Local structure distortion models for Cr3+ centers in Tl2MgF4 and Tl2ZnF4 fluorine compounds

Journal of Physics and Chemistry of Solids 88 (2016) 109–115

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Local structure distortion models for Cr3 þ centers in Tl2MgF4 and Tl2ZnF4 fluorine compounds Muhammed Açıkgöz n Faculty of Engineering and Natural Sciences, Bahcesehir University, Beşiktaş 34353, İstanbul, Turkey

art ic l e i nf o

a b s t r a c t

Article history: Received 4 June 2015 Received in revised form 28 September 2015 Accepted 3 October 2015 Available online 22 October 2015

Theoretical analysis of the EPR spectra of Cr3 þ centers in Tl2MgF4 (Tl2MgF4 and Tl2ZnF4) fluorine compounds have been carried out for the first time. The correlation between the experimental data and theoretical values regarding zero-field splitting (ZFS) provides suitable structural models to understand the local structure around the Cr3 þ centers in Tl2MgF4 and Tl2ZnF4. A clear compression of the MF6 octahedron around tetragonal (TE) Cr3 þ center has been shown in both crystals. The calculations for the monoclinic (MO) Cr3 þ center reveal that the length of the four equatorial F-ligands (R2) is about 1.5% longer than that of the octahedral ZnF6 in undoped Tl2ZnF4 and the length of the axial F-ligands (R1) is quite shorter (∼9.5%) than R2. Also, it yields a quite large b2−1 and declined angle (27.46°, ∼30%) for z-axis. Our results indicate that the presence of the different structural formations may be considered around the orthorhombic (OR) Cr3 þ center III and IV. It was suggested that the latter one can be attributed to an angular distortion relevant to the equatorial F-ligands along z∥[110]-axis. & 2015 Elsevier Ltd. All rights reserved.

Keywords: A. Magnetic materials D. Magnetic properties D. Crystal fields D. Electron paramagnetic resonance (EPR)

1. Introduction A2BF4-type layered perovskite-like crystals draw more attention of electron magnetic resonance (EMR) researchers due to their close relation to ABF3-type cubic perovskite crystals. It was experimentally observed that both group of crystals have various paramagnetic centers when they are doped with transition metal (TM) ions. EPR investigations of TM ion doped A2BF4 crystals reveal more interesting results with various extra centers having some lower symmetry than those of ABF3 crystals. Namely, in addition to the tetragonal (TE) and trigonal (TR) Cr3 þ centers formed in ABF3 crystals, some orthorhombic (OR) and monoclinic (MO) Cr3 þ centers have been found being formed in A2BF4 crystals. In particular, previously published EPR data for Cr3 þ in Tl2MgF4 (Tl2MgF4 and Tl2ZnF4) crystals have shown that the presence of four structurally different Cr3 þ centers. In the paper [1], Arakawa et al. reported the results of their investigation on Cr3 þ doped Tl2ZnF4. Aside from the previously observed centers (center I and IV) [2], they also observed two new centers: a MO center (center II) and another OR center (center III). A vacancy at the nearest Tl þ site was assigned to the Cr3 þ center II at the site of Zn2 þ ion as a result of the spin-Hamiltonian separation (SHS) analysis, which is based on separating the second-rank ZFSPs (fine structure terms) into an uniaxial term along the crystalline c-axis n

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http://dx.doi.org/10.1016/j.jpcs.2015.10.001 0022-3697/& 2015 Elsevier Ltd. All rights reserved.

and another uniaxial term along the crystalline b-axis [2]. It is known that paramagnetic impurity ions doped into A2BF4 fluorides substitute for host B2 þ cations and form paramagnetic impurity centers. When the impurity ions is a divalent M2 þ such as Mn2 þ and Ni2 þ , there is no need for a charge compensator, however, when a trivalent impurity ion such as Cr3 þ and Fe3 þ substitute for host divalent cation ion this situation is associated with a charge compensator for local charge neutrality. Based on the local charge compensation around the divalent sites after Cr3 þ substitution it is possible to consider some different formations for the TE and TR centers in ABF3 crystals. One of them is the Cr3 þ –Li þ center, where Li þ ion at the nearest B2 þ site compensates the excess monovalent positive charge on Cr3 þ ion [3]. The other one is the Cr3 þ –VA center, where a vacancy at the nearest A þ site occurs [4]. Even, through the creation of a B2 þ vacancy at the nearest B2 þ site, the formation of the Cr3 þ –VB center was also reported with an overcompensation of the positive charge on Cr3 þ by the B2 þ vacancy [5]. Similar various structural formations were reported for Cr3 þ doped A2BF4 crystals even with low symmetry centers. For not only the confirmation of the experimental observations but also to better understand the structural mechanism around the TM ion centers, a theoretical analysis is required. Nevertheless, no theoretical investigation of Cr3 þ centers in Tl2MF4 crystals has been done yet. Thus, in this study, we have investigated theoretically the Cr3 þ centers in Tl2MgF4 and Tl2ZnF4 crystals by means of semi-empirical calculations using superposition model (SPM), see, e.g. the papers [6,7] for the successful applications of this

110

M. Açıkgöz / Journal of Physics and Chemistry of Solids 88 (2016) 109–115

model on Cr3 þ ion doped systems. Based on the correlation between the crystallographic and EPR data we have carried out the modeling of the zero-field splitting (ZFS) parameters (ZFSPs) for all of the observed Cr3 þ centers and have enabled to determine the local structure of [Cr–F6]3  clusters through various modeling approaches.

2. Method for calculations

b20 = D =

Experimental spectra of Cr3 þ doped Tl2MgF4 and Tl2ZnF4 crystals can be analyzed by utilizing the spin Hamiltonian, suitable for the spin S¼ 3/2 systems, consisting of the Zeeman electronic terms and the ZFS terms [8,9,10]:

H = HZe + HZFS = μB B⋅g⋅S +

∑ Bkq Okq = μB B⋅g⋅S + ∑ fk bkq Okq

(1)

where μB is the Bohr magneton, B is the applied magnetic field, g is the spectroscopic splitting factor, S is the effective spin operator, and Bkq (or bkq ) are ZFSPs associated with the extended Stevens operators Okq , whereas fk ¼ 1/3, and 1/60 are the scaling factors for k ¼2, and 4, respectively [11,12]. Explicit form of the ZFS term in Eq. (1) can be written for each symmetry case [13–15]. ZFS of a d3 configuration Cr3 þ center with TE symmetry can be analyzed by the following explicit expression of the spin-Hamiltonian:

⎞ 1 0 0 1 ⎛ 2 1 b2 O2 = D ⎜ Sz − S (S + 1) ⎟ ⎠ 3 3 ⎝ 3

HZFS =

1 0 0 (b2 O2 + b2−1O20 + b22 O20 ) 3

(3a)

HZFS =

1 0 0 (b2 O2 + b2−2 O20 + b22 O20 ) 3

(3b)

HZFS =

1 0 0 (b2 O2 + b21O20 + b22 O20 ) 3

(3c)

which differ with respect to the choice of the MO direction, i.e. C2 ∥X-axis (Eq.(3a)), C2∥Z-axis (Eq.(3b)), and C2∥Y-axis (Eq.(3c)). On the other hand, for Cr3 þ center with OR symmetry we can use HZFS as:

(4)

In general, following the general definitions for the SPM quantities outlined recently in [16,17], the ZFSPs can be expressed as

bkq =

∑ b¯k (Ri )⋅Kkq (θi, φi ) i

(5)

where Kkq (θi, ϕi ) are the coordination factors [18] as functions of the position angles θi and ϕi of ligands. The intrinsic parameters (IPs) b¯k (Ri ) are assumed to obey the following power law:

⎛ R ⎞tk b¯k (Ri ) = b¯k (R 0 ) ⎜ 0 ⎟ ⎝ Ri ⎠

⎛ R 0 ⎞t 2 ⎟ (3 cos2 θi − 1) Ri ⎠ i=1 n

∑ ⎜⎝

(7)

n ⎛ R ⎞t 2 b2−1 = 3b¯ 2 (R 0 ) ∑ ⎜ 0 ⎟ sin 2θi sin ϕi ⎝ Ri ⎠ i=1

b22 = 3E =

3b¯ 2 (R 0 ) 2

(8)

⎛ R 0 ⎞t 2 ⎟ sin2 θi cos 2ϕi Ri ⎠ i=1 n

∑ ⎜⎝

(9) b2−1

Here we provide the expression for only ZFSP regarding the MO direction C2∥X-axis. Indeed, as mentioned above, depending on the choice of the C2 direction, we may have b2−2 or b21 instead of b2−1 for choosing C2∥Z-axis or C2∥Y-axis, respectively.

3. Results and discussion

HZFS =

⎞ 1 0 0 1 ⎛ 1 (b2 O2 + b22 O22 ) = D ⎜ Sz2 − S (S + 1) ⎟ + E (Sx2 − Sy2 ) ⎠ 3 3 ⎝ 3

b¯ 2 (R 0 ) 2

(2)

For the Cr3 þ centers with MO symmetry, for which only one symmetry axis C2 exists, can be represented by the following HZFS s:

HZFS =

included into a combined set, which is known as SPM parameter set for SPM applications [19]. Only one data set [20] of the model parameters, i.e. bk (R0 ) and tk with R0 , suitable for the ligand system of the Cr3 þ –F  bond configuration, exists in literature. These are: b2 (R0 ) ¼(467707800)x10  4 cm  1 and t2 ¼ 0.2470.03 with R0 ¼0.2113 nm. SPM provides the following general expressions for ZFSPs for the Cr3 þ centers in 6-fold coordination in terms of IPs:

The presence of TE center I and OR center IV in Tl2MgF4 [2] whereas TE center I, MO center II, and OR centers III and IV in Tl2ZnF4 [1] crystals are known experimentally. The types of Cr3 þ centers present in Tl2MF4 crystals and values of the previously determined experimental ZFSPs (D¼ b20 and 3E¼ b22) for them are tabulated in Table 1. It should be noted that the values of the ZFSP D¼ b20 in Tl2MgF4 and Tl2ZnF4 are rather higher than those in other A2BF4 crystals, even D¼ b20 of the TE Cr3 þ center is almost three times of that in K2ZnF4 (  381.0  10  4 cm  1 [1]) and Rb2ZnF4 ( 369.0  10  4 cm  1 [21]). Furthermore, it is worth noting that the rhombicity ratio λ ¼E/D measuring the deviation from axial symmetry for the OR and MO centers is much higher in these crystals. Even, it is 0.71 and 0.77 for OR center IV in Tl2MgF4 and Tl2ZnF4, respectively. Normally, the ratio λ yields 0 r λ ¼E/D r1/3 [22]. In SPM analyses, it is pertinent to know metal-ligand (M–F) distances for an appropriate prediction of the local structure distortion around the Cr3 þ centers. For Tl2MF4 crystals, there is no report about the host structure of Mg2 þ and Zn2 þ ions in terms of local structure parameters. However, it is known that the site of the binary cations Mg2 þ and Zn2 þ is exactly at the center of the unit-cell of Tl2MgF4 and Tl2ZnF4 crystals. The separation between two equatorial F-ligands (F–Mg/Zn–F distance: R2) coincides with the unit-cell parameter a, which means a/2 equals to R2. The TE Table 1 The values of the previously determined experimental ZFSPs [in 10  4 cm  1] for various Cr3 þ centers in Tl2MF4 crystals. Compounds

Center

D ¼ b20

3E ¼ b22

Refs

Tl2MgF4

I (TE) IV (OR)

 1041.7 843.6

– 598.0

[2] [2]

Tl2ZnF4

I (TE) II (MO) III (OR) IV (OR)

 866.1  1507.9 924.5 684.6

–  706.1  156.0 529.0

[2] [1] [1] [2]

(6)

where R0 is the reference distance, Ri are the ligand distances in the ML6 complex; b¯k (R0 ) is the intrinsic parameter, whereas tk is the power law exponent which are treated as adjustable parameters. The b¯k (R0 ), tk, and the reference distance R0 can be

M. Açıkgöz / Journal of Physics and Chemistry of Solids 88 (2016) 109–115

lattice parameters were reported to be a¼ 0.4007 nm and c ¼1.443 nm for Tl2MgF4 and a¼ 0.4105 nm and c ¼1.410 nm for Tl2ZnF4 [23]. Thus, these values provide R2 to be 0.20035 nm for Tl2MgF4 and 0.20525 nm for Tl2ZnF4. For the analyses in the next sections, we take these R2 values into account and adopt the SPM parameters provided in [20] with their accuracies for all centers, yielding satisfactory matching of both the size and the signs of the predicted and experimental ZFSPs. In the SPM calculations, the direct matching of the distortion parameters has been carried out based on comparison of the calculated ZFSPs and the experimental ZFSPs values. In order to enable discerning the effects of each type of distortions on the ZFSPs we have adopted different modeling approaches and steps in the calculations. Our results for each center are presented in the following sections. 3.1. Tetragonal (TE) center I For TE center I it should be noted that the ZFSP D for Tl2MgF4 and Tl2ZnF4 crystals are quite larger than that for other A2BF4 crystals. As discussed by Arakawa et al. [2], the reason of these large magnitudes of D in these crystals may be explained by the presence of a charge compensator on the c-axis around this Cr3 þ center. However, they ascribed no charge compensator for the center I in both crystals as a result of the analyses using SHS method. In our analysis we have calculated the ZFSP D and predicted the local structure parameters around Cr3 þ ion at Mg2 þ /Zn2 þ site (with space group D4h). The structural parameters for the six nearest-neighbor F  ions in the [Cr–F6]3  octahedral cluster have been determined based on the axis system (z∥c, y∥b, x∥a) as follows: (R1, 0, 0), (R1, 180, 0), (R2, 90, 0), (R2, 90, 90), (R2, 90, 180), (R2, 90, 270), where R2 is 0.20035 nm for Tl2MgF4 and 0.20525 nm for Tl2ZnF4. The configurations of the atoms around TE Cr3 þ center are shown in Fig. 1. Since R1 is not known for both undoped crystals we performed the SPM calculations by changing R2 between  0.004 nm and 0.004 nm, which corresponds to almost 2% of the M–F2 distances. This may be a moderate range if we take into account the change in ligand distances due to mismatch of the radius of the host atom Mg2 þ (rh ¼0.066 nm)/Zn2þ (rh ¼0.074 nm) ion and that of the substitution 1 Cr3 þ ion (rs ¼0.062 nm). The formula Ri ≈ Rhi + 2 (rs − rh ) [24], where Ri is the distance of the ith ligand and Rhi is the cation–anion distance in the host lattice, provides 70.002 nm change for Tl2MgF4 and 70.006 nm for Tl2ZnF4. We have carried out SPM calculations using the structural parameters and Eq. (7) based on the direct matching of calculated ZFSP D¼ b20 to the experimental D¼ b20 to reveal the change in R1 with ΔR2, which is the distortion of the equatorial F ligand–metal bond length R2. The results for b20 = D and the relative change of R1

Fig. 1. Configurations of the atoms around the TE Cr3 þ center in Tl2MF4 crystals.

111

and R2 are listed in Table 2 for the TE Cr3þ center in Tl2MgF4 and Tl2ZnF4 crystals. It is seen that R1 o R2 for both crystals, which indicates the compression of the MF6 octahedron of the Cr3 þ TE center in both crystals. This is the common situation for the TE centers, having negative ZFSP D¼ b20 , in all A2BF4 crystals [1,2,25,21,26]. The relation between the tetragonal distortion of the octahedral environment around a cation and ZFSP D ¼ b20 can be easily understood from the formula D ≈ − 3 (α − α0 ) G11[27,28], where G11 is the spin–lattice coupling coefficient and α is the angle characterizes the TE distortion of the octahedral environment with α0 ¼45°. Having a positive G11, negative D always provides α − α0 > 0. Based on the TE distortion R1, R2 and α can be related through the formula R1 = R2/ tan α . Then, R2 > R1 corresponds to the compression of the MF6 octahedron for all Cr3 þ doped A2BF4 crystals. Another important point can be derived from Table 2 is that D¼ b20 is clearly linearly dependent on the changes of the ligand lengths. Due to having much higher D¼ b20 values in Tl2MgF4 and Tl2ZnF4 with respect to those in other A2BF4 crystals, it can be expected that the TE distortion in these Tl2MF4 crystals would be higher than those in the other A2BF4 crystals. When we look at the R values in Table 2 we see that R2 − R1 is between 0.00939 nm (max.) and 0.00911 nm (min.), whereas it is between 0.00335 nm and 0.00345 nm for Rb2ZnF4[29]. It shows that the results are in accordance with the above argument. 3.2. Monoclinic (MO) center II This MO Cr3 þ center is only observed in Tl2ZnF4. Experimental data were analyzed by considering an OR approximation since only ZFSPs (D ¼ b20 and 3E¼ b22) corresponding to this symmetry case were determined. Indeed, for MO symmetry, depending on the choice of the C2 direction, we may have extra b2−1, b2−2 or b21 for choosing C2∥X-axis, C2∥Z-axis or C2∥Y-axis, respectively. Our structural model for this MO Cr3 þ center is based on the axis system (z*∥c, y∥[010]∥b, C2∥x∥a). Here, as shown in Fig. 2, the axis z* defines the declined z-axis from [001]∥c toward [100]∥a-axis by an angle ϕ. The corresponding ligand bond lengths and angular positions of F  ligands in [Cr–F6]3  cluster for this MO Cr3 þ center are (R1, ϕ, 180), (R1, 180  ϕ, 0), (R2, 90  ϕ, 0), (R2, 90, 90), (R2, 90þ ϕ, 180), (R2, 90, 270). For this Cr3 þ center SPM calculations have been carried out using EqS. (7)–(9) and by taking into account both the angular and bond lengths distortions by means of three definite modeling approaches (Calc.a  Calc.c), as defined in the footnotes of Table 3. The results of the SPM calculations are given in Table 3. As can be seen, for Calc.c, the length of the four equatorial F-ligands is about 1.5% longer than R2 of the octahedral ZnF6 in undoped Tl2ZnF4, whereas the length of the axial F-ligands (R1) is quite shorter (∼9.5%) than R2. Also, it yields a quite large b2−1 and declined angle (27.46°, ∼30%) for z-axis. The reason of the formation of such a MO center in A2BF4 crystals was attributed to a nearest A þ vacancy along the [111]axis [1]. However, there may be another option for a A þ vacancy along [001]∥c-axis. If we consider this option for Tl2ZnF4, due to the increase in the negativity of the effective charge, the closer close ) is expected to move more axial F-ligand to the vacancy ( Fax 3þ far towards the central Cr than the other axial F-ligand ( Fax ). The close far decrease in R1 of Fax results in an increase in that of Fax , by far providing the same ZFSPs. If we assume that Fax is distorted with close same amount of Feq in Calc.c, we find R1 of Fax ¼0.18538 nm and far ¼0.19196 nm. R1 of Fax

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M. Açıkgöz / Journal of Physics and Chemistry of Solids 88 (2016) 109–115

Table 2 The SPM calculated ZFSPs b20 = D (in 10  4 cm  1) and the assigned distortion parameters for the TE Cr3 þ centers Tl2MgF4 and Tl2ZnF4 crystals. All R values are in [nm]. Tl2MgF4

Tl2ZnF4

D ¼ b20

R1

*ΔR1 (t2 )

**ΔR1 (b2 )

R2

ΔR2

D ¼ b20

R1

*ΔR1 (t2 )

**ΔR1 (b2 )

R2

ΔR2

 1042.0

0.18724

70.0002

0.19635

 0.004

 866.1

0.19351

0.20125

 0.004

0.18821

70.0001

0.19735

 0.003

 866.2

0.19448

70.0001

0.20225

 0.003

 1041.9

0.18917

70.0002

0.19835

 0.002

 866.3

0.19545

70.0001

0.20325

 0.002

 1041.2

0.19014

70.0002

0.19935

 0.001

 866.4

0.19642

70.0001

0.20425

 0.001

 1041.8

0.19110

70.0002

0.20035

 866.4

0.19739

70.0001

0.20525

 1041.2

0.19207

70.0002

0.20135

þ 0.001

 866.5

0.19835

70.0001

0.20625

þ 0.001

 1041.7

0.19303

70.0002

0.20235

þ 0.002

 866.6

0.19933

70.0001

0.20725

þ 0.002

 1041.1

0.19400

70.0002

0.20335

þ 0.003

 866.7

0.20031

70.0001

0.20825

þ 0.003

 1041.7

0.19496

70.0002

0.20435

þ 0.004

 866.8

0.20128

þ0.0008  0.0011 þ0.0008  0.0011 þ0.0008  0.0011 þ0.0009  0.0011 þ0.0009  0.0011 þ0.0009  0.0011 þ0.0009  0.0011 þ0.0009  0.0011 þ0.0009  0.0011

70.0001

 1041.3

þ 0.0010  0.0013 þ 0.0010  0.0013 þ 0.0010  0.0013 þ 0.0010  0.0013 þ 0.0010  0.0013 þ 0.0010  0.0013 þ 0.0010  0.0013 þ 0.0010  0.0013 þ 0.0010  0.0013

70.0001

0.20925

þ 0.004

0

0

n

The change of R1 by t2; t2 ¼  0.27 yields þ ΔR1(t2), while t2 ¼  0.21 yields  ΔR1(t2). The change of R1 by b2 (R0 ) ; when b2 (R0 ) is changed by 7 800  10  4 cm  1 it corresponds 7ΔR1(b2).

nn

Table 3 The SPM calculated ZFSPs b20 = D , 3E¼ b22 , and b2−1 (in 10  4 cm  1) and the obtained

distortion parameters for the MO Cr3 þ center in Tl2ZnF4. All R values are in [nm] and ϕ values are in [degrees]. D ¼ b20 Calc.a β ε η

Calc.b β ε η

Calc.c β ε η

Fig. 2. Configurations of the atoms around the MO Cr3 þ center in Tl2ZnF4 crystal with a nearest Tl þ vacancy along [111]-axis. The arrows indicate the direction of structural distortions.

 1507.9  1507.6  1508.3  1507.0

3E ¼ b22 0 0 0 0

b2−1 0 0 0 0

R1

R2

ΔR2

0.19172 þ 0.0015  0.0019 7 0.0002

0.20525 0.20525 0.20525 0.20525

0 0 0 0

ϕ 0 0 0 0

 1508.0  1508.0  1508.2  1507.8

 706.3  706.3  706.3  706.2

5436.2 5436.3 5436.7 5435.6

0.18562 þ 0.0021  0.0026 7 0.0003

0.20525 0.20525 0.20525 0.20525

0 0 0 0

27.46 27.46 27.46 27.46

 1507.9  1508.3  1507.8  1508.0

 706.2  706.4  706.2  706.3

5435.8 5437.0 5435.5 5436.3

0.18867 þ 0.0021  0.0027 7 0.0003

0.20854 0.20854 0.20854 0.20854

0.00329 0.00329 0.00329 0.00329

27.46 27.46 27.46 27.46

a Calculations based on direct matching of R1 to the experimental ZFSP D¼ D = b20 only ΔR2 = ϕ = 0 . b Calculations based on the direct matching of R1 and ϕ to the experimental ZFSPs D = b20 and 3E = b22 . c Calculations based on the direct matching of R1, R2 and ϕ to the experimental ZFSPs D = b20 and 3E = b22 The change in R1 for βt2 ¼ -0.27; εt2 ¼  0.21; η b2 (R0 ) ¼ (467707 800)x10  4 cm  1.

3.3. Orthorhombic (OR) centers III and IV Experimentally, the OR Cr3 þ only center IV was observed in Tl2MgF4, while both center III and center IV were observed in Tl2ZnF4[2,1]. It was suggested from SHS method that these are two structurally different OR Cr3 þ centers and assumed to involve a nearest Zn2 þ /Mg2 þ vacancy (VM) along the [100] direction. The difference of the center IV is the presence of a Li þ ion located at this vacancy, which provides the charge compensation for the local structure. In order to analyze these centers we have carried out the SPM calculations by means of two models. The results of the SPM calculations are tabulated in Table 4 for the first model (model I) based on three different ligand lengths, R1, R2, and R3, which refers a different ligand length for the intervening F ligand between the

central Cr3 þ and the nearest M2 þ vacancy along [100]-axis. This model was suggested previously for OR centers in some other A2BF4 crystals [30]. The SPM calculations have been carried out on the basis of some definite modeling approaches (Calc.a  Calc.d), which are defined in the footnotes of Tables 4 and 5, to reveal the local structural distortion around OR Cr3 þ centers. From the results of Table 4, in addition to the quite different 3E = b22 parameters, we see that the characteristics of the distortions are opposite for the OR centers. It can be normally expected that the distortion on intervening F ligand should be negative due to the increase in the negativity of the electric charge of VM site, which results in electrostatic repulsion. When the presence of the M2 þ vacancy (center III) or Li þ ion substitution to the M2 þ vacancy site (center IV) is considered at

M. Açıkgöz / Journal of Physics and Chemistry of Solids 88 (2016) 109–115

113

Table 4 The SPM calculated ZFSPs b20 = D and 3E ¼ b22 (in 10  4 cm  1) and the obtained distortion parameters for the OR Cr3 þ centers at different temperatures regarding of model I. All R values are in [nm]. Compounds

Tl2ZnF4

III (OR)

Calc.a β ε η

Calc.b β ε η

Calc.c β ε η

Calc.d β ε η

Tl2MgF4

IV (OR) Calc.a β ε η

Calc.b β ε η

Calc.c β ε η

Calc.d β ε η

Tl2ZnF4

Calc.a β ε η

Calc.b β ε η

Calc.c β ε η

Calc.d β ε η

ΔR2

ΔR3

D = b20

3E = b22

R1

R2

R3

924.9 925.1 924.3 924.6 924.2 924.8 925.0 924.2 924.4 924.3 924.2 923.7 924.4 924.4 924.8 924.8

0 0 0 0  156.1  156.1  156.2  156.3  155.9  156.1  156.3  156.9  156.4  155.7  155.5  157.4

0.21390  0.0001 þ0.0013 ∓0.0002 0.21340  0.0009 þ0.0012 ∓0.0001 0.21538  0.0011 þ0.0015 ∓0.0002 0.21439  0.0010 þ0.0013 ∓0.0002

0.20525 0.20525 0.20525 0.20525 0.20525 0.20525 0.20525 0.20525 0.20717 0.20696 0.20745 0.20715 0.20621 0.20610 0.20634 0.20620

0.20525 0.20525 0.20525 0.20525 0.20334 0.20355 0.20307 0.20337 0.20525 0.20525 0.20525 0.20525 0.20429 0.20440 0.20416 0.20430

843.4 843.2 844.4 843.1 843.8 843.4 843.6 843.1 843.7 843.9 843.7 843.0 843.8 844.2 843.3 843.3

0 0 0 0 598.3 597.8 598.8 598.7 598.1 598.8 598.6 598.7 598.0 598.2 598.4 598.3

0.20809  0.0009 þ0.0011 ∓0.0001 0.20995  0.0011 þ0.0014 ∓0.0002 0.20258  0.0003 þ0.0003 ∓0.0001 0.20627  0.0006 þ0.0008 ∓0.0001

0.20035 0.20035 0.20035 0.20035 0.20035 0.20035 0.20035 0.20035 0.19324 0.19400 0.19225 0.19335 0.19680 0.19720 0.19629 0.19686

0.20035 0.20035 0.20035 0.20035 0.20766 0.20684 0.20872 0.20754 0.20035 0.20035 0.20035 0.20035 0.204008 0.20362 0.20452 0.20395

0 0 0 0 0 0 0 0  0.00711  0.00635  0.00810  0.00700  0.00355  0.00315  0.00406  0.00349

0 0 0 0 0.00731 0.00649 0.00837 0.00719 0 0 0 0 0.003658 0.00327 0.00417 0.00360

684.9 684.2 684.8 684.8 684.3 684.4 684.7 684.7 684.2 685.1 684.3 684.2 684.7 684.7 684.5 684.3

0 0 0 0 528.8 529.3 528.9 529.8 529.3 529.2 529.7 529.9 529.5 529.2 529.3 528.6

0.21163  0.0007 þ0.0009 ∓0.0001 0.21329  0.0009 þ0.0012 ∓0.0001 0.20668  0.0002 þ0.0002 ∓0.0000 0.20999  0.0005 þ0.0007 ∓0.0001

0.20525 0.20525 0.20525 0.20525 0.20525 0.20525 0.20525 0.20525 0.19883 0.19953 0.19793 0.19893 0.20204 0.20240 0.20158 0.20210

0.20525 0.20525 0.20525 0.20525 0.21182 0.21109 0.21277 0.21172 0.20525 0.20525 0.20525 0.20525 0.20854 0.20818 0.20900 0.20848

0 0 0 0 0 0 0 0  0.00642  0.00572  0.00732  0.00632  0.00321  0.00285  0.00367  0.00315

0 0 0 0 0.00657 0.00584 0.00752 0.00647 0 0 0 0 0.00329 0.00293 0.00375 0.00323

0 0 0 0 0 0 0 0 0.00192 0.00171 0.00220 0.00190 0.000960 0.00085 0.00109 0.00095

0 0 0 0  0.00191  0.00170  0.00218  0.00188 0 0 0 0  0.00096  0.00085  0.00109  0.00095

a

Calculations based on direct matching of R1 to the experimental ZFSP D = b20 only (ΔR2 = ΔR3 = 0) . Calculations based on the direct matching of R1 and the distortion parameter ΔR3 to the experimental ZFSPs D = b20 and 3E = b22 . c Calculations based on the direct matching of R1 and the distortion parameter ΔR2 to the experimental ZFSPs D = b20 and 3E = b22 . d Calculations based on the direct matching of R1 and the distortion parameters ΔR2 and ΔR3 to the experimental ZFSPs D = b20 and 3E = b22 The change in R1 for βt2 ¼  0.27; εt2 ¼  0.21; η b2 (R0 ) ¼ (46770 7800)  10  4 cm  1. b

the nearest Zn2 þ site, we can expect a move of the intervening F ligand towards Cr3 þ due to the change in electrostatic attraction, which results in a decrease in R3 (less decrease for the center IV). However, from the results in Table 4, we see that this is consistent only with the center III in Tl2ZnF4. For the OR center IV in both Tl2MgF4 and Tl2ZnF4R3 increases, thus we can conclude that first model is proper for only OR center III in Tl2ZnF4. The second model (model II) is based on the axis system (x∥c, ¯ ¯ ], y∥b) and consists of angular distortion () as well. The z∥ [110

corresponding ligand bond lengths and angular positions of F- ligands in the [Cr–F6]3  cluster are as follows: (R1, 90, 0), (R1, 90, 180), (R2, 45, 270), (R2, 135, 270), (R2, 135, 90), (R2, 45, 90). The results of the SPM calculations for this model are given in Table 5. The results yield very small distortion angle for the equatorial ligands, and indicate these ligands get closer to the z∥[110]-axis. The distortion on R2 is rather smaller with respect to that in model I. It can also be noted that R1 is found to be shorter than R2 unlike in model I. Contrary to the model I, it is seen that this model is

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M. Açıkgöz / Journal of Physics and Chemistry of Solids 88 (2016) 109–115

Table 5 The SPM calculated ZFSPs b20 = D and 3E ¼ b22 (in 10  4 cm  1) and the obtained distortion parameters for the OR Cr3 þ centers for model II. All R values are in [nm] and θ values are in [degrees]. D ¼b02

Compounds

Tl2ZnF4

Calc.a β ε η

Calc.b β ε η

Calc.c β ε η

Tl2MgF4

Calc.a β ε η

Calc.b β ε η

Calc.c β ε η

Tl2ZnF4

Calc.a β ε η

Calc.b β ε η

Calc.c β ε η

III (OR)

θ*

Δθ

3E ¼ b22

R1

R2

ΔR2

924.8 924.4 924.8 924.8 924.9 924.2 924.5 924.8 924.9 924.1 924.5 924.9

 2274.5  2773.2  2774.4  2774.3  156.0  156.2  156.5  156.5  155.8  156.8  156.5  156.5

0.18875 þ 0.0018  0.0022 7 0.0003 0.20032 þ 0.0005  0.0007 7 0.0001 0.19982 þ 0.0003  0.0000 7 0.0001

0.20525 0.20525 0.20525 0.20525 0.20525 0.20525 0.20525 0.20525 0.20474 0.20447 0.20474 0.20470

0 0 0 0 0 0 0 0  0.00051  0.00078  0.00051  0.00055

45.0 45.0 45.0 45.0 44.8654 44.8654 44.8656 44.8677 44.8653 44.8653 44.8653 44.8676

0 0 0 0  0.1346  0.1346  0.1344  0.1323  0.1347  0.1347  0.1347  0.1324

843.3 843.2 843.4 843.4 843.2 843.4 843.0 843.5 843.2 843.3 843.0 843.3

IV (OR)  2529.8  2529.7  2530.0  2530.2 598.0 598.2 597.7 597.7 598.2 598.3 598.0 598.2

0.18554 þ 0.0016  0.0020 7 0.0002 0.19924 þ 0.0001  0.0002 7 0.0000 0.19929 þ 0.0001  0.0001 7 0.0000

0.20035 0.20035 0.20035 0.20035 0.20035 0.20035 0.20035 0.20035 0.200395 0.20033 0.20047 0.200387

0 0 0 0 0 0 0 0 0.000045  0.00002 0.00012 0.000037

45.0 45.0 45.0 45.0 44.8383 44.8380 44.8386 44.8410 44.8383 44.8380 44.8386 44.8410

0 0 0 0  0.1617  0.1620  0.1614  0.1590  0.1617  0.1620  0.1614  0.1590

684.9 684.4 684.6 684.5 684.3 684.8 684.6 684.4 684.7 684.8 684.5 684.4

 2054.7  2053.2  2053.7  2053.4 528.8 529.0 528.3 529.1 528.1 528.3 528.2 528.8

0.19293 þ 0.0013  0.0017 7 0.0002 0.20454 þ 0.0001  0.0001 7 0.0000 0.20441 þ 0.0001  0.0001 7 0.0000

0.20525 0.20525 0.20525 0.20525 0.20525 0.20525 0.20525 0.20525 0.205125 0.20510 0.20518 0.205123

0 0 0 0 0 0 0 0  0.000125  0.000150  0.000070  0.000123

45.0 45.0 45.0 45.0 44.8673 44.8671 44.8674 44.8695 44.8672 44.8671 44.8674 44.8695

0 0 0 0  0.1327  0.1329  0.1326  0.1305  0.1328  0.1329  0.1326  0.1305

a

Calculations based on direct matching of R1 to the experimental ZFSP D = b20 only ( ΔR2 = Δθ = 0 ). Calculations based on the direct matching of R1 and the distortion parameter Δθ to the experimental ZFSPs D = b20 and 3E = b22 . c Calculations based on the direct matching of R1 and the distortion parameters ΔR2 and to the experimental ZFSPs D = b20 and 3E = b22 The change in R1 for βt2 ¼  0.27; ε t2 ¼  0.21; η b2 (R0 ) ¼ (467707 800)  10  4 cm  1. b

Fig. 3. Configurations of the atoms around the OR Cr3 þ centers in Tl2MF4 crystals with a nearest M2 þ vacancy (VM) along a∥[100]-axis; (a) model I and (b) model II. The arrows indicate the direction of structural distortions.

M. Açıkgöz / Journal of Physics and Chemistry of Solids 88 (2016) 109–115

reasonable for both OR centers in both crystals. Configurations of the atoms around the OR Cr3 þ centers with the chosen principal axes and a nearest Mg2 þ /Zn2 þ vacancy along b∥[100]-axis are depicted in Fig. 3 for both models.

4. Conclusions This present work is devoted to theoretically investigating the local structure of the Cr3 þ centers (tetragonal (TE) center I, monoclinic (MO) center II, orthorhombic (OR) centers III and IV) in Tl2MgF4 and Tl2ZnF4 crystals by means of semi-empirical calculations. Based on the correlation between the experimental data and theoretical values regarding zero-field splitting (ZFS), suitable structural models have been suggested to understand the local structure around the Cr3 þ centers in Tl2MgF4 and Tl2ZnF4. It is shown that a clear compression of the MF6 octahedron around TE Cr3 þ center has been occurred in both crystals. We found for the MO Cr3 þ center that (i) the length of the four equatorial F-ligands (R2) is about 1.5% longer than that of the octahedral ZnF6 in undoped Tl2ZnF4, (ii) the length of the axial F-ligands (R1) is quite shorter (∼9.5%) than R2, and (iii) a quite large ZFSP b2−1 and declined angle (27.46°, ∼30%) for z-axis from [001]||c toward [100]||a-axis. It was also shown that the previously suggested structural model for OR centers in A2BF4-type crystals, associated with a different ligand length for the intervening F ligand between the central Cr3 þ and the nearest M2 þ vacancy, is not proper for OR center IV in these crystals.

Acknowledgments The present work was supported by the Research Fund of Bahcesehir University.

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