Database of electron inelastic mean free path for
elemental solids
1. Electron inelastic mean free path (IMFP)
2. Calculation method of electron inelastic mean free path
3. Figures for electron inelastic mean free paths for 41 elemental solids over 10 eV
to 30,000 eV
Fig1. Li, Be, glassy carbon, graphite, diamond, and Na.
Fig2. Mg ,Al, Si, K, Sc, and Ti.
Fig.3 V, Cr, Fe, Co, Ni, and Cu
Fig.4 Ge, Y, Nb, Mo, Ru, and Rh.
Fig. 5 Pd, Ag, In, Sn, Cs, and Gd
Fig. 6 Tb, Dy, Hf, Ta, W, and Re.
Fig. 7 Os, Ir, Pt, Au, and Bi
4. Numerical data of electron IMFPs for 41 elemental solids over 50 eV to 30,000
eV
4.1 Table for IMFPs of Li, Be, graphite, diamond, glassy carbon, Na, Mg, Al, Si,
and K as a function of non-relativistic electron kinetic energy.
4.2 Table for IMFPs of Sc, Ti, V, Cr, Fe, Co, Ni, Cu, Ge, and Y as a function of
electron kinetic energy.
4.3 Table for IMFPs of Nb, Mo, Ru, Rh, Pd, Ag, In, Sn, Cs, and Gd as a function
of non-relativistic electron kinetic energy.
4.4 Table for IMFPs of Tb, Dy, Hf, Ta, W, Re. Os. Ir, Pt, Au and Bi as a
function of non-relativistic electron kinetic energy.
5. References
1
1. Electron Inelastic Mean Free Path
Data for elastic and inelastic scattering of electron in solids are needed for determining
the surface sensitivity of electron spectroscopies such as Auger-electron spectroscopy
(AES) and X-ray photoelectron spectroscopy (XPS) and for quantitative analyses with
these techniques.i,ii The inelastic mean free path (IMFP) is the key material parameter
that has been used to describe inelastic scattering of the detected signal electrons in AES
and XPS as well as of the primary electrons in AES.
We have reported calculations of IMFPs of 50 eV to 2000 eV electrons from
experimental optical data for 41 elemental solids, 15 inorganic compounds, and 14
organic compounds, as well as analyses of these results.iii,iv,v,vi,vii,viii ,ix,x The optical data
were checked for internal consistency using two sum rules;xi these checks indicated that
the optical data for the group of elemental solids and the group of organic compounds
were more reliable than those for the group of inorganic compounds. We analyzed
IMFPs for the groups of elemental solids and organic compounds to derive an equation,
designated TPP-2M,7 based on the Bethe equationxii for inelastic scattering of electrons
in matter. We found that the four parameters in the TPP-2M equation could be
empirically related to several material parameters (atomic or molecular weight, density,
number of valence electrons per atom or molecule, and the bandgap energy for nonconductors). The TPP-2M equation could then be used to estimate IMFPs for other
materials over the 50 eV to 2 000 eV energy range, the range of practical interest for
most AES measurements and for XPS performed with Al or Mg Kα X-ray sources.
In recent years, there has been growing interest in XPS and related
experiments performed with X-rays of much higher energies for both scientific and
technological purposes. So-called hard XPS is being applied with X-rays from
synchrotron-light sources (with energies up to 15 keV) and with Cu Kα X-ray sources
(with an energy of 8.048 keV) to characterize film composition and buried interfaces of
multi-layer thin-film samples and powders.xiii,xiv,xv In these applications, the higher X-ray
energies were needed to enable sample characterizations without removal of surface
layers by ion sputtering. We have therefore extended our earlier database by calculating
IMFPs for 41 elemental solids (Li, Be, graphite, diamond, glassy C, Na, Mg, Al, Si, K,
Sc, Ti, V, Cr, Fe, Co, Ni, Cu, Ge, Y, Nb, Mo, Ru, Rh, Pd, Ag, In, Sn, Cs, Gd, Tb, Dy,
2
Hf, Ta, W, Re, Os, Ir, Pt, Au, and Bi) and for electron energies from 10 eV to 30 keV.
The details were shown in the reference XVI.
3
2. Calculation method of electron inelastic mean free path
IMFPs were calculated at equal energy intervals on a logarithmic scale corresponding to
increments of 10 % from 10 eV to 30 keV. We first give a summary of our
implementation of the Penn algorithm.
The IMFP λ for an electron of energy E k =  2 k 2 2m in solids can be expressed
as
⎤

⎛ k ⎞⎡
⎟⎢
⎥ ,
⎝ m ⎠⎣⎢ 2 M I (k ) ⎦⎥
λ = ⎜
(1)
where k m is the electron velocity and 2M I /  is its inverse lifetime due to inelasticscattering processes.
For electron energies between 10 eV and 300 eV, we calculated MI(k) using the
full Penn algorithm (FPA):
M I (k) =
∫
∞
0
& 1
dω pG (ω p ) (
(' π a0 k
∫
Ek −EF
0
d ( ω ) ∫
q+
q−
))
dq &
1
++
Im (
q
('ε L ( q, ω; ω p ) +*+*
(2a)
q± = k #$1± 1 − ( ω Ek ) %&
(2b)
G (ω ) = −
2
1
,
Im
πω ε (ω )
(2c)
where a0 is the Bohr radius, εL is the Lindhard model dielectric function, ε(ω) is the
optical dielectric function, EF is the Fermi energy, ω is the frequency, q is the
momentum transfer, and ωp is the free-electron plasmon frequency.
For energies from 330 eV to 30 keV, we used the simpler single-pole
approximation (SPA) or simple Penn algorithm to calculate MI(k).
approximation,
4
In this
#
&
1
π ω P2
(=−
Im %
δ (ω − ω P ( q ))
2 ωP (q)
%$ε L ( q, ω; ω p ) ('
(3a)
2
& q 2 )
2
1"
$
ω ( q ) = ω + #vF (ω p ) q% + (
+ ,
3
' 2m *
2
p
2
p
(3b)
( )
where v F ω p is the Fermi velocity of a free-electron gas with plasmon frequency equal
to ωp. From Eqs. (2) and (3), MI(k) in the SPA can be expressed as
€
1
M I (k) =
2 π a0 k
q
1
%ω p + ω p ( q )
1
2 (
∫ d (ω p ) Im ε ω ln '' q 2 + 3ω ** ,
( p) &
p )q
2
(4)
where ω p = ω p E F ,
2
q = q k F , and ω p (q) = ω p2 + 4q 2 3 + q 4 . Analytical
expressions for q1 and q2 are given in Appendix A of Ref. XVII.
We note that the difference in IMFPs obtained using these two algorithms at 300
€
€
eV is very small (e.g., < 0.2 % for graphite).
€
€
5
3. Figures for electron inelastic mean free paths for 41 elemental solids over 10 eV
to 30,000 eV
Fig1. Li, Be, glassy carbon, graphite, diamond, and Na.
3
10
Na
Inelastic Mean Free Path(Å)
2
10
1
glassy
carbon
0
diamond
0
graphite
10
10
10
Be
0
3
10
10
Li
2
0
10
0
10
0
10
10
1
10
10
101
0
102
103
104
105
Electron energy (eV)
Plots of electron inelastic mean free paths as a function of electron energy for Li, Be,
graphite, diamond, glassy carbon and Na. The solid circles show calculated IMFPs from
the Penn algorithm. The solid lines show fits to these IMFPs with the modified Bethe
equation. The long-dashed lines indicate IMFPs calculated from the TPP-2M equation.
The ordinate scale on the right indicates the IMFP scale for Li. Successive plots have
been displaced vertically for clarity, and the ordinate scale at the left indicates these
displacements.
6
Fig2. Mg ,Al, Si, K, Sc, and Ti.
3
10
Ti
Inelastic Mean Free Path(Å)
2
10
Sc
1
10
K
0
10
Si
0
10
Al
3
0
10
10
Mg
2
0
10
0
10
0
10
10
1
10
10
101
0
102
103
104
105
Electron energy (eV)
Plots of electron inelastic mean free paths as a function of electron energy for Mg, Al,
Si, K, Sc and Ti. See caption to Fig. 1
7
Fig.3 V, Cr, Fe, Co, Ni, and Cu
3
10
Cu
Inelastic Mean Free Path(Å)
2
10
Ni
1
10
Co
0
10
Fe
0
10
Cr
3
0
10
V
10
2
0
10
0
10
0
10
10
1
10
10
101
0
102
103
104
105
Electron energy (eV)
Plots of electron inelastic mean free paths as a function of electron energy for V, Cr, Fe,
Co, Ni, and Cu. See caption to Fig. 1.
8
Fig.4 Ge, Y, Nb, Mo, Ru, and Rh.
3
10
Ru
Inelastic Mean Free Path(Å)
2
10
Mo
1
10
Nb
0
10
Y
0
10
Ge
0
10
3
10
2
0
10
0
10
0
10
10
1
10
10
101
0
102
103
104
105
Electron energy (eV)
Plots of electron inelastic mean free paths as a function of electron energy for Ge, Y,
Nb, Mo and Ru. See caption to Fig. 1.
9
Fig. 5 Pd, Ag, In, Sn, Cs, and Gd
4
10
Inelastic Mean Free Path(Å)
3
Cs
10
2
10
Sn
1
10
In
0
10
Ag
0
10
Pd
0
10
Rh
0
10
0
10
0
10
0
101
2
10
1
10
10
3
10
102
103
104
105
Electron energy (eV)
Plots of electron inelastic mean free paths as a function of electron energy for Rh, Pd,
Ag, In, Sn and Cs. See caption to Fig. 1.
10
Fig. 6 Tb, Dy, Hf, Ta, W, and Re.
3
10
W
Inelastic Mean Free Path(Å)
2
10
Ta
1
10
Hf
0
10
Dy
0
10
Tb
3
0
10
Gd
10
2
0
10
0
10
0
10
10
1
10
10
101
0
102
103
104
105
Electron energy (eV)
Plots of electron inelastic mean free paths as a function of electron energy for Gd, Tb,
Dy, Hf, Ta and W. See caption to Fig. 1.
11
Fig. 7 Os, Ir, Pt, Au, and Bi
3
10
Bi
Inelastic Mean Free Path(Å)
2
10
Au
1
10
Pt
0
10
Ir
0
10
Os
0
3
10
10
Re
0
10
2
10
1
0
10
0
10
10
10
101
0
102
103
104
105
Electron energy (eV)
Plots of electron inelastic mean free paths as a function of electron energy for Re, Os, Ir,
Pt, Au and Bi. See caption to Fig.1.
12
4. Numerical data of electron IMFPs for 41 elemental solids over 10 eV to 30,000
eV
4.1 Table for IMFPs of Li, Be, graphite, diamond, glassy carbon, Na, Mg, Al, Si,
and K as a function of non-relativistic electron kinetic energy.
Inelastic Mean Free Path (Å)
elereon
energy
(eV)
10.0
11.0
12.2
13.5
14.9
16.4
18.2
20.1
22.2
24.5
27.1
30.0
33.1
36.6
40.4
44.7
49.4
54.6
60.3
66.7
73.7
81.5
90.0
99.5
109.9
121.5
134.3
148.4
164.0
181.3
200.3
221.4
244.7
270.4
298.9
330.3
365.0
403.4
445.9
492.7
544.6
601.8
665.1
735.1
812.4
897.8
Li
5.1
4.5
4.0
3.7
3.5
3.4
3.4
3.4
3.4
3.5
3.5
3.7
3.8
4.0
4.1
4.3
4.6
4.8
5.1
5.4
5.8
6.1
6.5
7.0
7.4
8.0
8.5
9.1
9.8
10.5
11.3
12.1
13.1
14.1
15.1
16.4
17.7
19.2
20.7
22.4
24.3
26.3
28.5
30.9
33.5
36.4
Be
20.3
18.0
15.8
13.9
12.3
10.8
9.5
8.3
7.2
6.2
5.3
4.6
4.1
3.8
3.7
3.6
3.5
3.6
3.6
3.7
3.8
3.9
4.1
4.2
4.4
4.7
4.9
5.2
5.5
5.9
6.2
6.6
7.1
7.6
8.1
8.8
9.4
10.1
10.8
11.6
12.5
13.5
14.5
15.7
16.9
18.3
C
graphite
15.1
13.9
13.0
12.1
11.4
10.8
10.1
9.5
8.9
8.3
7.8
7.2
6.7
6.2
5.7
5.2
4.9
4.6
4.4
4.3
4.3
4.3
4.3
4.4
4.6
4.7
4.9
5.1
5.4
5.7
6.0
6.3
6.7
7.1
7.6
8.1
8.7
9.3
10.0
10.7
11.5
12.4
13.4
14.4
15.5
16.8
C
diamod
106.4
85.5
67.4
52.8
42.7
34.9
28.4
24.0
20.5
17.7
15.3
14.1
11.6
10.1
8.9
7.8
7.0
6.2
5.7
5.3
5.0
4.8
4.7
4.7
4.7
4.8
4.9
5.0
5.2
5.5
5.7
6.0
6.3
6.7
7.1
7.5
8.0
8.6
9.2
9.8
10.5
11.3
12.1
13.0
14.0
15.1
C
(glassy)
14.6
14.2
13.5
12.9
12.2
11.5
10.8
10.0
9.4
8.6
7.9
7.4
6.9
6.4
6.2
6.0
5.8
5.8
5.8
5.8
5.8
6.0
6.1
6.3
6.5
6.8
7.1
7.4
7.8
8.3
8.8
9.3
9.9
10.5
11.2
12.0
12.8
13.8
14.8
15.9
17.1
18.4
19.8
21.4
23.0
24.8
13
Na
3.9
3.5
3.3
3.2
3.1
3.1
3.2
3.3
3.4
3.5
3.6
3.8
4.0
4.2
4.4
4.7
5.0
5.2
5.6
5.9
6.3
6.7
7.1
7.5
8.0
8.5
9.1
9.7
10.4
11.1
11.8
12.7
13.6
14.6
15.7
17.0
18.3
19.7
21.2
22.9
24.7
26.7
28.9
31.3
33.8
36.7
Mg
14.3
12.4
10.9
9.6
8.1
6.2
5.0
4.4
4.0
3.8
3.7
3.6
3.6
3.7
3.7
3.8
4.0
4.1
4.3
4.5
4.7
4.9
5.1
5.4
5.7
6.1
6.4
6.8
7.2
7.7
8.2
8.7
9.3
9.9
10.6
11.4
12.2
13.1
14.0
15.1
16.2
17.5
18.9
20.4
22.0
23.8
Al
21.4
18.9
16.4
14.4
12.5
11.1
9.8
8.5
6.3
4.7
4.0
3.7
3.5
3.4
3.4
3.4
3.5
3.6
3.7
3.8
4.0
4.2
4.3
4.6
4.8
5.1
5.4
5.7
6.0
6.4
6.8
7.3
7.8
8.3
8.8
9.6
10.2
10.9
11.7
12.6
13.5
14.5
15.6
16.9
18.2
19.6
Si
24.3
21.2
18.3
15.9
13.8
12.1
10.4
8.9
7.5
6.4
5.4
4.8
4.4
4.2
4.1
4.1
4.1
4.2
4.3
4.4
4.6
4.8
5.0
5.2
5.5
5.8
6.2
6.5
6.9
7.3
7.8
8.3
8.9
9.5
10.2
11.0
11.8
12.6
13.5
14.5
15.5
16.7
18.0
19.4
20.9
22.5
K
4.2
4.3
4.3
4.4
4.5
4.6
4.8
5.0
5.2
5.3
5.5
5.8
6.0
6.2
6.5
6.8
7.1
7.4
7.7
8.1
8.5
8.9
9.4
9.9
10.5
11.2
11.9
12.7
13.6
14.6
15.6
16.8
18.1
19.4
21.0
22.8
24.6
26.6
28.7
31.1
33.6
36.4
39.5
42.8
46.3
50.2
992.3
1096.6
1212.0
1339.4
1480.3
1636.0
1808.0
1998.2
2208.3
2440.6
2697.3
2981.0
3294.5
3640.9
4023.9
4447.1
4914.8
5431.7
6002.9
6634.2
7332.0
8103.1
8955.3
9897.1
10938.0
12088.4
13359.7
14764.8
16317.6
18033.7
19930.4
22026.5
24343.0
26903.2
29732.6
39.5
42.9
46.6
50.7
55.1
59.9
65.2
71.0
77.3
84.2
91.7
99.9
108.9
118.7
129.4
141.1
153.9
167.9
183.2
199.9
218.2
238.2
260.1
284.0
310.2
338.8
370.1
404.4
441.9
483.0
527.9
577.1
631.0
689.9
754.5
19.8
21.4
23.2
25.1
27.3
29.6
32.1
34.8
37.8
41.1
44.7
48.6
52.8
57.5
62.6
68.1
74.2
80.8
88.0
95.9
104.5
113.9
124.2
135.5
147.8
161.2
175.9
192.0
209.6
228.8
249.8
272.8
298.0
325.5
355.6
18.1
19.6
21.1
22.9
24.8
26.8
29.1
31.5
34.2
37.1
40.3
43.8
47.6
51.7
56.3
61.2
66.6
72.5
78.9
85.9
93.6
102.0
111.1
121.1
132.0
144.0
157.0
171.3
186.9
204.0
222.6
243.0
265.3
289.7
316.4
16.3
17.6
19.0
20.5
22.1
24.0
25.9
28.1
30.4
33.0
35.8
38.8
42.1
45.8
49.7
54.0
58.8
63.9
69.5
75.6
82.3
89.6
97.6
106.3
115.9
126.3
137.6
150.1
163.6
178.5
194.7
212.4
231.8
253.0
276.2
26.8
29.0
31.4
33.9
36.7
39.8
43.1
46.8
50.8
55.1
59.9
65.0
70.7
76.9
83.6
90.9
99.0
107.7
117.3
127.8
139.2
151.7
165.3
180.2
196.5
214.3
233.8
255.1
278.4
303.8
331.6
362.1
395.4
431.8
471.6
14
39.8
43.1
46.8
50.9
55.2
60.0
65.3
71.0
77.2
84.0
91.4
99.6
108.4
118.1
128.6
140.2
152.8
166.6
181.6
198.1
216.1
235.8
257.3
280.8
306.5
334.7
365.4
399.1
435.9
476.3
520.3
568.6
621.4
679.2
742.5
25.7
27.8
30.2
32.7
35.4
38.4
41.7
45.3
49.2
53.5
58.1
63.2
68.7
74.8
81.4
88.6
96.4
105.0
114.4
124.7
135.9
148.1
161.5
176.1
192.1
209.6
228.7
249.6
272.4
297.4
324.7
354.6
387.3
423.0
462.2
21.2
22.9
24.8
26.9
29.1
31.6
34.2
37.1
40.3
43.8
47.6
51.7
56.2
61.1
66.5
72.4
78.8
85.8
93.4
101.7
110.8
120.8
131.7
143.6
156.5
170.7
186.3
203.2
221.8
242.1
264.2
288.5
315.1
344.1
375.9
24.3
26.3
28.5
30.8
33.4
36.2
39.2
42.5
46.2
50.1
54.5
59.2
64.3
70.0
76.1
82.8
90.1
98.1
106.9
116.4
126.8
138.2
150.6
164.2
179.1
195.3
213.0
232.4
253.6
276.8
302.2
329.9
360.3
393.5
429.8
54.5
59.1
64.1
69.6
75.6
82.1
89.2
97.0
105.5
114.8
125.0
136.0
148.1
161.4
175.8
191.6
208.8
227.7
248.3
270.8
295.4
322.4
351.8
384.0
419.2
457.7
499.8
545.9
596.3
651.4
711.8
777.8
850.1
929.2
1015.8
4.2 Table for IMFPs of Sc, Ti, V, Cr, Fe, Co, Ni, Cu, Ge, and Y as a function of
non-relativistic electron kinetic energy.
Inelastic Mean Free Path (Å)
elereon
energy
(eV)
10.0
11.0
12.2
13.5
14.9
16.4
18.2
20.1
22.2
24.5
27.1
30.0
33.1
36.6
40.4
44.7
49.4
54.6
60.3
66.7
73.7
81.5
90.0
99.5
109.9
121.5
134.3
148.4
164.0
181.3
200.3
221.4
244.7
270.4
298.9
330.3
365.0
403.4
445.9
492.7
544.6
601.8
665.1
735.1
812.4
897.8
992.3
1096.6
1212.0
Sc
19.5
16.8
14.8
13.2
11.8
10.6
9.3
8.4
7.5
6.8
6.3
5.8
5.5
5.2
4.9
4.7
4.6
4.6
4.6
4.6
4.6
4.7
4.8
4.9
5.0
5.2
5.3
5.6
5.8
6.2
6.5
6.9
7.3
7.8
8.3
8.9
9.6
10.2
11.0
11.8
12.7
13.7
14.8
16.0
17.2
18.6
20.1
21.8
23.5
Ti
20.3
17.3
14.8
12.5
11.1
9.8
8.7
7.9
7.2
6.6
6.1
5.6
5.2
4.8
4.5
4.3
4.2
4.1
4.1
4.1
4.1
4.2
4.3
4.4
4.5
4.6
4.8
5.0
5.2
5.5
5.8
6.1
6.5
6.9
7.3
7.8
8.4
9.0
9.6
10.3
11.1
11.9
12.8
13.9
14.9
16.1
17.4
18.9
20.4
V
18.8
16.1
14.1
12.3
10.5
9.5
8.4
7.7
7.1
6.6
6.2
5.8
5.5
5.2
5.0
4.8
4.6
4.5
4.5
4.5
4.5
4.5
4.6
4.7
4.8
5.0
5.1
5.3
5.5
5.7
6.0
6.3
6.6
7.0
7.4
7.9
8.4
8.9
9.5
10.2
10.9
11.7
12.6
13.6
14.6
15.8
17.0
18.4
19.8
Cr
18.9
16.2
13.9
12.0
10.5
9.3
8.3
7.5
6.9
6.4
6.0
5.7
5.4
5.1
4.9
4.7
4.5
4.3
4.3
4.2
4.2
4.2
4.3
4.4
4.5
4.7
4.8
5.0
5.2
5.4
5.7
6.0
6.3
6.7
7.1
7.5
8.0
8.6
9.1
9.8
10.5
11.2
12.1
13.0
14.0
15.0
16.2
17.5
18.9
Fe
16.2
14.2
12.3
10.9
9.6
8.7
7.8
7.2
6.6
6.1
5.7
5.3
5.1
4.8
4.6
4.5
4.4
4.3
4.3
4.3
4.3
4.4
4.5
4.6
4.7
4.9
5.1
5.3
5.5
5.7
6.0
6.3
6.6
7.0
7.4
7.9
8.3
8.9
9.4
10.1
10.8
11.5
12.4
13.3
14.3
15.4
16.6
17.9
19.3
15
Co
24.7
21.4
18.5
16.0
14.1
12.5
11.0
9.8
8.9
8.1
7.4
6.8
6.4
6.0
5.6
5.3
5.1
4.8
4.7
4.6
4.5
4.5
4.5
4.6
4.6
4.7
4.8
5.0
5.1
5.3
5.5
5.7
6.0
6.3
6.6
7.0
7.4
7.9
8.4
8.9
9.5
10.1
10.9
11.6
12.5
13.4
14.5
15.6
16.8
Ni
16.8
14.9
13.2
11.7
10.5
9.6
8.7
8.0
7.5
7.1
6.5
6.2
5.8
5.5
5.3
5.1
4.9
4.8
4.7
4.6
4.6
4.6
4.6
4.6
4.7
4.8
4.9
5.1
5.2
5.5
5.7
5.9
6.2
6.5
6.8
7.2
7.6
8.1
8.6
9.2
9.8
10.4
11.2
11.9
12.8
13.8
14.8
16.0
17.2
Cu
15.6
13.9
12.3
10.9
10.0
9.2
8.5
7.8
7.3
6.8
6.4
6.0
5.8
5.5
5.3
5.1
5.0
4.9
4.9
4.8
4.8
4.9
4.9
5.0
5.1
5.2
5.4
5.6
5.8
6.0
6.3
6.6
6.9
7.3
7.6
8.2
8.6
9.1
9.7
10.3
11.0
11.7
12.5
13.4
14.3
15.4
16.6
17.8
19.2
Ge
18.2
16.2
14.3
12.1
10.5
9.2
8.1
6.9
6.0
5.3
4.7
4.3
4.1
4.0
4.0
4.0
4.0
4.1
4.2
4.3
4.5
4.6
4.8
5.0
5.3
5.5
5.8
6.1
6.4
6.8
7.2
7.6
8.1
8.6
9.1
9.9
10.5
11.2
12.0
12.8
13.7
14.7
15.8
16.9
18.2
19.6
21.1
22.8
24.6
Y
11.9
11.1
10.2
9.6
9.0
8.5
7.9
7.4
7.0
6.5
6.1
5.8
5.5
5.3
5.2
5.1
5.1
5.0
5.1
5.1
5.2
5.3
5.4
5.5
5.7
5.9
6.2
6.5
6.8
7.2
7.6
8.1
8.7
9.2
9.9
10.7
11.5
12.3
13.2
14.2
15.3
16.5
17.7
19.1
20.6
22.2
23.9
25.8
27.9
1339.4
1480.3
1636.0
1808.0
1998.2
2208.3
2440.6
2697.3
2981.0
3294.5
3640.9
4023.9
4447.1
4914.8
5431.7
6002.9
6634.2
7332.0
8103.1
8955.3
9897.1
10938.0
12088.4
13359.7
14764.8
16317.6
18033.7
19930.4
22026.5
24343.0
26903.2
29732.6
25.5
27.6
29.9
32.4
35.1
38.1
41.3
44.9
48.7
53.0
57.6
62.6
68.1
74.1
80.6
87.8
95.6
104.1
113.4
123.6
134.7
146.8
160.1
174.6
190.4
207.8
226.7
247.4
270.1
294.8
321.9
351.5
22.1
23.9
25.8
28.0
30.3
32.9
35.7
38.7
42.0
45.7
49.6
53.9
58.6
63.8
69.4
75.5
82.2
89.5
97.5
106.2
115.7
126.1
137.5
149.9
163.5
178.3
194.6
212.3
231.7
252.9
276.1
301.5
21.4
23.2
25.1
27.1
29.4
31.8
34.5
37.4
40.5
44.0
47.7
51.9
56.3
61.2
66.6
72.4
78.8
85.7
93.3
101.6
110.7
120.6
131.4
143.2
156.1
170.2
185.6
202.5
220.9
241.0
263.0
287.1
20.5
22.1
23.9
25.9
28.0
30.3
32.9
35.6
38.7
41.9
45.5
49.4
53.7
58.4
63.5
69.0
75.1
81.7
88.9
96.8
105.5
114.9
125.2
136.4
148.7
162.1
176.8
192.8
210.4
229.5
250.5
273.4
20.8
22.5
24.4
26.4
28.5
30.9
33.4
36.2
39.3
42.6
46.3
50.2
54.5
59.3
64.4
70.0
76.2
82.9
90.2
98.2
106.9
116.4
126.8
138.2
150.6
164.2
179.0
195.2
212.9
232.3
253.5
276.7
16
18.1
19.6
21.1
22.9
24.7
26.8
29.0
31.4
34.0
36.9
40.0
43.4
47.1
51.2
55.6
60.4
65.7
71.5
77.7
84.6
92.1
100.3
109.2
118.9
129.6
141.2
153.9
167.8
183.0
199.6
217.8
237.6
18.5
20.0
21.6
23.4
25.3
27.4
29.7
32.1
34.8
37.7
40.9
44.4
48.2
52.4
56.9
61.8
67.2
73.1
79.5
86.5
94.1
102.5
111.6
121.6
132.4
144.3
157.3
171.5
187.0
204.0
222.5
242.8
20.7
22.3
24.1
26.1
28.2
30.5
33.1
35.8
38.8
42.1
45.6
49.5
53.7
58.3
63.4
68.9
74.8
81.4
88.5
96.3
104.8
114.1
124.3
135.4
147.5
160.7
175.2
191.0
208.2
227.1
247.7
270.3
26.6
28.7
31.1
33.6
36.4
39.5
42.8
46.5
50.5
54.8
59.5
64.7
70.3
76.4
83.1
90.4
98.4
107.1
116.6
127.0
138.3
150.7
164.2
179.1
195.2
212.9
232.2
253.4
276.5
301.8
329.4
359.6
30.2
32.7
35.4
38.3
41.5
45.0
48.8
53.0
57.5
62.5
67.9
73.8
80.3
87.3
95.0
103.4
112.6
122.6
133.5
145.5
158.5
172.8
188.3
205.3
223.9
244.3
266.5
290.8
317.4
346.4
378.2
413.0
4.3 Table for IMFPs of Nb, Mo, Ru, Rh, Pd, Ag, In, Sn, Cs, and Gd as a function of
non-relativistic electron kinetic energy.
Inelastic Mean Free Path (Å)
elereon
energy
(eV)
10.0
11.0
12.2
13.5
14.9
16.4
18.2
20.1
22.2
24.5
27.1
30.0
33.1
36.6
40.4
44.7
49.4
54.6
60.3
66.7
73.7
81.5
90.0
99.5
109.9
121.5
134.3
148.4
164.0
181.3
200.3
221.4
244.7
270.4
298.9
330.3
365.0
403.4
445.9
492.7
544.6
601.8
665.1
735.1
812.4
897.8
992.3
1096.6
1212.0
1339.4
Nb
27.28
24.73
21.70
19.10
16.55
14.29
12.51
11.33
10.41
9.68
8.99
8.36
7.81
7.21
6.67
6.13
5.76
5.50
5.36
5.26
5.21
5.20
5.24
5.30
5.38
5.47
5.59
5.75
5.95
6.20
6.49
6.82
7.20
7.62
8.09
8.62
9.21
9.85
10.55
11.31
12.14
13.03
13.99
15.02
16.15
17.37
18.70
20.13
21.70
23.41
Mo
31.13
27.64
24.12
20.72
17.74
14.94
12.44
10.72
9.56
8.67
8.00
7.39
6.87
6.36
5.89
5.41
5.06
4.77
4.56
4.44
4.37
4.34
4.35
4.39
4.47
4.56
4.66
4.79
4.96
5.16
5.40
5.68
5.99
6.34
6.72
7.15
7.63
8.16
8.74
9.37
10.06
10.80
11.60
12.47
13.40
14.42
15.52
16.71
18.01
19.42
Ru
25.21
22.17
18.82
16.46
14.46
12.57
11.12
9.89
8.89
8.06
7.30
6.80
6.36
5.94
5.60
5.27
4.96
4.68
4.46
4.29
4.16
4.09
4.05
4.05
4.09
4.15
4.25
4.37
4.51
4.67
4.86
5.08
5.34
5.63
5.96
6.30
6.71
7.16
7.66
8.20
8.79
9.44
10.15
10.91
11.73
12.62
13.59
14.63
15.77
17.00
Rh
23.46
19.98
16.80
14.51
12.76
11.52
10.30
9.29
8.48
7.76
7.11
6.51
6.10
5.69
5.38
5.09
4.83
4.57
4.37
4.21
4.08
4.01
3.96
3.96
3.99
4.05
4.14
4.25
4.39
4.54
4.72
4.92
5.16
5.43
5.73
6.04
6.43
6.85
7.32
7.84
8.40
9.01
9.68
10.41
11.20
12.05
12.97
13.97
15.06
16.23
Pd
19.36
16.60
14.61
13.11
11.77
10.90
9.94
9.13
8.42
7.79
7.12
6.59
6.13
5.77
5.42
5.13
4.87
4.64
4.44
4.27
4.16
4.08
4.04
4.04
4.07
4.13
4.21
4.33
4.47
4.63
4.81
5.02
5.26
5.53
5.85
6.16
6.56
7.00
7.48
8.01
8.58
9.21
9.90
10.64
11.46
12.34
13.30
14.33
15.45
16.66
17
Ag
15.51
14.17
13.09
12.34
11.57
11.02
10.57
10.01
9.52
9.08
8.57
8.08
7.66
7.31
6.92
6.56
6.18
5.91
5.63
5.39
5.18
5.05
4.94
4.88
4.87
4.89
4.94
5.01
5.13
5.28
5.46
5.66
5.89
6.16
6.47
6.74
7.15
7.61
8.11
8.66
9.26
9.92
10.63
11.42
12.27
13.19
14.15
15.23
16.39
17.65
In
17.43
15.66
13.70
12.20
10.78
9.47
8.10
6.58
5.62
5.15
4.88
4.76
4.69
4.66
4.66
4.69
4.73
4.79
4.86
4.95
5.05
5.16
5.28
5.43
5.59
5.78
6.00
6.24
6.51
6.81
7.15
7.52
7.93
8.37
8.87
9.34
9.96
10.64
11.39
12.21
13.10
14.08
15.14
16.30
17.56
18.94
20.44
22.08
23.85
25.77
Sn
21.52
18.47
16.28
14.54
13.22
12.12
11.00
9.98
8.95
7.91
7.03
6.45
6.16
5.93
5.83
5.77
5.79
5.82
5.88
5.94
6.03
6.12
6.26
6.39
6.57
6.78
7.01
7.27
7.55
7.87
8.22
8.62
9.05
9.53
10.06
10.53
11.20
11.94
12.75
13.64
14.62
15.68
16.84
18.11
19.49
20.99
22.64
24.42
26.38
28.49
Cs
3.78
3.83
3.90
3.98
4.08
4.18
4.31
4.46
4.61
4.77
4.95
5.13
5.32
5.53
5.75
5.99
6.26
6.57
6.92
7.31
7.74
8.22
8.73
9.29
9.89
10.54
11.26
12.05
12.90
13.82
14.83
15.94
17.14
18.45
19.85
21.40
23.03
24.83
26.79
28.94
31.28
33.83
36.62
39.66
42.97
46.58
50.52
54.81
59.50
64.60
Gd
13.95
12.11
10.73
9.60
8.60
7.92
7.09
6.45
5.89
5.44
4.99
4.69
4.49
4.35
4.28
4.24
4.13
4.14
4.15
4.19
4.26
4.36
4.48
4.61
4.79
5.01
5.25
5.51
5.79
6.11
6.46
6.86
7.28
7.74
8.24
8.93
9.51
10.16
10.86
11.63
12.48
13.40
14.40
15.50
16.69
18.00
19.42
20.97
22.65
24.49
1480.3
1636.0
1808.0
1998.2
2208.3
2440.6
2697.3
2981.0
3294.5
3640.9
4023.9
4447.1
4914.8
5431.7
6002.9
6634.2
7332.0
8103.1
8955.3
9897.1
10938.0
12088.4
13359.7
14764.8
16317.6
18033.7
19930.4
22026.5
24343.0
26903.2
29732.6
25.27
27.29
29.50
31.90
34.53
37.39
40.51
43.92
47.63
51.68
56.10
60.93
66.20
71.94
78.22
85.06
92.54
100.70
109.60
119.31
129.92
141.51
154.17
168.00
183.11
199.63
217.67
237.40
258.96
282.53
308.30
20.96
22.63
24.45
26.45
28.61
30.98
33.56
36.38
39.45
42.81
46.47
50.46
54.81
59.57
64.76
70.42
76.61
83.36
90.73
98.77
107.55
117.14
127.61
139.06
151.56
165.22
180.16
196.48
214.32
233.82
255.14
18.34
19.80
21.38
23.12
25.00
27.06
29.31
31.75
34.43
37.34
40.52
43.99
47.77
51.91
56.41
61.34
66.71
72.57
78.98
85.97
93.60
101.93
111.03
120.97
131.83
143.70
156.66
170.83
186.32
203.26
221.77
17.51
18.90
20.42
22.07
23.87
25.84
27.98
30.31
32.86
35.64
38.67
41.98
45.59
49.53
53.83
58.53
63.65
69.24
75.35
82.02
89.29
97.24
105.92
115.40
125.75
137.07
149.43
162.94
177.71
193.85
211.50
17.98
19.42
20.98
22.69
24.54
26.56
28.77
31.17
33.80
36.66
39.78
43.19
46.90
50.96
55.39
60.22
65.50
71.26
77.55
84.41
91.91
100.10
109.03
118.80
129.47
141.12
153.86
167.78
182.99
199.62
217.81
18
19.03
20.53
22.16
23.95
25.88
28.00
30.31
32.82
35.57
38.57
41.85
45.41
49.30
53.55
58.19
63.24
68.76
74.79
81.37
88.55
96.39
104.95
114.29
124.50
135.65
147.82
161.13
175.67
191.55
208.92
227.91
27.86
30.13
32.59
35.28
38.20
41.38
44.86
48.64
52.78
57.28
62.20
67.57
73.43
79.82
86.80
94.42
102.75
111.83
121.76
132.60
144.44
157.38
171.51
186.94
203.81
222.24
242.39
264.41
288.49
314.81
343.59
30.78
33.26
35.96
38.91
42.10
45.59
49.39
53.53
58.04
62.97
68.34
74.21
80.61
87.59
95.22
103.54
112.63
122.55
133.38
145.21
158.14
172.25
187.67
204.51
222.91
243.01
264.98
288.99
315.23
343.93
375.29
70.18
76.26
82.90
90.13
98.00
106.58
115.94
126.16
137.32
149.50
162.80
177.34
193.22
210.57
229.53
250.26
272.92
297.69
324.77
354.38
386.77
422.19
460.92
503.30
549.66
600.38
655.87
716.59
783.03
855.75
935.34
26.50
28.68
31.07
33.66
36.50
39.59
42.96
46.64
50.65
55.01
59.77
64.95
70.61
76.77
83.50
90.85
98.88
107.64
117.21
127.67
139.09
151.57
165.21
180.11
196.40
214.21
233.67
254.95
278.22
303.66
331.49
4.4 Table for IMFPs of Tb, Dy, Hf, Ta, W, Re. Os. Ir, Pt, Au and Bi as a function
of non-relativistic electron kinetic energy.
Inelastic Mean Free Path (Å)
elereon
energy
(eV)
10.0
11.0
12.2
13.5
14.9
16.4
18.2
20.1
22.2
24.5
27.1
30.0
33.1
36.6
40.4
44.7
49.4
54.6
60.3
66.7
73.7
81.5
90.0
99.5
109.9
121.5
134.3
148.4
164.0
181.3
200.3
221.4
244.7
270.4
298.9
330.3
365.0
403.4
445.9
492.7
544.6
601.8
665.1
735.1
812.4
897.8
992.3
1096.6
1212.0
1339.4
1480.3
1636.0
Tb
17.5
15.0
13.1
11.4
10.1
9.2
8.2
7.5
6.7
6.2
5.6
5.2
4.8
4.5
4.3
4.2
4.1
4.1
4.1
4.1
4.1
4.1
4.2
4.3
4.4
4.5
4.7
4.9
5.1
5.4
5.7
6.0
6.4
6.8
7.2
7.8
8.3
8.8
9.4
10.1
10.8
11.6
12.5
13.5
14.5
15.6
16.8
18.2
19.6
21.2
23.0
24.8
Dy
19.3
16.7
14.5
12.6
11.1
10.0
9.1
8.3
7.5
6.9
6.3
5.8
5.4
5.1
4.8
4.6
4.5
4.4
4.4
4.4
4.4
4.4
4.5
4.6
4.7
4.8
5.0
5.2
5.4
5.7
6.0
6.3
6.7
7.1
7.5
8.1
8.6
9.2
9.8
10.5
11.3
12.1
13.0
13.9
15.0
16.2
17.4
18.8
20.3
21.9
23.7
25.6
Hf
16.8
15.1
13.6
12.4
11.6
10.8
10.0
9.3
8.7
8.1
7.5
7.0
6.5
6.1
5.9
5.7
5.5
5.4
5.4
5.3
5.3
5.3
5.4
5.5
5.5
5.7
5.8
6.0
6.2
6.4
6.7
7.0
7.4
7.8
8.2
8.8
9.3
9.9
10.6
11.2
12.0
12.8
13.7
14.7
15.7
16.9
18.1
19.5
21.0
22.6
24.4
26.3
Ta
24.9
21.9
18.9
16.3
13.9
12.6
11.3
10.2
9.3
8.6
7.8
7.2
6.6
6.1
5.5
5.2
4.9
4.7
4.6
4.5
4.5
4.5
4.5
4.5
4.6
4.7
4.8
4.9
5.1
5.3
5.5
5.8
6.1
6.4
6.7
7.2
7.6
8.1
8.6
9.1
9.7
10.4
11.1
11.9
12.8
13.7
14.7
15.8
17.0
18.3
19.7
21.3
W
35.3
31.1
26.7
22.6
19.3
16.3
14.0
12.4
11.1
10.0
9.0
8.3
7.7
7.0
6.4
5.9
5.4
5.0
4.8
4.6
4.5
4.4
4.4
4.4
4.5
4.6
4.7
4.8
4.9
5.1
5.3
5.5
5.8
6.1
6.4
6.8
7.2
7.6
8.1
8.6
9.2
9.8
10.5
11.2
12.0
12.8
13.8
14.8
15.9
17.1
18.4
19.9
Re
32.3
28.7
25.2
21.7
19.1
17.0
14.4
12.4
10.9
9.7
8.9
8.2
7.6
7.0
6.4
5.9
5.4
5.0
4.7
4.5
4.3
4.2
4.2
4.2
4.2
4.3
4.3
4.4
4.6
4.7
4.9
5.1
5.3
5.6
5.9
6.3
6.6
7.0
7.5
7.9
8.5
9.0
9.7
10.3
11.1
11.8
12.7
13.6
14.7
15.8
17.0
18.3
19
Os
30.7
26.5
22.9
19.7
17.4
15.4
13.3
11.9
10.6
9.6
8.7
8.0
7.5
7.0
6.5
6.1
5.7
5.3
5.0
4.8
4.6
4.5
4.4
4.4
4.4
4.5
4.6
4.7
4.8
5.0
5.1
5.4
5.6
5.9
6.2
6.5
6.9
7.3
7.8
8.3
8.8
9.4
10.1
10.7
11.5
12.3
13.2
14.2
15.2
16.4
17.6
19.0
Ir
23.3
20.4
18.1
16.1
14.5
13.2
11.9
10.9
9.8
8.9
8.0
7.4
6.9
6.5
6.1
5.7
5.3
5.0
4.7
4.5
4.4
4.3
4.2
4.2
4.2
4.2
4.3
4.4
4.5
4.7
4.9
5.1
5.3
5.6
5.9
6.2
6.6
7.0
7.4
7.9
8.5
9.0
9.6
10.3
11.0
11.8
12.7
13.6
14.6
15.7
16.9
18.2
Pt
20.4
18.4
16.6
15.0
13.6
12.3
11.2
10.2
9.2
8.4
7.6
7.0
6.5
6.1
5.7
5.4
5.1
4.8
4.6
4.4
4.3
4.2
4.2
4.2
4.2
4.2
4.3
4.4
4.6
4.8
4.9
5.2
5.4
5.7
6.0
6.4
6.7
7.2
7.6
8.1
8.7
9.2
9.9
10.6
11.3
12.1
13.0
14.0
15.0
16.2
17.4
18.8
Au
18.0
16.4
14.9
13.7
12.5
11.5
10.5
9.7
8.9
8.3
7.5
7.0
6.5
6.1
5.7
5.5
5.2
5.0
4.8
4.6
4.5
4.4
4.4
4.3
4.4
4.4
4.5
4.6
4.7
4.9
5.1
5.3
5.5
5.8
6.1
6.5
6.9
7.3
7.8
8.3
8.9
9.5
10.1
10.8
11.6
12.5
13.4
14.4
15.5
16.7
18.0
19.4
Bi
14.0
12.8
11.4
10.1
9.2
8.1
7.4
6.6
6.1
5.6
5.3
5.1
5.0
4.9
4.9
4.9
4.9
5.0
5.0
5.1
5.2
5.3
5.4
5.5
5.7
5.9
6.1
6.3
6.6
6.9
7.2
7.5
7.9
8.4
8.8
9.4
10.0
10.6
11.4
12.2
13.0
14.0
15.0
16.1
17.3
18.7
20.1
21.7
23.3
25.2
27.2
29.4
1808.0
1998.2
2208.3
2440.6
2697.3
2981.0
3294.5
3640.9
4023.9
4447.1
4914.8
5431.7
6002.9
6634.2
7332.0
8103.1
8955.3
9897.1
10938.0
12088.4
13359.7
14764.8
16317.6
18033.7
19930.4
22026.5
24343.0
26903.2
29732.6
26.9
29.1
31.6
34.3
37.2
40.3
43.8
47.6
51.7
56.2
61.1
66.4
72.2
78.6
85.5
93.1
101.3
110.4
120.2
131.0
142.8
155.7
169.7
185.1
201.9
220.3
240.4
262.4
286.4
27.7
30.0
32.5
35.2
38.2
41.5
45.0
48.9
53.1
57.6
62.6
68.1
74.0
80.5
87.6
95.4
103.8
113.0
123.1
134.1
146.2
159.3
173.7
189.4
206.6
225.3
245.8
268.2
292.8
28.4
30.7
33.2
35.9
38.9
42.1
45.6
49.5
53.7
58.3
63.3
68.7
74.6
81.1
88.1
95.8
104.2
113.4
123.4
134.3
146.3
159.3
173.6
189.1
206.1
224.7
245.0
267.2
291.5
23.0
24.8
26.8
29.0
31.4
34.0
36.8
39.9
43.3
47.0
51.0
55.4
60.2
65.4
71.0
77.2
84.0
91.4
99.4
108.2
117.8
128.3
139.8
152.3
166.0
180.9
197.2
215.1
234.6
21.4
23.1
25.0
27.0
29.2
31.6
34.3
37.1
40.3
43.7
47.4
51.4
55.9
60.7
65.9
71.6
77.9
84.7
92.2
100.3
109.2
118.9
129.5
141.0
153.7
167.5
182.6
199.1
217.1
19.8
21.3
23.0
24.9
26.9
29.2
31.6
34.2
37.1
40.2
43.6
47.4
51.5
55.9
60.7
66.0
71.8
78.0
84.9
92.4
100.6
109.5
119.2
129.9
141.5
154.2
168.1
183.3
199.9
20
20.5
22.1
23.8
25.8
27.8
30.1
32.6
35.3
38.3
41.5
45.0
48.9
53.1
57.6
62.6
68.0
74.0
80.4
87.5
95.2
103.6
112.8
122.8
133.7
145.7
158.8
173.1
188.7
205.7
19.7
21.2
22.9
24.8
26.8
29.0
31.4
34.0
36.8
39.9
43.3
47.0
51.1
55.5
60.3
65.5
71.2
77.4
84.2
91.6
99.7
108.6
118.3
128.8
140.3
152.9
166.7
181.8
198.2
20.3
21.9
23.6
25.5
27.6
29.9
32.4
35.1
38.0
41.2
44.7
48.6
52.7
57.3
62.2
67.6
73.6
80.0
87.0
94.7
103.1
112.2
122.2
133.2
145.1
158.1
172.4
187.9
205.0
21.0
22.6
24.5
26.5
28.6
31.0
33.6
36.4
39.4
42.8
46.4
50.4
54.8
59.5
64.7
70.3
76.5
83.2
90.5
98.5
107.2
116.8
127.2
138.6
151.0
164.6
179.5
195.7
213.4
31.8
34.3
37.2
40.2
43.6
47.2
51.2
55.6
60.3
65.5
71.1
77.3
84.0
91.4
99.4
108.1
117.7
128.1
139.5
152.0
165.5
180.4
196.6
214.3
233.7
254.9
278.0
303.3
331.0
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C. J. Powell, A. Jablonski A, J. Electron Spectrosc. Relat. Phenom. (in press).
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C. S. Fadley, Nucl. Instr. Methods Phys. Res. A. 2005, 24, 547.
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21