Effect of Sintering on Structural and Physical ...

Author’s Accepted Manuscript Effect of Sintering on Structural and Physical Properties of Nickel and Lithium Co-Substituted Barium Titanate Ceramics Mahmoud. S. Alkathy, Rahul Gayam, Binoy Krishna Hazra, K.C.James Raju www.elsevier.com/locate/ceri

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S0272-8842(16)32416-6 http://dx.doi.org/10.1016/j.ceramint.2016.12.148 CERI14458

To appear in: Ceramics International Received date: 2 September 2016 Revised date: 30 December 2016 Accepted date: 31 December 2016 Cite this article as: Mahmoud. S. Alkathy, Rahul Gayam, Binoy Krishna Hazra and K.C.James Raju, Effect of Sintering on Structural and Physical Properties of Nickel and Lithium Co-Substituted Barium Titanate Ceramics, Ceramics International, http://dx.doi.org/10.1016/j.ceramint.2016.12.148 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Effect of Sintering on Structural and Physical Properties of Nickel and Lithium Co-Substituted Barium Titanate Ceramics Mahmoud. S. Alkathy, Rahul Gayam, Binoy Krishna Hazra, K.C.James Raju* School of Physics, University of Hyderabad, Hyderabad-500046, India. * Corresponding author Tel. No.: 040-23134305, Fax: +91 40 23010227. email [email protected] Abstract In this work, polycrystalline Ba0.90Li0.1Ni0.05TiO3 ceramics were prepared by conventional solid state reaction technique after microwave calcination of starting materials. The effect of sintering on structural, dielectric and activation energy of Ba0.90Li0.1Ni0.05TiO3 ceramics was investigated. Phase structure was confirmed by XRD and Rietveld refinement of the XRD patterns was carried out to estimate the lattice parameters and atomic positions. It was observed that distortion of the structure (c/a) increased as the sintering temperature increased and this leads to a shift in phase transition towards higher temperature. The average size of grains was affected by the sintering process. The Curie temperatures were observed to vary within an interval of 150-160oC with a degree of diffusivity γ>1. The dielectric constant of the different sintered samples increased from 500 to 1340 at ambient and from 1200 to 2512 at Curie temperature, while the dielectric loss decreased from 0.024 to 0.008 at RT and from 0.04 to 0.022 at Curie temperature as the sintering temperature is increased. The activation energies of all sintered samples were investigated using Arrhenius plots of the temperature dependence of AC conductivity at different frequencies. The result shows that the activation energy decreased with an increase of sintering temperature. The decrease of activation energy with an increase of sintering temperature is attributed to the reduction in a number of grains due to densification which leads to the individual grains come closer and the effective area of the grain to grain contact increases while the grains themselves begin to mimic single crystals. Keywords: Co-substitution, Sintering, Microwave calcination, Dielectric Permittivity, Grain Size, Porosity, Activation Energy.

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1. Introduction. Barium titanate (BaTiO3) is one of the most extensively used electro-ceramic materials. At room temperature, it has high dielectric permittivity. However, the losses are also high and hence to make BaTiO3 (BTO) a viable material for multilayer ceramic capacitor (MLCC) applications small quantities of metal ions are doped [1,2]. Electronics Industry is moving towards miniaturization and in this context passive circuit elements like capacitors have not kept pace with rapid miniaturization observed in transistors. There is a need for materials in MLCC with a potential for further miniaturization by having high permittivity with low dielectric loss and wide temperature stability [3]. With its tetragonal structure and polarization along the c axis, an introduction of dopant cations in BTO replaces the Ba2+ and Ti4+ ions at some sites. This alters the crystal structure [4], which affects the band structure and electronic properties thereby modifying the ferroelectric and dielectric properties while calcination and sintering process and conditions affect grain size and porosity [5-13]. The dielectric properties of BTO can also be enhanced by doping metals such as Ni, Cu, and Ag which creates BaTiO3 - metal composites which form a percolation structure [14-16]. Co-substitution as a method to change the properties of BTO with (La+3, Al+3) or (Ni+2, Nb+5) has been investigated in recent literature [17, 18]. A highly dense microstructure can be obtained at relatively low sintering temperature by adding low melting point materials or by using small particle size starting materials [11]. However, care must be taken to avoid secondary phase formation at higher temperatures or higher substitution concentrations as it negatively affects dielectric constant [19]. Co-substitution of Bi and Li in BaTiO3 ceramics led to reduced sintering temperature and increased dielectric constant [20]. The 2

work presented in this paper explores the effect of sintering temperature on structural and electrical properties of Ba0.90Li0.1Ni0.05TiO3 ceramics measured at different temperatures and in the frequency range of 100Hz -5MHz. 2. Experimental Polycrystalline ceramic pellets of Ba0.90Li0.1Ni0.05TiO3 were prepared using solid state reaction method with microwave calcination of the starting materials. The starting materials were BaCO3, NiO, Li2CO3 (Sigma-Aldrich, 99.99% purity) and TiO2 powders (Sigma-Aldrich, 99.98% purity). The raw materials were weighed according to Stoichiometric ratio and ball milled with acetone for 4 hrs using zirconia balls at 200 r.p.m. The mixture was dried in an oven at 150oC and calcined at 1000◦C for 20 minutes duration with heating and cooling rate of 50oC /minute using MWSS (Microwave Sintering System of ENERZI, India with 1.45KW magnetron). The calcined powders were again ball milled for 4 hrs under same conditions and dried. Disc-Shaped ceramic pellets with a 10 mm diameter were made by adding 1wt% Poly Vinyl Alcohol (PVA) as a binder under pressure of 200 Mpa pressure. The green pellets were heat treated to 500oC at a heating rate of 2oC/min for binder evaporation. The sintering was carried out in a conventional furnace at temperatures of 1150 oC, 1200 oC, 1250 oC, 1300 oC, and 1350oC respectively for 6 h duration with heating and cooling rate of 5◦C /min. Phase formation was confirmed by X-ray diffraction (XRD) study using Bruker D8 Advanced diffractometer with Cu-Kα radiation of wavelength 1.54058 Å.

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Experimental density was estimated by the Archimedes principle [20] with distilled water as the immersion liquid. The microstructure of sintering samples was collected using Field Emission Scanning Electron Microscope FE-SEM (Carl Zeiss, Ultra 55). For electrical studies, both sides of the sintered pellets were well-polished, and the silver paste was applied for electroding and is fired at 300oC. Dielectric properties were determined using an Impedance Analyzer, Agilent E4294A in the frequency range of 100Hz -5MHz from room temperature to 300oC. 3. Result and Discussion. 3-1. Structural analysis X-ray Diffraction pattern of Ba0.90Li0.1Ni0.05TiO3ceramics sintered at different temperatures are shown in Fig.1a. It is observed that the samples sintered at 1150, 1200, 1250 and 1300oC show similar XRD patterns with a splitting of diffraction peaks at 2θ

45º as shown in Fig.1. This

splitting corresponds to (200) and (002) planes of tetragonal phase with space group P4mm as per standard JCPDS file no 5-0626 of perovskite BaTiO3. No trace of oxides of nickel and lithium are observed as secondary phases in co-substituted BTO at these sintering temperatures. However, the secondary monoclinic phase of Ba6Ti17O40 was observed in the sample sintered at 1350oC as seen in Fig. 1a. The Rietveld refinement of the sintered samples was also carried out using fullprof program to estimate the structural parameters. The experimental and fitted XRD patterns for the present study are shown in Fig. 1b. The best fit is observed by using BTO phase with a tetragonal structure of P4mm space group and the peak profile analysis was carried out by Pseudo-Voigt function. The Rietveld refinement was confirmed the tetragonal symmetry for all sintered samples. The refined parameters such as lattice parameters (a, c and tetragonality (c/a), 4

unit cell volume, atomic position, X-Ray density and Goodness of fit index are listed in Table 1. From Fig 1a, it is observed that the (200) peak is shifted towards lower 2θ angle with an increase of sintering temperature and this corresponds to an increase in lattice dimensions and hence unit cell volume (Table1). Peaks of the crystal planes (110) were fitted using Gaussian fitting as shown in Fig.2. From this fitting, the FWHM was calculated. Substituting this in the Scherrer formula [22] the average crystallite sizes were estimated and reported in Table1. The SEM images of Ba0.90Li0.1Ni0.05TiO3 powders after calcinations are shown in Fig. 3(a). The particle sizes of the calcined powder are of the order of 100 nm. The images of the surface of Ba0.90Li0.1Ni0.05TiO3 ceramics sintered at different temperatures are shown in Fig. 3(b-f). It can be observed for samples sintered at 1150oC and 1200oC that small grains separated by pores are the dominant landscape. This indicates that the samples are not well sintered and hence have a lower density (Table 2). The average grain size is measured using linear intercept method [23], and it was found to be 0.85 µm, 1.1 µm, 2.21µm and 3.31 µm for the sintering temperatures of 1150oC, 1200oC, 1250oC and 1300oC respectively. As the sintering temperature increased, a dense microstructure was observed with an increase in average grain size (Table 2). This is due to increase in grain boundary mobility aided by co-substitution of lower melting point metal oxides [24] and is in agreement with the earlier report by Chaisan et al. [25]. The relative density of the samples sintered at 1150oC, 1200oC, 1250oC and 1300oC are 87%, 89%, 95% and 95% respectively. The increase in grain size at higher sintering temperature is due to small particles below a critical size dissolving and feeding larger grains through solid diffusion [2527]. When the sintering temperature was increased to 1350oC, the grain boundaries could not be 5

clearly observed as shown in Fig.3f, due to liquid phase formation. During the sintering process, grain size, the size of pores and some of the pores are affected. Usually, higher sintering temperature leads to decreased porosity as shown in Fig.3e. The reduction in porosity was caused by grain growth during the sintering process. 3-2 Dielectric study: Room temperature dielectric constant before and after porosity correction and loss tangent as a function of frequency for Ba0.90Li0.1Ni0.05TiO3 ceramics sintered at different temperatures has been estimated from impedance vs. frequency data in the frequency range of 100Hz -5MHz as shown in Fig 4 (a-c). From the figure 4(a, b), it is clear that for the samples sintered at 1150, 1200 and 1250oC, dielectric permittivity is approximately constant over a wide range of frequency of 100 Hz-5MHz. It was observed that the dielectric constant of the samples sintered at 1300oC is highest at low frequencies but shows relaxor behavior and reduces to below the permittivity values of samples sintered at lower temperatures as the frequency increases. The relaxation frequency corresponds to loss peak, as shown in Fig. 5a. This behavior agrees well with a Debye-like relaxation [28, 29]. It has been reported that relaxation in any system is a good example of dynamical heterogeneity in which under applied electric field the system gets disturbed from its equilibrium state and upon removal tends to relax back to its equilibrium state [30]. The dielectric constant is a complex quantity, and it is defined as [31]:

 *   ' j '' ……………………….. (1) Where (ɛ’) is the real part and  '' is the imaginary part of the complex dielectric constant. 6

The component that is out of phase with the applied field gives rise to dielectric loss (tanδ) which is the loss tangent given by: tan  

 ''  ''    tan 1 ( ) …………. (2) ' '

The complex dielectric constant given by [31] can be derived as following:

 *  1  [   1 

( s    ) ] …………… (3). 1  j

Equating equation (1) with equation (3) we can get:

 ' j '' = 1  [   1 

Now setting

( s    ) (   ) ] this leads to  '  j '' [   s  ] …… (4) 1  j 1  j

 ''  [

( s    ) ] ………………………….. (5) 1  j 2 2

Substituting equation (5) in equation (4) and taking the LCM of the obtained expression and canceling out common terms, we can get:

 '   

( s    ) …….. (6) (1  j 2 2 )

The equation (5) and (6) are defined as the Debye equations, which describe the behavior of polar dielectrics at various frequencies. For easily showing the dielectric behavior, it could be obtained from equations (5) and (6) that: tan  

 '' ( s    ) ……………... (7)   '  s    2 2  '   s   ( '') …… (8) 7

1   ''   '       …….. (9)  

Graphically, the relationship is illustrated in Fig.5 (b,c). The advantages of these relations are in explaining how well the experimental data fit the Debye relaxation model and for calculating some specific dielectric relaxation parameters from experimental data [32]. Similar behavior is reported by Tiwari et al. in BST ceramics [33]. The dielectric constant of Ba0.90Li0.1Ni0.05TiO3ceramics is enhanced with an increase in sintering temperature. This is partially due to increasing in grain size with increasing sintering temperature [25, 34]. The dielectric loss as a function of frequency is shown in Fig. 4c. It can be observed that the dielectric loss has high value at low frequency and decreases as the frequency is increased. According to Koop’s phenomenological theory [35] at the high-frequency region, dielectric loss is dependent on electrical properties of grain region and low-frequency loss is dependent on grain boundary properties. The charge carriers require more energy at low frequencies, and this translates into higher resistance of the grain boundary regions leading to a higher loss. However, low resistance is offered by grains at higher frequency, which results in decreased dielectric loss [36, 37] (1) Effect of porosity on dielectric constant Heidinger et al.[38] suggested a general relationship for pores in dielectric materials. 1 P  (

 m 1/3  ' 1 ………………….. (10) )  '  m 1

Equation (10) has no analytical solution regarding dielectric ɛ', so we consider a linearized approximation for  m   '   m 8

 '   m [1 

3P( m  1) ] ……………….. (11) 2 m  1

Where P is fractional porosity,  ' is the measured dielectric permittivity and  m is the dielectric permittivity after porosity correction. The fraction of porosity was calculated by using P= 1-D where D is the relative density of the materials. It can be observed from Fig. 6c that when the porosity increased the dielectric permittivity decreased as expected. The dielectric permittivity was calculated after porosity correction and plotted as a function of temperature in Fig (6a). (2) Effect of porosity on loss tangent To study the effect of porosity on loss tangent, it is assumed complex permittivity of the material is represented by Eq (1). The real part  ' describes the dielectric constant and the imaginary part

 '' describes the dissipation of electric field. The loss tangent is given by Eq (2).An additional contribution to the loss in the system will be added to  '' and consequently to tan  . The dependence of loss tangent on porosity could be written in the form of Eq-12 [39-40].

tan   APn …………………….(12) But this form is invalid if loss tangent becomes zero for fully dense materials. We modify the above equation by adding a non-zero loss tangent for fully dense material. The loss tangent at zero porosity is given by Eq (13):

tan   tan  o  APn

……………………… (13)

Where tanδ is loss tangent at zero porosity, (A) is an empirical constant obtained from the intercept of log-log plots. For unspecified pore character, (n) is the slope of log- log plot and the common assumption is that n is constant for a given pore character. Hence it allows accurate 9

extrapolation to other range of porosity (e.g., via log-log plots) and that n can be used to characterize the porosity. Since the loss tangent is due to full, dense micro-structure, this term should also depend on the porosity so that Eq13 becomes [39-40],

tan   (1  P) tan  o  APn ……………………. (14) By plotting a log-log graph of data and doing the least square fit, we get the slope is represented n=0.15, and the intercept is equal to A= 1.466 x 10-1 and tanδ=0.00338. In Fig. (6d) it is observed that, as porosity fraction increased the dielectric loss increased. The

temperature

dependence

of

dielectric

permittivity

and

loss

tangent

for

Ba0.90Li0.1Ni0.05TiO3ceramic measured at a temperature range of 30-300oC and frequencies of (1 kHz, 10 kHz, 100 kHz, and 1 MHz) are shown in Fig. 7 (a-d) and Fig. 8 (a-d) respectively. It can be seen that the dielectric constant increases with increase in temperature and reaches a maximum value ɛmax and then decreases. This corresponds to the phase transition in the material [37]. As the temperature increases, the space charge carrier concentration and mobility increases which lead to enhanced space charge polarization. Also, the ferroelectric phase got domains which respond to an oscillating electric field. As the temperature increases, the domains become more polarizable by inherent ferroelectric nature. These factors lead to an increase in dielectric constant with temperature. However, above the transition temperature the dielectric constant decreases due to the absence of domains in the paraelectric phase [37, 41]. From Fig 7 it is observed that the value of dielectric constant decreases with an increase in frequency, and this is due to inertial effects. The dielectric permittivity values of ceramics sintered at different 10

temperatures along with Curie temperatures are recorded in Table 2. It can be observed that as the sintering temperature increase the dielectric constant increases. In the present study the improved densification and reduction of porosity results in the enhancement of dielectric constant [42]. It can be seen that the phase transition slightly increased with an increase of sintering temperature. This increase in Tc could be attributed to large grain size, as it is reported that the internal stresses developed in constrained grains at phase transition lead to shifting of the Curie temperature to higher values [41, 43]. From Fig. 8 (a-d), it can be observed that the value of loss tangent is T c)

………………… (15)

Where To is Curie temperature and C is the Curie constant. It has been reported that the values of Curie –Weiss temperature and Curie constant of pure BaTiO3 are To =110oC and C=1.55x105 oC 11

respectively [46]. For Ba0.90Li0.1Ni0.05TiO3 ceramics sintered at different temperatures, the dielectric permittivity is fitted to Curie-Weiss equation. The deduced parameters are recorded in Table 3. The plots of temperature versus reciprocal dielectric constant at 1 kHz are fitted to Curie-Weiss law and shown in Fig. 9. It is clear that there is a deviation from Curie-Weiss law at Tcw which changes with a change in sintering temperature. The deviation parameter which is used to describe the degree of deviation from normal Curie –Weiss law is defined as [46]: Tm  TCW  Tm …………………….(16)

Where TCW refer to the temperature in which the dielectric permittivity start to deviate from normal Curie-Weiss law and Tm is the temperature at which the dielectric permittivity has a maximum value. All parameters are reported in Table 3, and it is observed that the value of deviation increased with an increase of sintering temperature. Uchino and Nomura [47] suggested an empirical expression describe the diffuseness of the phase transition in ferroelectric materials.

(T  Tm )   ,1  m C1 1

Where

1

……………………. (17)

and C1 are assumed to be constant. The

parameter provides us with the information

about the type of phase transition. For the case of

, a normal Curie-Weiss law is obtained

and if

, a complete diffuse phase transition is obtained [47, 48]. To determine the value

1 1 of , the plots of ln[  ] vs. ln[T  Tm ] was carried out. The plots show a linear relationship for  m

all different sintering Temperatures as shown in Fig.10 (a-d). The degree of diffuseness 12

can be

obtained from the slope of fitted data into Eq (15). The obtained values of γ are found to be in the range 1.55 to 1.62 (Table 4). Since ɛm and Tm used to determine the diffuseness parameters (γ) using Eq (17) are frequency dependent for diffuse materials, γ is not enough to describe the frequency independent behavior at high temperature (T>Tm) [49]. Furthermore, the dielectric data as a function in temperature ɛ(T) exhibited in Fig.7(a-d) was analyzed to understand the origin of diffused phase transition. It has been reported that the explanation of the slope of the dielectric peak at high temperature in ferroelectrics with or without diffused phase transition, can be strongly described above and below Tm with Lorentz type empirical relation [49,50]:

A T  TA ………………….. (18)  1  2 A2

 A is the parameter which reflects the diffuseness of the dielectric peak, TA and  A are the fitting parameters defining the temperature of the dielectric peak and the extrapolated value of  at T  TA . The temperature dependent dielectric data  (T ) measured in Ba0.90Li0.1Ni0.05TiO3 ceramic

sintered at different temperatures could be fitted well by Eq (18) in the two different ranges of temperature TTm respectively [49-50]. The typical Lorentz type fit for Ba0.90Li0.1Ni0.05TiO3 ceramic sintered at different temperatures measured at 1 kHz are summarized in Fig. 11 (a-d). The best fit parameters for all samples sintered at different temperatures have been listed in Table 4. It is observed that the parameter values of the fitting (ɛA, TA) are very close in the two ranges of temperatures suggesting that there is only one polarization process in the system. It is observed that, the variation in (  A ) is approx 9oC in the low-temperature region (TTm) a higher value in (  A ) for Ba0.90Li0.1Ni0.05TiO3 13

ceramics sintered at 1300oC suggests an increase in diffuseness of the dielectric peak. This could be due the complete crystallization at this sintering temperature [51] 3-3. Study of Activation Energy: Real and imaginary parts of dielectric permittivity were used to obtain the AC conductivity [52]. To investigate the activation energy of the Ba0.90Li0.1Ni0.05TiO3 ceramics sintered at different temperatures, the Arrhenius relation has been used.

 ac   o exp(

 Ea ) k BT

ln  ac  ln  o  (

Ea ) …………………. (19) kBT

The plots of lnσac as a function of 1000/T in various frequencies in the temperature range of (200-300oC) are given in Fig. 12. From the slope of linear least square fit of Eq.19, the activation energy has been measured and recorded in Table 4. The result shows a change in slope of the activation energy with sintering temperature. The noticeable results can be explained based on microstructure changes caused by the sintering process. The grain growth observed at higher sintering temperatures make the grains start mimicking larger crystallites with reduced grain boundaries where dipoles are less constrained to respond to an oscillating electric field freely. Higher densification or less porosity was observed at the higher sintering temperatures. The decreasing of activation energy with an increase of sintering temperature may be attributed to the reduction in some grains due to densification. As the number of pores is decreased, the individual grains come closer and the effective area of the grain to grain contact increases. The conductivity is directly proportional to the cross-sectional area of the conductor and at higher temperature the total conductance of the matrix may increase. The increase in conductivity is just 14

the consequence of the reduction in activation energy. A similar decrease in activation energy with an increase of sintering temperature was reported by Naik and Powar [53] in mixed nickelzinc ferrites sintered at 1100 and 1250oC. Also, it was observed that the activation energy tends to decrease with increasing frequency as found for amorphous materials. The increase of the applied frequency leads to enhance the jumping of charge carriers between the localized states, therefore the activation energy decline with increasing frequency [54-55]. Conclusion: Polycrystalline Ba0.90Li0.1Ni0.05TiO3 ceramics are prepared by conventional solid state reaction with microwave calcination of starting materials. The effect of sintering temperature on structural, dielectric properties and activation energy is investigated. All samples sintered at 1150, 1200, 1250 and 1300oC showed single phase perovskite structure. However, the secondary phase is appearing for samples sintered at 1350oC. Both porosity and grain size is affected by the sintering process. The result confirms that there was an enhancement in dielectric constant whereas the loss tangent decreased with an increase of sintering temperature. The Curie temperature is observed to vary within an interval of 150-160oC along with a degree of diffuseness γ>1. The dependence of dielectric constant and loss tangent on porosity is fitted theoretically using some simple modeling. The results confirm that the dielectric constant and loss tangent are strongly affected by porosity. The dielectric loss reduced as compared to pure BTO. The activation energies of all sintered samples were investigated using Arrhenius plots of the temperature dependence of AC conductivity at different frequencies. 15

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22

23

24

Fig.1a: X-ray diffraction of Ba0.90Li0.1Ni0.05TiO3 ceramics sintered at different temperatures. b: Rietveld refinement plots of Ba0.90Li0.1Ni0.05TiO3 ceramics sintered at different temperatures.

25

Fig.2: (110) X-ray diffraction peaks of Ba0.90Li0.1Ni0.05TiO3 ceramics sintered at different temperatures fitted to Gaussian profiles.

26

Fig. 3: FE-SEM images of calcined powder and Ba0.90Li0.1Ni0.05TiO3 pellets sintered at different temperatures.

27

Fig. 4: (A) Frequency dependence of dielectric constant before porosity correction, (B) frequency dependence of dielectric constant after porosity correction and (C) frequency dependence of dielectric loss of Ba0.90Li0.1Ni0.05TiO3 pellets sintered at different temperatures.

28

29

Fig.5: Frequency dependence of real (ɛ’) and imaginary dielectric constant (ɛ’’), (b) Straight-line fits between real dielectric constant (ɛ’) and ωɛ’’ and (c) Straight-line fits between real dielectric constant (ɛ’) vs.  '' of Ba0.90Li0.1Ni0.05TiO3 ceramic sintered at 1300oC. 

Fig.6: (a, b) Effect of sintering temperature in dielectric constant and loss tangent before and after porosity correction and (c, d) effect of porosity on the dielectric constant and loss tangent for Ba0.90Li0.1Ni0.05TiO3 ceramic sintered at different temperatures.

30

Fig.7 Temperature dependence of the dielectric constant measured at indicated frequencies for Ba0.90Li0.1Ni0.05TiO3 ceramics sintered at different temperatures

31

Fig. 8: Temperature dependence of the dielectric loss measured at indicated frequencies for Ba0.90Li0.1Ni0.05TiO3 ceramics sintered at different temperatures.

32

Fig.9: The reciprocal dielectric constant 1000/ɛ as a function of temperature at 1 kHz for Ba0.90Li0.1Ni0.05TiO3 ceramics sintered at different temperatures (Symbols: experimental data are points and solid lines are fits with Curie–Weiss law.

33

1 1 Fig. 10: ln[  ] as a function of ln[T  Tm ] for Ba0.90Li0.1Ni0.05TiO3 ceramics sintered at



m

different temperatures Solid line represents fitting with Eq. (14).

34

Fig. 11: Lorentz-type fitting for Ba0.90Li0.1Ni0.05TiO3 ceramics in low temperature region (TTm). Solid lines are the Lorentz fit curves.

35

Fig.12.

Arrhenius

plots

of

the

temperature

dependence

of

AC

conductivity

for

Ba0.90Li0.1Ni0.05TiO3 ceramics sintered at different temperatures and measured at different frequencies. Solid lines represent fitting with Eq. (19).

36

Table 1: Lattice parameters and unit cell volume from Rietveld refinement of XRD data of Ba0.90Li0.1Ni0.05TiO3 ceramics sintered at different temperatures. Sintering temperature (oC) Crystal system Space group Lattice constant a=b (Å) Lattice constant c (Å) Unit cell volume (Å3) Atomic position Ba x y z x y Ti z x O1

1150 Tetragonal P4mm (No.99) 3.9975 4.02244 64.4693




0.0000 0.0000 0.0000 0.5000 0.5000 0.5203

0.0000 0.0000 0.0000 0.5000 0.5000 0.5243

0.0000 0.0000 0.0000 0.5000 0.5000 0.5306

0.0000 0.0000 0.0000 0.5000 0.5000 0.5371

0.5000

0.5000

0.5000

0.5000

0.5000

0.5000

0.5000

0.5000

0.02364

0.02512

0.02996

0.06723

0.5000

0.5000

0.5000

0.5000

0.0000

0.0000

0.0000

0.0000

0.44098 1.0062 5.541 90 4.32 47 0.0022

0.4502 1.0085 5.606 90 3.42 60 0.0029

0.4529 1.0090 5.675 90 2.54 55 0.0024

0.4877 1.0127 5.928 90 4.33 58 0.0023

y z x

O2

y z

Tetragonality (c/a) Density (gm/cm3) Angles α=β=ɤ Ch2 Dp (nm) Strain

37

Table 2: Variation of relative density, porosity, loss tangent and dielectric loss before and after porosity correction with sintering temperature of Ba0.90Li0.1Ni0.05TiO3 ceramics Sintering ρm ρth ρm/ρth Grain size ɛexp at RT ɛcorr at RT tanδ at RT temperature (oC) (gm/cm3) (gm/cm3) % (µm) and 1kHz and 1kHz and 1kHz 1150 4.81 5.54 87 0.85 500 685 0.024 1200 5.02 5.61 89 1.1 737 854 0.017 1250 5.44 5.68 95 2.21 1125 1204 0.013 1300 5.65 5.93 95 3.31 1340 1424 0.008

Table 3: Summary of parameters of the Ba0.90Li0.1Ni0.05TiO3 ceramics sintered at different temperatures and measured at 1 kHz frequency Sintering temperature (oC) 1150 1200 1250 1300

Tm (oC) 150 150 150 160

To (oC) TCW (oC) 80 90 82 125

170 190 210 222

Tm(oC)

ɛ at Tc

tanδ at Tc

20 40 60 62

1200 1305 1982 2512

0.04 0.03 0.042 0.022

Curie constant (oC) 1.04 105 1.25 105 1.75 105 1.55 105

Table 4: variation of the diffuseness parameters (γ) from modified Curie Weiss low and the fitting parameters (  ,  A , TA ) from Lorentz- type relation which are investigated at 1 kHz for Ba0.90Li0.1Ni0.05TiO3 ceramics sintered at different temperatures Sintering temperature (oC)

γ (1 kHz)

 ( C)

1150 1200 1250 1300

1.55 1.59 1.60 1.61

8.41 9.43 9.43 9.44

o

TTm A 1255 1370 1800 2367

TA 155 150.61 149.8 164.22

Table 5: Variation of the activation energies measured at different frequencies with temperature of the Ba0.90Li0.1Ni0.05TiO3 ceramics. Sintering temperature (oC) 1150 1200 1250 1300

Ea (eV) at 1kHz 0.64 0.38 0.37 0.22

Ea (eV) at 10 kHz 0.61 0.31 0.30 0.20

39

Ea (eV) at 100kHz 0.57 0.27 0.25 0.18

Ea (eV) at 1MHz 0.50 0.22 0.21 0.15