2.3 BOLS-NEP-LBA Notion
37
E ν (I )
E ν (B)
= γ =
E I
E b
= 1 + H I
(2.10)
Figure 2.5b shows that alloy or compound formation evolves the E ν (B) into the
E ν (I ) with an intensity inversion of the two XPS components. The peak intensity
inversion happens and the total intensity conserves as the total number of electrons
in the particular energy level is subject to no loss.
2.3.4 Generalization of the Irregular-Coordination Effect
The following expressions formulate the irregular-coordination induced local entrapment and polarization of electrons in terms of Hamiltonian perturbation,
H (x l ) =
⎧
⎪ ⎪ ⎪ ⎪ ⎨
⎪ ⎪ ⎪ ⎪ ⎩
H (z i ) =
E zi −E b
E b
= C
−m
zi − 1
(Defect and skin)
H (K ) =
i≤3
γ i H (z i ) = τ K
−1
i≤3
C zi
C
−m
zi − 1
(Nanosolid)
H (I ) =
E I −E b
E b
= γ − 1
(Interface)
H (P) = [E ν ( p) − E ν (0)]//E ν (12) − 1
(Polarization)
(2.11)
The following correlates energies of component l and l
in an XPS spectrum from
a specimen (l = S 1 , S 2 , …),
E ν (x l ) − E ν (0)
E ν (x l ) − E ν (0)
=
1 + Hl
1 + Hl
,
l
= l
(2.12)
This formulation yields immediately [17],
⎧
⎨
⎩
E ν (0) =
E ν (x l )
1 + Hl
− E ν
x l
(1 + Hl )
Hl
− Hl
E ν (12) = E ν (12) − E ν (0)
E ν (x l ) = E ν (12)(1 + Hl )
(2.13)
Chemical reaction or coordination variation alters neither the E ν (0) nor the bulk
shift E v (12). Accuracy of determination of the E ν (0) and the E v (12) is subject to
calibration of the XPS and to determination in the shape and size of the nanocrystal.
Nevertheless, furnished with this formulation, one could elucidate, in principle, the
core level positions of an isolated atom E ν (0) and the bulk shift E v (12), as well as
the local bond length and energy from XPS measurement, as illustrated in subsequent
chapters.