EPR and optical absorption studies of Cu2+ doped lithium maleate dihydrate single crystal

Physica B 444 (2014) 14–20

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EPR and optical absorption studies of Cu2 þ doped lithium maleate dihydrate single crystal Ram Kripal n, Shri Devi Pandey EPR Laboratory, Department of Physics, University of Allahabad, Allahabad 211002, India

art ic l e i nf o

a b s t r a c t

Article history: Received 2 February 2014 Received in revised form 9 March 2014 Accepted 10 March 2014 Available online 21 March 2014

Electron paramagnetic resonance (EPR) study of Cu2 þ doped lithium maleate dihydrate single crystal is done at liquid nitrogen temperature (LNT). Four hyperfine lines are observed in all directions, i.e. only a single site is observed. The spin Hamiltonian parameters are determined from EPR spectra: gx ¼2.100 7 0.002, gy ¼ 2.1627 0.002, gz ¼ 2.215 70.002, Ax ¼ (5575)  10  4 cm  1, Ay ¼ (527 5)  10  4 cm  1, Az ¼(50 75)  10  4 cm  1. The results indicate that the copper ion enters the lattice interstitially. Using the spin Hamiltonian parameters obtained from EPR study the ground state wave function of Cu2 þ ion in the lattice is determined. The optical absorption study of Cu2 þ doped lithium maleate dihydrate at room temperature is also performed. With the help of optical and EPR data, the nature of bonding in the complex is discussed. & 2014 Elsevier B.V. All rights reserved.

Keywords: Organic compounds Crystal growth Crystal fields Optical properties Electron paramagnetic resonance

1. Introduction Electron paramagnetic resonance (EPR) studies of Cu2 þ impurities have been widely carried out in a variety of single crystals [1–8]. The hyperfine structure of copper ion was first investigated in solid state by the method of EPR. In Cu2 þ complexes the metal ions have either four or six co-ordination geometry and there are only few exceptions to this. The 3d9 configuration of Cu2 þ is of particular interest because it represents a simple one magnetic hole system. EPR and optical absorption are two supplementary tools to investigate the site symmetry of the impurity, the dynamic behavior of the dopant and its nature of bonding in crystals. The objectives of EPR studies of transition metal ions doped in crystals are to find the sites available for the impurity ion and their orientations, the study of phase transition and magnetic properties of unpaired electrons of transition metal ions. Lithium compounds are used as the standard in the treatment of bipolar disorder. Lithium salts may be helpful in diagnoses of schizoaffective disorder and cyclic major depression [9]. Organolithium compounds are used as strong bases, as reagents for the formation of carbon–carbon bonds, as catalysts in polymer synthesis or initiators in anionic polymerization of unfunctionalized olefins [10–12]. Such compounds are in turn very reactive and are the basis of many synthetic applications [13]. Lithium compounds are also used as pyrotechnic colorants and oxidizers in red fireworks and flares [14]. Some of these compounds (e.g. lithium

niobate) are used as non-linear optical materials. Due to reasons mentioned above, our interest developed in lithium maleate dihydrate. In the present study, EPR at liquid nitrogen temperature (LNT) and optical absorption at room temperature (RT) of Cu2 þ doped lithium maleate dehydrate (LMD) are carried out to find the location of impurity ion in the lattice. The study is also used to obtain the site symmetry, the energy level structure and the nature of bonding of Cu2 þ ion with its various ligands in the crystal.

2. Crystal structure LMD, Li2C4H2O4  2H2O single crystal is monoclinic, belongs to the space group Cc or C2/c and Z¼ 8 [15]. The unit cell dimensions are a ¼9.6306, b ¼12.1307, c¼ 12.7051 Å and β ¼ 107.961. The projection of the structure along the b-axis is shown in Fig. 1(a). The main plane of each maleate ion is approximately parallel to (001). The water molecules are sandwiched between layers of maleate ions and lithium ions. The structure is continuously bonded in three dimensions by either ionic or hydrogen bonds. Each lithium ion forms bonds with four oxygen atoms and each maleate ion is bonded by four oxygen atoms to lithium ions and water molecules.

3. Experimental details n

Corresponding author. Tel.: þ 91 532 2470532; fax: þ91 532 2460993. E-mail addresses: [email protected] (R. Kripal), [email protected] (S.D. Pandey). http://dx.doi.org/10.1016/j.physb.2014.03.021 0921-4526/& 2014 Elsevier B.V. All rights reserved.

Single crystals of LMD were prepared by slow evaporation of an aqueous solution of maleic acid with stoichiometric ratio of

R. Kripal, S.D. Pandey / Physica B 444 (2014) 14–20

15

O(1) O(5) Cu2+ gz

gy

gx

O(3)

O(2)

Fig. 1. (a) Projection of crystal structure along b-axis. (b) Morphology and orientation of axes of the LMD crystal. (c) Coordination of Cu2 þ in LMD (coordinates of Cu2 þ ion: (0.2100, 0.2862, and 0.1001)).

lithium hydroxide. For Cu2 þ doped crystals, an aqueous solution of 0.05 wt% of copper sulfate was added as dopant. Good, transparent and monoclinic prism shaped crystals were grew in about two weeks. The crystals are elongated parallel to a axis and show forms (010), (110) and (001). The maximum size of the grown crystals is 12 mm  1.5 mm  0.7 mm. The morphology of the crystal was found to be as shown in Fig. 1(b) together with the orientation of the crystal axes. The coordination of Cu2 þ in LMD is shown in Fig. 1(c).The coordinates of Cu2 þ ion are (0.2100, 0.2862, and 0.1001) and site symmetry is C2v. EPR spectra of single crystals were recorded at LNT using a X-band Varian E-112 EPR spectrometer with 100 kHz field modulation. The single crystals were mounted at the end of a quartz rod using quick-fix and crystal rotations were performed along the three mutually orthogonal axes a, b, cn at an interval of 101 using a goniometer. In the monoclinic system two of the crystal axes are perpendicular to each other, but the third is obliquely inclined. The LMD crystal is monoclinic so we choose a, b, and cn experimental axis system for single crystal studies. In this system a and b are orthogonal crystallographic axes and cn is orthogonal to both a and b. The optical spectra were recorded on a Unicam-5625 spectrophotometer in the wavelength range 195–1100 nm at room temperature.

4. Results and discussion The 3d9 system with S ¼1/2 and I¼ 3/2 exhibits four hyperfine lines from a single complex for two stable isotopes of copper: 63Cu (69.05% abundant) and 65Cu (30.95% abundant). The lines corresponding to the less abundant isotope of Cu2 þ (65Cu) could not be resolved perhaps due to the broadness of lines. EPR spectrum of Cu2 þ doped LMD single crystal taken at LNT in ab plane for the magnetic field at 01 from a axis (frequency 9.1 GHz) is shown in Fig. 2(a). The unit cell of host crystal contains eight molecules per unit cell but only one set of four hyperfine lines is observed. This is explained on the basis of interstitial doping. For a substitutional site of Cu2 þ in monoclinic crystal with two molecules per unit cell, two sets of four lines should be observed in two planes and only one set of four lines in one plane of rotation [16]. In the present

Fig. 2. (a) EPR spectrum of Cu2 þ doped LMD crystal in ab plane for the magnetic field at 01 from the a-axis (frequency 9.1 GHz). (b) Simulated EPR spectrum of Cu2 þ doped LMD crystal in ab plane for the magnetic field at 01 from the a axis (frequency 9.1 GHz).

study, the number of atoms per unit cell is eight in the monoclinic crystal. Therefore, we should get eight sets of four hyperfine lines in two planes and four sets of four hyperfine lines in third plane for substitutional site of Cu2 þ in place of Li þ . But we have observed only one set of four hyperfine lines in all three ab, bcn and cna planes. This indicates that the Cu2 þ ion enters the host lattice interstitially. Further, the ionic radius of Li þ ion (68 pm) is smaller than that of Cu2 þ ion (72 pm), which also suggests less possibility of substitution of Cu2 þ in place of Li þ . The simulation of EPR spectrum using EasySpin [17–20] and spin Hamiltonian parameters (obtained from the EPR spectra using Schonland procedure) gx ¼2.100 70.002, gy ¼2.162 70.002, gz ¼2.215 7 0.002, Ax ¼(55 75)  10  4 cm  1, Ay ¼ (52 75)  10  4 cm  1, Az ¼ (50 75)  10  4 cm  1 was performed. The simulation was based upon diagonalization of the entire S¼ 1/2, I ¼3/2 energy matrix.

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Fig. 3. (a) Angular variation of EPR line positions of Cu2 þ doped LMD in ab plane. (b) Angular variation of EPR line positions of Cu2 þ doped LMD in bcn plane. (c) Angular variation of EPR line positions of Cu2 þ doped LMD in cna plane. Table 1 Spin Hamiltonian parameters for Cu2 þ ion in LMD single crystal. Principal values of g-tensor

gx ¼ 2.100 gy ¼ 2.162 gz ¼2.215

Principal values of A-tensor(  10  4 cm  1)

Direction cosines n

a

b

c

 0.2165  0.5037  0.8363

 0.3159 0.8467  0.4282

0.9238 0.1715  0.3424

Ax ¼ 55 Ay ¼ 52 Az ¼50

Direction cosines a

b

cn

 0.5281  0.7959  0.2961

 0.6139 0.5988  0.5143

0.5867 0.0898 0.8048

Estimated errors for g and A values are 7 0.002 and 7 5  10  4 cm  1, respectively.

Lorentzian first derivative lineshapes were used. The simulated spectrum is in reasonable agreement with the experimental one. The simulated EPR spectrum of Cu2 þ doped LMD crystal in ab plane for the magnetic field at 01 from a axis (frequency 9.1 GHz) is shown in Fig. 2(b).The angular variation of hyperfine lines in all three ab, bcn and cna planes is shown in Fig. 3(a), (b) and (c), respectively. The direction of the maximum overall splitting of EPR spectrum is taken as the z-axis and that of the minimum as the x-axis [21]. The EPR spectra recorded in ab and cna planes showed a large anisotropy in g and A values; however the corresponding variation in bcn plane is small. The principal values of g and A tensors for Cu2 þ doped LMD single crystals were evaluated using the Schonland procedure [22], in which all the EPR line positions recorded for the magnetic field in the three planes were fitted to the spin Hamiltonian 1 [23] shown as follows:

where α, β and γ are functions of Gij. Fig. 4 shows the angular variation of g2 and g2A2 in ab, bcn and cna planes and indicates an approximate rhombic symmetry for copper ion in the LMD lattice. The quantities α, β and γ are determined by obtaining the best fit of Eq. (3) to a large number of g-value measurements at different angles. The quantities α, β and γ can also be expressed in terms of maximum (g þ ) and minimum (g  ) g-values in the plane and the angle θ þ at which the maximum g-value appears as

ℋ ¼ μB SgB þ SAI

2α ¼ g 2þ þ g 2

ð1Þ

where S ¼1/2 and I¼ 3/2 are the electronic and nuclear spins of Cu2 þ , μB is Bohr magneton, g is spectroscopic splitting factor and A is hyperfine structure constant. The spin Hamiltonian parameters g and A together with their direction cosines evaluated using the Schonland procedure [18] and self-developed computer program are given in Table 1. The procedure of obtaining principal values of the g-tensor is to rotate the magnetic field about three mutually perpendicular axes fixed in the crystal and to measure the g value variation in the plane perpendicular to each axis, respectively. If l1, l2 and l3 are the direction cosines of the magnetic field with respect to above axes, the square of corresponding g-value is given by 3

g 2 ¼ ∑ Gij li lj i;j ¼ 1

ð2Þ

When the coefficients Gij are known for a particular set of axes, the principal g values and principal axes are found by diagonalizing the matrix G. If θ is an angle specifying the direction of the magnetic field in the plane of measurement, the g2 variation in the plane must fit to the expression [22] g 2 ¼ α þ β cos2θ þ γ sin2θ

ð3Þ

2β ¼ ðg 2þ  g 2 Þcos2θ þ 2γ ¼ ðg 2þ  g 2 Þsin2θ þ

ð4Þ

To find all Gij, it is essential to measure the g-value variation in all three ab, bcn and cna planes. This gives nine equations to find the six independent Gij. The G matrix is then diagonalized and the principal values of g are obtained as the square roots of the diagonalized G tensor eigenvalues Gdiag ¼ R  1 GR gx ¼

pffiffiffiffiffiffiffiffi G11 ;

gy ¼

pffiffiffiffiffiffiffiffi G22

and

gz ¼

pffiffiffiffiffiffiffiffi G33

ð5Þ

where x, y and z are the principal axes of the g-tensor and R is the eigenvector matrix giving the direction cosines of gx, gy and gz with respect to the rotation axes in the laboratory axis system. The values are then transformed into the crystal and hence the

R. Kripal, S.D. Pandey / Physica B 444 (2014) 14–20

molecular framework using the direction cosines of the rotation axes. The principal values of the A tensor and their direction cosines can also be obtained by a similar procedure as for the g-tensor taking the angular variation of g 2 A2 in three perpendicular planes. The parameter errors are determined using a statistical method [24]. The values of spin Hamiltonian parameters of Cu2 þ doped LMD obtained here are similar to the results of earlier works [5,25,26] shown in Table 2. The direction cosines of different bonds in lithium maleate dihydrate crystal are calculated from X-ray data and compared with those obtained by an EPR method. The ionic distances and direction cosines of various bonds are given in Table 3. The direction cosines of O(1)–O(3) bond agree within experimental errors with those obtained for the principal axis of g-tensor of Cu2 þ ion. The observed EPR spectra are assigned to Cu2 þ ions on interstitial sites. An ion in an interstitial site has four nearest neighbor lithium ions at the corners of a cube; the ligands consist of a tetrahedron of oxygen ions and a tetrahedron of lithium ions (Fig. 1(c)). Cu2 þ ion has a small radius (72 pm) and fits readily into an interstitial site. The spectrum of Cu2 þ in LMD can be explained by assuming that Cu2 þ ions are associated with four neighboring lithium vacancies. This gives rise to the creation of an entity Cu (OH)24  in the crystal. The capture of the necessary lithium vacancies takes place either by migration to the Cu2 þ site of those already present in the lattice or by the removal of lithium ions migrating away as interstitials. The product of the concentrations of free lithium vacancies and interstitial lithium ions remains constant throughout the process. A similar effect has been found

17

for Fe3 þ ions incorporated in AgCl [27]. This indicates that Cu2 þ ion takes up interstitial position [27] (coordinates of Cu2 þ ion: (0.2100, 0.2862, 0.1001)) in the crystal showing tetrahedral structure (Fig. 1(c)) with O(1), O(2), O(3) and O(5) as the surrounding oxygen atoms.

4.1. Optical spectrum The optical absorption spectrum of Cu2 þ doped LMD single crystal at room temperature in the wavelength range 195– 1100 nm is shown in Fig. 5. There are five bands appearing at ν1 ¼ 11,253 cm  1, ν2 ¼ 12,183 cm  1, ν3 ¼14,239 cm  1, ν4 ¼15,770 cm  1, and ν5 ¼19,383 cm  1 in visible region and three bands in ultraviolet region at ν6 ¼ 23,280 cm  1, ν7 ¼31,746 cm  1 and ν8 ¼ 42,003 cm  1. From the nature of absorption spectrum in visible region, the band observed at ν1 ¼11,253 cm  1 is called as the d–d transition band between ground state dxy and the excited state dx2  y2 . The absorption band at ν4 ¼15,770 cm  1 may be called as d–d transition band between dxy and dxz,yz. The third absorption band observed at ν5 ¼19,383 cm  1 can be called as the d–d transition band between ground state dxy and the excited state d3z2  r2 . The bands at 12,183 cm  1 and at 14,188 cm  1 may be infrared spectral overtone and/or combination bands [28]. There are three bands observed in UV region. These bands are probably charge transfer bands, as they arise from the higher lying energy levels. The observed bands in UV region at 23,280 cm  1, 31,750 cm  1 and 2 42,003 cm  1 can be compared with the bands for CuCl4 complex 2 [29]. From the results of CuCl4 complex, the transitions 4e25b2, Table 3 Distances and direction cosines of various Li–O and O–O vectors in LMD single crystal. Bond

Fig. 4. Angular variation of g2 and g2A2 for B in ab, bcn and cna planes for Cu2 þ doped LMD.

Li(1)–O(1) Li(1)–O(2) Li(1)–O(3) Li(1)–O(4) Li(1)–O(5) Li(1)–O(6) Li(2)–O(1) Li(2)–O(2) Li(2)–O(3) Li(2)–O(4) Li(2)–O(5) Li(2)–O(6) O(1)–O(2) O(1)–O(3) O(1)–O(4) O(1)–O(5) O(1)–O(6) O(2)–O(3) O(2)–O(4) O(2)–O(5)

Distance (Å)

1.9107 6.0703 2.0151 11.0920 5.5747 8.9286 4.7869 5.9449 2.0217 12.2586 4.0475 6.7020 7.5737 2.9993 11.4658 6.2109 9.4413 10.1415 16.3904 11.942

Direction cosines a

b

cn

7 0.9827 7 0.95681 7 0.1115 7 0.1509 7 0.1691 7 0.1619 7 0.6814 7 0.7441 7 0.7960 7 0.2494 7 0.5749 7 0.4223 7 0.9960 7 0.5510 7 0.0177 7 0.1505 7 0.0457 7 0.5949 7 0.4565 7 0.5653

70.3016 70.179 70.9813 70.2193 70.9631 70.9843 70.7412 70.6828 70.4917 70.0439 70.5923 70.8679 70.0662 70.8515 70.2624 70.9572 70.9919 70.3022 70.2147 70.5406

7 0.4904 7 0.0782 7 0.1946 7 0.9184 7 0.1635 7 0.0357 7 0.0359 7 0.0487 7 0.1843 7 0.893 7 0.4142 7 0.1617 7 0.0598 7 0.1816 7 0.9702 7 0.2976 7 0.1331 7 0.0081 7 0.6505 7 0.1161

Table 2 Spin Hamiltonian parameters for Cu2 þ ion in different lattices performed in earlier works. Lattices

gx

gy

gz

Ax (  10  4 cm  1)

Ay

Az

Cs2ZnCl4: Cu2 þ C2H8N2ZnCl2: Cu2 þ ZnC28H36N6O6: Cu2 þ

2.083 70.004 2.058 70.002 2.02 70.002

2.1017 0.003 2.0627 0.002 2.09 7 0.002

2.4467 0.002 2.2977 0.00 2.1637 0.002

517 5 97 4 307 2

467 5 97 4 407 2

25 74 123 74 154 72

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R. Kripal, S.D. Pandey / Physica B 444 (2014) 14–20

Fig. 5. Room temperature absorption spectrum of Cu2 þ doped LMD in the wavelength range 195–100 nm.

3e25b2 and 2a125b2 correspond to the observed bands 23,280 cm  1, 31,750 cm  1 and 42,003 cm  1. In regular tetrahedral symmetry Td, the 2D term of the ion splits into a low lying doublet (E) and a high lying triplet (T2). The splitting between E and T2 is Dt ¼ ð20=27ÞqF 4 ðRÞ, where Dt is the tetrahedral cubic splitting, q is the effective charge of ligands in units of elementary charge, F4 is the fourth-order radial integral of the central field and R is the distance between ligand and central metal ion [30]. If there is small radial extension of the unpaired electron wave function, the fourth-order radial integral of the central field is F 4 ¼ 〈r 4 〉=R5 , where 〈r 4 〉 is the mean fourth-power radius of 3d orbital. Taking 〈r 4 〉 ¼ 0:19555 Å [30], Dt¼ 16885.488 ðq=R5 Þ, where Dt is in cm  1 and R in Angstrom. In our study, R¼ 2.3 Å and q¼ 6.3e [5,31,32], the value Dt¼ 1653 cm  1. The 3d energy levels can be expressed in terms of Ds, Dt and β as Eq. (16) of [5], where Ds ¼9539.055ðq=R3 Þ is a tetrahedron crystal field parameter in cm  1 , R in Angstrom and β is deformation angle between the z-axis of the complex and copper-ligand vector. The tetrahedral crystal field parameter Ds is related to Dt as Ds (cm  1) ¼0.5659 R2Dt. In tetrahedral complexes Ds exceeds Dt for all known copperligand separations. For regular tetrahedron, the deformation angle β is 54.741; for elongated tetrahedron β o54.741; for flattened tetrahedron β 4 54.741 and for a square planer complex β ¼901. Hoffmann and Goslar [32] have also shown in their study that in compressed tetrahedron, β is in the range 54.75–901 with |xy 4 ground state. When the tetrahedron undergoes elongation, ground state becomes |3z2  r2 4 and β lies between 0–451. When β ¼45– 54.741, the ground state is degenerated |xz, yz 4. The orbital splitting with respect to ground state is given in Fig. 6, where the experimental orbital splitting energies are shown by circles. The angle β is 801 with |xy 4 ground state. The experimental and theoretically calculated energies of d–d transition band are shown in Table 4. The poor agreement between the experimental and theoretical energies may be due to axial symmetry approximation. 4.2. Molecular orbital analysis of EPR data In a compressed tetrahedron copper complex with dxy ground state, the crystal field can admix 4pz state of the same symmetry. Due to similar hybridization effects for dxz, dyz and 4px, 4py states, wave functions can be expressed in terms of α, η, γ, ζ, δ and δ1 as Eq. (19) of [5]. Neglecting second-order terms in η and ζ, the spin Hamiltonian parameters become (assuming axial symmetry, as the difference

Fig. 6. The plot of orbital splitting with respect to ground state (Cu-ligand separation ¼ 2.3 Å and q ¼6.3 e are taken).

Table 4 Experimental and calculated energies together with Ds and Dt of d–d transition band. Band position (cm  1)

Transition from ground state dxy

Observed Calculated

dxy2dx2  y2 dxy2dxy,yz dxy2d3z2  r2

11,253 15,770 19,383

7998 15,815 19,186

Tetrahedron crystal field Ds (cm  1)

Tetrahedral cubic splitting Dt (cm  1)

4948

1653

between the values of gx, gy and Ax, Ay is small) 8α 2 λ d E1 2 2 2 2 ¼ 2:0023  ðγ α λd  αγλp ζ Þ E2

g jj ¼ 2:0023  g?

ð6Þ

    4 3 4 Ajj ¼ P d  K α2  α2 þ ðg jj  2Þ þ ðg jj 2Þ þP p η2 K þ 7 7 5     2 2 11 2 2 2 A ? ¼ P d K α  α þ ðg ?  2Þ þ ðg ?  2Þ þ P p η  K  7 14 5 ð7Þ where E1,and E2 are energy separations between the ground state dxy and excited states dx2  y2 and dxz,yz and K is the Fermi contact parameter.λd ¼  829 cm  1 and λp ¼150 cm  1 are the free ion spin–orbit coupling constants for the 3d and 4p orbital, respectively. Pd ¼0.0360 cm  1and Pp ¼0.0402 cm  1are Cu2 þ ion dipolar hyperfine structure parameters of the 3d and 4p orbital, respectively. The expressions (6) and (7) show that in our study, four molecular orbital (MO) coefficients α2, η2, γ2, and ζ2 and one Fermi contact parameter K are unknown. The values of MO coefficients α2, η2 and Fermi contact parameter K are calculated using expressions for g||, A|| and A┴. The rest two MO coefficients γ2 and ζ2 are obtained from equation for g┴ by fitting the MO coefficients using a least-square method to M¼ððg ? cal =g ? obs Þ  1Þ2 where the best-fit MO coefficients minimize the value of M. Here obs and cal indicate the observed and calculated value of g┴, respectively. The coefficients γ2 and ζ2 are characterized by the value M. The values of α2, η2, γ2, ζ2, K and M are 0.28, 0.21, 0.97, 0.001, 0.38 and 16.047  10  4, respectively. The value of α2 is equal to 1 for complete ionic s-bonding, but if overlap integral is too small that it can be neglected and α2 ¼0.5, the bond will be completely covalent. The smaller the value of α2,

R. Kripal, S.D. Pandey / Physica B 444 (2014) 14–20

the greater the covalent nature of bonding [33]. α2 ¼ 0.28 indicates that the s-bonding is completely covalent. The small value of α2 also indicates that the nature of bonding with the ligands along the axis is mostly ionic. The value of γ2 is 0.97, which is very near to unity. This indicates that the out-of-plane covalent π-bonding is very small. The Fermi contact parameter K, a measure of the polarization produced by uneven distribution of the d-electron density of the inner core s-electrons, for 3d transition metal ion is approximately 0.3 [34]. In the present study, K ¼0.38. The value of η2 is 0.21, which indicates that the ground state metal orbital contains 21% admixture of 4p state.

5. Theoretical g factors and defect structures For dn ions in tetrahedral clusters, the one electron basis function |Ψγ 4 (where γ ¼t or e, the irreducible function of Td group) in the two-SO parameter model can be expressed in terms of |dγ 4, |sγ 4, |πγ 4, Nγ and λβ as Eq. (1) of [35], where |dγ 4 is the d orbital of dn ion. |sγ 4 and |πγ 4 are the p orbital of the ligand. The molecular orbital (MO) coefficients Nγ (the normalization coefficients) and λβ (β ¼ s or π, the orbital mixing coefficients) are related by the normalization relationship [35,36] N e ¼ ½1 þ 3λπ þ 6λπ Sdp ðπ Þ  1=2 2

N t ¼ ½1 þ λπ þ λs þ 2λπ Sdp ðπ Þ þ2λs Sdp ðsÞ  1=2 2

2

ð8Þ

and the approximate correlation f e ¼ N 4e ⌊1 þ 9λπ S2dp ðπ Þ þ 6λπ Sdp ðπ Þc 2

f t ¼ N4t ⌊1 þ2λπ Sdp ðπ Þ þ 2λs Sdp ðsÞ þ 2λs Sdp ðsÞλπ Sdp ðπ Þ þ λπ S2dp ðπ Þ þ λs S2dp ðsÞc 2

2

ð9Þ

where fγ Efe E ft is a parameter concerning the covalence reduction effect of the studied dn cluster. For dn ions fγ can be written as the ratio of the Racah parameters in the crystal to that of free ion [35], i.e. B/B0 (or C/C0). fγ is treated as an adjustable parameter because of no Racah parameters for d1 and d9 ions [36]. Sdp(β) are the group overlap integrals. Sdp(β) can be calculated from the Slater type self-consistent field (SCF) functions [37,38] and the metal ligand distance R. As the direction cosines of O(1)–O(3) bond match with those obtained for the principal axes of g-tensor of Cu2 þ ion by EPR method, the copper ion sits in between O(1) and O(3) (coordinates of Cu2 þ ion: (0.2100, 0.2862, 0.1001)). The g values are calculated for various distances of copper ion to the ligand oxygen and at 2.3 Å a satisfactory result is obtained. For R¼ 2.3 Å, the evaluated values of group overlap integrals for Cu2 þ doped LMD are Sdp ðsÞ ¼0.1359 and Sdp ðπ Þ ¼ 0.0407,λπ ¼  0:6982. We can derive higher order perturbation formulas (based on two-SO parameter model) for g-factors of dn ions in tetragonally compressed tetrahedron (rhombic distortion small as the difference between the values of gx, gy and Ax, Ay is small) from the oneelectron basis function and perturbation method [39,40] as 0 0

0

0

g == ¼ g e þ

8k ξ ðg e þkÞξ 4k ξξ   E1 E 1 E2 E22

g ? ¼ ge þ

2kξ 2ξ k  2ξξ k ðg e ξ =2Þ  ξ k 2g e ξ  þ  E2 E1 E2 E21 E22

2

02

0 0

2

2

02

ð10Þ

The SO parameters ξ and ξ0 and orbital reduction factors k and 0 0 k are given in terms of Nγ, λβ, ξd and ξp by Eq. (4) of [36], where g e 0 0 is the free electron value.ξd E 829 cm  1 [39] and ξp E 150 cm  1 9 [41] are the SO parameters of the free d ion and the free ligand ion, respectively. The crystal field energy levels, E1 and E2 are given by E1 ¼ 10Dq and E2 ¼  3Ds þ5Dt, respectively, whereas the tetragonal field parameters Ds and Dt are often calculated from 0

19

superposition model [42]. In accordance with superposition model 4 A2 ðRÞð3cos2 θ  1Þ 7 4 Dt ¼ A4 ðRÞð35cos4 θ  30cos2 θ þ 3 þ 7sin4 θÞ 21 Ds ¼

ð11Þ

where Ak ðRÞ(k¼ 2, 4) are the intrinsic crystal field parameters. For dn ions in the crystals A2 ðRÞ=A4 ðRÞ ratio is found in the range of 8  12 [35,36,43–45]. We have taken A2 ðRÞ=A4 ðRÞ  12 here. The parameter A4 ðRÞ can be expressed in terms of cubic field parameter for dn tetrahedral clusters [41,46] as A4 ðRÞ ¼  ð27=16ÞDq. The value of Dq is estimated using the expression given by Ortolano [47]. The value of Dq is obtained as 930 cm  1. θ is the same as β as used in optical analysis, which is the deformation angle, the angle between the z-axis of the complex and copperligand vector. From the optical spectra of Cu2 þ doped LMD crystal, θ ¼801. The value of fγ is calculated getting the best fit to the experimental g-factors. From the calculation of g-factors, we find fγ ¼0.188 for Cu2 þ doped LMD single crystal. The best fitted values of g-factors are g// ¼2.18 and g ? ¼2.00. The MO mixing coefficients obtained from the value of fγ are λs ¼  0.8603, Ne ¼ 0.6606 and Nt ¼0.0589. The SO parameters ξ and ξ0 and orbital reduction factors k and k0 are calculated. The estimated values of ξ, ξ0 , k and k0 are 319 cm  1, 361 cm  1, 0.4566 and 0.5597, respectively. For dn ions in crystals, the covalence of dn ions increases. Due to increase in valence state of dn ions, the value of covalence reduction factor fγ decreases [48,49]. Here fγ ¼0.188, which shows that the covalence of Cu2 þ ion in LMD single crystal increases. A large local structural perturbation can be expected because copper ion enters the host lattice interstitially and also because there is a mismatch in the charge of copper ion and lithium ion. The large θ value is consistent with the expectation. The g-factors g// and g ? for copper ion in LMD crystal are explained satisfactorily. From the expression of g// one can find that signs of the third-order perturbation terms (third and fourth term) are opposite to that of second-order perturbation term (second term). Generally the contribution due to the third-order perturbation term is smaller than that of the second-order perturbation term. But the energy level E2 depends upon the tetragonal field parameter and hence upon tetragonal distortion. The tetragonal distortion of tetragonal tetrahedron can be characterized by |θ  θ0 |, where θ0 E 54.71 is the value in cubic tetrahedron. The small value of |θ  θ0 | leads to smaller tetragonal distortion than the value of energy level E2. From the calculation tetragonal distortion is 251, which results in large value of E2 approximately 42,386 cm  1. Thus the contribution due to thirdorder perturbation term becomes smaller than the second-order perturbation term to g//, which leads to large g// and small g ? .

6. Conclusion EPR study of Cu2 þ doped lithium maleate dihydrate single (LMD) crystal at LNT and optical absorption study at room temperature have been carried out. Only one site of Cu2 þ is observed. The principal g and A values are evaluated from the EPR spectra fitted to rhombic symmetry spin Hamiltonian. Cu2 þ ion enters the lattice interstitially (coordinates of Cu2 þ ion: (0.2100, 0.2862, and 0.1001)). The ground state wave function of Cu2 þ in the lattice is obtained that contains about 21% admixture of 4p state. The optical absorption has been explained well in terms of D2d symmetry of the oxygen ligands in Cu2 þ complex. The MO coefficients calculated for Cu2 þ doped lithium maleate dihydrate single crystal show that the s-bonding is strongly covalent while the bonding between Cu2 þ ion and its axial ligands is mostly ionic. The theoretical g values considering interstitial

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doping of Cu2 þ ion are in reasonable agreement with the experimental ones.

Acknowledgment The authors are thankful to the Head, Department of Physics, University of Allahabad for providing departmental facilities. We also thank the Sophisticated Analytical Instruments Facility (SAIF), IIT Mumbai, Powai, Mumbai, India for providing EPR spectrometer facilities. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17]

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