CHAPTER-3

EXPERIMENTAL TECHNIQUES.

CHAPTER-3

EXPERIMENTAL TECHNIQUES

3.1 Introduction

The first step in the preparation technique is to optimize the condition

required for preparation of material of desired composition, shape,

mechanical strength etc. The characteristics of the material are then

evaluated to ascertain its scientific and technological importance. The

establishment of physical and chemical characteristics and assessment of the

effect of constituents of the material on its properties is called

characterization. According to the United States Academy of Sciences and

National Academy of Engineering Committee of the Material Advising Board

the characterization is defined as "Characterization describes those features

of the composition and structure (including defects) of a material that are

significant for particular preparation and study of properties or use of and I or

suffice for the reproduction of the material".

In the present investigations on modified lead titanate ceramics

prepared by solid state method, the different characterization probes include

optical and scanning electron microscopy for microstructure analysis, X-ray

diffraction and microindentation for mechanical studies. Apart from this

dielectric, ferroelectric and piezoelectric studies were carried out, using

automated impedance analyzer, Hysterisis curve set-up, Birlincourt meter etc.

The various experimental techniques and instruments used are briefly

described in this chapter.

75

:1 -; Optical and scanning oloctron microscopy

,•, ' '' r·· . ' i' ~ \ ,) I I I i ! ' ! •, I \ ·: '(' •, o :

... ;1! Ull.dlllJil,t!IUI' ,,,II ltJrJ,Ift!flf•',', l!lt',l',tOft'fllt•!l!', t 1f {tit'

· • ~- ~-. 11 ~ !.!.1•·.ah• ( ni.IIIIU •1 w••rt• t .11111•d oul IJ'.IfHj fllll f() lrlth·n!.lflt!fl

3 2 1 lncidont light microscope (EPIGNOST)

I /11· flllt ftJ',r tiJlt' < .allt~d I pUJfiO',I ·,hown 111 l1q :~ l 1', dt",HIIH'd lor r.qlld

._, ... • .t!Hifl ,,, p<J!J·,/wd / n.!lur.tl ~-LHf.tu!:~ of Uw nl.llt•r~.tl:, II,., .111 IIH 1dc•rll

;' ~ !,t"' 1111( f()',( IJfH' Wtlh tfl;I)WIIlJ/Illll.ICjtllll< .t!Hlfl ,,, /H'JX (lilly I!•, tlhjt'( IIVt'

! .. t· •• 111 Hlflflllt· nll!'l',t•clronal dr~ol;mc:o, r n. Uu• spt~CHTH'rl lu•s 111 t/11~ front foc;1l

;• ,.,,.. "' l111• ni>J"c!rvo <111<! !110 llll<i<JO r:, lornll!d dl 11111111ly A liV l!>W lrldltl<!ltl

'.""I' .11 .\', '"' " litjhl sourcn wl1osn beam passes \ltrOli<Jtt Hw coHec\or ;111<1

1.111·, '"' ,,u,,, a 1>rrut1l fteld or a dark fteld adapter. It lt<ts a permanen\ly buill­

"' \trill' l<!ns wlt1clt 111 combination with eyepiece forms a telescope Th1s

1111provt!s tile total magnification by a factor of 0.63

Tile Epignost microscope can be used for the photography purposes,

. u~""J er\her the plate attachment or the combination of plate attachment and

:l~i mm camera.

3.2.2 Large Incident- light microscope NEOPHOT -2

Neophot-2 shown in fig. 3.2 is Carl-Zeiss Germany made inverted

metallurgical microscope designed according to Le-Chataliers Principle,

where the specimen to be examined is placed above the objective lens. The

magnifrcation factor of the microscope varies from 1 OX to 2000X, which is

attained by built-in integral magnification variators using different objectives. It

IS fitted w'rth two light sources of 12V 100W Halogen Lamp and d.c. operated

XBO 101 Xenon lamp. The former is employed for subjective observation and

76

ur IJrJ\)Ilt·fleld photomacrography and the latter for dark field and polarized-

1\Jht work as well as for photomicrography and projection. Filters for

1tlenuilt1on or spectral modifications are provided.

Rapid interchange of objectives is possible by simply pressing a lever

31ld the specimen stage gets lifted which facilitates change of the objective. A

retard mechanism slows down the lowering of specimen stage after which the

obJect gets again in focus and is sharply depicted by merely operating the

fine-adjustment knobs. Monocular or binocular observation with eye piece PK

12.5X always guarantees an apparent diameter of the image field of 200mm.

A turning control knob operates the magnification variater containing steps of

SX, 1 OX, 12.5X, 16X and 20X. All objects employed are of plane- field type

and are parfocalised hence there is no need to operate coarse motion knobs

after havmg changed objectives. The neophot-2 is equipped with a big size

13cm x 18cm plate attachment and 35mm camera for recording the

photographs of the specimen under analysis.

Apart from incident light observation in bright and dark fields, phase

contrast, polarization, measuring and counting, interference , microhardness

testing and test strip comparison can also be carried out with Neophot-2.

3.2.3 Scanning Electron Microscopy (SEM}

Scanning electron microscopy (SEM) provides a much higher

resolution more than 100A0 and magnification over optical microscopy. In the

present work scanning electron microscopy was utilized for analysis of grain

size. This technique reveals the individual crystals and grain boundaries of

polycrystalline materials.

When an electron beam is made incident on the surface of a solid,

various signals are generated by interaction of the solid with electron beam

VIZ., secondary and Auger electrons, back-scattered electrons. X-ray

fluorescence and other photons at different energies. The scanning electron

77

:n1c1oscopy mostly use back scattered and secondary electrons for analysis,

F1~ 3 3 depicts a schematic diagram of a scanning electron microscope. The

llkllll components of a scanning electron microscope are electron source,

electron optics, sample holder, electron detectors and display. An electron

CJUn consisting of a heated tungsten filament is used to produce electron

IJe<JITl. High potential of 1 to 50kV is used to converge the emitted electrons in

a tiny spot called 'cross over'. The scanning of electron beam on the sample

is accomplished by applying the electrical signals to sets of deflecting coils, X­

deflecting coils and Y-deflecting coils. By varying the electrical signal whose

amplitude varies linearly with time, the electron beam is moved in a straight

line across the sample and then returned to original positions. The beam is

deflected slightly in another direction (Y-direction) and scan in X-direction is

repeated. Thus, by moving the beam rapidly, the entire surface of the sample

can be irradiated with an electron beam. The detectors collect the secondary

and scattered electrons emitted from the sample surface. The image of the

sample is provided from the output of the electron on the screen of CRT

(Cathode ray tube). In scanning electron microscopes, mostly scintillation

detectors are used. The sample chamber is evacuated using oil rotatory

pump to maintain vacuum of the order of 1 o-3 Torr.

Samples which conduct electricity are easy to study. A variety of

techniques have been developed for obtaining SEM images of non­

conducting samples, but most common approach involves coating of the

surface of the sample with a thin metallic film (-500 A0) usually of gold using

sputtering or vacuum coating technique. In the present investigation, SEM

studies for grain size evaluation were carried out using JEOL JSM-80

Scanning Electron Microscope. The sample with a thin layer of gold sputter

coating on its surface was mounted on a copper stub using silver conducting

adhesive paint. The silver paste makes the surface on which the electron

beam impinges conducting to prevent accumulation of charge on it The

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;~tures of 1nterest are recorded on a photographic f1lm, using the camera

t<1ct1ment provided with the SEM .

. 3 X-ray diffraction (XRD)

Following the Roentgen's discovery of X-rays in 1985, Laue noted in

912 that these X-rays were believed to have wave lengths of the order of

0 8 em and that the crystals were believed to consist of periodic array of

toms with similar dimensions. Therefore, he concluded that crystals could

erve as grating for the diffraction of X-rays. The diffraction pattern obtained

·om the crystals depends upon shape and size of the unit cell of the

rystalline material.

The X-ray diffraction is one of the oldest of the non-destructive method

>f analysis of crystalline materials in all branches of science. Because of the

miqueness of the X-ray diffraction pattern of each crystalline material, the X­

ay diffraction provides a convenient and practical means for the quantitative

dentification of crystalline compounds. X-ray diffraction data can also be used

o quantitatively determine the domain structure etc., of the polycrystalline

naterials. The identification of the species from its diffraction pattern is based

)n the angular position of the times and their relative intensity. The diffraction

3ngle 28 is determined by the spacing between a particular set of planes and

.vith the aid of Bragg's equation

2dsin8= nA. (3.1)

and 'd' is calculated from wave length (A.) of source and measured angle.

The powder diffraction pattern can be recorded in two ways, one using

film and second by using electronic counting technique. In these methods, 28

angle and the relative intensity of each diffracted beam from the sample is

measured. The intensity of the radiation diffracted from the specimen is

monitored by using a Geiger-Miller counter or a similar counter with the

appropriately interfaced computer I bar chart recorder etc.

79

In the present investigations, Philips Analytical X-ray diffractometer

PW3710 based) was used in which the specimen is mounted in the centre of

he diffractometer and the X-rays get generated by Cuku radiation

) "1.54056A0 ). The counter is attached to the arm rotating around the same

ax1s by an angle of 20, which is twice the angle of sample rotation. The

diffraction patterns of the polycrystalline modified lead titanate ceramic disks

::Jf 1.5mm thickness -12mm diameter were studied. In polycrystalline

materials enormous number of small crystallites are oriented in every possible

direction, thus when an X-ray beam is traversed over the materials, significant

number of crystallites are expected to be having such orientations so as to

fulfil the Bragg's condition for reflection from every possible inter-planar

spacing.

In 1945 the American Society for Testing Materials began publishing

all known powder diffraction patterns in a file known as ASTM file. This

continued on till 1969 and thereafter the task was assigned to Joint

Committee on Powder Diffraction Standards. The data maintained by the

latter is known as I CPOS powder file. The data is used for identification of a

known material.

3.4 Impedance analyzer

The charge cannot flow freely in the insulators. However, if the

insulators are subjected to high electrical field, the internal electric field of

the insulator gives rise to lattice deformation and internal distortion which can

be studied in detail by knowledge of the dielectric behaviour of the insulator.

The Hewlett Packard model 4192A LF Impedance Analyzer (fig 3.4) is a fully

automatic, high performance test I measurement instrument designed to

measure wide range of impedance parameters as well as gain, phase angle

and group delay. The 4192A improves the efficiency and quality in the

development and production of many type of complex components.

80

semiconductors and other materials. Complete network analysis of devices

SiJCil as filters, crystals plus evaluation of the impedance characteristic of their

wcu1t components, can be performed. The two measurement display

scct1ons Display A and Display B, provide direct readout of the selected

measurement parameters with 4 Y, digit resolution along with appropriate

units. The speed of measurements depends on mode of measurements

selected viz, NORMAL, AVERAGE and HIGH SPEED. In normal mode

operation the instrument performs approximately five measurements per

second. The average mode is provided (one measurement per second) to

obtain data of higher resolution and repeatability than is poss'1ble in NORMAL

mode and HIGH-SPEED measurement mode perform approximately 10

measurements per second.

The 4192A Impedance Analyzer can provide measuring frequency,

oscillator level and d.c. bias voltage (impedance measurements only)

equivalent to actual operating conditions. The sweep capability of the built-in

frequency synthesizer and d.c. bias source permits quick and accurate

measurements. In impedance measurements, the 4192A Impedance

Analyzer can measure eleven impedance parameters with a basic accuracy

of 0.1% and 4 Y, digit display. The microprocessor base design of the

hardware design makes the operation of 4192A Impedance Analyzer simple,

yet improves the performance to realize the accurate measuring capabilities.

Desired parameters are fully programmable through front panel keys or via

HP-IB control, a standard capability of the 4192A Impedance Analyzer. The

self test function augments the high reliability design of 4192A Impedance

Analyzer. Convenient introspective testing is possible by pressing the SELF­

TEST key and confirms the functional operation of the instrument. The zero

offset adjustment function measures the residual impedance and stray

admittance inherent in the fixtures used, offsets the effects of these parasitic

parameter to zero with respect to measured values. The save 1 recall

functions can store five completely different front-panel settings, including

Rl

p<lfcHncter selection and sweep controls and recall them at any time (RECALL

key) Th1s feature can also be made to measure the same parameter on one

component under (five) different sets of test conditions. The standard memory

of the 4192A Impedance Analyzer preserves the stored data even when the

mstrument is off.

The impedance analyzer 4192A can measure all impedance

/gain/phase/transmission parameters at room temperature only. In order to

further automize the working of the Impedance Analyzer for measurements of

dielectric parameters at temperatures exceeding the room temperature, a set­

up based on 4192A Impedance Analyzer was designed , fabricated and

assembled. The setup is discussed in detail in the next chapter

3.5 Hysterisis curve set up

The most commonly accepted criterion of ferroelectricity is a hysterisis

loop on a P-E display. This is usually done using Sawyer and Tower circuits.

Briefly, the method consists of applying an alternating voltage and relating the

stored charge to the instantaneous voltage. The schematic diagram of the

Sawyer and Tower Circuit in its modified form is shown in figure 3.5(a). A

220V 50Hz variac is used to feed step-up transformer (1:10) to produce high

voltage of the order few kilo volts at the output of step-up transformer. The

high voltage capacitor filters out the harmonics and series resistance 1 OkQ

1 OW prevents damages due to short circuit.

The voltage divider in the circuit prevents the excessive voltage

applied to a horizontal input of cathode ray oscilloscope which prevents it

against damages. The capacitor C can be changed with the selection switch

to match the different thickness dielectric constant of different samples. The

hysteresis arises from energy needed to reverse the metastable dipoles

during each excursion of the field. The area of the loop represents the energy

82

11;1t 1S dissipated within the sample as heat. For this reason, the expenment is

Jsu;JIIy run at low frequencies, such as 50Hz or less

Typical hysterisis loop of a ferroelectric material is shown in figure

3.5(b). Spontaneous polarization Ps is given by Ps = (C.Vys) /A. Vys is the

1ntercept of straight line portion of the hysteresis loop, A is area of sample, C

1s series capacitance selected by the selector switch. The coercive field,

which is the applied negative field necessary to reduce the polarization to

zero is given by

Ec = (Vx/d) .(1+R2/R1), where Vx is horizontal intercept of the hysteresis loop,

d is the thickness of the sample and R1 and R2 are resistances which perform

as potential division.

The modern hysterisis measurement set-up are provided with analog

to digital converters which convert the analog vertical and horizontal signals

into digital for direct recording, displaying and analysis of P-E loops by

computer, thus eliminating the use of CRO's.

3.6 Berlincourt meter

It is used to measure the piezoelectric coefficients ( d33, d31) of a

piezoelectric material. It is the ratio of short-circuit electric charge developed

per unit area of electrode to the mechanical stress applied to the

piezoelectric element First subscript refers to the electrical direction (Electric

field or dielectric displacement) and the second refers to the mechanical

direction (stress or strain).

In the present studies Berlincourt meter manufactured by TAKE

CONTROL SYSTEMS, U.K was used. Schematic diagram of the Berlincourt

meter is shown in figure 3.6. The sample whose d33 is to be measured is

inserted between the upper and lower probe of the d33 meter and finite

pressure is applied on the sample by screw adjustment of the upper probe

and the d33 value in pC/N is directly read on the electronic unit d33 = CV/F.

83

'iler(' c rs capac1tance. V 1s voltage and F IS force. The shunt capacitance

onnecteu in parallel w1th the test spec1men should be at least 10 to 100

mes larger than the capacitance of test sample. Piezoelectric charge

·eveloped 1s collected on the shunt capacitance. This is converted to voltage

~ading usmg tube electrometer (0.1 to 10 V range) to give d33 directly.

t 7 Microindentation technique

The hardness of material can determined by using a variety of

echniques viz, indentation test, scratch plough test, rebound test, damping

est, cutting test, abrasion test etc. All these methods are associated with the

neasure of resistance to plastic deformation. Indentation induced hardness is

Jf two types i.e, macro indentation, where the testing load normally exceeds

5kgs (50N) and micro indentation hardness were the load range is generally

rom 1 Og to 5Kg (0.1 N to 50N). In this work, micro hardness studies are

·estricted to widely used Vickers's diamond pyramid indentation induced test

Jnly. For this purpose, Vickers microhardness tester mph-1 00 attached with

.he metallurgical microscope Neophol-2 is used and is described as under:

3. 7.1 Microhardness tester- mph-1 00

Design of mph-100 microhardness tester is shown in figure 3.7. The

diamond pyramid is in the shape of usual square-based Vicker's pyramid of a

slope angle p=22° The rest of diamond is shaped as short rod(1) of such a

small diameter that it can be mounted in the central bore of the front lens. A

sufficiently large angular portion of the front lens (2) is free for illumination and

imaging. The hardness tester is provided with an optical device for indicating

the test load. The objective is not so strongly attached with the instrument but

freely suspended from two disk springs (3) allowing the objective to move

parallel to the optical axis without friction. Any test load acting on the diamond

causes the suspension to deflect; the lift represents the measure of the test

load. The motion of the Llft is measured by second optical system. the

84

auxi11ary object1ve (6) which 1s attached to the rear element of the objective

(4) The auxiliary objective is equipped with a reflecting mirror (5) which

Illuminates the scale (12) and forms image of scale in the eye piece. The

auxiliary objective is rigidly attached to the main objective hence, move

together, while as the scale is stationary within the housing. Hence the action

of test load is read in the eyepiece as the motion of image of the scale. The

deflection of the load indicating scale can be calibrated so as to determine

and measure the effective test load precisely.

The rotation of lower rings (8) together with nutt (1 0) raises or Jowers

the scale holder thus adjusting the zero position of the scale. The upper ring

(7) connected to the eccentric ring (11) provides transverse motion of the

scale and objective and sharp focusing of the scale image. The space

between the rings is loosely filled with un-spun rayon to provide effective

damping of the trouble some vibrations. The bottom of instrument is made

dust proof by sealing with correction lens (9). Magnification factor of the mph-

100 is 32.

3.7.2 Eyepiece micrometer

The eyepiece micrometer (fig 3.8) resembles the standard screw

micrometer in design. It has two reticles, one stationary and one sliding. Each

of the reticles has right angled ruled on it. The displaced reticle has a dashed

line with the aid of which the diagonal length is measured. The angle on the

fixed reticle serves for marking the spot where point of the pyramid penetrates

the test piece. By displacing the movable angle, one of the two corners

forming thereby, is used as an indication for zero setting of the load indicating

scale.

3.7.3 Operation of microhardness tester

The objective of the Neophot -2 is replaced by microhardness tester

(mhp-1 00) by lifting the stage. The eyepiece micrometer with micrometer

85

rum <~I so Inserted in the eye piece tube is clamped in correct position· The

><lei HHl1cat1ng scale now becomes visible in the eyepiece on turning on the

l1illlii1<lllon light

The specimen is placed on the stage. The area to be tested is brought

1nder the fixed angular mark. The index mark of the eyepiece is then set to

he zero line of the load indicating scale. Load is now applied by continuously

Jwering the specimen stage until the scale reading corresponds to the

Jesired load. The load is removed by slowly raising the stage after few

;econds, until the zero line of the scale again returns to its index mark. For

Jccurate measurements of the indented impression, the microhardness tester

s replaced by another suitable objective. The micrometer drum is turned to

xing the straight line used for the measurement to the ends of the diagonal

3nd two settings are noted. The difference of the two readings indicates the

;ize of the impression in drum divisions and converted to size in micrometers

oy multiplication of the relevant scale factor. It is advisable to repeat the

measurements using several indentations by the same load to reduce error.

3.8 Hydraulic press

Shaping of ceramics used for making ceramic devices is generally

identical to the shaping methods used in other branches of ceramic industry.

The commonly used shaping method include, dry-pressing, isolate pressing,

extrusion, casting etc. The powder material is pressed in a die of desired

shape by applying high pressure (75- 300Mpa).

In the present studies a hydraulic press shown in figure 3.9 was used

to apply high pressure. It has a top punch which can be moved vertically up

and down vertically by screw rotation. Vertically under the top punch is a

piston which is moved up by hydraulic mechanism. The material to be

pressed /shaped is kept in a die (fig 3.1 0) with moving top and bottom

punches on the piston of the press and the top punch is lowered by screw

86

trun clo~e to top punch of the die. The piston is raised to apply high

essure by pumping the oil into the cylinder till the desired pressure indicated

' the pressure gauge is reached. The pressure is released by opening the

lease nut. Usually, organic binders are incorporated into the powered

1atenal The binder gives dry shape a sufficient strength to survive the

andling between shaping and sintering. One of the most important

;quirements of the binder is that it should be possible to eliminate it from the

ompact shape without any disruptive effect.

L9 Measurement of piezoelectric and electro­mechanical coefficients

~.9.1 Resonance method

Simple measurement of resonant and antiresonant frequencies is used

to evaluate piezoelectric effects. Elastic bodies show numerous resonance;

the most pronounced are those where the body can accommodate one half

wavelength of a wave. The piezoelectric effect is a convenient way to excite

such elastic wave to permit observation of the interaction of the mechanical

resonance with the electric behaviour. This is best seen in the electric circuit

idealized for a single resonance (fig.3.11 a). The values of L and C1 are such

that at resonance frequency f, the impedances 2nfrL1 and - 1 /(2nfrC1) are

opposite in sign and equal in magnitude and total impedance of the branch is

given only by the mechanical resistance R, which is comparatively quite

small. This mechanical branch is, however, in parallel with electric

capacitance C0 . The frequency of minimum impedance of resonance, f, is that

of the standing wave under zero field condition. For applied frequencies

above f, the mechanical branch becomes inductive. When the impedance of

the branch becomes opposite and equal to the impedance of Co the

impedance of the crystal becomes maximum since oppos'rte currents flow in

the two branches. This condition of parallel charge means constant charge on

the crystal.

87

T11r: values of prezoelectric properties of a material can be derived from

rr:sonance behaviour of suitably shaped specimens subjected to a

Jusordally varyrng electnc field. The frequency response of the equivalent

curt of piezoelectric material (fig 3.11 a) is shown in figure 3.11 c with various

aracteristics frequencies identified; f, and fa are resonant and antiresonant

~quencres when the reactance of circuit is zero (Xe=O); fs is the frequency at

1ich series arm has zero reactance (X1=0), f0 is frequency when the

sistive component Re is maximum; fm and fn are respectfully the frequencies

maximum and minimum impedance Z of the circuit as a whole.

The resonance frequencies are determined by using suitable bridge.

ransmission method as described in IRE standards [1] is also used for

1easurement of maximum and minimum impedance. Schematic diagram of

ansmission method is shown in figure 3.12.

:.9.2 Evaluation of piezoelectric and electromechanical coefficients

An important parameter of a piezoelectric material is the effective

)/ectromechanical coupling coefficient keff which is defined as the square root

i the ratio of mechanical energy converted to electrical energy to the

11echanical energy or vice versa. The effective coupling coefficient is related

to the values of Co and C1, and it can be shown that:

k 2 = c, efT

Co +cl

f 2 - f 2 p '

f 2 p

Planar coupling coefficient (k0)

Among the various modes of excitation and vibration, the planar mode

of excitation of disk is of practical importance as it allows ready evaluation of

the properties of piezoelectric ceramics, which are conveniently fabricated as

small thin disks. The fundamental planar extension mode requires coupling

88

Jetwecn expansion-contraction in a plane and electric field normal to the

Jl;me (fig 3.13)

The planar coupling factor is obtatned from the fundamental mode f~

_mu f., of a thtn disk with faces perpendicular to Z-axis as [2].

_k-"_,'~ ~ (1- a' p {11, + ~.fJ- ~,(l + ~.'}.rl,( l + ¥ J J

l-k,' (t+a'p{ll{l+~!)]

where J0 = Bessel function of first kind and zero order,

J1 == Bessel function of first kind and first order.

111 == Lowest positive root of

(1 + cr" pJ~] = nJ0 [~] for aE = 0.31 and ~1 = 2.05.

This relationship is plotted in fig. 3.14 where kp is shown as a function

of M/fs. This curve is drawn for tl = 0.31 but the deviation for aE between

0.27 and 0.35 is too small to show on the graph.

Values of planar coupling coefficients have also been determined

using the following relations [3,4]:

f2-f

2 2 8

r ' = pkP wherep =-2

[3] r2 n p

k 2 _P_ = 2.51 f,-f, 1-k 2 f p c

[4]

Thickness coupling coefficient (kt)

Measurement of laterally clamped thickness coupling factor k1 is not

recommended in general, since the fundamental thickness extensional

resonance of thin plates is not always free from unwanted resonances. The

coupling coefficient k, is directly related to piezoelectric stress constant h33

89

:Jr very tilm plate with Infinite lateral dimensions, the square of coupling

1ctor k, 1s g1ven by [1]

T( 1 ~ Tan[ IT_ !"fJ

7 r 2 r ... jl p

" . I [l J

Careful analysis of the free vibrations of a thickness mode piezoelectric

esonator with short-circuited electrodes indicate that the fundamental and

JVertone frequencies of resonance are given by a frequency equation of the

orm (5]:

X TanX =-2

k,

in which X= wT/2V, w is the angular frequency, Tis the thickness, Vis

the phase velocity of the elastic wave motion.

The roots of the above equation are obtained by the recurrence

formula [6]

The values of roots are tabulated as functions of k1 from 0 to 0.99 for

the first four modes of resonance by Onoe et al [6]. A knowledge of only two

frequencies of resonance is all that is required to determine the value of k1,

but in practice the two or more ratios of resonance frequencies provide check

on accuracy and consistency of results. The technique is applicable if the

ratio of diameter to thickness of the disk is around 10 or more.

Piezoelectric strain coefficients

The piezoelectric strain coefficient IS determined directly using

Berlincourt meter. A dynamic force is impressed on the electrode surfaces of

the specimen by a electromagnetic driven mechanical probe The

90

p1e;oelectncaly generated charge on specimen is measured and processed

tu work out t11e strain coefficient. The piezoelectnc coefficients d33 and d31,

r;Jtlo of strain developed along 3 axis to applied field along the same axis and

l<ltlo of strain developed along 1 and to the electric field applied along 3 axis

wspectively, are some of the important parameters of a piezoelectric material.

The ratio of (d33/d31 ) is referred as the anisotropy in the piezoelectric

coefficients.

A recommended procedure for measurement of d33 and d31 is the

shock free lifting of a previously applied weight from the specimen. The

generated charge flows into low loss capacitor, whose capacitance is at least

10 times and preferably 100 times that of the specimen, voltage across the

capacitor is measured by high input resistance voltmeter (a tube electrometer,

VTVM). Total generated charge is then calculated as the product of observed

voltage and sum of shunt capacitance and static capacitance of the

specimen.

The hydrostatic response can be measured at 1 0 to 1 00 Hz as

prescribed in the literature [7]. The hydrostatic strain coefficient is related to

d33 and d31 as·.

dh = 2d31 + d33

Piezoelectric voltage coefficients 933, g31 and gh are determined by

dividing the corresponding piezoelectric strain coefficients d33, d31 , dh

respectively with permittivity of the piezoceramic.

91

References

Proceedings of 1RE 61 (1961) 1161.

2 WP. Manson, Phys. Rev. 74 (1948) 1134.

:J B.Jaffe, W.R. Cook, H. Jaffe, Piezoelectric ceramics, Academic press

London (1971)

4 P R Chowdhary, S.B. Deshpande, Ind. J. Pure. Appl. Phys. 17 (1979)

571.

5. A.W. Lawson, Phys. Rev. 62 (1942) 71.

6. M. Onoe, H. F. Tiersten and A.H. Mectzler, J..Acc. Soc Am. 35 (1963)

36

7. WP. Mason, H. Jafte ,Proc. liRE 42 (1 954) 921.

92

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Magnetic objectrve lens

I I I I

oooru IF" oOoo J oooo ooco oooo oooo J oooo ooom [foo oooo I oOoo o~.o I 1~0_9.

I I I I / I

;;-::-0

~: 00

0 0 0

0 0

0 0 0 0

0 0 ' 0

0 0 ' 0

0 I 00 ~ 0 0 0

X-ray detector

I -I

I / I

I

Sample chamber

.---'--·-------Scan (magnlfrcalron)

cod controls

e detector r

l_s=-::3 CRT --L~ drsplay

Fig. 3.3 Schematic diagram of scanning electron microscope

95

.Z20V 50tpt

Fig.3.5(a) Schematic circuit diagram of experimental set-up of P-E loop tracer.

D

Fig.3.5(b) Typical hysteresis loop showing X-Y intercepts

97

TABLE

CAL. OUT

UPPER PRCBE

f"ORCE DRIVE IN

Fig. 3.6 Schematic diagram of Berlincourt meter

98

Fig. 3.7 Design of mhp-100 microhardness tester.

Fig. 3.8 Eyepiece micrometer.

99

®

CD --++---1~

---<3) CD--t+--JI-C::J

® ---~-~ r-;::=:::J--- 0 G>-tt=J;:==:::r--i ~;~~~~~~~~~~r-~==~~~=r~---·-----QW

®

Fig. 3.9 Schematic diagram of hydraulic press.

1. Screw with handle. 3. S.S. plate. 5. Pressure gauge. 7. Release handle 9. Flag. 11. Piston

100

2. Punch with '0' (rubber) ring. 4. Pressure plate foe felt seal. 6. Pump handle. 8. Rubber sheet 10. Breathing nut. 12.Ram

(a)

POl.ISH£0 ,~------ sunr,.,cc

A.NVIl 8rrvt'l

~~~7~5~=-CLF• f' 0 R<NG

S S ~IPPtr

{b)

Fig. 3.10 (a) Die (b) Schematic diagram of the die

101

L

/1,

(a) (b)

(c)

Fig.3.11 {a) Equivalent circuit for piezoelectric specimen vibrating close to resonance. (b} Equivalent of {a). (c) Characteristic frequencies of the equivalent circuit.

102

YI~L --,

:0 r SlONIIL

~ DETECTOR

Rr

-::: I

FREQUENCY MEASORINIJ EQ\.IIF~EtiT

Fig. 3.12 Transmission method for determining frequencies of maximum and minimum impedance.

..

Mechanical response

2

3 ·--o

~-

Fig. 3.13 Planar mode excitation of piezoelectric disk

103

k,

'

.. ~v"f . ~ v/ -r

.i v I/ , 1- i ' . I ~r.L

02 U4 r.G

,, I

(f,-f,)/f,

r !

I v.J: I~ 1C• DCI t>. 'o• • r.,-, '

~~< Q". ,)J

I ·-. ___ j_ .I

1--"

Fig.3.14 Planar electromechanical coupling coefficient (kp) as a function of Mlfs

104