Atomic jumps sequence

Equation 8.19 contains the correlation factor, f, which in this case is not unity since the self-diffusion of tracer atoms by the vacancy mechanism involves correlation. Correlation is present because the jumping sequence of each tracer atom produced by atom-vacancy exchanges is not a random walk. This may be seen by... 

Fig. 5.6 Schematic diagram showing the sequence of configurations when an atom jumps from one lattice site to another (a-c) and the corresponding change in the free energy of the lattice (d). Reproduced with permission from [1], Copyright 2003, CRC Press...

The wide range of diffusivity magnitudes evident in the diffusivity spectrum in Fig. 9.1 may be expected intuitively as the atomic environment for jumping becomes progressively less free, the jump rates, T, decrease accordingly in the sequence rs > rB rD(undissoc) > rD(dissoc) > VXL. The activation energies for these diffusion processes consistently follow the reverse behavior,... 

The periodic arrangement of atoms in a single-crystal surface causes a periodic sequence of potential wells separated by an energy barrier, the activation energy for surface diffusion E (Fig. 1.9). In fact, this barrier depends on the direction of motion, but the adsorbed particle will always jump to a neighboring site along the path of minimum activation energy, which is then... 

Fig. 15. (a) The monomer unit of trans- and cis-1,4-butadiene. The alternating sequence of CH—CH2 groups, for which the magnetization-exchange process is treated, (b) The geometry of the CH—CH2 spin system. The shaded circles represent protons and the black circles carbon atoms. The conformational jumps of the methylene protons lead to an average CH—CH2 proton distance rcH—CH2 Reproduced from Ref 65, with permission from American Institute of Physics. 

There is a jump in the sequential occupation of states of the Coulomb potential, namely we pass from atomic number 18 with the n = 3, / = 0 and / = 1 states filled to atomic number 21, in which the n = 3, / = 2 states begin to be filled. The reason for this jump has to do with the fact that each electron in an atom does not experience only the pure Coulomb potential of the nucleus, but a more complex potential which is also due to the presence of all the other electrons. For this reason the true states in the atoms are somewhat different than the states of the pure Coulomb potential, which is what makes the states with n = 4 and Z = 0 start filling before the states with n = 3 and Z = 2 the n = 4, Z = 0, m = 0 states correspond to the elements K and Ca, with atomic numbers 19 and 20. Overall, however, the sequence of states in real atoms is remarkably close to what would be expected from the pure Coulomb potential. The same pattern is followed for states with higher n and Z values. 

This sequence of configurations, which involves two ions at a time rather than just the one which we have been discussing so far, is susceptible to the same network analysis as already outlined. The points in this new network would now represent more complicated configurations than just single atom displacements, but the sequence of jumps between points and the branching between possible connecting paths could be analyzed in basically the same way. 

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