Indian Journal of Pure & Applied Physics
Vol. 44, January 2006, pp. 20-24
Bonding parameter, phase parameter and Ni K-edge position studies of
some Ni systems
Vinod K Singh
Department of Applied Physics, Indian School of Mines, Dhanbad 826 004, Jharkhand
Email: [email protected]
Received 17 November 2004; revised 17 August 2005; accepted 9 September 2005
Extended X-ray absorption fine structure (EXAFS) phase shift studies of some nickel compounds have been carried out
and the values of bonding parameter α1 and phase parameter β1 are evaluated by graphical method. α1 is then correlated
with nearest neighbour distance and ionicity of the corresponding systems. It has been observed that the bonding parameter
α1 decreases as bond distance decreases except in Ni3(PO4)2.XH2O and NiCl2.6H2O and decreases with increase of the
ionicity except for NiBr2. The phase parameter β1 has been correlated with oxygen atoms present in a system. The nickel Kedge position in the systems under study has been correlated with ionicity. No good relation has been observed between
ionicity and edge position. This has been attributed to different structure and coordination number of a system.
Keywords: EXAFS, XAFS, K-edge X-ray absorption spectra
IPC Code: G01J3/42
1 Introduction
Extended X-ray absorption fine structure (EXAFS)
observed on the high energy side of the absorption
edge is attributed to the scattering of the
photoelectron emitted by the absorption of the X-ray
by the atoms, surrounding the emitting atom. The
structures are observed in crystalline, glasses, liquids
and in gases except in monoatomic gases. The
structure appears over a few hundred eV on the higher
side of absorption edge. In contrast, the structure
close to the edge is generally dominated by strong
multiple scattering process and also local atomic
resonance in the absorption edge. This structure,
which lies within the 30 eV of the edge, is referred to
as X-ray absorption near edge structure1-3 (XANES).
Originally, Kronig4,5 explained the formation of
EXAFS structures. EXAFS was explained by Stern
et al.6,7, Lee and Pendry8, Ashley and Doniac9 and
others10-13. It has been proved to be highly useful for
determination of bond length, phase parameter,
bonding parameter etc. Stern, Sayer and Lytle6 have
given the following expression of EXAFS function
[χ (k)] of absorbing atom
χ (k) = -1/k ∑Aj sin[2kR j + δj(k)]
…(1)
where, k is the photoelectron wave vector and Aj is an
amplitude function containing the coordination
number, the scattering terms, the Debye-Waller
factor, the elastic loss terms, mean free path etc. The
term 2kR j in sine function of Eq. (1) is due to the
travel of the photoelectron from the absorbing atom to
the neighbouring atom and back and δj(k) is an
additional phase shift term.
Lytle et al.7 in the general theory of EXAFS
analysis assumed the linear form of δj(k) as
δj(k) = -2kαj + 2βj
…(2)
where 2kαj is an absorbing atom phase shift and βj is
a backscattering amplitude phase shift. We assume αj
to be linear in k over the EXAFS energy range. The
constants αj and βj are called bonding parameter and
phase parameter, respectively.
In the present paper, we have calculated the
bonding parameter α1 and phase parameter β1 using a
graphical method proposed by Sayer el al.7. This
method has been used because of its simplicity and
capability of giving good results and has also been
used by many researchers14,15. We are also reporting
the correlation of the bonding parameter with nearest
neighbour distance and ionicity. The nearest
neighbour distances have been calculated using the
method proposed by Chetal et al16,17. Ionicity has been
calculated using Pauling’s method18. The position of
the nickel edge in the present systems has been
correlated with the ionicity.
SINGH: EXAFS PHASE SHIFT STUDIES OF NICKEL COMPOUNDS
2 Experimental Details
A Cauchois type transmission X-ray spectrograph
with diameter 40 cm was used to record K-absorption
edge of Ni in the systems under study. X-ray radiation
was obtained from tungsten tube operated at 13 kV
and 10 mA. Mica with 2 01 planes was used for
recording the X-ray spectra of the systems under
study. Absorbing samples were prepared by spreading
uniformly fine powder of the compounds between two
cellophane tapes fixed on an aluminium frame.
Microphotometer traces of the spectra were recorded
using MD100 (Carl Zeiss, IRS) microphotometer. The
error in the measurement of the positions of the
maxima and minima in absorption spectra was of the
order of ±1eV. The Ni K-edge found to split into two
components K1 and K2 shown only for Ni metal in
Fig. 1. The measurements of edges were made from
the mid point of K1 component of the absorption edge.
This point is considered to be as zero energy.
3 Results and Discussion
The argument in the sinusoidal term given in Eq.
(1) determines the periodicity of EXAFS arising from
scattering from first co-ordination shell. From Eqs (1)
and (2), we have,
χ (k) = -1/k ∑Aj sin(2kR j -2kαj + 2βj)
…(3)
or, χ (k) = -1/k ∑Aj sin[2k(R j - αj) + 2βj]
…(4)
Lytle et al.7 have shown that EXAFS may be
visualized as a kind of electron diffraction where the
21
source of electron originates from the atom involved
in the absorbing event. The wave function of the
excited photoelectron has interference between the
outgoing and scattered part. The interference takes
place near the origin where the overlap of the initial
state occurs. Depending upon the wave number of the
photoelectron, the interference is either constructive
or destructive varying the dipole matrix element and
hence the transition rates. Substituting into the
argument of the sine function of the Eq. (4) and
rearranging for the co-ordination shell, it is
convenient to define n by
φ1(k) = (n+1/2)π = 2k(R1 - α1)+ 2β1
…(5)
where n = 0, 2, 4, ……. for the maxima and
n = 1, 3, 5,……...for the minima
The value of k (in Å-1) is obtained from equation
k=
0.263E
…(6)
where, E is the energy of the peaks in EXAFS in eV.
The microphotometer tracings between absorption
coefficient and energy are shown in Figs 1 and 2.
One can see from Eq. (5) that the value of bonding
parameter (α1) and phase parameter (β1) can be
determined provided we know the values of R1 and k.
The value of k is determined using Eq. (6) and R1 is
the crystallographic value of the nearest neighbour
distance and has been calculated using the following
formula developed by Mahto and Chetal16,
Fig. 1 — Absorption coefficient versus energy of Ni metal Ni-As mineral, NiBr2, NiS mineral, NiS and NiCl2.6H2O
INDIAN J PURE & APPL PHYS, VOL 44, JANUARY 2006
22
⎛ π⎞
Ru = Rs + ⎜ ⎟
⎝ 2⎠
1/ 2
⎡ 1
1 ⎤
−
⎢
⎥
⎣ Ku K s ⎦
…(7)
where, Ru is the nearest neighbour distances of
unknown systems, Rs, the nearest neighbour distance
of standard system and
K=
0.263( Er − Eb )
where, Er is the resonance energy corresponding to
the peak A and Eb is the bound energy corresponding
to the peak C as shown in Fig. (2) for NiSO4.6H2O.
The values of Er and Eb are given in Table 1.
The Ru values for the systems under study are
calculated by using Eq. (7), which we shall call as R1,
are given in Table 2. For calculating bonding
parameter (α1) and phase parameter (β1), we have
plotted φ1(k) versus k (not shown in the text). The
slope of the plot is 2(R1 - α1). By substituting the
values of R1 in (R1 - α1), the value of α1 of the
systems under study can be calculated easily (error ±
0.01 Å). The intercept of the plot of φ1(k) and k gives
2β1 (error ± 0.01Å). The values so obtained for α1 and
β1 for the systems under study are given in Table 2.
From Table 2, it can be observed that as R1
decreases the value of α1 also decreases except in
Ni3(PO4)2.XH2O and NiCl2.6H2O. The deviation may
be attributed to the complex nature of the systems.
The plot between the bonding parameter α1 and the
nearest neighbour distance R1 is shown in Fig. 3.
We have correlated α1 with the ionicity (I). The
ionicity of the systems under study was calculated by
using Pauling’s formula18 given below,
⎡ n
⎛ ( X − X a )2 ⎞ ⎤
I = ⎢1 − exp ⎜⎜ − l
⎟⎟ ⎥
4
⎝
⎠ ⎦⎥
⎣⎢ C
…(8)
where, Xl is the electronegativity of the ligand Xa, the
electronegativity of the absorbing atom C, the
Table 1 — Values of Er, resonance energy and Eb, the bound
energy
Sample Name of the systems
No.
Er (in eV)
Eb (in eV)
1
NiAs-Mineral
8348.52
8332.62
2
NiBr2
8349.12
8332.62
3
NiS-Mineral
8350.62
8333.52
4
NiS compound
8350.52
8332.52
5
NiCl2.6H2O
8353.62
8334.72
6
NiO
8352.62
8334.72
7
Ni3(PO4) 2.XH2O
8353.12
8334.92
8
LaNiO3
8352.62
8334.32
9
NiCO3
8353.52
8334.82
10
Ni(NO3)2.6H2O
8355.62
8333.62
11
NiSO4.6H2O
8354.62
8332.52
Fig. 2 — Absorption coefficient versus energy of NiO, Ni3(PO4)2 xH2O, LaNiO3, NiCO3, Ni(NO3)2.6H2O and NiSO4.6H2O
SINGH: EXAFS PHASE SHIFT STUDIES OF NICKEL COMPOUNDS
coordination number and n is the valence of the
absorbing atom.
The ionicities of the systems under study calculated
using Eq. (8) are given in Table 3. It can be seen from
Fig. 4 that the parameter α1 decreases with the
increase of ionicity of the corresponding system
except for the system NiBr2. The values of phase
parameter β1 in the systems under study are also given
in Table 2. It can be observed from Table 2 that the
Table 2 — Values of bonding parameter, nearest neighbour
distance and the phase parameter for the systems under study
Sample Name of the
No. systems
Bonding
Nearest
Phase
parameter neighbour parameter
α1 (in Å) distance
β1 (in Å)
R1 (in Å)
1
Ni-Metal
2.440
2.56*
0.52
2
NiAs-Mineral
2.170
2.29
0.33
3
NiBr2
2.160
2.28
0.27
4
NiS-Mineral
2.150
2.27
0.38
5
NiS compound
2.130
2.25
0.41
6
NiCl2.6H2O
2.080
2.24
0.17
7
NiO
1.990
2.09
8
Ni3(PO4) 2.XH2O
2.030
9
LaNiO3
10
23
greater the number of oxygen atoms in a system, the
higher is the value for the phase parameter β1 except
for the system NiCl2.6H2O. It is maximum for
Ni3(PO4)2.XH2O. In the case of NiO, the value may be
high due to the fact that the coordination number of
Ni is six in NiO and hence Ni is surrounded by six
oxygen atoms. In the case of NiCl2.6H2O, the effect of
oxygen in NiCl2 perhaps is not felt as it belongs to 2nd
coordination shell of water molecules. This work
Table 3 — Ionicities of the systems under study
Sample Name of the
No. systems
Ionicity Bonding
parameter
α1
(in Å)
K-edge
position
(in eV)
Author
K-edge
position
(in eV)
Choudhury17
1
NiAs-Mineral
0.67
2.170
8337.62
8333.70
2
NiS-Mineral
0.71
2.150
8338.62
8336.20
3
NiS compound
0.71
2.130
8340.22
8336.92
4
NiBr2
0.74
2.160
8336.82
8334.62
5
NiCl2.6H2O
0.77
2.080
8342.32
8339.52
0.68
6
Ni3(PO4) 2.XH2O
0.79
2.030
8342.92
8339.62
2.08
1.60
7
NiCO3
0.80
1.960
8341.90
8338.60
1.960
2.08
0.52
8
NiSO4.6H2O
0.81
1.917
8340.50
8339.60
NiCO3
1.960
2.07
0.53
9
Ni(NO3)2.6H2O
0.82
1.919
8342.80
8340.80
11
Ni(NO3)2.6H2O
1.919
2.03
0.63
10
NiO
0.84
1.990
8341.42
8338.32
12
NiSO4.6H2O
1.917
2.03
0.55
11
LaNiO3
0.87
1.960
8342.76
8342.62
* Crystallographic value
Fig. 3 — Bonding Parameter versus nearest neighbour distance
(in Å each)
Fig. 4 — Bonding parameter (in Å) versuss ionicity
24
INDIAN J PURE & APPL PHYS, VOL 44, JANUARY 2006
further suggests that for arsenic, sulphur, chlorine and
bromine the phase parameter β1 is less than that for
oxygen atoms.
The position of nickel K-edge has been studied in
the systems under study. The K-edge position of
nickel and corresponding ionicity are given in
Table 3. We have also given the measurements of the
edges carried out by Choudhury17. It can be seen from
the Table 3 that as ionicity increases K-edge position
also increases in the systems NiAs mineral, NiS, NiS
mineral, NiSO4.6H2O, NiO and LaNiO3. However, no
correlation has been observed in NiCl2.6H2O, NiBr2,
Ni3(PO4)2. XH2O, NiCO3 and Ni(NO3)2.6H2O. This is
due to fact that the shift of the edge does not only
depend upon ionicity but also on other factors20 such
as coordination number, crystal structure, valency etc.
Some time X-ray scattering also affects the edge
position.
4 Conclusion
We conclude that the EXAFS parameters α1 and β1
can be considered as chemical parameters as
they depend upon chemical parameters such as
ionicity, nature of the ligand and nearest neighbour
diatance etc.
Acknowledgement
Author is grateful to Prof A R Chetal for his
constant encouragement and guidance.
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