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Phase shifts and chemical bonding
383
Physica B 158(1989)383-385 North-Holland, Amsterdam
PHASE SHIFTS AND CHEMICAL
BONDING
M.N. GHATIKAR DEPARTMENT
OF PHYSICS,
1.1-T. BOMBAY
400 076, INDIA
Extended X-ray Absorption Fine Structure (EXAFS) SpeCtrOSCOpy involves measuring the cross-section of X-ray absorption for a range of X-ray photon energies (30-1000 ev) above the onset of absorption The physical origin of EXAFS is ascribed to the edge position. final state interference. The final state is the result of the outgoing wave and the wave back scattered by the atoms coordinating the The oscillatory behaviour of the absorption photoexcited atom. coefficient can be described in terms,of scattering amplitude and the phase function [1,2]. r/l(k) =
3 (k) sin [2krj + bj(k)j
is the amplitude function for the jth shell, Qj (k) the where Aj(k) scattering phase shift, r. the average separation of the absorbing 3 The atom from the atom of the jth shell and k the wave number. total scattering phase shift can be written as: 4(k) where
O,(k)
=
$a(k) + oh(k) is the phase shift due to the central atom (absorbing-
atom) and 4, (k) that due to the neighbouring backscattering atoms. Several workers [l-4] have shown that in a given class of bonding the phase shift is independent of the chemical environments. In our earlier work 151 we have established a linear relationship between the phase shifts and the atomic number of the backscattering atom in a large number of Rare-earth based compounds. In the present work we would like to study the dependence of the phase shifts on the effective charge, q on the absorbing ion. Theoretical calculations of the phase shifts involve certain approximations including the neglect of the chemical bonding between the central and the backscattering atoms. The total phase shifts for copper in different compounds have been calculated using the values of the backscattering phase shifts [4]. The coefficient of the term linear in k is obtained from the linear least-square fitting of the total phase shifts and are denoted by a(T) in the Table 1. The measured EXAFS major peak positions are used to estimate the experimental phase shift [l]. We have used the crystallographic values of the bond distance and the slope of the graph n versus k to obtain a(E) and are given in the table. 0921-4526/89/$03.50 @ Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
384
M. N. Ghatikar/ Phase shifts and chemical
bonding
The concept of effective charge has been used in understanding the chemical shifts in X-ray absorption spectra [6]. Several methods have been proposed to estimate the effective charge on ions and we have used the semi-experimental method of Gianturco and Coulson [6,7]. In order to study the dependence of the phase shifts, both theoretical and the experimental values and a(E) have been plotted a(T) as a function of the effective ionic charge, q. The plot shows a linear relationship between the phase shift and the effective charge for all the compounds. However, it is noted that the theoretical phase shifts are large compared to the experimental values and this is attributed to some of the approximations used in calculating a(T). This work suggests that the effective ionic charge on the central atom can be estimated from the EXAFS measurements. This will be of interest for a complex system in which one cannot calculate the effective ionic charge. In such system one can estimate the value of q provided you have the EXAFS data. Ke have used the plot of the phase shift vs the effective ionic charge on Cu to estimate the value of q on Cu in Cu(enJ3SO4 complex. The value is in good agreement with that obtained Table
1 :
from the chemical
shift meaurement
Phase shifts and the effective
Compound
Bonding type
a(T)
[6].
ionic charge.
a(E)
(A01
(A")
Effective Charge (electran/atom)
Cu (metal)
cu-cu
0.65
0.33
CuBr
Cu-Br
0.62
0.32
0.45
cuso4
cu-0
0.90
0.40
0.75
CuCl
cu-Cl
0.90
0.40
0.80
Cu(N03j2.3H20
cu-0
0.95
0.42
0.90
Cu(en3).S04
Cu-N
0.85
0.38
0.70
2
2
385
M.N. Ghatikar/Phase shifts and chemical bonding
I
1.0
IN-
a6 t t
(x7-
d
0.8OSOL03 t
O0
Figure
1
:
4
I
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0‘8 09 q-+
The plot of the phase charge in Cu compounds
1.0
shifts and the effective ionic [(a) for a(T) and (b) for (X(E)]
111. E.A. Stern, Phys. Rev. B 10, 3027 (1974). 120, 445 (1983). 121. M.N. Ghatikar, Phys.Stat.Sol.(b), [3]. [4].
P.H. Citrin, P.E. Eisenberger, and B.M. Kincaid, Phys. Rev. Letters, 36, 1346 (1976). 101, 2815 (1979). B.K. Teo and P.A. Lee, J.Amer.Chem.Soc.
[51. [6].
M.N. M.N.
[7].
Ghatikar, Phys.Stat.Sol.(b), 135, 487 (1986). Ghatikar and B.D. Padalia, J.Phys.C 11, 1941 F.A. Gianturco and C.A. Coulson, b:olec.Phys. 14, 223
(1978).
(1368).
Physica B 158(1989)383-385 North-Holland, Amsterdam
PHASE SHIFTS AND CHEMICAL
BONDING
M.N. GHATIKAR DEPARTMENT
OF PHYSICS,
1.1-T. BOMBAY
400 076, INDIA
Extended X-ray Absorption Fine Structure (EXAFS) SpeCtrOSCOpy involves measuring the cross-section of X-ray absorption for a range of X-ray photon energies (30-1000 ev) above the onset of absorption The physical origin of EXAFS is ascribed to the edge position. final state interference. The final state is the result of the outgoing wave and the wave back scattered by the atoms coordinating the The oscillatory behaviour of the absorption photoexcited atom. coefficient can be described in terms,of scattering amplitude and the phase function [1,2]. r/l(k) =
3 (k) sin [2krj + bj(k)j
is the amplitude function for the jth shell, Qj (k) the where Aj(k) scattering phase shift, r. the average separation of the absorbing 3 The atom from the atom of the jth shell and k the wave number. total scattering phase shift can be written as: 4(k) where
O,(k)
=
$a(k) + oh(k) is the phase shift due to the central atom (absorbing-
atom) and 4, (k) that due to the neighbouring backscattering atoms. Several workers [l-4] have shown that in a given class of bonding the phase shift is independent of the chemical environments. In our earlier work 151 we have established a linear relationship between the phase shifts and the atomic number of the backscattering atom in a large number of Rare-earth based compounds. In the present work we would like to study the dependence of the phase shifts on the effective charge, q on the absorbing ion. Theoretical calculations of the phase shifts involve certain approximations including the neglect of the chemical bonding between the central and the backscattering atoms. The total phase shifts for copper in different compounds have been calculated using the values of the backscattering phase shifts [4]. The coefficient of the term linear in k is obtained from the linear least-square fitting of the total phase shifts and are denoted by a(T) in the Table 1. The measured EXAFS major peak positions are used to estimate the experimental phase shift [l]. We have used the crystallographic values of the bond distance and the slope of the graph n versus k to obtain a(E) and are given in the table. 0921-4526/89/$03.50 @ Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
384
M. N. Ghatikar/ Phase shifts and chemical
bonding
The concept of effective charge has been used in understanding the chemical shifts in X-ray absorption spectra [6]. Several methods have been proposed to estimate the effective charge on ions and we have used the semi-experimental method of Gianturco and Coulson [6,7]. In order to study the dependence of the phase shifts, both theoretical and the experimental values and a(E) have been plotted a(T) as a function of the effective ionic charge, q. The plot shows a linear relationship between the phase shift and the effective charge for all the compounds. However, it is noted that the theoretical phase shifts are large compared to the experimental values and this is attributed to some of the approximations used in calculating a(T). This work suggests that the effective ionic charge on the central atom can be estimated from the EXAFS measurements. This will be of interest for a complex system in which one cannot calculate the effective ionic charge. In such system one can estimate the value of q provided you have the EXAFS data. Ke have used the plot of the phase shift vs the effective ionic charge on Cu to estimate the value of q on Cu in Cu(enJ3SO4 complex. The value is in good agreement with that obtained Table
1 :
from the chemical
shift meaurement
Phase shifts and the effective
Compound
Bonding type
a(T)
[6].
ionic charge.
a(E)
(A01
(A")
Effective Charge (electran/atom)
Cu (metal)
cu-cu
0.65
0.33
CuBr
Cu-Br
0.62
0.32
0.45
cuso4
cu-0
0.90
0.40
0.75
CuCl
cu-Cl
0.90
0.40
0.80
Cu(N03j2.3H20
cu-0
0.95
0.42
0.90
Cu(en3).S04
Cu-N
0.85
0.38
0.70
2
2
385
M.N. Ghatikar/Phase shifts and chemical bonding
I
1.0
IN-
a6 t t
(x7-
d
0.8OSOL03 t
O0
Figure
1
:
4
I
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0‘8 09 q-+
The plot of the phase charge in Cu compounds
1.0
shifts and the effective ionic [(a) for a(T) and (b) for (X(E)]
111. E.A. Stern, Phys. Rev. B 10, 3027 (1974). 120, 445 (1983). 121. M.N. Ghatikar, Phys.Stat.Sol.(b), [3]. [4].
P.H. Citrin, P.E. Eisenberger, and B.M. Kincaid, Phys. Rev. Letters, 36, 1346 (1976). 101, 2815 (1979). B.K. Teo and P.A. Lee, J.Amer.Chem.Soc.
[51. [6].
M.N. M.N.
[7].
Ghatikar, Phys.Stat.Sol.(b), 135, 487 (1986). Ghatikar and B.D. Padalia, J.Phys.C 11, 1941 F.A. Gianturco and C.A. Coulson, b:olec.Phys. 14, 223
(1978).
(1368).