300
15 Methodology: Parameterization
15.1.1.1 Conventional Approach
Conventionally, one normalizes the individual I–E curve independently. Both the
measured I exp -E and the computed I cal -E spectra are normalized by dividing the entire
spectrum with the maximal peak intensities, I eM and I cM , of the specific spectrum,
respectively; so that the maxima of all the normalized curves are equal to unit.
Comparison between calculation and experimental results is then performed with
the “least-square” R-factor method:
R = 1 −
N
i=1 [I c (E i ) − I e (E i )]
2
N (N − 1)
.
I c (E i ) and I e (E i ) are normalized intensities at selected energies E i (step size of E i
− E i−1 = 0.1 eV was used). The R-value determines the degree of satisfaction. For an
ideal agreement, R = 1. This convention is normally used and acceptable for qualitative simulation of a certain single VLEED spectrum. This treatment gives information
of shape-similarity between the calculated and experimental spectral curves.
However, this method is inadequate for the functionalized SPB, because it is
unable to differentiate with this method the intensity discrepancy among a series of
I–E curves such as those produced by varying oxygen-exposure. This treatment will
surely miss important information such as relative variation of the spectral intensity
during the reaction.
15.1.1.2 Common-Standard Normalization
The relative intensity of one curve to another in a complete set of dynamic I–E spectra gives important information. Data collection is done under stable instrumental
conditions. Therefore, it is necessary to calibrate all the experimental curves with
a common scale to all the I–E profiles. The reasonable way is to choose one maximum I eM (E i ) from among all of the experimental spectra to calibrate all the I–E
curves across. This ensures correct information on the relative change of intensities
during the data processing, because chemical reaction changes not only the shape
but also the intensity of the spectral peaks.
On the other hand, deviations of the absolute spectral intensities from the real
status can be modulated by the damping potential (1 ± 0.2) × ImV(E) that determines
the spectral intensity. Modifying damping constant will offset the computed curves.
Therefore, intensity change corresponds to the physical process that contributes to
the inelastic damping.
Digitization of VLEED spectra is subject to the following considerations:
(1) The incident current I 0 between 6.0 and 16.0 eV was assumed to be constant
within the instrumentation error. The inner potential constant V 0 was kept constant in calculation though it varies slightly with energy for the pure Cu(001)
15 Methodology: Parameterization
15.1.1.1 Conventional Approach
Conventionally, one normalizes the individual I–E curve independently. Both the
measured I exp -E and the computed I cal -E spectra are normalized by dividing the entire
spectrum with the maximal peak intensities, I eM and I cM , of the specific spectrum,
respectively; so that the maxima of all the normalized curves are equal to unit.
Comparison between calculation and experimental results is then performed with
the “least-square” R-factor method:
R = 1 −
N
i=1 [I c (E i ) − I e (E i )]
2
N (N − 1)
.
I c (E i ) and I e (E i ) are normalized intensities at selected energies E i (step size of E i
− E i−1 = 0.1 eV was used). The R-value determines the degree of satisfaction. For an
ideal agreement, R = 1. This convention is normally used and acceptable for qualitative simulation of a certain single VLEED spectrum. This treatment gives information
of shape-similarity between the calculated and experimental spectral curves.
However, this method is inadequate for the functionalized SPB, because it is
unable to differentiate with this method the intensity discrepancy among a series of
I–E curves such as those produced by varying oxygen-exposure. This treatment will
surely miss important information such as relative variation of the spectral intensity
during the reaction.
15.1.1.2 Common-Standard Normalization
The relative intensity of one curve to another in a complete set of dynamic I–E spectra gives important information. Data collection is done under stable instrumental
conditions. Therefore, it is necessary to calibrate all the experimental curves with
a common scale to all the I–E profiles. The reasonable way is to choose one maximum I eM (E i ) from among all of the experimental spectra to calibrate all the I–E
curves across. This ensures correct information on the relative change of intensities
during the data processing, because chemical reaction changes not only the shape
but also the intensity of the spectral peaks.
On the other hand, deviations of the absolute spectral intensities from the real
status can be modulated by the damping potential (1 ± 0.2) × ImV(E) that determines
the spectral intensity. Modifying damping constant will offset the computed curves.
Therefore, intensity change corresponds to the physical process that contributes to
the inelastic damping.
Digitization of VLEED spectra is subject to the following considerations:
(1) The incident current I 0 between 6.0 and 16.0 eV was assumed to be constant
within the instrumentation error. The inner potential constant V 0 was kept constant in calculation though it varies slightly with energy for the pure Cu(001)