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Optical basicity of metal oxides and XPS measurement
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. ..A..:.>>_?,.:.;
::;$y
Surface Science North-Holland
Letters
262 (1992) L144-L146
.::::
y,.,~,::
surface science letters
Surface Science Letters
Optical basic&y of metal oxides and XPS measurement W.M.
Mullins
School of Materials Engineering, Purdue University, West Lafayette, IN 47907, USA Received
11 October
A semi-empirical
1991; accepted
relationship
for publication
between
11 November
XPS measured
oxygen
To describe the solvent chemistry of oxide slags for metal ions, the optical basicity index [1,2] was developed. In principle, this one parameter empirical model relates reactions to the charge density associated with the oxygen ions in the network. It is easily measured using a heavymetal probe and a UV spectrophotometer. The number reflects a measure of the valence charge density surrounding the oxygen ion in the network. The larger the optical basicity index, the higher the charge density around the oxygen and the greater the tendency to act as a Lewis base. The optical basicity can be related directly to the electronic structure of the oxide network through a Mulliken type of approach. Assuming the mixing of two orbitals [31 of energies E, and E, the occupation number of the metal orbital is
a=hx/(&-Ed,
1991
Is binding
energy
and the optical
basicity
is developed.
(and neglecting differences in overlap etc.). Fig. 1 shows the observed relationship between optical basicity [1,2,4] and the Mulliken occupations calculated using the Herman-Skillman [5] atomic eigenvalues and experimental values for the band gap [61. The basic oxides are those with the least cation character in the bonding orbitals (valence band), as shown by the semi-empirical relationship A = 1.34 - 1.97a.
(4‘
Complete calculation for the species under
results are shown in table consideration.
(1)
where A is determined by the overlap and resonance integrals for the system and x is the metal-oxygen ratio. The antibonding orbital energy is Eanti = E,
+ (E,
- E,)a2/x2.
(2)
If the HOMO is the 02p orbital and the LUMO is one of the antibonding orbitals, the Mulliken occupation numbers can be estimated from the free atom valence energies and band gap by I
I;‘ LtZaP
a=X
i
2(E,-E,)
0039-6028/92/$05.00
1 1
(3)
--
2
0 1992 - Elsevier
Science
Publishers
02
o,....,,...,....,,...j.,../,.., 0
0.1
02 Mulllken
0.3
0.4
Occupation
Number
0.5
(
Fig. 1. Optical basicity as a function of calculated Mulliken occupation of cation for several oxides. The greatest uncertainty is associated with the Na. which is very sensitive to selected values of I?,,,.
B.V. All rights reserved
KM. Mdlins / Optical basic& of metal oxides and XPS measurement
in eV, where a is the Mulliken occupation number calculated above. This represents-a relaxation in the 0 1s state due to valence level screening. The measured XPS photopeak energy is referenced to the Fermi level of the sample [S], which is calculated above. The Madelung potential for the oxygen ion in the lattice has the form E Mad = -%at@/PO,
o~,,,,~,,,.J,,,,],,,,~,,,, -a
-7
-6
-5
-4
-3
CalculatedFermiEnergy Fig. 2. Optical basicity versus calculated Fermi energy for simple oxides.
The intrinsic Fermi energy should be half-way between the HOMO and LUMO. Using the relations above, this is Er-- &r&-tEo).
(5)
This can be substituted into the above relations to show a parabolic relationship between the optical basicity and Fermi energy as shown in fig. 2. As is expected, the higher the Fermi energy, the more basic the oxide. Chemical shifts in the XPS measured 0 Is is photopeak can be directly related to shifts in the 0 Is eigenvalue, changes in the Madelung potential for oxygen and shifts in the reference level of the measurement [7]. The separation interval between the Is and 2p eigenvalues was calculated as a function of 2p state occupation using the Herman-Skillman programme [5]. The results were fitted to obtain the empirical relationship
a = 0.468 + 1.272x,
(8) still assuming full ionization of the cations. This relationship should be within 10% of the true value for simple oxides. Setting r0 to the sum of the aluminum and oxygen ionic radii in bohr units, 3.66, including a term of (1 - a*) to account for the change in cation charge and converting from hartrees to eV gives 54.4cO.468 + 1.272x)( 1 - a’) E Mad =
-
2p-1s
=
-
4.0955a2 - 501.1991
*
3.66~
54.4(0.468 + 1.272x)(1
-a2) .
3.66~
(6)
Table 1 Semi-empirical model data Cation Na Mg Al Si P B Ca
E gap
Optical basicity
teV)
a
1.34 0.78 0.61 0.48 0.40 0.42 1.00
7.1 7.5 7.5 8.4 7.5 7.0 7.1
0~07876 0.25051 0.38540 0.42816 0.53654 0.42000 0.12738
X 2 1 0.66667 0.5 0.4 0.66667 1
(9)
Combining the three energy shift terms gives the estimate for the 0 1s binding energy E 4.0955a2 - 7 E 01s = -501.1991-
AE
(7)
where scat is the calculated charge on the cation, r,, is the equilibrium cation-anion separation distance and (Y is the Madelung constant for the structure. Values of the Madelung constant were obtained 191 for NaCl, P-quartz, corundum and other structures. These were then fitted as a function of stoichiometry to obtain the approximate relation
E Fermi
E HOMO
EL,,,
OlsBE
(eV1
&VI
(eV)
(eV)
-
- 7.418 - 7.826 -9.110 - 9.905 - 10.342 - 8.956 - 7.519
- 0.288 - 0.326 -0.610 - 1.505 - 2.842 - 1.956 -0.419
-527.168 - 529.696 - 531.381 - 533.389 - 532.452 - 529.917 -530.521
3.853 4.076 4.860 5.705 6.592 5.456 3.969
(10)
W.M. Mullins / Optical basicity of metal oxides and XPS measurement
servable. Attempts have been made to show a similar relationship for transition metal oxides. Though the results would be useful, the complexity of the model, and the large number of parameters makes it of limited practicality.
-525 6 z ; g
-530
6 ,” O
References
-535
111J.A. Duffy
-540 0
0.2
0.4
0.6
0.6
Optical
Basisity
1
1.2
Fig. 3. Optical basicity versus 0 1s binding energy; squares calculated values, circles are measured in ref. [lo].
1.4
are
Values for this function, along with experimental measurements [lo] for comparison, are shown in fig. 3. Based on these calculations, the 0 1s binding energy can be used to estimate the optical basic&y of a simple oxide. For heavy metal oxides, the relationships are more complicated, but the general trends for optical basicity should be ob-
and M.D. Ingram, J. Am. Chem. Sot. 93 (1971) 6948. @IJ.A. Duffy and M.D. Ingram, J. Inorg. Nucl. Chem. 37 (19751 1203. [31 R.S. Mulliken, J. Am. Chem. Sot. 74 (1952) 811. [41 D.R. Gaskell, Met. Trans. B 20 (19891 113. 151 F. Herman and S. Skillman, Atomic Structure Calculations (Prentice Hall, Englewood Cliffs, NJ, 19631. if51W.H. Strehlow and E.L. Cook, J. Phys. Chem. Ref. Data 2 (1973) 163. [71 W.F. Egelhoff, Surf. Sci. Rep. 6 (1986) 253. [81 W.M. Mullins and B.L. Averbach, Surf. Sci. 206 (1988) 29. 191J. Sherman, Chem. Rev. 11 (1932) 93. 1101W.M. Mullins and B.L. Averbach, Surf. Sci. 206 (19881 41.
. ..A..:.>>_?,.:.;
::;$y
Surface Science North-Holland
Letters
262 (1992) L144-L146
.::::
y,.,~,::
surface science letters
Surface Science Letters
Optical basic&y of metal oxides and XPS measurement W.M.
Mullins
School of Materials Engineering, Purdue University, West Lafayette, IN 47907, USA Received
11 October
A semi-empirical
1991; accepted
relationship
for publication
between
11 November
XPS measured
oxygen
To describe the solvent chemistry of oxide slags for metal ions, the optical basicity index [1,2] was developed. In principle, this one parameter empirical model relates reactions to the charge density associated with the oxygen ions in the network. It is easily measured using a heavymetal probe and a UV spectrophotometer. The number reflects a measure of the valence charge density surrounding the oxygen ion in the network. The larger the optical basicity index, the higher the charge density around the oxygen and the greater the tendency to act as a Lewis base. The optical basicity can be related directly to the electronic structure of the oxide network through a Mulliken type of approach. Assuming the mixing of two orbitals [31 of energies E, and E, the occupation number of the metal orbital is
a=hx/(&-Ed,
1991
Is binding
energy
and the optical
basicity
is developed.
(and neglecting differences in overlap etc.). Fig. 1 shows the observed relationship between optical basicity [1,2,4] and the Mulliken occupations calculated using the Herman-Skillman [5] atomic eigenvalues and experimental values for the band gap [61. The basic oxides are those with the least cation character in the bonding orbitals (valence band), as shown by the semi-empirical relationship A = 1.34 - 1.97a.
(4‘
Complete calculation for the species under
results are shown in table consideration.
(1)
where A is determined by the overlap and resonance integrals for the system and x is the metal-oxygen ratio. The antibonding orbital energy is Eanti = E,
+ (E,
- E,)a2/x2.
(2)
If the HOMO is the 02p orbital and the LUMO is one of the antibonding orbitals, the Mulliken occupation numbers can be estimated from the free atom valence energies and band gap by I
I;‘ LtZaP
a=X
i
2(E,-E,)
0039-6028/92/$05.00
1 1
(3)
--
2
0 1992 - Elsevier
Science
Publishers
02
o,....,,...,....,,...j.,../,.., 0
0.1
02 Mulllken
0.3
0.4
Occupation
Number
0.5
(
Fig. 1. Optical basicity as a function of calculated Mulliken occupation of cation for several oxides. The greatest uncertainty is associated with the Na. which is very sensitive to selected values of I?,,,.
B.V. All rights reserved
KM. Mdlins / Optical basic& of metal oxides and XPS measurement
in eV, where a is the Mulliken occupation number calculated above. This represents-a relaxation in the 0 1s state due to valence level screening. The measured XPS photopeak energy is referenced to the Fermi level of the sample [S], which is calculated above. The Madelung potential for the oxygen ion in the lattice has the form E Mad = -%at@/PO,
o~,,,,~,,,.J,,,,],,,,~,,,, -a
-7
-6
-5
-4
-3
CalculatedFermiEnergy Fig. 2. Optical basicity versus calculated Fermi energy for simple oxides.
The intrinsic Fermi energy should be half-way between the HOMO and LUMO. Using the relations above, this is Er-- &r&-tEo).
(5)
This can be substituted into the above relations to show a parabolic relationship between the optical basicity and Fermi energy as shown in fig. 2. As is expected, the higher the Fermi energy, the more basic the oxide. Chemical shifts in the XPS measured 0 Is is photopeak can be directly related to shifts in the 0 Is eigenvalue, changes in the Madelung potential for oxygen and shifts in the reference level of the measurement [7]. The separation interval between the Is and 2p eigenvalues was calculated as a function of 2p state occupation using the Herman-Skillman programme [5]. The results were fitted to obtain the empirical relationship
a = 0.468 + 1.272x,
(8) still assuming full ionization of the cations. This relationship should be within 10% of the true value for simple oxides. Setting r0 to the sum of the aluminum and oxygen ionic radii in bohr units, 3.66, including a term of (1 - a*) to account for the change in cation charge and converting from hartrees to eV gives 54.4cO.468 + 1.272x)( 1 - a’) E Mad =
-
2p-1s
=
-
4.0955a2 - 501.1991
*
3.66~
54.4(0.468 + 1.272x)(1
-a2) .
3.66~
(6)
Table 1 Semi-empirical model data Cation Na Mg Al Si P B Ca
E gap
Optical basicity
teV)
a
1.34 0.78 0.61 0.48 0.40 0.42 1.00
7.1 7.5 7.5 8.4 7.5 7.0 7.1
0~07876 0.25051 0.38540 0.42816 0.53654 0.42000 0.12738
X 2 1 0.66667 0.5 0.4 0.66667 1
(9)
Combining the three energy shift terms gives the estimate for the 0 1s binding energy E 4.0955a2 - 7 E 01s = -501.1991-
AE
(7)
where scat is the calculated charge on the cation, r,, is the equilibrium cation-anion separation distance and (Y is the Madelung constant for the structure. Values of the Madelung constant were obtained 191 for NaCl, P-quartz, corundum and other structures. These were then fitted as a function of stoichiometry to obtain the approximate relation
E Fermi
E HOMO
EL,,,
OlsBE
(eV1
&VI
(eV)
(eV)
-
- 7.418 - 7.826 -9.110 - 9.905 - 10.342 - 8.956 - 7.519
- 0.288 - 0.326 -0.610 - 1.505 - 2.842 - 1.956 -0.419
-527.168 - 529.696 - 531.381 - 533.389 - 532.452 - 529.917 -530.521
3.853 4.076 4.860 5.705 6.592 5.456 3.969
(10)
W.M. Mullins / Optical basicity of metal oxides and XPS measurement
servable. Attempts have been made to show a similar relationship for transition metal oxides. Though the results would be useful, the complexity of the model, and the large number of parameters makes it of limited practicality.
-525 6 z ; g
-530
6 ,” O
References
-535
111J.A. Duffy
-540 0
0.2
0.4
0.6
0.6
Optical
Basisity
1
1.2
Fig. 3. Optical basicity versus 0 1s binding energy; squares calculated values, circles are measured in ref. [lo].
1.4
are
Values for this function, along with experimental measurements [lo] for comparison, are shown in fig. 3. Based on these calculations, the 0 1s binding energy can be used to estimate the optical basic&y of a simple oxide. For heavy metal oxides, the relationships are more complicated, but the general trends for optical basicity should be ob-
and M.D. Ingram, J. Am. Chem. Sot. 93 (1971) 6948. @IJ.A. Duffy and M.D. Ingram, J. Inorg. Nucl. Chem. 37 (19751 1203. [31 R.S. Mulliken, J. Am. Chem. Sot. 74 (1952) 811. [41 D.R. Gaskell, Met. Trans. B 20 (19891 113. 151 F. Herman and S. Skillman, Atomic Structure Calculations (Prentice Hall, Englewood Cliffs, NJ, 19631. if51W.H. Strehlow and E.L. Cook, J. Phys. Chem. Ref. Data 2 (1973) 163. [71 W.F. Egelhoff, Surf. Sci. Rep. 6 (1986) 253. [81 W.M. Mullins and B.L. Averbach, Surf. Sci. 206 (1988) 29. 191J. Sherman, Chem. Rev. 11 (1932) 93. 1101W.M. Mullins and B.L. Averbach, Surf. Sci. 206 (19881 41.