Piezoelectric effect and ferroelectric properties in Mn₃B₇O₁₃I boracite

Article

Reference

Piezoelectric effect and ferroelectric properties in Mn

₃

B

₇

O

₁₃

I boracite

CROTTAZ, Olivier, RIVERA, Jean-Pierre, SCHMID, Hans

Abstract

Crystals of Mn3B7O13I boracite with transparent gold electrodes have been prepd. and, after an elec. poling, the single domain state of the sample verified by polarized light microscopy.

Ferroelec. hysteresis loops have been measured at room temp. Spontaneous polarization and pyroelec. coeff. of the orthorhombic phase are reported as a function of temp. Piezoelec.

measurements have been made using an admittance circle and motional capacitance method. The piezoelec. coeffs. are reported as a function of temp. for the cubic and orthorhombic phases. The effect of the magnetic phase transition on the series resonance frequency is also shown. A measurement has been made on a crystal showing multiple resonances due to the presence of tiny ferroelec./ferroelastic domains to illustrate the necessity of optical control during measurements on ferroelastic compds.

CROTTAZ, Olivier, RIVERA, Jean-Pierre, SCHMID, Hans. Piezoelectric effect and ferroelectric properties in Mn

₃

B

₇

O

₁₃

I boracite. Journal of the Korean Physical Society , 1998, vol. 32, Suppl., Proceedings of the 9th International Meeting on Ferroelectricity, 1997, Pt. 3, p.

S1261-S1264

Available at:

http://archive-ouverte.unige.ch/unige:31135

Disclaimer: layout of this document may differ from the published version.

1 / 1

Journal of the Korean Physical Society, Vol. 32, February 1998, pp. S1261-S1264

Piezoelectric Effect and Ferroelectric Properties in Mn

₃

B

₇

0

₁₃

1 Boracite

0. CROTTAZ, J. -P. RIVERA and H. SCHMID

Department of Inorganic, Analytical and Applied Chemistry, University of Geneva, CH-1211 Geneva 4, Switzerland Crystals of Mn3B1013I boracite with transparent gold electrodes have been prepared and, after

an electrical poling, the single domain state of the sample verified by polarized light microscopy.

Ferroelectric hysteresis loops have been measured at room temperature. Spontaneous polarization and pyroelectric coefficient of the orthorhombic phase are reported as a function of temperature.

Piezoelectric measurements have been made using an admittance circle and motional capacitance method. The piezoelectric coefficients are reported as a function of temperature for the cubic and orthorhombic phases. The effect of the magnetic phase transition on the series resonance frequency is also shown. A measurement has been made on a crystal showing multiple resonances due to the presence of tiny ferroelectric/ferroelastic domains to illustrate the necessity of optical control during measurements on ferroelastic compounds.

I. INTRODUCTION

Manganese iodine boracite Mn₃B₇0₁₃1 is a member of the boracite family with the general formula M₃B70₁₃X (hereafter M- X), where Mis usually a divalent tran- sition metal ion and X a halogen ion. Most of the bo- racites undergo a series of phase transitions from a high temperature cubic phase with 43m1' symmetry to phases with lower symmetry (42m1', mm21', 3m1', ml' , ... - see Ref. [1]). At low temperature some of these compounds become simultaneously ferroelectric and ferromagnetic.

The sequence of phases in Mn-1 is from a cubic 43m1' phase (with a= 12.3404(3)

A

at 421 K) [2) to an or- thorhombic mm21' one (with a= 8.7643(4), b= 8.6980(5) and c= 12.351(1)

A

at room temperature [3]) and to a weakly ferromagnetic m'm2' phase. The transition temperatures are 407 K [4) and 26 K [5], respectively.

All three phases, being non-centrosymmetric, allow the piezoelectric effect. In addition the polar orthorhombic phases permit ferroelectricity and pyroelectricity.

Piezoelectric measurements have previously been made on different boracites using either a resonance- antires- onance method (see Ref. [6) and references therein) or the admittance circle and motional capacitance method [7]. In this work we measured the ferroelectric hystere- sis cycles and the pyroelectric effect of Mn-I on a single domain crystal under optical control. The piezoelectric effect has been investigated using the admittance circle and motional capacitance method.

II. EXPERIMENTAL

The Mn-I single crystals used in these measurements are prepared by a chemical vapor transport method [8].

Elongated rods parallel to the <110>cubic direction were cut from a (001)cubic platelet using a wire saw. '!fans- parent gold electrodes were deposited on the (001)cubic

facets. After removing the gold on the sides of the rods a gold wire is attached to the centre of the electroded faces. In order to obtain a single domain sample poling with an electric field of 40 k V

f

em was necessary. During this procedure the crystal is put under a polarised light microscope in order to see if a single domain state is ob- tained. The size of the crystals for the piezoelectric mea- surements were 1.7 x 0.325 x 0.075 mm³ in the orientation 31 (crystal #1) and 2.96 x 0.44 x 0.075 mm³ in the orien- tation 32 (crystal #2), permitting a length extensionnal mode vibration along the long side of the crystal. The fer- roelectric/ pyroelectric measurements were also made on crystal # 1. The piezoelectric measurements on a twinned sample were made on another crystal ( #3) with dimen- sions 2.14 x 0.36 x 0.075 mm^3.

The form of the tensors for the piezoelectric coefficients

diJ and for the elastic compliances SiJ in the different point groups are given in Ref. [9). On the Mn-1 samples

G) orthorhombic: d31• S11

cubic: dw s'll

0

orthorhombic: d3_{2• s22}

cubic: dw s' 11

Fig. 1. The different piezoelectric and elastic coefficients obtainable on Mn-I boracite piezoelectric oscillators depend -ing on the temperature and the sign of the electric field ap- plied. The crystallographic directions a, b, c and the axes of the optical indicatrix no, na, n"Y (abbreviated o:, {3, "'( on the drawing) refer to the orthorhombic phase.

-81261-

-81262-

shown in Fig. 1 it can be seen that, depending on the sign of the electric field applied during poling, two dif- ferent sets of orthorhombic coefficient can be measured.

In order to simplify the notation the samples with the crystallographic direction a parallel to the long side of the rod (allowing measurement of the coefficient d31 ) are referred as "orientation 91" and when the direction b is parallel to the long side of the rod (allowing measure- ment of the coefficient d32 ) as "orientation 92". Note that in the cubic phase it is possible to determine only a linear combination of the 8ij cubic elastic compliances with 8~1 ⁼ 1/4{2su

+

2s12

+

^844).

The electric equivalent circuit of a piezoelectric oscil- lator consists in a series R1L1 C1 circuit in parallel with capacitance Co. The admittance circle and motional ca- pacitance technique that was used for the piezoelectric measurements has been extensively described elsewhere [7]. The main advantage of this technique is that, by measuring the whole admittance circle at the piezoelec- tric resonance, it allows the direct calculation of the en- tire set of parameters of the equivalent electric circuit.

The experimental details as well as the equations used for the derivation of these parameters are given in Ref.

(7] and are not repeated here. A new program has been written in HP Instrument Basic language for a PC.

III. FERROELECTRICITY AND PYROELECTRICITY

The Aizu species 43m1'Fmm21' being fully ferro- electric-fully ferroelastic [13], it is possible, in the or- thorhombic mm21' phase, to switch the spontaneous po-- larization and the coupled corresponding ferroelastic de- formation by applying a sufficiently strong electric field.

The ferroelectric hysteresis loop observed by applying an a.c. electric field is shown in Fig. 2. The spontaneous po- larization is found to be 2.5 p,C/cm2 and the remanent

3 N' E ²

~ (.)

..=.1

a.

z ⁰ 0 ~ ^-1

N

~ ^-2

~ ^-3

-4 -40

P ₅ = 2.5 11C/cm^{2 I}

~

~v ,..._...

;!"

~

P, = 2.0 11C/cm²-

I I

VJ L

I I

ll ^)v

Ec = 9 kV/cm ..._,_

J~

I

/ ^I

/

^...,...,.

/

^I

__..

_~

-30 -20 -10 10 20 30 40

ELECTRIC FIELD E [kV/cm]

Fig. 2. Hysteresis loop of Mn-I boracite at room tempera- ture on a 1.7 x 0.325 x 0.075 mm³ crystal (synthesizer HP 3325A, operational amplifier KEPCO BOP1000M, oscillo- scope HP 141B with a 1 pF capacitor and Sawyer and Tower electric circuit).

Journal of the Korean Physical Society, Vol. 32, February 1998

N"

E CJ

u

..:!.

a.~

c

~ 0 N -~

0 Q..

'E CIS

c

CIS E a: Q)

2.5

2.0

1.5

1.0

0.5

0.0 0

l

...--

- ^r--- ~I

I

7'\

I '

p

=-

^{dPr/ dT}

/ v

20

X

40 60 80 100 120

Temperature [⁰C]

140 200

Q=

§.

150

u

_::1.

a.

'E Q) 100 '()

:;

(.) 0

·c CJ 50 t) Q)

0 Gi

e

_>.

Q..

Fig. 3. Spontaneous polarization and pyroelectric coeffi -cient of orthorhombic Mn-I boracite vs. temperature (elec- trometer Keithley 617, t:t.T/t ~ 3 °C/min). The Curie tem- perature of the 43m1'-mm21' transition is 134 °C (407 K).

polarization 2.0 p,C/cm2 (at 300 K). The coercive field is 9 k V /em (measurement using the Sawyer and Tower method, [10] at 50 Hz).

The remanent polarization as a function of tempera- ture is shown in Fig. 3. The slight difference between its room temperature value and that reported in Fig. 2 is due to experimental inaccuracies. Contrary to what has been reported elsewhere [11] the phase transition is clearly of first order when measuring spontaneous polar- ization. This discrepancy is due to the fact that in Ref.

[11] the pyroelectric coefficient was measured and the spontaneous polarization obtained by integration, but without taking account of the integration constant. This makes the phase transition to appear of second order and gives an erroneous value of the spontaneous polar- ization {which is also indicated in [12], where the values for Mn-Br and Mn-Cl are probably also incorrect for the same reason). The pyroelectric coefficient, obtained as the derivative of the spontaneous polarization with re- spect to temperature, is also shown in Fig. 3. The values obtained are close to those determined in (12].

IV. PIEZOELECTRICITY

The series resonance frequencies as a function of tem- perature are shown in Fig. 4. The decrease of the se- ries resonance frequency close to the cubic-orthorhombic phase transition has already been observed in Cu-Cl and Cu-Br boracites and is due to an increase of the corre- sponding elastic compliances, indicating a softening of some vibration modes. The discontinuous change during the mm21'-43m1' phase transition is in agreement with the first order character of the transition. In Fig. 5 the dii piezoelectric coefficients are shown as a function of temperature. It can be seen that the coefficient corre- sponding to the orientation 32 shows erratic values. It has been found that this is due to a small crack in the crystal which created a perturbation in the resonance.

Piezoelectric Effect and Ferroelectric Properties in Mn3B1013I Boracite - 0. CROTTAZ et al. -Sl263-

F--:a~--~~~:v::-~

2.0 'N :I:

~ 1.8

>.

u c:

Q) 1.

:::::l 2.09l 15 20 25 30 35

C"'

f ₅ orientation 32

Q)

--- ... ·--- ...

u: ...

...._.

··---

Ill

··--.,

Q) 1.2

'a5

\f,AAO-

en

1.0

0 100 200 300 400 500

Temperature [K]

Fig. 4. Series resonance frequencies of Mn-1 boracite, corre- sponding to orientation 31 and 32 in the orthorhombic phase and 14 in the cubic phase, vs. temperature. Inset: Effect of the magnetic phase transition on the piezoelectric series res- onance frequency of Mn-1 boracite. The Neel temperature of the mm21'-m'm2' transition is 26 K and the Curie tempera- ture of the 43ml'-mm21' transition is 407 K.

16~---+---+---~---~·----~

~ ~ 14r---+---+---~---~A~--~

~~ 1

=

^~ 12~----~---+---~-4~----~+---~

8 J 10~---~---+---~~~--~/H-1~·~~~

2 -;;....:· ... .

100 200 300

Temperature [K]

· .. ,I' ?1.

;:

^-~

400 500

Fig. 5. Piezoelectric coefficients d31 and d32 (orthorhombic phase) and d14 (cubic phase) of Mn-1 boracite vs. temper- ature. The erratic values for d32 are due to a crack in the crystal. The Curie temperature of the 43ml' -mm21' transi- tion is 407 K.

Since this coefficient is calculated using the difference between frequencies with maximum and minimum sus- ceptance the accuracy needed on these data is no more sufficient. Other crystals have been prepared but showed either a problem with a crack or a spontaneous genera- tion of ferroelastic domains when the electric poling field is suppressed (as discussed in Section V below). The problem of erratic values for the orientation 32 does not appear in the measurements of the elastic compliances (see Fig. 6), because the calculation of this parameter is not based on a frequency difference.

The piezoelectric coefficients and elastic compliances in Mn-I have the same order of magnitude than those ob- served in others orthorhombic and cubic boracites (values for ^dij vary between 3.5 and 15 pm/V in the orthorhom- bic phase and between 4.5 and 15 pm/V in the cubic phase- see Table III in Ref. [6]).

As stated in the introduction, Mn-1 undergoes at 26 K a phase transition from the paramagnetic phase with

7

l. _-

~ E

.:=

!})".!.

Q) u c:::

.~ Q.

I

^s'11

51 1 -

,

~A--

r;:/

- ^....

E 0

0 .!::!

iii co 4

iii

... ^~.,:::1

-- ^{1 ·-}

^~22

0 100 200 300 400 500

Temperature [K]

Fig. 6. Elastic compliances su, s22 (orthorhombic phase) and s'₁₁ (cubic phase) of Mn-I boracite vs. temperature. The Curie temperature of the 43ml'-mm21' transition is 407 K.

point group mm21' to a weakly ferromagnetic phase with point group m'm2' [5]. The effect of this phase transition on the series resonance frequency can be seen in the inset in Fig. 4. This can be explained by a magnetostriction effect: the spontaneous magnetization appearing at the magnetic transition can induce a deformation of the sam- ple which creates a variation of the resonance frequency.

V. MEASUREMENTS ON TWINNED CRYSTALS

Some measurements have been made on a crystal con- taining some very small ferroelastic domains with an- other orientation than the majority of the crystal, as shown schematically in the inset in Fig. 7. When an elec- tric field is applied, these ferroelastic domains disappear but they are immediately reappearing when the electric field is suppressed. They are probably due to a stress induced by the epoxy used to fix the gold wires. On this sample it has been observed that, at some temperatures, the resonance is divided into numerous resonances due

2.0

[L 1.5

..e.

~ c::

·o ~

~ 10 CIS (,)

f--

0.5 100

~1,

~

' ..),~,J}

r . ' ·~ ~r

1000 Frequency [kHz]

22 20 18 16

14

~~y.

^{12 w"-}

• 10

..

10000

Fig. 7. Capacitance and relative dielectric permittivity of a twinned crystal of orthorhombic Mn-I boracite as a func- tion of frequency, showing numerous piezoelectric resonances (T= 128 K, crystal's size: 2.14 x 0.36 x 0.075 mm3). Inset:

Schematic representation of residual ferroelastic domains in a Mn-I boracite crystal after electrical poling.

-S1264-

to particular vibration modes (see Fig. 7). It is inter- esting to note that such domains, which represent only a very small percentage compared to the total volume, have such a large effect on the piezoelectric resonance.

VI. CONCLUSION

The ferroelectric and piezoelectric properties in Mn-I are consistent with the point groups determined by X ray diffraction (mm21' and 43ml') [2,3). The study of the spontaneous polarization and of the piezoelectric co- efficients as a function of temperature are in agreement with the first order character of the mm21'-43ml' transi- tion. The measurement on a crystal with small amounts of ferroelastic domains shows that an optical control of the sample under investigation is obligatory in order to avoid the possibility of obtaining incorrect results.

REFERENCES

[1] H. Schmid, Int. J. Magnetism 4, 337 (1973).

Journal of the Korean Physical Society, Vol. 32, February 1998 [2] 0. Crottaz and F. Kubel, Z. Kristallogr. 211, 926 (1996).

[3] 0. Crottaz, F. Kubel and H. Schmid, J. Solid State Chern. 120, 60 (1995).

[4] H. Schmid and H. Tippmann, Ferroelectrics 20, 21 (1978).

[5] 0. Crottaz, J. -P. Rivera, B. Revaz and H. Schmid, Fer- roelectrics, in press.

[6] P. Genequand, H. Schmid, G. Pouilly and H. Tippmann, J. de Phys. 39, 287 (1978).

[7] J. -P. Rivera and H. Schmid, Ferrolectrics 42, 35 (1982).

[8] H. Schmid, J. Phys. Chern. Solids 26, 973 (1965).

[9] J. F. Nye, Physical Properties of Crystals (Oxford Science Publication, 1990).

[10] C. B. Sawyer and C. H. Tower, Phys. Rev. 35, 269 (1930).

[11] A. J. Castellanos-Guzmann, Thesis (Queen Mary Col- lege, London, 1981).

[12] A. J. Castellanos-Guzmann, J. C. Burfoot, H. Schmid and P. Tissot, Ferroelectrics 36, 411 (1981).

[13] K. Aizu, Phys. Rev. B 2, 754 (1970).