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14 Principles: Bond-Band-Barrier Correlation
14.4.6 Significance and Limitations of the 3D-SPB
Instead of being independent conventionally, the ReV(z) and ImV(z, E) are tied
together through the surface charge distribution ρ(z). Except for the inner potential
constant V 0 , the parameters λ, α and z 1 are functional dependents of z 0 . The number
of variables for the SPB is hence reduced from four to one. Besides, the layout is more
physically meaningful than the independent treatment of the correlated parameters.
This single-variable parameterization allows the calculation code to optimize z 0
automatically to give intensity matching between calculation and measurement at
each value of energy. If the character z 0 remains constant, the ReV(z) and the ImV(z,
E) will degrade to the conventional form, namely, one-dimensional uniform and
monotonic energy dependence. Besides, as will be shown, the z 0 (E) profile varies
with atomic arrangement. The connection of the SPB to the crystal geometry represents that the crystal structure and the SPB are interdependent as they are consequences of surface bond formation and charge localization. It becomes now possible
to determine crystal and electronic properties simultaneously with VLEED by analyzing the structure dependent z 0 (E) profile. Therefore, the difficulty of VLEED in
conventional wisdom has been overcome completely. On the other hand, the variation
of the energy states represented by the z 0 (E) is an important aspect of chemisorption
studies, can also be probed because of this approach.
However, processes such as band-transition and single-excitation that add humps
to the monotonic damping (due to uniform DOS or constant work function) are not
clear in the present expression. Fortunately, this can be compensated for by a z 0 -
optimizing method based on the premise that the work function depends on the DOS
that is whatsoever not a constant.
This set of approaches correlate the chemical bond, valence DOS, and the SPB
with all the observations in terms of microscopy, crystallography and spectroscopy.
The significance of the approach is that it reflects the essential link of the quantities
in terms of bond forming and its consequences on the behavior of atoms and valence
electrons at the top layer of a surface by proper parameterization.
14.5 Summary
We have rationalized and formulated the energy dependent 3D-SPB and the M 2 O
tetrahedron models with expectation of the derivatives on the bond geometry, valence
DOS and morphology of the chemisorbed surface. Parameterization of the SPB and
crystal structures is necessary to correlate the features resolved using microscopy,
crystallography, and the electron spectroscopy. Calculation would be simplified by
reducing the number of independent parameters, which also reflects the real process
of reaction on the performance of atoms and electrons in the surface top layer.
14 Principles: Bond-Band-Barrier Correlation
14.4.6 Significance and Limitations of the 3D-SPB
Instead of being independent conventionally, the ReV(z) and ImV(z, E) are tied
together through the surface charge distribution ρ(z). Except for the inner potential
constant V 0 , the parameters λ, α and z 1 are functional dependents of z 0 . The number
of variables for the SPB is hence reduced from four to one. Besides, the layout is more
physically meaningful than the independent treatment of the correlated parameters.
This single-variable parameterization allows the calculation code to optimize z 0
automatically to give intensity matching between calculation and measurement at
each value of energy. If the character z 0 remains constant, the ReV(z) and the ImV(z,
E) will degrade to the conventional form, namely, one-dimensional uniform and
monotonic energy dependence. Besides, as will be shown, the z 0 (E) profile varies
with atomic arrangement. The connection of the SPB to the crystal geometry represents that the crystal structure and the SPB are interdependent as they are consequences of surface bond formation and charge localization. It becomes now possible
to determine crystal and electronic properties simultaneously with VLEED by analyzing the structure dependent z 0 (E) profile. Therefore, the difficulty of VLEED in
conventional wisdom has been overcome completely. On the other hand, the variation
of the energy states represented by the z 0 (E) is an important aspect of chemisorption
studies, can also be probed because of this approach.
However, processes such as band-transition and single-excitation that add humps
to the monotonic damping (due to uniform DOS or constant work function) are not
clear in the present expression. Fortunately, this can be compensated for by a z 0 -
optimizing method based on the premise that the work function depends on the DOS
that is whatsoever not a constant.
This set of approaches correlate the chemical bond, valence DOS, and the SPB
with all the observations in terms of microscopy, crystallography and spectroscopy.
The significance of the approach is that it reflects the essential link of the quantities
in terms of bond forming and its consequences on the behavior of atoms and valence
electrons at the top layer of a surface by proper parameterization.
14.5 Summary
We have rationalized and formulated the energy dependent 3D-SPB and the M 2 O
tetrahedron models with expectation of the derivatives on the bond geometry, valence
DOS and morphology of the chemisorbed surface. Parameterization of the SPB and
crystal structures is necessary to correlate the features resolved using microscopy,
crystallography, and the electron spectroscopy. Calculation would be simplified by
reducing the number of independent parameters, which also reflects the real process
of reaction on the performance of atoms and electrons in the surface top layer.