Ic

Qa

b

c

S

a

ARRA

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1

gcoc(

ilitsDtbddbg

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Materials Chemistry and Physics 132 (2012) 895– 901

Contents lists available at SciVerse ScienceDirect

Materials Chemistry and Physics

j ourna l ho me pag e: www.elsev ier .com/ locate /matchemphys

nvestigation of relationships between absorption band energies of Tl+ and therystalline environment

iang Suna, Hongyi Daib, Lili Wanga, Jing Wangc, Jinsheng Shia,∗

College of Chemistry and Pharmaceutical Sciences, Qingdao Agricultural University, Qingdao 266109, PR ChinaCollege of Landscape and Horticulture, Qingdao Agricultural University, Qingdao 266109, PR ChinaMinistry of Education Key Laboratory of Bioinorganic and Synthetic Chemistry, State Key Laboratory of Optoelectronic Materials and Technologies,chool of Chemistry and Chemical Engineering, Sun Yat-sen University, Guangzhou 510275, PR China

r t i c l e i n f o

rticle history:eceived 13 January 2011eceived in revised form 5 November 2011ccepted 11 December 2011

eywords:uminescence

a b s t r a c t

The relationships between sp energy levels (A, B and C bands) as well as charge transfer band (D band) ofTl+ center and the crystalline environment were systematically investigated for the first time by meansof dielectric theory of chemical bond for complex crystals. It is found that the coordination number of thecentral ion, the bond volume polarizability, the fractional covalence of the chemical bond between thecentral ion and the nearest anion, and the presented charge of the nearest anion in the chemical bondare the major factors influencing the positions of A, B, C and D bands of Tl+. Our model has successfully

+

hotoluminescence spectroscopyptical materialsrystal structure

built links between the EA, EB, EC and ED of Tl center and the environmental factor he. The results indicatethat both the energies of sp levels and the charge transfer band of Tl+ decrease with the increase of he.he has a linear relationship with the sp energy levels, and an exponential relationship with the CT band.The calculated results using our model are in good agreement with the experimental data. The currentmodel can serve as a predicting tool and be applied to assign and reassign the A, B, C and D band positionsof Tl+.

. Introduction

Ions with the outmost ns2 electronic configuration for theround state and nsnp for the first excited state (n = 4, 5, 6) arealled ns2-type ions [1]. Among these ions, Tl+ in alkali halides andther crystals has been studied most precisely, so ns2 ions are alsoalled Tl+-like ions [2]. This subject has been reviewed many timesexamples are in Refs. [1,3–5]).

Generally four absorption bands are observed when the Tl+ ions substituted by a host cation in a regular lattice site. The threeower bands are called A, B and C bands in the order of increas-ng energy, which have been attributed, respectively, to intra-ionicransitions from the 1S0 ground state to the 3P1, 3P2 and 1P1 excitedtates on the basis of Seitz model (see Fig. 1) [6]. The fourth band,

band, which does not fit in the Seitz model, is usually ascribedo a charge transfer (CT) transition [7,8]. A great deal of effort haseen devoted to understand the A, B and C bands of Tl+ ions embed-ed into alkali halides [9–14]. In 1951, quantitative approaches to

etermining them were taken by Williams and Hebb [9] on theasis of the ionic model. However, Knox and Dexter [10,11] sug-ested that a purely ionic description of the luminescence center

∗ Corresponding author. Tel.: +86 0532 88030161; fax: +86 0532 86080213.E-mail address: jsshiqn@yahoo.cn (J. Shi).

254-0584/$ – see front matter © 2011 Elsevier B.V. All rights reserved.oi:10.1016/j.matchemphys.2011.12.030

© 2011 Elsevier B.V. All rights reserved.

was not enough and that modifications would have to be made toobtain more accurate results. Subsequently, Sugano [12] proposedthe use of the molecular orbital in the Seitz model to explain the A, Band C absorption bands. Starting from this framework, he obtainedthe right value for the ratio of the C band dipole strength to theA band dipole strength. Bramanti and Mancini [13] noticed thatthe Sugano formula is independent of the representation and canalso be derived using a vacancy-centered model. So a semiempiri-cal molecular-orbital calculation was developed for describing theenergy levels by them. They described the positions of the A, B and Cbands by three parameters: Wo, G, �. The quantity Wo is the energydifference between the first excited state and the ground state,whereas G and � are the exchange and spin-orbit energies, respec-tively. This approach is conceptually more satisfactory than theionic one. Fujita [14] investigated the polarized absorption bandsof KH2PO4:Tl+ and RbH2PO4:Tl+. The observed A, B and C bandsare qualitatively explained by taking into account the spin-orbit,crystal-field, and electronic-vibrations. In a word, the theoreticalmodels mentioned above are useful to explain the qualitative fea-tures of the absorption spectra of Tl+ ions, but the quantitativerelationships between the positions of absorption bands for Tl+

centers and the crystalline environment are still unknown.In addition, several other centers, such as Tl0(1) [15,16], (Tl+)2

[5,17] and Tl2+ [18–20], could be formed for alkali halide dopedwith thallium. The presence of these centers introduces new

896 Q. Sun et al. / Materials Chemistry an

A

1P1 (1T1u)

3P2 (3Eu+3T2u)

3P1 (3T1u)

3P0 (1A1u)

1 1

C B

oTodosa6obbs6bebaaiCmrqttui

todRtaIbiptTosctt

2

[

S0 ( A1g)

Fig. 1. Energy level scheme of a free s2 ion.

ptical-absorption bands which make the absorption spectrum ofl+ in alkali halides very complex and difficult to assign. On thether hand, we note that the experimental data assignments byifferent groups are very contradictory. For instance, in the casef CsCl:Tl+, the absorption spectrum in vacuum ultraviolet (VUV)pectral region has been found to consist of several bands, peakingt 6.10, 6.34, 6.54, 7.13 and 7.32 eV [3,21–25]. In Ref. [21] the.10 eV band has been interpreted as 1S0→1P1 (C band) transitionf Tl+, whereas, in Ref. [22], it as a result of the CT transition (Dand). According to Refs. [3,23], the 6.34 eV band was assigned to Cand. In Ref. [24], the authors assumed that the D band of CsCl:Tl+

hould be located in the 6.8–7.7 eV energy range. However, the.34 and 6.54 eV bands have been, in Ref. [25], interpreted as the Dands of the Tl+ center; the 7.13 and 7.32 eV bands as the perturbedxciton transitions. The issue of the assignment for the absorptionands mentioned above should not be peculiar to thallium dopedlkali halides but should be observable in other ns2 ions dopedlkali halides (e.g., Pb2+ and Bi3+ ions). Therefore, it would be verynteresting to study the correlations between the positions of A, B,

and D bands of Tl+ and the crystalline environment. This wouldake it possible to solve the problem mentioned above. Once the

elationships are firmly established, not only qualitatively but alsouantitatively, a lot of useful information will be obtained for bet-er understanding of the energy level for Tl+ ions. The establishedrends can be used to predict A, B, C and D band positions of Tl+ inninvestigated materials. This study may also be very important

n the search for new hosts for phosphors.In this paper, the A, B, C and D band positions of Tl+ in 22 crys-

als were collected. The relationships between EA, EB, EC and ED

f Tl+ and the structure of the crystal were investigated using theielectric theory of chemical bonds for complex crystals [26,27].ecently, this theory has been successfully applied to the study ofhe hardness of crystal [28–32], nonlinear optical crystal [33,34],nd CT energies of Eu3+, Yb3+, Sm3+ and Zr4+ [35–37], and so forth.t is found that the coordination number of the central ion, theond volume polarizability, the fractional covalence of the chem-

cal bond between the central ion and the nearest anion, and theresented charge of the nearest anion in the chemical bond arehe major factors that determine the A, B, C and D band positions.he quantitative relationships between A, B, C and D band energiesf Tl+ and these four chemical bond parameters were establisheduccessfully, and four empirical formulas were obtained. The cal-ulated results based on our model are in excellent agreement withhe experimental results. Our method is also useful to investigatehe A, B, C and D band positions of any other ns2 ions.

. Theoretical methods

The dielectric theory of chemical bond for complex crystals26,27] is based on the bond charge model of Levine [38] and the

d Physics 132 (2012) 895– 901

dielectric theory of Phillips [39] and van Vechten [40], and regardsa complex crystal as the combination of all constituent chemicalbonds. The detailed theoretical method can be found elsewhere[26,27,35,41,42], so in this paper, only a brief description is given.

According to this theory, any multi-bond complex crystal con-taining cations A1, A2, . . ., Ai, anions B1, B2, . . ., Bj, and with formulaA1

a1A2

a2. . . Ai

aiB1

b1B2

b2. . . Bj

bjcan be decomposed into binary crystals

as shown in the following formula according to its crystal structuralinformation:

A1a1

A2a2

. . . Aiai

B1b1

B2b2

. . . Bjbj

=∑

ij

Aimi

Bjnj

(1)

where

mi = N(Bj − Ai)ai

NCAi

nj = N(Ai − Bj)bj

NCBj

(2)

Ai and Bj represent different elements or the different sites of thesame element of cations and anions in the crystal formula, respec-tively, and ai and bj represent the numbers of the correspondingelements. N(Bj − Ai) represents the number of Bj ions in the coor-dination group of the Ai ion, and N(Ai − Bj) has a similar meaning.NCAi

and NCBjrepresent the nearest total coordination numbers of Ai

and Bj ions in the crystal, respectively. Thus, complex crystals aredecomposed into the sum of different species of binary crystals,such as Ai

miBj

nj. For any binary crystal (AmBn)�, QA is the normal

valence of the cation A, and QB is obtained from QB = mQA/n. Givena complex example like KMgF3, we can obtain KMgF3 = KF2 + MgFin terms of Eq. (1). For KF2, let QK = 1.0; then the presented chargeof the F ion is QF = 1/2 = 0.5 in the K F chemical bond. For MgF, letQMg = 2.0; the presented charge of the F ion is QF = 2/1 = 2 in theMg F chemical bond. From that, we can find that the presentedcharges in various chemical bonds are different. Each chemical sub-formula forms a single chemical bond. For any � kind of chemicalbond, the chemical parameters such as ionicity f �

i, the covalency

f �c , and the polarizability of the chemical bond volume ˛�

bcan be

calculated by means of the dielectric chemical bond theory of crys-tals if the crystal structure and the refractive index (n) are known[39,40,43].

3. Results and discussion

Using the dielectric theory of chemical bond for complexcrystals, we calculated the chemical bond parameters for 17 com-pounds; the results are displayed in Table 1. The second columnshows the refractive index n of the crystals. Other columns inTable 1 give the chemical bond parameters: the bond distance (d�),the fractional covalence of the chemical bond (f �

c ), the polarizabil-ity of the chemical bond volume (˛�

b), the coordination number of

the central ion (CN).The experimental data of A, B, C and D bands of Tl+ in these crys-

tals can be obtained from reported experimental spectra and data[1,3,4,25,44–55], and the values are listed in Table 2. The data inTable 2 show that the positions of A, B, C and D bands depend notonly on the alkali ion but also on the halide ion in alkali halide. Forinstance, for Cl series, in the sequence of NaCl→KCl→RbCl→CsCl,the positions of A band were 4.881, 5.010, 5.061 and 4.999 eV,respectively. For K series, in the sequence of KF→KCl→KBr→KI, thepositions of A band were 5.435, 5.010, 4.750 and 4.320 eV, respec-tively. In the sequence of F→Cl→Br→I, the sp energy levels and CTband shift to lower energies, this was attributed to the nephelaux-

etic effect [56,57]. The nephelauxetic effect has been discussedin some detail by Jörgensen [56]. He found that the nephelaux-etic effect can be factored into the function of only a ligand andthe center metal: = 1 − h (ligand) k(center ion). Duffy and Ingram

Q. Sun et al. / Materials Chemistry and Physics 132 (2012) 895– 901 897

Table 1Chemical bond parameters and the environmental factors he.

Crystals n Bonds d� (A) f �c ˛�

b(A3) Q� CN he

Free ion 0.0000 0.0000 0.000NaCl 1.531 Na Cl 2.8100 0.0663 0.5462 1 6 0.466NaBr 1.640 Na Br 2.9869 0.0706 0.7639 1 6 0.569NaI 1.730 Na I 3.2350 0.0706 1.0753 1 6 0.675KF 1.362 K F 2.6835 0.0475 0.3411 1 6 0.312KMgF3 1.428 K F 2.8143 0.0218 0.0997 0.5 12 0.081

Mg F 1.9900 0.0642 0.1712 2 6 0.514KZnF3 1.440 K F 2.8673 0.0264 0.1358 0.5 12 0.104

Zn F 2.0275 0.0772 0.1771 2 6 0.573KCl 1.488 K Cl 3.1394 0.0483 0.7092 1 6 0.453KBr 1.557 K Br 3.2923 0.0490 0.9136 1 6 0.518KI 1.658 K I 3.5246 0.0513 1.2832 1 6 0.628RbCl 1.490 Rb Cl 3.2895 0.0445 0.8188 1 6 0.468RbBr 1.550 Rb Br 3.4384 0.0443 1.0305 1 6 0.523RbI 1.640 Rb I 3.6646 0.0457 1.4109 1 6 0.622CsCl 1.631 Cs Cl 3.5637 0.0379 0.7407 1 8 0.474CsBr 1.693 Cs Br 3.0273 0.1342 0.2993 1 6 0.491CsI 1.789 Cs I 3.9558 0.0372 1.2032 1 8 0.598TlCl 2.223 Tl Cl 1.9200 0.3467 0.3198 1 6 0.816TlBr 2.384 Tl Br 1.9850 0.3609 0.3794 1 6 0.906

n of thp rdinac

[1

[nagmo

TT

T

is the index of refraction; d� is the bond distance; f �c is the fractional covalence

resented charge of the nearest anion in the chemical bond; CN is the nearest-coorystals.

58] have proposed a quantitative relation between the position ofS0→3P1 transition of ns2 ions and Jörgensen’s h functions. Blasse57] and Bruce and Duffy [59] investigated the relationship betweens2 ions 1S0→3P1 transition as well as Eu3+ CT transition energy

nd h, and obtained some significant results. However, they did notet the detailed factors entering h. Gao and Zhang [60] studied theechanism of the nephelauxetic effect for the electronic structure

f 3d elements and identified the main factors responsible for the

able 2he A, B, C, and D band energy data of Tl+ monomer center in compounds from experimen

Crystals he EA,exp EA,cal EB,exp

Free ion 0 6.496a 6.447 7.653a

NaCl 0.466 4.881b 4.942 5.770c

NaBr 0.569 4.644b 4.609 5.462d

NaI 0.675 4.232b 4.267 4.940e

KMgF3 0.081 6.150g 6.185 7.380g

KZnF3 0.104 6.030g 6.111 7.200g

KF 0.312 5.435c 5.439 6.450c

KCl 0.453 5.010b 4.984 5.940c

KBr 0.518 4.750b 4.774 5.580c

KI 0.628 4.320b 4.419 5.060c

RbCl 0.468 5.061b 4.935 5.932j

RbBr 0.523 4.787b 4.758 5.535d

RbI 0.622 4.430k 4.438 5.080k

CsCl 0.474 4.999b 4.916 5.585d

CsBr 0.491 4.860m 4.861 5.560l

CsI 0.598 4.510n 4.515 5.210l

TlCl 0.816

TlBr 0.906

he experimental values of A, B, C and D band energies are from references:a Ref. [44].b Ref. [3].c Ref. [4].d Ref. [45].e Ref. [46].f Ref. [1].g Ref. [47].h Ref. [48].i Ref. [49].j Ref. [50].k Ref. [51].l Ref. [25].

m Ref. [52].n Ref. [53].o Ref. [54].p Ref. [55].

e chemical bond; ˛�b

is the polarizability of the chemical bond volume; Q� is thetion number for each element in the crystal; he is the environmental factor of the

effect, which are the covalency of chemical bond, the polarizabil-ities of ligand bond volume for the host and the valence, and thespin state of the center ion. Considering that the electric charge ofligands is different in different crystals, we redefined a new factor

he [41,42] which is written as follows:

he =[∑

f �c ˛�

b(Q �)2

]1/2(3)

tal and calculated results.

EB,cal EC,exp EC,cal ED,exp ED,cal

7.678 9.380a 8.969 12.0655.775 6.230b 6.262 7.0035.355 5.740b 5.664 6.2254.922 5.080e 5.049 5.500f 5.5217.347 8.270g 8.499 10.876h 10.9647.253 8.140g 8.365 10.6716.404 7.130c 7.157 8.560i 8.3675.828 6.358b 6.338 7.340f 7.1085.563 5.904c 5.960 6.500f 6.5985.114 5.300b 5.322 5.530f 5.8225.767 6.358b 6.251 7.100f 6.9875.543 5.848b 5.931 6.230f 6.5605.138 5.370k 5.356 5.900k 5.8625.743 6.294b 6.216 7.225l 6.9395.673 5.932j 6.117 6.600l 6.8055.236 5.620l 5.496 5.950l 6.023

4.974o 4.7174.258p 4.272

898 Q. Sun et al. / Materials Chemistry an

0.70.60.50.40.30.20.10.04.0

4.5

5.0

5.5

6.0

6.5

7.0

7.5

8.0

8.5

9.0

9.5

E /

eV

Tl+ A Band Tl+ B Band Tl+ C Band

F

w˛cafdot

ppo

h

ubmac

atAaie

he

ig. 2. The A, B and C band energies for Tl+ as a function of environmental factor he.

here f �c stands for the fractional covalence of the chemical bond,

�b

is the polarizability of the chemical bond volume in the � type ofhemical bonds, Q� stands for the presented charge of the nearestnion in the chemical bond, he is referred to as the environmentalactor. Using this new factor, we successfully explained the energyifference between the spin-allowed and the spin-forbidden statesf Tb3+ in crystals [41] as well as the barycenter of energy of lan-hanide 4fN−15d configuration in inorganic crystals [42].

Based on expression (3) and the corresponding chemical bondarameters (see Table 1), the environmental factors of the com-ounds were calculated. For instance, the environmental factor hef K site for KMgF3 can be obtained:

e =[∑

f �c ˛�

b(Q �)2

]1/2

= [12 × 0.0218 × 0.0997 × (0.5)2]1/2 = 0.081

The calculated results are listed in column 9 of Table 1 and col-mn 2 of Table 2. For a free Tl+ ion, its electron cloud is not affectedy any ligand, f �

c = 0, and ˛�b

= 0, so the corresponding environ-ental factor he = 0. The relations between the positions of A, B

nd C bands and the he are shown in Fig. 2, and Fig. 3 shows theorrelation between D band energy and he.

It is obvious from Figs. 2 and 3 that not only the sp levels (A, Bnd C bands) but also the CT band (D band) energies decreased withhe increase of he. It is worth noticing that the experimental data of

+

, B and C bands for Tl show a remarkably linear relation with he,nd an exponential relationship exists between D band and he. Thisnteresting phenomenon indicated that the influences of crystallinenvironment on sp levels and CT band are different. Four empirical

1.00.80.60.40.20.0

4

5

6

7

8

9

10

11

E /

eV

he

Tl+ D Band

Fig. 3. The D band energies for Tl+ as a function of environmental factor he.

d Physics 132 (2012) 895– 901

formulas are obtained by fitting the curves of A, B and C bands inFig. 2 and fitting D band in Fig. 3, which can be written as:

Tl+ A Band : EA = 6.447 − 3.230 × he (4)

Tl+ B Band : EB = 7.678 − 4.083 × he (5)

Tl+ C Band : EC = 8.969 − 5.808 × he (6)

Tl+ D Band : ED = 0.476 + 11.589e(−1.232he) (7)

EA, EB, EC and ED of Tl+ ion were calculated using expressions (4)–(7),and the corresponding results are listed in Table 2 (columns 4, 6,8 and 10). The model calculation results are in excellent agree-ment with the experimental data. In most cases, the relative erroris less than 2%. Especially for free Tl+ ions, the calculated val-ues (EA,cal = 6.447 eV, EB,cal = 7.678 eV, EC,cal = 8.969 eV), are in verygood agreement with the experimental data [44] (EA,exp = 6.496 eV,EB,exp = 7.653 eV, EC,exp = 9.380 eV). In the case of CT band (D band)for Tl+, as shown in Table 2 columns 9 and 10, we can see thatthe maximal error between calculated and experimental resultsis 0.330 eV for RbBr:Tl+, and the relative error is only 5.297%. Tothe best of our knowledge, this is the first successful quantitativeinvestigation of the relationship between D band of Tl+ ion and thecrystalline environment.

In addition, expressions (4)–(6) show that the slopes increasemarkedly in the sequence of A → B → C bands; the correspondingvalues are 3.230, 4.083 and 5.808, respectively. This means C bandis the most sensitive energy level compared with A and B bands.Moreover, as shown in Fig. 2, the distance of B and A bands as wellas C and B bands decrease with the increase of he. For example,�EB–A of Tl+ for KMgF3 (he = 0.081) and NaI (he = 0.675) are 1.230and 0.708 eV, respectively, and the corresponding �EC–B are 0.890and 0.140 eV, respectively. This trend indicates that the distance ofA, B and C bands of Tl+ will become too small to identify for eachband in the host whose he is larger than 0.7.

4. Applications

From the above discussion, it can be concluded that the absorp-tion band positions of Tl+ have direct relationships with theenvironmental factor, and four good empirical formulas betweenhe and EA, EB, EC and ED are obtained. Therefore, we think that thecurrent computational method can serve as a prediction tool andcan be applied to the assignments, reassignments, and predictionsof the absorption band position of Tl+ center in complex crystals.The applications of our model in these fields will be discussed inthis section.

4.1. Assignment and reassignment of the absorption bandpositions

In this section, RbI:Tl+, CsCl:Tl+, CsBr:Tl+, CsI:Tl+ and KMgF3:Tl+

were chosen to demonstrate the application of our model in theassignment and the reassignment of the absorption band positionsof Tl+.

In the case of RbI:Tl+, two absorption bands at 5.29 and 5.46 eVat 10 K were assigned to the C and D bands, respectively [51]. How-ever, we note that the structures of the emission spectra of RbI:Tl+

under 5.29 and 5.46 eV excitation are very similar: for 5.29 eV exci-tation, the strongest band is at 2.62 eV, and the three others are at2.82, 3.40 and 4.24 eV; for 5.46 eV excitation, the strongest bandis at 2.58 eV, and the three others are at 2.81, 3.40 and 4.24 eV. Inaddition, the intensity of these emission bands is also very sim-

ilar. The structures of emission spectra of KI:Tl+ excited in the Cand D bands at 12 K are different [61–63]. It is well known that theintensity of C and D bands are very close to each other [4], but the5.46 eV band is about one-third of the intensity of 5.29 eV [51]. In

try an

aoifcb(55rt

1

aobttoct

aatCrCtaebaoC

(tt[fvda(bMadi[baobctmwtttawTw

Q. Sun et al. / Materials Chemis

ddition, the intensity of 5.90 eV band is very close to 5.29 eV. More-ver, when the intensity of the 2.58 eV band decreases, the relativentensity of the peak at 5.90 eV also decreases. The aforementionedacts indicated that: (1) the 5.29 and 5.46 eV bands should be asso-iated with the same transition of thallium; (2) the origin of 5.90 eVand might be ascribed to the Tl+ center. According to expressions6) and (7), the predicted values of C and D bands of RbI:Tl+ are.356 and 5.862 eV, respectively. Thus, we suggest that the band at.29, 5.46 and 5.90 eV can be reassigned to the C1, C2 and D bands,espectively. The predicted values are in excellent agreement withhe observed values.

For CsCl:Tl+, in Ref. [21] the 6.10 eV band has been interpreted asS0→1P1 (C band) transition of Tl+, and in Ref. [3], the 6.34 eV wasssigned to the C band. According to our model, the calculated resultf C band was 6.216 eV, so we suggest that the 6.10 and 6.34 eV cane reassigned to the C1 and C2 bands, respectively. In Ref. [25],he 7.13 and 7.32 eV bands were regarded as the perturbed excitonransitions. In Refs. [21,24], the authors assumed that the D bandf CsCl:Tl+ should be located in the 6.8–7.7 eV energy range. Thealculated result of D band was 6.939 eV. Based on the above fact,he 7.13 and 7.32 eV bands may be assigned to the CT bands.

For CsBr:Tl+, in the higher energy region, two absorption bandst 5.56 and 5.94 eV were reported in Ref. [25]. Both of them weressigned to the CT bands by the authors. Sharan et al. [45] obtainedwo similar bands at 225 nm (5.510 eV) and 210 nm (5.904) forsBr:Tl+. These two bands were ascribed to the C and D bands,espectively. Using expressions (5)–(7), we predicted that the B,

and D bands of Tl+ in CsBr are 5.673, 6.117, and 6.805 eV, respec-ively. Therefore, we reassign the 5.56 and 5.94 eV bands to the Bnd C bands of Tl+, respectively. Moreover, we think that the D bandnergy should be around 6.805 eV. This hypothesis was confirmedy the absorption spectrum in which an intense absorption bandt 6.60 eV was observed in Ref. [64]. The author did not discuss therigin of this band, according to our model, we think it is due to theT transition (D band) of Tl+ in CsBr.

The CsI:Tl+ phosphor has been closely studied by many authors,see, e.g., Refs. [25,65–72]). Understanding of optical proper-ies of CsI:Tl+ is necessary to find an optimum performance forhis material which is widely used in scintillator applications65,66]. However, the optical properties of CsI:Tl+ differs essentiallyrom that of other alkali halide-thallium phosphors, and it givesery complicated absorption spectra which cannot be completelyescribed by a simple ionic model [21,66,67]. The assignment of thebsorption bands has not yet been successful [68–72]. The 4.51 eV276 nm) band had previously been identified as the B band [62]ut this interpretation has been questioned by Stillman [69] andasunaga et al. [70]. This band does not show any character of

forbidden transition [70], and moreover, the size of this bandecreases rapidly and steadily with increasing temperature and

ts appearance in the magnetic circular dichroism (MCD) spectrum69]. All these phenomena are strong indicators that the 4.51 eVand is not the B band. In Refs. [25,69] the 4.51 eV bands wasscribed to charge transfer from 5p orbital of I− to vacant 6p orbitalf Tl+. According to the study by Asami et al. [68] the feature of thisand is similar to the A band. According to expression (4), the cal-ulated value of A band for CsI:Tl+ was 4.515 eV. So, for 4.51 eV, wehink this band should be assigned to the A band of Tl+. The assign-

ent of 5.21 eV was also very contradictory: in Ref. [69], this bandas ascribed to the C bands; however, in Ref. [25], it was assigned

o the CT transition. Using expressions (5) and (6), we predictedhat the B and C bands of Tl+ in CsI are 5.236 and 5.496 eV, respec-ively. In Refs. [70,71], a band at 228 nm (5.438 eV) was observed

nd assigned to the CT transition of Tl+. According to our model,e reassign the 5.21 and 5.438 eV bands to the B and C bands of

l+, respectively. In addition, three bands at 5.78, 5.92 and 6.15 eVere observed by Babin et al. [53] and Zazubovich et al. [72]. To the

d Physics 132 (2012) 895– 901 899

best of our knowledge, these bands have not been assigned by anyauthor. In general, the D band is composed of three bands (namedas D1, D2 and D3 in order of increasing energy), and the peak posi-tions of the D band are higher than that of A, B and C bands [7,8].The calculated value of D band was 6.023 eV. Taking into consider-ation of the above fact, the 5.78, 5.92 and 6.15 eV may be assignedto D1, D2 and D3 bands, respectively. The agreement between thecalculated and experimental data is quite good.

The spectroscopic properties of single crystals of KMgF3:Tl+

were extensively investigated by several authors due to its possibleapplications in radiation dosimetry [47,48,73–77]. The absorptionof isolated Tl+ ions in the K+ site for KMgF3 exhibits the typicalA, B and C bands quoted in VUV spectral region [47,48]. Thesebands peaked at 6.15, 7.38 and 8.27 eV, respectively. As shown inTable 2, the calculated values are in excellent agreement with theexperimentally observed absorption bands. In addition, accordingto our model, we predict that the position of D band is 113.1 nm(10.964 eV). This hypothesis was confirmed by the absorption spec-trum, in which an absorption band at 114 nm (10.876 eV) wasobserved by Scacco et al. [48]. This band can be ascribed to theCT transition of Tl+ in the K+ site according to our model.

4.2. Prediction of the absorption band positions and clarifyingsite occupation

The most important application of our model is to predictthe absorption band positions and clarify the site occupationof thallium doped phosphors. Here, we chose complex crys-tals KH2PO4:Tl+, RbH2PO4:Tl+, Gd(BO2)3:Tl+, La(BO2)3:Tl+ andK2YF5:Tl+ to demonstrate the application of our model in this filed.

The crystal structures of KH2PO4, RbH2PO4, Gd(BO2)3, La(BO2)3and K2YF5 were reported in detail [78–82]. According to the methodmentioned previously, we can decompose KH2PO4, RbH2PO4,Gd(BO2)3, La(BO2)3 and K2YF5 into their subformula equations asthe followings:

KH2PO4 = KO4/3 + H2O4/3 + PO4/3

RbH2PO4 = RbO4/3 + H2O4/3 + PO4/3

Gd(BO2)3 = GdB(1)B(2)2O(1)2O(2)2O(3)2

= Gd2/5O(1)4/5 + Gd1/5O(2)1/2 + Gd2/5O(3)

+ B(1)1/2 O(1)2/5 + B(1)1/2 O(2)1/2 + B(2)2/3 O(1)4/5

+ B(2)2/3 O(2) + B(2)2/3 O(3)

La(BO2)3 = LaB(1)B(2)2O(1)2O(2)2O(3)2 = La2/5O(1)4/5

+ La1/5O(2)1/2 + La2/5O(3) + B(1)1/2 O(1)2/5

+ B(1)1/2 O(2)1/2 + B(2)2/3 O(1)4/5 + B(2)2/3 O(2)

+ B(2)2/3 O(3)

K2YF5 = K(1)K(2)YF(1)F(2)F(3)F(4)F(5) = K(1)2/9F(1)2/5

+ K(1)2/9F(2)2/5 + K(1)2/9F(3)2/5 + K(1)2/9F(4)2/5

+ K(1)1/9F(5)1/4 + K(2)1/4F(1)2/5 + K(2)1/4F(2)2/5

+ K(2)1/4F(3)2/5 + K(2)1/8F(4)1/5 + K(2)1/8F(5)1/4

+ Y1/7F(1)1/5 + Y1/7F(2)1/5 + Y1/7F(3)1/5 + Y1/7F(4)1/5

+ Y2/7F(5)1/2

900 Q. Sun et al. / Materials Chemistry and Physics 132 (2012) 895– 901

Table 3Experimental and calculated results of A, B, C, and D band energies of Tl+.

Crystals n Bond he EA,exp EA,cal EB,exp EB,cal EC,exp EC,cal ED,cal

KH2PO4 1.487 K O 0.149 5.660a 5.966 6.910a 7.070 7.485a 8.104 10.121RbH2PO4 1.485 Rb O 0.138 5.690a 6.001 6.960a 7.115 8.167 10.253Gd(BO2)3 1.75 Gd O 0.288 5.500b 5.517 6.800b 6.502 8.120b 7.296 8.603La(BO2)3 1.751 La O 0.308 5.800b 5.452 6.500b 6.420 8.300b 7.180 8.406K2YF5 1.45 K1 F 0.233 5.881c 5.694 6.727 7.616 9.173

K2 F 0.312 5.439 6.404 7.157 8.367

The experimental values of A, B, C and D band energies are from references:

UtpEaaTdeaofE

wVqsaiiu

hCcacoPbaedawfisi

5

ahfs(tla

[[[[[[[[[[

[

[

[[[

a Refs. [14,84].b Ref. [85].c Ref. [86].

sing the known refractive index n [83], the detailed bond parame-ers and he of each type of bond were calculated. The results of he areresented in Table 3. On the basis of expressions (4)-(7), the EA, EB,C and ED of KH2PO4:Tl+, RbH2PO4:Tl+, Gd(BO2)3:Tl+, La(BO2)3:Tl+

nd K2YF5:Tl+ are calculated and listed in Table 3 (columns 6, 8, 10nd 12). The predicted and observed values [14,84–86] shown inable 3 are close. This means that our model is a useful tool to pre-ict the absorption band positions of thallium doped phosphors,specially for complex crystals. For any compound, if the structurend the refractive index n are known, by using the dielectric theoryf chemical bond for complex crystals theory, the environmentalactor he of the crystal can be calculated, and then the EA, EB, EC andD of Tl+ can be predicted by expressions (4)–(7).

Recently, Tanimizu and Yasuda [85] found that the Tl+ co-dopedith Tb3+ ion in Ln(BO2)3 (Ln = La,Gd) is a new, efficient and greenUV phosphors. In the present work, it is found that there areuantitative relationships between energy levels and he, thus, weuggest the compound whose he is close to 0.29–0.30 would also be

suitable host for efficient and green VUV phosphors. Correspond-ng work is underway to confirm our hypothesis. If this hypothesiss confirmed, our model will be proven to be a very helpful andseful tool for the search of new phosphors.

For the past decades, a lot of studies had been focused on theost lattice dependence of the luminescence of ns2 ions [86–91].ompared to the effort devoted to experimental works, theoreti-al studies of the site selective spectrum have been very limited,nd the spectrum assignments were rather tentative. Here wehose K2YF5:Tl+ as an example to demonstrate the application ofur model. K2YF5 has an orthorhombic crystalline structure withna21, Z = 4 space group, the reticular constants are a = 10.791 A,

= 6.607 A, c = 7.263 A [88]. There are two K+ sites (K1 and K2) avail-ble for Tl+ in K2YF5. The K1 and K2 are coordinated by nine andight fluoride ions, respectively. Until now, only one experimentalata of 5.881 eV was reported by Demchuk et al. [86]. This band wasssigned to the A band of Tl+, however, it is very difficult to verifyhich site it comes from through experiments. The environmental

actor of K1 and K2 sites are 0.233 and 0.312, respectively. Accord-ng to expression (4), the calculated values of A band for K1 and K2ites were 5.694 and 5.439 eV, respectively. So, based on our model,t can be concluded that the 5.881 eV is from K1 site.

. Conclusions

In summary, a semi-empirical method for predicting thebsorption band positions of Tl+ center in any inorganic crystalsas been proposed based on the dielectric theory of chemical bond

or complex crystals. The environmental factors (he) affecting thep energy levels (A, B and C bands) as well as charge transfer band

D band) of Tl+ monomer centers are the coordination number ofhe central ion, the bond volume polarizability, the fractional cova-ence of the chemical bond between the central ion and the nearestnion, and the presented charge of the nearest anion. he has a linear

[[[[

relationship with the sp energy levels, and an exponential rela-tionship exists between D band and he. The agreement betweenexperimental and theoretical results is excellent. The currentsemi-empirical model can serve as a prediction tool and can beapplied to assign and reassign the absorption band positions of Tl+

centers in inorganic crystals. Based on the calculated results, wediscuss the origin of the absorption bands of RbI, CsX (X = Cl, Br,I), and KMgF3 doped with Tl+ ions, and assign and reassign theseabsorption bands. In addition, he of complex crystals KH2PO4,RbH2PO4, Gd(BO2)3, La(BO2)3 and K2YF5 were calculated, andEA, EB, EC and ED of Tl+ in these compounds were predicted.More importantly, using our model, the site occupation of Tl+ incomplex compounds can be assigned accurately. For K2YF5:Tl+,the absorption band at 5.881 eV from the site of K1 is confirmed.Moreover, our method is also useful for investigating compoundsdoped with other ns2 ions, such as In+, Sn2+, Pb2+, Bi3+, and soforth. Further systematic studies are underway.

Acknowledgement

This work was financially supported by the Project of Shan-dong Province Higher Educational Science and Technology Program(J10LD10).

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