ARTICLE IN PRESS

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doi:10.1016/j.ni

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Nuclear Instruments and Methods in Physics Research A 575 (2007) 390–394

www.elsevier.com/locate/nima

Computer simulation of Nb-doping PBWO4 crystal$

Teng Chen�, Tingyu Liu, Qiren Zhang, Fangfei Lii, Dongsheng Tian, Xiuyan Zhang

College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China

Received 9 September 2006; received in revised form 6 February 2007; accepted 13 February 2007

Available online 28 February 2007

Abstract

The existing forms of the impurity Nb5+ ions in the Nb:PWO crystals are simulated by the computer simulation technology. The

various kinds of defects and substitution reactions in the Nb:PWO crystals are also simulated. By analyzing the calculated results of

defect formation energies and solution energies, the optimal positions of the Nb5+ ions and the charge compensating mechanism

[NbO3+VO]+–[NbO4]

� in the Nb:PWO crystals are obtained; this charge compensating mechanism change the compensating form of

oxygen vacancies which relates to 350 nm absorption band, then the 350 nm absorption band is depressed.

r 2007 Elsevier B.V. All rights reserved.

Keywords: PbWO4; Doping; Charge-compensating mechanism; Computer simulation; GULP

1. Introduction

Owing to its potential application to electromagneticspectrometry in high energy physics, such as to electro-magnetic calorimeter for compact muon solenoid experi-ments in the large hadron collider at CERN [1], PbWO4

(PWO) crystals have attracted special interests and havebeen under investigations for some decades but till nowsome of its properties are still debated. A lot of problemsshould be solved in order to improve its scintillationproperties. Many studies show that doping some ions caneffectively improve the scintillation properties of PWOcrystals. Since Kobayashi [2–4] found doping La3+ ionscan enhance the radiation hardness and optical transmis-sion near UV regions of PWO crystals. In order to find theoptimal scintillant properties of PWO crystals, the dopingeffects for many kinds of ions in PWO crystals have beenstudied especially trivalent, tetravalent and pentavalentions. Up to now, the doping mechanism of trivalent andtetravalent ions doping in PWO crystals have been

e front matter r 2007 Elsevier B.V. All rights reserved.

ma.2007.02.077

by Shanghai Leading Academic Discipline Project,

ber: To501, and the Scientific Development Foundation

unicipal Education Committee under Grant No. 04EB09.

ing author.

esses: chen-teng@163.com (T. Chen), liutyyxj@163.com

commonly accepted. However, for the doping mechanismof pentavalent ions, there is seldom clear viewpoint up tonow. The appearance of Nb:PWO crystals has beenattracted extensive attentions, because doping niobiumcan enhance the transmittance near ultraviolet regions,restrain the 350 nm absorption band and enhance theradiation hardness [5,6]. However, there is no identicalviewpoint about the Nb doping mechanism, also there islittle direct experimental or theoretical evidence on theexistent form of the Nb5+ in the Nb:PWO crystals. F colorcenter, F+ color center and VO

2+, which is the main chargecompensatory form in Nb:PWO crystals have been debatedfor long time, Korzhik [6] proposed that Nb5+ ions occupythe W6+ positions in the (WO3+VO), forming hole centreNbO3+F+ in the Nb:PWO crystals; however, he did notexplain why Nb5+ ions occupy the W6+ positions in the(WO3+VO) instead of the normal W6+ positions.Furthermore, there are various opinions on the chargecompensating mechanism in the Nb:PWO crystals. Inorder to clarify the charge compensating mechanism inNb:PWO crystals, in this paper, the possible defect modelsand the possible substitution reactions in the Nb:PWOcrystals have been investigated using the free-softwaregeneral utility lattice program (GULP). The calculatedresults and various microcosmic mechanisms have beendiscussed.

ARTICLE IN PRESST. Chen et al. / Nuclear Instruments and Methods in Physics Research A 575 (2007) 390–394 391

2. Method of simulation

The lattice simulations were performed using the freesoftware GULP program that is based upon the Mott–Lit-tleton methodology for accurate modeling of defectivelattices. The program GULP optimizes the structure withrespect to the asymmetric unit fractional coordinates andcell strains, using analytical symmetry-adapted first andsecond derivatives within a Newton–Raphson procedurestarting from the exact Hessian matrix [7,8].

An important feature of these calculations is themodeling of defects. The simplification of the Mott–Lit-tleton method is to divide the crystal lattice that surroundthe defect into three regions known as I, 2a, and 2b, asshown in Fig. 1. In the inner region, all interactions aretreated at an atomistic level and the ions are explicitlyallowed to relax in response to the defect, while theremainder of the crystal, where the defect forces arerelatively weak, is treated by more approximate quasi-continuum methods. In this way, local relaxation iseffectively modeled and the crystal is not considered simplyas a rigid lattice through which ion species diffuse. In thestudy, the inner defect region was set at 7.5 A, which wasfound to be adequate for the convergence of the computedenergies, and the result almost approximates the one whenthe inner defect region was set at 12.0 A.

Both perfect- and defect-lattice calculations are formu-lated within the framework of the Born-like model. In thisapproximation, the potentials describing the interatomicinteractions between two ions, with distance r, arepresented as follows:

Uij ¼ZiZje

2

rþ A exp

�r

r

� ��

C

r6

Fig. 1. Mott–Littleton method deals with the lattice relaxation around a

defect.

Table 1

Empirically derived potential parameters used in PWO crystal

Short-range potential parameters

Interactions A/eV r/10�10m C/eV(10�10m)6 R

O2�–O2� 9547.960 0.219200 32.000 [8

Pb2+–Pb2+ 18912.114 0.313781 2.600 [8

Pb2+–O2� 8086.804 0.264866 3.564 [8

W6+–O2� 767.430 0.438600 0.000 [9

Nb5+–O2 3023.184 0.300000 0.000 [1

where the first part is the long-range Coulombic term andthe latter are the short-range term described by the two-body Buckingham form, which is composed of the short-range Pauli repulsion and the leading term of thedispersion energy. Therefore, Zi is the formal charge ofatom I. A, r, and C are the adjustable potential parameters,respectively.Because charged defects will polarize other ions in the

lattice, ionic polarizability(a) is also incorporated into thepotential model. A shell-model treatment of such effects isdescribed in terms of a shell with charge Y connected via anisotropic harmonic spring of force constant k to a massivecore of charge Z–Y, namely, a ¼ Y 2=k.In the calculations, all ions are treated as polarizable.

Table 1 gives the short-range potential parameters andshell-model parameters, where the maximum short-rangecutoff is 15.0 A.

3. Possible defect models

There are different charge compensating mechanismspossibly existing in Nb:PWO crystals, which correspondsto different defect clusters and different substitutionreactions.Firstly, the point defects possibly existing in the

Nb:PWO crystals were calculated, Nb5+ ions may occupynormal lattice Pb2+ positions and W6+ positions formingpoint defect NbPb

3+ and NbW�1,or enter into the crystals as

interstitial ions forming point defect Nbi5�; the formation

energies of intrinsic point defects lead vacancies VPb2� and

oxygen vacancies VO2+ were also calculated.

Secondly, in order to confirm whether Nb5+ ions occupythe W6+ position in the (WO3+VO) [5] and the chargecompensating mechanism on oxygen vacancies, five defectclusters relating to oxygen vacancies were calculated: (1)Nb5+ ions occupy the W6+ site in the (WO3+VO) formingdefect cluster (a) NbW1

�1 –F, (b) NbW1�1 –F+ and (c)

NbW1�1 –VO

2+; (2) Nb5+ ions occupy the W6+ site in the(WO4)

2� nearest to the (WO3+VO) forming defect cluster(d) NbW2

� –VO2+; (3) Nb5+ ions occupy the W6+ site in the

(WO4)2� further away to the (WO3+VO) forming defect

cluster (e) NbW3� –VO

2+.Lastly, the solution energies of possible substitution

reactions that correspond to different compensatingmechanism were calculated, the possible mechanism of

Shell parameters

eference Ions Y/e k/eV(10�10m)2 Reference

,9,10] Pb2+ �0.09 21006.539 [8,9,10]

,9,10] W6+ 5.89 7.690 [8,9,10]

,9,10] O2� 2.04 6.300 [8,9,10]

,10] Nb5+ 5.000 0.000 [11]

1]

ARTICLE IN PRESS

Table 2

Formation energies of isolated point defects and cluster defect

Lattice Energy (eV) Lattice Energy (eV)

(a) Lattice energy (eV)

PbWO4 �247.67 WO3 �213.38

PbO �37.89 Nb2O5 �327.35

(b) Isolated point defect

Defect Energy (eV) Defect Energy (eV)

VO2+ 18.72 NbW

� 34.12

VPb2� 25.21 NbPb

3+ ****

Oi2�

�9.83 Nbi5� ****

(c) Defect cluster

Configuration Cluster energy

(eV)

Configuration Cluster energy

(eV)

NbW1– F 53.586 NbW2–VO

2+ 50.181

NbW1– F+ 53.232 NbW3–VO

2+ 56.102

NbW1–VO2+ 50.179

(d) Solution energy

Substitution

reactions

Energy (eV) Substitution

reactions

Energy (eV)

3.1 3.265 3.3 4.015

3.2 10.382 3.4 5.234

T. Chen et al. / Nuclear Instruments and Methods in Physics Research A 575 (2007) 390–394392

Nb doping include four equations:

Nb2O5 þ PWO! ½NbO3 þ VO�þ þ ½NbO4�

� (3.1)

Nb2O5 þ PWO! 2½NbO3 þ VO�þ þ VPb

2� (3.2)

Nb2O5 þ PWO! 2½NbO3 þ VO�þ þOi

2� (3.3)

Nb2O5 þ PWO! NbO3 þ Fþ (3.4)

For Eq. (3.1), it means that a Nb5+ ion occupy thelattice of W6+ in a (WO3+VO), and another W6+ in the(WO4)

2� nearest to the (WO3+VO) is also replaced by aNb5+ ion; for Eq. (3.2), it means that two Nb5+ ionsoccupy two lattice of W6+ and make the two (WO4)

2�

change to (NbO3+VO), the charges of one VO2+ was

compensated by two NbW� and another VO

2+ was compen-sated by a VPb

2�; for Eq. (3.3), it means that two Nb5+ ionsoccupy two lattice of W6+ and make the two (WO4)

2�

change to (NbO3+VO), the difference from Eq. (3.2) is oneVO2+ was compensated by two NbW

� , but another VO2+ was

compensated by an interstitial oxygen ions Oi2� [12]; forEq. (3.4), it means that a Nb5+ ion occupy the lattice ofW6+ in a (WO3+VO), and the VO trap a electron formingF+ color center. The cluster defects formed from the fourequations have all achieved charge balance. By comparingthe solution energy of the four equations, the optimalcompensating mechanism could be found.

4. Simulation results and discussions

Table 2 presents the calculated formation energies ofisolated point defects, defect clusters and solution energiesin Nb:PWO crystals. Some of the computed results are ingood agreement with previous work [13].

Nb5+ ions only can in three forms enter into the PWOcrystals: occupying Pb2+ positions, occupying W6+ posi-tions and in the form of interstitial ions. The calculatedformation energies of point defect NbPb

3+ was not con-vergent (in Table 2 denoted with ***), it means that Nb5+

ions are difficult to occupy Pb2+ positions in Nb:PWOcrystals. This could be understood because a Nb5+ ionentering the Pb2+ lattice will produce excessively highcharge in the local structure. Because of its smaller radius,theoretically Nb5+ ions should easily enter into the crystalsin the form of interstitial ions. Several decade sites ofinterstitial Nb5+ ions embed in PWO crystals weresimulated, however, all the calculated results were notconvergent. It means that interstitial Nb5+ ions are alsodifficult to exist in Nb:PWO crystals. For Nb5+ occupyingW6+ position, the simulation result of defect formationenergy is convergent. It can be concluded that Nb5+ ionsshould occupy W6+ positions, not other positions inNb:PWO crystals. Meanwhile, the radius of Nb5+ is0.069 nm and its electronegative is 1.60. The radius ofPb2+ is 0.12 nm and its electronegative is 1.80. The radiusof W6+ is 0.062 nm and its electronegative is 1.70. The

radius and electronegative of Nb5+ is more close to that ofW6+, so Nb5+ ions should easily occupy the W6+ position.In the case of Nb5+ ions occupying W6+ positions, there

are three charge compensatory forms: F color center, F+

color center and perfect oxygen vacancies VO2+, which is the

main charge compensatory form has been debated for longtime. The simulation results show that the formationenergy of the NbW1–VO

2+ cluster is lower than that ofNbW1� –F and NbW1

� –F+ cluster. It indicates that the maincharge compensatory form is oxygen vacancies for NbW

� inNb:PWO crystals, not F or F+ color centers.The formation energies of cluster(c), (d), (e) were listed

in Table 2. For defect cluster (e), 30 cases were calculated(listed in Table 2 is the minimum of these 30 cases), fromthe calculated results it can be found that the Nb5+ shouldpreferentially occupy the W6+ lattice in (WO3+VO) in theNb:PWO crystal. However, we can also find the formationenergy of defect cluster (c) and (d) are very close to eachother, much less than that of cluster (e). Since theformation energy of (c) is so close to that of (d), we canspeculate that the W6+ ions nearest to the oxygenvacancies and next nearest to the oxygen vacancies possiblycould all be replaced by Nb5+ ions and this can achievelocal charge balance. The below calculated results furtherconfirm the speculation. The charge compensating mechan-ism can be expressed as cluster defect(h) ([NbO3+VO]

+–[NbO4]�)Fig. 2 shows its microscopic structure and

the substitution reactions can be expressed as Eq. (3.1).The solution energies of Eqs. (3.1)–(3.4) were calculated.

Whether interstitial oxygen ions can exist in Nb:PWO

ARTICLE IN PRESS

c

b

a

VO2+

NbW-

NbW-WO4

2-

Pb2+

Fig. 2. Micro-structural models of VO2+ and NbW

� color centre in the as-

grown PWO crystal.

T. Chen et al. / Nuclear Instruments and Methods in Physics Research A 575 (2007) 390–394 393

crystal should be confirmed before studied Eq. (3.3). WhenPWO crystal doping with Nb2O5, in the melting process,Nb2O5 will give out oxygen, make crystal grow in richoxygen conditions, so there may be some interstitial oxygenions exiting in the crystal. Several decades positions thatinterstitial oxygen ions may exist in the Nb:PWO crystalwere simulated in this paper, most of the defect formationenergies are convergent, the smaller one is listed in Table 2.It can be found that theoretically Eqs. (3.1)–(3.4) all couldoccur in the Nb:PWO crystals. The solution energy of Eq.(3.1) is 3.265 eV, which is the smallest of the four equations.The formation energy of Eq. (3.3) is 4.015 eV, which isclose to (3.1), however, the solution energy of Eq. (3.1) is10.382 eV, and is much bigger than the above two. Thismeans that cluster defect 2[NbO3+VO]

+–VPb2� described by

Eq. (3.2) is difficult to exist in the Nb:PWO crystalsbecause of its much higher energies. Comparing thesolution energy of Eq. (3.1) with that of Eq. (3.4), we canalso find the formation of defect cluster[NbO3+VO]

+–[NbO4]� is easier than that of defect cluster

NbO3+F+. It can further confirm the conclusion thatoxygen vacancy is the main compensatory form inNb:PWO crystals. We can also conclude that in Nb:PWOcrystals, Nb5+ not only occupy the lattice of W6+ in(WO3+VO), the W6+ in the (WO4)

2� nearest to the(WO3+VO) can also be replaced by Nb5+, which forms abalanced mechanism [NbO3+VO]

+–[NbO4]. For the caseof Nb2O5 heavy doping, there may also exist anothercharge compensating mechanism 2[NbO3+VO]

+–Oi2� in

Nb:PWO crystals, its amount is small because its solutionenergy is higher than that of [NbO3+VO]

+–[NbO4]� and

interstitial oxygen ions may not exist largely in the crystal.The experimental results also claim that Nb5+ ions

cannot occupy Pb2+ sites and lead vacancies in Nb:PWOcrystals, it can only occupy W6+ site and the maincompensatory form is not F color center or F+ colorcenter, but perfect oxygen vacancy, there will form thedefect cluster (NbO3+VO)

� in Nb:PWO crystals[14]. Our

calculated results are in good agreement with the experi-mental results. However, for the defect (NbO3+VO)

�,NbW�1 shows one negative valence and oxygen vacancy

shows two positive valence, this make local chargeexhibits one positive valence, namely, [(NbO3+VO)

�]+,so there should exist complex charge compensatingmechanism. Our calculated results indicate that theW6+ in the (WO4)

2� nearest to the (NbO3+VO) mayalso be replaced by Nb5+ ions forming defect cluster[NbO3+VO]

+–[NbO4]�.

Korzhik found that PWO doping with Nb can enhancethe transmittance near ultraviolet region, restrain the350 nm absorption band and enhance the radiation hard-ness [4]. In previous work, we found that the appearance ofthe 350 nm absorption band is related to oxygen vacanciesin the PWO crystal [15]. In that work, PWO crystalincluding an isolated oxygen vacancy was calculated, inorder to keep charge balance, the oxygen vacancy shouldcatch one or two electrons forming F+ or F color center, soit means that the appearance of 350 nm absorption bandhave relation with F color center, In Nb:PWO crystals,there will not form F or F+ color center, it will form a newcharge compensating mechanism [NbO3+VO]

+–[NbO4]�,

so the 350 nm absorption band is restrained.

5. Conclusion

The formation energies of point defects and defectclusters have been studied by a computer simulationtechnique. The calculated results indicate that Nb5+ willoccupy the site of W6+ forming defect cluster NbO3+VO

in Nb:PWO crystals. By further analyzing simulationresults, it shows that Nb5+ ions will not only replace theW6+ site in the(WO3+VO), the W6+ ions nearest to the(WO3+VO) also can be replaced by Nb5+. It will form thecharge compensating mechanism [NbO3+VO]

+–[NbO4]�,

this change the charge compensating mechanism of oxygenvacancies that are related to 350 nm absorption band, sothe 350 nm absorption band is restrained.

Acknowledgment

We are grateful to Prof. J.D. Gale and Dr. F.W. Zhangfor the interesting discussion in the program.

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