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Japanese Journal of Applied Physics 52 (2013) 09KH04 http://dx.doi.org/10.7567/JJAP.52.09KH04
Enhanced Microwave Resonance Properties of Pseudo-Tungsten-Bronze Ba63x R8þ2x Ti18 O54 (R = Rare Earth) Solid Solutions Explained by Electron–Phonon Interaction Wilfried Wunderlich1 and Hitoshi Ohsato2;3 1
Material Science Department, Graduate School of Engineering, Tokai University, Hiratsuka, Kanagawa 259-1252, Japan Nagoya Industrial Science Research Institute, Nagoya 464-0819, Japan 3 Nagoya Institute of Technology, Nagoya 466-8555, Japan E-mail:
[email protected] 2
Received May 21, 2013; accepted June 24, 2013; published online September 20, 2013 Microwave dielectrics consisting of pseudo-tungsten-bronze solid solutions form compositional ordering at x ¼ 2=3 with the Ba63x R8þ2x Ti18 O54 (R = La, Nd, Pr, Sm, Eu, and Gd) formula. The Qf value of the x ¼ 2=3 composition shows the highest value for Sm, but a discontinuity at Eu. When doping with heavier rare earth species, the crystal structure becomes unstable and needs stabilization with Nd. In this paper, we suggest for the first time that the electron–phonon interaction is responsible for this phenomenon. As the unit cells without Ba ions in the perovskite blocks caused tensile stress, the dielectric constant and dielectric losses increase by means of the ionic size of the dopant in the octahedral sites, but only when elements with a low electron–phonon interaction are used. # 2013 The Japan Society of Applied Physics
1. Introduction
Microwave resonators are technologically important dielectrics with a high quality factor Q, which is achieved by the highly symmetric crystal structure and inversion symmetry i, when the crystals are perfect and without defects or strain. In this paper we discuss the relationship between rare earth doping and microwave properties for the pseudo-tungsten-bronze type Ba63x R8þ2x Ti18 O54 (R = rare earth) solid solutions.1,2) The optimum sintering temperature of 1300 C2) has been confirmed by others3) and can be explained as the optimum between large grain size and ordering. Up to now, these solid solutions show the highest quality factor Qf at x ¼ 2=3, when Sm substitutes the A1 site in the perovskite block.3,4) The reason has been explained by compositional ordering and the lowest internal strain when substituting Ba by rare earth elements.4,5) The solid solutions are located on the tie-line with the ratio Ti : O ¼ 1 : 3 between BaTiO3 and R2 Ti3 O9 compositions. The ratio 1 : 3 shows the crystallographic feature, that is, all TiO6 octahedra are connected to each other by sharing all apexes, as shown in the crystal structures of BaTiO3 and tungsten-bronze. The crystal structure of pseudo-tungstenbronze solid solutions is compositionally disordered, when x is smaller than 2/3, and has compositional ordering, when x reaches 2/3. Moreover, different species of the R ions yield to different Qf values, namely, Sm with intermediate ionic radius shows the highest Qf value. In this case the internal strain is lowest.5–8) In the order R = La, Pr, Nd, and Sm the quality factor increases up to x ¼ 2=3, while the permittivity shows a small increase in spite of a general decreasing behavior with increasing x. When Gd and Eu are doped,9,10) the compositional stability range for the pseudo-tungstenbronze narrows remarkably. Detailed analysis of the fullwidth at half-maximum (FWHM) of the X-ray power diffraction (XRPD) showed that the highest Qf value is obtained when the internal strain is the lowest.1,4) In the case of the next element in this order, Eu, the quality factor decreases drastically. Doping of other lanthanides (Dy, Ho, Er, Yb) requires the structure stabilization with Nd, as expressed in the structural formula Ba4 (Nd28=3y Ry )Ti18 O54 .9) Understanding has gained progress,11) but Sr-
doping12,13) did not bring any improvement in dielectric properties. For further development of dielectrics, dependence studies on basic properties such as Young’s modulus or sound velocity are necessary.14) As elements are the smallest units for doping, some of their properties were examined15,16) by statistical data analysis, a new method of materials informatics.17) The dimensionless electron–phonon interaction (EPI) is one of the key parameters in transport theory.18–20) A large EPI is advantageous for a large critical temperature for superconductors as expressed by the McMillan formula.18–20) EPI can also be calculated from the Sommerfeld coefficient describing the temperature dependence in specific heat, from electric resistivity or from optical conductivity.18–24) In this paper, besides the mentioned origins of the internal strain examined by crystallographic considerations, we examine the discontinuity in the quality factor and structural instability when doping rare earth elements with different ionic sizes and by means of the electron–phonon interaction parameter. 2. Experimental Methods
This crystallographic study is based on experiments resolved on previously prepared samples.1–6,8,9,11–13) Additionally, transmission electron microscopy (TEM) observations were performed in high-resolution mode on a JEOL 3000FX operated at 300 kV. The preparation was performed by depositing crushed powder on a carbon-coated Cu grid. In the second part of this paper, the literature data for EPI20–24) are drawn against the Mendeleev number MN1,17) which is used to plot the so-called Pettifor maps of the stability region of binary compounds. 3. Results and Discussion
The pseudo-tungsten-bronze solid solution consists of two 2 2 perovskite blocks per unit cell as confirmed by the HRTEM micrograph in Fig. 1 showing the unit cell with dimensions a ¼ 2:271 and b ¼ 1:271 nm. The crystallographic sites A1, A2 (Ba), and C (empty) are marked. When doping such crystals with smaller values of x, namely x < 2=3, at first the Ba ions at the A1 sites within the
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Fig. 1. (Color online) HRTEM micrograph of Ba63x Sm8þ2x Ti18 O54 with x ¼ 0:67 showing lattice fringes, diffraction pattern, and the unit cell of the crystal structure with the 2 2 perovskite blocks.
perovskite block become statistically occupied with R such as [R8þ2x Ba23x Vx ]A1 , in which three Ba ions are substituted by two R ions and one vacancy. The internal strain due to doping of rare earth elements changes with composition. In the case of x < 2=3, a small size unit cell without Ba ions in the perovskite block is strained by tensile stress from the surrounding large cells with Ba ions in the block. The case with Sm concentration x ¼ 2=3 for the Ba63x R8þ2x Ti18 O54 formula has the lowest internal stress as determined from XRPD measurements. As microwave dielectric properties depend on the internal strain, the quality factor has the highest value, as shown in Fig. 2(a). Eu and Gd have smaller ionic radii than Sm, but in contrast such doped specimens have a quality factor much smaller than those doped with Sm. In order to explain this phenomenon, even smaller rare ions were doped. However, when doing so, the tungsten-bronze structure becomes unstable.9,10) So, the alloy Ba63x Nd8þ2x Ti18 O54 with x ¼ 2=3 was partially substituted as Ba4 (Nd28=3y Ry )Ti18 O54 9) by R = Eu, Dy, Ho, Er, and Yb and the quality factor is shown in Fig. 2(b). Instead of the expected increase in Qf due to internal stress, in all cases a decrease in Qf is observed. In the case of Gd,10) a stable pseudo-tungsten-bronze solid solution was reported for x ¼ 0:5 only, but not for x ¼ 2=3, where it should be noted that their x has a different definition than ours.10) The quality factor reaches only Qf ¼ 2050 GHz a value similar as for La. For clarification, we study in the following only the case x ¼ 2=3 and draw dielectric properties as a function of the ionic radius (Fig. 3) by omitting Gd with its small stability range of x value. As found in a detailed crystallographic analysis,5) the coordination numbers (CN) for A2 and A1 sites are similar (CN ¼ 10 and 9), we use in the following the Shannon radius CN ¼ 10 and valence +3 for the rare earth ionic
Fig. 2. (Color online) Qf values of tungsten-bronze composite materials
for (a) Ba63x R8þ2x Ti18 O54 with R = La, Pr, Nd, Sm, Eu,6) and Gd,10) and (b) Ba4 (Nd9þ1=3y Ry )Ti18 O54 with R = Eu, Dy, Ho, Er, and Yb.9)
radius. As shown by the dark line in Fig. 3, the dielectric properties follow the order of rare earth elements in the periodic table La, Pr, Nd, Sm, but at Eu there is a discontinuity and for all the following elements the crystal structure needs stabilization with Nd with different concentrations y as marked (dotted line in Fig. 3). The (a) volume, (b) temperature coefficient, and (c) permittivity show almost the same behavior, while the (d) quality factor shows strong inverse linearity for La, Pr, Nd, and Sm and also the discontinuity for Eu. The values are almost constant for heavy rare earth elements (Eu to Yb) with their Nd stabilization. The quality factor shows opposite behavior, but an additional strong decrease for the case of small-sized rare earth elements. When doping La instead of Ba with its radius of 0.152 nm, the internal strain is lowest, so the changes of Qf are not so large,6) but Sm with the largest strain shows the highest Qf value. In spite of the fact that Sm and Eu have the same Shannon radius, their dielectric properties change discontinuously when they are doped into the tungsten-bronze crystal. This phenomenon is clarified in the following. For studying the dependence of different atomic specimens, the ordering in the sequence of the Mendeleev number is an appropriate approach.16) The electron–phonon interaction is a dimensionless parameter describing the disturbance of a propagating electron wave by phonons and vice versa. The plot of EPI and Mendeleev number was first reported
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(a)
(b)
(c)
(d)
Fig. 3. (Color online) Dielectric properties of the tungsten-bronze compounds with x ¼ 2=3. Ba4 (Nd9þ1=3y Ry )Ti18 O54 (left, y ¼ 0:5 and 1) and Ba4 R9þ1=3 Ti18 O54 (right) as a function of the ionic radius of the rare earth dopant. In detail: (a) volume of the unit cell, (b) temperature coefficient, (c) permittivity, and (d) Qf values.
Fig. 4. (Color online) EPI is shown as a function of the Mendeleev number MN116) for two classes of elements, alkali, and transition metals. Full symbols represent experimental values (Ex.) as shown in Table I, open symbols are predicted values (Pr., this paper) according to the correlation lines from averaging (Av.).
elsewhere15) and its correlation is shown in Fig. 4 and Table I. Although there is data scattering due to experimental difficulties, the correlation is very good and two
groups of elements can be categorized. While alkali elements up to the fourth column of the periodic table have a low EPI in the order of 0.3, the transition elements from the fifth column show a large EPI, such as V (1.1921)), and Nb (1.2618)). As for rare earth elements no experimental data are yet available, the data correlation allows now for the first time the following interpolation. With the above described experimental results on rare earth doped tungsten-bronze, it is now possible to define the border between low EPI (Sm, Pm, Nd, Pr, La) and high EPI (Eu, Dy, Ho, Er, Yb) elements. While the above described discontinuity in Fig. 2(a) and Figs. 3(a)–3(d) between Eu- and Sm-doped tungsten-bronze electro ceramics could not be clearly explained geometrically, it now becomes clear by considering the EPI. The ionic Shannon radii of Eu and Sm are equal, but the dielectric properties of doped tungsten-bronze change discontinuously. The electron–phonon coupling is a parameterization of interactions caused by internal or external stresses on the outer electron cloud compared with the atomic core and the Coulomb field provided by the crystal structure. A large EPI means the atom is sensitive to such stresses caused by thermal vibrations or external pressure. A large quality factor, however, can only be achieved when the electron cloud can vibrate freely, which means a low electron– phonon interaction. In other words, good resonance of electron waves requires atomic vibrations independent from external strain provided by phonons, hence a low EPI. The tungsten-bronze structure is a kind of model system, because the rattling effects of cations in the oxygen polyhedra
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Table I. Experimental values for EPI parameter for some alkali and transition metals. Values without a reference are predicted values according to the correlation in Fig. 3 of this study.
EPI with reference
Element
Atomic number
Mendeleev number15)
Na
11
11
Ca
20
9
0.28
Sc
21
13
0.26
Ti
22
45
0.3820Þ
V
23
48
1.1921Þ
Cr
24
75
0.90
Sr
38
10
0.30
Y
39
14
0.2422Þ
Zr
40
46
0.2022Þ
Nb
41
49
1.2618Þ
42
52
22Þ
0.42
Ba
56
11
0.30
La
57
15
0.23
Ce
58
17
0.24
Pr
59
19
0.24
Nd Pm
60 61
21 23
0.25 0.25
Sm
62
25
0.26
Eu
63
27
1.65
Gd
64
29
1.55
Tb
65
31
1.48
Dy
66
33
1.44
Ho
67
35
1.38
Er Tm
68 69
37 39
1.32 1.26
Yb
70
41
1.2
Lu
71
43
1.15
Hf
72
47
1.00
Ta
73
50
0.8318;20Þ
W
74
53
0.2820Þ
0.2119Þ
with d-electrons
Mo
Ti18 O54 (R = rare earth) solid solutions, the quality factor depends strongly on the ionic radius of different rare earth species (R ions) doped on the pseudo-tungsten-bronze compounds, causing internal strain and structural instability when the mismatch of the R ions becomes too large. 2) The discontinuous change of dielectric properties between Eu and Sm when doping different rare earth elements is explained for the first time by the change in the electron–phonon coupling parameter as the correlation between Mendeleev numbers clearly showed that rare earth elements up to Sm have a low EPI value, while beyond Eu they have a large one. 3) For further improvement of dielectrics, doping elements with a small EPI seems favorable. Acknowledgements
The authors would like to express their thanks to H. Sakashita, M. Imaeda, and Y. Futamata for study in Nagoya Institute of Technology, and Professor Ken’ichi Kakimoto for the experimental support and discussions. A part of this work was supported by JSPS KAKENHI Grant Number 25420721. Another part of this work was supported by Grant-in-Aid for Scientific Research (C), and Adaptable & Seamless Technology Transfer Program from the Ministry of Education, Culture, Sports, Science and Technology, Japan.
with f-electrons
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become large when doping elements increase the volumes of polyhedra particularly the TiO6 octahedra. The rattling yields an increasing dielectric constant "r and dielectric losses tan . Here, the Qf value shows reverse behavior to that of the dielectric losses tan . The dielectric constants "r values are also increasing, as they depend on the ionic radius of R ions. They are affected by the rattling factor of cations, which depends on the size of polyhedra, as the lattice constants increase by R ions as shown in Fig. 3(a). In this study all the doping elements for dielectrics with a high quality factor consisted of elements with a low EPI. Further studies are necessary to determine, whether this is a general rule. In particular it is not yet clear why Tacontaining perovskites show a large quality factor24) in spite of the not so small EPI of 0.86. Further progress can be expected from ab-initio calculations of the electron–phonon interaction.
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4. Conclusions
1) In the case of pseudo-tungsten-bronze Ba63x R8þ2x -
