions and let them crystallize. Filter off the crystals on a Buchner funnel, wash them with a small amount of cold water, and dry them on filter paper. Weigh the salt and calculate the yield in per cent. 

The coordinated phenanthroline ligand is almost planar while the two pyridyl groups in coordinated bipyridyl are twisted with respect to each other (less than 10°) as a consequence of steric repulsion between non-bonded atoms. Mixed complexes of the type [Ni(bipy)(phen)2]2+ and [Ni(bipy)2(phen)]2+ have been also reported.849... 

In precursor processing, shelf life is rarely a problem as noncovalent bonding interactions between molecules and solvent content define processability. Furthermore, atomic mixing and multimetallic compounds are readily accessible as will be amply demonstrated below. Thus, there is recent interest in developing oxide precursors for processing... 

Note that reaction of Al(OH)3 with triethanolamine produces a tetrameric alumatrane159. Despite the fact that this material is likely to be only a homogeneous mixture, it behaves as if it is atomically mixed. The following sections provide an example of how this mixture pyrolytically transforms to phase pure mullite. The purpose is to provide an example of... 

Finally, it is worth noting that the mullite precursors shown above can be made at the kilogram scale in a matter of hours, whereas sol-gel derived materials can require up to one month to obtain atomically mixed gels. To date, no attempts have been made to form transition metal precursors via the OOPS or the Kemmitt and Milestone processes. However, the following section suggests that there are good reasons to explore this approach. 

In another review, Magee and Honig [24] discuss three important aspects of depth profiling by SIMS depth resolution, dynamic range and sensitivity. First, the depth resolution is a measure of the profile quality. They point out that the depth resolution is limited by atomic mixing effects and the flatness of the sputtered crater within the analyzed area. Second, the dynamic range of depth profiles is limited by crater edge... 

Fig. 4.5 Hybridization is forming new atomic orbitals, on an atom, by mathematically mixing (combining) original atomic orbitals on that atom. Mixing two orbitals gives two hybrid orbitals, and in general n AOs give n hybrid AOs. Orbitals are mathematical functions and so can be added and subtracted as shown in the figure...

In Table 2 the results of calculations on Ge ad-dimers on Si(0 01) are shown. Their relative agreement is similar to that of Si/Si(0 0 1) with the exception of the results of Ref. [86], The origin of this discrepancy is not clear to us. Experimentally, for Ge/Si(0 0 1) isolated A,B and C dimers are observed after room temperature deposition and subsequent imaging [87, 88], As has been pointed out by Lu et al. [88], there is strong evidence that even at room temperature the deposited Ge atoms mix with Si atoms of the Si(0 0 1) surface, which results in the formation of mixed Si-Ge dimers, or even pure Si dimers. The dynamic appearance of such a mixed dimer is distinctively different from that of a Si-Si or Ge-Ge dimer. Lu et al. [88] found that these mixed dimers exhibit a rocking mode, i.e. a 180° rotation of the dimer rather than a 90° rotation as has been found for Si dimers on Si(0 01) see Section 5. 

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