The effect of second phase La0.67TiO2.87 on the phase structure and impedance spectroscopy of La2Ti2(1 + x)O7 piezoelectric ceramics

Ceramics International 45 (2019) 12742–12756

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The effect of second phase La0.67TiO2.87 on the phase structure and impedance spectroscopy of La2Ti2(1 + x)O7 piezoelectric ceramics

T

Yueyi Li, Laiming Jiang, Chao Wu, Zichen Liu, Xiaoji Zhao, Qiang Chen, Jie Xing, Jianguo Zhu∗ College of Materials Science and Engineering, Sichuan University, Chengdu, 610064, China

A R T I C LE I N FO

A B S T R A C T

Keywords: La2Ti2(1 + x)O7 ceramics Phase structure Impedance spectroscopy

The Ti excess La2Ti2 (1+x) O7 (x = 0, 0.005, 0.01, 0.02, 0.05, 0.1) piezoelectric ceramics have been prepared by sol-gel technology and solid state synthesis method. Through refinement analysis, the phase structure of the ceramics varies with Ti content. Most monoclinic phase (∼93%) and a handful of orthogonal phase (∼7%) coexist in La2Ti2 (1+0) O7 ceramics. Pure monoclinic phase La2Ti2O7 with space group P21 appears in La2Ti2 (1+0.005) O7 and La2Ti2 (1+0.01) O7 ceramics. Monoclinic phase La2Ti2 O7 and a certain proportion of tetragonal phase La0.67TiO2.87 coexist in La2Ti2 (1+0.02) O7, La2Ti2 (1+0.05) O7 and Ti2 (1+0.1) O7 ceramics. With the excess of Ti content, the monoclinic phase ratio and distortion angles in a-b projection plane of the ceramics increase first and then decrease, which is consistent with the variation tendency of piezoelectric constant d33. The excellent piezoelectric constant for Ti2 (1+0.01) O7 ceramics is 2.8 pC/N. Impedance analysis shows that the conductive mechanisms of all samples include both grain and grain boundary conductivity at temperature range T ≥ 500 °C. The formation of tetragonal phase La0.67TiO2.87 derives from Ti excess in pure monoclinic phase La2Ti2O7. The existence of tetragonal phase La0.67TiO2.87 can obviously increase the capacitance of ceramics at x ≥ 0.05. All prepared piezoelectric La2Ti2 (1+x) O7 ceramics have highly frequency stability and are candidates for ultrahigh temperature piezoelectric application.

1. Introduction High-temperature piezoelectric materials can be applied in hightemperature sensors, ferroelectric random storage [1], ferroelectric gate field effect transistors [2], gas turbine engine control (1273 K), petroleum, geological exploration, power generation industry and other fields [3]. One of the high-temperature piezoelectric materials Ln2Ti2O7 (Ln = Lanthanide) is layered perovskite structure, which can be applied in high-temperature field due to its high Curie temperature. The structural stability of Ln2Ti2O7 is determined by the radius ratio of Ln3+ and Ti4+.When r

appears. r

and

(Ln3 +)

r

(Ti4 +)

(Ln3 +)

r

(Ti4 +)

r

(Ln3 +)

r

(Ti4 +)

= 1.46 ∼ 1.78, the pyrochlore structure

> 1.78 is corresponding to the perovskite-like structure

< 1.46 to the defective fluorite structure.

r

(La3 +)

r

(Ti4 +)

= 1.92 is for

La2Ti2O7 (LTO) which belongs to the perovskite-like structure [4]. LTO whose Curie temperature is about 1500 °C is one kind of Ln2Ti2O7 materials. A lot of literature have reported that LTO is monoclinic phase with space group P21 [3]. In 1970, it was reported that the piezoelectric coefficient d33 of single crystal La2Ti2O7 was about 16 pC/N [5]. At room temperature, the cell parameters of monoclinic LTO were ∗

a = 7.81 Å, b = 5.55 Å, c = 13.02 Å and β = 98.43. The spontaneous polarization of LTO is along the b-axis [6]. In 2009, Haixue Yan et al. reported that LTO with an orientation factor of 0.79 had a favorable piezoelectric coefficient 2.6 pC/N and high Curie temperature 1461 ± 5 °C. This kind of materials could be used in high temperature fields [7]. At present, the main methods for improving properties of LTO ceramics are: (i) prepare LTO precursors by new methods to obtain uniform and highly activated powders, such as sol-gel method [8], precipitation method [7], organic matter decomposition method [9] and hydrothermal method [10]; (ii) LTO is made into textured ceramics, such as using SPS sintering [7]; (iii) Other elements are added to A or B or A/B positions of LTO to improve its electrical properties, such as La2−xCexTi2O7 (x = 0.15, 0.25, 0.35) [11], La2Ti1.97T0.03O7 (T = Co, Fe, Mn, Cr) [12] and (Sr1-xLax)2(Ta1-xTix)2O7 [13] ceramics. It is well known that presence of excess B-site element can lead to

Corresponding author. E-mail address: [email protected] (J. Zhu).

https://doi.org/10.1016/j.ceramint.2019.03.160 Received 14 January 2019; Received in revised form 20 March 2019; Accepted 21 March 2019 Available online 26 March 2019 0272-8842/ © 2019 Elsevier Ltd and Techna Group S.r.l. All rights reserved.

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optimization of density, dielectric and piezoelectric properties [14]. In this article, in order to fine-tune the phase structure and electrical properties of LTO ceramics, Ti excess La2Ti2(1+x)O7 (x = 0, 0.005, 0.01, 0.02, 0.05, 0.1) ceramics were prepared. Impedance spectra are non-destructive to the analysis of microstructure and electrical properties of materials. It can be used to evaluate various kinds of relaxation frequencies, such as bulk defects, grain boundary effects, and electrode surface effects [15]. It is an important tool for studying localized relaxation (dipoles) and delocalized conduction (long-range conduction) of ferroelectric materials [16]. The advantage of impedance lies in measuring and analyzing some frequency correlation functions and plotting these functions in a complex plane. These graphical plots help to explain the small-signal ac response of the materials to be studied [17]. In this paper, the piezoelectric ceramics of Ti-site excess LTO were prepared and their phase structure and impedance spectroscopies were analyzed to investigate the relaxation phenomenon of ceramics from the microscopic level. 2. Experimental procedure The LTO piezoelectric ceramics with excessive Ti content were prepared by sol-gel method combined with solid state synthesis method. The detail processes of obtaining LTO sol, gel, powders and ceramics were the same as the reference elsewhere [18]. X-ray diffraction (EMPYREAN), with scan type continuous and the rays Kα1 1.540598 and Kα2 1.544426 emitted by Cu target was used to determine the general phase structure of La2Ti2(1+x)O7 ceramics. The flat panel detector (PIXcel, A Medipix3 collaboration) was 256 × 256 points array. The scan step size, time per step and minimum step size omega were 0.013°, 16.32 s and 0.0001°, respectively. Software JADE [19–22] and MAUD [23,24] were employed to analyze explicit the samples' phase structure, cell parameters, and atomic site occupations. Software DIAMOND [25,26] was used to reveal a clear cell structure as well as the distortion angles of TiO6 oxygen octahedrons. These parameters are the fundamental elements of LTO ceramics. The scanning electron microscope (SEM) (JSM-7500, Japan) was used to observe the grains’ microscopic appearance of the sintered ceramics. The frequency and temperature dependences of dielectric permittivity and impedance of the ceramics were measured using an LCR meter (HP4980, Agilent, USA). Samples for piezoelectric measurements were poled under DC electric field (15 kV/mm) in silicone oil at a temperature of 180 °C for 30 min. After poled for 24 h, the piezoelectric coefficients d33 of the ceramics were measured by Belincourt meter (ZJ-3AN, Chinese Academy of Sciences, China). 3. Results and discussions 3.1. Phase structure analysis Fig. 1 shows the X-ray diffraction spectra of La2Ti2 (1+x) O7 ceramics with different Ti content at room temperature. The spectra of prepared La2Ti2 (1+x) O7 ceramics, standard monoclinic phase La2Ti2O7, orthogonal phase La2Ti2O7 and tetragonal phase La0.67TiO2.87 are shown in Fig. 1 (a). The magnified views of La2Ti2 (1+x) O7 peak positions are shown in Fig. 1(b) and (c) and (d). In Fig. 1 (a), it can be seen that all of the prepared ceramics are perovskite structures. With the increase of x, the monoclinic La2Ti2O7 phase or orthogonal phase La2Ti2O7 turns to the coexistence of monoclinic La2Ti2O7 phase and a bit of orthogonal phase La0.67TiO2.87 existing in the ceramics. The peaks’ positions and intensities of monoclinic phase La2Ti2O7 and the orthogonal phase La2Ti2O7 are similar, so that they are difficult to be distinguished. On the contrary, the peaks in tetragonal phase La0.67TiO2.87 are quite different from them. In Fig. 1(b) and (c) and (d), when x ≤ 0.01, only pure monoclinic phase or orthogonal phase or their mixed phases exist in the ceramics.

The tetragonal phase La0.67TiO2.87 with space group P4/mmm appears when x ≥ 0.02. The obvious peaks belonging to La0.67TiO2.87 in these samples correspond to the crystal plane indices (001), (011) and (012) in (a), (b) and (c), respectively. When x = 0.1, the peaks belonging to plan (012) become the strongest. This phenomenon indicates that the quantity of tetragonal phase reaches the highest level among all samples, shown in Fig. 1 (d). In order to further clarify the exact phase composition of La2Ti2 (1+x) O7 with different Ti contents, the cell structure diagrams of three standard PDF cards monoclinic La2Ti2O7 (1950-ICSD), orthogonal La2Ti2O7 (4132-ICSD) and tetragonal La0.67TiO2.87 (77674-ICSD) are provided and drawn in Fig. 2. It has reported that the monoclinic phase La2Ti2O7 is distorted layered perovskite structure, which is layered along the a-axis and its spontaneous polarizations are along b-axis [6]. If the angles between the TiO6 oxygen octahedrons and b-axis change, the spontaneous polarizations of La2Ti2O7 will change simultaneously. In the unit cell diagrams of standard monoclinic La2Ti2O7 with space group P21, it is defined that the angle between the two oxygen octahedrons in the upper half cell is a0 in a-b projection plane. The angle a0 is shown in the left of Fig. 2. The same definition method is applied in other two phases. The angle b0 is belonging to orthogonal phase La2Ti2O7 with space group Pna21 and c0 for tetragonal phase La0.67TiO2.87 with space group P4/mmm. The essential difference between monoclinic and orthogonal La2Ti2O7 is that whether they are twin crystal. There is a mirror surface perpendicular to c-axis. The twinning operation can only affect the position of oxygen ions. The rotation angle in orthogonal La2Ti2O7 between the twins is 17.12° [4]. Therefore, the unit cell size of orthogonal La2Ti2O7 is twice of the monoclinic La2Ti2O7. It has been reported in the literature in which the twins’ spontaneous polarization is 0 [7]. However, there are few articles with this view. It is possible that the spontaneous polarizations of this structure can neutralize each other along a fixed direction, while that can exists along with other directions. This viewpoint requires further verification. Software MAUD is employed to analyze the phase composition and unit cell parameters of the prepared La2Ti 2 (1+x) O7 ceramics. The cell structures the samples shown in Fig. 3. The refinement results indicate that all samples meet the refinement requirements, reliability factors sig < 2, Rwp (%) < 10%. The specific refinement parameters for all samples are shown in Table .1. It reveals that monoclinic phase La2Ti2O7 and orthogonal phase La2Ti2O7 coexist in sample La2Ti2 (1+ x) O7, x = 0. When x = 0.005 or x = 0.01, the samples only possess pure monoclinic phase La2Ti2O7. The tetragonal phase La0.67TiO2.87 appears and coexists with monoclinic phases La2Ti2O7 when x ≥ 0.02. The angles a0, b0 and c0 are measured by software DIAMOND and have been listed in the blank position of Fig. 3. The distortion angles in a-b projection plan of monoclinic phase La2Ti2O7, orthogonal phase La2Ti2O7 and tetragonal phase La0.67TiO2.87 are defined as αi = | ai - a0| (i = 1, 2, 3, 4, 5, 6), βj = |bj - b0| (j = 1), γk = |ck - c0| (k = 4, 5, 6). (1, 2, 3, 4, 5, 6) for La2Ti2 (1+x) O7 (x = 0, x = 0.005, x = 0.01, x = 0.02, x = 0.05, x = 0.1) samples. The specific values are shown in Table 2. It can be seen that the distortion angles of monoclinic phase is the largest for all samples. With the increase of Ti content in La2Ti2 (1+x) O7 ceramics, the distortion angles for monoclinic phase La2Ti2O7 increase first and decrease then, reaching the maximum value α4 = 34.8° when x = 0.02. The distortion angles for tetragonal phase La0.67TiO2.87 increase with the increase of Ti content in La2Ti2 (1+x) O7 ceramics. Considering on the refinement results, it has discovered that the phase composition and proportion will change with the excessive Ti content in La2Ti2 (1+x) O7 ceramics. It's wondered whether the micromorphology will be affected in Ti excess La2Ti2 (1+x) O7 ceramics. The SEM is employed to analyze the morphology of all samples. The surfaces of samples need to be gold plated before testing. The scanning electron microscope (SEM) spectra (the left pictures), zoom-in spectra (the left pictures) and grain size distributions of La2Ti2 (1+x) O7

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Fig. 1. (a) X-ray diffraction (XRD) spectra and local enlarged XRD spectra (b) 2θ = 10.8–12°, (c) 2θ = 25–27.5° and (d) 2θ = 31.5–34.25°of La2Ti2(1+x)O7 (x = 0, 0.005, 0.01, 0.02, 0.05, 0.1) ceramics at room temperature.

Fig. 2. Standard PDF cards of 1950-ICSD, 4132-ICSD and 77674-ICSD that would be employed to analyze La2Ti2

ceramics are shown in Fig. 4. The grain size distributions are obtained from software Nano Measure. The specific procedures to obtain the grain size distributions are shown in enclosure 1. The densities of all La2Ti2 (1+x) O7 ceramics are measured through Archimedes method. The specific parameters of grain sizes and densities for all samples are listed in Table .3. It is obvious that all samples are dense and non-porous. With the increase of Ti content in La2Ti2 (1+x) O7 ceramics, the grain size decreases and grains gradually change from long strips to polygons then to small particles. When x ≤ 0.01, the samples possess plenty of long strips grains and some irregular grains. The influence of orthogonal phase La2Ti2O7 on the grain size of La2Ti2 (1+x) O7 ceramics can be negligible. When x = 0.02, most of the grains become uniform hexagonal, and their boundaries are connected by small polygonal grains or strips. This

(1+x)O7

ceramics.

phenomenon suggests that excess Ti can restrain the grains' growth directions in monoclinic phase La2Ti2O7 ceramics. The grain sizes in this sample are mainly concentrated between 16 and 22 μm. When x ≥ 0.05, a large number of small particles (< 10 μm) are precipitated from the long-slab grains, and the larger the amount of Ti, the more precipitation grains form. Taking the refinement results into account, it's supposed that monoclinic phase La2Ti2O7 is easy to form long flaky large grains, while tetragonal phase La0.67TiO2.87 prefers to precipitation grains. Therefore, the tetragonal phase La0.67TiO2.87 can be obtained from monoclinic phase La2Ti2O7 when the content of Ti excesses x ≥ 0.02 in the La2Ti2 (1+x) O7 ceramics. The trend of relative densities of La2Ti2 (1+x) O7 ceramics increases to the maximum 97.41% when x = 0.01, and then decreases with the increase of Ti content. It is suggested the La2Ti2 (1+0.01) O7 ceramics should possess perfect

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Fig. 3. Refinement and cell structure of La2Ti2

(1+x)

O7 (a) x = 0, (b) x = 0.005, (c) x = 0.01, (d) x = 0.02, (e) x = 0.05 and (f) x = 0.1.

electrical performances. 3.2. Impedance spectroscopy analysis Fig. 5 shows the dielectric relaxation of La2Ti2 (1+x) O7 samples at frequency range 100 Hz–1 MHz before Curie temperature. It is obvious that the dielectric constants of all samples increase slowly till 400 °C, and then rapidly after 400 °C. This phenomenon could be attributed to the grain boundary effect and various types of polarizations or space charges existing in ceramics [27]. The dielectric constants of all samples

decrease rapidly with the increase of frequency at low frequency range f < 104 Hz. This phenomenon corresponds to the appearance of dielectric loss peaks, shown in the insert diagrams in Fig. 5. The relaxations exist in La2Ti2 (1+x) O7 ceramics in this process. The dielectric constant peaks of all samples merge when the frequency range is f > 104 Hz. It indicates that various relaxations are frozen. In the insert diagrams of Fig. 5, some non-conspicuous peaks which could be the characteristic peak of monoclinic phase La2Ti2O7 appear at high frequency range when x ≤ 0.02. However, these peaks disappear in the whole frequency range when x ≥ 0.05. It's suggested that the tetragonal

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Table 1 The specific refinement parameters for La2Ti2 the parameter doesn't exist).

(1+x)

O7 ceramics (M: monoclinic phase La2Ti2O7; O: orthogonal phase La2Ti2O7; T: tetragonal phase La0.67TiO2.87;/:

Parameters

La2Ti2O7

La2Ti2.01O7

La2Ti2.02O7

La2Ti2.04O7

La2Ti2.1O7

La2Ti2.2O7

Sig Rwp (%) Rb (%) Symmetry Space group Phase fraction (%) a (Å) b (Å) c (Å) α (°) β (°) γ (°) Z V (Å3)

1.8929 8.4240 6.6870 M&O P21&Pna21 93.38&6.62 7.8160 & 25.7368 13.0215 & 7.8331 5.5518 & 5.6043 90.00 & 90.00 90.00 & 90.00 98.59 & 90.00 4&8 558.70 & 1129.82

1.9275 8.7107 7.0120 M P21 100.00 7.8010 13.0142 5.5481 90.00 90.00 98.60 4 557.57

1.9223 8.6993 6.8870 M P21 100.00 7.8179 13.0247 5.5525 90.00 90.00 98.61 4 559.01

1.9835 8.9603 7.0098 M&T P21&P4/mmm 97.29&2.71 7.8115 & 3.8980 13.0129 & 7.7949 5.5483&/ 90.00 & 90.00 90.00 & 90.00 98.60 & 90.00 4&2 557.65 & 118.44

1.9039 8.5770 6.8033 M&T P21&P4/mmm 85.87&14.13 7.8169 & 3.8903 13.0214 & 7.7308 5.5526&/ 90.00 & 90.00 90.00 & 90.00 98.59 & 90.00 4&2 558.85 117.00

1.8579 8.1851 6.4849 M&T P21&P4/mmm 82.29&17.71 7.8106 & 3.8851 13.0129 & 7.7240 5.5470&/ 90.00 & 90.00 90.00 & 90.00 98.63 & 90.00 4&2 557.41 & 116.59

phase La0.67TiO2.87 could shift these characteristic peaks' situations to a certain extent. In order to verify whether the results obtained from frequency spectra are precise, the temperature dependence of dielectric permittivity for La2Ti2 (1+x) O7 (x = 0.01) ceramics are obtained from Fig. 5 and shown in Fig. 6 (a). The directly tested dielectric permittivity is shown in Fig. 6 (b). It can be seen that the (a) and (b) diagrams fit well except. It demonstrates that the test results are guaranteed. In order to study the relaxation mechanism of the first peaks at lower frequency in the insert diagrams of Fig. 5, the relaxation activation energy is necessary to be calculated. The frequencies corresponding to the peak are fp , and the angular frequencies are ωP = 2πfp , so

ωp τp = 2π

(1)

The relaxation activation energy can be calculated from Arrhenius' law:

temperature, the arcs’ radius become smaller first and then two arcs with different radius are formed at high temperature interval. It suggests that negative temperature coefficient effect exists in the La2Ti2 (1+x) O7 ceramics. The grain and grain boundary conductivity are both dominate relaxation mechanisms at high temperature. In general, the grain conductance and grain boundary conductance appears as a high-frequency semi-arc and a low-frequency semi-arc in the complex impedance diagram [31]. The centers of all samples' arcs do not fall above the real axis. This phenomenon can be explained by the statistic distributions of relaxation time [17]. The large arc consists of two small arcs and it can be separated at high temperatures. There is a distribution of relaxation times rather than a single relaxation time existing in samples. It's called non-Debye type relaxation. Many factors can have an effect on this kind of relaxation, such as grain orientation, grain boundaries, stress-strain, and atomic defect distribution [32]. In the non-Debye relaxation model [33,34],

ZCPE =

E ⎞ τ = τ0 exp ⎛ ⎝ kB T ⎠ ⎜

φπ φπ 1 1 1 ⎞ ⎞−i sin ⎛ cos ⎛ = A 0 ωφ YCPE A 0 ωφ ⎝ 2 ⎠ ⎝ 2 ⎠

⎟

(2)

Fig. 7 shows the fitted results. The relaxation time and relaxation activation energy of each sample can be obtained from the intercept and slope [28]. The specific values are shown in Table .4. In Fig. 7, it can be seen that the relaxation activation energy of La2Ti2 (1+x) O7, x = 0.01 is the highest (E0.01 = 1.58 eV) . The calculated relaxation frequency of La2Ti2.02O7 ceramics is f0 = 1.07987 × 1011 Hz, which is close to atomic or ions’ resonance frequency in crystal (1012–1013 Hz). E. Bruyer et al. used the firstprinciples to calculate the band gap of La2Ti2O7 in monoclinic phase La2Ti2O7 and found its value is 3.2 eV [29]. For La2Ti2.02O7 ceramics, the theory value is close to the twice of relaxation activation energy. The result manifests that resonance dispersion exists in La2Ti2.02O7 ceramics at high frequency and high temperature interval. The relaxation activation energies of other samples are near 1 eV, which is from the conduction activation energy of the second ionized electrons from the oxygen vacancies VO⋅⋅ [30]. Complex impedance spectroscopy is employed to investigate the relaxation mechanisms. Fig. 8 shows the ac impedance spectra of La2Ti2 (1+x) O7 samples at different temperatures. With the increase of test Table 2 The distortion angles of La2Ti2

(1+x)

At φ = 0 , the CPE is a pure resistor and its value is R = the CPE is a pure capacitor A 0 . At 0 < φ < 1,

(3) 1 . A0

At φ = 1,

2

2

R R R 2 ⎛Z′ − ⎞ + ⎛Z′ ′ + tanθ ⎞ = ⎛ ⎞ (1 + tan2θ) 2⎠ 2 ⎠ ⎝2⎠ ⎝ ⎝

(4)

( ) φπ 2

. When the grain and grain boundary In equation (4), tanθ = cot both contribute to the ceramic conductance, it is equivalent to two sets of R-CPE series. The two partial arcs can be fitted by equation (4). The AC conductivity of La2Ti2 (1+x) O7 ceramic can be obtained from the complex impedance spectrums. Fig. 9 describes the frequency dependence of ac conductivity for the Ti excessed ceramic La2Ti2 (1+x) O7 (x = 0, 0.005, 0.01, 0.02, 0.05, 0.1) at definite temperatures. The ac conductivities disperse at low frequency region for all samples. The increase of ac conductivities at low frequency region can attribute to the disordering of cations between adjacent sites and the presence of space charge [17]. The ac conductivity increase with the increase of x at temperature range T ≤ 400 °C. When T ≥ 500 °C, the ac conductivity increase first and then decrease with the increase of x from 0 to 0.1. This trend indicates that the tetragonal phase La0.67TiO2.87 can reduce the electrical conductivity of La2Ti2 (1+x) O7 ceramics and increase its

O7 ceramics.

Angles (°)

La2Ti2O7

La2Ti2.01O7

La2Ti2.02O7

La2Ti2.04O7

La2Ti2.1O7

La2Ti2.2O7

αi βj ϒk

27.0 0.6 /

20.5 / /

28.9 / /

34.8 / 4.6

20.6 / 5.3

16.2 / 6.3

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Fig. 4. Scanning electron microscope (SEM) spectra (the left pictures), zoom-in spectra (the left pictures) and grain size distributions of La2Ti2 (1+x) O7 (a) x = 0, (b) x = 0.005, (c) x = 0.01, (d) x = 0.02, (e) x = 0.05 and (f) x = 0.1. Table 3 The grain sizes and densities for La2Ti2

(1+x)

O7 ceramics.

Parameters

La2Ti2O7

La2Ti2.01O7

La2Ti2.02O7

La2Ti2.04O7

La2Ti2.1O7

La2Ti2.2O7

Average grain size (μm) Maximum grain size (μm) Density (g/cm3) Theory density (g/cm3) Relative density (%)

29.17 98.02 5.54 5.79 95.68

33.18 130.81 5.56 5.80 95.86

24.69 139.33 5.65 5.80 97.41

19.42 31.36 5.58 5.78 96.54

19.24 121.24 5.53 5.72 96.68

8.68 59.21 5.51 5.70 96.67

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Fig. 5. Frequency dependence of the dielectric permittivity εr and dielectric loss tanδ (insert figures) of ceramics La2Ti2 x = 0.01, (d) x = 0.02, (e) x = 0.05 and (f) x = 0.1 at temperature range 200 °C–700 °C.

(1+x)

O7 (a) x = 0, (b) x = 0.005, (c)

Fig. 7. Arrhenius plot of the dielectric relaxation peaks and linear fitted solid lines of La2Ti2 (1+x) O7 ceramics. Table 4 Exponential logarithm of the relaxation time and relaxation activation energy parameters of La2Ti2 (1+x) O7 ceramics. Fig. 6. Temperature dependence of dielectric permittivity εr for La2Ti2 (1+x) O7 x = 0.01 (a) obtained from Fig. 5 and (b) obtained from directly test.

resistivity to a certain extent. According to the analysis of complex impedance in Fig. 8, the relaxation mechanism is dominated by both grain and grain boundary conductance for all samples. The ac conductance mode is [35]:

σac (ω) = σdc + Aωng + Bωngb

(5)

In equation (5), σac (ω) is the ac conductivity which can be obtained from the complex impedance spectra. σdc is the fitted dc conductivity. Aωng and Bωngb are the influences of conductive relaxation on conduction for grain and grain boundary, respectively. The index ng and ngb lie in high frequency and low frequency regions, respectively. Parameters A and B are constant. For the La2Ti2 (1+x) O7 ceramics at T = 600 °C, the fitted results are shown in Fig. 10. Fig. 10 shows the fitted ac conductivity curves and resistivity for La2Ti2 (1+x) O7 ceramics at 600 °C. The fitted results in (a)-(f) are considerable. That denotes the model in equation (5) is favorable. In Fig. 10 (g), with the increase of x, the resistivity of La2Ti2 (1+x) O7

La2Ti2(1+x)O7

x=0

x = 0.005

x = 0.01

x = 0.02

x = 0.05

x = 0.1

Ln(τ0) E (eV)

- 20.71 1.16

- 19.57 1.15

- 25.41 1.58

- 21.53 1.30

- 21.17 1.00

- 18.90 0.86

ceramics increases first and then decreases at 600 °C. The interpretation is that the excess Ti in La2Ti2 (1+x) O7 ceramics can form pinning [36] and increase resistivity before x ≤ 0.02. When 0.02 < x < 0.05, the excess Ti reacting with monoclinic phase La2Ti2O7 can form tetragonal phase La0.67TiO2.87, which can improve ceramic resistivity. This conclusion has been obtained from the analysis of Fig. 9. However, the resistivity decreases rapidly from x > 0.05, which can be attributed to the occurrence of excessive defects in ceramics and the appearance of leak current. Fig. 11 shows the constant phase angle element CPE-T, CPE-P and resistances R of grains and grain boundaries for La2Ti2 (1+x) O7 ceramics. The parameters are obtained by fitting circuit model using software ZView. The impedance is defined as [37]:

Z = 1/[T (j × ω) P ]

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Fig. 8. Nyquist curves of La2Ti2 200 °C–700 °C.

(1+x)

O7 (a) x = 0, (b) x = 0.005, (c) x = 0.01, (d) x = 0.02, (e) x = 0.05 and (f) x = 0.1 ceramics in the temperature range

Fig. 9. Frequency dependence of ac conductivity for La2Ti2 (1+x) O7 ceramics at (a) T = 200 °C, (b) T = 300 °C, (c) T = 400 °C, (d) T = 500 °C, (e) T = 600 °C and (f) T = 700 °C. 12749

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Fig. 10. The frequency dependence of ac conductivity for La2Ti2 (1+x) O7 (a) x = 0, (b) x = 0.005, (c) x = 0.01, (d) x = 0.02, (e) x = 0.05, (f) x = 0.1 ceramics and (g) the resistivity ρ for La2Ti2 (1+x) O7 at T = 600 °C.

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Fig. 11. Temperature dependence of (a–f) CPE-T for grain and grain boundary; (g–l) CPE-P for grain, grain boundary of La2Ti2 (1+x) O7 ceramics; (m–r) resistance R for grain and grain boundary.

In which

Pπ Pπ ⎞ ⎞ + i sin ⎛ j P = cos ⎛ ⎝ 2 ⎠ ⎝ 2 ⎠

(7)

And the phase angle is

φ∗

= −Pπ/2

(8)

The meaning of P is equivalent to φ in equation (3) and P is defined as CPE − P (0 ≤ CPE − P ≤ 1) . When P = 1, the T is equivalent to a pure capacitor and is defined as CPE − T . The impedance for all samples mainly includes both grains and grain boundaries. The analog circuit consists of two parallel R-CPE elements in series which is shown at the lower left corner in Fig. 11 (m) [38]. This circuit is corresponding to the equations (3) and (4). From (a)-(f), as the test temperature increases, the ceramic grain capacitance CPE-T increases first and then decreases slowly when x ≤ 0.02 at the temperature interval 300–700 °C. The variation trend of grain boundary capacitance is inconsistent due to insufficient effective fitted points. When x ≥ 0.05, the grain capacitance CPE-T remains stable, while the grain boundary capacitance gradually increases. This result attributes to the influence of the tetragonal phase La0.67TiO2.87 on the ceramic grain boundary at high temperature. In diagrams (g)-(i), the CPE-P for grains are less than 1.0 and always larger than grain boundaries'. It's indicated that the grains are closer to a pure capacitor. In diagrams (m)-(r), both of the grain and grain boundary resistances decrease with the rise of temperature at 300–700 °C. It's also indicated that all prepared La2Ti2 (1+x) O7 ceramics have negative temperature coefficient effect. The grain resistances are dominate at T < 500 °C. With the increase of temperature, the decreasing of grain resistances mainly attributes to the presence of hot carriers. The grain boundary resistances appear at temperature range T > 500 °C. At this temperature interval, all samples' grain boundary resistances are always larger than the grain resistances. It demonstrates that the grain intrinsic carrier conductance dominates in the high temperature stage. Fig. 12 shows the frequency dependence of real and imaginary parts of impedances for La2Ti2 (1+x) O7 ceramics with different x. At low frequency, Z′ decreases rapidly and merges at a certain frequency with increasing frequency. Temperature also has a large influence on the real and imaginary parts of impedance. The merge point of Z’ can be seen lower than 400 °C, while that has excessed 1 MHz higher than 500 °C. This phenomenon explains that the temperature rise can cause thermionic relaxation, Whose frequency range is 102–108 Hz. This phenomenon is more apparent in the insert diagrams Z″-f in Fig. 12. The

relaxation peaks appear at temperature range T > 400 °C. As the test temperature increases, the relaxation peaks of all samples move toward to high frequency. It means that the relaxation times become shorter with the increase of temperature. This result can lead to the decrease of capacitance. The Z″ peak for x = 0.01 ceramics is the largest at 500 °C while the same peak for x = 0.1 ceramics appears at 600 °C. It is probably that the tetragonal phase La0.67TiO2.87 in La2Ti2.2O7 ceramics can thin grains and form relaxation. To distinguish the contribution of grains and grain boundaries to the static dielectric constant at various temperatures, Fig. 13 shows the calculated dielectric permittivity of grain and grain boundary for La2Ti2 (1+x) O7 (x = 0.01) ceramics. If two peaks do not coincide in the Z″-f curves,

ωmax(g ) = 1/ Rg Cg ωmax(gb) = 1/ Rgb Cgb

(9)

In equation (9), the frequency corresponds to the maximum Z ′′max is the characteristic angle frequency, ωmax = 2πf . Rg , Rgb , Cg and Cgb are the resistance and capacitance for grain and grain boundary, respectively. When the peaks Z ′′max appear,

Z ′′max = εr =

Cl ε0 S

R 2

(10)

(11)

In equation (11), εr is the static dielectric permittivity, C is the capacitor, ε0 is the vacuum dielectric constant, l is the thickness of sintered ceramics and S is the round surface area of ceramics. In Fig. 13 (a), the grain dielectric permittivity decrease first and then increase with the increase of temperature at interval 425 °C–700 °C. The decreases of dielectric permittivity owe to the negative temperature coefficient effect, while the increases of it attributed to the phase transition from monoclinic phase La2Ti2O7 to orthorhombic phase La2Ti2O7. This result is consistent with the fact that the La2Ti2O7 has an exothermic peak at 780 °C which may be a monoclinic orthotropic phase transition point reported by Zhenmian Shao in 2010 [4]. The grain boundary dielectric permittivity decreases first and gradually increases at around 670 °C. The analysis result is the same as the phenomenon in grain dielectric permittivity. It is interesting that the trends of grain and grain boundary dielectric permittivity are consistent with the CPE-T in Fig. 11 (c). That means the model of two RCPE series is suitable for grain and grain boundary relaxations.

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Fig. 12. The real Z′ and the imaginary Z’’ (insert diagrams) parts of complex impedances for La2Ti2

(1+x)

O7 ceramics.

The normalized Z''/Z″max diagrams can demonstrate more clearly the contribution of grains and grain boundaries to conductance in La2Ti2 (1+x) O7 ceramics. Fig. 14 shows the frequency dependence of Z''/Z″max for La2Ti2 (1+x) O7 ceramics at temperature range 500–700 °C. It is obvious that two peaks arise above 650 °C when x ≤ 0.02. The first peak in low frequency region and the second in high frequency region correspond to grain boundary and grain conductance, respectively. The value of x has little effect on the position of these two peaks. When x ≥ 0.05, only one peak exists under test conditions, T = 500–700 °C, f = 103∼106 Hz. This phenomenon ascribes to the presence of the tetragonal phase La0.67TiO2.87 which can restrain grain boundary conductance. It is worth noting that when x < 0.05, the peaks shift to higher frequency with the increase of temperature. That ascribes to a decrease in the grain capacitance [39]. When x = 0.1, T < 650 °C, the peaks shift to higher frequency region and then to lower as the temperature increases. At this process, the capacitances keep stable and the resistances decrease owing to negative temperature coefficient effect. When T > 650 °C, as the temperature increases, the grain capacitances increase rapidly ascribing to the influence of tetragonal phase La0.67TiO2.87. The two peaks appearing in Fig. 14 at x ≤ 0.02 and they correspond to both grain boundary and grain relaxation mechanisms. The equivalent circuit can be described by the following formula [28]: Fig. 13. Temperature dependence of static dielectric permittivity εr of grain and grain boundary for La2Ti2.02O7 ceramic.

Rg Rgb ⎤+R ⎡ ⎤ Z′ ′ = Rg ⎡ gb ⎢ 2⎥ ⎢ 1 + (ωRg Cg )2 ⎥ + 1 ( ωR gb Cgb ) ⎦ ⎦ ⎣ ⎣

(12) ′

The normalized peaks of the imaginary part Z′ in the impedance 12752

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Fig. 14. Frequency dependence of normalized impedance Z’‘/Z’‘max for La2Ti2(1+x)O7 (a) x = 0, (b) x = 0.005, (c) x = 0.01, (d) x = 0.02, (e) x = 0.05, (f) x = 0.1 ceramics at temperature range 500 °C–700 °C.

diagrams are corresponding to the characteristic angle frequencies ω . The characteristic frequencies ω obey Arrhenius' law:

E ωmax = ω0exp ⎛− a ⎞ k ⎝ BT ⎠ ⎜

⎟

(13)

In equation (13), Ea is relaxation activation energy, kB is Boltzmann constant, and T is the absolute temperature. The fitting results are shown in Fig. 15. The peaks appearing at 650 °C at low frequency region are not obvious compared with the peaks at high frequency region.

So, no fitting analysis is done for this kind of peaks in this part because the fitting result is meaningless. Fig. 15 shows the fitting results of peaks for La2Ti2 (1+x) O7 ceramics in high frequency region in Fig. 14. The grain relaxation activation energies of La2Ti2 (1+x) O7 ceramics can be obtained from fitted slopes, shown in the blank area in Fig. 15. It has reported that the theory band gap for pure monoclinic phase La2Ti2O7 is 3.2 eV [29], which is twice of the relaxation activation energy of grains. Therefore, the main conductance mechanism for La2Ti2 (1+x) O7 ceramics is grain conduction at temperature interval 500–700 °C. Compared with the insert diagrams in Fig. 12, the normalized Z’‘/ Z’‘max in Fig. 16 can reveal the influence of different Ti excess on La2Ti2 (1+x) O7 ceramics at specific temperatures more clearly. In Fig. 16, no peak exists at 300 °C while some peaks arise at 400 °C at x ≤ 0.01. The Z’‘/Z’‘max peaks for all La2Ti2 (1+x) O7 ceramics move toward to higher frequency region as test temperature increases, that means the relaxation phenomenon is a thermal activation process. For different x, the values of Z’‘/Z’‘max tend to merge at high frequency region. This phenomenon attributes to the release or disappearance of space charge [17,31]. In La2Ti2 (1+x) O7 ceramics, the Z’‘/Z’’max peaks arise above 500 °C for x ≤ 0.02, while that phenomenon appears in La2Ti2 (1+x) O7 (x ≥ 0.05) ceramics until 600 °C. That means the presence of tetragonal phase La0.67TiO2.87 can increase the thermionic activation energy. The insert diagrams in Fig. 16 shows the normalized electrical modulus M’‘/M’’max of La2Ti2 (1+x) O7 ceramics. The merit for electrical modulus is that it significantly suppresses electrode polarization effects [40].

Fig. 15. Arrhenius fitted lines of La2Ti2 (1+x) O7 ceramics from frequency dependence of Z’‘/Z’‘max peaks in high frequency region. 12753

M′ ′ = ωε0 Z ′

(14)

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Fig. 16. Frequency dependence of normalized Z’‘/Z’‘max and Electrical modulus M’‘/M’‘max (insert diagrams) for La2Ti2 (1+x) O7 (x = 0, 0.005, 0.01, 0.02, 0.05, 0.1) ceramics at (a) T = 300 °C, (b) T = 400 °C, (c) T = 500 °C, (d) T = 600 °C, (e) T = 650 °C and (f) T = 700 °C.

All samples' M’‘/M’‘max peaks exist at temperature interval 300–500 °C. When T > 600 °C, the peaks which reflect the attribution of capacitance in tetragonal phase La0.67TiO2.87 for x ≤ 0.02 disappear while that still exist for x ≥ 0.05. The same conclusion has already obtained from the analysis in Fig. 11. In M’‘/M’’max spectra, the carriers are limited and can only jump in the potential well when the frequency is higher than fmax . In contrast, long-distance conduction is dominated at frequency range f < fmax [41,42]. The characteristic frequency positions in Z’‘/Z’‘max and M’‘/M’‘max spectrums should coincide When the relaxation mechanism of the same ceramic is identical. Fig. 17 shows the normalized Z’‘/Z’‘max and M’‘/ M’‘max spectra for La2Ti2.02O7 ceramic. It is obvious that the peaks of Z’‘/Z’‘max and M’‘/M’‘max haven't overlapped. This phenomenon demonstrates that local conduction current exists in the ceramics [16]. Fig. 18 shows the normalized modulus M’‘/M’‘max for La2Ti2 (1+x) O7 with different content of Ti at temperature interval 300 °C–700 °C. As the temperature increases, the M’‘/M’‘max peaks move towards to higher frequencies for all ceramics. The trend is consistent with the Z’‘/ Z’’max spectra in Fig. 16. It reveals that thermal activation relaxation or dipole reorientation exists in all prepared ceramics [43,44]. It needs special attention that two peaks present at T = 300 °C when x = 0.1, the possible reason is that the first peak corresponds to the grain conductance relaxation of monoclinic La2Ti2O7 at lower frequency region,

and the second peak is attributed to the grain conductance mechanism of tetragonal phase La0.67TiO2.87 at higher frequency region. Fig. 19 is the piezoelectric coefficient diagram of La2Ti2 (1+x) O7 ceramics. The piezoelectric coefficient increases to the maximum value at x = 0.01 and then decreases with the increase of x. It can be found that electric domains are easier to form in monoclinic phase La2Ti2O7 (long strips) than in tetragonal phase La0.67TiO2.87 (precipitated grains). This result can also be obtained from the refinement and SEM analysis. In addition, high piezo-response is consistent to high relative density in La2Ti2 (1+x) O7 ceramics. Therefore, it is indicated that adjusting different content in Ti element for La2Ti2O7 ceramics can regulate the phase structure and electrical properties of LTO ceramics. 4. Conclusion Through the analysis of Ti excess La2Ti2 (1+x) O7 (x = 0, 0.005, 0.01, 0.02, 0.05, 0.1) ceramics prepared by sol-gel method combined with solid state reaction technology, it can be found that monoclinic coexisting with orthogonal phase, pure monoclinic phase and monoclinic coexisting with tetragonal phase La0.67TiO2.87 appear in ceramics with x = 0, 0.005 ≤ x ≤ 0.01 and 0.02 ≤ x ≤ 0.1, respectively. The maximum piezoelectric coefficient d33 = 2.8 pC/N presents in La2Ti2 (1+0.01) O7 ceramics with the highest relative density 97.41%. Impedance analysis reveals that only one conductance mechanism at lower temperature (T ≤ 500 °C) at x ≤ 0.02, which can be attributed to the presence of hot carriers. Grain and grain boundary conductance dominates at higher temperature (T ≥ 500 °C). At x ≥ 0.02, the grain conductance exists both in monoclinic phase La2Ti2O7 and tetragonal phase La0.67TiO2.87 at lower temperature (T ≤ 400 °C). However, when the temperature is higher than 600 °C, the presence of tetragonal phase La0.67TiO2.87 can inhibit the relaxation of grain boundaries and increase the ceramic capacitance. It is hoped that this study can promote the exploration of the phase structure and impedance of LTO ceramics. Acknowledgements

Fig. 17. Frequency dependence of normalized Z’‘/Z’‘max and electrical modulus M’‘/M’‘max for La2Ti2.02O7 ceramic at T = 600 °C.

This work was supported by the National Natural Science Foundation of China (No. 51332003) and Sichuan Science and Technology Program (2018G20140). The authors are grateful to Ms Wang Hui for SEM measurement. 12754

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Fig. 18. Frequency dependence of normalized electrical modulus M’‘/M’‘max for La2Ti2 (1+x) O7 (a) x = 0, (b) x = 0.005, (c) x = 0.01, (d) x = 0.02, (e) x = 0.05 and (f) x = 0.1 ceramics at temperature interval 300 °C–700 °C.

[6]

[7]

[8] [9]

[10]

Fig. 19. The piezoelectric coefficient d33 for La2Ti2

(1+x)

[11]

O7 ceramics.

Enclosure 1

[12]

The specific procedures to obtain the grain size distributions are shown below:

[13]

(1) Download the software “Nano Measure ” online (2) Open the software and click “File” to open a picture with format “bmp” or “jpg”. (3) Draw a line depending on the test condition, and then click “setting” to define the scale length. (4) Choose a region or the whole picture to mark all grains in by moving the mouse from one edge to another edge. (5) Click “Report” to obtain all grains' sizes. (6) Software Origin is employed to analyze the obtained data.

[14]

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