THE RELATION BETWEEH THE MEOHANXCAL

AND PIEZO.ELECTRIOAL PROPm:lTIES OF A·ROCm:u.E SALT CRYSTAL

by

Frank o. Isely

A.B. Fairmount College 1921

A thea1a. subin1~1~ed to the Department og Pllya1os

and the Fncul ty ot the Grtl.dua.tc~ School of

the Un1vera1ty ot Ka.nsa.s,in part1al

tulf'1llmont of. the requirements

for the degree · of

Mnatc:r of Arts.

Approved by,

T A B T"' E 0 F 0 0 N T E N T S •

I. Intrrodunt!on. • • • • t. l?tll''poae of Reaan.rch. • •

I

2. Pl"'evi.ous !nveBt1e;n.tion. • •

• • • • •

• • •

• •

• • 'b. Const,1'·uction Rnd Ce1ihraM.on cf

Extonsomct,nr •. • •

c. Corop1.,osni.n~Ap;ie,rntuc..

!!. Temperritu:re Control.

•

" • •

. ·• 8. Summary. • •

•

•

•

..

•

• •

•

• . .

•

•

•

•

•

• 0

•

•

•

4

6

6

6

32

BIBLIOGRAPHY.

Anderson,J .A.

Poynt1ng and ThomHon.

Valasek,J.

Valasek,J.

Valasek,J.

Ruesall,E.w.o. and Cotton,A.F.R.

Wood,Har:ry O.

Williams, S .R •.

Reports to National Research Council, March and April 1918.

Eleatric1ty and Magnetism. Page, 148• (1914) P1ezo Electric R.nd Allied Phe-nomenon in Rochelle Salt. Phyaioal Review .!11 475-491.

Piezo Electric Aot1v1ty, of Rochelle Salt under various Condi t1ons. Physical Review ~~' ~78-491.

The Property of Rochelle Salt Re-later to the P1ezo Electrio Effect. Phys1oa.1 Review 20,639-664.

P1e7'o Electr1o1ty. Electrioa.l Review .2B,. 284~?.87.

P1ezo-Electr1o~l- Acoeleograph Bulletin of Seismological Society of America • .1.l. no.1,Maroh 192t.

An Extenaometer Amplifier. Journal or the Optical Society of America, 1,no.t1 Nov.1923,p.loU.

I N T R 0 D U C T I 0 N •

It wn.s.the purpose of this pieoe of resen.rch to investigate the relation between the mechanicaland p1ezo-

eleotr1oal properties of a Rochelle Salt Oryatal,under

v.9.rious temperature conditions and w1 th varying stresses

applied..

*P1ezo-electric1ty we.a discovered 1n t880 by the

brothers,Ja.oquas and Pierre Ourie,while investigating the

similar phenomenon af pyro-electric1ty in various crystals.

This latter is the property of a oryatnl to produce an

electric charge on its ands clue to a. tempera.ture change.

While the former,with which this pa.per de~la>is the proper-

ty of A. crystal to produce a ohRrge on i ta s1clea or ends

due to A. s t1"esa along the long1 tudinal axis.

Since the discovery of the p1ozo-eleotrical

phenomenon mru:iy crystals have been found to possess this

property to a greater or lesser degree. In all crystals

with polar axes, 1.e. those of which the opposite ends c5f

an axis are not alike in the grouping of the a.toms,thero -Hi-t.Y ~ .._,.(_

is at least one and usually~many directions along which

the application of force will produce a oharge,e1ther

on the planes where the force is applied,or on the

- -* Poynting and ThompAon. Elect. and Mag. P• 148.

(1.)

:gerp end1 cular surf'a.oe1to this. The aooumula.tion of eleotrica.1 charges

are of opposite signs and on opposite ands or aides.

Only in a tew crystals is this chn.nge very approa1able

and in o1b.ly a vary few is it comparatively lnrge.Roohelle

Salt crystals are one of these very few.Poynting and

Thomy,son,1n their text on Electricity and Magnetism page

148, give the best discussion of the effect of any of the

standard works on physics.

Until recently (1917) little work ha.a been done

on this subject.But durlng the Great War,a study of 1t

was again tnken up. A number of men in this country have

ta.ken an interest in worlting on the crystal. W.G.Oadyt

of Wesleyan Univers1ty,M1ddletown Connecticut,has done

consideralbe work in determining the crystal properties.

J.Valaaek2 of.Minnesota.has perhaps done more than any

other man.His work h~s been espec1aly wit~he application

of a potenti~l difference acroaa the surfaces of the

c~yst~l.He found that a dilation was produoed,also that

there is q permanent polarization in the naturRl state

thnt,, o.tiused a tTl(!t.rlced hystcreaio effect. He further worked

with the optio~l .refrRction and temperature. effects on

the oxw1st:il. ~"lderaon3 ans Viood4 made 111v~at1gat1ons

en (2) <:.H (4)

Reports to the Mat1ona.l Research Couno11 1 May 1918. Physical Rov1ew, lZ 475, 12 478, ail 639. Reports.to the National Research Council, March and April, 1918. Bulletin of the Se1amoloe1cal Soc1aty of Am~rtoa, .ll,no •. t,. March 1921.

(3)

with the idea.a in v!.ew of ad.a.pting the oryata.l to signal

Md seismographic uaes respectively.Taylor and Yoder 1 for )

their Master's Thes1s,1n 1922,at the Un1verslty of Kansas,

worked on the correlation of the mecha.n1crl nnd. piezo-

eleotrion.l properties.But, 1;ho they arrived a.t a. value of

Young's modulus,for both open and short cirouit of the

cryatal,the1r results were not definite and thetr method

a.eemed inaccurate and 1nconclua1ve. -( t) Thesis Physics Gept. Untvera!ty of Kanan.s 19?.2. An

Investigation of the Electr1oal and Mechanical Phenomenon in the Rochelle Salt Cryntal.

PHEPARATION.

In the study of thia problem,it was desired to

devise a method whereby the streas,strain,and charge

could be meA.sured a.a. nearly simultaneously as possible.

Also it vms necessary to keep the atmospheric concU. M.ona

fa11--ly constant or var1a.ble n.s desired.

The apparatus use1 by ~raylor and. Yoder in 19?.?. w~a

still available.So the firat thot WR.A to uAe aa much as

possible of their apparR.tua :ind yet change th,.~ parts that

seemed to be unaten.dy.With th1A 1deR. in m1nd,the1r appar-

atua w~s carefully looke1 over.It consisted of a solenoid

with an iron plunger attached to the cryst~l for applying

the foroe,and nn interferometer arrangeraent for determ1n-

inp; the oontr.,.ction or strain.

The method of applying the. force seemed good so

thRt part was kept but tho interferometer method of ir} length rea<ling the ohange/WtHJ, tins table ~.nd 1na.ccura.te due to

the great change in forces applied.This p~rt was

oh'l.nged A.ncl an optical extensomet,er,descr1bed lt:J.ter,wa.s

used.

After the extensometer W8.s in place Rnd ~,he prooes s

of ca.11 bra ting the solenoid bjr megas of a. Jolly balance

arrangement waa in progress .1 i:, wA.s decided that because

of the he~ting effect of the solenoid(which was considerable

{5)

for some of the forces deaired) that th1o meth0d of

applying the force would ~lso be d1scarded for a simple

lever arm.

Temperature control vm.a thot to be socured eR.aiest

by an electric light bulb for heat1ne; A.nd R. co1l of copper

pipe for cooling.

For measuring the qmmt1 ty of the chR.rge n Leeds·

and Northrup grtlvanometo:r wlth a sAna1t1v1ty factor of

?.~4t megohms,was considered adequate. This galvanometer

h;;id Ar crl t,ion.l .dn.mptng raaiat,a.nce of 8100 ohma, vrt th a

rea1atance of 525 ohma,and a period of 5.85 seconds.

EXPERIMENTAL WORK.

Rochelle Salt, NaKC4H406· .4rr2o .• cryst,allizee. in

the hem1hec1ra.1 form as cUs tinguiehecl fl"om t,ho hem1.morph1o

clt1.Ss of the ort,ho1ihol:lbic Hystem. It is in e. class 1n wlh1oh

the cri1atal for'roa arc rcfe:nned. to the thr,!}a axes at right

angles to each other,but in which the planes of the ntmpleat

prismatic bounding surfaces interoopt these axes at diff-

erent d.1atancea from the common cent8r of· tho crystal.Fig.

( t). Further' the claaa ha.a no center of symmetry and eonse-

quently the enda of the axes,or any other direction thru

the cryatal,have different physical characteriatica.There-

fore each axia is a p1ezo-eleotr1c axis.

All .. of the principle axes are pole.r ancl therefore

mrtny ways would present themselves for cutting the crystal

into a slab that.would yield. the plezo-electric effect.

The best way.howevertis considered ao follows: A thin

plate of given .thickness. ,&,Figure (2), was cut from the

.29. plane and. from the central portion of the crystal.

From. th1a plate a sls-~b of length l,, and width ,:z,wa.s cut

so thA.t 1 ts side a were inclined a.t ·arr_ansle of 450 with

the odge of the original crystal.

The cutting ofthe crystal had to be undertalten •'

with great care for any uneven strain would cause the

orystA.l to. era~~ ancl break.The method. of. cutt.1ng is one

that has been used by most of those working with this

( 7)

I I I I I I I

I I

I I I I I I I

I I I I I I I I I I I I I I I I I I I I I I I I I -l. I I

.. L- .._., ..... ... ....

flj ./.

( 8)

--~ --- ' -- ' --- ' _.,,,,,. .... ---- ' . .:::::-------- --- ----- -----.:::........__ ,-,, - - -- -- - - --__.,..- -- --- -- ---...,;111'1 f, _,,.,,. I

b

_.,,,,. I _,,..,,,,.-"' ' .,,,,..,,.' I

~ ,, I ~ C I

' J

b

{9)

type of cryatal.Figure (3) shows the apparatus.It cons1sts

of a platform on whibh the orvstal rests A.nrl to which is . ...

fastened four pulley wllr;eln.Two of which-are under water

so th~t ~n endl~aa thre~d,drivon by a motor, pas3ef) thru

the wnt~r,mrer the pulleys,a'bd a3A.tnat the crystal.The

cryAtal was thus dinaolved 1J1.way 'hy the water.

The al::tb that was loft wa.s in a rough ~n(1 uneven

condition.It was ground to a perfect rectangular form

with eme~yan(! 'vat!;lr on a ~gia'sa plate and. later polished

by w.~.ter nn ·-t. ·piece of ground gla.s D.

In order. to t-~limitla'lie·::any change in vapor tension

of the crystn.l and to minimize the change in the crystal

due to ~,ny oh~nge il" humid'\. ty .1 t was coated with an aaphal-

tum cement 41 Thi a cen1ent vm.a macle by .dis-sol v1ng powdered

a.aphaltum guro 1.n. Benzine( 00H6 ) and waH udec1 both beoause

of 1 ta t~naci ty And r-ap1.clly fu•ytng property and also

beoa.uae ne1 ther t.he asphal tum nor the berrnlne hnd any

hnrmfttl effeota on tho erystf:,llogrR.phic structure.

To ~A.ch aide of the crystal w;-~s cemented, with the

same ocment,A. p1ece of t1nfo1l>the .tinfoil. coming within

a few millimeters of the edge of the cryatal.

The crysta.l, thus prepnrerl, was ccmen.terl to. a brass

base and supported byf, two aeta of glasa.rods,wedgea

being placed betwei:m the rods and the 011 ystal .After the

cement h?,d ha:rdenP.d t~1e weclgon were romovad leaving the

crystal free to move up and down without any friction.

--c -

( 11)

Figures (5) and (6) show the cryst~l 1n 'lace.

Construction and Calibration of Extensometer.

Tht3 lna·crmnent, usod in meaaurtng ·t;ha chnugc in

10ngth of the crystFi.l war-~ e.n opt:tcnl. extensomet1er,made

2c~cor(linc; to a description of sunh an instrument by

fl.R.Williama* of Oberlin.It was made in the machl.ne shop of the physics depa.rtrnentrv1ith the exception of the

jo:vclern wo:rJr. on the pt~mt n.nd bearings.

Flgur•e (4) shows the oonatruction of the piece.

The le'!el:-· arm wr.is ma.cle eighteen contimetel:'tt long, w1 th three

centimet,ors a.fJ the distance from pivot to the grr,ova in · w·hioh the at1r:rup raAted. T~~e. pivot of the levM:~ a.rm wFtsvf

ma.do of a fine oamb1--10· needle rtnd rested in a "vtt groovB.

At tho end of. the lever arm P.. fine phosphor-bronze v11re

was fnstened.Th1s wire passed. arotmd another small pivot

and to a. weight, which held 1 t tight to the pivot.Thia

lr;.tter ptvot WAS made of M.ghly tempe1--ec1. steel ancl 'Wr-LS

perllnps two millimeters in d.i.smeter, except where the

fine rd~re p~ssed a.round. 1 t .• J\t this polr..t it had been out

to a diameter of nh:mt one rn1111.Jeter.The bearings were

~1ewels.The etirl"Up wn.a made w!.th thelower part of

nteel in order to ron.1te ns 1<:aen t:i k11ife edf5e a;.1 possible

for the lever arm to reat on.The mil''ror w~s n. small gn.lvanomater mirror s:,1d 'f'r;.oten.ed_to the pivot by wa;,

I - -* An Extenaometer Amplifier. Journal of ~he Optical Society of America. z,n~1' Nov.1923 p, to11.

l To :s.Jcll c:

\ ·-

Fi.J. +.

( 13)

1 t was count~rba.lanoed so that there would be no ten-dency of the mirror to creep.

In the calibration of the 1netrument,a wire from

the atirr.1Up WRa fastened to the micrometer sorew o! a cathe-

torneter .A telescope waa focused on the mirror image ot a

soale. The miorometer screw WRS then irurned so aa to give

the mirror an even number of cmplete rotations.From the

micromet,er movement and number of rotations• the distance

the stirrup moved for one complete revolution could be

cnlculateclFrom this va.lue the movement of the stirrup

for a centimeters movement of: t,he m1r1'lor at any scale .

distance could be computod.Vl1th a sea.le three meters

distant ~ movement of leas that a twentieth of the wave

ltingth of sodium light could be detected.Thie w~a thot to

be fine enough 1 as a matter Of fact the scale WA.S used a.t

a distance of onlv two metera. v

After the calib11 ation of the extensometer,which

is shown 1n Ta:ble I, it was securely fasten eel upside down

to t,he SA.roe. base thnt supported the crystal.This is

clearly shown in Figures (5) and (6).

On top of the crystal a small block, was placed.~hru this block a hole w~s cub ao that a small brass ro4 cou~d

Pass .thru.Th1a rod wns the top part of a saddle that sur-

rounrled tho aryo tal. In. the center of this rod a small

noedle waa f~stened so th~t its point rested in a small

con1cal hole in tha bloc!'=.Thu.s any movement of the cryat.al

(14)

TABLE .I

Calibration of Extenaomoter.

Feb.7,1924. Micrometer

Readi?1e;. M1oromater No. of. Turns Movement !4f.1v·arn'·ent. ntade by IUrror. p(}?' yu:rn.

to3 -?5 4 •• 11.

101 15.2 .5230 t .5130 mm. to1 16.2 10:; ~7.8

.5282 1 .5282

103 20.5 tot rm.s 10 t no.s 99 14.9

99 14.9 to 1 25. t

101 as. 1 V03 36.o to:; ;5.o 105 44.5

105 43.9 103 35.8

'103 35.8 101 e6.9

.5200

.5t4o

.5248

.c::~72

.5262

.520:;

.5223,

1 .5200

1 .s•4o

.5248

t .5272

t .526?.

1 .sno3

t .~~2~ Average

.5229 Fcb.8, 19H4

Avernc;e. of ·t11:('le :rea.11ngs. .5230 mm. (with various number of complete turns made by th.~; mi :r>1'lor)

Feb.9, 1924

.Average of five l''ead1ngs .522.7.

Final. a,verage of three. aet.s of da.ta .52287 mm for e~oh complete turn of mirror.

mm.

With scale d1st:i,,nt two met,e4a,?n.e <1m. def-leat1on:rAoor<i.s 8. movement of .315. x 10- · om. .

(15)

TABLE II Crystal Dimensions. Feb.22tt924

Lengt,h Width '1~1.ckneas

1,575" .795~ .08911

1.560 .788 .088 1.58o .1a2 .uB9

.79, .osa

.792 .o87 .o84 .090

Avt:Jrage 1.57163 .7895" .,0883 1~

Converted to me trio a~rAtHm. ?·292 orn. ~.qp!2 om. .a24cm.

finfoil Dimensions. Length Width

:;.5 om. t .39 cm.

{16)

( 17)

0j.6.

( H~)

gave,thru the bloc1t,a movement to the and.dle,wlli.oh in turn tranafer1"ed this movement to the e;.:tenaometer.

Oomp1"'eo~:tng 1\ppn.rntua.

This a.ppliratus wna a a1mple lever arm.ThG a.rm wa.:l ~ ma.de of, steel rod lesa than a oent1meter in diam~ter and

11.early thirty aentimet,ers long. It was j>ivoted at one edd

bjt a long needle m~u11ted 1n oon;Lcal steel bea.r1nc;a.The bloolts comp(asing the beP.rings were ~aa tnned toge the~ and

clamped to a ~1tand. At the other e11d a small hook waa taat ..

ened to the arm~on s1hich the weights were to be hung. At

the· cerrter• of the ftrm,.a threaded hole for a. machine &Cl"'9W

was ma.de.This aorev1 had a. Bhar!)ent.id end thR.t was made to

rest 111 a amall hole in the brass block that w~ia pla.oed

on th 11 aryatal.Thus t,he foroo could be o.ppl1ed directly

to the ·crystal.Of. ooui'\se the f'.orce applied was twice

the 11a1uo of the weights applifld at the l&ver arm.

The apparatus as thus made gave an 1nit1al atreaa to the crystal.. In orr1er to over.<Jome thia,n. spring waa

fa.fltened by means of two v1i:rea to the 1)raas block aa shown 1n Figul"'e CG l . The spring wa.a a tretohed enough

.1ust to oireroome the i.nl tlal weight on the crystal.

(19)

In order to keep the conditions of the crystal ta1rly constant a tln crl.ae \Vas made t,o surround the

aryatal and to rest on the ha~d l"Ubbor base. A glass top wa.a made to go over tho oase,~t having a sma.11 hole in tts center foi-- the spring to pn.se thru.

Thia .tin oase was actually a double walled oaae

fo·rming R oi:rcul~ ·b11ough~Thus,vrn.tcr could l)e pm.ired indlo tht1 ·fjr~1ugh to regulate the tempei,,n.tu1 .. o .This method of

temperature oont1.,ol was not sa.tisiSi? .. ctory so that a coil

of coppe1'l tu.bl.ng Wt' .. S placan in thn tro.ueh of water a.ntt

could be lowered and kept at n...Yiy po:tn t b'3°bwecn room 0 tf1mpe:rn.ture a.nd a mim.mum of H5 oentigrada.

In order -to r·~1ir:!e the temperature a nituogen

mazcla. lamp was placed abo".re the glass case, care being

taken to lreep the J..ight f.rom shini11g clirectly on the

Ol.'yatal.

A holo waa made near the top of the inner tin oaae so 'f:,hA.t Fv the:rmometer,clividec1 1nt,entha of de.5:reea,

could be inserted into the case and the buli placed in 1ntimRte contac!t with the lowerf edge of the

crystal.

(20)

Calibration of Galvanometer.

The electr101 ty p.roo.uced by t.1'HJ crystal le a

charge so t,hat the gn.lvrmometer ha.d to be oa11 bra.tad for

this charge.'rhe met.hod of aal1brat1on W3.o the ate.ndal"d

oondeneer mBthod.

Table III shows ·th1a data. n.nd Figure ( '"() shows

the 5raph !')f these values. From the t.1me the instrument vrn .. s calil>ratad until

after( the after) the ftna.l dR.ta. wtis taken, 1,he suspension

w.!:.is not changed. ,All the3e o1rou1 ts ware mounted on

plate glass 1~ order to reduce le~kage to a rn1n1mum.

UH)

TABLE !II

Cal1bra.t1on of Gal vanometel'. !fa.rnh ~7 .. 19r?4

E a Q. R.oac1tng Det. 1n 1n 1n in 1n.

i;ol·t,s. fa.rr:i .. dn coulombs cma., oma • • 1 .osx10

... 6 -fl .5xtn 25.5 .5 .a .os t.o ~6. t7 t.17 ,.,4 .os 2.0 ~7.1 ~.t .5 .05 ?..5 27.58 2.sa :~. t .lQ;: l,o ~5-9 .9 .a • 2.0 ?.7. 1 ~~. 1 • • .4; • 1 4.o ?.8.r;.5 3.95 .5 . , 5.0 30.0 5 .(l .o • 1 a.a 33.1 8.l

Lo • t to.o 35.1 10.1 1.3 .. 1 ,,.o ;;s.s 13.5 , .. s • 1 15.0 40.35 115 .35 t~.o • 1 20.0 46.o 2't.o

• 1 .a 2f0 n6.a5 1.85 .:J .a 4.o ~8.7 3.7 .~ .2 B.o 33.1 8.t .5 .~ iO~o 35.0 10.0 .7 ,2 t4.o 39.25 14.?.5

1 .. 0 .2 ?.O.o 45.7 20.7 t .• 1 .2 ?2.0 48.o .. :n .o 1.2 • :".! ~4.o 50.2 25.a.

• 1 .J 3.0 a1.1 ~.2

.2 . :; 6.o 30,,7 5.7

.4 .3 1~.o 37._4 1?. ,4

.5 ,; 15,0 40.3 15.3

.6 .; 1a.o 43.95 18.95

.7 .3 ?.1.0 46.4 ?.1.4 ,3 .3 ~4~() 110.?. ~5,.2

• 1 .5 s~~ 30.6 5.6 .2 . t: 10,0 35.1 10.1 • ::.> .4 .5 20.0 45.9 20.9

5

(22)

. C.q/J"brqTion C"i-ve Of

I

6c:r/ va nom~Te r

::;cede de flecf-irm · I>'> cm:s.,

Proceedure •

With the P..ppa.ratua C(>:'"!lPleted r,.n 1nitL~.1 at:ce~r;­

strr-tin run W'.1.s t~.1ten. In t.h!.s run 1 t W9.8 fmmrl t.hn.t there

w:::is an 1ni ti al chang~: ln cr7:J tri.1 lenr;th ~n'"l ~.l BO th'!'.t t th.ere

was a creep 1n thi3 ch~nee for a sh~rt ~eriod of time.

Whffll the lo~v1 w0 .s 1 .. 0moved t,,he1"'e "lm.s ·~n 0qual 1ni tlal

, mo1retnent tn re,rerserl direction .::1.nd 1. erHep unt,11 t,hA

extenaometer ren.rlinc; w~s bi:tck at th\'3 01~tg!nal.

When the br:=iss b10c1-t on to!1 d>f tho cry;1t:il W"tA

moved,a-\rn?t very slightly,i.;h0 j.niti-:tl read1n_g ns ~.vell Ra

time off.e0t w~1s 0h1ngP-1.0ne.¢pn1nt, vns founrt. to .c;lve ~

minimum chrrnge n.s ·we).1 as ~1 minlrnum of tine effect.It

WA.s decide~l that the minimun condition W.'1.n t,h1t in wh1ch

the stress W!'.l.~ bei~g npp11e'1. t'} the cry3t~1 an nearly as

possible along the line "F'! of Figure (q). At nth.Gr pp1nts

a bending of the c~yat~l w~s obtainad,whictr <l!d not give

the des ire(l results. The t1mr.; ef fGa.t in th1 s c en trn.l position

WRS a very sm~ll one cornpRrei to that ~t ~ny othor point.

Vl:l th thls ml.n1tnUm potnt of. defJ..Gctton ~rnm.trncl,a

series of runs ·N:.:;..n t-1.:-<en fln--'.i.ng the =1t~:-rnr~-str81n r~~la.tions

for the cryat~l un~er v~~tous f1xoi t~~'9r1turee wtth

various la~ . ..-1s.Thin st:res$ went ~;.s htgh ~.a ?.~25gr./ sq •.

cm. star·tlne; w1 th the smnJJ.est RS :-rn~.5 gr./sci. mp •. s.nd

going up 1n tan even atcps.

These rune were t~ken on both open :1..ndahort circu1 t

(24)

and at the same time the charge profu1ced on each short

circuit run vns taken f:rom the gRlvanomoter reacU.ng.

i.i.'hn maximum oha;-.,g{~ nhnwod ri.t ~~?. ?.5° no tho.t at

thRt t;amrrnrA.t1.lre an open cJ.rcut t run wnd r;;:i.do r:;b;ing

lnit1al Rnd finnl vnluon of cxtcnsometor rending.

22~5 gr./nq.cm. at various tempara~1r0H from 35° to

16° finding both tlrn otr~i5.n nnd plu;~o-electrio · chrt.ree.

RJi~SULTi3 •

Only typic~l a~ts of data are e1ven in the follow-

~Rble I\.1 g1"'TeS the omnplet.,e Calculations Of the.

Stress '1':1'~. st~n1.n v11J.ueH ori. both open :ind short c1rctt1t

for a. tmmper9.ture of 20° c0ntic;!'\ad.e.

TRble V given t~e end results for atrena and

str.1.in at t,em'.)oratures of ~o0 , 25(), n.11.d 390 • These V8.lu es are sh,,wm g!''1Ph1c'1ly 1n Fisur-e UP. It l 8 to '1Jo notetl

tha.t :tt "'.:,h(:} tem~·iEH'.'atUl'.'9 Of ;;oO . the AhO!'t ?.nd Opt:Jn cir-out t VBJ.u1-rn al"e the same and th~.t ttt thi.a teroperature the

at.rain is greatest. At the t~mperqture of ?.oo thert~ is a

difference betw08n opnn a.nrl short circuit values, the open circut t h~:~r1ne; the less st:ratn.

Tables VI and VII gtve the str~es-charge relations for ·the same set of rlms tn ~~h1ch the streH s-Htl'nin data wa.a t;:tken.The grq,phs of Ftgi.ire (9_) show thene values vary,

0 ·. well. It will be no:bed thq,t, a.t 20 (as ahown from these ttuns)

cr..a .. rit;E: :tn ol thnr direction vrlll re,luce this ch!t:~ge. A.a is

A. co:rrelation of Ftgures (8) anfl. (9) sht')W t..hat a.t the terope:rq_ture of l'east p1ezo-electrtc chRrge there

ls the ereRteAt ntrain,the stresa being the s~me.Al80 that at the temperature where t,here 1a conai.dHrable charge

Force gr.

100 aoo 300 400 500 600 700 800 900

lOOO

1~0

200 300 400 500 1)()0 700 800 900

1000

(26)

TAB1...E tir

Stress Stratn Values. 0 = 20°

April 14,t924

Stress Oontraotio~4 Stra1g r;r./sq.cm •• 315x10om. 10-

0pen Circuit ~2~··5 445.0 667.5 840.0

11l2.5 !.335.0 ' 1~~7 5 .? .) '. t78o.o ~oo~.5 ..,'?"?5. 0

'.5 a.5 4.8 6.5 "'l .5 8.5 9~0 9.5

10.0 ro.5

Short Clrou1 t

0~1:?.5 ~.o

445.o 4.o 667.5 5.5 840,0 7 .• 5

.t11'?,5 9.0 13.35 ,o 10.0 15?7.5 u .o 17BO~O ~ l • 5 ~~00~.5 1 ~~ .o ~Y?~5.0 13 ,l)

t .575 3. 15 4.33 5. 9·~ 7. 1 7 .• 88 8.67 9.07 9.4n

10.25

St1ress gr./oc1.cm.

~?.~.5 445.o 667.5 890.0

n 12.5 n:;s.o 1557.5 tlfliJO .o 2002.5 22~!a.O

?.~e!?.5

445.0 067.5 890.0

i112.5 1 :335 .o 15!37.5 7780,0 i:OO'?. 5 ~825.0

TABLE V'

Sreas Strain Values.

Open Circutt

t .97 1.77 3.5 3.31 4-.73 4.33 r;. '7

,t • • 5.52 7.~8 6.7 9. 1 7., 9.86 '7 .88

11. 5 G,67 1re.22 ·~.85 tJ .o 1t. 1

Short Ciro1J.i t.

l .97 , .97 - r: :h'..) ~5.47 4.73 4.7:) 6;7 6. :; 7,oe 7,4e 9.1 7;88 9.86 . 8,67

t 1 .5 9.86 'f?..22 HJ.65 t3.o 'i. 85

April ?4, 1924

1 • , 8} 1,97 ;.78 5.1~5 5.92 6.7 7.1 7,5 7.88 8,28

1.575 :~. '5 4.3} 5. 9?": ' 7. 1 7.6:3 8,67 9.07 9.47 10.~5 '

Force t;;ro

too 200 ;JOO 400 500 600 700 800 900

lOC10

(28)

TABLE VI Forae Charge Values.

o= 20° Apr·11 t 4, 1924.

Stress Cha1~g~8 Charge/cm~ gr./o~.am. . . 10 Coulombs.

2iH~ .5 l"'J ,., 'f°• • .r, .565

4-45.0 4.5 ~.156 667.5 6.8 1 71· .. • :.I 8900 9.0 2.31

.tn2.5 ,, .o ~.a:;

t3:;5.o tn.7 3.:;6 1557.5 M.5 3.7r:? 17f3\),.0 16.0 4. 12 Rtma .5 17.0 4.7/"( ~2:15.o H1.o 4.62

.. Aprtl 14.,.1924

S·~rese Charge /Hq.cm. in to-B Coulombs. 0 £5~./sq.cm. g:-:;;;5° o:-:3c1° 0::::?5° ~-::200 o=c6 ·

,..,n~ e (. 1:. (~ • ,.) ~05 '4- .P77 .2055 .565 .463 445.0 • 103 .154 .4G~~ 1. ,56 t.,53 66"! ~ 5 • 154 .~nt .693 1.75 l.9~

sso.o .206 .32t .937 2.3t 2.13 1112.5 --~5? .411 ' 1 C)f'.:' 2.8;; .2. 4)1 l})~.Q .;Qo .478 i :,st3 }.35 2.88 155·7 .5 .36. .;~t -1 .645 3 7'71 ;,zt .... 1780.0 .412 .666 .t.825 4.12 ;;.4~

2002.5 .46.) .745 2.055 4.6a 4. ta

i.

(2~)

Fi1.B ..

. ,-Sit-e,,ss -.~ f-_rq;">-> C.vrve.s

'. /OUO

.-STress.;_C hctr-Je ·. CvV-ves.

/ti(J(J

CIJ(!()

C,'() uo '

the short circu! t. valucn of ~.trn.tn cl!fi'e:1 , the open ctr-cui t atrain bein5 the less.

The st~oss-strain 5rnphs ar nll c1u ... vtxl, U10 leas

only where .~ lnrge ohHrgo '·s ol,.tJrdncc1.

Figut"e ( 10,) nhc\ws. n cU1---ect., correlation betvmnn t,heee two sets of gr~:.phs.?1o apeci.Gl conclt1s1.·:m appears

T.ableVIII and Figure ( t t) show anothr-.;r flc~·t of

the mRXi.rnum vnlue of chnrge.Eoth inHt~.ntaneoua atrt. .. .tn a.nd

tl~e change ir. crystal length haf. come to .?. C<>mplete stop.

g:l"ten stress 0f 2~213 gr./cc:.c.!!1. Tho J.0vrnr curve shovrn

th t t \" 1 .... ~ .. .s rill~.,.,.. O')~""l·'""o t::·" 'tT••n n·.,f ~.J. OIA <:)C:o J\ R. r"l•:.l""fJ S '1.IDr: .... · .. ..1..J.1.1,:iJ f.::.} .. e:.,· t.l~··:· 1..·J . .:~IJ :.!..,•i-.:1 • .t•B

ao qui cltly. The upppl" curve ehows that at ·the point of mRximum chr·u."ge thAre ia a rn1.n1muro ·ins t~mtRneoua s t:r?.in while the mnximum instantaneous strain comes at the temp-erRture where the charee ia negligible. It albo shows the

Foroa

~00 400 600 aoo

1000

T.ABI.iE VII! Stress Btr.1.1n Values.

\') ·= 22.5° Aprll 15,1924

Stress Oontract1on Strain Contraction Strain ( i:ai ti!,t.l) 4 { !J.uul) 4 5 gr./sq.om. .315x10- cm. 10-5 .315x10· om. hr

445 3.7 2.9~ ,,.. 4.7 3.7 aso 6.3 4.97 a.::; .6.7 t3}5. 9.J 7.33 11.a 8.67 ~fl~I .11.5 9.,07 t4. 1 l i. ' r~2a5 13.4 1~.58 t7.Q 13.4

.,

• i~ : I

~' ........

·t ..

(32)

j

'/lL_:....___;~~~l~~--~-2=-~------3----~~-A--:------:

/0

. ;

r ....

F1j.JI. ?ft·ess :..._::;f~4 ;>->

Cur- Vc::-.s c? l1S0

,

J l'-rf) J 5'" I'"()

2t.,-ess '"' ~ %6. c-Jor'I.

r-;;,4/~.

2U VO

Temp.

:~5.0 32.5 30.0 '?.7.5 ~-?5. () 24.5 ~4.o :;3.5 ~;3.Q

22.5 22.25 th: .n 2 l .5 21.0 ~0.5 rw.o ~?.5 ~6.o

'.Pemp ~

35.0 3?..~ 3g.o 27.5 25.0 ?.t!?. 5 20QQ 17.5 16.o

Temperature Charge Values

April ·17 • 1924

Q. co?~~e~~ _:,(a~. cm •. Q.ne7·~~B~ n Q/~q.cro. ---co. i&.~d~--- ---~O. ·!ardda--· f) .~~ .504 2.5 .642 3.2 .<'.32} 5.1 1.31 9.0 "'• :; t '". to.4 2.67

12.6 J.24 i4.8 3.83 t7.6 4. :1:.: '.11 .t 5.44 ~! 1 • Ji 5.47 20.0 5. 14 1::1.:; 4.96

. t8.4 4.73 ta.o '"•6) 17.0 4.:;*; 16,4 4.2P. 16, f') 4. rn

TABT ... E X

Cont~:t~act,ion Strain (in1tia~) .3t5xto~~cm~ 10-5

17. 1 13.5 l6.0 \3.25 t6.5 13.0 16.0 18.6 1·5.0 n.n3 12.0 9.46 13.0 10.25 1}.J 10.5 . 13.5 lO.n5

9.o 2.:;1 10.5 2.1 1a.5 3.21 \4.8 :;.BJ 17.5 4.5 21 .o 5.4 rd .3 5.47 2, .o 5.14· 19.2 4,9:; 18.5 4.75 18.0 4.63 l7.t; 4.42

Contraction Strain (final)

.• 315x10-#crn to-5

17. 1 13.5 16.G 13.25

t7.~ t3.55 . \ 'i' .o ':;.4 16.9 t3.31 4 'l. t 13.49 17.0 .13.4 l '"'(. 1 t3.49 ........

f '-I ~ Vl :.. ·1-~

Ill ...Q s

()

~ \)

\J ~ ·;3

I

·~ ...... {::' ......

I

. G) . :

. Final_,}

, Tbe. op P-~ o·,. >n4'."~~:l,t" J

pf:, . .se·c. v\""~d by h ~ ~1,.,' : /· .... • . (' . • ~ 4

rh.~'.x .·/JjcJitq. fi"?.J pt s Securtd 67 cooH~.

(34)

Temf'erQture Contrac.t lo11

C:.urve,s, ' ,.s·n-~slz2Z.Z·~~ t"Q m~

• ~gem.,

Tempe~C<"tt..lt-e C.ha.r-9 e C-v•-vf."

1-or<E' 22.ZS Jr-~~ . ~ C.n",

..

(35)

final. atrCJ .. tn to .1J'3 a .hor.iz.t)ntt-J.l .line w~.th a value the aame

as th~t of the maxtmum instant~neoua a"'i.;rai.n.

Figux•e ( 13) shows a correlation of. the two curves

of Fie;ure ( t?.).It shows a etl'aight llne reJ.?..tion batween

charge n.ncl atrnln, except R,t, low vP.luas of ol-uirge, whore

the a1u~e seems to change d5.1"act1011 slightl~,.

All of these oul"ves show ccmcluaiv.ely th~t tho

s·t.rain a.nfl consequently th~l v~.lL!e of Young' f1 modulus for the c1 .. yat>3,l dependa def1n1 tely on the charge of the crystal.

SJ.nee this is true, the l"'eason for a difference tm

open and shox•t airou1 t strain VHlues {Figure 8 )° can easily

be seen. On sho1~t uircui t tha oharga goes off pr.9.ctiually

inat,a.ntaneoualy,whi.le on opon c1.rcu1 .. i; it iB hAld for a

g1~e.q,t,er length of time dep:~n(line on t.hf3 ·ltHl11 t.y of ineul-at1.on. 'I111ere is ~ ama.11 amount of chEn"'ge on or>en a:J.:rcui t

that. is not g:.bren up lmmea.<Uately i;his ta the :roaf'1..,n for

:bhe. up1ler \llll"a\re .~f li"'1gure ( i?.) • A.s t,he ahA.rgA tno:r'Mta es

the1~a it-1 a gre3.ter a.mount th.g.t, ls no·t given off immoadi-

a tely; t11i s cht=tr§e will then tand to k cep tho orytt taJ.. front

oontraC"?ttng. T!:ie value of Young• C:J modulus obtained from .the

final value of strain as shown in Figure ( 12) for aa25 gr.

per aq.om. 1a t .6.~ 7 . to&.P. : ?. • 31 x lo 10 betng the value

at point of minimum strain. 'rho value of the modulus

m~y be fouwl a;t any rc1nt .for the crystal b~r takin5 the

ta.nge?lt to the atreas.,str•ain curve at the stress desired.

/

:( 36)

,S 'lrtt i,,, - C h4' 't' j t'

C"'t'Vt::.

3 /t; ... B. C1wl'a-n.b;)/-,. ~.

·. ·- ... "'O

It will be noted from the curvas of Figures (8)

and (9) that where the atrefrn-charge curves approach a

stx•a1ght line the stress-stra.in curvea are also more

nearly a straight .11ne., Since 1 t 1a when thoPe 1tl a

m1n1mmn or charge that the stresr:~charg'a curves do become • straight 11nes,1t would seem thnt when there is no charge

thee~ linea would bec~me. f~.baoluteJly ~strate;ht a.nd alaiJ· the

which would be expected. wer(~ t.hm~e no chH.rgA on the oryatll

the st:resR-atrain. cu1"Ve is a str,J .. ght lina.

int1ebtec1nesa to the Physics :!)epar•tment of the tTniv•&rs1ty

of K&nsss for making this invest1~at1on p~3aibla,to the

General Electric Comp.":tny for supplying the. C~cystq_ls,

and to the va1~.1ous members of the stnff o~ the Physics

Department f \>r their helpful suggest1·3l10. Eap<rnia.ly

he wishes to thenk Dr.F.F.Kaster for sugs~stlng the

·problem A.n.d for his (Jonttnued help in d.irccting ~lte

work.

Elt:ik e ?hyrii c :~l !.,a born tory. Univernity of Kansas.