Determination of the elastic properties of ceramic A1:Yig systems by ultrasonic techniques

Materials Chemistry and Physics, 23 (1989) 464-472

464

ON OF -ELASTIC AI:YIG

SYSTEMS

BY ULTRASONIC

PR-

OF Cw

TECHNIQUES

G. SOCINO Dipartimento di Fisica, Universitl di Perugia(Italy) N. SPARVIERI Selenia Direzione Ricerche, Via Tiburtina km 12.4, Rome (Italy) F. TREQUATTRINI,

E. VERONA

CNR, Istituto di Acustica, Via Cazsia, 1216 - I-00189 Rome (Italy).

ABSTRACT The elastic properties of polycrystalline garnets have been analyzed by means of an acoustic investigation technique. The method relies on measurement of the phase velocity of both the Lamb and Love modes propagating along a sample having the shape of a plate. Because of the structure of the acoustic modes, each consisting of a different combination of longitudinal and shear partial waves, the information obtained permits in evaluation of the elastic constants of the material. Measurements performed on a ceramic YlG plate , enabled us to determine the two independent constants cl1 and cI1 of the material. An analysis of ceramic garnets with different percentages of Al’+ ions in the tetrahedral sites of Fe in the basic structure of YlG, has shown a strong dependence of the elastic constants on the concentration of the substitutional ions.

INTRODUCTION A large amount of work has been done in recent years on the technology of production and on the investigation of physical properties of magnetic garnets for microwave applications. The importance of these materials lies on their magnetic properties and low electrical conductivity which allow electromagnetic wavea to propagate in the medium with characteristics which depend on its magnetization state. As thii can be varied by means of an external bias magnetic field, magnetic garnets are suitable for applications to microwave devices such as tunable delay lines, phasers, magnetic’ field sensors and nonreciprocal devices [l-6]. 0254-0584/89/%3.50

0 Elsevier Sequoia/Printed

in The Netherlands

465 The magnetic properties of these garnets can be widely changed because of their capacity to selectively incorporat,e a large numher of ions in crystal

sites which

depend

on the

radius of the substitutional ions. This paper presents the results of an investigation of the elastic properties of ceramic Ys Al. Fes-. Oi2 for different concentrations of AIS+ ions. The mechanical properties of these ceramic materials differ from those of the single crystal and can be highly affected by the process of their production,so that a direct characterization of these materials is of great importance.

The experimental method used for determining the

elastic constants relies on measurement of the phase velocity of acoustic modes propagating along the sample under investigation. Both Lamb and Love modes were analyzed in order to determine the two independent elastic constants ~11, and 1244.The experimental results show a strong dependence of these constants on the concentration of substitutional A13+ ions. MAGNETOELASTIC

WAVES

IN THIN

PLATES

The structure under investigation consists of an elastically isotropic ferrimagnetic plate of thickness h, magnetized beyond its saturation magnetization x

by a uniform bias magnetic

field z?, parallel to the surface of the plate. A rectangular Cartesian coordinate system (zyz) is chosen, with the z-axis along the magnetic field direction and the y-axis along the normal to the faces of the plate. Because of the magnetoelastic coupling , the characteristics of the acoustic modes propagating along the plate are affected by the presence of the magnetic field and depend on the relative direction between the field itself and the acoustic wavevector p. We assume that the acoustic frequencies of interest lie in the low megahertz range, so that exchange-free conditions are satisfied and, moreover, the quasistatic approximation can

I-

CERAMIC

YIG PLATE

I, Fig. 1. Schematic of the magnetoelastic structure under investigation.

466

apply.

With these approximations,

and Maxwell equations,

the complete

for a small dynamic

set of coupled

particle

spin motion

motion,

on a large static bias magnetic

field superposed

field is given by [7-lo]: PC

= CII(%~S + %,yz + UW) + c~~(%yy + u.,.. - uy,yz - u,,,,)

pii,

=

Cd%”

+

%/,yy +

%#.Y)

+

C44(%,z.

+

uy,rr

-

uz,sy

-

uz,xy ) +

2Mb44my,x

pii,

=

C11(%,1

+

%/d/z +

l+)

+

c44(uz,.z

+

%,yy

-

u.,..

-

uy,y. ) +

2Mb44(m.,.

- Mb,,,

+ 2M,b44m.,,

-

M,4.ur

+ mvJ) + (1)

-MdP,ZZ -k/r

= Km,

-%/7

= -%m,

- 2K%4(uz,.

-4r(m,#,

+ my,“) + 47~M,(u.,,,

+ +,,

in the differential

equations

V24

f 2Mzb44(uy,, + Q)

The six variables vector

8, the two transverse

constants

and the gyromagnetic a derivative

We consider

1 are the components

of the dynamic

ratio of the material,

with respect

magnetoelastic

x-axis.

Each mode consists,

waves.

This number

of symmetry

+ u,,,~) = 0

the elastic

respectively.

to the corresponding

modes that propagate

system

xi shown

xs-axis

along the normal

vector

spatial

eqns.

in Fig. 1, with the xl-axis

1.

by a

along the plate at an angle 0 from the

On referring

along the acoustic

to the plate , the particle

followed

coordinate.

in the more general case, of a linear combination

in the coupled

Ri and the

and magnetostrictive

A comma

is lower when some of the partial waves uncouple

conditions

of the displacement

magnetization

4. p, cij, b,, and 7 are the mass density,

potential

denotes

+ u,,,) - i&P,

components

magnetic

letter

+ M.4,”

of twelve partial

from the others because

to the laboratory propagation

displacement

coordinate

direction

components

and the

can be written

in the form: ui = cA,a!P)

,

exp ipb(P)zs exp i(&

- wt)

(2)

p=l

where

p is the acoustic

normal

to the plate

wavenumber

of the mode,

of the p’th partial

are given by A, and c$‘), respectively. quantities

associated

differential

equations

free surfaces ber component coupling

with

the acoustic

/3b(p) the propagation

wave, whose amplitude Similar field.

1 and the mechanical

expressions These

and mechanical

can be written

acoustic

and electromagnetic

modes

is fairly strong

the transverse

at the crossover

resonance

conditions.

points of the dispersion

must

boundary

of the plate [8] . Thii implies that the modea are dispersive /lb(p) must satisfy

constant

along the polarization

for the magnetic satisfy conditions

both

the

at the

since the wavenumThe magnetoelastic

curvea, where the uncoupled

467

spin and elastic

waves have the same frequency

away from the crossover predominant

elastic

ELASTIC

or magnetic

CONSTANTS

The elastic frequencies

where

the acoustic

garnets

modes

have been studied

are almost

can be considered

exclusively

plane (zizs)

together.

purely elastic and isotropic.

and consist of two longitudinal

The dispersion

by operating

elastic.Under

along the plate : Lamb and Love modes

modes can propagate

expressed

waves are still coupled

far

but with a

character.

of ceramic

medium

in the sagittal

and magnetic

[g-12]. For frequencies

EVALUATION

properties

the propagation

coupled

values, the acoustic

and wavenumber

relations

u(h/X),

in a range of

these

conditions,

Two types of acoustic

[13]. Lamb modes are polarized

and two shear vertical

depending

on both

partial

waves

cl1 and ~44, can be

in the form:

(3) where the plus or minus sign of or antisymmetric

modes,

of two shear horizontal ~44 by the dispersion

c44

respectively. partial

on the right hand side of eqn. 3 refers to symmetric

Love modes,

waves.

polarized

Their phase velocity

along the zz direction, is related

to the elastic

consist constant

relations: 1

( >

1

P

-=-

the exponent

1+_

2;

v’

with n = 0 91 , 2 >**Equation putation

4 can be solved analytically

technique.

The dispersion

along an undoped

YIG ceramic

using the effective

elastic constants

of the phase velocity iterative

computation

elastic constants

technique,

curves

plate,

of a number

relative

are shown

of the ceramic of acoustic exploiting

are those which minimize

from the theoretical

while eqn. 3 requires

the use of a numerical

to Love and Lamb

modes

com-

propagating

in Fig. 2. These curves were calculated garnet

modes.

as determined

The procedure

the linear regression the standard

deviation

by

from measurements

followed

method.

is based on an

The values of the

of the experimental

values

ones.

RESULTS The material trations

under

investigation

of AIS+ substitutional

ions:

is ceramic

yttrium

iron garnet

YsA~~Fc~-~O~~. Its preparation

with

different

followed

concen-

the standard

468

6000

1

(h/l)

(a)

Fig.

(b)

2. Dispersion curves for (a) Lamb and (b) Love modes propagating along an undoped

YIG ceramic plate.

I

WEIGHT STARTING MATERIALS

I

I

I

(Y20s,Fe203,A1203) 1

WET

MIX I

I

DRY AND GRANULATE

I

ATOMIZER

PRESINTER (lOOO°C 1 hour)

I

SIEVE

I

1

BINDER (polyvinyl alchool or acrylic resin)

WET MILL I I

DRY ANJJ GRANULATE

ATOMIZER

SIEVE

1 PRESS (1000 Kg/cm21 1 EVAPORATE I

BINDER I

I (02 flow

SINTER 1200-1400°C

PHYSICAL

1 CHARACTERIZATION

I Fig.

I MECHANICAL

FINISH

10 h)

MAGNETIZATION DIELgCTRIC LOSS MAGNETIC LOSS HYSTERESIS LOOP DENSITY 1

3. Schematic diagram of the procedure followed for preparing the ceramic garnets.

469

ceramic

technology

investigated, plates,

as schematized

corresponding

1 mm thick,

generated

to z = 0,0.4,0.8

with the two surfaces

and detected

tolithographic

by means

techniques.

in generating

and detecting

field is parallel

generated (v,h/X)

and detected.

having

velocity

The corresponding

The

propagation

the dispersion

by standard

pho-

periodicity

transducers

provided

that

direction,

are effective

the bias magnetic

respectively

(see Fig. 4)

of the transducer

can be

is given by the intersection vertical

The relation

in the

line at a value

between

the phase

f of the mode is given by: u = Xf.

two independent

~44. They are related

waves were

with a spatial

curve and a straight conditions.

as thin

24 mm apart were implemented

X equal to the period phase velocity

Acoustic

configured

of 11 meanders

and Love waves,

a wavelength

were shaped

and well finished.

delay line. Meanderline

to the specific experimental

and frequency

The specimens

Two transducers,

to the acoustic

plane of Fig. 2, between

(h/X) corresponding

Lamb

of A13+ ions were

concentrations

transducers,

consist

an acoustic

both

or orthogonal

(14,151. All the modes

of meanderline

length of 4mm.

so to configure

and 1.1. parallel

The transducers

X=0.6 mm and an electrode on each sample,

in Fig. 3. Four different

elastic

constants

to the wavelength

of the material

and velocity

to be determined,

of the acoustic

are

cl1

modes, by the dispersion

relations given in eqns. 3 and 4. The mass density p, which also enters into these equations, measured almost

by means

of a pycnometer.

Its value p = (5.08 f 0.02)10sKg/ms

of the Al’+ concentration

independent

ii

within

BIAS MAGNETIC FIELD

0

the experimental

/

and

turned

error.

was

out to be

Measurements

II0

TRANSDUCERS

'CERAMIC

YIG

SUBSTRATES/

(al Fig. 4 Schematic waves.

(b) of the acoustic

delay lines used for investigating

(a) Love and (b) Lamb

470

Table I. Elastic constants cl1 and c4 of the four samples analyzed with different concentrations of substitutions

AI’+ ions.

ceramic

material

elastic

constants

(10”

N/m*)

c11

c44

Y3Fe5012

1.486

0.738

Y3A10.4Fe4.6012

1.492

0.798

Y3A10.8Fe4.2012

1.513

0.825

Y3A11.1Fe3.9012

1.549

0.863

of the frequency

of the acoustic modes were performed by means of an HP 8753A network

analyzer.

Love modes were analyzed

frequency

corresponding

experimental

at firzt, in order to evaluate the cd4 constant.

to the fnzt three modes was measured

The

for each sample, and the

data processed according to the procedure outlined in the previous section, in

order to minimize the experimental

error.

A symilar analysis, performed on the first three

Lamb modes, allowed uz the evaluation of the cli constant.

The measured elastic constants err

and cM of the four samples analyzed arc reported in Table I. The values relative to undoped YIG ceramic are in a fairly good agreement with thoze calculated by the single crystal constants [ 16) on using the procedure outlined in [ 171 (c,, = 1.61, cM = 0.79). elastic stiffnezz verzuz per cent substitutionz

5.6% and 16.5% waz observed for the cl1 and ~44 constants,

1.50

,/-

/--*

0-’

iz seen. An increase of about respectively,

between undoped

2

.’ 1.45

17

10 A13*substitutionz

0

20

f%)

of the

of AISi in Fe can be zeen in Fig. 5. An almost

lineax increase of both the constants with Als+ concentration

1.55

The behaviour

0

10

A13+substitutiona

20

f%)

Fig. 5. Elastic constants cl1 and cd4 of Y~Al~Fe~_+01~ versus AIS+ concentration.

471

and 22% Al’+ doped the process

YIG. In order

of production

of the ceramic,

having the same concentration turned

to evaluate

measurements

of substitutional

out to differ by amounts

the dependence

of the these

were performed

constants

on different

on

samples

A13+ ions. The values of the elastic constants

not larger than 2.5%.

CONCLUSIONS In summary, constants velocity

an ultrasonic

of ceramic of a number

plate.

Measurements

of substitutional turned

garnets.

is bound increase

has been exploited

The experimental

of acoustic

method

modes propagating

were performed

for the evaluation

of the elastic

relies on measurement

of the phase

along a sample having the shape of a thin

on ceramic

Al:YIG systems,

Alat ions. The two independent

elastic constants

out to be strongly

linear increase

technique

of both

dependent

of the lattice

force and, consequently,

was observed.

with Al’+ concentration,

parameter

a stiffening

concentrations

~11 and ~44 of the material

of substitutional

with Alst substitutions

the constants

to the decrease of the cohesive

on the concentration

for different

ions. An almost This behaviour that

implies

an

of the material.

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B. Lax and K. J. Button, Microwave ferrites and ferrimagnetics,

2 F.F.Y.Wang rication 3

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