3TiO3 ceramics

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Journal of the European Ceramic Society 32 (2012) 3791–3799

Structures and microwave dielectric properties of Ca(1−x)Nd2x/3TiO3 ceramics R. Lowndes, F. Azough, R. Cernik, R. Freer ∗ Materials Science Centre, School of Materials, University of Manchester, Manchester, M13 9PL, UK Received 18 December 2011; received in revised form 14 May 2012; accepted 16 May 2012 Available online 12 June 2012

Abstract Ca(1−x) Nd2x/3 TiO3 microwave dielectric ceramics were prepared by the mixed oxide route; powders were calcined at 1100 ◦ C and sintered at 1450–1500 ◦ C. High density, single phase products were obtained for all compositions. Grain sizes ranged from 1 ␮m to 100 ␮m. There was evidence of significant discontinuous grain growth in mid range compositions; all ceramics were characterised by complex domain structures. With increasing Nd content there was a evidence of a transition from an orthorhombic Pbnm structure to a monoclinic C2/m structure. This was accompanied by a decrease in relative permittivity (εr ) from 180 to 78, and decrease in the temperature coefficient of resonant frequency (τ f ) from +770 ppm K−1 to +200 ppm K−1 . The product of dielectric Q value and resonant frequency (Q × f) varied in a grossly non-systematic way, exhibiting a peak at 13,000 GHz in Ca0.7 Nd0.2 TiO3 . © 2012 Elsevier Ltd. All rights reserved. Keywords: Perovskites; Dielectric properties; Electron microscopy; X-ray methods

1. Introduction Microwave dielectric ceramics are used extensively in the filter units of communications systems, removing unwanted frequencies by a resonance technique.1 Such materials are exploited in mobile telephone base stations, radar and global positioning systems. Candidate materials for such applications must have (i) high relative permittivity (εr ), (ii) a high dielectric Q value (usually described in terms of a high Q × f product, where f is the resonant frequency) and (iii) a temperature coefficient of resonant frequency (τ f ) close to zero.2 The relative permittivity should be as high as possible to minimise the size of the resonator component. However, the relative permittivity is often restricted to values between 20 and 100 to take account of other criteria placed on the material. For the most demanding applications the Q × f product should be above 35,000 GHz to enable the resonator to be highly selective to the target frequency. Finally, the temperature coefficient of resonant frequency should be as close to zero as possible to ensure temperature stability of the system. Research into such materials is driven by the need for increased bandwidth for future generations of devices and economic constraints to reduce component costs. ∗

Corresponding author. E-mail address: [email protected] (R. Freer).

0955-2219/$ – see front matter © 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jeurceramsoc.2012.05.024

Much attention has been paid to the microwave dielectric properties of CaTiO3 based materials.3–10 CaTiO3 offers the opportunity to reduce the size of the resonator component because of its high relative permittivity of 180, but with a highly positive τ f of +800 ppm K−1 and low Q × f of 6000 GHz, the end-member material is not suitable for commercial applications.3 The microwave dielectric properties of CaTiO3 -based resonators have been improved by additions of rare earth aluminates,4,5 rare earth cation deficient titanates7–9 and MgTiO3 .10 For example Yoshida et al.6 showed that additions of Nd2/3 TiO3 improved the Q × f value (from 6000 GHz for CaTiO3 ) to 17,200 GHz for Ca0.61 Nd0.26 TiO3 , and reduced τ f from +800 ppm K−1 to approximately +270 ppm K−1 . Yoshida et al.6 did not identify a mechanism for the changes, but a more recent study by Fu et al.7 suggested that changes in charge distributions affected the vibrational properties of the lattice. An important aspect of understanding loss processes in dielectrics is knowledge of the structure of the ceramic. There are specific difficulties in investigating the structures of ceramics involving rare earth, cation-deficient formulations because the high concentrations of vacancies tend to destabilise the structure, leading to decomposition into two or more unwanted phases.11 However, small additions (typically <10 wt%) of NiO,12 CaTiO3 ,7–9 or rare earth aluminates,13,14 or adjustments of the oxygen deficiency15 can stabilise the structure and

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maintain a single phase. Yoshii15 and Yoshida et al.6 were able to stabilise cation deficient Nd2/3 TiO3 (NT) by adjustment of oxygen stoichiometry and to stabilise CaTiO3 by doping; the NT X-ray diffraction pattern was indexed on the basis of an orthorhombic P222 space group. This yielded a unit cell of a = b = ac and c = 2ac where ac is the lattice parameter for the ideal cubic perovskite structure. Recently Zhang et al.16 used NdAlO3 to stabilise the cation deficient Nd2/3 TiO3 phase at room temperature. By a combination of group theoretical analysis and high resolution structural diffraction techniques Zhang et al. suggested the structure of Nd2/3 TiO3 was monoclinic (C2/m), with lattice parameters of a ≈ b ≈ c ≈ 2ac . This proposal was supported by simulation and experimental electron diffraction patterns. The nature of the ordering in the cation deficient ceramics is alternate layers of cations and vacancies as described by Zhang et al.16 and Wang.17 Wang17 noted that the crosshatched satellite reflection in the electron diffraction patterns of Ca0.1 Nd0.6 TiO3 closely resembled the electron diffraction patterns for ThNb4 O12 .18 Labeau et al.18 attributed the appearance of the satellite reflections to the formation of ordered superlattice due to A-site cation-vacancy ordering. The primary objective of the current study is to understand structural and microstructural control of dielectric properties in Ca(1−x) Nd2x/3 TiO3 microwave dielectric ceramics. It is well known that CaTiO3 -based perovskites undergo two structural phase transitions on cooling from the sintering temperature to ambient19 and that internal strain associated with these transitions is relieved by twinning. Although the microstructure of Ca(1−x) Nd2x/3 TiO3 ceramics have been studied previously,7,8 little consideration has been given to the twin domains. Specific attention is therefore given to structural and microstructural changes as a function of composition and the development of twin domains within the microstructure. 2. Experimental Ceramic samples of Ca(1−x) Nd2x/3 TiO3 with x = 0, 0.21, 0.3, 0.39, 0.48, 0.57 and 0.9 were prepared by the conventional mixed oxide route. Starting materials were high purity (>99.5%) powders of CaCO3 (Solvay, 99.5%), Nd2 O3 (AMR Limited, 99.9%) and TiO2 (Tioxide, 99.9%). The Nd2 O3 was dried at 900 ◦ C for 6 h prior to use. The powders were weighed in batches according to the required formulations and wet milled for 24 h in a vibratory mill using zirconia balls and propan-2-ol. The powders were then dried at 85 ◦ C for 24 h and calcined at 1100 ◦ C for 4 h. To prevent reduction of Ti4+ to Ti3+ during heat treatment,20 0.2 wt% Mn2 O3 was added and the batches were wet milled for a further 24 h. Powders were uniaxially compacted into pellets of 20 mm diameter and 15 mm thickness at a pressure of 25 MPa prior to sintering at 1450–1500 ◦ C for 4 h in air. The heating and cooling rates were 180 ◦ C/h; samples were sintered in alumina crucibles with sacrificial powder below the sample to prevent contamination from the substrate. Densification was assessed from mass and dimension measurements. Structural analysis was undertaken by X-ray diffraction using a Philips PW1830 system operating at 50 kV

and 40 mA. The samples were first ground flat using 400 grade SiC and then scanned from 10◦ to 85◦ 2θ in steps of 0.05◦ with a dwell time of 18.5 s per step. Rietveld analysis of the data was undertaken using TOPAS 4.2.21 Microstructures were examined by scanning electron microscopy (Philips XL30 FEGSEM and Zeiss EVO60 equipped with EDX capability). Samples were ground using 240, 400, 800 and 1200 grade SiC and polished using 6 ␮m and 1 ␮m diamond paste. The final polishing stage employed Oxide Polishing Suspension (OPS). Samples were etched in warm (100 ◦ C) sulphuric acid (80 vol%)–H2 O (20 vol%) prior to carbon coating. Microwave dielectric properties (relative permittivity, εr , product of dielectric Q value and resonant frequency (Q × f) and the temperature coefficient of resonant frequency, τ f ) were determined using a silver-plated aluminium cavity at 2–3 GHz. The temperature coefficient of resonant frequency (τ f ) values were determined at temperatures between −10 and +60 ◦ C. 3. Results and discussion 3.1. Microstructure All samples sintered in the range 1450–1500 ◦ C attained at least 95% of the theoretical density. Typical micrographs of the ceramic microstructures are shown in Fig. 1 (low magnification) and Fig. 2 (higher magnification). There is no evidence of any second phases; porosity is located at the grain boundaries and trapped within the grains. The lack of any second phases contrasts with the work of Fu et al.7 on Ca(1−x) Nd2x/3 TiO3 who reported the presence of TiO2 . Furthermore, the most Nd-rich formulation, having x = 0.9 (Ca0.1 Nd0.6 TiO3 ), has been stabilised by the presence of CaTiO3 ; neither of the anticipated breakdown products of Nd2/3 TiO3 (Nd2 Ti2 O7 and Nd4 Ti9 O24 )22 could be detected (Fig. 1). The grains in Ca0.79 Nd0.14 TiO3 (Figs. 1a and 2b) are generally equiaxed in shape with a bimodal grain size distribution; most individual grains are in the 10–40 ␮m range. With increasing Nd content the bimodal distribution becomes more pronounced (Fig. 2b–e) reaching a maximum in Ca0.52 Nd0.32 TiO3 (Fig. 2d) and Ca0.43 Nd0.38 TiO3 (Fig. 2e) with grain sizes ranging from 5 to 100 ␮m. When the composition reaches Ca0.1 Nd0.6 TiO3 the average grain size is much smaller with many grains as small as 1 ␮m (Fig. 1c). The bimodal grain size distributions in the mid range compositions are probably the result of discontinuous grain growth with some grains growing rapidly at the expense of smaller grains. This has been observed in several systems including BaTiO3 24 Pb(Mg1/3 Nb2/3 )O3 –PbTiO3 ,25 and columbite structured ceramics.26 Fisher et al.24 suggested that the development of very large grains was encouraged by the faceting of interfaces between adjacent grains, and that the presence of a liquid phase would reduce the critical driving force required for abnormal grain growth. At higher magnification (Fig. 2) details of the domain structures in the samples become apparent. In general there is a high density of twin domains which is typical for perovskite ceramics based on CaTiO3 .19 In the end member CaTiO3 (Fig. 2a) twin

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Fig. 1. SEM micrographs of Ca(1−x) Nd2x/3 TiO3 ceramics after thermal etching: (a) Ca0.79 Nd0.14 TiO3 ; (b) Ca0.43 Nd0.38 TiO3 and (c) Ca0.1 Nd0.6 TiO3 (scale bars 20 ␮m).

domains are predominant, having the form of needle-like lamellae, tapered at one end. As Nd3+ is added to the formulation the domain morphology changes and the tendency to form welldefined lamellar twin domains is lost and there is a wider variety of morphologies (Fig. 2b–e). These include well-defined regular triangular and quadrilateral shapes and multi-sided domains, some with curved edges (Fig. 3). The tendency for random domain morphologies appears to end with Ca0.52 Nd0.32 TiO3 and there is a return to the familiar, almost straight-sided lamellae on reaching the composition Ca0.1 Nd0.6 TiO3 (Fig. 2f). Fig. 4 shows the domain widths as a function of composition as determined by a linear intercept method. The domain widths increase from 1.7 ␮m for CaTiO3 to 4.1 ␮m for Ca0.61 Nd0.26 TiO3 and subsequently fall to 1.7 ␮m for Ca0.1 Nd0.6 TiO3 partly due to the

change in the morphology of the domains. However, there is an anomalous reduction in domain sizes at Ca0.52 Nd0.32 TiO3 . This trough coincides with the maximum in both grain size and discontinuous grain growth in the system (Fig. 2d), although it was significantly more difficult (because of poor optical contrast) to measure domain sizes in Ca0.52 Nd0.32 TiO3 than in other ceramics. The domains form after sintering as the samples cool and pass through two structural phase transitions. The first transition is from cubic to tetragonal at approximately 1300 ◦ C and the second is from tetragonal to orthorhombic at approximately 1150 ◦ C.23,27 Since the phase transitions involve substantial structural changes and reorganisation of the unit cell, it is inevitable that the transitions induce significant strain in the

Fig. 2. SEM Micrographs of Ca(1−x) Nd2x/3 TiO3 ceramics showing twin domains in: (a) CaTiO3 ; (b) Ca0.79 Nd0.14 TiO3 ; (c) Ca0.7 Nd0.2 TiO3 ; (d) Ca0.52 Nd0.32 TiO3 ; (e) Ca0.43 Nd0.38 TiO3 ; (f) Ca0.1 Nd0.6 TiO3 . Scale bars: (a), (b), (c), (d) and (e) 10 ␮m; (f) 1 ␮m.

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Fig. 5. Collected X-ray diffraction spectra for Ca(1−x) Nd2x/3 TiO3 ceramics. Fig. 3. Scanning electron micrograph showing domain types in Ca0.61 Nd0.26 TiO3 : triangular domains (A), a curved domain wall (B) and multi-walled single domain (C). Scale bar 20 ␮m.

lattice. The mechanism by which this strain is relieved is through the formation of twin domains, of which there are three types i.e. the so-called (1 1 2), (0 1 1) and [0 0 1]90 .19 The formation of the twins is rapid and twin healing may occur at high temperatures by diffusion. Twin healing in CaTiO3 ceramics gives rise to the characteristic needle shapes that are observed in the microstructure.28 The change in the morphologies of the domains from needles in CaTiO3 to random morphologies in Ca0.61 Nd0.26 TiO3 and the return to lamellae in Ca0.43 Nd0.38 TiO3 suggests a change in the thermodynamics and kinetics of the phase transitions as a result of Nd3+ doping levels. It is possible that the addition of Nd3+ suppresses the phase transitions closer to room temperature, as noted by Ravi et al.29 and Moon et al.30 for additions of LaAlO3 to CaTiO3 . This would reduce the amount of time available for the diffusion processes required for the formation of needle shaped twin domains. 3.2. Phase analysis and structure X-ray diffraction spectra for Ca(1−x) Nd2x/3 TiO3 ceramics for x = 0.0 to x = 0.90 are shown in Fig. 5. There are clearly differences between the structures of the samples as a function of composition, but all the data could be indexed on the basis of

Fig. 4. Domain widths in Ca(1−x) Nd2x/3 TiO3 ceramics as a function of composition.

a single perovskite phase; there was no evidence of TiO2 second phase in the Ca(1−x) Nd2x/3 TiO3 ceramics as reported by Fu et al.7 There are two possible reasons for this difference. The first relates to the heat treatment schedules employed. Fu et al.7 cooled samples at 120 ◦ C/h to 1100 ◦ C, followed by natural cooling to room temperature; in contrast our samples were cooled at a constant rate of 180 ◦ C/h. Detailed structural analysis of the Ca(1−x) Nd2x/3 TiO3 ceramics began with the end members. The structure of CaTiO3 at room temperature is well established3,23,27 ; our sample was confirmed to have an orthorhombic Pbnm structure (Fig. 5). The structure of Nd2/3 TiO3 ceramic is less well defined due to its instability and tendency to break down into two separate phases.22 In the present investigation Nd2/3 TiO3 was stabilised by addition of CaTiO3 , yielding a single phase product at 0.1CaTiO3 –0.9Nd2/3 TiO3 . The X-ray diffraction spectra were refined on the basis of previously reported and predicted space groups for Nd2/3 TiO3 : (i) Pbnm, (ii) C2/m, (iii) P222, (iv) P2/m, (v) Amm2 and (vi) Pmma.6,16 Zhang et al.16 proposed P2/m, C2/m and Amm2 on the basis of group theoretical analysis. The P222 space group assigned to Nd2/3 TiO3 by Yoshida et al.6 did not in fact appear in that analysis. Indeed the earlier studies of Zhang et al.16 and Lee et al.22 employed NdAlO3 to stabilise the Nd2/3 TiO3 phase instead of CaTiO3 in the present case. The best refinements were achieved on the basis of the monoclinic space groups P2/m and C2/m. In order to distinguish between these two possible structural models for Ca0.1 Nd0.6 TiO3 the data and models were examined in detail. The analysis of the Wyckoff positions for the P2/m structure indicated that some of the oxygen atoms share the same positions as the titanium atoms. Clearly this is not an acceptable proposition and therefore the P2/m structure must be rejected as a candidate. It is therefore proposed that the C2/m space group best describes the structure of Ca0.1 Nd0.6 TiO3 ceramics. Thus in the system Ca(1−x) Nd2x/3 TiO3 , the CaTiO3 ceramics (x = 0.0) have an orthorhombic Pbnm structure, whilst Ca0.1 Nd0.6 TiO3 ceramics (x = 0.9) have a monoclinic C2/m structure. This is similar to the transitions in related rareearth doped perovskite system Ca(1−x) La2x/3 TiO3 , where Zhang et al.31 found structural transitions of Pbnm-Ibmm–Cmmm across the composition range. In an attempt to determine the composition at which there is a transition from orthorhombic

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Table 1 Lattice parameters for ceramics in the system Ca(1−x) Nd2x/3 TiO3 after refinement based upon (A) Pbnm space group and (B) C2/m space group.a x 0 (A) Pbnm space group a (Å) 5.3820 b (Å) 5.4465 c (Å) 7.6341

0.21

0.3

0.39

0.48

0.57

0.9

5.4333 5.4565 7.7017

5.4009 5.4352 7.6559

5.4038 5.4789 7.6842

5.4006 5.4245 7.6437

5.4282 5.4526 7.6722

5.4124 5.4134 7.7094

x 0.21 (B) C2/m space group a (Å) b (Å) c (Å) Beta (degrees) a

7.6695 7.6574 7.6619 89.51

0.3 7.6874 7.6588 7.6681 89.61

0.39

0.48

0.57

7.7224 7.6662 7.6713 89.77

7.6685 7.6589 7.6574 89.80

7.6678 7.6682 7.642 89.92

0.9 7.6336 7.6333 7.6811 90.05

The end member CaTiO3 was not refined on the basis of C2/m as it is accepted to have Pbnm structure.3,23

Pbnm to monoclinic C2/m in the Ca(1−x) Nd2x/3 TiO3 system, the X-ray diffraction data for compositions with x > 0 were refined on the basis of both orthorhombic Pbnm and monoclinic C2/m space groups. Whilst the refined data indicated differences along the compositional series, the quality of the laboratory X-ray diffraction data was inadequate to unambiguously define the relative amounts of the two closely related structural variants in each product, and therefore the location of the structural transition. However, the lattice parameters, refined using the Topas suite of software,21 do reveal distinct and important differences (Table 1). The most obvious feature in the data is a maximum in the lattice parameters (and therefore cell volume) at composition Ca0.61 Nd0.26 TiO3 . This maximum is clearest in the data for C2/m and is shown graphically in Fig. 6. This significant change in lattice parameters is indicative of structural distortion or change between Ca0.61 Nd0.26 TiO3 (peak in lattice parameters) and Ca0.52 Nd0.32 TiO3 (reduction in lattice parameters at higher Nd content) and may indeed represent the change from a structure which is predominantly orthorhombic (Pbnm) to monoclinic (C2/m). High resolution synchrotron data will be necessary to confirm this transition. However, the

Fig. 6. Lattice parameters for Ca(1−x) Nd2x/3 TiO3 ceramics after refinement on the basis of C2/m space group: a lattice parameter (䊉); b lattice parameter (); c lattice parameter ().

change in lattice parameters between these two compositions correlates directly with the anomalous changes in domain sizes (Fig. 4). In terms of absolute values, the lattice parameters of materials having a predominantly orthorhombic Pbnm structure (low values of x) are consistent with data previously reported for the system.6,7 The average changes in lattice parameters as Nd replaces Ca in the A-site of the perovskite structure (Table 1) are comparatively modest, reflecting the similarity in the ionic radii ˚ and Nd3+ (1.27 A) ˚ ions.32 In the monoclinic of Ca2+ (1.34 A) regime (high values of x), there is very limited published data for direct comparison. Zhang et al.16 reported lattice parameters for a single composition Nd0.7 Ti0.9 Al0.1 O3 ). Their results (a = 7.676, b = 7.643, c = 7.7114) are broadly comparable with our data for Nd-rich compositions having monoclinic symmetry, taking compositional differences into account. The lattice parameters can be used in the assignment of the tilt system related to the oxygen octahedra. The compositions √ that the Pbnm structure have lattice parameters of a = possess 2ac , √ b = 2ac , c = 2ac , where ac is the lattice parameter for cubic ˚ Using the Glazer CaTiO3 found at high temperature (3.83 A). notation,33 gives the structure a tilt system of a− a− c+ meaning that there are two approximately equal out of phase tilts about the a and b axes and an in-phase tilt about the c axis. The equal antiphase tilts about the a and b axes are expected to give rise to X-ray diffraction peaks with (h k l) values which are all odd; the in-phase tilting will give (h k l) values of odd–odd–even. The tilt system is confirmed by the presence of (1 3 3) and (1 1 5) type peaks for the antiphase tilting, and (3 1 0) and (3 3 2) peaks for the in-phase tilting. The lattice parameters for the ceramics with the P2/m structure are a = b = c = 2ac indicating that all three axes are doubled relative to the cubic perovskite. The C2/m structured ceramics were assigned the a− b◦ c− tilt system indicating that there are three unequal in-phase tilts about each of the three principal crystallographic axes. This tilt sys/ l (a− ) and tem would give peaks of type odd–odd–odd with k = − h = / k (c ) and this is confirmed by the presence of the (1 3 1), and (3 1 1) peaks in the X-ray diffraction patterns (Fig. 5). In

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0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

800

τf

600 400

Q x f (GHz)

200 0 12000 10000 8000 6000 4000 2000 0 150

εr

100 50

Fig. 7. Visualisation of structure for Ca0.1 Nd0.6 TiO3 (C2/m). The Nd1 sites are fully occupied by Nd atoms. The Nd2 sites are shared Nd atoms and vacancies. The dark spheres in the diagram represent oxygen atoms at the corners of Ti octahedra.

moving from the Pbnm structure of CaTiO3 to the C2/m structure of Ca0.1 Nd0.6 TiO3 the lattice becomes increasingly distorted as Nd2/3 TiO3 is added to CaTiO3 . Fig. 7 shows a visualisation of the structure of Ca0.1 Nd0.6 TiO3 . The Nd1 sites are filled with cations whilst the Nd2 sites are partially filled with cations but contain most of the vacancies. The ordering of cations in the perovskite crystal lattice is important in understanding dielectric loss. In a study of Nax Nd(2−x)/3 TiO3 , Kagomyia et al.34 found superlattice peaks in the diffraction patterns at approximately 11◦ , 35◦ , 48◦ , 55◦ , 60◦ and 65◦ (for Cu K␣ radiation). Examination of the X-ray diffraction spectra for the current Ca(1−x) Nd2x/3 TiO3 ceramics with compositions between CaTiO3 –Ca0.43 Nd0.38 TiO3 revealed no superlattice peaks at the positions reported for Nax Nd(2−x)/3 TiO3 . This suggests that the cations are either randomly distributed in the structure or that there is only short range order. No superlattice peaks were identified in Ca0.1 Nd0.6 TiO3 ; this is possibly due to the fact that the superlattice peaks are too weak to be observed above the background. Based on the work of Wang17 on the system Ca(1−x) Nd2x/3 TiO3 we expect the ordering in our Nd-rich ceramics to involve alternate layers of cations and vacancies within the lattice. However, no superlattice peaks were observed in the Ca0.52 Nd0.32 TiO3 and Ca0.43 Nd0.38 TiO3 ceramics indexed on the basis of the monoclinic C2/m structure, suggesting that the ordering is either weak or absent in these structures. 3.3. Microwave dielectric properties Fig. 8 and Table 2 summarise the microwave dielectric properties of Ca(1−x) Nd2x/3 TiO3 , as a function of composition. The relative permittivity falls rapidly from 180 for CaTiO3 to 80 for Ca0.3 Nd0.2 TiO3 and then there is very limited change in εr to Ca0.1 Nd0.6 TiO3 . The Q × f values of the ceramics follow a different trend, rising from 6000 GHz for CaTiO3 to 13000 GHz

0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Composition (x) Fig. 8. Microwave dielectric properties of Ca(1−x) Nd2x/3 TiO3 as a function of composition: temperature coefficient of resonant frequency (τ f ), Q × f and εr .

for Ca0.7 Nd0.20 TiO3 and subsequently falling to 1000 GHz for Ca0.1 Nd0.6 TiO3 . For τ f there is an approximately linear variation with composition, falling from +800 ppm K−1 at x = 0 (CaTiO3 ) to +200 ppm K−1 at x = 0.48 (Ca0.52 Nd0.32 TiO3 ); τ f could not be determined for compositions richer in Nd because of the low Q × f values. Our microwave dielectric data are in excellent agreement with the published data for this system.6,7 There are however some interesting similarities and differences from the trends occurring in other rare earth, cation deficient microwave dielectric ceramics. Ca(1−x) Sm2x/3 TiO3 shows a similar Q × f peak as a function of composition8 whilst Ca(1−x) La2x/3 TiO3 shows no such peak in Q × f9 and Q × f remains high after the initial increase. For all three rare earth (Nd, La and Sm) substitutions, Q × f increases remarkably from 6000 GHz to values as high as 15,000 GHz. The mechanism for this is not yet well understood yet as the factors controlling the Q × f values of Ca(1−x) Nd2x/3 TiO3 ceramics are complex.7 From a microstructural perspective, porosity can affect the Q × f value because the presence of pores will modify lattice vibrations. However, except for increasing overall dielectric losses, porosity is not expected to have any significant impact on Q × f values here as all densities were at least 95% theoretical and did not vary by more than a few percent. Similarly, there was limited variation in the average grain size (Fig. 2) and so it is unlikely that grain size variation would have had a significant effect on Q × f values.35 Samples with x ≥ 0.39 were shown to exhibit discontinuous grain growth (DGG); it has been reported that this phenomena can cause rapid decreases in the Q × f value of columbite niobates with no significant change in εr or density.26 The very largest grains (and extent of DGG) were observed in samples of x = 0.48, and the transition from x = 0.39 to x = 0.48 coincides with a rapid fall in Q × f values and the anomalous fall in the width of domains. From changes in lattice parameters it is inferred that the

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Table 2 Microwave dielectric properties of Ca(1−x) Nd2x/3 TiO3 ceramics. x

εr Q × f (GHz) τ f (ppm K−1 )

0

0.21

0.3

0.39

0.48

0.57

0.9

180 5900 770

101 8000 –

79.7 13,000 295

87.5 12,400 242

82.8 7850 200

96.7 3140 –

78 1000 –

transition from Pbnm to C2/m also occurs in this composition range. Together these indicate that local structure can play an important role in controlling Q × f values. Ohsato et al.36 found that the symmetry of the structure had a strong effect on the Q × f values of (Mg(1−x) Nix )2 Al4 Si5 O18 ceramics, leading to significant improvements in the Q × f over a short range of composition. The increase in Q × f was attributed to an increase in the unit cell symmetry, whilst subsequent falls in Q × f were associated with the development of NiAl2 O4 secondary phase. It is possible that the microwave properties Ca(1−x) Nd2x/3 TiO3 are affected by subtle changes of structure or symmetry. In related systems it has been found that secondary phases adversely affect the Q × f values of rare earth, cation deficient ceramics, particularly where the secondary phases have lower Q × f values than the primary phase. Suvorov et al.13 found that the Q × f value of La2/3 TiO3 stabilised by LaAlO3 increased with the amount of LaAlO3 in the formulation. They attributed the change in Q × f values to the reduction in the amount of the secondary phases of La2 Ti2 O7 and La4 Ti9 O24 . However, in the present investigation none of the analogous phases Nd2 Ti2 O7 or Nd4 Ti9 O24 (or TiO2 ) were detected by X-ray diffraction. There is much evidence to suggest that dielectric Q × f values of microwave dielectric ceramics are sensitive to cation ordering, particularly for complex perovskite structured materials; frequently Q × f values increase with cation ordering.37,38 However, for the current Ca(1−x) Nd2x/3 TiO3 there was no evidence of cation-vacancy ordering in the X-ray diffraction analysis (except for Ca0.1 Nd0.6 TiO3 ), and therefore no evidence of cation ordering in the ceramics exhibiting the highest Q × f values (Fig. 5). It is interesting to note that Ca(1−x) Nd2x/3 TiO3 is an example where ordering does not automatically lead to optimal Q × f values. This contrasts with the behaviour in related systems such as Ca(1−x) La2x/3 TiO3 where the highest Q × f values coincide with the highest degree of ordering.9,31 There is no documentary evidence of ordering in Ca(1−x) Sm2x/3 TiO3 . One further structural factor which may have a significant effect on the Q × f values of Ca(1−x) Nd2x/3 TiO3 is the change in the domain morphology as a function of composition. The development of complex domain structures within individual grains can enhance the scattering of phonons and increase dielectric losses. Evidence to support this assertion for microwave dielectric systems comes from the work of Lowe on CaTiO3 .28 He measured the domain density in ceramics cooled at different rates after sintering and found that for slow cooling (1 ◦ C/h) there was a high Q × f value (∼7000 GHz) and a low domain density, whereas the rapidly cooled samples had a lower Q × f value (5700 GHz) and a higher density of domains. Preliminary

analysis of the Ca(1−x) Nd2x/3 TiO3 ceramics suggests that specimens with higher Q values are associated with lower domain wall densities, but accurate quantification of such phenomena requires more detailed investigations. Initial studies of the La and Sm analogues (unpublished data) suggest that reductions in domain wall densities have similar effects on their Q × f values. Kim et al.8 collected infrared reflectivity spectra for the Ca(1−x) La2x/3 TiO3 system and concluded that the substitution of Sm3+ for Ca2+ affected the vibration modes resulting in decreased dielectric loss. There is no comparable published reflectivity data for the Nd and La analogues to test the generality of this observation. The interpretations of the permittivity and τ f data are relatively straightforward in that the properties show a strong dependence on composition over at least parts of the composition range. Although the phase stability of Nd2/3 TiO3 ceramics prohibits the direct measurement of the relative permittivity for this composition, it is possible to estimate the value from other ceramics in the same compositional series. The relative permittivity data was fitted using an exponential function and the relative permittivity of Nd2/3 TiO3 was estimated from this function. On this basis the relative permittivity and τ f were predicted to have values of approximately 79 and 40 ppm K−1 respectively. It is anticipated that the trends in τ f are related to distortion of the crystal lattice in response to changes in the charge and size ions substituted in the A site. The Goldschmidt tolerance factor can be used to quantitatively explore the degree of distortion of the perovskite unit cell.39 For Ca(1−x) Nd2x/3 TiO3 , the tolerance factor decreases from 0.996 for CaTiO3 to 0.792 for Ca0.1 Nd0.6 TiO3 indicating that the structure becomes increasingly distorted. The structural phase transition that we have identified will have a significant impact on the τ f values. As there is loss of symmetry at the structural transition there will be an increase in the distortion of the structure, and this will tend to encourage reduction in τ f .

4. Conclusions High density (>95% theoretical), single phase Ca(1−x) Nd2x/3 TiO3 ceramics were prepared for compositions in the range 0.1 ≤ x ≤ 0.9. Grain sizes were in the range 1–100 ␮m, and all ceramics were characterised by complex domain structures which varied with composition from needle-like lamellae to triangular and quadrilateral shapes. Relative permittivity decreased from 180 to 78 and τ f decreased from +770 ppm K−1 to +200 ppm K−1 with increasing Nd substitution (increasing x value) across the composition range.

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Dielectric Q × f values varied in a grossly non-systematic way, peaking at 13,000 GHz for Ca0.7 Nd0.2 TiO3 . X-ray diffraction analysis showed that samples having compositions which were rich in Ca (typically x ≤ 0.39) could best be described by√an orthorhombic Pbnm structure based on a √ unit cell of a = 2ac , b = 2ac , c = 2ac . This was associated with a tilt system of a− a− c+ . In contrast, the structural data for ceramics rich in Nd (typically x ≥ 0.48) could best be fitted to a monoclinic C2/m space group, which was associated with the a− b◦ c− tilt system. It was inferred that a structural transition from Pbnm space group to C2/m space group occurred between Ca0 .61 Nd0 .26 TiO3 and Ca0.52 Nd0.32 TiO3 . There was very little evidence of cation ordering in any of the ceramics except for Ca0.1 Nd0.6 TiO3 . The structures of twin domain, within individual grains, depended on composition. In both end member compositions needle-like lamellae were dominant, but triangular and quadrilateral shaped domains were found in the intermediate compositions. The dielectric Q × f values depend on a combination of morphological factors. With no second phases, very limited variation in specimen density, and minimal evidence of superlattice peaks and cation ordering, it is inferred that the combination of (i) structural changes (from orthorhombic to monoclinic), (ii) domain structural changes (in terms of morphology, domain widths and possibly domain density), and (iii) the presence of discontinuous grain growth, are important factors controlling the losses in the Ca(1−x) Nd2x/3 TiO3 system. Acknowledgements The authors would like to thank Dr David Iddles of Powerwave Ceramics Division, Wolverhampton, UK for the supply of powders and for assistance in the measurements of the microwave dielectric properties. The EPSRC are thanked for financial support in the form of a doctoral training account (DTA) for RL. References 1. Vanderah TA. Talking ceramics. Science 2002;298:1182–4. 2. Freer R, Azough F. Microstructural engineering of microwave dielectric ceramics. J Eur Ceram Soc 2008;28:1433–41. 3. Kay HF, Bailey PC. Structure and properties of CaTiO3 . Acta Cryst 1957;10:219–26. 4. Nenasheva E, Mudroliubova LP, Kartenko NF. Microwave dielectric properties of CaTiO3 –LnMO3 system (Ln – La, Nd; M – Al, Ga). J Eur Ceram Soc 2003;23:2443–8. 5. Suvorov D, Valant M, Jancar B, Skapin SD. CaTiO3 -based ceramics: microstructural development and dielectric properties. Acta Chim Slov 2001;48:87–99. 6. Yoshida M, Hara N, Takada Seki A. Structure and dielectric properties of (Ca(1−x) Nd2x/3 )TiO3 . Jpn J Appl Phys 1997;36:6818–23. 7. Fu MS, Liu XQ, Chen XM. Structure and microwave dielectric characteristics of Ca(1−x) Nd2x/3 TiO3 . J Eur Ceram Soc 2008;28:585–90. 8. Kim WS, Kim ES, Yoon KH. Effects of Sm3+ substitution on the dielectric properties of Ca(1−x) Sm2x/3 TiO3 at microwave frequencies. J Am Ceram Soc 1999;82:2111–5. 9. Kim IS, Jung WH, Inaguma Nakamura T, Itoh M. Dielectric properties of A-site cation deficient perovskite type lanthanum calcium titanium oxide solid solution system [(1 − x)La2/3 TiO3 –CaTiO3 (0. 1–0.96)]. Mater Res Bull 1995;30:307–16.

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