Piezoelectric measurements of Ni-I boracite by the techniques of admittance circle and motional capacitance

Article

Reference

Piezoelectric measurements of Ni-I boracite by the techniques of admittance circle and motional capacitance

RIVERA, Jean-Pierre, SCHMID, Hans

Abstract

Piezoelec. expts. on Ni-I boracite were made between 4.2 and 320 K. An automatic measuring technique permitting the detn. of the entire set of parameters of the elec. series equiv. circuit was developed and is described. It is based on the measurement of the whole admittance circle at piezoelec. resonance. The electromech. parameters d31, g31 and k231 were obtained by means of a motional capacitance method and using an independent measurement of ε33τ. Measurements were done under optical control of ferroelec. and ferromagnetic domain states. Internal loss (1/Qm) peaks were obsd. The only phase transition which can unamibiguously be confirmed is the phase transition at 61.5 K.

RIVERA, Jean-Pierre, SCHMID, Hans. Piezoelectric measurements of Ni-I boracite by the techniques of admittance circle and motional capacitance. Ferroelectrics , 1982, vol. 42, p.

35-46

DOI : 10.1080/00150198208008099

Available at:

http://archive-ouverte.unige.ch/unige:32134

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

1 / 1

Ferroelecrrics, 1982, Vol. 42, pp. 35-46 0015-0193/8214201-0035/$06.50/0

C> 1982 Gordon and Breach, Science Publishers. Inc.

Printed in the United States of America

PIEZOELECTRIC MEASUREMENTS OF Ni-l BORACITE BY THE TECHNIQUES OF ADMITTANCE CIRCLE

AND MOTIONAL CAPACITANCE

J.-P. RIVERA and H. SCHMID

Department of Mineral, Analytical and Applied Chemistry, University of Geneva, Sciences II, 30 quai Ernest-Ansermet, CH-1211-Geneva 4, Switzerland

(Received July 13. 1981; in final form October 26. 1981)

Piezoelectric experiments on Ni- I boracite have been made between T

=

4.2 K and 320 K. An automatic measuring technique permitting the determination of the entire set of parameters of the electric series equivalent circuit has been developed and is described. It is based on the measurement of the whole admillance circle at piezoelectric resonance.

The electromechanical parameters iJJ,, iJ1 and k~, have been obtained by means of a motional capacitance method and using an independent measurement of "Ef3• Measurements have been done under optical control of the ferroelectric and ferromagnetic domain states.

Internal loss (1/Qm) peaks have been observed and were found to increase in temperature (18 K- 20 K and 142 K- 152 K) with frequency (2 MHz- 6 MHz).

The only phase transition which can unambiguously be confirmed is the one at 61.5 K.

INTRODUCTION

The natural boracite (Mg3B10nCI) is one of half a dozen crystals in which the piezoelectric effect was discovered for the first time by the brothers Jacques and Pierre Curie¹ in 1880.

The boracites form a family of isotypic com-

r

pounds with the general formula M3B10nX, ab- breviated henceforth M-X, where M stands for Mg, Cr, Mn, Fe, Co, Ni, Cu, Zn or Cd and X for OH, N03, F, Cl, Br or I. Other variants of bora- cites with somewhat different formulae are known with X=S, Se or Te and M=Li. The properties of boracites have recently been reviewed by R. J. Nelmes.² They are also collected in .. Landolt- Bornstein's Tables".³

Most of the boracites are characterized by a se- quence of ph!!_se transitions, for example with the point groups 43m - mm2 - m - 3m in the sense of decreasing temperature.

At low temperatures some of the compositions become simultaneously ferroelectric and weakly ferromagnetic.

All phases of boracites are non-centrosymmetric and consequently allow the measurement of the piezoelectric effect.

Some piezoelectric measurements on differ- ent compositions of boracite have already been reported. 3'⁴

In this paper we present measurements of piezo- electric data on the boracite composition Ni-l which is one of the most interesting ones owing to the simultaneous onset of ferroelectricity and ferro-

ma~netism at one and the same temperature (61.5 K).!.6

Piezoelectric experiments on Ni-l have been performed by W. Rehwa.ld⁷ between 35 K and 250 K on an unpoled specimen, but without simul- taneous observation of the domain states. In that paper⁷ an unusual temperature dependence of the coefficient c •• was observed near 130 K, and a tiny dip around 60 K. A contour-shear mode specimen served for the experiment.

Preliminary piezoelectric measurements on Ni-l under simultaneous visual control of the domain states have been initiated at Battelle⁸ following a technique already used for other boracite compo- sitions:• the crystal is excited by an oscillator via a weak coupling capacity and the resonances are measured by means of an oscilloscope.

Owing to heavy internal losses ( l!Qm) of our Ni-l crystals at about 140 K, a too high capaci- tlV!Ce of the sample holder and unstable spring- like mounting of the sample, that technique did not allow measurements between 100 K and 200 K.⁸ However, the main advantage was the possi- bility of applying a relatively high electric poling field.

[423]/35

•

36/[424] J.-P. RIVERA AND H. SCHMID As R. Holland and E. P. EerNisse have already

pointed out,⁹ the piezoelectric measurement tech- niques proposed by the Standards on Piezoelec- tricity10 only allow the amplitude of the electric signal to be obtained. This means that one loses all information on the phase and it is necessary to use correction formulae. 14 The "IEC Recommen- dation"16 suggests measurements at zero phase, a technique which is not much more satisfactory.

In order to obtain more information than by the techniques described in the "Standards" and the "IEC publications," a Vector Impedance Meter (HP4815A) has been used in the present work, where we have automated data acquisition and handling.

We recorded the whole admittance circle at the fundamental piezoelectric resonance. Thereafter, by using the motional capacitance method, 12 we computed the piezoelectric coefficient

a

31 from the special points

J-,

^fs,

f..

and IIR1 of the circle.

Other coefficients of interest, such as ultrasonic velocity, piezoelectric coefficient K11 and mechani- cal coupling factor k~1 are also presented. For these last two coefficients the low frequency ca- pacity at 100 kHz, has been used.

ELASTIC AND PIEZOELECTRIC COEFFICIENTS

There exist several sets of equations linking the electric and mechanical properties of a crystal. 15 We have chosen the length-extensional mode for the piezoelectric measurements of Ni-l boracite.

Figure 1 shows the relationship between the cubic and orthorhombic coordinates. The axes x 1 to x3

of the oscillator (see also Figure 8 of Ref. 15) are

FIGURE I Orientation of the "Standard" axes (i,, i2, i1) of the oscillator crystal with respect to the cubic axes. For Ni-l boracite sample #48-11, I= 1.86 mm, w = 0.66 mm and t = 0.118 mm.

parallel to the orthorhombic axes of boracites (compare Figure 2 of Ref. 4).

However, for Ni-l boracite, recent results⁶ have shown that the symmetry is most probably mono- clinic below 61.5 K, hence in this work, axes x1 to X3 are pseudo-orthorhombic axes below that temperature. The longest axis of the resonator (x1) is paraJiel to the (I IO)cub direction, i.e. to the face diagonal of the cube.

Semi-transparent electrodes have been applied to the cubic (001)cub facets. Therefore the compo-

nents of the electric field E1 = E2 = 0. Because the -~

crystal can vibrate freely, the stress components T2 to T6 are equal to zero.15

The relevant pair of equations is therefore15 St = .Sft·TI

+ all·E1l

D1 =

a1,.

^T1

+ £f1·EJ

⁽¹⁾

The carets C) have been ·placed on the constants to indicate that the constants are referred to the coordinates i~, i2,

x

3 and the compressed matrix notation has been employed.

Moreover

(2)

(3) The wave equation15'17"18 yields the ultrasonic velocity

- 2 - 1

Vt-~

p ·su and for the fundamental resonance

(4)

Vt

=

^{2•/•/1 (5)}

For Eqs. (1) to (5) we recall the following notation: 15

S =strain.

T =stress.

E = electric field.

D = electric displacement.

s£

= compliance at constant E.

a

^{and ~} are piezoelectric coefficients.

E is the low frequency permittivity, usu- ally for

f

between 50 kHz and 1 MHz.

For some of our Ni-l crystals, the dispersion of E(/) at 295 K is described by a Cole-Cole formalism when e.g.

J<

50 kHz.⁶

•

PIEZOELECTRIC MEASUREMENTS OF Ni-l BORACITE {425]/37

k

= electromechanical coupling factor.

/1

is a resonance frequency. Experimen- tally/.. the series resonance frequency, is taken for

f

1•

15

I

=

^length of the crystal.

p = the density, using Ref. 19, the x-ray densit~ of Ni-l, at 295 K, is 4.46 · 10³ Kg/m.

In case of dissipation of ener~f'· complex coeffi- cients have to be introduced. ²⁰-

. For the non-zero components of thc:_piezoelectric .r and elastic coefficients of the cubic (43m) and or-

thorhombic (mm2) phase of boracites see Ref. 4.

ELECTRIC EQUIVALENT CIRCUIT The electric equivalent circuit¹⁴•18

•23

of a mechani- cally unloaded piezoelectric oscillator is composed of a series circuit R1, L1 and C1 (see Figure 2) in parallel with Co, which is also in parallel with the stray capacitance C,. In this work, C, is mainly due to the coaxial line between the probe of the Imped- ance Meter, located outside the dewar, and the crystal. The index 1 in R1 , L1 and C1 refers to the fundamental mode of vibration. For the overtone i the series circuit is composed of R;, L; and C;.

Using Eq. (11) of the Standards of 1958,¹² the relationshi? between the measured low frequency capacity C -being larger than Co-and Co can be derived as

T 7r 2

C =Co+ -·CI 8

for an elongated platelet as shown in Figure 1.

,---a.--..,----,

I I I

_._

I cfZl "'T' c.

I I I I

~---....1-

___

^.J

(6)

FIGURE 2 Eleclric equivalenl circuit of a piezoelec1ric vi- brator near to resonance, with a stray capacitance C, (sample holder).

ADMITTANCE CIRCLE MEASUREMENTS When the frequency (f = w/2rr) increases, the locus of the impedance

zl

= Rl

+

j(wLI - 1/wCI) of the series equivalent circuit forms a straight line parallel to the imaginary axis in the R-X plane. This is shown in Figure 3a. The imaginary part of

zl

vanishes at

w = Ws

=

2rr/.

=

IIVL1C1, (7) where/. stands for the series resonance frequency.

The admittance Y1

=

1/Z1 is a special case of a conformal transformation. The straight line in the impedance plane transforms into a circle in the admittance plane. This circle is centered on the real axis, i.e. on the conductance axis G, and its di- ameter equals IIRt. The series frequency [. is given by the intersection of the circle with the real axis at maximum conductance, Gmu: = 1/R^1•

If the motional quality factor Q, (see below) of the series circuit is not too weak, say at least about forty, one can admit that the effect of the capacities Co

+ c.

will only be to translate the admittance circle parallel to the imaginary axis, Figure 3, by a value

B = w(Co

+c.)=

Ws(Co

+c.).

For very small boracite samples, Co is of the order of 2 pF whereas the capacity of the coaxial sample holder and the probe of the Impedance Meter is C, = 7.5 pF

+

0.3 pF = 7.8 pF.

For 2 • Ws • R1 ·(Co

+

C,)

>

l the circle no longer cuts the real axis and there is no longer resonance and antiresonance. This means that the phase no longer reaches zero. Then the parallel resonance frequency

J,

is no longer measurable by means of approximation methods¹⁴ as used in Ref. 4.

The particular points of the circle, f-, j. and f+

together with the diameter of circle IIR 1 (Figure 3), allow the straight forward calculation of R1, C~,

L1, Q, and 1/Q,, (because for f- and f+, [w L1

- (llw'~'CI)]/Rl = tg(±45°) =

±

1) "' Ct = - 1- · (f+

-f-)

(8)

2rrRI f+·f-

RI 1

L~=-·----

2rr (f+

-f-)

⁽⁹⁾

(10) Q, must not be confused with the dielectric Q fac-

•

38/[426] J.-P. RIVERA AND H. SCHMLD

o>

X

8

f_

f.,.

o)

Z•R+jX 8 / f'.,.

y

w<C •C

a o

G

b)

d)

Y•G+j8

•1/Z

f,.

G

y

G

FIGURE 3 Locus of serie equivalent circuit (L1 R1 C1) ver- sus frequency in the Z and Y planes; special points of interest

<f-, fs, f.) are indicated.

a, Z(j) = R + jX(j) b. Y(j) = G(j)

+

jB(j)

In c. and d. the effect of the translation of the circle by w,C.

and w,(C.

+

C,) respectively, is shown.

tor. 1/Qm describes the internal mechanical losses of the piezoelectric crystal.

From Eqs. (4) and (5) which link the compliance with the ultrasonic velocity, and the latter one with the series resonance frequency, one obtains

(11) More precisely²⁰'21

'2

z.²• .s

=

^{.s' - j.s" and therefore}

expression (11) gives the real part of

sf.

whereas the imaginary part is linked to Qm bl ²•24

.sfj' l.sfl = 1/ Qm (12)

neglecting losses due to mounting, roughness, etc.

In principle, the ultrasonic velocity v. = 2/[s would have to be corrected for the effect of inter- nal friction. One finds²³

v. = 2/[s J l - 11(4Q~)

In the case of our Ni- l boracite crystals, the low- est value of Qm found at T = 140 K equals- 40, for which a correction turns out to be unnecessary

on the basis of the preceding formula, however, the problem should be studied in more detail using a more modern theoretical approach.

MOTIONAL CAPACITANCE METHOD Following the 1958 Standards,¹² the motional capacitance constant

r

can be related to the piezo- electric constant a 31• For the length-extensional mode of a narrow bar one obtains

t 32 ~2 2 2

r

= c~·-

1

^-·w ^{= 2 · p}7r ^•a3.·1

^{·f •.}

hence

~

(13)

(131 =

± ~._!_. J

^{t •}

^JC;.

⁽¹⁴⁾

4/ Is 2 • p • I· w

Thus in this expression the parallel resonance fre- quency [p and the dielectric constant do not occur.

For the length-extensional mode the electrome- chanical coupling factor is defined by Eq. (2).

From Eqs. (11) and (14) it follows that k~1 is linked to Ct and Cf3 by

(15) where

CE

^is the low frequency capacity.

Another method, the so called "Capacitance Ratio Method, ¹² which can be derived from the preceeding one, allows us to calculate a31 from [s, ..._

Efh / ,

p and the capacitance ratio r

=

CalC, of a vibrator!·¹² The ratio r is linked to the parallel resonance freguency [p by the expression [p

=Is

J

^l

+

llr which likewise defines [p. ¹⁴ In principle r can be obtained from experimental values of[p and[s, however, the exact value offp is not easily accessible by experiment. ¹⁴

Knowing

sf

1 and

k i

1 one can calcu.late

sf ,:

sf.= s f10 - kL)

(16) In principle it is possible⁹'21

-although more delicate-to determine the imaginary parts of d and E by measurement of the admittance. A more elaborate method using an iteration procedure has been described by J. G. Smits.²⁵

INSTRUMENTATION

In order to observe the crystals at low temperature during the measurements, the tail of a standard

PIEZOELECTRIC MEASUREMENTS OF Ni-l BORACITE [427)/39

Raman Oxford Instruments CF 204 dewar has been modified in such a way, according to our plans, that the distance between the outer windows was reduced from 80 to 40 mm. This allows the use of 3.2x and 4x objectives (Leitz) as well as a special 20x objective for long-working distance, together with lOx or 16x oculars mounted on an "Ortho- plan" Leitz polarizing microscope. The dewar has been conceived so as to fit between the pole gaps of different Varian electromagnets, with the dewar being mounted on an optical bench.

r

The capacitance of the coaxial sample holder (l.D. 19 mm, length 500 mm) was 7.5 pF at I MHz.

In the described experiment,

IZI

and its phase have been measured by an Impedance Meter Hewlett Packard HP4815A. The active probe of this apparatus supplies a constant current of

4~ARMS· Hence the output voltage of the meas- urement circuit is proportional to the magnitude of the impedance. The capacitance of the probe was 0.3 pF. A synthesizer HP3325A commands the Impedance Meter. The latter one is equipped with two analog outputs, one for

IZI,

the other one for the phase, both being read by a digital voltmeter. These two voltmeters and the synthe- sizer are linked by a HP-IB bus to a desktop computer HP9825T for data acquisition and treatment. The calculator is equipped with a ROM matrix HP982I lA for matrix calculation. A plotter (HP9872B) allows controlling the form of the ad- mittance circle for every temperature and to plot all parameters of interest versus temperature at the

nd of the experiment.

The temperature was controlled to better than

±0.1 K (with DTC2 and VC30 Oxford Instr.). An exchange gas pressure of about 50 mbar (at 295 K!) of He gas was used inside the dewar.

Figure 4 shows the experimental set-up.

In order to eliminate stray capacities the dielec- tric constant is measured by a three point method using Boonton bridges 75C (5 kHz to 500 kHz) or 72BD (1 MHz). The analog output of the 72BD bridge conveniently allows continuous measure-

MICROSCOPE

ments as a function of temperature, although the relatively high frequency may sometimes be inconvenient.

For the determination of DC resistance versus temperature⁶ a Keithley 417 electrometer was used.

DATA ACQUISITION AND TREATMENT Because the HP4815A Impedance Meter was not programmable, it was necessary to conceive an in- teractive program for the HP9825T.

At the beginning of a measurement one is look- ing for the frequency at which the phase equals zero, or in case of the phase not becoming zero, for the frequency at minimum absolute phase.

Thereafter one comes back to a starting frequency for which the phase is of the order of -85° to -80°.

The value of twice the difference between these two frequencies yields the frequency interval to be scanned. Sixty to eighty points (N) are sufficient to describe the resonance curve around the series resonance frequency. It is not necessary to go through the "parallel" resonance because in addi- tion to the reasons already pointed out, the Imped- ance Meter is lacking a scale above IOO k!l.

The variation of the frequencies is chosen such to avoid an excessive density of experimental points far off the series resonance.

Thereafter the points i = I to N are plotted in the admittance plane Y = G

+

jlJ. At this stage one can already check the absence of an eventual secondary resonance. Then the program sets out to seek the "best circle" with center ( G, B), radius r and running through N points ( G;, lJ;). This circle is found by a least squares fit, i.e. when the min- imum of the function S( G, B, r) is reached, where

S(G, B, r)

=

E

N ^{(J(GI- G/}

⁺

^{(B;- JJ)2- r)2• (17)} I= I

There exist several methods for minimizing a

SYNTHESIZER DVM DVM

DESKTOP COMPUTER PLOTTER

FIGURE 4 Experimental set-up for piezoelectric measurements under visual control of the ferroelectric domain state.

40/[428] J.-P. RIVERA AND H. SCHMID function with N variables, their particular appli-

cability depending on the knowledge or ignorance of the first and second derivatives of that func- tion.26 In the present case it is easy to calculate the gradient 'V S (x) as well as the hessian or Hesse matrix H which is the matrix of the second derivatives

H={iJ²S(x')).

OX;OXj

In our case this real and symmetric matrix is of order three.

The minimum of S is given by 'V S(x) = 0.

By developing a Taylor seri.es around the point x giving the minimum, and by retaining only the first terms of the development, one obtains

x

=

x'-Jr¹(x')· 'VS(x'), (18) where x' is a point in the neighborhood of x.

Hence the gradient is modified in magnitude and direction by the inverse of the Hesse matrix. Thus one has to check that

IHI >

0.

In reality the search of the minimum is even more speeded up by the following method:26

Instead of calculating x = x' + d, where d

=

^{-Ir1·g and g}

=

^'VS taken at the point x', one seeks

(19) where t• is a scalar calculated at point x' and de- fined by

(20) Here gT and dT indicate the transpose vectors of g and d, respectively.

The minimum is approached by iteration; the convergence being very fast, three or four itera- tions are sufficient.

In principle one has always to check that the obtained minimum is not a local one. This can be done by using for x pseudo-random numbers gen- erated by the calculator.

Figure 5 shows the experimental points and the circle obtained for a Ni-l crystal (#48-11) at T = 140 K as well as the printout of the calculator.

The circle is drawn rapidly by the use of the SQ:

called rotation matrix operating on a small vector tangent of the circle.

The frequenciesf-,/s and/+ are calculated by in- terpolation between two adjacent points as indi- cated on Figures 3 and 5.

For a given temperature and by choosing about 60 points around the frequency fs, the data acqui- sition takes about 10 minutes, the response of the Impedance Meter HP4815A being relatively slow.

However, the computation of the "best circle" by means of the program shortly discussed above, takes only 5 to 10 seconds. In one day 80 to 100 temperatures are registered and thereafter the pa- rameters are automatically plotted versus temper- ature, e.g. between 4.2 K and 320 K. The program length is of 18 kilobytes whereas the numeric and string variables require 10 to 20 kilobytes more.

Adaptation of this program for a Gain Phase Meter is now in progress.

SAMPLE PREPARATION

The single crystals were obtained by chemical vapor transport. ²⁷ Elongated rods were cut with a wire saw, ground with SiC paper and polished with diamond paste (3 and 1 ~m). After careful cleaning in a stripping solution, transparent gold (on chromium) electrodes were evaporated. For ob- taining adequate adherence a substrate tempera- ture of about 150°C and a vacuum of 10-⁵ to 10-6 mbar proved satisfactory. After electroding, the lateral edges of the rods have to be freed from eventual spurious gold by means of diamond paste.

Finally, gold wires (D.40 ~m) are attached to the center of the .eJectroded faces by means of

"Epoxy", using a micromanipulator.

POLING

With a view to obtaining a ferroelectric single domain state the samples have to be cooled from 62 K to 4.2 K in a DC electric field. For one po- larity, denoted+ (plus), the monoclinic b axis was aligned-even at zero bias field-along the direc- tion of observation .i2 (extinction directions rotat- ing with temperature, absence of Faraday rota- tion). For the reverse polarity, denoted-(minus) the monoclinic b axis was aligned along it as could be judged from the observation of magnetic do- mains. It was not always possible to lift the degen- eracy of the two allowed monoclinic domains be- cause the polarization vector in both of them is forming the same angle with the applied electric field (compare Figure 20 of Ref. 28 describing the purely ferroelectric monoclinic domains) .

. .

,...__

r

PIEZOELECTRIC MEASUREMENTS OF Ni-l BORACITE [429]/41

0.17~---~

T ^~-. Jo

f-

_tib^{T; i'IF>} . ;:.·t.::. ^{0 K} ~ ~l p ¹⁴⁰ 8^{0 fj} 0

l't(tX 8 1 ^8<?-~14

,.,in 8 13. ^{4-: -(15} p.,:;.(r/50•3• 4

*

^{J I~} s 3. ::;51 -:--€!!:· ⁴

8 , _{• :;>} . _I <:H: e-u4

, .

_'3 ~:I sr:.t. o?-05

~; s·rz ^{I 502 e-1 I}

L 0

til E

f + Hz 20 u<:::::z

f ~- Hz 1':< (1154 f- Hz I·~ 7i)€,4

'--' p 0 1 .40 e •H

( F 1 • 2::: .;--1.3

CD L H ^~ -'• 16 .; -·~2

l~ 4 0 E>l .: 0 I

1/0 2. 1t· ^F.-02

w u 0. 12 :z <

I -a..

w u

til :::l til

f+

140.0K

0.07+----+----~--~----;---~----~---~----~----~--~

CONDUCTANCE G [ mS J

FIGURE 5 Example of an admittance circle for Ni-l Boracite (lf48-Il), at the temperature (140 K) where the inter- nal loss (1/Q.,) reaches a maximum for the fundamental resonance frequency.

RESULTS

In the Figures 6, 7, 8, 9, 10 and 11 the respective pararneters.fs, Rt, Ct, Lt, Q,. and 1/Q, are repre- sented as a function of temperature for one and the same Ni-l boracite sample (#48-11) vibrating in the fundamental length-extensional mode.

In Figure 6, representing fs(T), the righthand scale gives the ultrasonic velocity (v = 2 ·I ·fs) for the given orientation of the rod.

Figures 12 and 13 show the temperature behav- ior of II /;-being proportional to compliance

sf1

(Eq. 11)-and of the piezoelectric coefficient ^a31,

calculated by Eq. (14), respectively. Because of lack of data for p(T) and /(T) for the used crystal, we can only give

111;

instead of

sf1

(Eq. 11) in Figure 12. From Ref. 29, it ensues for the temperature range 4.2 K to 300 K that

tlpl p

=

+0.5% and tl/²//2

= +0.3%

(total: +0.8%) become comparable with

tlf;/ f; =

^{+ 2.4%!}

In the calculation of

a

31 (Eq. 14, in which

.JC;

is the dominating term) the value of p = 4.46 10³[kg/m^3] has been taken for the density. ¹⁹

42/[430] J.-P. RIVERA AND H. SCHMID 2. 010

...

₇₄₅₀

,....,

.

N I

3 ^(II 1. 990

.·· ··· ...

7400 ⁽⁰

...

. .

...

:

. .

_c.S

,.._

.

u

. . .

c

. _. ^.

^,.._

II)

l ^{. ..,}

::J

. .

_{7350 0}

rr

...

II) 0

L 1. 970

u..

,

_al

:61. SK >

al

..

u

"

^{7300 0}

c

. ..

0 _c

. .. .

^{c 0}

0

..

^(II

(II

..

⁰

II>

..

^L

a:: 1. 950

.. ^..,

-:·

7250

(/)

~::

^::l

al L al

t.n 7200

1. 930

0 50 100 150 200 250 300 350

Temperature [KJ

FIGURE 6 Series resonance frequency of the fundamental mode. The right hand scale indicates the ultrasonic ve- locity v, = 2 ·l·j.. where I is the length of the crystal (Ni- l (1148-11) I = 1.86 mm).

We reca!t that dt4(43m) = 2 ·

d11

^{for cubic}

symmetry (43m) at T

>

61.5 K and d₃₁(mm2) or d32(mm2)

=

d31 for pseudo-orthorhombic symme-

try at T

<

61.5 K. By analogy sft(mm2) or

sf2(mm2)

= sft

in the_ orthorhombic phase, whereas for the cubic phase (43m) one obtains4

i

(2sft

+

2sf2

+

s!'4) =

sft.

8

=

oc

10.00

•

u c

., 0

• ;;

"'

• ...

0 _c

~ 5. 00

.,

X 0

· ... ··

0. e0 c..A...,._ ... ....,."-. __..__.'--~-'---...___.___.___._'---'

0 50 100 150 200 250 300 350

T emp•~otv~e [J{)

FIGURE 7 Motional resistance R1(T) of Ni- l (1148-11).

Other crystal cuts would be needed in order to deduce the various compliances.

Figure 14 shows the temperature dependence of the real part of the low frequency capacity

crl

^at

100kHz. An electric field of 100V/0.0118 em= 8.5 kV /em is applied below 62 K in order to polarize-~

the crystal and to maintain it in the ferroelectri'- single domain state. At the frequency of 100 kHz peaks of dielectric Joss are observed at T = 12 K and T= 110 K.⁶

;:;:

_g.

-,.:.

...

_.,

u

• ^{0. 20}

u c

.., 0

0 c a. c u 0.10 0 _c

0

....

0 X

..,

··:1

1- · ..

... . . ...

···· ··· ....

· · · · ··· ···· ··· ··.

50 100 I 50 200 250 300 350

T emperoture [KJ

FIGURE 8 Motional capacitance C1(T) of Ni-l (1148-11), calculated from Eq. (8).

•

PIEZOELECTRIC MEASUREMENTS OF Ni-l BORACITE [431)143

• 0

c c

" ⁰

~ c

c 0

., 0 X 0

l~~

80 60

40

,..,- .

20 ._,.,.. I

0 s~

. · .. · ··· ·

100 150

.... .. ··· · · · ···

20~ 250

T emperoturo (K]

···

300 350

FIGURE 9 Motional inductance L1(T) of Ni-l (#48-11), calculated from Eq. (9).

E Q

l;

" ⁰

0 2~000

~

..

1~000

,

0

0 I

.

^:

~ ... i

0

:'\.

. !·

50

· .

100

· · ···

150 200 250 300 350 T emper-otur-e (Kl

FlGURE 10 Motional quality factor Qm(T) of Ni-l (1148-11). calculated from Eq. (10).

r '

Figure 15 refresents the electromechanjcal cou- pling factor

k

3 ., calculated by means of Eq. (15) where

C'f3

is measured at 100 kHz (Figure 14).

Finally, Figure 16 shows the temperature dependence of the piezoelectric coefficient

g31 = a3.1Er3.

Table I gives some coefficients of Ni-l boracite for particular temperatures. By comparison with Table III of Ref. 4, also reproduced in Table 250, p. 267 of "Landolt-Bornstein",³ it can be seen that the electromechanical coefficients of Ni-l are of the same order of magnitude as those found for other boracite compositions.

In Figure 17 the series resonance frequencies are compared for one and the same crystal for the fundamental mode and a mode at higher frequency (-3x/runc1.) whereas in Figure 18 the internal losses for the same two modes are compared. It can be seen that the anomalies at T

=

18 K - 20 K and T = 142 K - 152 K depend upon the frequency of measurement!

.

_•

--' 0

0 c

L • ., c

20

10

0 :'\ ..

0 j 50

···· ···

...

.·

100 150 200 250 300 350

T emperctvre (Kl

FIGURE II Peaks of the internal loss 1000/Qm(T) of Ni-l (#48-11).

• g 0. 250

0

•

Q. 0 u

50

.···· ··· ... ..

100 150 200 250 300 350

T emper-otur-a [K]

FIGURE 12 Compliance 1/.f. versus temperature of Ni- l (1148-Il).

} IS "

~,.._.,... ··--._ -r---r--r---r--.- -..--.~..----r--~ l

f;j 10.00 ·,·l., ~

,.: ...,

• 0 0 0

~ s. e0

•

,- ·.. ... j

... J

J

j

j

0. 00

L,__..___.._-'---'---'-'--..__-'--'-~--'----''---'-j

0 100 150 200 250 300 350

T ernpe,..oture [K)

FIGURE 13 Piezoelectric coefficient lt1li(T)! of Ni- l (#48-11).

44/[432] _J.-P. RIVERA AND H. SCHMID

2. Hl 23

J''

22

~ 2.00

..

u..

..., o

._g-.

.

·.

21 ^...

(\') I. 90

.... . I

^(\')

1-C't'l (LJ 1-C't'l

"'

>-.

\

^{20 ....}

....

1. 80 0 ^c

0 ....

0

.

19 ^Ill

a.. 0

.

^c

u 1. 70

.

u ⁰

>-.

... ...

18 ⁰

0 c

....,. . _{· •.}

_L

CD 1. 60 ....

:>

.

₀

cr

. .

₁₇ ^CD

CD

L

a;

u.. _{1. 50}

. .

^C)

"'

0

. .

16

_. . _.

1. 40

. . . . . .. .. .. _..

15

I. 30

. . . .

0 50 100 150 200 250 300 350

Temperature [K]

FIGURE 14 Low frequency (100 kHz) capacity C i1(T) of Ni-l (1148-11).

0. 19 0. 16 1-,..:..

N "'• ·

~ 0.14 '·

( :!

^{0. 12}

l; 0. 10

~

..

0. 08

r0.

^0s

10.04

u 0.02

· .. _.... :..

·.

·· . ... .

··· · ··· ··· · ··· ...

0 50 100 1 50 200 250 300 350

T empe,..otut'e U<l

FIGURE 15 Electromechanical coupling factor k~1^{(1) of} Ni-l (1148-11).

""

'"'

... ...

• 0 u u

" t:

~ u

• 0

~ 0:

0. 05

0. 04

..

..,,:·_..,._

_{. ,}

. _,

'

..

^(• .

·.

·":

·.

0 50 100

.. . .. · .. .··· . .

. . . ....

· · · ··· ...

150 200 250 300 350

T ompero<u,..e CKJ

FIGURE 16 Piezoelectric coefficient )i1t(1)) of Ni-l (1148-11).

CONCLUDING REMARKS

Having initially encountered great difficulties in measuring the piezoelectric properties of Ni-l due to strong internal losses and to the small size of crystals, a more elaborate method based on the...__

automatic plot of the admittance circle had to b<

developed in this work. One of the advantages of the method is the possibility of using tiny oscilla- tors that can be cut out from small defect-free re- gions of the crystaL To the best of our knowledge/⁰ there was so far a great paucity of piezoelectric measuring techniques for very small crystals.

The most important result of the present work appears to be the observation that the temperature of the internal loss peaks of Ni- l is shifting with frequency. Thus these peaks do not seem to be re- lated to phase transitions as believed earlier. ³1-3³

In a-quartz similar loss peaks ( 1/Qm) have been observed. ³⁴ One of the peaks (at 25 K) was attrib- uted earlier to the motion of dislocations and is now known to be due to phonon-phonon interac- tions. ³⁵ Another one (at 50 K) is caused by sodium impurities. ³⁴•36 The origin of the peaks in Ni-l has still to be clarified.

The behavior of the Joss peaks in Ni-l is cor- roborated by Faraday effect, birefringence, rota-

PIEZOELECTRIC MEASUREMENTS OF Ni-l BORACITE [433)145 TABLE I

~

~ I. 990

)...

0 0

, 0

J:

r .

I. 970

~

₀

.

_•

': I. 950 .!

L

"' 0

NiJB,OIJ[

(#48-11)

pseudo- orthorhombic

cubic

Temperature [K]

4.2 61.5"

61.5.

295.0

Jdlll""ldnl I0-12[m/V]

11.7

9.81 Jdl•l 10-12[m/v]

19.6 11.8

5. 13 5. II 5. 09 6. 07 6. 05 6. 03 6. 01 5. 99

I. 930 L...__.__.___.___..__.._~..__....__.__.___.___..__J 5. 97

0 50 100 150 200 250 300 350

T emperotvre [KJ

.-'1GURE 17 Comparison of the series resonance frequency

versus temperature of Ni-l (#48-11) for the fundamental res- onance (0) and the 3rd overtone resonance (*), showing the ,frequency dependence of the "anomalies" at 18 K and

142 K-152 K. Lines are only a guide for the eyes.

E 20

0 ....

""

""

~

•

.

0

...

0 _< ¹⁰

L

•

""' .!:

Slil 100 150 200 250 300 350 T emperoture [KJ

FIGURE 18 Frequency dependence of the peaks of internal loss (1/Q.,) at 18 K and 142 K for the fundamental resonance (0) and at 20 K and 152 K for the 3rd overtone(*). Lines are only a guide for the eyes.

•T fJ]

I Kll I .., I Knl to

10-z[mz/q kil-k~l @100[kHz]

5.86 0.161 22.62

5.56 0.132 19.93

lgul sn ^•£ Kil

10. 2[m²/C] 10-¹²[m2/N]

11.12 0.132 19.66

9.32 4.06 0.067 14.29

tion of the optical indicatrix and domain observa- tions. all of which indicate the existence of only one phase between 4 K and 61.5 K, a phase being simultaneously ferroelectric, ferromagnetic and f.erroelastic, most probably with Aizu species

43ml'Fm'.⁶

At this stage it is timely to recall once more the name of Pierre Curie. Nickel-iodine boracite is the first material in which the simultaneous occurrence of ferromagnetism and ferroelectricity was discov- ered. ⁵ As already pointed out by O'Dell/ ⁷ Pierre Curie-in his famous 1894 paper on symmetry/^8-

propbetically supposed that such kind of materials might exist:

"Les conditions de symetrie nous permettent d'imaginer qu'un corps

a

molecule dissymetdque se polarise peut-etre magnetique- ment lorsqu'on le place dans un champ electrique".

He would have been astonished to learn that such an exotic compound-being by the way also piezoelectric!- did already exist during his life- time in Paris, where H. Allaire³⁹ synthesized Ni- l boracite for the first time in 1898. Curie would probably also have been pleased to learn that piezo- electric measurements proved to be a powerful tool that finally helped to clarify a subject surrounded for many years with controversy: the tricky prob- lem of symmetry of ferroelectric/ferromagnetic/

ferroelastic nickel-iodine boracite.

ACKNOWLEDGEMENTS

The present work was initiated in 1976 by experiments at Battelle Geneva Laboratories together with Dr. David Lockwood to whom the authors wish to extend their gratitude.

Particular thanks go to Roland Boutellier, Ernest Burkhardt

. .

46/[434) J.-P. RIVERA AND H. SCHMrD

and Roger Cros for their painstaking preparation of samples and the careful construction of sample holders. M. Bostdeche of the "Department de physique nucli:aire et corpusculaire"

has kindly lent the Impedance Meter and Dr. J.-J. Combremont of the "Laboratoire de chimie thi:orique appliquee" gave in- valuable information on methods of optimalisation of functions.

The support of this work by the "Fonds National Suisse de Ia Recherche Scientifique," contracts No 2.274.0.79 and No 2.691.-{).80 is gratefully acknowledged.

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I. J. and P. Curie, Bull. Soc. Jr. Miner .• 3, 90 (1880).

2. R. J. Nelmes, J. Phys. C. Solid Stare Phys .. 7, 3840 (1974).

3. Landolt-Bornstein, New Series, Ferroelectrics: Oxides, 111/16a, pp. 261-284, pp. 597-614. Ed. K.-H. Hellwege Springer-Verlag Berlin, Heidelberg, New York 1981.

4. P. Genequand, H. Schmid, G. Pouilly et H. Tippmann, J.

de Phys., 39, 287 (1978).

5. E. Ascher, H. Rieder, H. Schmid and H. Stossel, J. Appl.

Phys., 37, 1404 (1966).

6. J.-P. Rivera and H. Schmid, IMF-5 State College PA (USA) 1981; Ferroelecrrics. 36,447 (1981).

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9. R. Holland and E. P. EerNisse, IEEE Trans. Sanies and Ul- trasonics, SU-16, 173 (1969).

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II. Standards on Piezoelectric Crystals. Proc. IRE, 37, 1378 (1949).

J 2. IRE Standards on Piezoelectric Crystals. Proc. IRE. 46, 764 (1958).

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14. ANSI/IEEE Std 177-1966 (Revised edition of the IRE Standards on Piezoelectric Crystals Proc. IRE, S1, 353 ( 1957)).

15. IEEE Standards on Piezoelectricity, IEEE Std 176-1978.

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17. W. P. Mason, Piezoelectric Crystals and Their Application to Ultrasonics, D. van Nostrand Co Toronto New York London, 1950 (out of print).

18. W. P. Mason Ed. Physical Acoustics, Vol. 1-Part A, Aca- demic Press New York 1964, (Ch. 3, Don A. Berlincourt, D. R. Curran and H. Jaffe, Piezoelectric and Piezomagnetic Materials}.

19. R. J. Nelmes and F. R. Thomley, J. Phys. C: Solid State Phys .. 9, 665 (1976).

20. R. Holland, IEEE Trans. Sanies and Ultrasonics, SU-14, 18 (1967).

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22. M. Marutake. Ferroelectrics. 10, 55 (1976). ...,.

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Inc. New York 1946 Revised Edition, Dover Publications, Inc. New York 1964 (out of print).

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Sanies and Ultrasonics. SU-11, 8 (1964).

25. J. G. Smits, IEEE Trans. Sanies and Ultrasonics, SU-23, 393 (1976).

26. J.-1. Combremont, Introduction aux methodes d'optimisa- tion de fonctions de N variables.-Private communication.

27. H. Schmid, J . .Phys. Chem. Solids. 26, 973 (1965).

28. H. Schmid and H. Tippmann, Ferroelecrrics, 20,21 (1978).

29. A. V. Kovalev and G. T. Andreeva. Fiz. Tverd Tela (Leningrad), 21, 1744 (1979) [Sov. Phys. Solid Stare, 21, 999 (1979)].

30. C. Solbrig, Z. Phys., 184, 293 (1965).

31. B. I. Al'shin and L. N. Baturov, Fiz. Tverd. Tela (Leningrad), 18, 3539 (1976) [Sov. Phys. Solid State. 18, 2062 (1976)].

32. A. F. Murray and D. J. Lockwood, J. Phys. C: Solid State Phys., 11, 4651 (1978).

33. J. Holakovsky and F. Smutny, J. Phys. C: Solid State Phys .. 11, L 61 I ( 1978).

34. G. Mossuz and J. J. Gagnepain, Cryogenics. 652 (1978). 35. J. J. Gagnepain, J. Uebersfeld, G. Goujon and P. Handel,

35th Annual Symposium on Frequency Control, Phila- delphia, USA (1981).

36. J. J. Gagnepain, private communication.

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"Oeuvres de Pierre Curie," Gauthier Villars, Paris, (1908).

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•