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An investigation of the ferroelectric properties of barium titanate Nasmyth, Patrick Walden 1952

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fly  hi-  i r  AN INVESTIGATION OP. THE FERROELECTRIC PROPERTIES OF BARIUM. TITANATE by PATRICK.WALDEN NASMYTH  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS  i n the Department of PHYSIOS  We accept this thesis as conforming to the standard required from candidates f o r the degree of MASTER OF .ARBS  Members of the' Department of PHYSICS THE UNIVERSITY OF BRITISH COLUMBIA November  1951  ABSTRACT  The theory of f e r r o e l e c t r i c i t y , and i n p a r t i c u l a r the f e r r o e l e c t r i c behavior of barium titanate, are discussed and q u a l i t a t i v e agreement i s obtained with experimental r e s u l t s . Limitations of the theory are pointed out. Experimental procedure used to manufacture samples of polycrystaline barium titanate ceramic, and to investigate t h e i r f e r r o e l e c t r i c properties i s outlined. The phenomena of permanent p o l a r i z a t i o n and hysteresis are investigated i n the f e r r o e l e c t r i c temperature range, and are discussed.  An e l e c t r i c equivalent of the  Barkhausen e f f e c t i s observed.  ACKNOWLEDGEMENT The research reported i n this thesis was supported i n part by a grant from the Defence Research Board of Canada. I am indebted to Dr. A.J.Dekker i n p a r t i c u l a r , and to the other members of the Department of Physics of the University of B r i t i s h Columbia f o r t h e i r suggestions and assistance during the course of the research.  P.W.Nasmyth . November 195i  TABLE-OF CONTENTS Page I  INTRODUCTION  1  II  FERROELECTRIGITI.  3  1.  Analogy to Theory of Ferromagnetiem  4  2.  Theory of Mason and Matthias  III  IV  EXPERIMENTAL PROCEDURE  17;  1.  Preparation of Samples  17  2.  Polarization  19,  5.  External Field  20  4.  Hysteresis Loops  EXPERIMENTAL RESULTS  ' •  21 22  . 1.  Composition  22  2.  Polarizatioh  24  5.  External Field  26  4. Hysteresis 5. V  12  28  "Barkhausen" Effect ;:  52  CONCLUSIONS  35-  REFERENCES  $6  APPENDIX A - Auxiliary Equipment  37  1.  Furnace  37  2.  High Voltage Supply/  37  LIST OF ILLUSTRATIONS  Figure  Facing Page  1  P o l a r i z a t i o n by External F i e l d  5  2  l / " ^ versus 1'.  5  3  Condition f o r Spontaneous P o l a r i z a t i o n  7  4; BatiO^ L a t t i c e  8  5  Ionic Spacing i n EaTiOj L a t t i c e  8  6  (deleted!)  7 7  Barium Titanate Samples  18  8  Sample holder  18  9  Device f o r measuring External F i e l d  18  10  C i r c u i t to show,Hysteresis: Loop  21  11  Hysteresis Loop  25  12  P o l a r i z a t i o n Process  26  13  Variation of Hysteresis Loop with Temperature  29  14  D i s t o r t i o n of Hysteresis Loop  30  15  Potential Minima i n BaliOj Lattice.  30  16  Action of T i Ion  30  17  C i r c u i t to show E l e c t r i c a l Equivalent, of Barkhausen Effect  32  18  Pulses caused by " Barkhausen" E f f e c t  J.1'9  :  High Voltage Power Supply  33 37;  I  INTRODUCTION  I t i s known that i n the temperature range between about 0  o  o . . and 120 C a single c r y s t a l of barium titanate (BaTiO^) consists of  domains which develop a spontaneous e l e c t r i c p o l a r i z a t i o n .  Polycrystal-  l i n e barium titanate ceramic also consists of a large number of randoml y oriented polarized domains which can, to a degree be brought into alignment along a chosen axis by the application of a high DC f i e l d along t h i s a x i s .  Once aligned i n t h i s way, there i s a tendency f o r the  domains to remain i n alignment, with a r e s u l t i n g remanent p o l a r i z a t i o n ; and under these conditions piezoelectric  the material exhibits both f e r r o e l e c t r i c and  properties. During the past few years much study has been given to  these properties  of barium titanate, and to i t s related c h a r a c t e r i s t i c  of extremely high d i e l e c t r i c constant. In t h i s thesis i t i s not attempted to review the f i e l d , but only those aspects are discussed with which we are d i r e c t l y concerned.  The purpose of the present investigation i s  three-fold: (^a) To learn the procedure of manufacturing polarized elements of barium t i t a n a t e .  (2) (b) To reproduce the experimental results of other workers; to investigate i n more d e t a i l -the phenomena of spontaneous p o l a r i z a t i o n , f e r r o e l e c t r i c i t y , and p i e z o e l e c t r i c i t y ; and to consider the use of barium titanate ceramic as the active element of an electro-mechanical transducer. (c) To attempt a t h e o r e t i c a l explanation of the phenomena involved.  (?)  II  FERROELECTRICITY  In 1912  Debye postulated the existence of permanent e l e c -  t r i c dipoles i n molecules which have no centre of symmetry.  Such dipoles  he argued, are bound to a r i s e when two atoms of d i f f e r e n t electron a f f i n i t i e s combine, the electron clouds being displaced towards the nucleus having the higher binding energy.  I f we place such a material  i n an e l e c t r i c f i e l d , the dipoles w i l l obviously tend to a l i g n themselves i n the d i r e c t i o n of the f i e l d .  I t can be shown, however, by the method  f i r s t used by Langevin f o r the case of magnetic dipoles, that unattainably high f i e l d s would be required to produce an appreciable.degree of alignment'. Many years e a r l i e r , i n I8y0, Mosotti had developed an expression f o r the l o c a l l y acting f i e l d within a polarized d i e l e c t r i c , but despite the implications of a combination of these two ideas, i t was  not  u n t i l quite recently that the phenomenon of f e r r o e l e c t r i c i t y , involving the 8pontaneouBlalignment of e l e c t r i c dipoles, was  discovered, or even  suspected. We s h a l l f i r s t outline the Debye-Langevin theory, and de— 1 velop i t to the point where we can predict such a spontaneous alignment.  (4) 1.  Analogy to Theory of Ferromagnitism Consider a group of N e l e c t r i c  absence of any external f i e l d .  dipoles of momentyc*. i n the  The dipoles w i l l be randomly oriented  owing to t h e i r thermal a g i t a t i o n , and the average dipole moment,^ , of the group w i l l be zero.  Now i f we apply an external f i e l d , E , i t can  e a s i l y be shown that the potential energy of each dipole, due to E, i s given by  ^ £f  i c V 9 • </&  yu£(\-<i#i^  where &  (1)  i s the angle between^, and  .  There w i l l be a tendency f o r  the dipoles to a l i g n themselves i n the d i r e c t i o n of the applied f i e l d , i . e . to reduce 0 , and therefore the potential energy to a minimum, but t h i s tendency w i l l be counteracted by thermal motion, and i f we assume e q u i p a r t i t i o n of energy, we can use the Boltzmann d i s t r i b u t i o n function to calculate the number of dipoles,  per unit volume having an angle  6 with E. We get  •  .  •  .  ('-co*®)Ar  ,  where k i s Boltzmann's constant, T i s the absolute temperature, do* i s an element of s o l i d angle, A i s a proportionality f a c t o r . We can put  d<^> - m  5<VP cl&  a^-cC  I. ^cos&.fie^  Y '. ws**e<to ki  rt  () 2  bo face paqp  (5)  f\e  ft  •  y  st~e  4e  =. number of dipoles per unit volume.  Then  /-—  ^ Putting  e  =• —=i  (2 =y—~  /  k  ' .  -i an* integrating; we get the, r e s u l t that  —  a  -a  _  e  +e  =  a  a  i  -  i  Slotting the r a t i o of f i e l d energy to thermal energy,  Q_ =  » as abcissar and the: r a t i o of the average dipole moment to  the i n d i v i d u a l dipole moment,/^ , as ordinate, we get. the curve shown in. Fig.1, which, f o r small  a  ( i . e ^ E * * * 0 approximates to /5« a  Now  take, f o r example, yU. - 1 x. 10"^ esu cm.,,' of. the order of magnitude we would expect, and require a very low value, of. 0.01 tor/~  , corres-  ponding to a = 0.0J. We would require  di  1200 esu / cm. or. 5.6 x 10^ v o l t s / cm. at 20°C. r  This derivation can be considered  correct only f o r  completely free-dipoles, as approximated i n the case of a gas, and i t i s seen that the p o l a r i z a t i o n w i l l be extremely low f o r ordinary  (6) temperatures and permissible f i e l d s .  In a s o l i d , however, the interact-  ion between each dipole and i t s neighboring dipoles must be considered. It i s apparent that the e f f e c t w i l l be to increase the f i e l d w i t h i n the medium i n the way suggested by Mosotti.  The following theory,is outlined  as an analogy to the Curie-Weiss theory of ferromagnetism. Let  us represent the f i e l d within our d i e l e c t r i c by  -  £i  €  +X P  where P i s the p o l a r i z a t i o n per unit volume produced by the applied f i e l d , E, and i s given by ^ y y Z T , and \ . i s an unknown f a c t o r defining the  contribution by P to the t o t a l internal f i e l d .  _  iP— - -  rt-lL a- -  <?olU  I  J-  where  w h e r e  From ( j ) *  /-> ~ <2i =  X H ^ L '  and again f o r low f i e l d or high temperature^**,(ti <^ L l ) we get  or  Now  %— .  "X  3  must have the dimensions of temperature.  Then say  T-TX  3  3k(T--T~ )  ~  /VC  c  -i— _  /v^i"  (7) and y(_ may be a function of T, E, and the h i s t o r y of the sample i n the case of a f e r r o e l e c t r i c material. Now p l o t  ' a g a i n s t I as i n Fig.2, and the r e s u l t i s a  straight l i n e of slope  ^ (<  o -  (10)  So f a r we have used the approximation (6) high temperature or low f i e l d .  f o r the case of  For normal temperatures we must use  (5)  where  k I Solving f o r P and dividing by  Now From (5)  v\  ( F i g . j ) plot ^ ^ a g a i n s t  <Z- from. (11) and from C  1/5.  we get a curve s i m i l a r to F i g . l with an. i n i t i a l slope of  From ( l l ) we get a series of straight l i n e s of constant T. the case f o r E  =  0,  we recognize immediately, the  eous polarization^below a c r i t i c a l temperature> tangent to the curve of (5)'at the o r i g i n .  Taking f i r s t spontan-  p o s 8 i b i l i t y ; o f  T. Q  The i T  (5).  2  T  Q  line i s  At any temperature below T , G  the value of the predicted spontaneous p o l a r i z a t i o n i s given bytthe i n t e r cept of the two curves,, as shown.  There are, of course, two intercepts  i n each case, but a consideration of the free energy i n the two possible, stable conditions indicated shows, a much higher p r o b a b i l i t y f o r the upper one, and i n every case we may neglect the intercept at the origin.. Above T  Q  the curves do not intercect and we expect no p o l a r i z a t i o n .  (8) The slope of the T_ l i n e i n F i g . 3 i s  " • ^ Therefore  T~  2^ .  (12)  1  and We a r r i v e at the same value as before f o r the high temperature case, ( 9 ) . From (10) and (12) we now get  A  -  (  1  5  which can be evaluated experimentally from a knowledge of the d i e l e c t r i c constant, € , above the c r i t i c a l or Curie temperature, and the known r e l a t i o n that  <f-/  A. "  TTTr-  (14)  Let us now consider i n p a r t i c u l a r barium t i t a n a t e (BaTiO^ ) the simplest of the known f e r r o e l e c t r i c materials i n i t s c r y s t a l s t r u c ture.  The unit c e l l of the barium t i t a n a t e l a t t i c e i s of the "pervos-  k i t e " form, consisting of a single titanium ion (T1 "'" ) surrounded <  M  symmetrically by eight barium ions (Ba*"*") on the corners of a cube, and six oxygen ions ( 0 ~ ) centered on the faces of the cube, (see. Fig.4)..  By  X-ray study the edge of the cube has been found to be yery^nearly 4 R. The radius of an oxygen i o n i s approximately 0.64 R .  1.J2 £  and of a Mtaniumeion  I t i s seen (Fig.^) that the titanium ion has a freedom of move-  1  )  (9) ment of at l e a s t 0.86 A i n any d i r e c t i o n without coming i n c l a s s i c a l 3  contact with another i o n . Techniques have recently been developed by which single crystals of barium titanate can be grown up to several millimeters i n s i z e , and i t has been demonstrated by a number of workers 1»2) that the barium titanate l a t t i c e i s a pure cubic structure above a c r i t i c a l temperature of about 120°0, which we have already referred to as the Curie temperature.  As the temperature i s lowered through this Curie point,  the l a t t i e e stretches along one of i t s cubic axes into a tetragonal font. In the tetragonal phase, X-ray study ^  shows the titanium ion to be d i s -  placed from the centre of the l a t t i c e , i n the d i r e c t i o n of one of the oxygen ions, by a distance which varies with temperature and reduces to zero a t the Curie point.  At 20°0 the displacement i s approximately 0.16 A . 3  Under these conditions each unit c e l l of the l a t t i c e becomes a permanent e l e c t r i c dipole, and as soon as a number of adjacent dipoles become l i n e d up i n the same d i r e c t i o n , whether by an external f i e l d or thermal a g i t a t i o n , an i n t e r n a l f i e l d of the Mosotti type i s set up, which spreads as more dipoles f a l l into l i n e .  Thus the entire c r y s t a l  would develop a spontaneous p o l a r i z a t i o n , P, per u n i t volume, and under controlled conditions c r y s t a l s have been made to do so.  Under normal c i r -  cumatances, however, due to impurities, or to other factors not f u l l y understood, the c r y s t a l usually breaks up into polarized domains with t h e i r p o l a r i z a t i o n vectors, P, oriented more or less at random to eachrother so that the resultant o v e r a l l p o l a r i z a t i o n of the c r y s t a l i s very  (10) low. Much study '3>4, and o t h e r s ) 2  h a B  b  e  e  n  g  i  v  e  n  t o  t  h  e  f  o m a  tion  and behavior of these f e r r o e l e c t r i c domains, but since the present work i s concerned with p o l y c r y s t a l l i n e barium titanate ceramic rather than with single crystals,, we are not d i r e c t l y interested here, a l though we s h a l l have reason to mention the subject again l a t e r . There are two other phase changes at approximately  5° Gand -70°0 to which some study has been given 5*6)  w  e  s  h ].l a  confine ourselves to the tetragonal phase and the temperature region of the cubic phase immediately above the Curie point. Now,  applying the foregoing theory to barium titanate  we f i n d experimentally that Tf l i e s between 120 and 125° C, and we c  ;have the empirical r e l a t i o n  developed by Jonker and van Santen ^ ) . lead to a value f o r A of 0.05.  These experimental values  Then from (12) we get 3 k To  and from X-ray measurement we have  a = 4 x 10  dimension of the u n i t c e l l of the l a t t i c e .  V\ = 1.56 x 1 0  2 2  cm. where a is,the  Thus by c a l c u l a t i o n  and yt»* = l4.4 x 10" . 18  If we take the displacement of the titanium i o n as  0.16  at room temperature as observed by X-ray d i f f r a c t i o n , and assume that, the oxygen i o n moves an equal distance to meet i t , the dipole moment  f  (11) would be  6 x 4.8 x I O  - 1 0  x 0.16  x 10"  8  =  4.6 x  =  4.6  IO  - 1 8  debye units.  We wimA4 see that our theoretical value fory^. i s too large by a factor of 5*  We would, i n f a c t , expect i t to be too large  since  we have attributed the entire p o l a r i z a t i o n to the displacement of the ions, whereas i t i s actually due, atomic p o l a r i z a t i o n .  i n part, to electronic  However, we would hardly expect the  to be as great as indicated.  and  difference  In order to correct f o r t h i s error,  we would have to know, i n d e t a i l , the configuration  of the  field  within the l a t t i c e , and: even i n such a comparatively simple l a t t i c e ^ as barium titanate, the mathematics involved turn out to be formidable.  Either assumptions and approximations must be made which  probably render the r e s u l t useless, so involved  quite  or else the mathematics become  as to be p r o h i b i t i v e .  Continuing, i f we assume a l l dipoles to be i n one d i r e c t i o n , we obtain from our theory a saturation  directed polarization  5) Hulm  has  experimentally measured the spontaneous  p o l a r i z a t i o n , S, of a single c r y s t a l of barium titanate at 20-  G  (12)  S a 16 x IO" " coulombs / cm. 0  2  Now, i f on Fig. J, we plot the line corresponding to 20°C we read a P value of 0.60 for  , which, for zero external f i e l d , is the  ratio of spontaneous to saturation polarization. gives us  Thus our theory-  A A S = 0.60 x 75 x 10~° = 45 x 10~° coulombs/cm.  2  which is greater by a factor of almost J than the experimental value. This difference is attributed, at least in part to the effect mentioned above and to the fact that there is no apparent justification for assuming that our value for A , calculated from data observed above the Curie temperature, should hold below the  Curie temperature with  a modified crystal structure. 2.  Theory of Mason and Matthias A somewhat more elaborate theory i s due to Mason and 8)  Matthias  who consider a model of the barium titanate lattice as  shown in Fig. 15. It is assumed that the titanium ion forms a covalent bond with one of the oxygen ions and is displaced from the centre of the lattice in that direction.  Above the Curie temperature,  the thermal energy: is sufficient to cause any one of the six positions to be equally: probable and, from X-ray measurement, the cell appears to be cubic.  Below the Curie temperature the thermal energy is no  longer sufficient to cause each position to be equally probable and the displacements of adjacent ions tend to litie up spontaneously as:  (13)  previously, described.  A dipole moment develops i n the direction of  displacement, and the crystal becomes ferroelectric,, and,, since the unit cell has now lost i t s centre of symmetry,., i t also becomes piezoelectric.  The axis in the direction of the displacement: becomes  longer, and the crystal assumes i t s tetragonal form. Suppose,, now, that, a l l the minima of Eig. 15 have i n i t i a l l y the same value... Then apply an external f i e l d , E, along the Z-axis, say. An internal f i e l d will be produced, as before, given by where now we consider P to be made up of P due to electronic and e  atomic polarization and  due to the displacement of the titanium  ions.  (£ +. \  or where  Thus  £. *  K  +. O^ t  G *Aft .1 - \l  =  (15)  is the polarizability per unit volume due to a l l causes  except the titanium dipoles.  X can be determined from the dielec-  t r i c constant,. €, measured at low fields and at very low or very high temperature where Pd is not effective.  4tp Thus  ~ - s -K.—  •  £"  Under these conditions e  -i-M  and from a measured value of 550 for <?o (  '  •« /'+ \(^7.a)  (16)  (14) The internal f i e l d causes an increase i n potential energy at minimum 2 equal to  where Ax A>% & =  /^+.\P \  _  , i n which 4e » charge on Td ion  /  r 0 = displacement from centre of  and a s i m i l a r decrease at 1.  lattice,  The potentials of the other four minima  remain unchanged. We then apply the Boltzmann d i s t r i b u t i o n function i n  - O^yx  the usual way and put..  where K  (  and  Y\  numbers of titanium ions per unit volume in. minima 1 and tively.  ,  2"respec-  /r-*\PITT  U7)  Nov? consider the condition for, spontaneous p o l a r i z a t i o n .  <~r-  E^";= 0 and a »  aP  P  Q  (18)  kT  equation (17) becomes  ——  Setting  —-  l -  Eor  are the  Thus we derive the r e l a t i o n f  i n which  x  x+ ~*  #  i i ss d i f f e r e n t from zero only :f o r values of c a n  Cl9)  A  ^-5  have positive:.-or negative values between  zero and one, corresponding to spontaneous p o l a r i z a t i o n along the positive or negative Z-axis.  Here, of course,, i n the absence of  external f i e l d , the Z-axis may be chosen i n any one of the possible six  directions.  .  (15)  From (18) we get T^. »  ^- •  '(jZ^)  w  h  i  c  h  i  e  /  the same, expression we had before with the a d d i t i o n a l factor - — r ~ r / - A o  to. correct f o r electronic and atomic p o l a r i z a t i o n . Y \  i s now eliminated from a knowledge of  £  0  ^ and,  i s evaluated,, as before, by experimental measurement of £ above For barium titanaterwe get. A. = 0.124 which leads  to a value f o r the dipole moment of yU.  = if.344x I O  -18  -  esu  cm  which agrees quite well with,the experimental value of 4.6; x.. 10" as derived from X^ray data.As before we get. a value f o r saturation p o l a r i z a t i o n  For 27^ 0JMason and Matthias calculate  ——  => 0 . 0 0 =  —  Then S = 61,000 esu  = 20.5 x IO"""•-'coulombs/cm. 0  2  which i s greater by a factor of approximately 2 than t h e i r experimental value of 11.8 x 1 0 " . 6  In correcting f o r the atomic and electronic p o l a r i z ation, t h i s theory: approaches more .closely to the' true s i t u a t i o n . However the two l i m i t a t i o n s remain that.' ' (a)  There i s no apparent reason to expect the value, A,  same above and below the Ourie temperature.  to be:, the  There i s , however,, no  (16)  simple means of obtaining a value for \  in the temperature range  below U Q . (b)) The value of A  would be expected to vary considerably,  depending on the configuration of changes in the immediate neighborhood of the point in question and will vary from.one point of the lattice to another.  Owing to the complexity of the mathematics,  however, we are forced to assume a constant value.  ?  .  •  •  •  (17))  III:  1.  EXPERIMENTAL PROCEDURE..  Preparation of Samples After some experimentation, a manufacturing procedure  very similar to that used by von Hippel and his co-workers at the  9) Laboratory for Insulation Research, M.I.T>.  , was adopted.  The  dry barium titanate powder, obtained from the Titanium Manufacturing; Company, is pressed in a steel mold into cakes 1 inch in diameter and approximately 3 / l 6 inch thick.  Pressures varying from 1000 to  20,000 psi were tried and i t was found that, over this range, results are almost independent of pressure except that at very low pressures the cakes are weaker mechanically and d i f f i c u l t to handle without damage, and at pressures above about 6000 psi the powder tends to compact diBContinuously (as a snow-ball packs) and cleavage faces develop which are indiscernable at the time but: show up after f i r i n g . A pressure of 5000 psi was used for most of the samples made. The cakes are thgn stacked 5 f o i l separators in a small crucible.  o r  6" high with platinum  The following firing cycle  was found to be most satisfactory and was used throughout the ex-  (18) periments: (a)  Increase temperature at a rate- of  100°© per hour from room  temperature to 1350°G"i (b) ) Hold at 1550°0 f o r six hours. (c)  Qool at the cooling rate of the furnace.  I t takes about 43  hours to reach.a temperature 10°0 above room temperature. Prepared i n this way the samples are homogeneous and vitreous and have very good mechanical properties.  Some of the f i r s t  samples prepared had very small blow holea throughout t h e i r volume. These, however, were e n t i r e l y eliminated i n l a t e r batches by s i f t i n g the powder through a 200 mesh per inch screen d i r e c t l y into the mold. In f i r i n g the samples shrink to about 7/8 inches i n diameter. to 4 mm.  The two faces are ground f l a t and the thickness i s reduced with carborundum powder i n water on a plate glass surface.  The faces are then polished.in a similar manner with very f i n e a l undum powder. Electrodes are applied to one or both faces by painting with DuPont s i l v e r paste No. 4351 which i s baked on i n another short heating cycle at.600°G.  A l/32 inch wide s t r i p around the edge i s  l e f t unpainted i n order to reduce the tendency to. break down e l e c t r i c a l l y over the surface during the p o l a r i z i n g process.  Flexible  leads about 6 inches long are soldered to the s i l v e r electrodes. (See F i g . 7)  .o~:  :  (19) 2.  Polarization The samples are polarized i n a d i r e c t i o n perpendicular  to t h e i r f l a t faces by the a p p l i c a t i o n of a high DC f i e l d i n that direction.  The power supply used to supply the DC f i e l d i s described  i n Appendix A. A simple device ( F i g . 8),was made to hold the sample between two bakelite discs with a l i g h t pressure applied by springs,, while the p o l a r i z i n g voltage i s applied between, the electrodes. In the case of the samples with only one s i l v e r electrode, one of the bakelite discs i s replaced by one of brass, ground and polished to a smooth f l a t surface to make good contact with the surface of the sample. At., f i r s t some d i f f i c u l t y was experienced with sparking over the edges or electrical.* breakdown through the sample at. voltages:, of about 5000 v o l t s .  With the following precautions, however, the  voltage can be successfully raised to"16,000 or a f i e l d strength of 40,000 v o l t s per centimeter without breakdown: (a)  The entire assembly, including holder and sample i s placed i n  a bath of transformer o i l . (b)  Before applying the voltage the sample i s heated i n the o i l  bath to 120°C f o r 10 or 15 minutes i n order to remove any  moisture  which might be absorbed by the sample. The o i l bath i s also used as a means of c o n t r o l l i n g the temperature of the sample during p o l a r i z a t i o n .  (20) Details and variations of the p o l a r i z a t i o n procedure w i l l be discussed under " Results" . ::  3..  External F i e l d The external f i e l d of the polarized sample i s measured  q u a l i t a t i v e l y i n the following way.  A sample with only one plated  electrode i s placed i n a horizontal p o s i t i o n with i t s exposed face up.  A mechanical device ( F i g . 9) i s used to raise and lower a brass  electrode from contact with the sample to a maximum spacing of about 3 cm. where, i n a l l cases, the field.has dropped to an unmeasurably low value.  The two electrodes are connected through a b a l l i s t i c g a l -  vanometer or an electrometer, and deflections are observed as the spacing between the removable electrode and the sample i s v a r i e d . See F i g . 12(b) and ( c ) . Results obtained by t h i s method have not been so usef u l as had been hoped.  Quantitative measurements have been quite  impossible due to leakage of surface charges, probably through a t h i n layer of absorbed moisture on the surface of the sample, and due to n e u t r a l i z a t i o n of the surface charges by ions i n the a i r .  To obtain  r e l i a b l e quantitative data i n this way, the sample, should be enclosed i n an evacuated chamber, and t h i s has not been attempted. some q u a l i t a t i v e remarks are made under " "Results" . :i  However,  rvt  6C?  /v  a n a c  3ok <?3 5 rvic  t t<y o r e to  O  0.5  p ie  (21)  4.  Hysteresis Loops. The. c i r c u i t , of F i g . 10 i s used to display the ferro--  e l e c t r i c hysteresis loop of the samples under varying conditions, on the screen of an-oscilloscope.  Some of the loops: have been photo-  graphed and are reproduced i n F i g . 15.  For these experiments, the  sample i s supported i n an o i l bath i n the same way as f o r p o l a r i z a t i o n , and, as well as preventing breakdown over the surface of the sample, the o i l bath again acts as a means of c o n t r o l l i n g the temperature of the sample.  By means of the.variac, the voltage across the sample  can be varied from zero to about, of  6000 v o i t s RMS a t the l i n e frequency  60 c/s. In F i g .  10, the resistance divider,  R].R2*  provides a  l i n e a r horizontal sweep, proportional to the applied voltage.  The  capacitive divider, C i C , provides a v e r t i c a l d e f l e c t i o n proportional x  to the displacement,  of the sample.. Gj_ i s a paper capacitor and  i s assumed to be l i n e a r over the range of voltages  involved.  serves only to prevent:.a s t a t i c charge from building up on the upper v e r t i c a l deflection plate.  The resistance, R, was added to damp out  shocked o s c i l l a t i o n s i n the secondary of the transformer.-  Various  values up to 50*000. ohms are used under d i f f e r e n t conditions. necessity f o r this addition w i l l be explained  later.  The  (22)  IV.  1.  N  EXPERIMENTAL  RESULTS:.  Composition It i s knovm 9) that small quantities of other titanates  i n dilute solution i n barium titanate have pronounced effects on the d i e l e c t r i c constant, the Curie temperature, the degree of p o l a r i z a t i o n , and other c h a r a c t e r i s t i c s .  Most substances are found to lower the  Curie point and decrease the d i e l e c t r i c loss, making the r e s u l t i n g mixture more suitable as a d i e l e c t r i c material than pure barium t i t a n a t e . Lead titanate, on the other hand, i s found to r a i s e the Curie point and increase the area of the hysteresis loop with a r e s u l t i n g higher remanence and higher coercive force.  The remanence, i s also found  to be more t r u l y permanent than i n the case of pure barium t i t a n a t e . For use as a p i e z o e l e c t r i c material, i t i s , of course, desirable to obtain as high and as permanent' a remanence as possible, since the p i e z o e l e c t r i c c o e f f i c i e n t s depend d i r e c t l y on the remanent., p o l a r i z a t i o n . To this end some experiments were  doTte  with barium t i t a n a t e .  A reasonable homogeneous mix of the two powders was obtained-by placing them i n a small b a l l - m i l l f o r several hours.  (23))  .  Only two mixtures - 2.3% and 10% lead were t r i e d and compared with pure barium t i t a n a t e . Samples containing 2.5% lead t i t a n a t e showed both remanence and coercive force greater by a f a c t o r of about 2 than;samples of pure barium t i t a n a t e under equivalent conditions.. They are found to saturate a t . a lower f i e l d and to require a shorterp o l a r i z a t i o n , time.  The remanent p o l a r i z a t i o n a l s o shows a greater  permanence than;in the case of pure barium t i t a n a t e . : At the end of the maximum period of observation - about 6 weeks - the p o l a r i z a t i o n of the pure barium t i t a n a t e i s s t i l l observed to decline at a very slow r a t e , whereas the 2.5% mixture appears to have reached a constant, value.  A.much longer period of observation w i l l be required however  before a statement can be made about.the long, term permanence of polarization.  The 10%imixture does not appear t o be s i g n i f i c a n t l y -  d i f f e r e n t i n c h a r a c t e r i s t i c s from the 2.5% mix, and i t . i s concluded that: the percentage of lead t i t a n a t e i s not c r i t i c a l within, quite broad l i m i t s .  However it.does show a higher c o n d u c t i v i t y and lower  d i e l e c t r i c strength above the Curie point and f o r t h i s reason most of the experimentation  was done^with: pure barium t i t a n a t e and a 2.5%  s o l u t i o n of lead t i t a n a t e . No f u r t h e r experimentation out i n t h i s d i r e c t i o n s  was,, c a r r i e d  (24) 2.  Polarization In general, three polarizing procedures were tried. (a) . The polarizing voltage of up to 16,000 volts was merely applied  across the sample at room: temperature and maintained- for periods varying up to one. hour.  The resulting polarization was found to be  very low and from the results of later observations i t is believed that i n order to reach anything approaching saturation polarization, in this way, the voltage would have to be maintained for days, at least.  It appears that, before the spontaneously polarized domains,,  of which the crystals are composed, will align themselves to any degree with an applied field, they must f i r s t be "loosened" by heating or by application of a high AO voltage. (b)  The polarizing voltage is applied at room temperature and is  maintained at about 10 Kv while the temperature of the sample is slowly raised to above the Gurie temperature and lowered again. While above the Curie point, the voltage should not be raised above this value because at highu temperatures the conductivity of the material increases and i t s dielectric strength decreases and there is danger of electric breakdown. When the temperature has been lowered again, however, the voltage may be increases to 15 or 16 Kv for a short time before the end of the polarizing cycle.  The best results, i.e. the  highest and most permanent, remanence, have been produced by this method. (c) An AC voltage of J-4 Kv is applied to the sample and the hysteresis loop is observed.  The sample is run through a temperature  p  •to face page %y  (25) cycle as before u n t i l a maximum value of remanence i s observed. The AG; i s then removed and a W. p o l a r i z i n g voltage of perhaps 15 Kv, immediately applied.  In the cases t r i e d the DG voltage was l e f t on  f o r only about 5 minutes and results were not so good as i n ( b j ) above.  A longer application of the p o l a r i z i n g voltage might produce  better r e s u l t s , because, as observed i n a number of other experiments,, i t appears that once the dipoles have become "used" to behaving i n one fashion, i t takes minutes and sometimes hours to adapt themselves to any sudden.change.  No further investigation was carried out. A  study of the phenomena involved here could, i t s e l f , be the subject of an entire paper., By projecting backwards the f i n a l slope of the hysteresis loop at saturation, as i n F i g . 11,  from the equivalent v e r t i c a l de-  f l e c t i o n voltage, v, of the P intercept, P , and from the c i r c u i t B  constants, of F i g . 10., and the area, a, of the electrodes on the sample we get the expression P  s  = G-^v/a microcoulombs/cm. where  2  i s i n microfarads, v  i s i n volts  a  is- i n cm.  2  x  10"^  coulombs/cm. at a f i e l d of 20 Kv/cm. after heat treatment.  This  In this way we measure a "saturation" 2  p o l a r i z a t i o n of 5>5  &e no y/eG ipie  *~ 1  T  +  +  T +  7 c?/ecf  r o d e  or  to)  Cc)  ( b )  Fx'j o Fb(oxln<i.i c'o rt  is tic- C^al ^/a/i o ot e "fcr £~fec i r o ^ ^ e r  /2 ir?o oess  (26) is in close agreement with,Hulm's: ^) value.of 5»3  x  10"^ for poly-  crystalline ceramic. As. Hulm points, outi; however,; i t is.probable that.a ceramic: sample is s t i l l far from truly/saturated at this field.. The 2»5%' lead titanate mixture saturates more easily and gives a value of about 8 x 10  : .coulombs/cm. under the same conditions,,  (This seems reasonable compared to the value reported by a number of. workers of about 16 x 10" 3.  for a single domain crystal.)  External.. Field; The external.field of the samples is determined as  described under "Experimental Procedure"".  For reasons previously  stated, no reliable- quantitative results have been obtained, but. the following remarks are made. We first:polarize the sample as in Fig. 12(a), and we assume that the dipoles align themselves as shown.. Removing the polarizing voltage and connecting a b a l l i s t i c galvanometer as in Fig. 12(b) we measure a steady discharge current (electron flow) of the order of 0.01 x. 10"^ amperes: in the direction of arrow #2.  This  current decreases exponentially to an unmeasureable value over a period of 2 or 3 days, and is assumed to be due to a relaxation of some, of the dipoles.  As the polarization of the sample decreases,  some of the induced charge oh the electrodes is released and/ippears as a discharge current in the external circuit. How we remove the upper electrode completely out, of  (27)  range of the external f i e l d of the sample.  At: f i r s t i t was. expected  that the induced charges on the electrodes would, be released and would neutralize each other through.the external circuit, causing a current, again in the direction of arrow # 2 .  A current in the direction  of arrow #1 was expected when.the electrode was replaced.  As observed,  however, these last two deflections actually occur in the opposite directions.  ^ Hie theories advanced  to explain similar phen-  omena in wax: electrets cannot be applied here because,, in most, cases,; they assume a migration of ions in the molten wax under the influence of'the polarizing f i e l d .  In our case the ions are tightly bound, in  the lattice and cannot be assumed to migrate at,a rate fast.enough to explain the observed phenomena. The following explanation is offered. Under the influence of the high intensity polarizing f i e l d , some electrons may; "soak" into the dielectric: from the negative: electrode and become trapped i n the lattice, forming a negative, surface charge.  A similar positive surface charge may be formed on the  other side, and in the interior the dipoles would s t i l l be oriented as expected.  Now when the polarizing voltage is removed these.sur-  face charges remain and induce an external f i e l d in opposition toe. the f i e l d of the dipoles.  If we assume the f i e l d of the surface  charges to be greater than the f i e l d of the dipoles (Fig. 12(c)) the directions of the deflections would then be as observed.  (28) The only piece of experimental evidence in support: of this theory is that, the removal of, the surface layers of the sample decreases the observed external f i e l d . off the faces after polarization.  This was. done by grinding  On: one occasion, also,, three pieces  of titanate were polarized in series. Then assuming a l l of the surface charges-to be on the two outside pieces, i t . was thought: that the centre piece alone might: give,deflections in the opposite directions.. This was. actually not observed, but: the deflections caused by the centre piece were unobservably small, while i t s polarization was  ap-  parently j u s t as high as that.of the outside pieces which-produced high deflections. This indicates that the phenomenon is at least partly one of surface charges, and i t may be that, owing to the finite conductivity of the titanate, the charge penetrates, with reduced intensity,., into the interior of the sample.  In the final steady  state, reached some days after polarization,, i t is assumed that.this charge reaches an equilibrium with the:field of the dipoles. Under these conditions then, the observed external f i e l d should be a relative measure of the polarization, and from measurement; of piezoelectric, voltages,, i t appears that this is approximately true. 4.  Hysteresis The remarks concerning the size and shape of the :  hysteresis loops observed for different-mixtures andunder different, conditions w i l l not be repeated here.  (29) P  Eig. 1J illustrates the variation with temperature^  of the hysteresis loop of a new sample containing 2.5$:lead titanate, at a constant peak AG) f i e l d of 12,000 volts per centimeter.. The upper limit of the ferroelectric: range is clearly observed at., about 120°G.  The fact that the hysteresis curve appears to open out. again  above this point is misleading.  This is not a true hysteresis loop,  but is caused by a phase shift introduced i n the C^G network of X  Fig. 10 by greatly increased^conductivity of the sample at:high temperatures.  Et. is this phase shift,also, which makes the slope of the.,  resulting ellipse continue to decrease above the Gurie point. Actually this slope should remain constant, and equal to the slope of the f i r s t curve of Eig. 15> and. to the slope of the saturation portion of the; other curves where only the electronic and atomic polarization is effective and the dipoles do!notcontribute appreciably.  The necessity  for heat treatment in the polarizing cycle is clearly.seen by comparing: the curves at equivalent temperatures before and after the heating cycle.  Actually the i n i t i a l shape can be made to approach the final  shape without heating, but this requires unpleasantly high fields with danger of dielectric breakdown,, and long polarizing time. Ah: interesting effect was observed! and is illustrated in.Pig. l 4 .  It was found that, a t some temperatures and at some  value8 of applied f i e l d , the small hook seen near the tips of the hysteresis loop in Fig. l4(a), and expanded i n (b), appeared. In an effort to explain i t s appearance, the wave-form of the applied.  2T  fe> feee p a g e 3&  (?o) voltage (across AB: i n F i g . 10) was. checked and the form corresponding: to F i g . l4'£a);and (b) i s shown: i n ( c ) .  (Note: The f a c t that the  upper and lower halves of the cycle are not:symmetrical i s due to a non-linearity i n the oscilloscope sweep,., and i s not s i g n i f i c a n t ) . The following explanation, i s offered on a simplified, and purely c l a s s i c a l basis. Consider two of the s i x potential minima assumed to existtwithin the unit c e l l of the barium titanate l a t t i c e ( F i g . 15) to be i n l i n e with the applied f i e l d , and, f o r the present", neglect ;  the other four.  We represent a section through these two minima  graphically i n E i g . 16, and assume the. titanium ion to be a t . p o s i t i o n 1 as the AC) f i e l d increases: through zero:in the d i r e c t i o n indicated. Now we associate a displacement current with the horizontal motion of the titanium ion.  In a region around position 1 the motion of  the ion i s comparatively unhindered by the i n t e r n a l f i e l d of the l a t t i c e and i t i s free.to move.under the action of the applied f i e l d . During this part of the cycle the displacement.current i s large. At 2 the motion of the i o n i s slowed down by the central p o t e n t i a l hump, and the corresponding:;current i s small.  Having reached 3 with  the applied f i e l d , s t i l l increasing, the ion w i l l jump to p o s i t i o n 4 with.a r e s u l t i n g high pulse of current.of very short, duration.  The  ion w i l l then continue to move i n the d i r e c t i o n of 5-with a corresponding small current: u n t i l the peak of the applied f i e l d i s reached. Now the transformer used to provide the alternating  (3D ' f i e l d is of very high impedance and has poor regulation.  As the  load (i.e. the real current iri the external circuit, corresponding: to the displacement, current in the sample) increases,, the output, voltage of the transformer decreases, and vice versa. The output wave-form of the transformer on no load! (shown dashed on Eig.. l4(c))) is a reasonably good sine wave,, and i t is recognized immediately, that the distorted form is exactly as one would expect from the process described i n the previous paragraph.  The corresponding numbers on  Eig. l4(a) and (c) and Eig. 16 identify corresponding parts of the cycle.  The hook in the hysteresis loop is thus identified with the?  sudden.transition of a large group of titanium ions from, one potential minimumi to the other.  In: Eig. l4(c))the peak of the distorted wave  projecting;; above the undistorted form at 3? is  a n  overshoot caused  by the inductance of: the transformer. Attempts, so far, to calculate the height: of the central potential hump by the f i e l d at which this transition takes place, have resulted; in answers: which are too low by at least one order of magnitude. However the observed phenomena do appear to f i t the proposed theory-very nicely, in.a qualitative way, and further investigation of the effect mighttprove a useful means of increasing our knowledge off the process of permanent polarization..  O  W V W N A  c  £ < J U I  L/Q '^n T  o/-  Bar  (?2) 5.  " Barkhausen"  Effect  During the course of investigations i t was observed that on close inspectiontthe steep portions of the hysteresis, curve, marked ABiand GDI on Fig. 11, were of a different!: texture on the oscilloscope screen than the rest of the loop. No deflections were observed, but these portions of the curve appeared to sparkle, while the remainder was quite solid.  It was recognized immediately that,  this is exactly the part of the cycle where the Barkhausen effect i s observed in ferromagnetic materials, and that this might be.the electric equivalent, which, so far as the writer is aware, has not previously been observed i n ferroelectric materials., i  •  In order to check this possibility.,, apparatus was set up as shown in block form in Fig. 17.  A sample: containing 2.5%  lead titanate was used.. The amplifier has a low cut-off at about. 1000 c/ssand would therefore differentiate any discontinuities in the polarization curve, and we would see a pulse on the oscilloscope.. This,,in fact, was observed. As the large condenser,. G:, is slowly charged through the high resistance,.. R, pulses begin to appear at a field., of about: 5000 volts per centimeter at room temperature.  The amplitudes of the  pulses, appear to be randomly distributed over a range, of about 6 to 1.  Fig. I8(a),(b) and (c)) is a series of photographs taken as the  f i e l d was slowly increased. The oscilloscope was allowed to sweep continuously at 60 c/ssand the exposure in each case was l/lO second.  (3?)) (The negative overshoot following each pulse i s caused by the amplifier,)) It w i l l be noted, that at low f i e l d , small amplitude pulses predominate, and that there.is a very well defined minimum: ( F i g . 18(a));.  As we increase the f i e l d ( F i g . 18(b)) the proportion  of large amplitude pulses increases,, artd.it appears that there i s ah equally well defined maximum,., although an occasional pulse of much, higher amplitude (usually o f f screen) was observed but not, caught i h a photograph.  (Note: This series of pictures was taken a t 65°C.  and the range of amplitudes  ;  i s somewhat less than at room temperature)..  A t . s t i l l higher f i e l d ( F i g . 18(c)) the pulse rate increases very abruptly and almost a l l pulses are of the maximum amplitude.  Beyond  t h i s pointl the amplifier became confused and the resulting picture had the appearance of c i r c u i t noise.. Aa w i l l be seen i n F i g . 17, the sample i s completely isolated from any sources of noise, i n the charging c i r c u i t , andAt i s believed that this i s t r u l y an e l e c t r i c a l , equivalent of the Barkhausen effect.  I t can be further proven that the pulses are not due to  extraneous  causes by charging the condenser,, Q, and then completely  removing;the power supply. by leakage.  The pulses continue as & slowly discharges  Again, no quantitative investigation has yet been under-  taken,., but the following comments are made. The maximum and minimum pulse s i z e seems to indicate sharp l i m i t s to the permitted range of domain sizes.. The occasional very high pulse may be caused by an exact coincidence of two or more  normal pulses.  As the temperature of the sample i s raised towards  the Curie point, the amplitudes of a l l the pulses decrease, as would be expected from the:fact that the displacement; of the titanium ion i s known to decrease, and the pulses also become fewer i n number. Also, as the temperature i s raised, pulses can be observed, at lower; and lower f i e l d , , as would also be expected from the f a c t that the l a t t i c e i s known to contract-along i t s tetragonal axisj i . e . i t approaches more closely to cubic, and the height of the potential hump at i t s centre.-should decrease, while a t the. same time the thermal energy of the titanium ion increases and i t requires less additional energy to r a i s e i t over the hump.  Above the Curie temperature, where,  by the theory, the permanent dipoles and, therefore, the f e r r o e l e c t r i c ; domains have;; ceased to exist,, only a very few very small amplitude pulses are seen, and i t i s probable that i f the sample were maintained at a high temperature f o r an extended length of time, these also would disappear.  (35)  W  CONCLUSIONS  It i s d i f f i c u l t to state s p e c i f i c conclusions stage, since the results reported and are not e a s i l y condensed.  in  t h i B  at t h i s  thesis are mainly descriptive  I t appears, however, that the p a r a l l e l be-  tween f e r r o e l e c t r i c i t y and ferromagnetism can be carried even f a r t h e r than i n the theory outlined e a r l i e r , to include an e l e c t r i c of the Barkhausen e f f e c t , and i t . i s believed that valuable  equivalent information  on the f e r r o e l e c t r i c behavior of barium titanate could be gained by further study of the d i s t o r t i o n of the hysteresis loop attributed to the action of the titanium ions, and of the " Barkhausen " e f f e c t . Very l i t t l e has been said i n the foregoing pages about the o r i g i n a l intention of investigating the use of barium titanate as the active element of an electro-mechanical transducer. The investigations, however, indicate that i t should be at least as good as other known p i e z o e l e c t r i c materials f o r t h i s purpose, provided the long term permanence of i t s remanent p o l a r i z a t i o n can be demonstrated, and i t has, of course, the obvious advantage that i t can be moulded as a ceramic into any desired form and polarized i n any desired d i r e c t i o n .  (36)  REFERENCES  1)  H. Megaw  2)  P.W.  3)  C.C., D a n i e l s o n ,  Forsberg  Nature (Jr)  B.T..  l ^ L , 484 (19^5)  Phys. Rev, Matthias,  J6 , 1187 (1949)  J.M. R i c h a r d s o n  Phys.Rev.  J4. , 986: (1943)  4)  W.J. Merz  Phys. Rev. TJL*  5)  J.K. Hulm  Nature  6)  H.F. Kay, P. 7»busden  P h i l . Mag.  7)  C H . J o n k e r , J.H. v a n Santen. S c i e n c e  8)  W.P. Mason, B.T. M a t t h i a s  Phys. Rev. ] ± 1 6 2 2  9)  A. v o n H i p p e l  I n d . and Eng. Chem.  10)  A. Gemant  11)  F. Gutmann  (and o t h e r s )  R.S.I.  687 (19^9)  160 , 127 (1947) (7) 4<D »  1 0 1  ? (1949)  10£ , 632 (1949) (1948) 3j3 , 1097 (1946)  11 , 65 (l94o).  Rev.Mod.Phys.  20 , 457 (1948)  2 SI  1^ s Sealed in oil  500  •AW  10 k  0.001 h 0  o  f 10k' O.lyut  _  X  0-1500  r-  —< <  ! ^ 1  1  6  6  20 Fit}  %Jf€  19  Ki  (37)  APPENDIX A 1.  -  Auxiliary Equipment  Furnace The furnace used f o r f i r i n g the samples consists of  a 2" I.D. alundum tube 18" long, wound with a platinum heating element. The tube i s set i n a v e r t i c a l p o s i t i o n and packed i n a thermally i n sulating material.  During operation the ends of the tube are sealed  with f i r e b r i c k . The furnace temperature i s controlled by a platinum thermocouple i n contact with the alundum tube and coupled to a Wheelco Pbtentiotrol, Model 2J24l.  A maximum temperature of about 1500°C can  be reached safely,, and, with careful c a l i b r a t i o n the chamber temperature can be controlled to within plus or minus 2°0.  2.  High Voltage Supply The c i r c u i t of the high voltage supply, used f o r  p o l a r i z a t i o n of the sample, i s shown i n F i g . 19. By a combination of the two controls (the grid-leak resistance of the o s c i l l a t o r and the tuning of the tank c i r c u i t ) a range of voltages from 2 to 20 Kv can be obtained. The only remarkable feature of the c i r c u i t i s the r . f . transformer which i s of a common type often used i n t e l e v i s i o n receivers and designed f o r an output of 3 or 4 Kv. I t was found that t h i s could  (38) be raised s l i g h t l y but that r . f . breakdown occurred at 5 or 6 Kv. The transformer was  therefore sealed i n i n s u l a t i n g o i l i n a l u c i t e  container, and has been successfully operated at 12 Kv.  A conven-  t i o n a l voltage doubler i s used to r e c t i f y and increase this to 20 Kv/.  

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