2.5 Numerical Strategies: Formulation and Quantification
41
Proper calibration of the equipment can remove the artifacts like ionizationinduced core-hole relaxation and radiation-induced surface charging. Upon background correction and peak-area normalization, one can decompose a skin XPS
spectrum into the B and the S i components in a positive CLS order. The best fit to
the spectral peak can estimate the number of components and the width of each for
a given spectrum. One can take the effective z 1 = 4 for the outermost layer of the
fcc(100) flat skin as the standard reference. A fine-tuning of the component energies
of all involved sublayers can optimize their z values collectively. The optimized set
of z values are only geometry dependent. Repeated fine-tuning optimizes the z value,
intensity, energy, and width of each component. The least deviation σ justifies the
accuracy and precision of the spectral analysis derivatives.
An incorporation of the BOLS-LBA-NEP notion into the TB approach and the
PES measurements not only clarifies the physical origin of the CLS but also enables
quantification of several parameters. These parameters include the energy level of an
isolated atom E ν (0) and its bulk shift E ν (12), the CN dependent CLS E ν (z) and
component width E νW (z), local bond length d z , bond energy E z , energy density E den ,
atomic cohesive energy E coh , in addition to the charge distribution—entrapment or
polarization. Polarization happens only to atoms with an effective CN smaller than
that of an atom in the flat skin.
2.5.2 Local Energy Density and Atomic Cohesive Energy
Traditionally, the surface free energy (γ s ) is defined as the energy required for cutting
a given crystal into two halves, or the energy costs in making a unit area of a surface
[44]. The interface energy (γ I ) is what required to form the unit area of an interface.
The unit of the γ s and γ I is sometimes in eV/nm
2 (density perunit area) and some
other times in eV/atom (cohesive enenrgy). Magnitude of the former is often higher
than that of the latter for the same substance. The γ s , the γ I , and their functionalities
arise from nothing more than interaction between the irregularly-coordinated atoms.
In fact, instead of the energy cost for forming a surface or an interface, the energygain per unit volume E den or the cohesive energy remnant per atom E coh in the skin
or in the interface region dictates the performance of atoms and electrons in these
irregularly-coordinated atomic sites. To effectively describe phenomena and processes at the skin and interface, the following concepts are necessary to complement the conventional terms of surface and interface free energy. Table 2.2 summarizes the formulation, physical origin, and the functionality of E den and E coh in the
irregularly-coordinated atomic sites based on the BOLS notion [45]. The concept of
skin of a certain thickness is much more meaningful than the surface or interface in
two-dimension [2].
41
Proper calibration of the equipment can remove the artifacts like ionizationinduced core-hole relaxation and radiation-induced surface charging. Upon background correction and peak-area normalization, one can decompose a skin XPS
spectrum into the B and the S i components in a positive CLS order. The best fit to
the spectral peak can estimate the number of components and the width of each for
a given spectrum. One can take the effective z 1 = 4 for the outermost layer of the
fcc(100) flat skin as the standard reference. A fine-tuning of the component energies
of all involved sublayers can optimize their z values collectively. The optimized set
of z values are only geometry dependent. Repeated fine-tuning optimizes the z value,
intensity, energy, and width of each component. The least deviation σ justifies the
accuracy and precision of the spectral analysis derivatives.
An incorporation of the BOLS-LBA-NEP notion into the TB approach and the
PES measurements not only clarifies the physical origin of the CLS but also enables
quantification of several parameters. These parameters include the energy level of an
isolated atom E ν (0) and its bulk shift E ν (12), the CN dependent CLS E ν (z) and
component width E νW (z), local bond length d z , bond energy E z , energy density E den ,
atomic cohesive energy E coh , in addition to the charge distribution—entrapment or
polarization. Polarization happens only to atoms with an effective CN smaller than
that of an atom in the flat skin.
2.5.2 Local Energy Density and Atomic Cohesive Energy
Traditionally, the surface free energy (γ s ) is defined as the energy required for cutting
a given crystal into two halves, or the energy costs in making a unit area of a surface
[44]. The interface energy (γ I ) is what required to form the unit area of an interface.
The unit of the γ s and γ I is sometimes in eV/nm
2 (density perunit area) and some
other times in eV/atom (cohesive enenrgy). Magnitude of the former is often higher
than that of the latter for the same substance. The γ s , the γ I , and their functionalities
arise from nothing more than interaction between the irregularly-coordinated atoms.
In fact, instead of the energy cost for forming a surface or an interface, the energygain per unit volume E den or the cohesive energy remnant per atom E coh in the skin
or in the interface region dictates the performance of atoms and electrons in these
irregularly-coordinated atomic sites. To effectively describe phenomena and processes at the skin and interface, the following concepts are necessary to complement the conventional terms of surface and interface free energy. Table 2.2 summarizes the formulation, physical origin, and the functionality of E den and E coh in the
irregularly-coordinated atomic sites based on the BOLS notion [45]. The concept of
skin of a certain thickness is much more meaningful than the surface or interface in
two-dimension [2].