Structural, microwave dielectric properties and dielectric resonator antenna studies of Sr(ZrxTi1−x)O3 ceramics

Journal of Alloys and Compounds 528 (2012) 126–134

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Structural, microwave dielectric properties and dielectric resonator antenna studies of Sr(Zrx Ti1−x )O3 ceramics S. Parida a , S.K. Rout a,∗ , V. Subramanian b , P.K. Barhai a , N. Gupta c , V.R. Gupta c a b c

Department of Applied Physics, Birla Institute of Technology, Mesra, Ranchi 835215, India Department of Physics, Indian Institute of Technology Madras, Chennai 600036, India Department of Electronics and Communication Engineering, BIT Mesra, Ranchi 835215, Jharkhand, India

a r t i c l e

i n f o

Article history: Received 16 February 2012 Received in revised form 6 March 2012 Accepted 11 March 2012 Available online 19 March 2012 Keywords: Powders X-ray diffraction Raman spectroscopy Ceramics Microwave dielectric properties Phase transformation Dieletric resonator antenna (DRA) High frequency structure simulator software (HFSS)

a b s t r a c t Compositionally induced phase transitions in the system Sr(Zrx Ti1−x )O3 were analyzed using a combination of X-ray diffraction, FT-Raman and FTIR spectroscopy. Sr(Zrx Ti1−x )O3 system showed at least two tilting of phase transitions, pm3m–I4mcm and I4/mcm–pnma. The structural transition occurred due to tilting of BO6 octahedra. Dielectric constant measured with Hakki–Coleman technique decreased from 253 to 25 with increase of Zr content. The value of  f found 1771 ppm/◦ C for SrTiO3 which decreased to −82 ppm/◦ C for the SrZrO3 . The dielectric resonator antenna (DRA) was investigated experimentally and numerically using a monopole antenna through an infinite ground plane and Ansoft’s high frequency structure simulator software, respectively. The required resonance frequency and bandwidth of DRA were investigated in the composition between 0 ≤ x ≤ 1.0. © 2012 Elsevier B.V. All rights reserved.

1. Introduction Due to the rapid development of technology the microwave region of the electromagnetic spectrum has been of special interest since a long time [1–3]. Day by day there is a strong increase in the demand for special dielectric materials (high dielectric constant and low loss) in the microelectronics industry as well as in shortand long-range communications [4]. Microwave dielectric materials play a key role in global society as they have a wide range of applications from terrestrial and satellite communications including, global positioning system (GPS), and direct-broadcast satellite (DBS) TV for environmental monitoring via satellites [5]. Recently progresses in microwave telecommunication, satellite broadcasting and intelligent transport systems (ITS) have resulted in an increasing demand for dielectric resonator antenna (DRA) [6]. Low dielectric constant (εr ) which minimizes cross-coupling with conductors and shortens the time for electronic signal transition [7], a high quality factor (Q × f), and a near-zero temperature coefficient of resonant frequency ( f ) are required for a microwave substrate and antenna application [8,9]. Many techniques have been developed for the measurement of material permittivity.

∗ Corresponding author. Tel.: +91 9471555277. E-mail addresses: [email protected], [email protected] (S.K. Rout). 0925-8388/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2012.03.047

Some general descriptions of those methods are provided in the literature [10,11]. Among these methods, the TE01␦ mode method is superior for the accurate measurement of a microwave dielectric constant of low loss materials with cylindrical shapes [12]. In recent years, the application of dielectric resonators as antennas in a microwave band has been extensively studied due to advantages such as light weight, low cost, small size and low profile [13–15]. DRA can be designed with different shapes to accommodate various design requirements. Moreover, DRA can also be excited with different feeding methods such as probes, microstrip lines, slots and co-planar lines [16]. Among the different DRA shapes, cylindrical DRA offers greater design flexibility where the ratio between the radius to height (a/h) controls the resonance frequency, the quality factor (Qf ) and bandwidth of antennas [17,18]. Ceramic materials with perovskite-type structures have a varied property that makes them applicable in displays, electronic/piezoelectric devices, sensors, actuators, transducers, wireless communications, etc. [19–21]. SrTiO3 and SrZrO3 are such materials that have been of recent interest of study. They have diverse technological application whether from integrated microelectronics or in electronic ceramic industry and microwave devices. These features are attributed by their high dielectric permittivity, tunability and low microwave loss high breakdown strength and low leakage current density [22–24].

S. Parida et al. / Journal of Alloys and Compounds 528 (2012) 126–134

Sr(Zrx Ti1−x )O3 is formed by the substitution of Ti4+ ions (atomic weight of 47.9 g/mol, ionic radius of 74.5 pm) by Zr4+ ions (atomic weight of 91.2 g/mol, atomic radius of 86 pm) at B-site of ABO3 perovskite [25,26]. Many fundamental research including elastic behavior and structural analysis of Sr(Zr,Ti)O3 ceramics have been already studied [27]. An even ultra wide range dielectric spectrum from kHz to THz has already been discussed using IR-reflective method [28]. Though much work has been done on microwave properties of Sr(Zrx Ti1−x )O3 series. However, their application as DRA has not been explored. Here, we make an effort to report on the structural analysis, and microwave dielectric properties Sr(Zrx Ti1−x )O3 ceramics prepared by a solid state reaction method that will hopefully support the recent researches being carried out in this field. 2. Experimental and computational details

mode. The relative dielectric constant and loss factors were calculated from the following formula (2) [18]:



εr = 1 +

tan ı =

The compounds were mixed in an agate mortar stoichiometrically to obtain a homogeneous mixture followed by heat-treatment, with intermediate grinding and mixing, successively at 1400 ◦ C for 5 h and finally at 1450 ◦ C for 5 h. The calcined powders were then milled in liquid medium using a planetary ball milling unit (Pulverisette 5, FRITSCH Germany) in which the sun wheel and the grinding jar rotate in opposite directions. Milling was used with spherical agate balls and agate bowls rotating at a speed of 300 rpm of the sun wheel for 5 h. The ball to powder weight ratio was maintained as 10:1. The planetary ball mill was set to change the direction of rotation after each 30 min with a rest interval of 1 min. Finally milled powders were calcined at 1500 ◦ C for 5 h. The obtained powders were then dried and uniaxially pressed into pellets. The pellets of compositions from x = 0.0 to 0.4, from x = 0.5 to 0.6, from x = 0.7 to 0.8 and from x = 0.9 to 1.0 were sintered at 1550 ◦ C for 5 h, 1580 ◦ C for 5 h, 1610 ◦ C for 5 h and 1650 ◦ C for 5 h respectively. For all cases, a heating rate 5 ◦ C/min was employed followed by furnace cooling to room temperature. The bulk densities of the sintered pellets were determined by the Archimedes method and were found to be about 95% of their respective theoretical density.

2.2. Structural characterizations measurements The pellets were crushed and structurally characterized by using PANAlytical X’pert pro MPD in Bragg-Brentano geometry with an X’Celerator detector. XRD patterns were obtained using Cu K␣ radiation in the 2 range from 20◦ to 90◦ with a scanning rate of 0.02◦ min−1 and a step size of 0.017◦ . Raman studies were performed using STR500, Seki Technotron spectrometer with an excitation wavelength at 514.5 nm, from an Ar laser. The Fourier-infrared (FT-IR) absorption spectrum was recorded by the standard KBr pellet technique using FT-IR spectrometer (IR-Prestige 21, SHIMADZU, Japan). Morphological analyses of the sintered pellets were studied by using back scattered electron mode of scanning electron microscope (SEM; JEOL, Model: JSM-6390LV).

2.3. Microwave dielectric constant measurements The dielectric constants and unloaded Q values at microwave frequencies were measured using the TE01␦ resonance mode using the Hakki–Coleman [18] dielectric resonator method as modified and improved by Courtney [29]. These values were measured inserting the cylindrical pellets in a shielding cavity by Agilent PNA E8364B network analyzer in the transmission setup with a weak or moderate coupling [10,30]. In the TE01␦ method, the field confinement is not complete in the z direction and hence TE011 mode is designated as TE01␦ . This mode is widely used in materials property characterization because in this mode there is no current crossing the dielectric and the conducting plates, so possible air gaps between the dielectric and the conducting plates have no effects on resonance properties of this mode [31]. The theoretical model is properly described for the configuration mentioned by Courtney and as modified from Kobayashi and Tanaka [32]. The TE01␦ resonance mode has been found most suitable for the real part of the relative dielectric constant (εr ), and a gain/loss factor (tan ı) of the specimen was obtained from the measured resonance frequency (f1 ) and unloaded quality factor (Q0 ) for the TE01␦ resonance

(˛21 + ˇ12 )

(2)

A − BRs Qu

(3)

W εr

(4)

A=1+

 3 l 2L

B=

1+W 302 εr l

(5)

J12 (˛1 ) K0 (ˇ1 )K2 (ˇ1 ) − K12 (ˇ1 )

(6)

K12 (ˇ1 ) J12 (˛1 ) − J0 (˛1 )J2 (˛1 )



(1)



where

2.1. Synthesis of Sr(Zrx Ti1−x )O3 ceramic by solid state reaction

SrCO3 + xZrO2 + (1 − x)TiO2 → Sr(Zrx Ti1−x )O3 + CO2

c Df1

where c is the velocity of light, ˛1 is given by the mode chart [18] and ˇ1 is obtained from the resonance frequency (f1 ) and the sample dimension. The tan ı is given by Hakki–Coleman [18] as described in Eq. (3):

W=

Sr(Zrx Ti1−x )O3 ceramics were prepared by solid state reaction method. In this synthesis method, strontium carbonate (SrCO3 ) (99.9%, S.D. Fine-Chemical Limited), titanium oxide (TiO2 ) (99.0%, Merck) and zirconium oxide (ZrO2 ) (99.0%, Himedia Laboratories, Mumbai) were used as raw materials. Formation of these compounds occurs by the inter diffusion process at high temperature, according to chemical reaction presented in Eq. (1):

127

Rs =

f1  

(7)

The function W is the ratio of electric field energy stored on the outside of the rod to the energy inside the rod. The  is the free space wavelength and L is the length of the dielectric specimen. The  is the conductivity of the shorting plate, and Q0 is the unloaded quality factor of the dielectric resonator. If the dielectric material is isotropic then the characteristic equation for such a resonance structure for the TE01␦ mode is given by Eq. (8) ˛

K0 (ˇ) J0 (˛) = −ˇ J1 (˛) K1 (ˇ)

(8)

where J0 (˛) and J1 (˛) are the Bessel functions of the first kind of order zero and one, respectively. K0 (ˇ) and K1 (ˇ) are the modified Bessel functions of the second kind of orders zero and one, respectively. A method for the experimental determination of Rs is given in Ref. [33] which employs on two rod samples cut from the same dielectric rod with equal diameters but different lengths. The expression of Rs is given by

 3

Rs = 302

2L l

εr + W l 1+W l−1



1 1 − Q01 Q0l



(9)

Then substitution of Eq. (9) into Eq. (3) yields: tan ı =

A l−1



1 l − Q0l Q01



(10)

This calculation facilitates the precise measurement of (tan ı). Temperature coefficients of the dielectric resonator were measured using a temperature controlled hot plate in the temperature range from 40 ◦ C to 70 ◦ C using the equation below

 

f =

1 f

f T



(11)

where f/ T is the resonance frequency change with respect to temperature. 2.4. Dielectric resonator antenna (DRA) measurements An Agilent PNA E8364B network analyzer was employed to make the measurements of DRAs. In an experiment introduced by Long et al. [34], the DRAs were excited by a wire antenna above a ground plane. Similar configuration is employed in the present investigation for study of Sr(Zrx Ti1−x )O3 ceramic antenna and is shown in Fig. 1 As shown in Fig. 1, each cylindrical (a/h ≈ 1.11) DRA was placed on a conducting ground plane (copper conductor of size 5 cm × 5 cm × 2 mm) and excited by a coaxial probe (length = 5 mm). The probe is located on the x-axis at x = a and ϕ = 0. In practical basis, locating the probe feed adjacent to the DRA is preferred since it does not required drilling into the DRA and again the probe adjacent to the DRA can excite HE11␦ mode which is the basis mode for cylindrical DRA. The coaxial probe goes through the ground plane and was connected to a SMA connector. Since the cylindrical DRA works at the HE11␦ mode whose resonant frequency f0 can be approximated as [35] 2.007 f0 = √ 20 εr



1.184 a

2   2  +

2h

GHz

(12)

Eq. (12) is obtained with the hypothesis that the lateral and upper surfaces of the DRA are perfectly magnetic conductors (PMC). This assumption can be verified only for a sample with an infinite permittivity. Therefore, Eq. (12) is the only approximation that leads to an error around 10% [36].

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S. Parida et al. / Journal of Alloys and Compounds 528 (2012) 126–134

Fig. 1. The geometry of cylindrical DRA.

A comparison of the values from Eq. (12) to the following closed form of expression for the HE11␦ resonant frequency published in Refs. [37,38] are interesting (see Eq. (13)):



6.324c



f0 =

2a

0.27 + 0.36

2 + εr

 a 2 a + 0.02 2h 2h



GHz

(13)

where h and a are the height and radius of DRA respectively. The f0 is called as resonant frequency given in GHz. Radiation Q-factor of the isolated cylindrical DRA can be written as per Eq. (14) and the bandwidth (return loss < −10 dB) is calculated as given in Ref. [39]. Similar calculations were also employed in earlier literatures [17,40,41]. Qrad =

a 1.2 ε 2h r



0.01893 + 2.925e

−2.08 a



2h

1−0.08 a



2h

(14)

2.5. Numerical simulation The characteristic of designed dielectric resonator antenna has been simulated using high frequency structure simulator (HFSS) based upon the finite element method (FEM), which characterizes the 3D designs. The variation of return loss versus frequency and far field radiation patterns of the DRA are determined experimentally and compared with the simulated results. It is important to note that both experimental and simulation results show a great variability of the results according to the probe. This problem, that finds its origin in the presence of air gap between the DR and the metallic conductors, have been thoroughly studied by Junker et al. [42,43].

radii Ti4+ by the higher radii Zr4+ ions. It is reported that the composition Sr(Zr0.05 Ti0.95 )O3 of space group I4/mcm illustrates the existence of tetragonal phase [44]. From Fig. 1(b), it is observed that the peak (1 1 2) is splitted into (3 2 1) and (2 4 0) in the composition x = 0.1 which confirms the existence of tetragonal phase. This splitting of peaks continues upto the composition x = 0.5. When percentage of Zr is increased to 60%, the two peaks (3 2 1) and (2 4 0) splits into (3 2 1), (2 4 0) and (1 2 3) which confirms the formation of orthorhombic phase in the compositions. The orthorhombic phase with space group pnma was also observed in the composition Sr(Zr0.6 Ti04. )O3 by Wong et al. [44]. With further increase of Zr content, these three peaks to becomes prominent suggesting the development of orthorhombic phase and become strongest at the compositions x = 1.0. The composition x = 1.0 (SrZrO3 ) is in good agreement with JCPDF card no-70-0283. This type of compositionally induced structural transition from cubic through tetragonal to orthorhombic structure is mainly due to the tilting of the BO6 (B = Ti or Zr) octahedra. Wong et al. [44] reported that, the interoctahedral B O B angles gradually decrease as the Zr content is increased, indicating the formation of more disorder structure. Hence in this case it can be a result of increase of the tilting of BO6 octahedra at higher Zr content. The tilt of angles may be increased suddenly with just only 10% substitution of Zr content in the Ti site causing the splitting of peak in the x = 0.1 composition. This type of distortion increases steadily as the amount of Zr content in the sample is increased, leading to an orthorhombic phase. Fig. 3 shows the FT-Raman spectra of Sr(Zrx Ti1−x )O3 powders with different ‘x’ compositions in the frequency range 150–800 cm−1 . Generally the 1:1 B site ordering is reported in cubic structure of space group pm3m [45]. This perovskite structure has 5 atoms per unit cell, therefore, there are 12 optical vibration modes. In the cubic phase, the zone center optical phonons belong to 3F1u + F2u irreducible representations. Each of the F1u modes is triply degenerate and infrared active, while the F2u modes are Raman active [46]. opt = 3F1u (IR active) + 1F2u (Raman active) Splitting in modes is resulted for any change in symmetry of the material. The IR active modes break into (A1 + E) modes and the Raman active modes break up into (B1 + E) modes. opt = 3(A1 + E)(IR active) + 1(B1 + E)(Raman active)

3. Results and discussion opt = 3A1 (IR active) + 1(B1 )(Raman active) Fig. 2(a and b) shows the XRD patterns of the Sr(Zrx Ti1−x )O3 powders with different (x) compositions. According to the XRD patterns, all diffraction peaks correspond to the perovskite structure. The Sr(Zrx Ti1−x )O3 powders with x = 0.0 compositions is indexed as cubic with space group Pm3m. This is in good agreement with JCPDF card no-73-0661. Increase of Zr content into SrTiO3 lattice promotes an increase in lattice parameters and unit cell volume as illustrated in Table 1. This is due to the replacement of lower

+ 4E(Raman and IR active) According to the group theory calculation no first order Raman active modes are possible in materials with cubic symmetry [47]. It is reported [48,49] that SrTiO3 shows an ideal cubic perovskite structure with space group pm3m because of odd symmetry of all the zone-center optical phonons produce in the lattice. Therefore

Table 1 Details of lattice parameter and cell volume calculated from the XRD patterns using CCPI4 program “check cell”. Sr(Zrx Ti1−x )O3

a (nm)

b (nm)

c (nm)

Cell volume (nm3 )

Symmetry and Space group

x = 0.0 x = 0.1 x = 0.2 x = 0.3 x = 0.4 x = 0.5 x = 0.6 x = 0.7 x = 0.8 x = 0.9 x = 1.0

0.39035 0.55537 0.55825 0.56218 0.56313 0.56782 0.56864 0.57091 0.57496 0.57402 0.58045

0.39035 0.55537 0.55825 0.56218 0.56313 0.56782 0.57096 0.57253 0.57621 0.57801 0.58206

0.39035 0.78295 0.78682 0.79370 0.79329 0.79982 0.80472 0.81022 0.81122 0.81144 0.81949

0.05947 0.24148 0.24520 0.25084 0.25156 0.25787 0.26124 0.26483 0.26875 0.26922 0.27687

Cubic (pm3m) Tetragonal (I4/mcm)

Orthorhombic (pnma)

S. Parida et al. / Journal of Alloys and Compounds 528 (2012) 126–134

129

Fig. 2. (a) XRD patterns of Sr(Ti1−x Zrx )3 powders (b) XRD patterns show the compositionally induced phase transition.

no first-order Raman activity is expected on the basis of factor group symmetry analysis, only the second-order scattering is observed at room temperature. From Fig. 3 it is observed that the phonons of SrTiO3 are dominated by two strong and broad second-order Raman bands at 200–500 cm−1 and 600–750 cm−1 which are in agreement with literature [50,51]. The optical phonon bands of SrTiO3 are observed near 181 cm−1 corresponding to TO2 LO1 band. This band is associated with the active vibrational modes of F1u and is mainly due to the translations vibration of Sr2+ against TiO6 octahedra [52]. P. A. Fleury et al. [53] reported that the activation of the six R-zone corner phonons (A2u + Eu + 2F1u + F2u + F2g ) due to the folding of the cubic Brillouin zone lead to a seven Raman active modes A1g + B1g + 2B2g + 3Eg of tetragonal phase. Wong et al. [44] reported that the cubic–tetragonal phase transition occurs in the composition range 0 ≤ x ≤ 0.05. This phase transition actually occurs due to the R point instability in cubic Brillouin zone which leads to a tetragonal structure I4/mcm (D4h 18 ). When transition takes place from cubic to tetragonal, Raman inactive F1u softmode

of cubic phase becomes the 1st order Raman scattering of A1g and Eg modes and the so called silent mode F2u transforms to the Eg + B1g mode [54] and along with that B2g mode is also observed. With 10% adding of Zr content on B-site of SrTiO3 , three basic modes B1g , B2g and Eg which are the signature of tetragonal phase [49,55,56] are observed near 240 cm−1 , 454 cm−1 and 505 cm−1 respectively (see Table 2). This confirms the existence of tetragonal phase in x = 0.1 composition. These three modes are observed clearly upto the composition x = 0.5 confirming the presence of tetragonal phases in the powders. The presence of mode Eg in compositions 0.1 ≤ x ≤ 0.5 would imply the presence of anti-phase tilted TiO6 and ZrO6 octahedra in the powders [56]. The weak band TO3 has also been identified (see Table 2) in the composition between x = 0.1 and x = 0.5 indicating the presence of long-range lattice distortion in the powders. This type of phenomenon is also reported in literature [57]. For the orthorhombic structure (pnma), 24 irreducible Raman active phonon modes (7Ag + 5B1g + 7B2g + 5B3g ) are observed [58,59]. When transition takes place from tetragonal to

784.11

S. Parida et al. / Journal of Alloys and Compounds 528 (2012) 126–134

635.69 671.21 663.41 370.9 333.07 333.65 337.11 338.56 313.72 284.27 284.27 284.27

B2g 426.63 426.23 418.83 417.39 414.21 Ag B3g B2g

Ag 162.14 162.41 163.86 165.30 169.92 x = 0.6 x = 0.7 x = 0.8 x = 0.9 x = 1.0

Ag Raman frequency shift (cm−1 ) Compositions

x = 0.0

Orthorhombic

Ag

208.6

B1g 222.47 185.22 228.83 240.95 250.48

TO2 175.22 176.27 179.45 179.45 183.85 Tetragonal x = 0.1 x = 0.2 x = 0.3 x = 0.4 x = 0.5

B1g 240.95 233.45 231.71 232.00 237.16 Raman frequency shift (cm−1 ) Compositions

No Raman active mode is being observed Cubic

Raman frequency shift (cm−1 ) Compositions

Table 2 Raman shifts of Sr(Zrx Ti1−x )O3 compounds of their cubic (pm3m) tetragonal (I4/mcm) and orthorhombic (pnma) structures.

B3g 491.60 476.01 446.84 445.11 443.46

Ag 508.64 511.81 476.29 477.45 488.71

TO3 293.51 275.03 276.76 279.94 289.67

B1g

572.86 564.37 558.30

Ag

609.12

B2g

Eg 505.17 505.46 508.64 507.19 510.10

Ag

685.07 694.31 691.13

B1g

723.7

B2g 774.87 769.96 753.22 740.80 757.84

B2g 454.35 429.80 434.14 431.25 429.60

B1g

130

Fig. 3. The FT-Raman spectra of the Sr(Zrx Ti1−x )O3 powders with increase of Zr content.

orthorhombic phase, the degenerate Eg phonons splits into nondegenerate B2g + B3g phonons and annihilates some Ag phonons. As a result number of phonon modes increase to 24 irreducible Raman modes. This increase of phonons might be attributed to doubling of formula units per primitive unit cell (Z = 2 for I4/mcm and Z = 4 for pnma space group) [56,60] and the additional phonons condensations of the X- and M- boundry points of the primitive cubic perovskite Brillouin zone [61]. The splitting of Eg band (Table 2) into B3g and Ag is observed in composition x = 0.6 confirms the transition from tetragonal to orthorhombic phase [56]. With increase of Zr content the intensity of the B3g and Ag gradually increases alongwith evolvement of orthorhombic phase. The Raman spectrum of SrZrO3 shows a number of sharp peaks superimposed on a broad band between 100 and 750 cm−1 . The observed frequencies of Raman modes and their assignments are obtained by comparing with those reported in the literature [62] and are given in Table 2. Fewer bands are observed in the Raman spectra possibly due to peak overlap or very low polarizability. The transition of Sr(Zrx Ti1−x )O3 from pm3m through I4/mcm to pnma may involve the rotation of the octahedra and thus the metal oxygen bond distances are expected to change systematically with change in composition.

S. Parida et al. / Journal of Alloys and Compounds 528 (2012) 126–134

Fig. 4. FT-IR spectrum of Sr(Zrx Ti1−x )O3 powders prepared by solid state reaction. The inset shows the variation of wave number with of x component.

Fig. 4 shows the FTIR spectra of Sr(Zrx Ti1−x )O3 powders. In the spectrum of SrTiO3 , the broad and strong absorption band observed around 610 cm−1 can be assigned to Ti O stretching normal vibration of TiO6 octahedra, while the weaker and sharper peak at around 412 cm−1 can be attributed to Ti O bending normal vibration [63,64]. From Fig. 3 it can be observed that the absorption bands shift toward lower wave number with increase of Zr content (inset of fig. 3). This shifting of peaks toward higher or lower wave number can be correlated with the formation of shorter and stronger M O bonds in the ceramic [26]. Shifting of absorption peaks toward lower wave number with increase of Zr substitution can be attributed to change of lattice parameter, as radius of Ti4+ is smaller than that of Zr4+ . Since the distance between Ti4+ and O2 2− is smaller than the distance between Zr4+ and O2 2− so the interaction between Ti O becomes stronger than that of Zr O. Therefore the bond strength of Zr O is smaller than Ti O. Likewise increase of zirconium content, which induces more O-vacancies, promotes shifting of peaks toward lesser wave number gradually. The composition x = 1.0 (SrZrO3 ) shows absorption peak at 572 cm−1 [65].

131

This absorption peak is due to the Zr O stretching vibration in SrZrO3 [66]. It may be due to the change in lattice parameter in perovskite structure. When Zr content is increased gradually, M O bond energy gets lowered in the perovskite. This may be due to the systematic change in metal oxygen bond distance during the phase transition from pm3m through I4/mcm to pnma, which results in decrease of force constant for which the absorption band is shifted toward lower wave number. Fig. 5 shows the representative scanning electron microscopic (SEM) images of some selected compositions. It shows grains of different sizes homogeneously distributed. The observed difference in grain sizes may be due to structural disorder, strain developed in the lattice due to different ionic radii and/or cluster in the particles incorporated at the B site. The diffusion rate of the two ions at the B site is different which results in differently sized grain growth. Probably this is the reason behind the local disorder in the system. Table 3 contain εr (permittivity),  f (temperature coefficient at resonant frequency), Q × f and tan ı (loss tangent) values of Sr(Zrx Ti1−x )O3 series. The permittivity of SrTiO3 was measured to be 253 which is quite close to that reported in literature [62]. Tsurumi et al. [28] reported that the permittivity of SrTiO3 is mainly due to ionic polarization rather than dipolar polarization at room temperature. The permittivity of SrTiO3 single crystal is 320 [28], slightly higher than that of the measured SrTiO3 ceramic in this case. This obvious reduction of permittivity is mainly due to presence of pores and defects in the ceramic samples. In the Sr(Zrx Ti1−x )O3 solid solution, Ti and Zr ions are randomly distributed at the B-site of the perovskite structure which inhibits the in-phase motion of cations. The contribution of electronic and dipolar polarization are quite small in this system and the decrease in permittivity from x = 0.0 (SrTiO3 ) to x = 1.0 (SrZrO3 ) is due to the decrease in ionic polarization [28]. The value of εr in SrZrO3 was found to be slightly less than those already reported in Ref. [67]. This may be due to the insertion loss in the samples. With increase in Zr content Q × f values decreases up to the composition x = 0.1, then increases at x = 0.2, again decreases gradually up to the composition x = 0.4 and finally increases from composition x = 0.5 to x = 1.0. This type of variation in Q × f values is attributed to the inhomogeneous grain growth in the ceramic samples. When the Zr content is increased, temperature coefficient at resonant frequency ( f ) value changes from 1771 ppm/◦ C to −82 ppm/◦ C. The values of  f of SrTiO3 and SrZrO3 are quite close to those reported [68]. The decrease of temperature coefficient at resonant frequency ( f ) from x = 0.0 (SrTiO3 ) to x = 1.0 (SrZrO3 ) can also be attributed to decrease in ionic polarizability. This may be due to the systematic changes of octahedral in the structure [69]. Variation and loss in microwave dielectric properties is caused not only by the lattice vibrational modes, but also by the pores, impurities, lattice defects or secondary phases present in

Table 3 Microwave dielectric properties of sintered Sr(Zrx Ti1−x )O3 samples. Compositions Sr(Ti1−x Zrx )O3

Frequency (GHz)

εr

Q×f

 f (ppm/◦ C)

x = 0.0 x = 0.1 x = 0.2 x = 0.3 x = 0.4 x = 0.5 x = 0.6 x = 0.7 x = 0.8 x = 0.9 x = 1.0

1.45 1.67 1.71 1.79 2.09 2.33 2.57 2.90 3.49 4.09 4.81

253 183 179 165 123 101 82 65 43 32 25

2013 1189 1511 1323 889 1051 1105 1218 1760 3639 11,646

1771 1655 1577 1312 819 567 478 405 331 113 −82

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Fig. 5. SEM micrographs of Sr(Zrx Ti1−x )O3 composite ceramic samples: (a) x = 0.0; (b) x = 0.3; (c) x = 0.7; (d) x = 1.0.

the samples, and any kind of phase change occurring in the material [70–72]. The results obtained from TE01␦ resonator method are used for the simulation of dielectric resonator antenna (DRA). The measured return loss and simulated return loss versus frequency of cylindrical dielectric resonator antennas are presented as Supplementary data (see Fig.SD-1). The estimated resonant frequency and Q-factor of Sr(Zrx Ti1−x )O3 DRA having different dimensions are calculated using Eqs. (13) and (14). The resonant frequency, Q-factor and bandwidth values are given in Table 4. The computed resonance frequency results obtained by HFSS simulations have been found to be in reasonably good agreement with experimental resonance frequency. The difference between experimental and simulated results may be attributed to variations in permittivity, manufacturing tolerance and the frequency excursion caused by the air gap between the probe, resonator and ground plane [73] (see Table 4). The resonance frequency of the antenna increases as the permittivity of the DRA decreases; similar behavior has been reported in the

literature [74]. Van Bladel [75] reported that Qrad is proportional to εr for dielectric resonators and is related as Qrad ˛εnr

(15)

where ‘n’ is the numerical value for HE11␦ mode. From Table 4 it is observed that the value of Qrad is gradually decreasing with decreasing of εr value. Smaller value of Qrad exhibits larger bandwidth as well as better broad side of radiation pattern (see Fig.SD-2; Supplementary data). The larger the bandwidth, the more coverage over the frequency space that can be utilized by the antenna. The relationship between the Q-factor and the bandwidth is given by Mongia and Bhartia [17] where the Q-factor is inversely related to the bandwidth (Table 4). The radiation characteristics of cylindrical DRA with a coaxial feed are obtained at different resonance frequencies for different composition (0 ≤ x ≤ 1.0) with different dielectric constant of Sr(Zrx Ti1−x )O3 ceramic (see Fig.SD2; Supplementary data).

Table 4 Characteristics of the cylindrical dielectric resonator antenna obtained from both experiment and simulation of different ‘x’ compositions. Sr(Zrx Ti1−x )O3

Radius (mm)

Height (mm)

εr

Experimental frequency (GHz)

Simulated frequency [HFSS](GHz)

Estimated frequency

Error [HFSS](%)

Error theoretical frequency (%)

Q-factor

Band width (MHz)

x = 0.0 x = 0.1 x = 0.2 x = 0.3 x = 0.4 x = 0.5 x = 0.6 x = 0.7 x = 0.8 x = 0.9 x = 1.0

7.145 7.355 7.255 7.165 7.15 7.075 7.105 7.115 7.245 7.22 7.235

6.82 6.94 6.83 6.78 6.71 6.61 6.57 6.5 6.55 6.57 6.48

253 183 179 165 123 101 82 65 43 32 25

1.75 1.94 1.98 2.105 2.41 2.65 3.765 4.83 4.958 5.258 6.32

1.7 1.89 1.96 2.124 2.465 2.78 3.663 4.854 4.911 5.308 6.362

1.771 2.034 2.088 2.194 2.555 2.852 3.166 3.567 4.304 4.948 5.817

2.857 2.577 1.010 0.902 2.282 4.905 2.709 0.496 0.947 0.950 0.664

1.204 4.881 5.476 4.246 6.019 7.648 15.903 26.131 13.186 5.892 7.945

420.360 285.031 277.577 251.720 176.951 139.688 108.776 82.296 50.111 35.158 26.132

14 20 23 25 33 40 45 49 52 70 119

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The patterns are plotted in both an E-Plane (˚ = 0◦ ) and an H-Plane (˚ = 90◦ ) (experimental H-planes are almost omnidirectional). The ideal characteristics of an E-plane should resemble a half-wave dipole pattern parallel to the ground plane. In practice the feeding mechanism may excite more than one mode, so that the patterns differ from the ideal pattern. Moreover, simulation and experimental characteristics at different frequencies for different compositions having different dielectric constant show some back radiation in the lower half of the plane. The back radiation is more significant in experimental results than in simulated results due to the use of a finite ground plane used in the experimental setup. 4. Conclusion The structural and microwave dielectric properties of the Sr(Zrx Ti1−x )O3 system were investigated. XRD and Raman analysis confirmed the occurrence of phase transition for composition x = 0.1 and 0.6. For the composition x = 0.0 a cubic structure (pm3m), x = 0.1–0.5 a tetragonal structure and for x ≥ 0.6 an orthorhombic structure were observed. Moreover, the increase of Zr content into the lattice promoted an increase of lattice parameters and consequently in unit cell volume due to the higher radius of (Zr4+ ions) than that of (Ti4+ ions). In spite of that Raman and FTIR spectrum suggested a structural distortion with increase in Zr content. This is due to the rotation of the octahedra and change in metal–oxygen distance in the material. The SEM micrograph of sintered disc showed well defined grains and grain boundaries. The microwave dielectric constant and quality factor were measured by the method as proposed by Hakki–Coleman. The microwave dielectric constant decreased from 253 to 25 and the value of  f changed from 1771 ppm/◦ C to −82 ppm/◦ C. This type of variation was attributed to change in ionic polarizability. The variation in Q × f values was attributed to the inhomogeneous grain growth in the sample and phase changes in the material. Cylindrical DRAs have been investigated experimentally and numerically by taking advantage of the configuration of a monopole through an infinite ground plane and using Ansoft’s HFSS, respectively. DRA studies show that the resonance frequency and bandwidth depend upon the permittivity of the materials and can be applicable to different fields of communication. The measurements of DRAs confirm the use of such materials for small DRAs. Acknowledgment The authors are pleased to acknowledge Department of Science and Technology, Government of India, New Delhi, for providing financial support through SERC research grant no. SR/S2/CMP37/2007. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.jallcom.2012.03.047. References [1] J.R. Swanson, V.E. Rose, C.H. Powell, Am. Ind. Hyg. Assoc. J. 31 (1970) 623–629. [2] E.C. Niehenke, R.A. Pucel, I.J. Bahl, IEEE Trans. Microwave Theory Technol. 50 (2002) 846–857. [3] Y.C. Lee, K.W. Weng, W.H. Lee, Y.L. Huang, J. Ceram. Soc. Jpn. 117 (2009) 402–406. [4] U. Kaatze, Metrologia 47 (2010) S91–S113. [5] L. Bin, J.F. Aujol, Y. Gousseau, S. Ladjal, H. Maitre, IEEE Trans. Image Process. 16 (2007) 2503–2514. [6] J. Bian, Z. Liang, L. Wang, J. Am. Ceram. Soc. 94 (2011) 1447–1453. [7] Y. Ohishi, Y. Miyauchi, H. Ohsato, K. Kakimoto, Jpn. J. Appl. Phys. 43 (2004) L749–L751.

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