Structural and dielectric characterizations of the mixed crystal Li0.8Na0.2NbO3

Pergamon

00223697(93)EOOll-P

J. Phys. Chem. Solids Vol. 55, No. 3, vv. 293-298. 1994 Copyright 0 1994 Elkier Science Ltd Printed in Great Britain. All rights reserved om-3697p4 s7.00 + 0.00

STRUCTURAL AND DIELECTRIC CHARACTERIZATIONS OF THE MIXED CRYSTAL Li,, Na,,NbO, JEONG-BAE KIM? and JUNG-NAM KIM$ TDepartment of Physics, Inje University, Kimhae 621-749, Korea SDepartment of Physics, Pusan National University, Pusan 609-735, Korea (Received 24 September 1993; accepted 12 November 1993) Ah&ret-Ferroelectric mixed crystals LiO,sN~,zNbO, were grown from the melt by the Czochralski method. It has been found from the structural analysis that a mixed crystal Lis, Na,,rNbOl is rhombohedral with a hexagonal unit cell of dimensions aH= 5. 1736A and cH= 13.9381 at 25°C. To confirm the thermal expansion, high-temperature X-ray diffraction was carried out in the temperature range from 25 to 900°C and the longitudinal thermal expansion coefficients turned out to be a,, = 11.501 x 10-5”C-’ and a3r = 7.712b310-5”C-1. The temperature characteristics of dielectric constants and a.c. conductives of the mixed crystals Lii,N~,,NbO, have been investigated in detail from room temperature to above the Curie temperature, 1108°C. Significant low frequency dielectric dispersions were observed over a wide temperature range, including the Curie temperature. It is believed that this low frequency relaxation process is due to mobile charged-point defects presumably connected with the substitution of Na+ for Li+ in the LiNbO,, frame. Keywork Mixed crystal Li,,NaslNbO,, dispersion, mobile charged-point defects.

rhombohedral,

1. INTRODUCTION

LiNbO, undergoes a second order phase transition at 1210°C [l] from a paraelectric R% to a ferroelectric R3c and NaNbO, undergoes a phase transition at 643°C [2] from a paraelectric Pm3m to an antiferroelecttic P4/mbm. In the mixed crystals of these crystals, a ferro-antiferroelectric mixture Li, _,Na,NbO, is expected to exist in the form of the frustrated states due to the competition between two kinds of order-disorder arrangements. Polycrystalline Li, _ ,Na,NbO, has been investigated by various workers for many years. An application for high-frequency piezoelectric devices was reported by Nitta [3]. Structural and dielectric properties [4], electromechanical properties for the pressure-sintered Li, _ 1Na,NbO, in the range 0.85 < x < 0.985 were reported by Henson et al. [S]. Kus et al. investigated the ferroelectricity in the range 0.80 G x < 0.99 [6]. A few results have been reported for the crystalline Li,_.Na,NbO, with low concentration of Li+ ion (0.97 GX). Megaw reported that antiferr+paraelectric phase transition temperature T, decreases rapidly with substituting Li+ for Na+ in the compositional range from x = 1.O to 0.97 [A. The in the mixed crystal L&.0zNa,,gBNb09 and Li,,,N~,97Nb0, were reported by Sadel ef al. [8] and Zhang et al. [9], respectively. Dielectric dispersion of Li0,0ZSNa,,,,,Nb03 at low temperature was also reported by Zhong et al. [lo]. and sol-gel process-

pyroelectricity

thermal expansion, low frequency dielectric

ing was developed by Balbaa and Gowda [ 111.But no detailed studies have been reported for low concentrations of Na+ ion. We have grown the mixed crystal Li, _ .Na,NbO, in the range 0
2. EXPERIMENTAL

PROCEDURE AND RESULTS

2.1. Crystal growth The starting materials used to prepare the mixed crystals of Li,,Na,,rNbO, were 99.99% L&CO,, Na,C03 and Nb205. They were weighed in the appropriate stoichiometric ratio and mixed together, ball milled for 10 h, then fired at 600°C for 20 h, then ball milled again and fired at 900°C for 20 h. The synthesized Li,,,Na,,2Nb0, was then RF heated in a 60ml platinum crucible. A personal computer was adopted to control the furnace. Typical growth conditions were as follows: seed crystal direction-c-axis; rotation speedpulling speed-l-3 mm h-‘; above 15-25 rpm; and temperature gradient interface--60°C cm-i. The grown solid-liquid

293

JEONG-BAEKIM and JUNG-NAMKIM

294

crystals were light brown and transparent and had three-fold symmetrical ridges along the c-axis like

changes in the values of the Miller indices are obtained. The determined indices of Li,, Na, zNbO,

LiNbOl. The typical diameter and length of the grown crystals were 15 and 40 mm, respectively.

at 25°C are presented in Table 1. In analogy with Li,,gNa,,,NbO, reported previously [12], conditions limiting possible reflections -h + k + I= 3 n for Ml reflections and I= 2n for hi/ reflections, allow R3c or Rk as a possible space group [16]. In addition, the same diffraction angles were re-indexed on condition that the negative values of indices were allowed. The resultant indices different from the previous values are represented in parentheses in Table 1. These new reflections hhOl are satisfied with the conditions 1 = 2n [16]. Anticipating this result, one may therefore say that the space group is R 3c at room temperature. To confirm the space group assigned, the structure factors were obtained by analytic application of the Lorentz and polarization corrections together with the multiplicity factor, assuming that the value of the atomic form factor of the Li+ ion is substitutable by 0.8fLi + 0.2& in the LiNbO, framework. The structure factors obtained at 25°C in this study were collected in Table 1 under F,,,,,, and were in excellent

2.2. Investigation

of structure

Pre-investigation of structure was composed of the conoscope on a polarizing microscope, a chemical etching and the back Laue photography, as the previous work [12]. As a result, it is confirmed that Li,,,Na,,,NbO, has a rhombohedral unit cell at room temperature. High-temperature X-ray diffraction of powdered crystals was carried out in the temperature range from 25 to 900°C. The crystal-powder was annealed at 1000°C for 10 h in order to remove the strain resulted from powdering. The X-ray diffractometer used was a RIGAKU GDX-1193A model, and the diffractometric data were obtained using Ni-filtered Cu-Kcr 1 radiation. The tube voltage was 30 kV with 10 mA. The measured range of 2 0 was from 0” to 160” and the scanning step was 0.01” with a holding time for 2 s. To index the diffraction pattern, a BASIC computer programme was specially written. The programme incorporates a continuous re-indexing of the diffraction peaks by using Lipson’s analytical method [ 151, which is based upon minimizing the difference A sin* 0 (= sin* 8,,,-sin* e,,,,), many times, until no

agreement

in all cases.

As in the previous work [ 121, Cohen’s least-squares analytical method was adopted for the best estimates of the hexagonal lattice parameters from the powder X-ray diffractometric measurements. cedure, we found that Li,,,Na,,,NbO, dral with a hexagonal unit cell

Table 1. Miller indices and structure factors of L&Na,,NbO, 20

hk

21.03 23.38 32.39 34.36 38.81 39.48 42.18 48.14 52.85 55.69 56.73 60.67. 62.01 68.20 70.9 1 73.20 75.72 78.08 78.89 81.33 82.30 83.39 86.08 88.43 91.76 92.62 93.62 97.55

1 0 0 1 1 0 1 1 0 0

1

Asin% /sin20,,,

F,,,,,

F,,,

20

1 2 4(1 i4) 0 6

0.0188 0.0195 0.0101 0.0183 0.0020 0.0202 0.0094 0.0064 0.0048 0.0063 O.OOll 0.0046 0.0045 0.0000 0.0006 0.0002 0.0000 0.0012 0.0012 0.0003 0.0022 0.0040 0.0005 0.0004 0.0018 0.0000 0.0039 0.0001

23 175 178 170 112 291 93 284 198 157 135 161 360 117 126 151 151 108 208 115 114 232 268 102 225 312 149 77

23 176 174(175) 163 107 286 91(90) 283 (281) 190 153 136 155 356 114(115) 121 148 149 106 211 114(115) 113 229 270 98 219 318(315) 150 77

98.62 99.46 102.34 102.95 104.21 105.55 110.10 112.81 llS.00 116.56 117.95 118.43 121.30 123.18 124.58 125.60 126.11 126.97 127.54 128.68 129.25 132.06 132.55 133.34 138.12 139.68 140.45

: A &2I2) 0 2 4 (2 z 4) 11 6 12 2 01 8 21 4 30 0 2 0 8(2 2 8) 1 1 9‘ 22 0 30 6 3 1 2 I 2 8 0 2 lO(22) I 3 4 0 0 12 2 2 6 0 4 2 3 0 9 4 0 4(4z4) 1 1 12‘ 3 2 1

hk

2 3 2 3 4 0 0 1 3 2 4 0 2 1 4 0 2 3 1 1 5 2 4 0 4 2 0

3 1 2 2 1 2 4 3 2 1 1 5 3 I 0 5 2 3 2 0 0 4 2 4 1 4 5

at 25°C

I

Asin28/sin28,,,

8 15 IO 4(554) 12 0 14 16(l i 16) 5 1 2 11 9 4 7

0.0000 0.0022 0.0059 0.0006 0.0013 0.0024 0.003 1 0.0040 0.0018 0.0012 0.0030 0.0073 0.0016 0.0047 0.0050 0.002 I 0.0017 0.0013 0.0029 0.0006 0.0006 0.0031 0.0040 0.001 I 0.0028 0.0034 0.0054

2 8 9 4 0 13 8 10 7 13 6

1

In this prois rhomboheof dimensions

F,,,,

93 100 87 98 161 132 135 491 160 91 178 179 108 101 87 122 101 194 72 137 103 55 55 154 73 113 Ill

F,,

92 101 83 99 157 127 132 500 156 88 177 180 104 100 84 119 (123) 102 191 1:: (138) 103 56 55 152 70 114 109

Structural and dielectric characterizations of Li,,,Na,,*NbO,

1::: I”““‘“I t

0 E *z z

14.0 15.9

y.....................................w...-

13.8 l

15"_; .I

0

5.4

-

: 5

5.3

-

'; -I.

52-

*.*__._o....o"'-

5.1 3.0

paramrtw parom9ter

e Q

* o__..O___.O....O....o~--

I 0

I

I

I1

I

I&

I

100200300400500~00700~002001000

Temperature

(“C)

Fig. 1. The change of the lattice parameters of L&,8N%,,Nb0, along the crystal axis with increasing temperature.

a,,= 5.1736A and cH= 13.938 8, and volume V H = 323.09 A’ at 25°C. The dimensions of the rhombohedral transformed from the hexagonal unit cell of L&,Nat,rNb03 are aR= 5.5234& a = 55”51’, and VR= 107.70 A’. L& Na,,? NbO, has a formula weight fw = 151.05336 and a density measured at room temperature P,,,= 4.672 g cm-‘. There are six jii per hexagonal (two per rhombohedral) unit cell in which Ap (=p, - pthm) is O.O14gcm-‘. Considering the size of the unit cell of Li0,BNa,,2Nb0, compared with LiNb03 (a” = 5.174337 A and c, = 13.87359 A), the apparent elongation of cu in contrast to the negligible reduction of a,, is the evidence for the substitution of Na+ ions on the site of Li+ ions located along the c-axis. In addition, the changes of the lattice parameters obtained by above procedure were investigated with increasing temperature. The variations of the lattice parameters in the 25-900°C temperature range were shown in Fig. 1. Due to the symmetry of point group 3 m there are two coefficients of thermal expansion, a,, describing the longitudinal effect in every direction in the x-y plane, CL”describing the longitudinal effect in the z-direction. In Fig. 1, the circular points are data points and the dotted straight lines are fitted by the method of least squares. The thermal expansion of LiNbO, parallel to the c-axis is characterized by an irregular behaviour, becoming negative in this direction above 600°C. Kim and Smith have explained this irregular behaviour is due to the tilting of the octahedra in LiNbO, [17]. However, the thermal expansion of Li,,Na,,NbO, reveals a regular behaviour in this work. The longitudinal thermal expansion coefficients corresponding to the inclinations of the

295

fitted lines are a,, = 11.501 x lo-s0c-’ and aj3 = 7.712 x 10-s”C-‘. Since the ionic radius of Na+ (0.95 A) is larger than Li+ (0.68 A), the substitution of Na+ for Li+ in the LiNb03 frame may give rise to a structural rearrangement caused by a size mismatch. Thus large thermal expansion coefficients compared with LiNbO, is explained as a result that a structural rearrangement weakens the crystal bonding. The thermal expansion of L&Na,,,NbO,, as well as L&,pNh,, Nb03 [12], is believed to be affected more by the change in the size of the octahedra than by a change in the tilting of the octahedra. 2.3. Dielectric properties Dielectric constants c3) and electric conductivities uj3 were determined at several frequencies, between 10 kHz and 13 MHz, using a Hewlett Packard impedance analyzer 4192 A. Samples used for these measurements were cut into plates perpendicular to the c-axis. The typical sample size is 1Omm in diameter and 0.7 mm in thickness. The electrodes on the large faces were made with platinum paste, fired at 900°C to diminish the effect of the residual resistance of the electrode in the initial warm up. The samples were placed in the electric furnace and connected by 1Ocm parallel Pt lead wires with HP standard test cable. A personal computer was adopted to control an electric furnace and processing of data. Measurements on 6)’ and crs3were carried out in the temperature range from 20 to 118O”C, where loss tan 6 was lower than 20. We first tried to observe the D-E hysteresis loop over the wide temperature range. However, no hysteresis effects have been observed at room temperature under ext)emely high fields of 385 kV cm-‘. We

10’1. . .1040’ -. 1000

.

‘.

1080

Temperature

. ‘. 1120

. . ‘.

1160

(‘C)

Fig. 2. Dielectric constant .zjj as a function of temperature in Li,,,Na,,,NbO,. The inset is a view of the complete temperature range.

296

JEONG-BAE KIM

and

JUNG-NAM KIM

0 0

0

200

400

600

Temperature

800

1000

1200

0.75

NbO,.

then measured the dielectric constant as a function of temperature. Figure 2 shows dielectric constants 6 and Fig. 3 shows the loss tan 6 in the Li,* Na,,, NbOj . Because of the elastic resonance, the dielectric constant t,, above 1 MHz was not determined in the vicinity of T, = 1108°C. The dielectric constant c3, exhibits a maximum at T, and its maximum value reaches as high as 1.44 x lo6 at 1 kHz. However T, shift depending on the frequency, which is expected in the frustrated state, is not observed. All values of cjj over the measured temperature range as well as frequency range were considerably larger compared with those of LiNbO, [18]. As expected, dielectric loss along the c-axis exhibits a minimum at T,. The Cur&Weiss law is satisfied in a narrow temperature range about T, + 7°C. The obtained Curie constant at 100 kHz in the paraelectric phase is C = 6.56 x lO’K, which is a typical value for the displacive phase transition. The ratio of slopes below and above T, for 100 kHz is calculated as 1.7 which is smaller than the 2.6 for LiNbO,. This indicates that Li,.,Na,.2Nb0, reveals a diluted character of ferroelectric second-order phase transition. There are significant dispersions in cJ3over the wide temperature range, including the Curie temperature. A dielectric dispersion and a diluted character of phase transition are in genera1 related with a conducting process. However, as shown in Fig. 4, no dispersive behaviours through a dependence of the electrical conductivity crjj on angular frequency w is observed over the same temperature range as revealed by the dielectric dispersion. Moreover, such dispersive behaviour in the dielectric constant of Li,.,NaO,,NbO, was not satisfied with a semicircular Cole-Cole relation based on the Debye response. Figure 5 shows a log-log plot of the imaginary part

rJ..so

'.'*'.'*'*'.'*'* 0.7 0.8 0.0 1.0

(V)

Fig. 3. Loss tan a,, as a function of temperature in LG%2

0.70

alo-9

1.1

1.2

1.3

1.4

1.5

1 OOO/T( 1 /K)

Fig. 4. Arrhenius plot of the conductivities bj) at several frequencies for Li,,,Nat,,NbO,. With the exception of the anomalous part, related to the phase transition, a plot of log (rj3 vs l/T falls on a straight line. +3 varies approximately with ionic activation energy as exp (- Q/k,,T) Q = 0.527 eV. The inset i;; letailed view in the vicinity c

E&(W) versus the real part E;~(o) at several temperatures including Curie temperature. The logarithmic Cole-Cole plot in the measured frequency range cannot be described by the Debye relaxation equation. These are, however, satisfied by the relation c”(w) = c1ac’(tw) in the low frequency side and attenuate quickly in the high frequency range, such behaviour is respected in the ferroelectric dielectric response corresponding to the equivalent circuit made up by a capacitor in parallel with a resistor [19]. The linear relattonship, t “(w) = a t ‘(co), has been previously interpreted in terms of the low-frequency dielectric response due to mobile charged-point

10' Y

k

g :

.

. . . ...... l

8

0

926.C 97d*C 107Pc

10'

10'

Real

. . . ...

..I

.

.

.

.

.

. ..(

.

:

c-a+ : i

10'

Dielectric

.

.

.

:=

10'

10'

Con&ant

Fig. 5. Logarithmic Cole-Cole plots of I” vs c’(w) at several temperatures for L&Nat,, NbO,

Structural and dielectric characterizations

fects presumably connected with the substitution of Na+ for Li+ [14]. In the previous work, we have introduced the modified Debye model of re-orientable permanent dipoles allowing for the possibility of point-charge migration within a network of partially vacant potential wells in the lattice, all acting under the influence of a low-frequency field [14,20]. Resulting expressions for E’(O) and E”(W) are given as

1

of Li,,,Na,,zNb03

291

o-’

zK 6’(0)=6,+

4n2~~~T~J,+2) [I -exp(-t/r)],

(1) 10-•

B

E“(O) =

0.7

a [Nxe *a *(cm+ 2)/3/c, T] Wt

0.8

1000/T (2)

0.0

1.0

(1 /K)

Fig. 6. Semi-log plot of the relaxation time as a function of inverse temperature.

respectively, where N is the average number of mobile charged defects per unit volume, e is the magnitude of the charge, 2a is the distance between the nearest Li+-sites and r is the relaxation time. These two expressions for L’(W) as given by eqn (1) and c”(w) as given by eqn (2) show a frequency dependence to describe the low frequency behaviour of the real and imaginary parts of the dielectric constant of Li,, Na,,* NbO, . The dimensionless geometric factor 01appearing in eqn (2) can be obtained from Fig, 5, using the ratio of the low frequencyimaginary and real contributions to the dielectric constant, as lx N L”(W)/E’(O) % 20.

(3)

Substituting values for N, e and a in either eqn (1) or eqn (2) one can obtain the relaxation time 7. Where the value of N can be approximately estimated as 9.9849 x lO*Odefects cmw3, from the difference of the measured density from the theoretical density, Ap = 0.014 g cmm3, and 2a (Li-Li) estimated as 3.785& from the structural data. Since e = 4.80325 x lo-*’ esu, em = 1.66 x 105, the relaxation time at 1020°C is

T =

aNne *a*(cm+ 2)/3k, Tot"(w) = 7.389 x 10-4s.

(4)

This value is not unreasonable for point defects at high temperature. Taking into consideration that, from t = [2oexp( -qb/k,T)]-’ in Fig. 6 we obtained 4 N 0521 eV, it is in good agreement with 0.527 eV obtained from the Arrhenius plot in Fig. 4. This energy probably corresponds to the defect formation energy at a Li+ sublattice, accompanied with substiPCS

55:3-F

tution of Na+, because the ionic conductivity of dielectrics usually consists of the motion of the light ions and, moreover, is probably the main reason for the electric current generation.

3. SUMMARY The ferroelectric mixed crystal Li,,, Na,,, Nb03 was grown from the melt by the Czochralski method. It has turned out that mixed crystal L&,,Nao,,Nb03 is rhombohedral R3c with a hexagonal unit cell of dimensions uH = 5.1736 A and cH= 5.1736 8, and cH = 5.1736 t% and c, = 13.938 A at 25°C. The longitudinal thermal expansion coefficients in the temperature range from 25 to 900°C are a,, = 11.501 x 10-5”C-’ and aj3 = 7.712 x 10-5”C-‘. The enlargements in the size of the unit cell and the large thermal expansion coefficients are due to the substitution of Na+ ions for Li+ ions and due to the structural rearrangement caused by a size mismatch, respectively. The dielectric variation of Li,,*Na,,, Nb03 reveals a diluted character of ferroelectric second-order phase transition in the vicinity of T,, 1108”C, lower than 1143°C for Lio,,Nao., Nb03. In the high temperature including T,, the low frequency tails of both real and imaginary part of the dielectric constant in Lio,,Na,,lNb03, which are proportional to l/o, were well explained by the modified Debye’s model of reorientable permanent dipoles allowing for the possibility of point-charge migration under the influence of a low frequency ac. field. It is believed that this low frequency relaxation due to the point defect causes a marked dispersion of temperature dependent dielectric constants of Lio,,Nao,2Nb03 at high temperature.

JEONG-BAEKIM and JUNG-NAMKIM

298

Acknowledgements-This work was supported in part by the Korea Science and Engineering Foundation (KOSEF) through the Science Research Center (SRC) of Excellence Program.

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