Using JPF1 format

Electrical and structural characteristics of lanthanum-doped barium titanate ceramics Finlay D. Morrison, Derek C. Sinclair, and Anthony R. West Citation: Journal of Applied Physics 86, 6355 (1999); doi: 10.1063/1.371698 View online: http://dx.doi.org/10.1063/1.371698 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/86/11?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Grain growth kinetics and electrical properties of lanthanum modified lead zirconate titanate (9/65/35) based ferroelectric ceramics J. Appl. Phys. 105, 014110 (2009); 10.1063/1.3063693 Direct observation of potential barriers in semiconducting barium titanate by electric force microscopy J. Appl. Phys. 100, 104501 (2006); 10.1063/1.2382454 Dielectric properties of barium titanate ceramics doped by B 2 O 3 vapor J. Appl. Phys. 96, 6937 (2004); 10.1063/1.1814167 Relaxor properties of lanthanum-doped bismuth layer-structured ferroelectrics J. Appl. Phys. 96, 5697 (2004); 10.1063/1.1807029 Microstructure and dielectric properties of Mg-doped barium strontium titanate ceramics J. Appl. Phys. 95, 1382 (2004); 10.1063/1.1636263

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JOURNAL OF APPLIED PHYSICS

VOLUME 86, NUMBER 11

1 DECEMBER 1999

Electrical and structural characteristics of lanthanum-doped barium titanate ceramics Finlay D. Morrison,a) Derek C. Sinclair, and Anthony R. West Department of Engineering Materials, University of Sheffield, Sheffield, S1 3JD, United Kingdom

共Received 30 April 1999; accepted for publication 27 August 1999兲 Single phase La-doped BaTiO3 with the formula Ba1⫺x Lax Ti1⫺x/4O3: 0⭐x⭐0.20 was prepared by solid state reaction of oxide mixtures at 1350 °C, 3 days, in O2. The tetragonal distortion in undoped BaTiO3 decreased with x and samples were cubic for x⭓0.05. Both the tetragonal/cubic and orthorhombic/tetragonal transition temperatures decreased with x, but at different rates, and appeared to coalesce at x⬃0.08. The value of the permittivity maximum at the tetragonal/cubic phase transition in ceramic samples increased from ⬃10 000 for x⫽0 at 130 °C to ⬃25 000 for x⫽0.06 at ⬃⫺9 °C. At larger x, the permittivity maximum broadened, showed ‘‘relaxor’’-type frequency dependent permittivity characteristics and continued to move to lower temperatures. Samples fired in O2 were insulating and showed no signs of donor doping whereas air-fired samples were semiconducting, attributable to oxygen loss. © 1999 American Institute of Physics. 关S0021-8979共99兲04423-0兴

T c ⫺T 0 ⫽0. In addition to the order of the phase transition, several other factors have been shown to affect T c ⫺T 0 , including porosity, grain size, and poorly defined grain boundary regions.5–9 Porosity and poorly defined grain boundary regions which exhibit low capacitance are also reported to affect C W , 5,7 whereas grain size does not.7,9 Smolenskii2 also observed that the deviation from Curie–Weiss-like behavior exhibited by ferroelectrics with diffuse phase transitions obeyed a quadratic equation

INTRODUCTION

Tetragonal barium titanate, BaTiO3 is a ferroelectric perovskite at room temperature which exhibits high permittivity, ⑀ ⬘ , making it a desirable material for capacitor applications. On heating, it undergoes a ferroelectric/paraelectric phase transition to the cubic polymorph at a Curie temperature, T c , of ⬃130 °C, at which ⑀⬘ passes through a maxi⬘ , and typically reaches values of ⬃10 000 in unmum, ⑀ max doped ceramic samples. The phase transition is first order,1 and the peak in ⑀⬘ is correspondingly sharp. In the paraelectric state above T c , ⑀ ⬘ of undoped BaTiO3 follows a temperature dependence described by the Curie–Weiss law

⑀ ⬘ ⫽C W / 共 T⫺T 0 兲 ,

1/⑀ ⬘ ⫽A⫹B 共 T⫺T c 兲 2 ,

⬘ and B⫽1/2⑀ max ⬘ ␦, where ␦ is a parameter where A⫽1/⑀ max describing the degree of diffuseness of the phase transition. Uchino and Nomura,10 however, reported that not all diffuse phase transitions obey this relationship exactly, and developed Eq. 共2兲 into a more general expression, viz.

共1兲

where C W is the Curie constant and T 0 is the Curie–Weiss temperature. Many classic ferroelectric materials obey Curie–Weiss behavior in the paraelectric state. For undoped BaTiO3, T 0 is typically ⬃8 – 10 °C lower than T c . Some ⬘ behavferroelectric perovskites, however, exhibit broad ⑀ max ior as a function of temperature, and show deviations from the Curie–Weiss law at temperatures just above T c . 2,3 The most common group of ferroelectric perovskites which exhibit such, so-called diffuse phase transitions are Pb-based ‘‘relaxor’’-type materials, such as Pb共Mg1/3Nb2/3兲O3. These deviations from the Curie–Weiss law close to T c result in a change in the temperature difference between T c and T 0 , whereby T 0 can be significantly higher than T c . In addition, relaxor-type materials exhibit frequency dependent ␧⬘ values below T c . 4 Smolenskii2 suggested that the degree of deviation, T c ⫺T 0 , indicates the order of transition; T c ⫺T 0 ⬎0 indicates a first order transition and sharp d ⑀ ⬘ /dT profiles close to T c ⬘ peak, whereas, for second order transitions with a broad ⑀ max

1 ␧⬘

⫺

1

⬘ ␧ max

⫽

共 T⫺T c 兲 ␥

c⬘

,

共3兲

where c⬘ and ␥ are constants and 1⭐ ␥ ⭐2. The limiting values of ␥ relate to the Curie–Weiss law, Eq. 共1兲, for ␥ ⫽1, and Smolenskii’s quadratic expression, Eq. 共3兲, for ␥ ⫽2. A physical interpretation of the temperature dependence of paraelectric data which exhibit deviations from conventional Curie–Weiss behavior, however, has not been made. For many years A- and B-site dopants have been used to modify the electrical properties of BaTiO3-based ceramics. For example, isovalent dopants are commonly used to alter T c and the lower temperature orthorhombic/tetragonal (o/t) and rhombohedral/orthorhombic (r/o) phase transition temperatures, hereafter referred to as T o/t and T r/o , respectively. ⬘ and In this way, either or both the temperature of ⑀ max d ⑀ ⬘ /dT may be modified and in some cases lead to diffuse phase transition-type behavior. The effect of some common A- and B-site isovalent dopants on the phase transition temperatures are summarized in

a兲

Electronic mail: [email protected]

0021-8979/99/86(11)/6355/12/$15.00

共2兲

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© 1999 American Institute of Physics


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J. Appl. Phys., Vol. 86, No. 11, 1 December 1999

FIG. 1. Effect of several substitutions on the temperatures of 共in order of increasing temperature兲 the rhombohedral/orthorhombic, orthorhombic/ tetragonal, and tetragonal/cubic phase transitions in ceramic BaTiO3. Adapted from Ref. 11.

2⫹

Fig. 1. A-site doping with Sr decreases both T c and T o/t whereas T r/o is unaffected. T c increases linearly with Pb2⫹ substitution, however Ca2⫹ doping has a negligible effect up to ⬃10 at. %, i.e., Ba0.90Ca0.10TiO3 . On the other hand, both dopants cause a dramatic decrease in T o/t and T r/o . The behavior observed with Sr2⫹ doping is normally explained as a cation size effect, whereby the smaller ionic radius of Sr2⫹ compared to Ba2⫹ stabilizes the cubic polymorph, thus decreasing T c . The effect of A-site doping with Pb2⫹ or Ca2⫹ on T c , however, cannot be explained on the basis of cation radii, and as far as we are aware, no universal explanation for the effects of various A-site dopants on T c or the phase transition temperatures, T o/t and T r/o , exists. Although many isovalent A-site dopants are effective in displacing or ‘‘shifting’’ T c they do not have a dramatic effect on the value of ⬘ or on the profile of d ⑀ ⬘ /dT. ⑀ max The introduction of isovalent cations on the B site, how⬘ and d ⑀ ⬘ /dT. Comever, can have a significant effect on ⑀ max mon nonferroelectric active B-site dopants such as Zr4⫹ and Sn4⫹ cause a linear decrease in T c , whereas both T r/o and T o/t increase, Fig. 1. The reduction in T c is initially accom⬘ , but with continued substitupanied by an increase in ⑀ max ⬘ decreases and becomes increasingly broad. This tion ⑀ max behavior is commonly known as ‘‘pinching’’ and is attributed to the coalescence of the three phase transition temperatures at a dopant level of ⬃10 at. % Zr, Fig. 1, and thus overlap of the three permittivity maxima associated with the individual phase transitions. Hennings et al. used a combination of T c ⫺T 0 data, differential thermal analyses and calculation of Devonshire coefficients to show that, with increasing Zr doping, the ferroelectric to paraelectric phase transition becomes increasingly second order.12 The exact origin of this effect, however, is not discussed. Aliovalent, A-site dopants such La3⫹ are known to induce n-type semiconductivity in BaTiO3, 13–16 but their influ-

Morrison, Sinclair, and West

ence on the various polymorphic phase transition temperatures is less well documented. Data for Ce3⫹-doped BaTiO3, which is reported to form according to a Ti vacancy solid solution mechanism, Ba1⫺x Cex Ti1⫺x/4O3, 17,18 indicate that T c decreases linearly at a rate of ⬃21 °C per at. % Ce3⫹. 18 Due to the mixed 3⫹/4⫹ valency of Ce, problems arise as any Ce4⫹ present is likely to occupy the B site as opposed to the A site. The rate of change of T c on Ce doping may not therefore be representative of A-site doping by Ce3⫹ alone. Such problems may be avoided by using lanthanum as a dopant. Lanthanum has a fixed valency of 3⫹ and, with an ionic radius of 1.36 Å compared with 1.61 Å for Ba2⫹ and 0.74 Å for Ti,19 will only occupy A sites within the lattice. The charge balance compensation mechanism when Ba2⫹ is replaced by La3⫹ has long been a matter of debate. Due to the semiconducting behavior commonly observed at low dopant levels, ⬃0.03 at. %, for air-heated materials, compensation is generally believed to occur via the electronic, ‘‘La donor-doping’’ mechanism,13–16 where Ba2⫹⇒La3⫹⫹e ⫺ .

共4兲

At higher La contents it is now widely accepted that compensation occurs via an ionic mechanism with partial replacement of Ba2⫹ by La3⫹ and the creation of titanium vacancies, Ba2⫹⫹ 41Ti4⫹⇒La3⫹⫹ 41䊐Ti

共5兲

forming a solid solution Ba1⫺x Lax Ti1⫺x/4O3, where 0⭐x ⭐0.25.20–23 We have recently shown that the electronic, La donordoping mechanism is unlikely to exist and that titanium vacancies are the primary means of compensation at all La concentrations.23 These materials, however, are susceptible to small amounts of oxygen loss 关Eq. 共6兲兴 especially when heated in air at temperatures ⭓1350 °C. O2⫺⇒ 21O2⫹2e ⫺

共6兲

It is this small amount of oxygen loss which is responsible for the semiconducting behavior commonly observed in airheated La-doped BaTiO3 samples. Although it is well known that mechanism 共6兲 also occurs in undoped BaTiO3, the connection between oxygen loss and the so-called La donordoping effect in La–BaTiO3 has only recently been made.23 Oxygen loss is dependent on a number of factors including heating atmosphere and temperature, heating/cooling rate, ceramic microstructure, and pellet density.24 Depending on the amount and distribution oxygen loss, samples may be insulating or semiconducting,23 alternatively, they may be electrically heterogeneous and exhibit a number of regions with different conductivities.24 By processing samples in O2 rather than air, we have recently shown that it is possible to suppress oxygen loss 关Eq. 共6兲兴 and consequently, produce single phase, insulating materials with Ti vacancies as the primary compensation mechanism. Preliminary data for such materials, over the narrow compositional range 0⭐x⭐0.06 have shown these



materials to exhibit a linear decrease in T c and an increase in ⬘ with increasing x: for x⫽0.06 the value of ⑀ max ⬘ is in ⑀ max excess of 25 000.22 In this article, we report the results of a comprehensive study of Ti-vacancy solid solution materials prepared in O2. The effect of La content on the lattice parameters, phase transition temperatures, and electrical properties are all reported. The unusual combination of A-site doping and B-site vacancies leads to complex and diverse ⑀⬘ behavior as a function of x. The observed behavior is discussed in terms of what is currently known about the influence of A- and B-site dopants on the phase transition temperatures and ⑀⬘ behavior of doped-BaTiO3 materials.


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514.5 nm. A 300 ␮m slit and integration time of 5 s were used, giving a resolution of 0.47 cm⫺1 . Data were collected over the range of 200–700 cm⫺1 . Microstructural properties such as grain size distribution and morphology were determined using an ISI SS40 scanning electron microscope 共SEM兲. Samples were either in the form of fractured pellets or polished, etched specimens. For etching a 0.3 vol % HF-6 vol % HNO3 solution was used, and etching times varied between 20 and 45 s. Fractured samples were mounted on an aluminum stub and gold coated to avoid charging under the electron beam. Polished, etched samples were carbon coated for the same reason. IMPEDANCE DATA ANALYSIS

EXPERIMENT

Samples of general composition Ba1⫺x Lax Ti1⫺x/4O3, with a range of x, were prepared by the conventional solid state, mixed oxide route. Appropriate amounts of BaCO3 共Aldrich, 99.98%兲, La2O3 共Aldrich, 99.99%兲, and TiO2 共Aldrich, ⫹99.9%兲 were intimately mixed in acetone in an agate mortar and pestle until dry. The powders were placed in an alumina boat lined with Pt foil and fired in flowing O2. Firing schedules were 1000 °C overnight to decarbonate, 1200 °C for 3 h, and 1350 °C for 3 days, with daily regrinding for 5 min in an agate planetary ballmill. X-ray diffraction 共XRD兲, using a Ha¨gg Guinier camera, was used to follow the progress of reaction and as a first indication of phase purity. Lattice parameters were calculated using data obtained from a Stoe Stadi P diffractometer which was calibrated using an external Si standard. Pellets were prepared by uniaxial pressing of powders to 200 MPa in an 8 mm stainless steel die. The green bodies were placed in an alumina boat lined with Pt foil and heated overnight at 1350 °C in flowing O2. Pellets for impedance measurements were prepared as above. Electrodes were fabricated from Au paste 共Engelhard T-10112兲; electroded pellets were fired to 800 °C to remove organics and harden the Au residue. Pellets were attached to the platinum measuring leads of a conductivity jig and placed in a horizontal tube furnace whose temperature was controlled to ⫾1 °C. Subambient temperatures were obtained using an Oxford Optistat Bath Dynamic Variable Temperature Cryostat controlled by an Oxford ITC4 temperature controller. Impedance measurements were made over the frequency range 10⫺2 to 107 Hz using a combination of Solartron 1250/1287 and Hewlett–Packard 4192A instrumentation with an applied voltage of 100 mV. All data were corrected for sample geometry. Differential scanning calorimetry 共DSC兲 measurements were carried out on pellet fragments using a Polymer Laboratory DSC Auto between ⫺50 and 200 °C with various heating rates between 5 and 20 °C min⫺1. Samples were heated, cooled, and reheated to check reversibility and to determine if any hysteretic behavior occurred. Transition enthalpies were calculated from peak areas using the instrument software. Raman spectroscopy was carried out using a Jobin Yvon T64000 spectrometer with a 100 mW Ar laser, wavelength

Conventionally, impedance data on dielectric BaTiO3 are analyzed using an equivalent circuit consisting of two parallel resistor-capacitor 共RC兲 elements connected in series.8 One RC element represents the bulk 共intragranular兲 response, while the second represents thin layer effects associated with the grain boundary 共intergranular兲 response. Based on this equivalent circuit the frequency dependence of the parallel capacitance of the sample, C P , where C p ⫽ ⑀ ⬘ ⑀ 0 and ⑀ 0 is the permittivity of free space, will consist of low and high frequency plateaus, C lf and C hf , respectively, separated by a dispersion.8 The magnitudes of C lf and C hf are given by Eqs. 共7兲 and 共8兲, C lf⫽C gb ,

共7兲

⫺1 ⫺1 ⫹C ⫺1 , C hf⫽ 共 C gb b 兲

共8兲

where C gb and C b are the grain boundary and bulk capacitances, respectively. Certain important assumptions are made in this derivation, namely that C b ⬍C gb and R b ⰆR gb , where R b and R gb are the bulk and grain boundary resistances, respectively.8 In order to use Eqs. 共7兲 and 共8兲 in data analysis, it is clearly important to have information on the resistance and capacitance associated with both bulk and grain boundary responses to ensure the assumptions are valid. Each parallel RC element used to represent an electroactive region within the sample will result in a semicircular arc in the complex impedance plane, Z*, plot. The frequency at which the semicircular arc maximum occurs is determined by the time constant or relaxation time, ␶, of the parallel RC element as described by

␻ max⫽ ␶ ⫺1 ⫽ 共 RC 兲 ⫺1 ,

共9兲

where ␻ max is the angular frequency 共and ␻ ⫽2 ␲ f , where f is the frequency in Hz兲 at the top of the semicircular arc. Below ⬃250 °C the resistance of insulating BaTiO3-based samples is generally too high to measure with the equipment currently available. In such circumstances, it is only possible to measure the effective parallel capacitance, C p , as a function of frequency. At high temperatures 共above ⬃250 °C), however, it is possible to extract bulk and grain boundary R and C values from Z* plots. A typical data set obtained at high temperature for a La-doped sample with x⫽0.20 heated in O2 is shown in Fig. 2共a兲. The Z* plot is dominated by a large semicircular arc at low frequency, with a smaller, partially resolved semicircular


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dure of obtaining capacitance 共and ⑀⬘兲 data at a fixed frequency is common for ferroelectric materials, however, few studies consider the possible contribution of C gb to the measured capacitance, C hf . Although it is quite straight forward to check the validity of this method for data extraction at TⰇT c , several points for consideration arise with respect to data analysis at lower temperatures. 共i兲 Without any direct information on C b and C gb from Z* plots at temperatures near T c in the paraelectric state, it is only possible to determine C P . It is therefore no longer possible to check the validity of Eq. 共10兲 and therefore to assume that C hf is a suitable estimate of C b . In addition, data analysis depends critically on whether or not the grain boundary component is ferroelectric. If the grain boundaries are not ferroelectric then the assumption that C b ⰆC gb does not hold at temperatures close to T c where C hf values can be in the nF range and are comparable to typical C gb values of several nF, as determined at TⰇT c . 共ii兲 In the ferroelectric region below T c , the presence of ferroelectric domains and domain walls will require a more complex equivalent circuit to model the ac response than that of two parallel RC elements connected in series. Without any knowledge of the equivalent circuit below T c , C hf can only be interpreted as the effective parallel capacitance of the sample, C P . Despite these problems, capacitance data obtained from C hf remains the most feasible way of presenting capacitance data of ferroelectric BaTiO3-based materials, especially at TⰇT c where C gb can be quantified. RESULTS FIG. 2. Complex impedance plane, Z*, plot at 382 °C 共a兲 and C P spectra at several temperatures for x⫽0.20 共b兲. Filled circles in Z* plot represent selected frequencies in Hz.

arc at higher frequency 共inset兲. From the intercepts of each semicircular arc with the real, Z⬘, axis, the large, low frequency semicircular arc has an associated R of ⬃560 k⍀ and the smaller, high frequency arc has an associated R of ⬃6.6 k⍀. Using Eq. 共9兲 at the arc maxima, the low and high frequency responses have associated capacitances of ⬃0.4 nF and 15 pF, respectively. From the magnitudes of the capacitances these responses were assigned to grain boundary and bulk components, respectively25 and confirms the validity of the assumptions that C b ⬍C gb and R b ⰆR gb for x⫽0.20 at 382 °C. C P spectra for x⫽0.20 at various temperatures are shown in Fig. 2共b兲. Since Z* plots indicate that C b ⰆC gb , Eq. 共8兲 can be further simplified to give the expression C hf⬵C b .

共10兲

The high frequency plateau therefore gives a close representation of the bulk capacitance value. Bulk capacitance data for all samples were therefore obtained from the middle of the high frequency plateau, typically at ⬃100 kHz, with the proviso that in the paraelectric state C b ⰆC gb . This proce-

XRD, SEM, and electron probe microanalysis 共EPMA兲 indicated that all samples with 0⭐x⭐0.20 were single phase. They had the essential XRD pattern of BaTiO3 with varying degrees of tetragonality, or cubic symmetry, depending on the La content. The XRD pattern for x⫽0 was indexed on a tetragonal cell with a⫽3.9951(6) and c ⫽4.0303(9) Å, in good agreement with the reported values for tetragonal BaTiO3 where a⫽3.994 and c⫽4.038 Å.26 The variation in lattice parameters and unit cell volume at room temperature as a function of x is shown in Fig. 3. The effect of increasing x on the lattice parameters can be described by three regions of behavior. For 0⭐x⭐0.05 a decrease in tetragonality is observed with increasing x up to 0.05, which has cubic symmetry with a⫽4.0022(4) Å. With further increase in x, cubic symmetry is retained, and a decreases up to ⬃x⫽0.10 where a⫽3.9963(3) Å. For x ⭓0.10, increasing La content has little effect on the unit cell, which remains cubic and, for x⫽0.20, a⫽3.9948(2) Å. Raman spectroscopy was also used as an indication of the room temperature symmetry of the samples. Spectra obtained at room temperature for 0⭐x⭐0.06 are shown in Fig. 4. The spectrum for x⫽0 shows a sharp peak at ⬃305 cm⫺1 , which is characteristic of the B 1 mode of the tetragonal polymorph.27 The intensity of this peak decreases with increasing x, indicating a decrease in tetragonality. For x ⫽0.06, the peak is very weak, but indicates the presence of




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FIG. 4. Raman spectra, obtained at room temperature, for 0⭐x⭐0.06.

FIG. 3. Variation in lattice parameters 共a兲 and unit cell volume 共b兲 at room temperature, as a function of x.

distorted TiO6 octahedra, although XRD indicates that this composition is macroscopically cubic at room temperature. SEM was used to determine the microstructure of compositions with a range of x. Secondary electron images of fracture surfaces indicated a uniform morphology consisting of smooth, rounded grains with no evidence of any secondary, intergranular phase共s兲. Micrographs of fracture surfaces for two compositions are shown in Figs. 5共a兲 and 5共b兲. x ⫽0.04 has a uniform grain size of ⬃3–4 ␮m, as indicated in Fig. 5共a兲. Compositions 0⭐x⭐0.06 all displayed similar morphology, grain size, and grain size distribution. Where x⭓0.06 the grain size increased with increasing x, but a similar morphology of smooth surfaced grains and narrow grain size distribution was retained. The micrograph of the fracture surface for x⫽0.20 indicates a smooth grained material with a fairly uniform grain size of ⬃7–10 ␮m, Fig. 5共b兲. The grains also exhibited ‘‘ring-like’’ growth steps which were not apparent in the more lightly doped compositions. Backscattered electron 共BSE兲 micrographs of etched samples of x⫽0.04 and 0.20 are shown in Figs. 5共c兲 and 5共d兲, respectively. These micrographs indicate the uniform grain size for both compositions and, again, there was no evidence of any secondary phase共s兲. Pellet densities, calculated from pellet dimensions and x-ray density, were in excess of ⬃95%. No secondary phases were detected by EPMA. The starting compositions and measured EPMA values, for a range of x are given in Table I. The results indicate that, within errors,

the materials form according to the Ti-vacancy solid solution mechanism. DSC of compositions 0⭐x⭐0.05 indicated an endotherm, during heating, associated with the t/c phase transition. The transition enthalpies, ⌬H, were calculated from the peak areas. For x⫽0, ⌬H⬇192 J mol⫺1, close to the reported value of 210 J mol⫺1. 28 A dramatic decrease in ⌬H is observed with initial additions of La, and for x⫽0.01, ⌬H ⬇77 J mol⫺1. After the initial drop, ⌬H decreases steadily with increasing x, Fig. 6, and for x⭓0.06, ⌬H was too small to detect. T c decreases linearly with increasing x, as described in more detail in our previous work.22 No information on T o/t or T r/o was obtained. All DSC data showed good reproducibility on heating and cooling cycles and also for heating/cooling rates ranging from 5 to 20 °C min⫺1. Capacitance, C hf , and ⑀⬘ data, where ⑀ ⬘ ⫽C hf / ⑀ 0 , were extracted, as described above, over a wide temperature range for compositions 0⭐x⭐0.10, Fig. 7. In each case, high temperature impedance data indicated that C b ⰆC gb , as a result C hf was considered a suitable estimate of C b . For clarity, only selected compositions are shown; more complete data for 0⭐x⭐0.06 are presented in Ref. 22. x⫽0 showed behavior typical of an undoped BaTiO3 ceramic, exhibiting a ⬘ ⬇10 000 at the Curie temperature, T c ⬇137 °C, and a ⑀ max shallow maximum ⬃10 °C associated with the o/t transition. On doping with La, the ⑀⬘-temperature profiles for compositions 0⭐x⭐0.06 retained the essential signature of undoped BaTiO3, but were displaced to lower temperatures with in⬘ decreased and became increascreasing x. For x⬎0.06, ⑀ max ingly broad with increasing x. T o/t also decreased with increasing x, but at a less dramatic rate than T c , and for x ⬘ associated with the o/t transition was barely ⫽0.08, ⑀ max discernible as a shoulder on the low temperature side of ⬘ . For x⭓0.10, it was not possible to detect two phase ⑀ max transition temperatures from the C hf data. The change in T c and T o/t as a function of x are shown in Fig. 8 and indicate a rapid decrease in both phase transition temperatures with increasing x. T c decreased approximately


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FIG. 5. SEM micrographs of fracture surfaces of compositions x⫽0.04 共a兲 and 0.20 共b兲. BSE images of etched samples for the same compositions are shown in 共c兲 and 共d兲, respectively.

linearly at a dramatic rate of ⬃24 °C per at. % La3⫹ substitution. T o/t also decreased, but at a less dramatic rate, and displayed a degree of curvature making it difficult to determine dT o/t /d 关 La兴 . For compositions x⬎0.08 the phase transition temperatures coalesce and T c appears to be displaced to lower temperature by the overlap of the o/t phase transition. As a result, it is difficult to estimate the true T c for x ⭓0.08. With increasing x, the parallel capacitance, C p , showed an increasing degree of frequency dependence at temperatures below T c . C P spectra for x⫽0.04, at several temperatures, are shown in Fig. 9共a兲. For T⭓T c , C P was essentially

frequency independent over several decades of frequency. Below T c , however, C P showed a monotonic decrease with increasing frequency. This effect becomes more pronounced with increasing x; Fig. 9共b兲 shows data for x⫽0.10. Again, for T⭓T c , C P was essentially frequency independent, but below T c , the data showed a strong frequency dependence. Capacitance data as a function of frequency and temperature for x⫽0.10 are shown in Fig. 9共c兲 and indicate that these materials exhibit ‘‘relaxor’’-type behavior. All compositions 0⭐x⭐0.10 exhibit Curie–Weiss behavior, Eq. 共1兲, over a wide temperature range, Fig. 10共a兲. The similarity in gradients of the fitted data shows that C W

TABLE I. Starting compositions for titanium vacancy compensation solid solutions, Ba1⫺x Lax Ti1⫺x/4O3, and observed compositions of the solid solutions formed, as determined by EPMA, for samples fired at 1350 °C in O2. Values given are averaged from 10 to 20 spot analyses.

a

Starting composition 共mol %兲

Composition of solid solution formed 共mol %兲

Starting x in Ba1⫺x Lax Ti1⫺x/4 O3

BaO

La2O3

TiOx

BaO

La2O3

TiOx

0 0.01 0.02 0.03 0.04 0.05 0.06 0.10 0.20

50.00 49.62 49.25 48.87 48.48 48.10 47.72 46.15 42.10

••• 0.25 0.50 0.75 1.01 1.26 1.52 2.56 5.26

50.00 50.13 50.25 50.38 50.51 50.64 50.76 51.29 52.64

49.15⫾0.22 49.28⫾0.90 48.51⫾0.94 48.16⫾0.28 48.18⫾0.53 47.77⫾0.25 47.31⫾0.36 47.03⫾0.44 44.00⫾0.21

••• 0.28⫾0.05 0.67⫾0.43 0.77⫾0.10 0.94⫾0.27 1.25⫾0.03 1.47⫾0.07 2.48⫾0.04 4.70⫾0.07

50.85⫾0.15 50.44⫾0.60 50.82⫾0.28 51.07⫾0.20 50.88⫾0.18 50.98⫾0.18 51.22⫾0.20 50.49⫾0.28 51.30⫾0.18

Calculated formulaa Ba1.00⫾0.01Ti1.04⫾0.01O3 Ba0.99⫾0.02La0.01⫾0.01Ti1.01⫾0.01O3 Ba0.97⫾0.02La0.03⫾0.02Ti1.02⫾0.01O3 Ba0.97⫾0.01La0.03⫾0.01Ti1.03⫾0.01O3 Ba0.96⫾0.01La0.04⫾0.01Ti1.02⫾0.01O3 Ba0.95⫾0.01La0.05⫾0.01Ti1.01⫾0.01O3 Ba0.94⫾0.01La0.06⫾0.01Ti1.02⫾0.01O3 Ba0.90⫾0.01La0.10⫾0.01Ti0.97⫾0.01O3 Ba0.82⫾0.01La0.18⫾0.00Ti0.96⫾0.01O3

Formula calculated after normalizing Ba⫹La⫽1.



FIG. 6. Transition enthalpy, ⌬H, for the tetragonal/cubic phase transition vs x as determined by DSC.

does not change significantly with La doping. At temperatures close to T c , however, the data show small deviations from Curie–Weiss behavior; these deviations increase with increasing x. The degree of deviation is indicated by the temperature difference between T c and T 0 , where T c is ob⬘ and T 0 from extrapolation of the linear tained from ⑀ max region of the Curie–Weiss plot. T c , T 0 and T c ⫺T 0 data and Curie constants, C W , for a range of x are summarized in Table II. The paraelectric data for x⫽0.10 exhibits the largest deviation from the Curie–Weiss law. A Curie–Weiss plot for x⫽0.10, Fig. 10共b兲, indicates the deviation at temperatures below ⬃⫺40 °C. The temperature dependence of the paraelectric data below ⫺40 °C was investigated using both Smolenskii’s quadratic expression, Eq. 共2兲, and Uchino’s modified expression, Eq. 共3兲. The data fit the (T⫺T c ) 2 dependence, Eq. 共2兲, reasonably well, Fig. 10共c兲. Using linear regression the data had a residual, R⫽0.0362. The data below ⫺40 °C were replotted according to Eq. 共3兲, Fig. 10共d兲,


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FIG. 8. Variation of T c and T o/t as a function of x as determined by C hf data.

and again the data showed good linearity. Using linear regression of the data, the exponent, ␥, was calculated as 1.82 and R⫽2.25⫻10⫺5 . At temperatures greater than ⬃250 °C it was possible to extract conductivity data, ␴ (⫽R ⫺1 ), for bulk and grain boundary regions using impedance spectroscopy, as described above. Bulk conductivity ( ␴ b ) data are shown in the form of an Arrhenius plot, Fig. 11, and all show Arrheniustype behavior described by

␴ ⫽ ␴ 0 exp共 ⫺E A /kT 兲 ,

共11兲

where ␴ 0 is the pre-exponential factor and k is the Boltzmann constant. The activation energy, E A , calculated in eV and the pre-exponential factor for each composition is shown in Table III. Undoped BaTiO3, x⫽0, has an activation energy of ⬃1.56 eV. On addition of La, a dramatic change in E A occurs, suggesting a change in conduction mechanism. All La-doped compositions exhibit E A values between 0.64 and 0.72 eV, Table III, with no apparent trend on La concentration. The pre-exponential factor, ␴ 0 , also showed no dependence on La concentration. Grain boundary conductivity data ( ␴ gb) also exhibit Arrhenius-type behavior for all compositions, Fig. 12. As with the bulk data, x⫽0 had the highest E A of 1.84 eV. All other compositions exhibited similar E A values ranging from 1.40 (x⫽0.03) to 0.97 eV (x⫽0.06), Table III. As with the bulk data, no systematic trend in E A or ␴ 0 was observed with increasing x. DISCUSSION

FIG. 7. Capacitance, C hf , and permittivity data as a function of temperature for various compositions, 0⭐x⭐0.10.

The physical and electrical properties of insulating Ba1⫺x Lax Ti1⫺x/4O3 solid solution compositions must be discussed from the viewpoint of combined A- and B-site doping. Since partial replacement of Ba2⫹ by La3⫹ with the creation of Ti vacancies are intrinsically linked to each other, it is difficult to attribute specific effects to either A- or B-site effects alone.


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FIG. 9. Parallel capacitance, C P , spectra, at several temperatures, for x ⫽0.04 共a兲 and 0.10 共b兲. C P and ⑀⬘ data as a function of temperature and frequency for x⫽0.10 are shown in 共c兲.

The decrease in tetragonality, observed by a combination of XRD and Raman spectroscopy 共Figs. 3 and 4兲 can be explained as a cation size effect. The smaller La3⫹ cation stabilizes the cubic form as predicted by Goldschmidt’s tolerance factor for undistorted and distorted perovskites.29 Why the unit cell parameter, a 共and hence unit cell volume兲 should appear to reach a lower limit of a⬇3.995 Å with increasing x is unclear. The value is significantly lower than for cubic BaTiO3, a⫽4.031 Å,30 and significantly larger than for SrTiO3, a⫽3.905 Å,31 which has the ideal, cubic perovskite structure. The limit may signify the highest possible packing density for a 共Ba,La兲O3 cubic close packed lattice. DSC data indicate that with increasing x, ⌬H for the ferroelectric phase transition decreases, Fig. 6. This may indicate that the transition becomes increasingly second order with increasing x.

The effect of La concentration on T c and T o/t is dramatic. The rate of change in T c and T o/t with La doping is compared with other A- and B-site dopants in Figs. 13共a兲 and 13共b兲, respectively. The effect of La doping on T c is greater than for any other A- and B-site dopant, decreasing it approximately linearly at a rate of ⬃24 °C per at. % La compared with 21 °C per at. % Ce3⫹, Fig. 13共a兲. To our knowledge, this is the largest reported dT c /d 关 dopant兴 . La doping also has the greatest reported effect on T o/t which decreases at a greater rate than both A-site Ca2⫹ and Pb2⫹ doping, Fig. 13共b兲. As a result, La-doping ‘‘pinches’’ T c and T o/t together in a similar manner to Zr doping. The main difference is that La-doping decreases both T c and T o/t , whereas Zr doping decreases T c , but increases T o/t and T r/o until they coalesce at approximately 50 °C for ⬃13 at. % Zr. For La doping, the phase transition temperatures coalesce at a similar dopant




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FIG. 10. Curie–Weiss plots for x⫽0 共䊊兲, 0.01 共䊐兲, 0.02 共䉮兲, 0.03 共䊉兲, 0.04 共䊏兲, 0.05 共䉭兲, 0.06 共⫹兲, 0.08 共丣兲, and 0.10 共〫兲 are shown in 共a兲. Also shown are data for x⫽0.10, plotted according to the Curie–Weiss law 共b兲, Smolenskii’s quadratic equation 共c兲, and Uchino’s modified expression of Smolenskii’s quadratic equation 共d兲.

concentration of ⬃10 at. % La, the decrease in both T c and T o/t is so dramatic, however, the temperature at which they coalesce is much lower, ⬃⫺130 °C, Fig. 13共c兲. The permittivity behavior of La-doped compositions, Fig. 7, resembles that of Zr-doped samples.12 Both dopants ⬘ followed by a result in an initial increase in the value of ⑀ max ⬘ . In both cases the broadenbroadening and decrease in ⑀ max ⬘ can be attributed to the coalescence of the ing of the ⑀ max

individual phase transitions. It should also be noted that Zr and La doping produce defects in the form of nonferroelectric ZrO6 octahedra or Ti vacancies, respectively, both of which will disrupt the cooperative linking between the ferroelectric-active TiO6 octahedra. The rate of displacement ⬘ , however, is much greater in the case of La doping of ␧ max

TABLE II. T c , T 0 , and T c ⫺T 0 data and Curie–Weiss constants, C W , for a range of compositions with 0⭐x⭐0.10.

a

Ba1⫺x Lax Ti1⫺x/4O3 共x兲

Tc (°C)

T0 (°C)

T c ⫺T 0 (°C)

CW (105 °C)

0 0.01 0.02 0.03 0.04 0.05 0.06 0.08 0.10

135⫾1 106⫾1 82⫾1 64⫾1 36⫾1 13⫾1 ⫺9⫾1 ⫺75a⫾1 ⫺128a⫾1

127⫾2 102⫾2 84⫾3 64⫾4 42⫾3 31⫾2 6⫾2 ⫺37⫾2 ⫺92⫾2

8⫾3 4⫾3 ⫺2⫾4 0⫾5 ⫺6⫾5 ⫺18⫾4 ⫺15⫾3 ⫺38⫾3 ⫺36⫾3

1.24 1.25 1.24 1.09 1.23 1.11 1.15 1.16 0.95

T c at 100 kHz.

FIG. 11. Arrhenius plot of bulk conductivity data for 0⭐x⭐0.20. Symbols as in Fig. 10, and also x⫽0.02 共*兲.


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TABLE III. Activation energies, E A , and pre-exponential factors, ␴ 0 , calculated from the bulk and grain boundary conductivity data shown in Figs. 11 and 12, respectively. bulk Ba1⫺x Lax Ti1⫺x/4O3 x 0 0.01 0.02 0.03 0.04 0.05 0.06 0.10 0.20

grain boundary ⫺1

E A 共eV兲

log ␴0 共⍀ 兲

E A 共eV兲

log ␴0 共⍀⫺1兲

1.56 0.66 0.72 0.69 0.71 0.72 0.65 0.64 0.66

6.23 1.73 1.78 0.96 2.03 1.94 1.98 2.19 1.29

1.84 1.02 1.09 1.40 1.00 1.03 0.97 ••• 1.17

6.84 2.47 3.35 4.20 2.70 3.03 2.92 ••• 3.38 FIG. 12. Arrhenius plot of grain boundary conductivity data for 0⭐x ⭐0.20. Symbols as in Fig. 11.

compared to Zr doping, as indicated by Fig. 13共c兲. La doping also results in relaxor-type behavior, which increases with increasing x, Figs. 9共a兲 and 9共b兲. No evidence for increasing frequency dependence of ⑀⬘ with Zr doping has been reported, despite the overall similarity in ⑀⬘ behavior; however, only single, fixed frequency ⑀⬘ data have generally been presented. The origin of the relaxor phenomenon in La-doped BaTiO3 is unclear, however, as the effect increases with increasing x, it may result from aggregation of defects, i.e., association of La3⫹ and Ti vacancies, resulting

in a compositional fluctuation model similar to that used to describe other relaxor materials such as Pb共Mg1/3Nb2/3兲O3 .32 To our knowledge, this relaxor behavior has not been observed previously in a B-site deficient, cubic close packed perovskite. At temperatures well above T c , ⑀⬘ data for all compositions obey the Curie–Weiss law, Eq. 共1兲, but exhibit increasing deviations, T c ⫺T 0 , close to T c with increasing x. The change in T c ⫺T 0 is unlikely to be linked to a change in

FIG. 13. Comparison of the effect of La doping on T c 共a兲 and T o/t 共b兲, with various A- and B-site dopants. Also shown, comparison of the effect of doping with La and Zr 共c兲.



porosity or low C gb values due to poorly defined grain boundaries as SEM and impedance analysis showed no variation in either as a function of x. The grain size, however, increases slightly with increasing x and may make a small contribution. The change in T c ⫺T 0 is therefore likely to indicate a change in the order of the ferroelectric phase transition from first to second, in agreement with the DSC data. ⬘ , is also consistent with a change The initial increase in ⑀ max to a second order transition.12,33 The deviations from the Curie–Weiss law fit the treatments of both Smolenskii2 and Uchino,10 Eqs. 共2兲 and 共3兲, respectively, reasonably well, but are better described by the latter. The usefulness of describing such data using either expression is unclear as each is only valid over a relatively small temperature range and neither method has an associated explanation of the physical processes occurring within the material. 共Although the exponent, ␥, of Uchino’s treatment may be used to indicate the diffuseness of the phase transition in a similar manner to Smolenskii’s diffuseness coefficient, ␦ 兲. Instead, some explanation of the general temperature dependence of all paraelectric data is required. The overall behavior is described by a combination of Aand B-site effects whereby the smaller La3⫹ cation on the Asite has a similar effect on T c as Sr doping, and the Ti vacancies on the B site disrupt the cooperative effects between octahedra in a similar manner to Zr4⫹ and Sn4⫹ doping. The effect on T o/t is unusual in that it is more similar to Pb2⫹ and Ca2⫹ doping. These dopants, however, do not decrease T c as is observed for La doping. The reason for unusual effect of La doping on T o/t is not clear, but may involve distortion/ tilting of octahedra. The high temperature conductivity data for both bulk and grain boundary components follow Arrhenius-type behavior, Eq. 共11兲, as shown in Figs. 11 and 12, respectively. The bulk data, ␴ b , for all La-doped compositions exhibited E A values between 0.64 and 0.72 eV, Table III, with no apparent trend with varying La concentration. Conductivity may be described by the relation ␴ ⫽ne ␮ , where n is the carrier concentration, e is the charge on each carrier, and ␮ is the carrier mobility. The similarity in E A values suggests the same conduction mechanism is present in all La-doped compositions. Since e is a constant and ␮ does not have a strong dependence on x, as indicated by their similar activation energies, ␴ 0 is proportional to the number of carriers, n. As ␴ 0 does not vary proportionally with La concentration, Table III, the carrier共s兲 cannot be directly related to the concentration of La. As the oxygen stoichiometry of these materials has been shown to be particularly sensitive to heating conditions and has a dramatic effect on the electrical properties,23,24 the source of conduction at these high temperatures may be associated with oxygen vacancies, Eq. 共6兲. CONCLUSIONS

The effect of La doping on the permittivity-temperature profile of BaTiO3 is explained by a combination of A- and B-site doping effects. The replacement of Ba2⫹ by the smaller La3⫹ cation on the A-site and the presence of B-site vacancies result in a rapid decrease in T c . The presence of


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La3⫹ on the A-site is analogous to Sr doping, while the B-site vacancies are analogous to Zr doping. In combination, the effect on T c is greater than any A- or B-site substitution alone, decreasing T c at a rate of ⬃24 °C per at. % La, one of the highest reported for any dopant, to date. The effect on T o/t is also the greatest reported, decreasing T o/t at a greater rate than for both Ca and Pb doping. The decrease in T o/t with La doping is not easily compared to either dopant as they do not also decrease T c . The general permittivity behavior of the La-doped BaTiO3 solid solution is similar to Zr-doped BaTiO3. Although T o/t increases with increasing Zr doping whereas La doping has the opposite effect, the rate at which T c decreases as a function of x still results in the phase transition temperatures coalescing at dopant levels of ⬃10 at. %. As a result, ⬘ the ferroelectric phase transition becomes diffuse and ⑀ max decreases. The increasing frequency dependence of ⑀⬘ below T c , with increasing x, is attributed to the increase in concentration of A- and B-site defects. The presence of either will have a decoupling effect on the surrounding octahedra, and result in a distribution of local T c values. The relaxor-type behavior in La-doped BaTiO3 materials may therefore be similar to the compositional fluctuation model for Pb-based perovskite relaxors. The decrease in ⌬H at T c and the change in T c ⫺T 0 with increasing x both suggest increasing second order character for the ferroelectric phase transition. This is also consistent ⬘ . with the initial increase observed in ⑀ max Bulk conductivity data indicate that electronic conduction at high temperatures is not directly controlled by La doping, but may be dominated by oxygen vacancy donor states. Even when heated in O2, therefore, the high temperatures required to produce dense ceramics still results in a small amount of O2 loss from the samples. ACKNOWLEDGMENTS

The authors would like to thank the EPSRC for a studentship 共FDM兲, Dr. A. Coats for EPMA and Dr. E. E. Lachowski for advice on SEM. Thanks also to Dr. T. Takeuchi and Dr. N. Ohtori of Osaka National Research Institute, Japan for assistance with Raman Spectroscopy. 1

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