Flux growth and low temperature dielectric relaxation in piezoelectric Pb[(Zn 1/3 Nb 2/3 ) 0.91 Ti 0.09 ]O 3 single crystals

Cryst. Res. Technol. 44, No. 9, 915 – 924 (2009) / DOI 10.1002/crat.200900294

© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Flux growth and low temperature dielectric relaxation in

piezoelectric Pb[(Zn1/3Nb2/3)0.91Ti0.09]O3 single crystals

B. K. Singh1, K. Kumar

1, N. Sinha

2, and B. Kumar*

1

1 Crystal Lab, Dept. of Physics and Astrophysics, University of Delhi, Delhi-110007, India 2 Dept. of Physics and Electrics SGTB Khalsa College, University of Delhi, Delhi-110007, India

Received 16 May 2009, revised 2 June 2009, accepted 5 June 2009

Published online 19 June 2009

Key words crystal growth, flux, X-ray diffraction, perovskites, piezoelectric, dielectric.

PACS 61.10.Nz, 77.22.Gm, 77.80.Bh, 77.80.Dj, 77.84.Dy, 81.10.Fq

Single crystals of Pb[(Zn1/3Nb2/3)0.91Ti0.09]O3 (PZNT 91/9) have been grown by flux method after

modifications in temperature profile, flux ratio and addition of excess ZnO/B2O3 which resulted in enhanced

perovskite yield (more than 95%). Only a few crystals showed the presence of pyrochlore phase/variation in

composition. A comparative characterization of these crystals were carried out in respect of piezoelectric

charge coefficient d33, dielectric constant, ac conductivity and hysteresis loop after cutting and poling the

crystals along [001] direction. The total activation energy for conduction has been found to increase with Ti-

content in the sample. The effect of ZnO on growth behavior has been analyzed. A detailed analysis of PZNT

(91:9) has been carried out at low temperature in respect of the various thermodynamic parameters related to

the dielectric relaxation mechanism, like optical dielectric constant, static dielectric constant, free energy of

activation for dipole relaxation, enthalpy of activation and relaxation time, have been calculated in the

vicinity of transition temperature in the lower temperature region. The activation energy for relaxation at -10

and -49 °C have been found to be 0.09 and 0.02 eV respectively. The results were analyzed and a detailed

dielectric analysis and low temperature relaxation behavior of PZNT crystals were interpreted.

© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

1 Introduction

High performance Pb (Zn1/3 Nb2/3)0.91 Ti0.09 O3 (PZNT) crystals are considered as next generation piezoelectric material. It exhibits ultrahigh piezoelectric charge coefficient (d33 > 2000 pC/N) and electromechanical coupling coefficient (k33 >90%) at room temperature when poled along the pseudocubic [001] direction. Further it exhibits a very high dielectric constant (~40,000 at Curie temperature) near its morphotropic phase boundary (MPB) (~ 9% PT) [1-3]. The binary system can be visualized as a complete solid solution formed between (1-x)PZN and xPT (Lead Zinc Niobate and Lead Titanate) with a morphotropic phase boundary (MPB) at x = 0.09, which separates the rhombohedral and tetragonal phases at room temperature [3]. Various dielectric and piezoelectric properties of these crystals are influenced by deviation of PT content from its MPB value (9%). So far, much work had been undertaken on the growth and characterization of PZNT single crystals by the flux method [4-8] but very limited work has been undertaken to study the effect of Ti4+ variation on the performance of the crystals obtained from the same growth run. Further, a common problem with flux growth of PZNT crystal is the growth of unwanted pyrochlore phase and additional compositions in significant volume of the ingot [5]. First serious attempt to increase the perovskite percentage was undertaken by Mulvihill et al. in which composition to flux ratio (C:F) was changed in the range 26:74 to 40:60 and it was concluded that higher C:F ratio is beneficial [6]. Harada et al. and Arunmozhi et al. used C:F ratio as 45:55 [7-

____________________

* Corresponding author: e-mail: [email protected]

916 B. K. Singh et al.: Piezoelectric Pb[(Zn1/3Nb2/3)0.91Ti0.09]O3 single crystals

© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.crt-journal.org

8]. Further, on the basis of TG/DTA curve, Mulvihill et al. suggested that the nucleation for perovskite and pyrochlore phases takes place at 950 °C and 850 °C, respectively. However, Mulvihill cooled the temperature slowly upto 900 °C while Arunmozhi started fast cooling just below 950 oC. In the present work various measures have been taken to enhance the perovskite yield of PZNT crystals and the effect of variation of PT content on various dielectric and piezoelectric properties have been reported. Further, the effect of excess ZnO on the growth behavior was interpreted. A low temperature dielectric relaxation behavior for PZNT single crystals has been analyzed.

2 Experimental

High purity Pb3O4, ZnO, Nb2O5, TiO2 (>99.99% from M/s Aldrich Chemicals) chemicals were used as starting materials with Pb3O4 as flux. To enhance the chances of higher percentage of perovskite formation, the crystal composition to flux ratio is increased so as to keep the lower temperature limit (LTL) of slow cooling at the higher end, thus omitting the temperature range which assists the formation of pyrochlore phase. A small trace (2 wt %) of B2O3 (purity 99.99% Aldrich) was added to the flux to obtain a stable growth of pure perovskite and to minimize the evaporation of PbO at higher temperature [9]. The PZNT: Flux: B2O3 ratios were maintained as 65:33:2. To minimize the chance of pyrochlore formation due to Zn2+ deficiency, an excess of ZnO was added such that ZnO:Nb2O5 =1.15:1. The self explanatory temperature profile is shown in figure 1. Finely grinded single crystals obtained from different parts of the crucible were subjected to XRD in the range 20o to 70o of 2θ with a step angle of 0.02° with step time 0.2 s using PW3710 Philips diffractometer (Cu Kα radiation). The hysteresis loop was traced by using computer controlled P-E loop tracer. Crystals were poled by applying a field of 1.2 kV/mm at 100 °C for 10 minutes. The piezoelectric charge coefficient d33 (pC/N) was measured using piezometer (PM300, PiezoTest, UK). The variation of dielectric constant and ac conductivity at different frequency (100Hz-100 kHz) of as grown samples was studied from room temperature to 200 °C using a HP 4284A impedance analyzer.

Fig. 1 Temperature profile for crystal growth. The figure

in the inset shows the as grown PZN-PT 91/9 single

crystals. (Online color at www.crt-journal.org)

Fig. 2 XRD patterns of (a) Sample A (b) Sample B and (c)

Pyrochlore at room temperature.

3 Result and discussion

Crystal growth PZNT crystals with dimensions ranging from 4 x 3 x 2 mm3 to 8 x 6 x 6 mm3 were obtained after dissolving flux in hot concentrated HNO3 (inset Fig 1). The crystals were collected from different parts of the crucible. All the samples obtained from the bottom & middle portion of the crucible are

Cryst. Res. Technol. 44, No. 9 (2009) 917

www.crt-journal.org © 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

found to be pure perovskite with PT content as 9% (sample A). Only few crystals obtained from the top layer of the ingot have shown perovskite phase of varying PT content and/or the presence of pyrochlore phase. Two samples are selected from this portion with PT content < 9% and >9 % which are labeled as sample B and C, respectively. The growth of the pure perovskite phase in the ingot is found to be more than 95%, which is more than that of the earlier reported results by Harada at el. [5]. This is due to the more precise ratio of the ZnO:Nb2O5 (i.e 1.15:1) and reducing the LTL to 880 oC during growth, which assisted the stable perovskite phase formation. Reduction in LTL increases the chances of getting a good quality, bigger perovskite crystals since the perovskite phase has got more time to grow bigger and defect free after nucleation at 950 oC. Further, we obtained the crystals in all parts of the crucible, while normally in flux growth good quality crystals are mostly confined to the lower contour of the crucible [8], which is a result of increased C:F ratio.

XRD studies X-ray diffraction analysis confirmed that crystals extracted from nearly 95% volume of the crucible (A type sample, Fig. 2a) have no sign of any pyrochlore phase in it. Few samples from the surface portion of the ingot did show the presence of pyrochlore phase (Fig. 2c) along with crystals of type B (Fig. 2b) and type C. The obtained XRD pattern of the pyrochlore crystal is subjected to cell refinement using High Score Plus software and found to consist of Hexagonal symmetry (space group P63/mmc) with cell parameters

10.043, 16.521a b c= = = Å and 090, 120α β γ= = = . Amongst the crystals with compositional variation,

most of them were found to be of type B (lower PT%). The reduced PT content brings the crystals towards the rhombohedral side of the morphotropic phase boundary (MPB). The XRD pattern is subjected to cell refinement and the pure rhombohedral symmetry (space group R3m) is found with cell parameters

4.069a b c= = = Å and 89.77oα β γ= = = . This shows that these crystals are slightly towards rhombohedral

side from the MPB (Fig 2a, b). This might be due to the presence of excess ZnO, as in the excess of ZnO and PbO (as flux) with pyrochlore (Pb2Nb2O7), the perovskite formation is promoted which can be explained on the basis of following reactions:

Thus in the presence of excess ZnO, the formation of PZN phase is assisted on the expense of unwanted pyrochlore Pb2Nb2O7. Further, as the LTL of slow cooling is kept at 880oC, instead of 950oC, the formation of excess and stable PZN is enhanced, thus increasing the perovskite phase. Due to reduced PT content, a reduced Tc for type B sample is expected, which has been confirmed in the dielectric analysis. Pure perovskite phase having high piezoelectric properties was confirmed in all of the crystals of type A. The refined values were found to be of low symmetry unstable monoclinic (space group Cm) MB phase. In addition, the coexistence of rhombohedral (R3m) and tetragonal (P4/mm) phases is confirmed and report elsewhere [10]. XRD with slow

scan rate of 0.02 degree/min for the range 2θ=43o-46o were taken to locate the peaks corresponding to the rhombohedral and tetragonal phases and were found to be at 44.6° and 44.81° respectively. The (200) reflection shows a single narrow peak in the rhombohedral phase, while in the tetragonal phase it splits into two peaks with the intensity of the former being half of the latter. The splitting of (200) reflection into two peaks of nearly equal intensity in the present case can be attributed to the overlapping of the multiple phases coexisting in the sample and that the composition is always within the MPB region [11-12].

Dielectric and ac conductivity analysis Figure 3 shows the variation of dielectric constant of the three unpoled samples with temperature at 1 kHz. A large variation in the dielectric property was found in the samples. The dielectric constant of the sample A was found to be 43,000 with Tc at 181 °C. For samples B and C these values were 33,000 with Tc at 161 °C and 41,000 with Tc at 221 °C, respectively. The variation of the Tc for the samples is due to the variation of Ti4+ concentration in different samples, which causes PT content to vary (with increasing PT content Tc increases and vice versa).

The ionic conductivity σ can be expressed as "o

σ ε ωε= , where "ε is the imaginary part of dielectric

constant. Further deducing Einstein relation [13], it can also be related to diffusion constant (D) as 2

/ /B

D Ne k Tσ = ,

where N is the number of carriers, e is the charge on ion, kB is the Boltzmann’s constant and D is the diffusion



constant associated with the migration of ion vacancy. Further the relation can be extended and written as 2

0 0ln( ") ln( / ) ln( ) ( )

B t Bk T Ne D E k Tε ε ω= − − ,

where D0, Et are the maximum diffusion coefficient and total activation energy due to bulk and surface

conduction respectively [14]. Hence a plot between ln( ")Bk Tε and 1 T (Fig. 4) will give a straight line whose

slope will represent /t B

E k . Almost a linear variation is observed below and above the transition temperature

Trt and Tc. A sharp rise is seen near Tc due to ionic hopping of the mobile ion through vacancy defects (oxygen vacancy), which increases with the increasing temperature. The value of Et was calculated from the slope of the curve below the transition from rhombohedral to tetragonal for all the samples at 1 kHz. The observed change in the Et below Trt for the sample A, B and C are found to be 0.40 eV, 0.32 eV and 0.42 eV, respectively. The observed increase in the Et value is found to increase with the increase in Ti content, which is highest for the sample C. The rhombohedral to tetragonal transition (Trt) for Sample A, B and C is observed at 97, 81 and 119 °C, respectively. The presence of Trt for all the samples confirmed that the samples are within the vicinity of the MPB (8-10% PT).

Fig. 3 Variation of real part of dielectric constant with

temperature for (a) Sample A (b) Sample B and (c) Sample

C at 1 kHz. (Online color at www.crt-journal.org)

Fig 4 Variation of ln( ")Bk Tε with temperature for (a)

Samples A (b) Sample B and (c) Sample C at 1 kHz.

(Online color at www.crt-journal.org)

Hysteresis behavior Figure 5 shows the electrical polarization versus electric field (P-E) for [001]

oriented sample of type A, B and C at room temperature. From the Hysteresis loop, the values of coercive field (Ec) for the samples A, B and C were found to be 14.5, 12.5 and 14.5 kV/cm respectively while remnant polarizations (Pr) were found to be 20, 12.5 and 12 µC/cm2 respectively. These values purely depend on the polarization orientation, but due to the coexisting phases having different polarization orientations, these values of Ec and Pr cannot be explained on the basis of PT content. However, in lead based ferroelectric materials, these piezoelectric properties are strongly influenced by composition and its homogeneity, defects, external field and domain wall motions, which eventually contributes to the material response. A uniform domain structure actually increases the material properties. The various ferroelectric domains as observed by Leite et al. [15] include nano-domains, tweedlike domains and micro domains. The differences in the size and mobility between various coexisting domains weaken the interaction between them and results in low remanent polarization. However, the presence of a single domain structure, and the combined interaction between them, yield higher value of Pr and lower Ec. Thus in the present case, the higher value of Pr for sample A with nearly same Ec as compared to sample B & C can be attributed to better uniformity in the domain structure of sample A as compared to B & C. According to Haertling and Zimmer [16] the empirical relation between remanent polarization, saturation polarization and polarization at fields above coercive field is given by the relation:



1.1c

Er

sq

s r

PPR

P P= + ,

where, Rsq, Ps and P1.1Ec are the squareness of Hysteresis loop, saturation polarization and polarization at an electric field equal to 1.1 times the coercive field, respectively. For an ideal Hysteresis loop the squareness parameter is equal to 2. Using this relation, a quantification of changes in the Hysteresis behavior for each sample can be done. The squareness parameter for all the three loops were calculated and found to be 1.97, 1.92 and 1.96 respectively. It may be mentioned that the squareness in the case of polycrystalline phase of PZNT & PMNT is around 1.2-1.5. The value of squareness close to 2 indicates good switching behavior of polarization in PZNT crystal.

Fig. 5 Hysteresis loop of unpoled as grown single crystal

of (a) Type A (b) Type B and (c) Type C at room

temperature. (Online color at www.crt-journal.org)

Fig. 6 The variation of (a) d33 with frequency at room

temperature for sample A poled along [001] and [111]

direction. (Online color at www.crt-journal.org)

Poling and d33 measurements The crystals were subjected to poling (along [001] and [111] directions) at

electric filed 1.2 kV/mm at a temperature of 100 °C for 10 minutes. The d33 value as high as 2.382 pC/N was observed for the sample A poled along [001] direction. However, the sample B and C showed comparatively lesser values of d33 viz. 750 and 950 pC/N, respectively. When these crystals were poled along [111] direction a reduced d33 of the order of 630, 310 and 408 pC/N was observed for sample A, B and C, respectively. The variation of d33 with frequency for the sample A (poled along [001] and [111] direction) is shown in figure 6. The value of d33 is found to rise exponentially with frequency. However, the rise is much rapid in the former case. Similar variation was observed for other samples as well. This behavior is due to domain wall pinning. As the frequency increases, new micro domains are formed in the crystals, which results in the increased number of dipoles per unit volume of the crystals and hence there is an increase in d33 value.

Detailed dielectric analysis (Sample A) Figure 7a shows the variation of the real part of dielectric constant with temperature for different frequencies. Figure 7b shows the variation of real part of dielectric constant with freqeucny at different temperatures. A slight shift in the temperature of dielectric maxima (Tm) with frequency is observed, which shows the relaxational behaviour of the system which is also evident from the deviation from the curie weiss law as shown in figure 7c. The relaxational behaviour of the system is studied by using modified Vogel-Fulcher equation [17]

( )a B m fE k T T

oeω ω− −

= ,

where ω is the probing frequency, o

ω is the attempt frequency, Ea is the activation energy, kB is the Boltman

constant, Tm is the temperature of dielectric maxima and Tf is the freezing temperature for the clusters. A plot

between Tm vs. ln( )ω (Fig. 7d) is fitted with Vogel-Fulcher model and o

ω , Ea and Tf is found to be



108.89 10× Hz, 0.0323 eV and 171 °C respectively. Jonscher [18] suggested that the behavior of dipolar system

can be characterized by fractional power laws in frequency above the loss peak frequency as 1"( ) nf fε

−

∝ ,

where (0<n<1). Figure 8a shows the variation of ε” with frequency at different temperatures near its Tc. After fitting the curve the exponent n is found to increase from 0.88 to 0.93 as temperature increases from 179 to 200 oC.

Fig. 7 Variation of (a) real part of dielectric constant with temperature for different frequencies (b) real part

of dielectric constant with freqeucny at different temperature (c) curie constant with temperature at different

frequency and (d) ln( )ω with temperature of dielectric maxima (Tm). (Online color at www.crt-journal.org)

Fig. 8 The variation of (a) imaginary part of dielectric constant (ε”) with frequency at different

temperatures near its Tc and (b) log (1/ε -1/εm) vs. log (T-Tm) at different frequencies. (Online color at

www.crt-journal.org)



Combination of PZN with PT introduces dielectric peak broadening due to diffuse phase transition. For better insight of this dielectric behavior of PZNT system, we can look at these behaviors through Curie–Weiss law. A material such as PT, which shows normal ferroelectric behavior, follows Curie–Weiss law above Tc as

o

C

T Tε =

−

,

where c is the Curie constant and To is the Curie–Weiss temperature. For PZNT, which shows a diffuse phase transition (broad peak), the equation 1/ε = (T − Tm)2 has been shown to be valid over a wide temperature range instead of the normal Curie–Weiss law, where, Tm is the temperature at which the dielectric constant is maximum. If the local Curie temperature distribution is Gaussian, the reciprocal permittivity can be written in the form

2

( )1 1

2

m

m m

T Tγ

ε ε ε δ

−

= + ,

where εm is maximum permittivity, γ the diffusivity and δ is diffuseness parameter [19-20]. The values of γ and δ are both materials constants depending on the composition and structure of materials [21]. The value of γ is the expression of the degree of dielectric relaxation, while the parameter δ is used to measure the degree of diffuseness of the phase transition. The plot shown in figure 8b show that the variation is almost linear and the values of γ is found to vary between 1.13 and 1.93, which confirms that diffuse phase transition occur in PZNT system.

Fig. 9 (a) The variation of ac conductivity with temperature at various frequency (b) Calculation of activation energy by

fitting the arrhenius plot for conductivity and (c) The variation of ac conductivity with frequency at different temperature.

(Online color at www.crt-journal.org)

Figure 9a shows the variation of ac conductivity of the PZNT crystals with temperature at variation frequency. In these systems the B-site niobium ion may coexist as Nb3+ or Nb5+ ions on equivalent crystallographic sites and contribute to conduction due to the jumping of additional 4d electron between adjacent Nb3+ or Nb5+ ions [10]. In higher temperature region above 150 °C (Fig. 9a), the ac conductivity is strongly temperature dependent and increases sharply with the increase in the temperature. Similar behavior is observed near Tc. The activation energy was calculated for the regions below 150 °C by fitting the equation

a BE k T

ac oeσ σ−

=

and is as shown in figure 9b. It is found that the activation energy slightly increases with frequency. Fig. 9c shows the variation of ac conductivity with frequency at different temperature. It is found that as frequency increase the ac conductivity increases sharply beyond 50 kHz. A convenient formalism to investigate the frequency dependence of conductivity in a material is based on the power-law relation proposed by Jonscher [17-18]:

( ) SAσ ω ω= ,

where, σ is the total electrical conductivity, 2 fω π= and the coefficient A and exponent s are temperature



and material dependent parameters [22]. The term A comprises the ac dependence and characterizes all dispersion phenomena. The exponent s (0<s<1) depends on the nature of material, temperature [23-24], etc. The plot is fitted with the above equation and the exponent s is found to vary from 0.88 to 0.98 for a variation in temperature from 100 to 200 °C.

Fig 10 Variation of (a) real part of dielectric constant (b) imaginary part of dielectric constant and (c) dielectric loss in

lower temperature region at various frequencies. (Online color at www.crt-journal.org)

Low temperature dielectric relaxation (Sample A) The as grown crystals were subjected to dielectric characterizations in the lower temperature region. The variation of real part of dielectric constant and dielectric loss with temperature at various frequencies is shown in figure 10a and b, respectively. A continuous increase in the dielectric permittivity with temperature is observed with few discontinuities at -132, -49 and -10 which is related to freezing temperature, monoclinic (MC) to orthorhombic and orthorhombic to rhombohedral phase transitions, respectively [10]. Similar behavior is observed in the dielectric loss vs temperature plot. For analyzing the distribution of dielectric relaxation time, a cole-cole plot between real and imaginary dielectric constant is drawn at the transition temperature viz. -49 °C and -10 °C (Fig. 11). An arc is drawn, intersecting x-

axis at value ε∞

(optical dielectric constant) and s

ε (static dielectric constant), with center lying below the x-

axis. The radial vector at the point ε∞

makes an angle equal to / 2απ with the x-axis from which α is

calculated. The macroscopic relaxation time ( )o

τ is related to α as

1( )o

v uα

ωτ−

= ,

where, v and u are the distance of the experimental point from s

ε and ε∞

, respectively and ω is the angular

frequency. The molecular relaxation time ( )τ is related to ( )o

τ , s

ε and ε∞

as [25]

[(2 ) / 3 ]s s o

τ ε ε ε τ∞

= + .

( )τ can also be related to free energy of activation for dipole relaxation ( )FΔ as [26]

( / ) exp( / )h kT F RTτ = Δ ,

where h, k and R are Plank’s, Boltzman’s and gas constant, respectively. Further, ( )FΔ is related to the

enthalpy of activation ( )HΔ as

( )F H T SΔ = Δ − Δ ,

where SΔ is the energy of activation. Here ( )HΔ is calculated from the slope of the plot between ln( . )Tτ and

1/T (Fig. 12a and b). ( )FΔ is related to ( )τ as

2.303 log( / )F RT kT hτΔ = .

Using the above equations the various parameters are calculated and are listed in table 1. The occurrence of arc in the cole-cole plot at high frequency is due the high DC conduction loss at high frequency. This shows the existence of distribution of relaxation times in the sample. The relaxation time is found to decrease with



increasing temperature. The variation of relaxation time can be expressed as

exp( / )o t

E kTτ τ= Δ ,

where, t

EΔ is the activation energy of dielectric relaxation. The obtained value of s

ε , ε∞

, α , ( )o

τ , ( )τ ,

( )HΔ , ( )FΔ and t

EΔ at different temperature is as indicated in table 1.

Table 1 Dielectric relaxation and thermodynamical parameters of PZNT single crystal at transition in lower temperature

region.

Tem-

perature

(oC)

ε∞

s

ε α ( )o

τ

Relaxation time

from Cole-Cole

( )τ

Relation time

from ln ( )τ

Enthalpy of

activation

HΔ eV

Activation

free energy

FΔ eV

Dielectric relax-

ation activation

energy t

EΔ eV

-49 1130 1640 0.56 5

4.044 10−

× 53.625 10

−

× 54.706 10

−

× 0.21 0.37 0.09

-10 1800 2150 0.44 55.892 10

−

×5

5.573 10−

× 55.151 10

−

× 0.14 0.44 0.02

Table 2 Comparison of physical and electrical properties of PZNT 91/9 Single crystal.

PZNT (91/9)

[27]

PZNT (91/9)

[28, 29]

PZNT (91/9)

[5]

PZNT (91/9)

[This work]

Dielectric constant (unpoled) ~ 60000 2500-10000 5000-8000 43000-45000

Dielectric constant (poled) 1500-4000 3000-3500 41000-42000

Tc oC 173-176 175-185 170-175 179-182

Trt 70-84 ~75 81-105

tan δ (%) 1.3-3.5 1.0-2.0 1.2-1.5 2.0-5.0

k33 81-83 90-94 92-94 86-89

d33 pC/N for poling direction (001) 2000 1500-2000 1600-2000 2300-2400

Fig. 11 Cole-Cole diagram for PZNT in the vicinity of transition temperature -49 oC and -10 oC.

Fig. 12 ln( . )Tτ vs. 1000/T plot at (a) -49 °C and (b) -10 °C.



4 Conclusions

A meticulously chosen value for limit of fast and slow cooling rate, composition to flux ratio and addition of

ZnO/B2O3 has resulted in higher perovskite and growth yield in PZNT crystals. The higher value of C:F

(65:35) helps in increasing the perovskite percentage while saving the cost on flux material. The influence of

PT content (in the vicinity of MPB) on dielectric, piezoelectric and conduction process in PZNT system has

been studied. The total activation energy for conduction for the three samples (0.40 eV, 0.32 eV and 0.42 eV,

for A, B & C, respectively) was found to increase with the Ti content in the sample. A detailed dielectric

analysis of PZNT (91/9) has been carried out at high temperature while dielectric relaxation mechanism has

been studied at various transitions observed at low temperature. Various thermodynamic parameters related to

dielectric relaxation mechanism viz s

ε , ε∞

, α , ( )o

τ , ( )τ , ( )HΔ , ( )FΔ and t

EΔ in the vicinity of the

transition temperatures in lower temperature region are calculated and analyzed. The activation energy for

relaxation at -10 and -49 °C have been calculated and found to be 0.09 and 0.02 eV, respectively. The various

experimental observations for the present work have been compared with the earlier reports and are shown in

table 2. However, the dielectric relaxation and thermodynamical parameters of PZNT 91/9 single crystal in

lower temperature region are not included in the table as they are being reported for the first time. It is evident

from the comparison that the excess of ZnO during growth has improved the properties of the PZNT 91/9

crystals.

Acknowledgements We are thankful for the financial support received form the Department of Science & Technology

for the Project “Growth and quality control of high performance piezoelectric PZNT crystals (SERC Sanction No

100/(IFD)/1637)”. B. K. Singh is thankful to DST for Junior Research Fellow position.

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Flux growth and low temperature dielectric relaxation in piezoelectric Pb[(Zn 1/3 Nb 2/3 ) 0.91 Ti 0.09 ]O 3 single crystals