82 Trends in activity and stability
far, is compared to the Cumpson-Seah formula for the estimate of the electron
mean free paths. A decrease in the estimated thicknesses can be easily observed
in all cases. This is just a consequence of the fact that the Cumpson-Seah formula
predicts in general lower electron mean free paths 112. However the decrease
is very similar in all cases, always leading to 15% lower values of d, indicating
that the energy dependence of the formula is very similar for both TPP-2M and
Cumpson-Seah expressions. Since the main interest of this work is to compare the
thickness of the Pt overlayers for different alloys, the choice of the two formulas will
basically be equivalent and only the TPP-2M formula will be used in the following.
Figure 4.13: Thickness d of the Pt overlayer as calculated by method 2 for different values
of t (thickness of the C-O-H contamiantion layer). Results from the use of the TPP-2M
formula (dotted lines) and of the Cumpson-Seah formula (full lines) are compared.
A final test of this method concerns the quality of the fit; in Section 4.5.2
it was shown how equation 4.11 can be simplified to equation 4.13 under the
assumption of EP t EGd . In Figure 4.14 the left side of equation 4.13 is plotted vs.
, which should give a linear relationship with a slope equal
to thickness d of the Pt overlayer. Clearly, with the choice of the Gd 3d5=2 peak
the assumption is not verified and a simple line does not fit well the experimental
points. In particular, the intercept of the line lies far above the origin of the graph
and the estimated value of d = 14.9 Å is far from the values presented above.
Contrarily, the approximation works quite well in the case of the Gd 4d peak. The
measured points lie on a line approximately crossing the origin of the axis and the
estimated thickness of the Pt overlayer is d = 9.8 Å, which only slightly higher than
the values of Figure 4.12. Figure 4.14 also shows that at very high emission angles
the model fails. This is probably due to the presence of elastic scattering effects
112 and to the difficulties in achieving an accurate quantification of the XPS