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Dielectric relaxation in double potassium yttrium orthophosphate K3Y(PO4)2 doped by praseodymium and dysprosium ions
Journal of Molecular Structure 1006 (2011) 166–172
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Journal of Molecular Structure journal homepage: www.elsevier.com/locate/molstruc
Dielectric relaxation in double potassium yttrium orthophosphate K3Y(PO4)2 doped by praseodymium and dysprosium ions S. Szulia a,⇑, M. Kosmowska a, H.A. Kołodziej a, D. Mizer b, G. Czupin´ska b a b
Faculty of Chemistry, University of Wrocław, Poland Department of Inorganic Chemistry, Wrocław University of Economics, Poland
a r t i c l e
i n f o
Article history: Received 12 July 2011 Received in revised form 1 September 2011 Accepted 1 September 2011 Available online 22 September 2011 Keywords: Dielectric relaxation Double orthophosphate Electric properties
a b s t r a c t We report the paper presents the results of electric properties of double potassium yttrium orthophosphates doped by lanthanide ions K3Y(1x)Lnx(PO4)2 (x = 0.01, 0.05, Ln = Pr3+, Dy3+). Electric permittivity and dielectric loss measurements have been performed on polycrystalline samples in the temperature range 50–120 °C and frequency range 1 kHz–1 MHz by means of HP 4282A impedance meter. The frequency and temperature dependence of electric properties were analyzed by theoretical models of dielectric relaxation in order to obtain information abut molecular dynamic of our solids in external electric field. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction In the previous report was presented dielectric properties in double potassium yttrium orthophosphates K3Y(1x)Ybx(PO4)2 (x = 0.01, 0.05) [1]. This paper is the second part of our investigation on double potassium yttrium orthophosphates doped by lanthanide ions. In this part general formula of our samples is K3Y(1x)Lnx(PO4)2 (x = 0.01, 0.05), where Ln = Pr3+ and Dy3+. The structure data of K3Y(PO4)2 was presented by Ushakov [2] and Komissarova et al. [3]. The authors reported a monoclinic system with space group P21/m with the cell parameters: a = 7.358 (Å), b = 5.613 (Å), c = 9.349 (Å), b = 90.92° and Z = 2. This structure can be described as a distortion of glaserite structure, where structural subunit is formed by octahedron [LnO6]. Alternately arranged up and down [PO4] groups are connected with octahedron in its five vertices but one tetrahedron group divided one of its edge with a polyhedron containing Ln. In this way the number of coordination of LnIII rises into 7 and symmetry of space group decreases from the hexagonal to the monoclinic. The potassium ions are situated along c axis among layer formed by a tetrahedron and a octahedron. This monoclinic distortion of the glaserite structure reminds the arcanite – type K3Na(SO4)2 (Fig. 1). The spectroscopic properties of double alkali metal yttrium orthophosphates, with formula M3Y(PO4)2, where the molar ratio of YPO4:M3PO4 is 1:1 (M = Rb, Na, Lu) doped with Pr3+, Dy3+ have been studied by several authors
⇑ Corresponding author. E-mail address: [email protected] (S. Szulia). 0022-2860/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.molstruc.2011.09.002
[4,5]. However, there is a few information about the dielectric properties of M3Y(PO4)2 doped with the lanthanide ions. The crystal structures of the obtained compounds were confirmed by X-ray diffraction using a diffractometer Siemens D 5000th. The resulting diffraction patterns were compared with the crystallographic data sheet number 049-0497 double potassium yttrium orthophosphate – K3Y(PO4)2 in a crystal base ICCD PDF – 4+. The X-ray diagrams received for non-doped materials and with admixture depict that peaks derived from doped samples by lanthanide ions coincide with the peaks originating from pure K3Y(PO4)2 (Fig. 2). It was found that the process of doping material and the fusion did not cause any changes in the crystalline structure of the compounds. So far, we obtained in the system where amount of doped material is 1% of Dy3+ and Pr3+ the dielectric relaxation can be described by two-parametric dielectric response function of the Havriliak– Negami (HN) [6]. The real and imaginary part of permittivity were calculated using the following equations: 1 1a 1a f C B b a tan f cosð a 2 p Þ=1 sin ð a 2 p Þ C B fc fc C e0 ¼ e1 þ ðe0 e1 Þ cos B C B" # b=2 2 2 C B 1a 1a A @ f f sinða 2pÞ þ fc cosða 2pÞ 1 þ fc 0
1 1a 1a f C B b a tan f cosða 2pÞ=1 fc sinða 2pÞ C B fc C e00 ¼ ðe0 e1 Þ sin B B" # 2 2 b=2 C C B 1a 1a A @ sinða 2pÞ þ ffc cosða 2pÞ 1 þ ffc 0
ð1Þ
S. Szulia et al. / Journal of Molecular Structure 1006 (2011) 166–172
167
recalled models on double potassium yttrium orthophosphates doped by lanthanide ions was presented in previous part of this work [1]. 2. Experimental Electric properties were investigated in double potassium yttrium orthophosphates K3Y(1x)Lnx(PO4)2 (x = 0.01. 0.05, Ln = Pr, Dy). All compounds were synthesized by means of solid phase reaction by sintering a stoichiometric mixture of the initial orthophosphates of YPO4, K3PO4 and Ln2O3 at 1200C for 4 h. The obtained orthophosphate were melted in closed platinum–rhodium tube in the argon atmosphere at 1440 °C [14]. Complex electric permittivity has been performed, as was written previously [1], on polycrystalline samples in the temperature range from 50 °C to +120 °C and frequency range 1 kHz–1 MHz by means of HP 4282A impedance meter. Samples were made as pellets 10 mm in diameter and about 1–2 mm thick. Copper-foil electrodes were affixed to the prepared pellets. Before experiment samples were annealed at a temperature of 170 °C in vacuum in order to decrease the amount of water absorbed from the air thus a number of electric charges is also reduced rather substantially. All measurements were carried out in a dry nitrogen atmosphere. The shape of measurements configuration was described previously [15].
Fig. 1. Projection of the arcanite-type structure of K3Y(PO4)2.
3. Results 3.1. K3Y(1x)Prx(PO4)2. (x = 0.01, 0.05)
Fig. 2. The X-ray diagrams for K3Y(PO4)2 (black), K3Y0.99Pr0.01(PO4)2 (red) and K3Y0.99Dy0.01(PO4)2 (green line). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
In the case 5% Pr3+ and Dy3+ our analysis prove that one-parametric dielectric response function of the Cole–Cole [7] better describe the dependence of complex permittivity in whole temperature range.
e0 e1 1 þ ðf =fc Þð1aÞ sinðap=2Þ ¼ es e1 1 þ ðf =fc Þ2ð1aÞ þ 2ðf =fc Þð1aÞ sinðap=2Þ e00 ðf =fc Þð1aÞ cosðap=2Þ ¼ es e1 1 þ ðf =fc Þ2ð1aÞ þ 2ðf =fc Þð1aÞ sinðap=2Þ
ð2Þ
where es and e1 is the static and optical permittivity, a and b are the empirical coefficients (0 6 a, b 6 1) and fc is the frequency of the relaxation process. The average values of relaxation times ðs ¼ 1=2p f c Þ were obtained from the fitting of the Havriliak– Negami equation (for 1% Dy3+ and Pr3+) (e.g. 1) and Cole–Cole equation (e.g. 2, 5% of impurity of Ln) in the whole range of frequencies. Unfortunately, experimental points are located in a high frequency region of the spectrum what results in large uncertainty of the fitted parameters. All the tested compounds have a complex dielectric characteristics. The diagrams of the real and imaginary part of the permittivity as a function of temperature are in the form of broad bands, generated by the partial overlapping of several smaller components. Matching models Cole–Cole and Havriliak–Negami also indicates the polydispersive nature of the studied systems. In order to analyse the dielectric loss line shape the model of Dissado–Hill [8,9] based on Jonscher’s theory [10–13] was used. The application of
Fig. 3 presents temperature dependence of the real and imaginary part of electric permittivity in materials doped by 1% and 5% praseodymium. Below 40 °C no dispersion and absorption is observed, this situation is similar for both ions. In discussed temperature range relaxation process is retarded because of the rigidity of crystallographic lattice. In a higher range of temperature (20 °C to +100 °C) a dielectric dispersion and absorption is significantly illustrated. The dielectric response for a material doped by 1% of Pr, presented in the Fig. 3a, depicts one broad peak with a maximum at 24 °C. The absorption curve (e00 ) at the frequency below 4.5 kHz two separated bands are clearly indicated. When the frequency increasing the maxima approaching and one broad peak is appeared, with maximum value at 24 °C. For temperature lower than 20 °C absorption maxima shift towards higher frequencies with temperature (color violet in the Fig. 4a), for the temperatures from 20 °C to 30 °C the maximum band does not change the position (Fig. 4a color red). With a further increasing of temperature the decreasing of the value of critical frequency is observed (Fig. 4a color green). In the Fig. 3c, for dependency of real part of permittivity, two peaks are observed, but the absorption diagram is more complex (Fig. 3d). First of all, it is noticeable that the broad absorption band is due to the imposition of three narrower bands. Beside, at the T = 80 °C the addition peak also appears. For the temperature lower then 10 °C maxima of the band are not clear separated, due to the appearance of a new band. Although the trend is visible of shifting the maxima with temperature towards to higher frequency (color violet in Fig. 4b). For the band in the range of temperature 15–20 °C characteristic is that the absorption reaches the highest value at temperature about 25 °C (color red Fig. 4b) independently apart from the frequency. The third maximum of the band shifts towards lower frequency with the increasing of the temperature (in the Fig. 4b color green). The dielectric response data obtained for the material doped by 1% Pr in whole range of the temperature were evaluated by the Havriliak–Negami model. In compounds with 5% of Pr the
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S. Szulia et al. / Journal of Molecular Structure 1006 (2011) 166–172
Fig. 3. The real and imaginary part of electric permittivity versus temperature and frequency for K3Y0.99Pr0.01(PO4)2 and K3Y0.95Pr0.05(PO4)2.
Fig. 4. The imaginary part of electric permittivity versus frequency for (a) K3Y0.99Pr0.01(PO4)2 and (b) K3Y0.95Pr0.05(PO4)2.
one-parametric dielectric response function of the Cole–Cole better described experimental data. Matching dielectric parameters: the
relaxation time s, a and b parameters, dielectric increment (es and e1 ), for chosen temperature, are shown in Table 1.
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S. Szulia et al. / Journal of Molecular Structure 1006 (2011) 166–172 Table 1 Temperature dependence of dielectric parameters: relaxation time and distribution parameters for (a) K3Y0.99Pr0.01(PO4)2. (b) K3Y0.95Pr0.05(PO4)2 materials. T (°C)
10.8
0.4
10.1
19.5
30.0
40.6
49.9
60.2
58.36 4.66 0.153 0.789 521.1
67.78 4.72 0.178 0.824 200.8
74.52 4.80 0.180 0.843 78.2
77.48 4.90 0.152 0.829 42.7
77.45 4.90 0.168 0.859 46.7
73.31 4.74 0.196 0.875 91.7
69.32 4.63 0.217 0.891 168.8
66.53 4.54 0.252 0.936 284.6
(a) K3Y0.99Pr0.01(PO4)2
e0 e1 a b
s 106 s T (°C)
10.1
(b) K3Y0.95Pr0.05(PO4)2 41.53 5.02 0.373 834.5
e0 e1 a s 106 s
0.2
10.6
20.3
30.1
40.4
50.4
60.3
69.9
74.9
75.9
76.8
77.8
79.8
80.8
48.94 4.74 0.414 268.9
52.06 4.73 0.396 74.5
60.30 4.62 0.396 59.7
63.33 4.90 0.358 63.1
61.67 5.26 0.303 66.4
60.06 5.33 0.285 99.5
60.43 5.27 0.291 239.5
59.38 5.22 0.284 582.8
60.55 5.24 0.285 918.4
67.44 5.27 0.303 1256.7
63.49 5.26 0.394 1170.5
61.78 5.26 0.290 1110.9
61.24 5.26 0.289 1013.0
59.68 5.22 0.284 985.8
Assigned for different temperature the relaxation times were provided to draw the dependence of lns = f(1000/T). According to Arrhenius relation, the resulting graph is presented in Fig. 5. The points on the graph are consists of three sections with different slope of straight line. For occurring at temperatures below 20 °C process for 1% of Pr and 10 °C for 5% of Pr was determined the activation energy. The value of estimated energy is 57.7 kJ/mol and 71.7 kJ/mol, respectively. The non-activated nature was assigned to the other processes, both K3Y0.99Pr0.01(PO4)2 and K3Y0.95Pr0.05(PO4)2. For description the model of Dissado–Hill is proposing. The Arrhenius graph suggests that the processes in the middle range of temperature occur with zero activation energy, while the processes run at higher temperatures with evolution of energy. The first process can be defined as non-activated tunneling ‘‘flipflop’’ second as transition ‘‘flip’’. In case of material doped by 5% of praseodymium additional peak appeared at about 75 °C is connected with the second thermally activated transition. As was proved previously in material with 5% of ytterbium ions [1], those process is due to alteration of the direction of polaron coupling. This effect is distinctly observed in ionic crystals, where exists a strong interaction between ions and electrons. When temperature is growing up the number of phonons plays major role in the electron scattering by lattice vibration. As a consequence the electric resistance decrease is noted. The value of calculated activation energy in those region of temperature is 50.2 kJ/mol. 3.2. K3Y(1x)Dyx(PO4)2 (x = 0.01, 0.05) Fig. 6 presents the 3D graphs of the dielectric response for double potassium yttrium orthophosphates doped by 1% (Fig. 6a and b) and 5% of dysprosium ions (Fig. 6c and d). The complex permittivity in
both compounds versus temperature and frequency is characterized as symmetrical bands with maximum value in T = 27 °C, independently on frequency. In the absorption diagram (Fig. 6b) for temperature lower than 10 °C, e0 and e00 data were described by the Havriliak–Negami equation, although, for higher temperature the Cole–Cole model is sufficient. Matching dielectric parameters: the relaxation time s, a and b parameters, dielectric increment (es and e1 ), for chosen temperature, are shown in Table 2. In case of K3Y0.95Dy 0.5(PO4)2 the imaginary part of the permittivity consists of three imposing bands and additional bands with maximum at 85 °C (rys.6d). Unfortunately, the increment of permittivity is insignificant and matching any model describing the dielectric relaxation is difficult. Below 10 °C the maximum at band is shifted with temperature towards the higher frequency. In the middle temperature range the second band begins to dominate. In this band the highest value of absorption marked at 27 °C for all frequencies from range 10 to 1000 kHz. For temperature higher then 40 °C outlines another bands, with changing maximum in direction of lower frequency with increasing of the temperature. Arrhenius plot reflects the complexity of the absorption band as a function of temperature. Activation process marked in the temperature range from 14 to 15 °C is shown in the Fig. 7. Next, appears the transition ‘‘flip-flop’’ and, above 40 °C, flip transition. The value of activation energy calculated from linear slop is equal 68.6 kJ/mol for sample doped by 1% of Dy3+ and 91.9 kJ/mol for 5% of dysprosium. For both compounds doped by praseodymium and dysprosium ions, the middle and higher range of temperature cannot be explained by means of Debye concept. We suggest that such process could be explained by the configurational tunneling mechanism proposed by Dissado–Hill model based on Jonscher’s
Fig. 5. Arrhenius plot of the relaxation times for (a) K3Y0.99Pr0.01(PO4)2 and (b) K3Y0.95Pr0.05(PO4)2.
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S. Szulia et al. / Journal of Molecular Structure 1006 (2011) 166–172
Fig. 6. The real and imaginary part of electric permittivity versus temperature and frequency for K3Y0.99Dy0.01(PO4)2 and K3Y0.95Dy0.05(PO4)2.
Table 2 Temperature dependence of dielectric parameters. Relaxation time and distribution parameters for (a) K3Y0.99Dy0.01(PO4)2. (b) K3Y0.95Dy0.05(PO4)2 materials. T (°C)
9.8
0.2
9.5
19.8
29.7
40.5
50.2
60.7
(a) K3Y0.99Dy0.01(PO4)2 e0 33.67 e1 4.51 a 0.000 b 0.591 s 106 s 1754.5
31.52 4.51 0.000 0.596 846.8
41.15 4.50 0.167 0.739 308.8
51.81 4.53 0.263 0.880 120.2
77.38 4.25 0.364 – 102.8
91.39 4.05 0.388 – 147.8
84.87 4.21 0.378 – 262.0
64.63 4.59 0.332 – 521.3
61.95 4.59 0.323 – 1712.6
T (°C)
10.2
0.5
10.5
20.7
30.3
40.9
50.2
60.3
45.04 5.14 0.384 3621.6
42.36 5.11 0.374 568.6
42.39 5.10 0.358 142.6
47.06 5.09 0.354 66.0
49.89 5.16 0.332 59.1
51.37 5.29 0.316 103.2
57.37 5.32 0.336 465.2
96.09 5.26 0.399 6130.8
14.1
14.5
(b) K3Y0.95Dy0.05(PO4)2 e0 43.86 e1 5.10 a 0.391 s 106 s 7004.6
theory. Similar results was obtained for K3Y1xYbx(PO4)2 (x = 0.01, 0.05). For such materials, Jonscher proposed by introducing the
coefficients m and n, description of susceptibility function as a power law:
S. Szulia et al. / Journal of Molecular Structure 1006 (2011) 166–172
171
Fig. 7. Arrhenius plot of the relaxation times for a) K3Y0.99Dy0.01(PO4)2 and b) K3Y0.95Dy0.05(PO4)2.
1
v
00
¼
x xc
m
þ
x xc
ð1nÞ ð3Þ
where 0 < m < 1 for x < xc and 0 < 1 n < 1 for x > xc. xc is a frequency equal or near to the frequency of the relaxation process. For pure Debye response m = 1 n = 1, which corresponds to the symmetric peaks of dielectric loss. Where m is equal 1 n probable is Cole–Cole relation, for m = 1 and 1 n – 0 Cole–Davidson equation. The physical meaning of exponents have been proposing by Nigamtullin [16,17]. Author attributed ‘‘m’’ and ‘‘n’’ with the dimension of energy. In the first stage of relaxation, for times shorter than 1/xp, that is, for frequencies x > xp, the energy is mainly spread through a large number of high-speed transitions called as flip, which represents the cooperative configurational tunneling mechanism. In the surrounding of the dipole exists local structural distortion, that can allow realignment of the dipole. Energies needed for the configurational adjustments are stored in the local structure around the dipole and form a narrow band of configurational states on the bottom of the potential well. As a dipole has reoriented a net change and the polarization occurs in the system. Loss of energy to reverse the polarization is constant their measure is the size of the exponent ‘‘n’’, regardless of the degree of polarization reversal. In the second stage of relaxation, for times longer than 1/xp, that is, a frequency x < xp, another process dominates. The flipflop transitions have the same nature as the configurational tunneling and can be considered as a local fluctuations in the medium. The point is that two configurational tunneling processes occur synchronously but dipolar movements involved are in opposing directions at different points in the medium. Microscopically dipoles reorient but macroscopically net change of dipole moment is not observed. After each abrupt transition followed many transitions among the neighboring dipoles, which causes a gradual dissipation of stored energy. Loss of the energy during the flip-flop transitions is in a constant ratio of the additional energy that can be accumulated through the static field. The size of wasted energy is expressed with the coefficient ‘‘m’’. The table below is presenting the value of m and n obtained in range of temperature were the ‘‘flip-flop’’ and ‘‘flop’’ processes are presented. Table 3 The value of coefficients m and n calculated for processes non-activated thermally. Compounds
m for x < xc
n for x > xc
K3Y0.99Pr0.01(PO4)2 K3Y0.95Pr0.05(PO4) K3Y0.99Dy0.01(PO4)2 K3Y0.95Dy0.05(PO4) K3Y0.99Yb0.01(PO4) [1] K3Y0.95Yb0.05(PO4) [1]
0.271 0.096 0.099 0.00 0.102 0.148
0.353 0.376 0.399 0.447 0.344 0.377
The values of ‘‘m’’ and ‘‘n’’ exponents for reported materials with contained Pr3+, Dy3+ and Yb3+ ions are shown in Table 3. According to the Table 3 it is difficult to see any tendency in value of the ‘‘n’’ and ‘‘m’’ exponents. The coefficients ‘‘m’’ was obtained for frequencies saddle with big measured errors. In case ‘‘n’’, the value is more or less 0.4. The extra energy that can be stored in the sample by the static field of the order of 60% of the energy lost per cycle of frequency. 4. Conclusion In summary, we have measured temperature and frequency dependence of electric permittivity of K3Y0.99Pr0.01(PO4)2, K3Y0.95Pr0.05(PO4)2, K3Y0.99DDy0.01(PO4)2 and K3Y0.95Dy0.05(PO4)2 in range of frequency 1 kHz–1 MHz and temperature from 50 °C to +120 °C. The obtained data of real and imaginary part of electric permittivity can be described by the Cole–Cole and Havriliak– Negami equation. The relaxation times were used to calculated the activation energies. From the Arrhenius plot the processes with different nature were observed. The one area of the thermally activated transition was designated for 1% doped by Dy3+and Pr3+ material and two in case of 5% Dy3+and Pr3+. That additional process can be connected with alteration of the direction of polaron coupling. Non-activated processes called as flip and flip-flop transitions in Dissado–Hill theory were observed in both compounds. The behavior with frequency of these materials suggests that the Jonscher’s power law is held good. In our interpretation we have presumed that particular molecules in considered materials have different freedom of motion. Dipoles in solids are not free to rotate as in pure Debye concept, but are constrained to assume discrete orientations in the system with respect to the nearest neighbors. Acknowledgements This work was supported from the Republic of Poland scientific funds as a research project, within Grant No. N N204 166436. References [1] S. Szulia, M. Kosmowska, H.A. Kołodziej, M. Sobczyk, G. Czupin´ska, J. Mol. Struct. 996 (2011) 135–140. [2] S.V. Ushakov, A. Navrotsky, J. Mater. Res. 19 (7) (2004) 2165–2175. [3] L.N. Komissarova, M.G. Zhizhin, A.A. Filaretov, Russ. Chem. Rev. 71 (2002) 619– 650. [4] M. Guzik, T. Aitasalo, W. Szuszkiewicz, J. Legendziewicz, J. Holsa, J. Alloys. Compd. 380 (2004) 368–375. [5] M. Guzik, J. Legendziewicz, W. Szuszkiewicz, A. Walasek, Opt. Mater. 29 (2007) 1225–1230. [6] S. Havriliak, S. Negami, J. Polym. Sci. Part C 14 (1966) 99–117. [7] K.S. Cole, R.H. Cole, J. Chem. Phys. 9 (1941) 341. [8] L.A. Dissado, R.M. Hill, Nature Lond. 279 (1979) 685–689. [9] L.A. Dissado, R.M. Hill, Phil. Mag. B 41 (1980) 625.
172 [10] [11] [12] [13]
S. Szulia et al. / Journal of Molecular Structure 1006 (2011) 166–172 R.M. Hill, Contemp. Phys. 24 (1) (1983) 75–110. A.K. Jonsher, Nature 253 (1975) 717–719. A.K. Jonscher, Nature 267 (1977) 673–679. A.K. Jonsher, Dielectric Relaxation in Solids, Chelsea Dielectric Press, London, 1983.
[14] G. Czupin´ska, T. Znamierowska, J. Therm. Anal. 39 (1993) 539–544. [15] S. Szulia, H.A. Kołodziej, W. Szuszkiewicz, G. Czupin´ska, J. Non-Cryst. Solid 356 (2010) 805–808. [16] R.R. Nigamtullin, Phys. Stat. Sol. (b) 123 (1984) 739–745. [17] R.R. Nigamtullin, Phys. Stat. Sol. (b) 124 (1984) 389–393.
Contents lists available at SciVerse ScienceDirect
Journal of Molecular Structure journal homepage: www.elsevier.com/locate/molstruc
Dielectric relaxation in double potassium yttrium orthophosphate K3Y(PO4)2 doped by praseodymium and dysprosium ions S. Szulia a,⇑, M. Kosmowska a, H.A. Kołodziej a, D. Mizer b, G. Czupin´ska b a b
Faculty of Chemistry, University of Wrocław, Poland Department of Inorganic Chemistry, Wrocław University of Economics, Poland
a r t i c l e
i n f o
Article history: Received 12 July 2011 Received in revised form 1 September 2011 Accepted 1 September 2011 Available online 22 September 2011 Keywords: Dielectric relaxation Double orthophosphate Electric properties
a b s t r a c t We report the paper presents the results of electric properties of double potassium yttrium orthophosphates doped by lanthanide ions K3Y(1x)Lnx(PO4)2 (x = 0.01, 0.05, Ln = Pr3+, Dy3+). Electric permittivity and dielectric loss measurements have been performed on polycrystalline samples in the temperature range 50–120 °C and frequency range 1 kHz–1 MHz by means of HP 4282A impedance meter. The frequency and temperature dependence of electric properties were analyzed by theoretical models of dielectric relaxation in order to obtain information abut molecular dynamic of our solids in external electric field. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction In the previous report was presented dielectric properties in double potassium yttrium orthophosphates K3Y(1x)Ybx(PO4)2 (x = 0.01, 0.05) [1]. This paper is the second part of our investigation on double potassium yttrium orthophosphates doped by lanthanide ions. In this part general formula of our samples is K3Y(1x)Lnx(PO4)2 (x = 0.01, 0.05), where Ln = Pr3+ and Dy3+. The structure data of K3Y(PO4)2 was presented by Ushakov [2] and Komissarova et al. [3]. The authors reported a monoclinic system with space group P21/m with the cell parameters: a = 7.358 (Å), b = 5.613 (Å), c = 9.349 (Å), b = 90.92° and Z = 2. This structure can be described as a distortion of glaserite structure, where structural subunit is formed by octahedron [LnO6]. Alternately arranged up and down [PO4] groups are connected with octahedron in its five vertices but one tetrahedron group divided one of its edge with a polyhedron containing Ln. In this way the number of coordination of LnIII rises into 7 and symmetry of space group decreases from the hexagonal to the monoclinic. The potassium ions are situated along c axis among layer formed by a tetrahedron and a octahedron. This monoclinic distortion of the glaserite structure reminds the arcanite – type K3Na(SO4)2 (Fig. 1). The spectroscopic properties of double alkali metal yttrium orthophosphates, with formula M3Y(PO4)2, where the molar ratio of YPO4:M3PO4 is 1:1 (M = Rb, Na, Lu) doped with Pr3+, Dy3+ have been studied by several authors
⇑ Corresponding author. E-mail address: [email protected] (S. Szulia). 0022-2860/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.molstruc.2011.09.002
[4,5]. However, there is a few information about the dielectric properties of M3Y(PO4)2 doped with the lanthanide ions. The crystal structures of the obtained compounds were confirmed by X-ray diffraction using a diffractometer Siemens D 5000th. The resulting diffraction patterns were compared with the crystallographic data sheet number 049-0497 double potassium yttrium orthophosphate – K3Y(PO4)2 in a crystal base ICCD PDF – 4+. The X-ray diagrams received for non-doped materials and with admixture depict that peaks derived from doped samples by lanthanide ions coincide with the peaks originating from pure K3Y(PO4)2 (Fig. 2). It was found that the process of doping material and the fusion did not cause any changes in the crystalline structure of the compounds. So far, we obtained in the system where amount of doped material is 1% of Dy3+ and Pr3+ the dielectric relaxation can be described by two-parametric dielectric response function of the Havriliak– Negami (HN) [6]. The real and imaginary part of permittivity were calculated using the following equations: 1 1a 1a f C B b a tan f cosð a 2 p Þ=1 sin ð a 2 p Þ C B fc fc C e0 ¼ e1 þ ðe0 e1 Þ cos B C B" # b=2 2 2 C B 1a 1a A @ f f sinða 2pÞ þ fc cosða 2pÞ 1 þ fc 0
1 1a 1a f C B b a tan f cosða 2pÞ=1 fc sinða 2pÞ C B fc C e00 ¼ ðe0 e1 Þ sin B B" # 2 2 b=2 C C B 1a 1a A @ sinða 2pÞ þ ffc cosða 2pÞ 1 þ ffc 0
ð1Þ
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167
recalled models on double potassium yttrium orthophosphates doped by lanthanide ions was presented in previous part of this work [1]. 2. Experimental Electric properties were investigated in double potassium yttrium orthophosphates K3Y(1x)Lnx(PO4)2 (x = 0.01. 0.05, Ln = Pr, Dy). All compounds were synthesized by means of solid phase reaction by sintering a stoichiometric mixture of the initial orthophosphates of YPO4, K3PO4 and Ln2O3 at 1200C for 4 h. The obtained orthophosphate were melted in closed platinum–rhodium tube in the argon atmosphere at 1440 °C [14]. Complex electric permittivity has been performed, as was written previously [1], on polycrystalline samples in the temperature range from 50 °C to +120 °C and frequency range 1 kHz–1 MHz by means of HP 4282A impedance meter. Samples were made as pellets 10 mm in diameter and about 1–2 mm thick. Copper-foil electrodes were affixed to the prepared pellets. Before experiment samples were annealed at a temperature of 170 °C in vacuum in order to decrease the amount of water absorbed from the air thus a number of electric charges is also reduced rather substantially. All measurements were carried out in a dry nitrogen atmosphere. The shape of measurements configuration was described previously [15].
Fig. 1. Projection of the arcanite-type structure of K3Y(PO4)2.
3. Results 3.1. K3Y(1x)Prx(PO4)2. (x = 0.01, 0.05)
Fig. 2. The X-ray diagrams for K3Y(PO4)2 (black), K3Y0.99Pr0.01(PO4)2 (red) and K3Y0.99Dy0.01(PO4)2 (green line). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
In the case 5% Pr3+ and Dy3+ our analysis prove that one-parametric dielectric response function of the Cole–Cole [7] better describe the dependence of complex permittivity in whole temperature range.
e0 e1 1 þ ðf =fc Þð1aÞ sinðap=2Þ ¼ es e1 1 þ ðf =fc Þ2ð1aÞ þ 2ðf =fc Þð1aÞ sinðap=2Þ e00 ðf =fc Þð1aÞ cosðap=2Þ ¼ es e1 1 þ ðf =fc Þ2ð1aÞ þ 2ðf =fc Þð1aÞ sinðap=2Þ
ð2Þ
where es and e1 is the static and optical permittivity, a and b are the empirical coefficients (0 6 a, b 6 1) and fc is the frequency of the relaxation process. The average values of relaxation times ðs ¼ 1=2p f c Þ were obtained from the fitting of the Havriliak– Negami equation (for 1% Dy3+ and Pr3+) (e.g. 1) and Cole–Cole equation (e.g. 2, 5% of impurity of Ln) in the whole range of frequencies. Unfortunately, experimental points are located in a high frequency region of the spectrum what results in large uncertainty of the fitted parameters. All the tested compounds have a complex dielectric characteristics. The diagrams of the real and imaginary part of the permittivity as a function of temperature are in the form of broad bands, generated by the partial overlapping of several smaller components. Matching models Cole–Cole and Havriliak–Negami also indicates the polydispersive nature of the studied systems. In order to analyse the dielectric loss line shape the model of Dissado–Hill [8,9] based on Jonscher’s theory [10–13] was used. The application of
Fig. 3 presents temperature dependence of the real and imaginary part of electric permittivity in materials doped by 1% and 5% praseodymium. Below 40 °C no dispersion and absorption is observed, this situation is similar for both ions. In discussed temperature range relaxation process is retarded because of the rigidity of crystallographic lattice. In a higher range of temperature (20 °C to +100 °C) a dielectric dispersion and absorption is significantly illustrated. The dielectric response for a material doped by 1% of Pr, presented in the Fig. 3a, depicts one broad peak with a maximum at 24 °C. The absorption curve (e00 ) at the frequency below 4.5 kHz two separated bands are clearly indicated. When the frequency increasing the maxima approaching and one broad peak is appeared, with maximum value at 24 °C. For temperature lower than 20 °C absorption maxima shift towards higher frequencies with temperature (color violet in the Fig. 4a), for the temperatures from 20 °C to 30 °C the maximum band does not change the position (Fig. 4a color red). With a further increasing of temperature the decreasing of the value of critical frequency is observed (Fig. 4a color green). In the Fig. 3c, for dependency of real part of permittivity, two peaks are observed, but the absorption diagram is more complex (Fig. 3d). First of all, it is noticeable that the broad absorption band is due to the imposition of three narrower bands. Beside, at the T = 80 °C the addition peak also appears. For the temperature lower then 10 °C maxima of the band are not clear separated, due to the appearance of a new band. Although the trend is visible of shifting the maxima with temperature towards to higher frequency (color violet in Fig. 4b). For the band in the range of temperature 15–20 °C characteristic is that the absorption reaches the highest value at temperature about 25 °C (color red Fig. 4b) independently apart from the frequency. The third maximum of the band shifts towards lower frequency with the increasing of the temperature (in the Fig. 4b color green). The dielectric response data obtained for the material doped by 1% Pr in whole range of the temperature were evaluated by the Havriliak–Negami model. In compounds with 5% of Pr the
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Fig. 3. The real and imaginary part of electric permittivity versus temperature and frequency for K3Y0.99Pr0.01(PO4)2 and K3Y0.95Pr0.05(PO4)2.
Fig. 4. The imaginary part of electric permittivity versus frequency for (a) K3Y0.99Pr0.01(PO4)2 and (b) K3Y0.95Pr0.05(PO4)2.
one-parametric dielectric response function of the Cole–Cole better described experimental data. Matching dielectric parameters: the
relaxation time s, a and b parameters, dielectric increment (es and e1 ), for chosen temperature, are shown in Table 1.
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S. Szulia et al. / Journal of Molecular Structure 1006 (2011) 166–172 Table 1 Temperature dependence of dielectric parameters: relaxation time and distribution parameters for (a) K3Y0.99Pr0.01(PO4)2. (b) K3Y0.95Pr0.05(PO4)2 materials. T (°C)
10.8
0.4
10.1
19.5
30.0
40.6
49.9
60.2
58.36 4.66 0.153 0.789 521.1
67.78 4.72 0.178 0.824 200.8
74.52 4.80 0.180 0.843 78.2
77.48 4.90 0.152 0.829 42.7
77.45 4.90 0.168 0.859 46.7
73.31 4.74 0.196 0.875 91.7
69.32 4.63 0.217 0.891 168.8
66.53 4.54 0.252 0.936 284.6
(a) K3Y0.99Pr0.01(PO4)2
e0 e1 a b
s 106 s T (°C)
10.1
(b) K3Y0.95Pr0.05(PO4)2 41.53 5.02 0.373 834.5
e0 e1 a s 106 s
0.2
10.6
20.3
30.1
40.4
50.4
60.3
69.9
74.9
75.9
76.8
77.8
79.8
80.8
48.94 4.74 0.414 268.9
52.06 4.73 0.396 74.5
60.30 4.62 0.396 59.7
63.33 4.90 0.358 63.1
61.67 5.26 0.303 66.4
60.06 5.33 0.285 99.5
60.43 5.27 0.291 239.5
59.38 5.22 0.284 582.8
60.55 5.24 0.285 918.4
67.44 5.27 0.303 1256.7
63.49 5.26 0.394 1170.5
61.78 5.26 0.290 1110.9
61.24 5.26 0.289 1013.0
59.68 5.22 0.284 985.8
Assigned for different temperature the relaxation times were provided to draw the dependence of lns = f(1000/T). According to Arrhenius relation, the resulting graph is presented in Fig. 5. The points on the graph are consists of three sections with different slope of straight line. For occurring at temperatures below 20 °C process for 1% of Pr and 10 °C for 5% of Pr was determined the activation energy. The value of estimated energy is 57.7 kJ/mol and 71.7 kJ/mol, respectively. The non-activated nature was assigned to the other processes, both K3Y0.99Pr0.01(PO4)2 and K3Y0.95Pr0.05(PO4)2. For description the model of Dissado–Hill is proposing. The Arrhenius graph suggests that the processes in the middle range of temperature occur with zero activation energy, while the processes run at higher temperatures with evolution of energy. The first process can be defined as non-activated tunneling ‘‘flipflop’’ second as transition ‘‘flip’’. In case of material doped by 5% of praseodymium additional peak appeared at about 75 °C is connected with the second thermally activated transition. As was proved previously in material with 5% of ytterbium ions [1], those process is due to alteration of the direction of polaron coupling. This effect is distinctly observed in ionic crystals, where exists a strong interaction between ions and electrons. When temperature is growing up the number of phonons plays major role in the electron scattering by lattice vibration. As a consequence the electric resistance decrease is noted. The value of calculated activation energy in those region of temperature is 50.2 kJ/mol. 3.2. K3Y(1x)Dyx(PO4)2 (x = 0.01, 0.05) Fig. 6 presents the 3D graphs of the dielectric response for double potassium yttrium orthophosphates doped by 1% (Fig. 6a and b) and 5% of dysprosium ions (Fig. 6c and d). The complex permittivity in
both compounds versus temperature and frequency is characterized as symmetrical bands with maximum value in T = 27 °C, independently on frequency. In the absorption diagram (Fig. 6b) for temperature lower than 10 °C, e0 and e00 data were described by the Havriliak–Negami equation, although, for higher temperature the Cole–Cole model is sufficient. Matching dielectric parameters: the relaxation time s, a and b parameters, dielectric increment (es and e1 ), for chosen temperature, are shown in Table 2. In case of K3Y0.95Dy 0.5(PO4)2 the imaginary part of the permittivity consists of three imposing bands and additional bands with maximum at 85 °C (rys.6d). Unfortunately, the increment of permittivity is insignificant and matching any model describing the dielectric relaxation is difficult. Below 10 °C the maximum at band is shifted with temperature towards the higher frequency. In the middle temperature range the second band begins to dominate. In this band the highest value of absorption marked at 27 °C for all frequencies from range 10 to 1000 kHz. For temperature higher then 40 °C outlines another bands, with changing maximum in direction of lower frequency with increasing of the temperature. Arrhenius plot reflects the complexity of the absorption band as a function of temperature. Activation process marked in the temperature range from 14 to 15 °C is shown in the Fig. 7. Next, appears the transition ‘‘flip-flop’’ and, above 40 °C, flip transition. The value of activation energy calculated from linear slop is equal 68.6 kJ/mol for sample doped by 1% of Dy3+ and 91.9 kJ/mol for 5% of dysprosium. For both compounds doped by praseodymium and dysprosium ions, the middle and higher range of temperature cannot be explained by means of Debye concept. We suggest that such process could be explained by the configurational tunneling mechanism proposed by Dissado–Hill model based on Jonscher’s
Fig. 5. Arrhenius plot of the relaxation times for (a) K3Y0.99Pr0.01(PO4)2 and (b) K3Y0.95Pr0.05(PO4)2.
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Fig. 6. The real and imaginary part of electric permittivity versus temperature and frequency for K3Y0.99Dy0.01(PO4)2 and K3Y0.95Dy0.05(PO4)2.
Table 2 Temperature dependence of dielectric parameters. Relaxation time and distribution parameters for (a) K3Y0.99Dy0.01(PO4)2. (b) K3Y0.95Dy0.05(PO4)2 materials. T (°C)
9.8
0.2
9.5
19.8
29.7
40.5
50.2
60.7
(a) K3Y0.99Dy0.01(PO4)2 e0 33.67 e1 4.51 a 0.000 b 0.591 s 106 s 1754.5
31.52 4.51 0.000 0.596 846.8
41.15 4.50 0.167 0.739 308.8
51.81 4.53 0.263 0.880 120.2
77.38 4.25 0.364 – 102.8
91.39 4.05 0.388 – 147.8
84.87 4.21 0.378 – 262.0
64.63 4.59 0.332 – 521.3
61.95 4.59 0.323 – 1712.6
T (°C)
10.2
0.5
10.5
20.7
30.3
40.9
50.2
60.3
45.04 5.14 0.384 3621.6
42.36 5.11 0.374 568.6
42.39 5.10 0.358 142.6
47.06 5.09 0.354 66.0
49.89 5.16 0.332 59.1
51.37 5.29 0.316 103.2
57.37 5.32 0.336 465.2
96.09 5.26 0.399 6130.8
14.1
14.5
(b) K3Y0.95Dy0.05(PO4)2 e0 43.86 e1 5.10 a 0.391 s 106 s 7004.6
theory. Similar results was obtained for K3Y1xYbx(PO4)2 (x = 0.01, 0.05). For such materials, Jonscher proposed by introducing the
coefficients m and n, description of susceptibility function as a power law:
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171
Fig. 7. Arrhenius plot of the relaxation times for a) K3Y0.99Dy0.01(PO4)2 and b) K3Y0.95Dy0.05(PO4)2.
1
v
00
¼
x xc
m
þ
x xc
ð1nÞ ð3Þ
where 0 < m < 1 for x < xc and 0 < 1 n < 1 for x > xc. xc is a frequency equal or near to the frequency of the relaxation process. For pure Debye response m = 1 n = 1, which corresponds to the symmetric peaks of dielectric loss. Where m is equal 1 n probable is Cole–Cole relation, for m = 1 and 1 n – 0 Cole–Davidson equation. The physical meaning of exponents have been proposing by Nigamtullin [16,17]. Author attributed ‘‘m’’ and ‘‘n’’ with the dimension of energy. In the first stage of relaxation, for times shorter than 1/xp, that is, for frequencies x > xp, the energy is mainly spread through a large number of high-speed transitions called as flip, which represents the cooperative configurational tunneling mechanism. In the surrounding of the dipole exists local structural distortion, that can allow realignment of the dipole. Energies needed for the configurational adjustments are stored in the local structure around the dipole and form a narrow band of configurational states on the bottom of the potential well. As a dipole has reoriented a net change and the polarization occurs in the system. Loss of energy to reverse the polarization is constant their measure is the size of the exponent ‘‘n’’, regardless of the degree of polarization reversal. In the second stage of relaxation, for times longer than 1/xp, that is, a frequency x < xp, another process dominates. The flipflop transitions have the same nature as the configurational tunneling and can be considered as a local fluctuations in the medium. The point is that two configurational tunneling processes occur synchronously but dipolar movements involved are in opposing directions at different points in the medium. Microscopically dipoles reorient but macroscopically net change of dipole moment is not observed. After each abrupt transition followed many transitions among the neighboring dipoles, which causes a gradual dissipation of stored energy. Loss of the energy during the flip-flop transitions is in a constant ratio of the additional energy that can be accumulated through the static field. The size of wasted energy is expressed with the coefficient ‘‘m’’. The table below is presenting the value of m and n obtained in range of temperature were the ‘‘flip-flop’’ and ‘‘flop’’ processes are presented. Table 3 The value of coefficients m and n calculated for processes non-activated thermally. Compounds
m for x < xc
n for x > xc
K3Y0.99Pr0.01(PO4)2 K3Y0.95Pr0.05(PO4) K3Y0.99Dy0.01(PO4)2 K3Y0.95Dy0.05(PO4) K3Y0.99Yb0.01(PO4) [1] K3Y0.95Yb0.05(PO4) [1]
0.271 0.096 0.099 0.00 0.102 0.148
0.353 0.376 0.399 0.447 0.344 0.377
The values of ‘‘m’’ and ‘‘n’’ exponents for reported materials with contained Pr3+, Dy3+ and Yb3+ ions are shown in Table 3. According to the Table 3 it is difficult to see any tendency in value of the ‘‘n’’ and ‘‘m’’ exponents. The coefficients ‘‘m’’ was obtained for frequencies saddle with big measured errors. In case ‘‘n’’, the value is more or less 0.4. The extra energy that can be stored in the sample by the static field of the order of 60% of the energy lost per cycle of frequency. 4. Conclusion In summary, we have measured temperature and frequency dependence of electric permittivity of K3Y0.99Pr0.01(PO4)2, K3Y0.95Pr0.05(PO4)2, K3Y0.99DDy0.01(PO4)2 and K3Y0.95Dy0.05(PO4)2 in range of frequency 1 kHz–1 MHz and temperature from 50 °C to +120 °C. The obtained data of real and imaginary part of electric permittivity can be described by the Cole–Cole and Havriliak– Negami equation. The relaxation times were used to calculated the activation energies. From the Arrhenius plot the processes with different nature were observed. The one area of the thermally activated transition was designated for 1% doped by Dy3+and Pr3+ material and two in case of 5% Dy3+and Pr3+. That additional process can be connected with alteration of the direction of polaron coupling. Non-activated processes called as flip and flip-flop transitions in Dissado–Hill theory were observed in both compounds. The behavior with frequency of these materials suggests that the Jonscher’s power law is held good. In our interpretation we have presumed that particular molecules in considered materials have different freedom of motion. Dipoles in solids are not free to rotate as in pure Debye concept, but are constrained to assume discrete orientations in the system with respect to the nearest neighbors. Acknowledgements This work was supported from the Republic of Poland scientific funds as a research project, within Grant No. N N204 166436. References [1] S. Szulia, M. Kosmowska, H.A. Kołodziej, M. Sobczyk, G. Czupin´ska, J. Mol. Struct. 996 (2011) 135–140. [2] S.V. Ushakov, A. Navrotsky, J. Mater. Res. 19 (7) (2004) 2165–2175. [3] L.N. Komissarova, M.G. Zhizhin, A.A. Filaretov, Russ. Chem. Rev. 71 (2002) 619– 650. [4] M. Guzik, T. Aitasalo, W. Szuszkiewicz, J. Legendziewicz, J. Holsa, J. Alloys. Compd. 380 (2004) 368–375. [5] M. Guzik, J. Legendziewicz, W. Szuszkiewicz, A. Walasek, Opt. Mater. 29 (2007) 1225–1230. [6] S. Havriliak, S. Negami, J. Polym. Sci. Part C 14 (1966) 99–117. [7] K.S. Cole, R.H. Cole, J. Chem. Phys. 9 (1941) 341. [8] L.A. Dissado, R.M. Hill, Nature Lond. 279 (1979) 685–689. [9] L.A. Dissado, R.M. Hill, Phil. Mag. B 41 (1980) 625.
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