Microscopic origin of spontaneous polarization and absolute sense of pyroelectric and piezoelectric coefficients in α-LiIO3

Solid State Communications, Vol. 75, No. 6, pp. 535-538, 1990. Printed in Great Britain.

0038-1098/90 $3.00 + .00 Pergamon Press plc

MICROSCOPIC ORIGIN OF SPONTANEOUS POLARIZA;FION AND ABSOLUTE SENSE OF PYROELECTRIC AND PIEZOELECTRIC COEFFICIENTS IN ~t-LilO3 M. Szafrafiski Institute of Physics, Adam Mickiewicz University, Grunwaldzka 6, 60-780 Poznafi, Poland

(Received 19 March 1990 by G.S. Zhdanov) Using a point-charge and dipole model, the spontaneous polarization P, of 0t-LilO3 is calculated to be parallel to the direction in which the apices of IO~- pyramids are pointed. The magnitude of P, is found to decrease with increasing temperature. It is shown that pyroelectric coefficient P3 and piezoelectric coefficient at33are negative, which is quite the contrary to the results obtained by Liminga and Abrahams model [J. AppL Cryst. 9, 42 (1976)].

1. INTRODUCTION

X-ray anomalous scattering. It was also proved that accommodation of the morphology of ~-LiIO3 on HEXAGONAL lithium iodate (0t-LilO3, space group determining its polarity may lead to erroneous results. P63) is one of the most intensely studied crystals. It The + c direction may be a direction of either slower exhibits many interesting properties, among others or faster growth of the crystal, depending on pH. pyroelectric and piezoelectric ones. A few studies have Therefore, the results obtained by YZCL made us been devoted to the issue of these properties as well as undertake another attempt at explaining a microscopic to the correlation between the crystal polarity, strucorigin of spontaneous polarization in ~t-LiIO3. In this ture, and morphology. Rosenzweig and Morosin [1] paper we also study the pyroelectric and piezoelectric observed that under compressive stress along the effects. c-axis, a positive charge is generated at the larger end of the crystal. Moreover, Morosin [2] found that the 2. MODEL FOR SPONTANEOUS apices of IO~- pyramids were pointed to the smaller POLARIZATION end of the crystal. Using Morosin's piezoelectric test, Determination of spontaneous polarization P3 in Turner [3] defined the absolute sign of pyroelectric polar, but nonferroelectric crystal, is a problem. A coefficient Pa of ~t-LilO3 as positive at room temperastudy of crystal structure from the point of view of its ture. Liminga and Abrahams (LA) [4] proposed a model, in which they postulate a positive sign of polarity may be helpful in determining the absolute piezoelectric d33 and of pyroelectric P3 coefficients. A sense of Is- In lithium iodate the unit cell contains two positive sign of p3 was also obtained in the model given molecules. As can be seen in Fig. 1, Li ÷ ions are located in the planes perpendicular to the c-axis and by Coquet et al. [5]. Temperature dependence of pyroelectric coef- distant by c/2. Similar layers are formed by IO~- ions. ficient was studied by Bhalla [6] and Poprawski et al. A comparison of electronegativity of iodide and oxy[7]. In both papers, P3 > 0 and the polarization gen atoms lets us suppose that the negative charge of IO3 ion will be distributed on oxygen atoms. Thus, it change Ap, > 0 with increasing temperature. On the basis of this short review, it would be follows that a dipole moment resulting from the possible to draw a conclusion that in 0t-LilO3, P3 and displacement of ionic charges will depend on the Li-O d33 coefficients are positive for the + c axis appointed distance. There are two different Li-O distances in in the same direction (according to the piezoelectric at-LilO3 structure. We can see in Fig. 1 that any 103 ion forms with Li ÷ ions from two adjacent layers standard [8]) as the apices of the IO3 pyramids. However, recently Yang Hua-guang, Zhang dipole moments with antiparallel components/~1 and Dao-fan, Chen Wan-chun and Li Yin-yuan (YZCL) /a2 pointed in the c direction. As follows from crystal[9] reported on achieving the opposite results, i.e. lographic data, z-coordinates of lithium and oxygen negative signs of d33 and P3 coefficients. YZCL studied atoms obey the following relation: z2 - zl > z3 - z2 polar properties for many samples and the results were (according to the notations in Fig. 1), which implies correlated directly with structural measurements by that the dipole moment: Ap = p~ + P2 is pointed 535

MICROSCOPIC ORIGIN OF SPONTANEOUS POLARIZATION

536

c

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oxygen charge Q0 = _ 0.826e, - 0.828e, - 0.825e for 20, 215 and 500 K respectively. On studying temperature induced structural changes, Svensson et al. [11] described O(z) and Li(z) coordinates by polynomial functions:

................ -i--it ° 0--[,

o--0,

"--Li

Fig. 1. Schematic view of ~-LiI03 structure with the contribution of dipole moments marked. The absolute sense of spontaneous polarization P~ is marked with an arrow. toward - c. At the same time, the dipole moment # of IO; ion is pointed toward + c. The charge distribution and dipole moment for IO; were determined using the INDO method. Details concerning these calculations may be found in [10]. Geometrical parameters of IO; pyramid for different temperatures were taken from the paper of Svensson et al. [11]. The calculated temperature dependence #(T) is shown in Fig. 2. A decrease in the value of # with increasing temperature results mainly from a reduction of the height of the pyramid. On the other hand, charge distribution in IO; depends on the length of I-O bond in the first place, whereas the temperature has a slight effect on it. For example,

Li(z) -- 0.3808A + 167 x 10-gT2AK -2,

(1)

O(z) =

(2)

- 0 . 8 4 3 5 A + 62 x 10-gT2AK -2.

Using the equations (1) and (2) and a charge distribution of I O ; calculated for particular temperatures, A# was calculated. Temperature dependence of dipole moment A# is presented in Fig. 2. A comparison of the values and signs o f f and Ap leads to a conclusion that a resultant dipole moment is pointed in the same direction as the dipole moment of I O ; ion, so P, is pointed toward + c. The spontaneous polarization can be derived from the dependence: 20~ + a#) V '

P~ =

(3)

where V is a volume of the unit cell. Temperature changes of unit cell volume calculated from the data given in [11] are illustrated in Fig. 3. The V(T) dependence has a significant influence on P,(T). The obtained temperature dependence of spontaneous polarization is shown in Fig. 3. It is easy to notice that P, decreases with increasing temperature. The nature of this dependence does not change even if we assume that IOn- pyramid remains stiff within the whole temperature range.

0.45

137 O.~A. 135~ -

~.e

33.5

os.3

a.,,,

>

? ~.5

z~.~,

~

3

3

.

~.OO

200

OA2

3

331

T (K)

Fig. 2. Temperature dependence of dipole moment # of IO; ion and A# moment originating from ioncharge displacements. Solid line denotes the best fit of polynomial temperature function.

0.~,1 0

133

' 200

' 400

131

T (K)

Fig. 3. Temperature dependence of the volume V of unit cell and of calculated spontaneous polarization P, in ~t-LiIO3. Solid line denotes the best fit of polynomial temperature function.

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MICROSCOPIC ORIGIN OF SPONTANEOUS POLARIZATION

537

3. PRIMARY PYROELECTRIC EFFECT

via simple model calculations describe only the primary pyroelectric effect. The measurement of the As follows from Ps(T) dependence (Fig. 3), the primary pyroelectric coefficient for lithium iodate is pyroelectric coefficient P3 is negative. This result is in hindered due to a considerable secondary pyroelectric agreement with the results of measurements reported contribution [6, 7]. Moreoever, ~-LiIO3 is a quasi-oneby YZCL. The temperature course of pyroelectric dimensional ionic conductor and relatively high coefficient may be determined from the following conductivity may be the reason for the differences relation: between the experimental results [7]. It seems that the dP, contribution of the primary pyroelectric effect to p3(T) = dT" (4) the experimentally determined effective pyroelectric coefficient is the highest within the range of low temThe quantites from equation (3) describing the peratures. A comparison of the p3(T) dependence spontaneous polarization can be approximated by from Fig. 4 with the results obtained by Poprawski the polynomial temperature functions. The results et al. [7] within the temperature range 20-100 K indiof the best fit are as follows: cates a good qualitative agreement (under the assumption that the signs of p3 are the same). bt(T) = (33.922 + 3.922 x 10-4TK -' -2.888

A/z(T) =

x

10-6T2K -2) x 10-3°Cm

-(4.524 + 1.175 x 10-3TK -I -- 2.409 x 10-7T2K -2 - 4 . 7 5 3 x 10-gT3K -3) x 10-3°Cm

V(T) = (132.069 + 2.814 x 10-3TK -I + 2.275 10-5T2K -2 - 1.235 x 10-ST3K -3) x 10-3°m 3. (5) The use of expressions (5) and equation (3) enabled us to derive from equation (4) a p3(T) dependence. This dependence is shown in Fig. 4 (curve a). For comparison, the course ofp3 (T) for a stiff pyramid IO; is also shown (curve b). Naturally, the results obtained

4. MODEL FOR ORIGIN OF PIEZOELECTRIC d33 COEFFICIENT For the same coordinate system of axes as accepted in this paper, YZCL determined the piezoelectric d , coefficient as negative. This implies that upon compression of the crystal along c, a positive charge develops on (00 1). We hope to explain this by using the proposed model of PsIn the first approximation, we can assume that IOn- ion is fairly stiff, so that an application of moderate stress does not change its dipole moment. Such an assumption is justified even from the point of view of the studies of pressure dependence of the Raman spectrum in ~t-LiIO3 [12]. If the charge of oxygen atom I Q0[ ~< e, then the dipole moment A# is given by the following expression: A/z = 31Q°lAz,

6

(6)

where Az = zl + Za - 2z2. Under compression Li + layers are shifted with respect to IO; layers. In consequence, more readily deformed, longer distance Li-O is reduced, whereas the shorter distance, obeying the requirement that the distance between Li + layers be c/2, will increase. Consequently, IAzl will also decrease. The decrease in I A/~l and in the volume of unit cell results, as can be seen from equation (3), in an increase in P,. Therefore, an application of compressive stress to the crystal toward c should cause positive polarity development on (001), which is in agreement with the results of YZCL.

2 I

0

0

m

I

200

600 T (K)

Fig. 4. Temperature dependence of primary pyroelectric coefficient calculated from equations (3)-(5) - (a) and under the assumption that #(T) = ~(20 K) -- (b).

5. FINAL REMARKS According to the LA model, the dipole moment Ap generated by ion-charge displacements is parallel to the dipole moment p of I O ; . In this paper it has

538

MICROSCOPIC ORIGIN OF SPONTANEOUS POLARIZATION

been proved that contributions of Ap and/~ are antiparallel. This finding is of a great importance in explaining the microscopic origin of piezoelectricity in ~-LilO3. Moreover, as follows from the performed calculations, the dipole moment of IO~- ion is about ten times larger than that taken by LA, and it has a decisive influence on the value of P,. The estimated spontaneous polarization is pointed to + c. In the presented model, P,, unlike in the LA model, decreases with increasing temperature. These results as well as the absolute sense of P3 and d33 coefficients corroborate the experimental results obtained by YZCL. On examining the p3(T) dependence, Bhalla [6] found a clear local minimum at ca. 210K. Such a minimum was not reported in [7] and [9], but it seems that such an anomaly may be related to, and even justified, by structural changes. If we compare geometrical parameters of IO~- pyramid for different temperatures [11], we can notice that the length of I-O bond slightly decreases over the temperature range 20 K-215 K, and increases again above 215 K. If these changes are related to a real shift of average positions of iodide and oxygen atoms, then they cause changes in charge distribution, thus leading to slight changes of dipole moment of 103 ion. Such changes may, however, significantly influence the course of p3(T) dependence. Therefore, it would be purposeful to study in detail the pyroelectric effect and the length of I-O bond in the vicinity of 210K.

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Acknowledgements - The author wishes to thank Dr M. Koralewski for providing a few references and Dr A. Katrusiak for helpful discussion. This work was partially supported by the Polish Academy of Sciences under the project CPBP 01.12.6.4. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

A. Rosenzweig & B. Morosin, Acta Cryst. 20, 758 (1966). B. Morosin, private communication quoted as [25] of J.G. Bergman & G.R. Crane, J. Chem. Phys. 60, 2470 (1972). E.H. Turner, J. Appl. Cryst. 9, 52 (1976). R. Liminga & S.C. Abrahams, J. Appl. Cryst. 9, 42 (1976). E. Coquet, J.M. Crettez, J. Pannetier, J. Bouillot & J.C. Damien, Acta Cryst. B39, 408 (1983). A.S. Bhalla, J. Appl. Phys. 55, 1229 (1984). R. Poprawski, J. Shaldin & S. Matyjasik, Phys. Status Solidi (a) 90, 167 (1985). IRE Standard 176, Proc. IRE 37, 1378 (1949). Yang Hua-guang, Zhang Dao-fan, Chen Wanchun & Li Yin-yuan, J. AppL Cryst. 22, 144 (1989). M. Szafrafiski & M. Koralewski, Acta Phys. Polon, A75, 705 (1989). C. Svensson, J. Albertsson, R. Liminga, A. Kvick & S.C. Abrahams, J. Chem. Phys. 78, 7343 (1983). V. Lemos, F.E.A. Melo & F. Cardeira, Solid State Commun. 40, 1035 (1981).