DIPOLAR FIELD FLUCTUATION EFFECTS ON PHONON ECHOES IN PIEZOELECTRIC POWDER

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DIPOLAR FIELD FLUCTUATION EFFECTS ON PHONON ECHOES IN PIEZOELECTRIC POWDER

S. Yoshikawa, T. Kimura

To cite this version:

S. Yoshikawa, T. Kimura. DIPOLAR FIELD FLUCTUATION EFFECTS ON PHONON ECHOES IN PIEZOELECTRIC POWDER. Journal de Physique Colloques, 1981, 42 (C6), pp.C6-873-C6-875.

�10.1051/jphyscol:19816259�. �jpa-00221347�

JOURNAL DE PHYSIQUE

Colloque C6, suppldment au n o 12, Tome 42, ddcembre 1981 page C6-873

DIPOLAR F I E L D FLUCTUATION EFFECTS ON PHONON ECHOES I N PIEZOELECTRIC POWDER

S. Yoshikawa and T . ~ i m u r a *

TechnoZogicaZ Univ. of Nagaoka, Nagaoka, Niigata, Japan

"Musashino Electrical Corn. Lab., N . T. T., Musashino, Tokyo, Japan

ABSTRACT: One-shot phonon echo i n piezoelectric powder was studied i n order t o simplify the experimental condition and c l a r i f y the basic mechanism on t h i s phenomenon. One-shot phonon echo i s observed by t h e application of the s i n g l e sequence of the incident e l e c t r i c pulses. The one-shot two-pulse echo was exp(-&). ob erved t o have relaxation c h a r a c t e r i s t i c s with the function of 1 The dynamic relaxation i s c l a r i f i e d t o originate i n the e f f e c t of t h e l o c a l f i e l d fluctuation i n a large number of the o s c i l l a t i n g piezoelectric p a r t i c l e s .

1.EXPERIMENTS.- LMb03 and LiTa03 powder with 74-88 pm center grain size was dehumidified a t 250°C, enclosed into 0 . 1 ~ a ( 1 0 - ~ T o r r ) glass tubes with a diameter 15 mm. The number of particles were about 10 7 . The echo signal measurements were made by using a transient recorder, which can sample a real time signal a t a r a t e of 8 bits/0.2 p s , and carries out the one-shot echo observation. The relation between the incident two-pulse separation and the observed two-pulse echo hight

ea

2. RESULTS. - The measured relation between 'T- and e2 is shown in Fig. 1 . This result indicates that the observed relation is expressed a s e 2 exp(-dc(: 2 ).

Coefficient d changes a s the driving frequency f changes. The relation between d and f is shown in Fig.2. Figure 2 indicates that f 2 . ^{On the}

contrary, three-pulse echo e3 characteristics a r e quite different from those f o r e 2 . The one-shot experimental results a r e shown in Fig.3. Figure 3 indicates that the decay of e3 does not depend on the driving frequency. I t also suggests that the one-shot phonon echo has long life time, a s has been observed in the ordinary experiment. F u r t h e r , the mechanism for the decay behavior in t h e one-shot two-pulse echoes originates in the quite different mechanism from that f o r e3.

3. DIPOLAR FIELD FLUCTUATION MECHANISM.- The two-pulse echo decay with the

2 2

function of exp(- d T ), where docf , suggests that t h e phonon echo in piezoelectric powder possibly has a similar mechanism to that of spin echo 1 .

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19816259

C6-874 JOURNAL DE PHYSIQUE

In the present study, a dipolar field fluctuation mechanism is assumed and developed on the basis of the torque rotation2 and the dipolar field models. 3

For the particle with resonant frequency fi ,the angle 0 between the incident pulse field and the induced dipolar orientation is given by the following dynamic equation 3 .

9 ⁺

r6 -

=

4

e e i s the initial orientation. It is considered that the second force is small because ,through the one-shot experiment within the interval in the order of

T

ee

is divided into two components,

of

^so.

so

ef

are assumed to be independent from time. The fluctuating effect also induces the fluctuation 66 on the angular moment. This process is a Markoff process. The conditional probability density is given by ⁴

where C is the coefficient,and W is the noise power. From fluctuation for the angular moment , the expected dipolar field strength is derived as follows.

x other term dependent on and go . (3)

If 1/IWLT

>>

Therefore, coefficient 0 ( , observed in the present experiment, can be defined to be O( = 1/IWr . This theoretical result further explains the dependence of d on driving frequency f . The relevant moment of inertia I is given by I -= ^f d2, where P is the averaged grain density and d is the diameter. The piezoelectric resonant condition has been observed to be f

-

In summary, it is concluded that a large number of dipoles, which a r e caused by induced piezoelectric oscillation, should be considered in the light of dipolar field fluctuation. The effect like this short time fluctuation mechanism is further expected to explain the real compLicated phenomena on phonon echoes in piezoelectric powder.

1. P.Hu and S. R.Hartmann, Phys. Rev.

E ,

2. R.L.Melcher and N . S . Shiren, Phys. Rev. L e t t . , 36, 888 (1976) 3. T.Kimura and S.Yoshikawa, J . Appl. P h y s . , 51, 2817 (1980) 4. T.K.Caughey, J. of Acoust. Soc. of Amer., 2 , 1683 (1963) 5 . N.S.Shiren and R.L.Melcher, 1975 IEEE Proc.SU Symp., 572 (1975)

t I I 1 1

- .

T' ( p a 1 DRIVING FRMUENCY ( w z )

Fig.1 Relation between one-shot two-pulse Fig.2 Relaxation coefficient

echo e2 and pulse separation

T .

6

t.2 ^{* 4}

0 :P

o s * a x ~ , x 0 Ooo e0',3'

.5

'F'

lo 100 nnnl

I E A O C M T I M ( )IS

Fig. 3 . One-shot three-pulse echo relaxation