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Journal of Physics and Chemistry of Solids 68 (2007) 1652–1655

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EPR parameters and defect structures of the off-center Ti3+ ionon the Sr2+ site in neutron-irradiated SrTiO3 crystal

Zheng Yuana, Wu Xiao-Xuana,b,d, He Lva,c, Zheng Wen-Chena,d,�

aDepartment of Material Science, Sichuan University, Chengdu 610064, PR ChinabDepartment of Physics, Civil Aviation Flying Institute of China, Guanghan 618307, PR China

cCollege of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua 321004, PR ChinadInternational Centre for Materials Physics, Chinese Academy of Sciences, Shenyang 110016, PR China

Received 18 November 2006; received in revised form 6 March 2007; accepted 30 March 2007

Abstract

The EPR parameters (g factors and hyperfine structure constants A) for the tetragonal Ti3+ center in cubic phase and the rhombic

Ti3+ center in tetragonal phase in the neutron-irradiated SrTiO3 crystals are calculated from the third-order perturbation formulas of

EPR parameters for d1 ions. These low-symmetry Ti3+ centers in both phases of SrTiO3 are due to the Ti3+ ion at ‘‘off center’’ on the

Sr2+ site. From the calculation, the defect models (including the direction and magnitude of the Ti3+ off-center displacement) of the two

Ti3+ centers in SrTiO3 are estimated and the EPR parameters of both Ti3+ centers are reasonably explained on the basis of the defect

models. The results are discussed.

r 2007 Elsevier Ltd. All rights reserved.

Keywords: A. Oxides; D. Crystal fields; D. Defects; D. Electron paramagnetic resonance

1. Introduction

Irradiation can cause defects in crystals. For example,after irradiation with fast neutrons, the undoped pureSrTiO3 crystals show electron paramagnetic resonance(EPR) arising from Ti3+ ion on Sr2+ site [1]. As is known,SrTiO3 is a classical ABO3 perovskite-type crystal whichundergoes a displacive soft mode type phase transitionfrom cubic to tetragonal at TCE105K [2]. The EPRmeasurements for the above neutron-irradiated SrTiO3

suggested that the Ti3+ center in cubic phase is tetragonalsymmetry and that in tetragonal phase is rhombicsymmetry [1]. The anisotropic g factors and hyperfinestructure constants A for the tetragonal and rhombic Ti3+

centers in SrTiO3 were obtained from the EPR measure-ments [1]. Schirmer et al. [1] thought that the low-symmetryTi3+ center in both phases is due to Ti3+ at ‘‘off-center’’

front matter r 2007 Elsevier Ltd. All rights reserved.

s.2007.04.001

ng author. Tel.: +8628 85412371; fax: +86 28 85416050.

ss: zhengwc1@163.com (Z. Wen-Chen).

site, i.e., Ti3+ ion is not at an ideal position of Sr2+, but ismoved off center towards one of the twelve surroundingoxygen ions, because of the smaller radius of Ti3+

compared with the replaced Sr2+ ion. However, the moveddirection is one of the twelve [1 1 0]-type C2 axis, whichshould result in the rhombic Ti3+ center in cubic phase andthe monoclinic Ti3+ center in tetragonal phase. Thesesymmetries of Ti3+ centers are in disagreement with theobserved ones. In addition, the experimental tetragonalaxis of g factors in the tetragonal Ti3+ center in cubicphase is one of cubic [1 0 0]-type C4 axes rather than [1 1 0]-type C2 axes. So, we suggest that the Ti3+ off-centerdisplacement from Sr2+ site is not along one of C2 axes,but along one of C4 axes, thus, the symmetry and symmetryaxes for the low-symmetry Ti3+ centers in both phasesof SrTiO3 are consistent with those in the experiments.This displacement direction is the same as that of Mn2+

ion in similar perovskite crystal KTaO3 (where becauseof its smaller radius, Mn2+ ion does not occupy the idealK+ site, but is shifted by about 0.9 A along one of six[1 0 0]-type C4 axes, this displacement is confirmed by the

ARTICLE IN PRESSZ. Yuan et al. / Journal of Physics and Chemistry of Solids 68 (2007) 1652–1655 1653

first-principles study [3], the density functional theory ingeneralized gradient approximation (GGA) [4] and thedipole moment study [5]) and can be regarded as possible.In order to confirm this suggestion and to explainreasonably the anisotropic g factors and hyperfine struc-ture constants A for the two Ti3+ centers in both phases ofSrTiO3 crystals (note: these EPR parameters have not beenexplained reasonably until now), in this paper, we calculatethese EPR parameters form the high-order perturbationformulas of EPR parameters for 3d1 ions in tetragonal andrhombic symmetries. The results are discussed.

2. Calculations

2.1. Calculation for tetragonal Ti3+ center (T4TC)

Ti3+ ion at the Sr2+ site of SrTiO3 is in a 12-foldcoordinated tetrakaidecahedral crystal field. For a 3d1 ionin this crystal field, the 2D energy level splits into a lowerdoublet 2E and a higher triplet 2T2. The tetragonaldistortion further splits the 2E level into 2B1 and 2A1(E)and the 2T2 into 2E and 2A1(T). From the experimental g

factors of the tetragonal Ti3+ center in SrTiO3 (T4TC),one can expect that the ground state is 2A1ðEÞðjdz2iÞ Sincethe observed hyperfine structure constants AJ and A? arevery small (see Table 1, note: for the tetragonal Ti3+

center, the parameters AJ and A? were not reported, wereasonably estimate them by AJ ¼ Az, A? ¼ (Ax+Ay)/2,where Ax, Ay and Az are the experimental values in therhombic Ti3+ center. Since the experimental values g||Egz,g?E(gx+gy)/2 [1], the above estimation is suitable), asshown in Ref. [6] for the 3d1 ion V4+ in some crystals, aparameters N(E) (note: N(E)o1. If N(E) ¼ 1, itdenotes the reduction being not considered) is used torepresent the effective John–Teller reduction in thestudy of hyperfine structure constants. Thus, from theperturbation method, we derive the third-order perturba-tion formulas of EPR parameters for a 3d1 ion in

Table 1

g factors and hyperfine structure constants A (in units of 10�4 cm�1) for

the tetragonal and rhombic Ti3+ centers in SrTiO3 crystal

Calculation Experiment [1]

Tetragonal center g|| 1.9985 1.9940(30)

g? 1.8904 1.8905(10)

A|| 2.7 2.7 (1)a

A? 14.96 14.95 (45)a

Rhombic center gx 1.9229 1.9228(5)

gy 1.8346 1.8530(5)

gz 1.9964 1.9945(5)

AX 14.51 13.50(5)

AY 15.78 16.4(4)

AZ 2.7 2.7(1)

aEstimated from the values in rhombic symmetry, see text.

tetragonal symmetry as

gjj ¼ ge þ3x2ðk�geÞ

E21

;

g? ¼ ge �6xkE1�

3ðkþge=2Þx2

E21

;

Ajj ¼ P½�k þ 4NðEÞ=7þ ðgjj � geÞ � ðg? � geÞ=7�;

A? ¼ P½�kþ 2NðEÞ=7þ 15ðg? � geÞ=14�;

(1)

where ge(E2.0023) is the free-electron value, k and K arethe orbital reduction factor and the core polarizationconstant, respectively. x and P are the spin-orbit couplingparameter and the dipolar hyperfine structure constant incrystals. It should be pointed out that the widely usedformulas given in Ref. [7] are the approximate expressionsof our above formulas when we take k ¼ 1(i.e., the orbitalreduction effect is neglected) and geE2.For 3dn ions in crystals, since the covalence reduction

effect [8–10], we have k � N2; x ¼ N2x0 and P E N2P0,where N2 is the covalence reduction factor (which is oftentaken as an adjustable parameter), x0 and P0 are thecorresponding parameters in free state. For free Ti3+ ion,we have x0E154 cm�1 [11] and P0E�25.6� 10�4 cm�1

[12]. For Ti3+ ion, the core polarization constantkE0.6�0.725 [10,13,14], we take kE0.63 here. E1 inEq. (1) is the energy difference between 2E state and theground state 2A1ðEÞ dz2

�� �. From the crystal-field theory, it

can be expressed as

E1 � Eð2EÞ � E½2A1ðEÞ� � �B20=7� 10B40=21, (2)

where B20 and B40 are the tetragonal field parameters. Theycan be calculated from the superposition model [15]. Fromthis model, for the studied tetragonal Ti3+ center, we have

B20 ¼ 4A2ðR0ÞP3i¼1

R0

Ri

� �t2ð3 cos2 yi � 1Þ;

B40 ¼ 4A4ðR0ÞP3i¼1

R0

Ri

� �t4ð35 cos4 yi � 30 cos2 yi þ 3Þ

(3)

in which the power-low exponents t2E3, t4E5 because ofthe ionic nature of bonds [9,15,16]. A2ðR0Þ and A4ðR0Þ arethe intrinsic parameters with the reference distance R0. Wetake R0E2.758 A [17], the metal–ligand distance at the Sr2+

site in the cubic phase of the host SrTiO3 crystal. The ratioA2ðR0Þ=A4ðR0Þ � 9� 12 obtained for 3dn ions in manycrystals [10,16,18,19], we take the mean value, i.e.,A2ðR0Þ=A4ðR0Þ � 10:5 here. The parameter A4ðR0Þ dependsupon the cubic crystal field strength. As is known, the cubicfield strength (characterized by the cubic field parameter Dq)of 3dn ions at the tetrakaidecahedral A site is much weakerthan that at the octahedral B site in ABO3 perovskite (e.g.,the cubic crystal field strengths for Fe 3+ ion at both sites inKTaO3 [20]) because of the larger metal–ligand distance anddifferent coordination number. For Ti3+ in oxygen octahe-dra, e.g., Ti3+ in Al2O3, A4ðR0Þ � 3Dq=4 � 1400 cm�1

[21], thus for Ti3+ in oxygen tetrakaidecahedra understudy, we take A4ðR0Þ � 650 cm�1. Ri and yi are thestructural data of the studied tetragonal Ti3+ center. They

ARTICLE IN PRESSZ. Yuan et al. / Journal of Physics and Chemistry of Solids 68 (2007) 1652–16551654

can be expressed as

R1 ¼R2

0

2þ

R0ffiffiffi2p � Dz

� �2" #1=2

; cos y1 ¼ðR0=

ffiffiffi2pÞ � Dz

R1,

R2 ¼ R20 þ ðDzÞ2

1=2; cos y2 ¼

Dz

R2,

R3 ¼R2

0

2þ

R20ffiffiffi2p þ Dz

� �2" #1=2

; cos y3 ¼ðR0=

ffiffiffi2pÞ þ Dz

R3,

ð4Þ

where Dz is the off-center displacement of Ti3+ from Sr2+

site along C4 axis. Thus, in the above formulas, theparameters N2, N (E) and Dz are not known and are takenas adjustable parameters. By fitting the calculated gJ, g?, AJ

and A? to the experimental values, we obtain

N2 � 0:6; NðEÞ � 0:77; Dz � 0:24 A (5)

The comparisons of EPR parameters between calculationand experiment are shown in Table 1.

2.2. Calculation for rhombic Ti3+ center (ToTC)

When the temperature ToTC, the cubic phase of SrTiO3

becomes tetragonal phase and the symmetry of the off-center Ti3+ defect center changes from tetragonal torhombic. Thus, the energy level 2E in tetragonal centersplits into 2B2 and

2B3. The energy separation is 2d. Thus,we have

E2 � Eð2B2Þ � E½2A1ðEÞ� � gE1 � d;

E3 � Eð2B3Þ � E½2A1ðEÞ� � gE1 þ d(6)

The ground state is still 2A1ðEÞðjdz2Þ. The second-orderperturbations of gi (i ¼ x, y, z) for d1 ions in rhombicsymmetry with dz2

�� �as the ground state were given in

Ref. [22]. It is too simple because gz(EgeE2.0023) is in pureagreement with the observed value. So, we derive the third-order perturbation formulas of EPR parameters for 3d1 ionsin the rhombic symmetry with dz2

�� �ground state as

gx ¼ ge �6kxE3� 3x2ð

k

E2E3þ

ge

2E22

Þ,

gy ¼ ge �6kxE2� 3x2ð

k

E2E3þ

ge

2E23

Þ,

gz ¼ ge þ3x2kE2E3

�3

2x2geð

1

E22

þ1

E23

Þ,

Ax ¼ P½�k� 2NðEÞ=7þ ðgx � geÞ þ ðgy � geÞ=14�

Ay ¼ P½�k� 2NðEÞ=7þ ðgy � geÞ þ ðgx � geÞ=14�

Az ¼ P½�kþ 4NðEÞ=7þ ðgz � geÞ � ðgy � geÞ=14

� ðgx � geÞ=14�. ð7Þ

From the crystal-field theory, the rhombic splittingd ¼

ffiffiffi6p

B22=7� 2ffiffiffiffiffi10p

B42=21, where B22 and B42 are therhombic field parameters related to the defect structuraldata. Since the tetragonal phase of SrTiO3 is the result of

alternate rotations of the oxygen octahedra surroundingTi4+ ion (i.e., the B site in ABO3 crystal) around atetragonal axis, the displacements of the 12 oxygen ionssurrounding Ti3+ ion (i.e., the A site in ABO3 crystal) aredifferent and complex. In addition, the phase transitionbehavior in the impurity center may be different from that inthe host crystal. So, it is difficult to calculate the rhombicsplitting d from the defect structural data. Also, since thepositions of 12 oxygen ions in rhombic center are unlikethose in tetragonal center, the level E1 calculated usingEq. (2) in rhombic center may be slightly different from thatin tetragonal center. Thus, in Eq. (6), we apply a changefactor g (g ¼ 1 represents the E1 being unchanged). We taked and g as the adjustable parameters. Substituting the sameparameters (e.g., N2 and N(E)) as those in the tetragonalTi3+ center into Eq. (7) and fitting the calculated EPRparameters to the observed values, we yield.

g � 1:08; d � 2200 cm�1. (8)

The calculated EPR parameters are compared with theobserved values in Table 1.

3. Discussion

The off-center displacement of impurity ion in a crystal isdue to its much smaller ionic radius compared with thereplaced host ion [23–28]. In fact, the off-center displace-ment in magnitude is related to the size and valence state ofimpurity ion [24]. For the isovalent impurity ions in acrystal, the off-center displacement of impurity along thesame direction increases with the deceasing ionic radius r ofimpurity. For example, for Mn2+ (rE0.80 A [29]) and Fe2+

(rE 0.74 A [29]) ions in SrO crystal (note: for Sr2+,rE1.12 A [29]), the off-center displacements along /1 1 1Saxis are, respectively, 0.33 and 0.4 A and those along/1 1 0S axis are, respectively, 0.27 and 0.33 A [26].However, for the impurity with different valence state,although the ionic radius of impurity decreases withincreasing valence state [29], the off-center displacementdecreases rather than increases with the increasing valencestate of impurity. For instance, the off-center displacementsalong /1 1 1S axis for Ni+, Ni2+ and Fe3+ in SrO crystalare, respectively, 0.32, 0.27 and 0.18 A [27,28]. So, thesmaller off-center displacement of Ti3+ ion along C4 axis inSrTiO3 crystal obtained above than that (E0.90 A [3–5]) ofMn2+ along the same direction in similar perovskite KTaO3

crystal can be regarded as rational in physics.Based on the above suitable defect model, the EPR

parameters gi and Ai for the off-center Ti3+ ion at Sr2+ site

of SrTiO3 crystal in cubic and tetragonal phases arereasonably explained from the high-order perturbationformulas (see Table 1). There is very small disparitybetween calculation and experiment for some EPR para-meters in the rhombic Ti3+ center in the tetragonal phase.The causes may be as follows: (i) The slight changes onsome parameters (e.g., N2 and N(E)) from cubic totetragonal phase are not considered. (ii) The perturbation

ARTICLE IN PRESSZ. Yuan et al. / Journal of Physics and Chemistry of Solids 68 (2007) 1652–1655 1655

formulas are approximate. (iii) The EPR parameters atvarious temperatures come from the static contributionrelated to the defect structure of paramagnetic center andthe vibrational contribution related to electron–phononinteraction [30–33]. In the above calculations, the vibra-tional contributions to EPR parameters are not included.Considering these, the small errors in the calculated EPRparameters can be understood.

Acknowledgments

This project was supported by the National NaturalScience Foundation of China (Grant no.10274054) and theCAAC Scientific Research Base of Civil Aviation FlightTechnology and Safety.

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