Revealing the Spin-Hamiltonian and CharacteristicParameters of Paramagnetic Centers in Cu2+-DopedPotassium Metabisulfite (K2S2O5) Single Crystalby Electron Paramagnetic Resonance Technique

Ilkay Yıldırım • Bunyamin Karabulut

Received: 15 July 2013 / Revised: 20 August 2013 / Published online: 29 November 2013

� Springer-Verlag Wien 2013

Abstract The present study is mainly related to finding out spin-Hamiltonian

parameters of Cu2?-doped potassium metabisulfite [K2S2O5] single crystals using

electron paramagnetic resonance (EPR) technique which has been applied in the

temperature range from 297 to 113 K for single and powder crystals of the title

compound. The existence of two complexes and two Cu2? sites for each complex

was concluded from the angular variation of the EPR spectra. Having constructed

the g and the hyperfine tensors, the spin-Hamiltonian parameters have been obtained

for these two complexes. Using these parameters, the covalency parameter (a2),

mixing coefficients (a and b) and Fermi contact term (K) have been calculated.

1 Introduction

Electron paramagnetic resonance (EPR) has been used commonly as an effective

method in getting information on the magnetic properties of the paramagnetic

samples. The Cu2? ions were used extensively as a dopant for the complexes to

show paramagnetic properties [1–14]. Among a few transition metal ions, the Cu2?

ion is the most stable cation which is doped in a divalent or monovalent manner into

the host lattice.

Potassium metabisulfite [K2S2O5; hereafter PMbS], also known as potassium

hydrogen sulfite, is a white crystalline powder. It is used as a general purpose food

additive anti-oxidant and disinfectant [15]. Therefore, it is important to have

I. YıldırımDepartment of Physics, Faculty of Arts and Sciences, Ondokuz Mayis University,

Kurupelit 55139, Samsun, Turkey

B. Karabulut (&)

Department of Computer Engineering, Faculty of Engineering, Ondokuz Mayis University,

Kurupelit 55139, Samsun, Turkey

e-mail: bbulut@omu.edu.tr

123

Appl Magn Reson (2014) 45:1–8

DOI 10.1007/s00723-013-0493-3

Applied

Magnetic Resonance

detailed knowledge on physical properties of such a material with a wide spectrum

of usage in food sector. Tapramaz and Koksal [16] reported EPR studies of gamma-

irradiated PMbS single crystals. However, a literature survey shows no report on the

EPR study of Cu2? although this technique can possibly give valuable information

on the magnetic properties of this material. In the present study, the EPR

investigation of single crystal and powder Cu2?-doped PMbS samples has been

performed. Spin-Hamiltonian parameters and other characteristic quantities such as

covalency parameter, mixing coefficients and Fermi contact term (K) have been

calculated and the ground state wave function of the Cu2? ion has been constructed.

2 Experimental

K2S2O5 [PMbS] was prepared by slow evaporation at room temperature from its

aqueous solution. CuCl2 (0.05 %) was added to the solution as a dopant and the

single crystals were grown by slow evaporation of their saturated aqueous solution.

After about a week, the well-developed single crystals of suitable size were selected

for the EPR study. Zachariasen [17] determined the crystallographic structure of

potassium pyrosulfite, reporting a monoclinic space group P21/m (a = 6.95 A,

b = 6.19 A, c = 7.55 A and b = 102.41�) for the crystal structure. EPR experi-

ments were performed on a Varian E-109 C X-band spectrometer (9.5 GHz) with

about 20 mW microwave power and 100 kHz magnetic field modulation. The

angular variation spectra were recorded for every 10� interval in three mutually

perpendicular planes. DPPH (g = 2.0036) was used for calibrating magnetic field

lines.

3 Results and Discussion

The Cu2?-doped PMbS single crystals yield many lines in EPR spectra. Considering

allowed transitions (DMI ¼ �0 and DMS ¼ �1), four EPR hyperfine transition lines

are expected for a single Cu2? ion with S = 1/2 and I = 3/2.

The EPR spectra of Cu2?-doped PMbS single crystals exhibit eight lines, when

the magnetic field is along the crystallographic b-axis or in the a*c plane, the

spectrum consists of two sets of four hyperfine lines (Fig. 1a). However, the spectra

consist of four sets of four hyperfine lines (Fig. 1b), when the magnetic field is in

the ba* and cb planes. The 63Cu and 65Cu lines are not distinguishable in all planes

since the spacing of the lines changes rapidly with orientation and overlapping

occurs. Spectra in Fig. 1a, b seem to be incompatible with the monoclinic

crystalline symmetry, for which in all planes except a*c plane the hyperfine lines do

not merge into double set since there are two different complex centers. The angular

variation studies exhibit the presence of two complex groups, each having two sites

Cu2? in the PMbS host lattice as shown in Fig. 2. This is an indication of the two

sites and is in agreement with the monoclinic symmetry of the crystal. As given in

the crystal structure, the unit cell contains two molecules and hence two sets of four

2 I. Yıldırım, B. Karabulut

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hyperfine lines are observed. The two outer four lines in the spectrum may be

ascribed to two molecules in unit cell of different bond lengths.

The observed EPR spectra of Cu2? in PMbS have been explained by the

following spin Hamiltonian:

H ¼ bðgxxBxSx þ gyyBySy þ gzzBzSzÞ þ AzzIzSz þ AxxIxSx þ AyyIySy; ð1Þ

which includes only electronic Zeeman and hyperfine interactions.

The angular variations of observed g2 lines about a*, b, c axes are given in Fig. 2

for two complex centers. These three axes are perpendicular to each other. Four sets

Fig. 1 EPR spectra of the Cu2?-doped PMBS single crystal a when the magnetic field in the a*c plane is by160� away from the b-axis and b when the magnetic field in the ba* plane is by 40� away from the c-axis

Cu2?-Doped Potassium Metabisulfite (K2S2O5) Single Crystal by EPR 3

123

of four hyperfine lines can be measured in cb and a*b planes and two sets of four

hyperfine lines can be measured in the a*c plane. Each of four lines consists of two

sets of four hyperfine lines in this plane known as the monoclinic plane. EPR

information can be extracted from these measurements. The g2 variation of each line

should fit the expression

g2kðhÞ ¼ g2

ii cos2 hi þ g2jj sin2 hj þ 2g2

ij sin hi cos hj; ð2Þ

where i; j; k ¼ x; y; z are the cyclic laboratory coordinates and h is the rotation angle.

g2ii; g2

jj and g2ij are the g tensor elements which can be found by fitting [18, 19]. This

process is known iterative numerical technique as given in ref [18, 19]. The EPR

parameters g and A tensors were evaluated using this technique and it was also used

to resolve the spectra [18, 19]. This technique is a least squares computer analysis of

the measured values of g2 and A2 tensors, and and gives the terms of the tensors in

current coordinate system, consisting of a*, b and c axis. These tensors were then

diagonalized by the unitary transformation to yield the principal g and A values and

direction cosines related to the a*, b and c coordinate system. The values obtained

for spin-Hamiltonian parameters, g and A of Cu2? in PMbS along with the direction

cosines are given in Table 1. Both g and hyperfine values of all complex sites

correspond to the rhombic symmetry. It is seen from Table 1 that the principal axes

of the g and hyperfine values almost coincide since they have nearly the same

direction cosines. These results are consistent with monoclinic symmetry properties

and indicate that the Cu2? ion substitutes with the K? ions in PMbS single crystal.

The ionic radius of K? (95 pm) is large enough for the substitution of Cu2?

(72 pm). We have deduced that the paramagnetic center has the rhombic symmetry.

Cu2? ions substitute with K? ions in the host and compensate the negative charge

deficiency via oxygen atoms of (SO4)3- groups in the ligand positions. They are

relatively close and equidistant to oxygen atoms of each [SO4]3- group where

oxygen atoms are bridged via hydrogen atoms with the corresponding oxygen atom

of the next group.

Fig. 2 Angular variations of the g2 lines in Cu2?-doped PMbS single crystals

4 I. Yıldırım, B. Karabulut

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The X-band EPR powder spectrum of Cu2? ion in the PMbS complex is shown in

Fig. 3. The principal values of g and A tensor obtained from the powder spectrum

are as follows: gx = 2.182, gy = 2.043, gz = 2.381, Ax = 40G, Ay = 70G,

Az = 87G. These values correlate well with data obtained from the single-crystal

data.

There are two K2S2O5 molecules in the unit cell. In the lattice, the potassium

atoms are surrounded by nine or seven oxygen atoms. The K? ions of the first kind

are surrounded by nine O atoms. These are two OI atoms, two OI atoms, two OII

atoms, two OIII atoms, and one OIII atom at distances of 2.88, 2.91, 3.02, 3.21 and

3.01 A, respectively. The K? ions of the second kind are surrounded by seven O

atoms. These are two OI atoms, two OII atoms, two OII atoms, and one OIII atom at

distances of 2.69, 2.74, 2.95 and 2.71 A, respectively [17]. The Cu2? ions substitute

with the either kind of K? ions in the host lattice and form an octahedron having two

aqua ligands in axial positions and two bidentate metabisulfite ligands in equatorial

plane as in Fig. 4. Here, probably, two distinct oxygen bond distances are formed

compared to the equatorial plane in coordination sphere of either kind of K? ions of

either kind. Due to these two distinct equatorial planes, two Cu2? complexes are

formed as complex I and complex II in the crystal lattice. In this case, each complex

group shows one site for the a*c plane and two sites for ba* and bc planes as is

clearly seen in EPR spectra (Fig. 2). On the other hand, along the crystalline b-axis

and in the a*c plane two sets of four hyperfine lines and in the other planes four sets

of four hyperfine lines were observed. These lines were grouped as complex I and

complex II in Fig. 1b. The intensity difference between these two groups may be

due to their population at these orientations. From these results it is inferred that

there are two magnetically inequivalent, but chemically equivalent two Cu2? ions in

the unit cell of the PMbS single crystals. These results are consistent with

monoclinic symmetry properties.

Table 1 The principal values and direction cosines of g and A tensors of Cu2?-doped PMbS single

crystal (Dg = ±0.005 and DA = ±5G)

Complex g Direction cosines Hyperfine Direction cosines

a* b c* A (G) a* b c*

Site I gx = 2.185 -0.863 -0.0013 0.504 Ax = 41.1 0.826 -0.274 -0.493

gy = 2.006 -0.328 0.777 -0.537 Ay = 83.2 0.558 0.509 0.654

gz = 2.409 0.384 0.628 0.676 Az = 91.7 -0.073 0.816 -0.572

Site II gx = 2.196 0.349 0.818 0.455 Ax = 39.7 0.862 0.110 -0.494

gy = 2.022 -0.831 0.053 0.545 Ay = 77.0 0.392 0.470 0.790

gz = 2.383 0.423 -0.571 0.703 Az = 93.9 -0.320 0.875 -0.362

Site I gx = 2.241 -0.878 -0.268 0.395 Ax = 51.2 0.945 -0.114 0.305

gy = 2.022 -0.455 0.721 -0.521 Ay = 70.5 -0.159 0.653 0.739

gz = 2.363 0.145 0.638 0.756 Az = 88.7 0.283 0.748 -0.599

Site II gx = 2.236 0.903 -0.296 -0.308 Ax = 47.1 0.911 0.304 0.277

gy = 2,037 0.421 0.738 0.525 Ay = 71.1 0.304 -0.541 0.837

gz = 2.358 0.072 -0.605 0.792 Az = 86.2 -0.405 0.873 0.470

Cu2?-Doped Potassium Metabisulfite (K2S2O5) Single Crystal by EPR 5

123

The ground state of Cu2? seems to be predominantly the dx2�y2 state.

Formulation of the admixture of the dx2�y2 and d3z2�r2 orbitals in the ground state

wave function of the Cu2? in a rhombic symmetry has been established and applied

by many authors. The ground state wave function including also the covalency

effect of the metal ion [20–22] is written as

W ¼ a0 a x2 � y2��

�

þ b 3z2 � r2��

�� �

; ð3Þ

where the square of a0 is the probability of finding unpaired electron in the d-orbital

of central copper ion and the measure of the covalency [20–22]. a and b are the

normalization coefficients. The coefficients should satisfy the relation

Fig. 3 EPR spectrum of Cu2?-doped PMbS powder samples atroom temperature

Fig. 4 Schematic view of the Cu2? ion in the PMbS complex

6 I. Yıldırım, B. Karabulut

123

a 2 þ b 2 ¼ 1: ð4ÞUsing Eq. (2) together with the experimental values (Table 1), a02, a, b and j

parameters were calculated and are given in Table 2 where j is Fermi contact term/

spin-exchange polarization parameter, P is hyperfine interaction parameter and aand b are in plane r-bonding and out-of-plane p-bonding coefficients, respectively.

The ground state wave functions of the sites using the parameters in Table 1 are

constructed as

WI ¼ ð0:982Þ12 0:953 x2 � y2

��

�

þ 0:305 3z2 � r2��

�� �

; ð5aÞ

WII ¼ ð0:937Þ12 0:954 x2 � y2

��

�

þ 0:300 3z2 � r2��

�� �

: ð5bÞThe value of the covalency parameter a02 (0.982) for the site I indicates that the

unpaired electron spends 1.8 % of its time on the ligand orbitals and 98.2 % is spent

on the d-orbitals of the copper ion in the site I (K2S2O5I). Due to that the a value is

larger than the b value, the unpaired electron spends most of its time on the dx2�y2

orbital of the copper ion. For the site II, the fraction of time spent on ligand orbitals

is larger than that for the site I. The ground state wave function parameters of Cu2?

ions observed in different lattices are listed in Table 2 [22–28]. The parameter j is a

measure of the polarization produced by the uneven distribution of the d-electron

density on the inner core of 4s-electrons.

Table 2 Ground state wave function parameters of Cu2? ions observed in different environments

Lattice Site a02 a b j References

K2S2O5 I 1 0.982 0.953 0.305 0.266 Present study

2 0.937 0.954 0.300 0.284 Present study

K2S2O5 II 1 0.907 0.934 0.356 0.314 Present study

2 0.886 0.940 0.341 0.314 Present study

Powder 0.880 0.960 0.279 0.302 Present study

MCD 0.856 0.824 0.201 0.380 [22]

C6H5O7Na3�2H2O 0.931 0.878 0.027 0.262 [23]

DGCCT 0.837 0.754 0.336 0.404 [24]

KDP 1 0.880 0.980 0.160 0.400 [25]

2 0.940 0.990 0.150 0.390

3 0.910 0.970 0.210 0.380

4 0.880 0.980 0.190 0.390

5 0.850 0.970 0.230 0.370

Na3PO4�8H2O 1 0.911 0.986 0.084 0.298 [26]

2 0.931 0.997 0.074 0.263

LSAP 1 0.563 0.926 0.377 0.975 [27]

2 0.590 0.909 0.418 0.960

LAP 1 0.429 0.994 0.113 0.705 [28]

2 0.460 0.958 0.288 0.713

j is the Fermi contact term

Cu2?-Doped Potassium Metabisulfite (K2S2O5) Single Crystal by EPR 7

123

4 Conclusions

EPR studies of Cu2? doped in PMbS single crystal reveal that the Cu2? ions enter

the lattice in the substitutional position in the host lattice with the rhombic

symmetry of the electrostatic field around the ion. The Cu2? spectra and the angular

variation show the presence of two magnetically distinct sites for the Cu2? ion. The

principal g and hyperfine values of Cu2? complex are evaluated. Both values show

rhombic symmetry. The detailed study indicates that the octahedron formed around

the Cu2? ion is slightly distorted to the tetragonal symmetry (Table 1). The ground

state wave function confirms the delocalization of the unpaired spin density and the

probability of finding the unpaired electrons in the metal d-orbital is 97.4 % in site I

and 97.3 % in site II. The site symmetry of Cu2? ion in PMbS has a distorted

octahedral sites (D4h) elongated along the z-axis and ground state of the unpaired

electron is dx2�y2 .

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