Relaxor Ferroelectric-cross

5Relaxor FerroelectricsL.E.Cross5.1IntroductionIt is interesting to note that as with almost all initial advances in the study of ferroelectric oxides the impetus for studies of relaxor ferroelectrics stemmed from early work on polycrystalline ceramic systems.In the case of the relaxor ferroelectrics,the advance originated from studies in Professor Smolensky’s group at the Ioffe Institute in Leningrad(now St.Petersburg)on perovskite structure electroceramics of complex composition.Originally classified as fer-roelectrics with diffuse phase transitions,it slowly became clear that the very high dielectric maximum being highly dispersive could not mark a classical ferroelectric phase transition.Now,following studies at Penn State University, the suggested designation as relaxor ferroelectrics has become internationally adopted.The name is nicely compact and does highlight two key features, the combination of massive dielectric relaxation with almost classical lower-temperature ferroelectric response.Over the last20years there has been an explosive growth of interest in the topic.Not surprising perhaps,as relaxor studies combine a focus on materials with properties of very strong practical importance,but underpinned also with challenging fundamental considerations,a nearly ideal mix for current applied research funding.The current,very high level of interest is nicely reflected in a recent excellent review by G.Samara“Ferroelectrics Revisited: Advances in Materials and Physics”[1],which devotes some30%of the text to the topic of relaxor ferroelectrics.In this short chapter,the focus will be upon the relevance of relaxor studies to the basic understanding of elasto-dielectric transducing functions in oxide ferroelectrics.Early realization of the importance of relaxor ferroelectrics for transducing structures came with the exploration of the large,stable electrostrictive strains that could be controlled in lead magnesium niobate(PbMg1/3Nb2/3O3) (PMN):a Smolensky group discovery[2]that has became the prototype for perovskite-structure relaxors.The utility of this ceramic was highlighted132L.E.Crossby the incorporation of PMN-based multilayer actuators to drive remote-controlled tilt mirrors in the replacement wide-field and planetary camera II of the Hubble Space Telescope.These PMN tilt mirrors permitted ground control to makefinal,precise alignment of the corrector optics required to compensate for the original primary mirror problem and bring the Hubble to its present fantastic performance.Relevance of the relaxor ferroelectric studies to the deeper understanding of the strong piezoceramics in the lead zirconate titanate(PZT)family,which still underpin all most important electro-elastic transducer applications,is further clarified by discussion of the relaxor fer-roelectric lead titanate solid solutions which incorporate morphotropic phase boundaries(MPBs),where,unlike the PZTs,respectable single-crystals can be grown and the orientational behavior of the intrinsic elasto-dielectric prop-erties fully studied.5.2Relaxor Ferroelectric CompositionsRelaxor ferroelectric properties occur in a number of perovskite and tungsten-bronze structure compounds and solid solutions.In perovskites,the properties to be described are most often associated with mixed cations of different valen-cies occupying one of the lattice sites in this ABO3structure.Typical examples of A-site substitutions are bismuth strontium titanate,(Bi2/3x Sr1−x)TiO3,and lead lanthanum zirconate titanate,(Pb1−x La2/3x)(Zr y Ti1−y)O3(PLZT),and for the B-site substitution the compounds lead magnesium niobate,(PbMg1/3 Nb2/3)O3(PMN),and lead scandium tantalite,Pb(Sc1/2Ta1/2)O3(PST).It should be noted that in the A-site system x must be above a critical value for the relaxor properties to be manifest.In the tungsten bronze structure,which is much more open than the per-ovskite,aliovalent cations are not necessary,and typical examples are the solid solution barium strontium niobate,(Ba x Sr1−x)Nb2O6,and lead barium niobate.Neither barium nor strontium forms a stable bronze,but in solid solution in the range0.25<x<0.6relaxor properties occur,while in lead barium niobate,Pb1−x Ba x Nb2O6,relaxation is confined to solid solution near the x=0.4composition.From its early discovery and because of outstanding properties and ease of preparation in both ceramic and single-crystal forms, lead magnesium niobate has become the prototype for perovskites and,simi-larly,barium strontium niobate for the bronzes.5.2.1B-Site-Substituted Perovskite Relaxor Ferroelectrics5.2.1.1Lead Magnesium Niobate(PMN)Three of the key features of this typical relaxor are illustrated in Fig.5.1. In the weak-field dielectric response(Fig.5.1a),the permittivity reaches a high peak value∼20,000typical for a ferroelectric perovskite near T c,but5Relaxor Ferroelectrics133ЊC no line1α2Pb (Mg Nb )O ’⑀Fig.5.1.Characteristic features of the ferroelectric relaxor,lead magnesium nio-bate,Pb(Mg 1/3Nb 2/3)O 3(PMN).(a )Dielectric dispersion in PMN as a function of temperature and frequency.(b )Dielectric hysteresis in PMN as a function of temperature.(c )Optical and X-ray evidence for the absence of a macroscopic phase change below the dielectric maximum at T mthe maximum clearly does not mark a phase change to a ferroelectric form as the maximum temperature T m moves to higher temperature with increasing measuring frequency in a manner typical for a relaxation dielectric.There is also an associated maximum in tan δ,again typical of relaxor response (not shown).Behavior at lower temperatures under high alternating fields does,however,exhibit bonafide hysteretic response,a necessary and sufficient con-dition for ferroelectricity.However,unlike a normal ferroelectric,the hysteretic response is not lost suddenly at T m but decays more slowly into just nonlinear response (Fig.5.1b).The third surprising feature is that to longer-coherence-length probing radiation,samples even at very low temperature show no evidence of optical anisotropy or X-ray line splitting,which would be characteristic of the domains in a normal ferroelectric (Fig.5.1c).The early explanation that this could be due to a nanoscale structure of polar regions has proven correct,but only recently has its origin been correctly diagnosed.134L.E.CrossFig.5.2.(a )Refractive index of PMN at optical wave length showing the departure from linear behavior due to the onset of polar nano regions.(b )Thermal contraction in PMN showing the change from linearity induced by electrostriction in the polar nano regionKey forward progress came from the realization that even though in such a structure of compensating nanoscale polarizations,macro P =0,RMS polarization √P 2=0so that examination of properties that depend on P 2such as quadratic electro-optic effects or electrostriction could indicate the onset of nanoscale polarization fluctuations.The first clear evidence for the presence of nanoscale polar regions came from refractive index measurement on PMN by Burns and Dacol [3](Fig.5.2a).Normal,linear decrease of index n with temperature is enhanced beginning at a temperature T B much above T m through contribution from the electro-optic constants g 33and g 31of the form∆n =−n 3o 2 g 33+2g 313P 2d showing the onset of nanoscale polarization that did not perturb optical isotropy.5Relaxor Ferroelectrics 135This diagnosis was supported by thermal contraction measurements by Bhalla et al.[4](Fig.5.2b),which confirmed a departure from linear contrac-tion again at ∼345◦C so that the total strain becomesS 11(T )=α(T −T o )+(Q 11+2Q 12)P 2dfrom whichP 2d =S 11(T )−α(T o −T )(Q 11+2Q 12)A microscopic picture of the polarization situation is now also emerging from X-ray [5]and neutron diffraction [6],high-resolution transmission elec-tron microscopy [7],and neutron pair distribution function analysis [8].The consensus appears to be that there are nanopolar regions that begin to appear at ∼618K,which grow from 2–3nm in size near TB to ∼10nm at 160K,and that the volume fraction increases to near 30%at low temperature.It does appear generally agreed that above T m the polar nanoregions are dynamic and that they do probably carry a major fraction of the system polarizabil-ity so that the dynamics of the nanopolar regions must tie in closely with the massive dielectric relaxation near T m .Analysis of the major dispersion reveals departure from Arrhenius behavior,which can be very satisfactorily described by the empirical Vogel–Fulcher relation [9]that takes the form:τ−1=ω=ωo exp(E/k (T −T f ))where ωo is the attempt frequency,E the energy barrier between equivalent polar orientations,and T f can be viewed as a dipolar freezing temperature for the relaxation process.In PMN the fit is remarkably good [10](Fig.5.3)with E =0.079eV ,T f =217.7K,and k and ωo =1012Hz.It should be noted,however,that in fact there is a very broad distribution of relaxation times in PMN that changes at T f ,the freezing temperature,so it is thelargest1081061041021003.43.63.84.04.23.2I /T m a x × 103ω (H Z )Fig.5.3.The non-Arrhenius character of the dielectric relaxation in PMN.Solid line is a Vogel–Fulcher fit to the data.E =0.079eV ,T f =217.7K ,ωo =1012Hz136L.E.CrossFig. 5.4.Suggested temperature-dependent relaxation time spectrum for PMN. G(τ,T)is the number of polar micro regions having a relaxation timeτ,T f is the freezing temperature,andτd is the Debye relaxation timerelaxation times that became macroscopic.A suggested response profile is given in Fig.5.4.Thus the Vogel–Fulcher relation suggests that the zero-field,cooled PMN freezes into a random array of micropolar regions in a spin-glass-like state[11]. The micropolar regions are dominantly polarized along the(111)orientation, but because of the random arrangement there is no macroscopic anisotropy. Under high electricfield,however,a static change can be induced,and the nanopolar region can be reoriented to form macro-domains,which then lead to the observed ferroelectricity at lower temperatures.The importance of the local B-site cation arrangement for the onset of the relaxor nanopolar structures is very nicely demonstrated in lead scan-dium tantalate.Material quenched from high temperature shows a disordered Sc:Ta arrangement and initial relaxor ferroelectric response[12];however,un-der high-temperature annealing,the Sc:Ta order1:1in NaCl-like ordering and the ordered structure exhibits a sharpfirst-order phase change at T m into a conventional ferroelectric[13,14].In fact,it does appear in PST that even for the disordered structure with careful preparation to avoid oxygen vacancy effects,the more perfect disordered structure goes through the major relaxor dispersion,but at lower temperature crosses over into the ferroelectric form as evidenced by the loss of dispersion and the onset of a macrodomain structure[15].In PMN,because of the1:2(Mg:Nb)composition on the B-site and the fact that the structure chooses to order1:1in(111)-oriented(Mg2Nb)and pure Nb composition sheets in which the Mg-containing sheet is still disordered,it is not possible to induce a highly ordered state and even1:1order is strongly kinetically limited.None the less,it does appear that limited ordering is an aid to relaxor behavior[16]and there is gathering evidence that thefirst onset of micropolar regions at T B occurs in the most highly ordered regions[17]and that it is in these regions that the nanopolarization is most mobile.5Relaxor Ferroelectrics 1375.2.2A-Site-Substituted Perovskite Relaxor Ferroelectrics5.2.2.1Lead Lanthanum Zirconate Titanate (PLZT)Probably the most widely studied mixed A -site perovskite system is lanthanum-modified lead zirconate titanate (PLZT).One of the first electronic ceramics to be hot-pressed to optical transparency,much original work was focused on the optical properties,which hinge upon relaxor ferroelectric be-havior closely similar to PMN.As in pure PZT,there is a pseudo-morphotropic phase boundary separating rhombohedral and tetragonal phases at lower La 3+concentration.Most interesting are compositions in the Pb 1−3/2x La x (Zr 0.65Ti 0.35)O 3system,with x between 0.06and 0.12.PbZr 0.65Ti 0.35O 3is in the rhombohedral phase field of the solid solution and completely free of radio fre-quency dispersion in dielectric properties.The 0.06mole fraction La 3+induces weak relaxor properties (Fig.5.5)and,as in disordered lead scandium tanta-lite,this composition is close to cross-over into ferroelectricity.The relaxor phase can be stabilized by additional La 3+or by increasing hydrostatic pres-sure (Fig.5.6).A most interesting feature of the whole range of La-substituted 65/35PZTs is the manner in which the phase diagram changes with La con-centration (Fig.5.7).Again,thermal expansion and optical index show that000000000000000000000000120001000080006000400020001600014000120001000080006000PLZT-6PLZT-7PLZT-8PLZT-6.5100150200250050100150100150200250TEMPERATURE (C)TEMPERATURE (C)D I E L E C T R I C C O N S T A N I E L E C T R I C C O N S T A N T (b)138L.E.CrossPLZT 6/65/351 bar 1 bar 103 Hz 105104103 Hz 10 kbar 20 kbar 103104105 Hz 20 kbar T m T F-R 128400 2.02.42.83.23.64.0510152025280320360400440T (K)ε’ x 10–3T T T PARAELECTRICKINETICALLY DISORDERED (K.D.)a) polarization F.E.ROMB. II ROMB. I F.E.T000000000000000K.D.a) polarization a) polarization a) polarization b) orientation b) orientation b) orientation c) elastic a) elastic c) elastic Glassy Glassy K.D.5Relaxor Ferroelectrics139Fig.5.8.(a)Structure of nanoscale domains revealed in PLZT8.2/65/35composi-tion by dark-field TEM.(b)Modification of the domain pattern by beam charging showing the induction of larger macrodomain stripesadded La.One of the best demonstrations of NPR in PLZT is the TEM study by Randall[18]showing for an8.2:65:35PLZT composition darkfield contrast from NPR(Fig.5.8a)and by charging from the beam current the evolution towards more normal continuous ferroelectric macro-domains(Fig.5.8b).5.2.2.2Bismuth Strontium TitanateA second A-site-substituted system that gives additional insight into relaxor ferroelectric behavior is bismuth-substituted strontium titanate,(Bi2/3x Sr1−x) TiO3,originally classified as Skanavi dielectrics in honor of its Russian discov-erer.More recent studies have again shown clear relaxor ferroelectric behavior for higher bismuth concentrations.In pure strontium titanate,SrTiO3,the weak-field dielectric permittiv-ity follows the Curie–Weiss law from high temperature down to50K with a Curie–Weiss temperatureθ=35.5K;however,no permittivity peak appears below50K and the permittivity levels offat a very high value that persists to a very low temperature.The suppression of ferroelectricity is attributed to quantumfluctuations and often described by a model due to Barrett[19,20]. Interestingly,at thefirst introduction of Bi3+at low levels,the quantum para-electric behavior is modified by two weak dispersions(A,B)exhibiting nicely separated tanδmaxima(Fig.5.9).At higher Bi3+concentrations,a more mas-sive relaxation(C)appears,and with further increase in Bi3+concentration digests both A and B.Dispersions A and B follow the simple Arrhenius law over the frequency range10–109Hz:τ=τo exp(E/kT),and display nicely symmetric Cole-Cole arcs,typical for dielectric dispersion.Relaxation C,however,is not of the Debye type and follows the Vogel–Fulcher law:140L.E.CrossFig.5.9.(a )Temperature dependence of ε for Sr 1−1.5x Bi x TiO 3with x ranging from 0to 4%at 0.1,1,10,100and 1,000kHz.Note the log T scale.(b )Temperature dependence of ε for similar compositions and temperature rangeτ=τo exp Ek (T −T f ) of a relaxor ferroelectric .Dispersions A and B increase in amplitude with Bi 3+concentration but do not move in frequency with Bi 3+concentration or applied bias field.Dis-persion εalso increases markedly with Bi 3+concentration,but moves to lower temperatures with concentration and with bias field.For a simple defect-dipole-induced relaxation as in A and B ,it is expected that the dielectric step height follows a simple Debye–Langevin relation:∆ε=(n (qδ)2/3kT )εoFor both A and B relaxations the observed∆εwould require a totally unrealistic displacementδs,suggesting that the effective electric movement is massively augmented by high lattice polarizability,i.e.,∆ε=(n(Nqδ)2/3KT)εowhere for realisticδ,N∼100is required.It is suggested that A and B dispersions are associated with local displace-ments of the Bi3+ion and are distinguished by the absence or near-presence of the associated strontium vacancy,which appears reasonable.For the C dis-persion,however,the very different character might suggest that,as in the original Skanavi model,Ti4+is participating.Again,polar clusters form at the higher Bi3+concentration,but now the clusters communicate much more effectively through the oxygen framework to give positive feedback and the slowing down evidenced in the Vogel–Fulcher model.Clearly,the system offers important clues as to the origin of relaxor re-sponse,but much more work is needed to pin down the possibilities.5.3Polycrystalline Ceramics Relaxor Based Actuators Realization of the absence of stable domain states in PMN in the temperature range from T m to T B suggested that the carefully prepared ceramic should be free from aging effects.In fact,the ceramic is not easy to prepare from mixed oxide powders because of the very refractory nature of magnesium oxide,and often early ceramics were heavily contaminated by a pyrochlore phase or by the excess MgO that was used to alleviate the problem.This difficulty was nicely solved by the columbite method of fabrication[21],in which the necessary MgO was pre-reacted with niobium pentoxide(Nb2O5) to form the columbite phase,which could then be reacted with PbO to form PMN.In the pure stoichiometric PMN,absence of aging is evidenced over a wide temperature range(Fig.5.10),andfield-induced polarization leads to useful electrostrictive strain(Fig.5.11).As a function of electricfield,the strain is not quadratic because of dielectric nonlinearity;none the less,it leads to impressive induced piezoelectricity at modest biasfield levels and is age-free over a suitable range of temperature.Fortunately,the age-free range of T can be manipulated by limited solid solution with lead titanate(PbTiO3) to give performance superior to the best hard PZT at room temperature.It was this longer-term stability of the bias-induced displaced states that led to PMN being chosen for Hubble corrector tilt mirrors,a decision that has been amply justified by its subsequent performance.Interesting to note also is that many of the actuator controlled atmospheric densityfluctuation corrector mirrors now incorporated into most very large ground-based telescopes also use ceramic PMN-based compositions.1709010–70100 000Hz10 000Hz1000Hz100Hz00000ELECTRIC FIELD (kV/cm) 26812x10–4STRAIN 10010102020PZT=Pb(Zr 0.5Ti 0.5)O 30.9PMN-0.1PT.Pb(Mg 0.3Nb 0.6Ti 0.1)d 33~1500p C/NAT 3.7 kV/cm1. 1KHZ2. 10 KHZ3. 1000 KHZ12300000000101102103104NO aging3 h aging10 h100 h1000 h00000000 0(a) (I)(II)(III)(IIII)100000 Hz100000 Hz10 000 Hz10000 Hz1000 Hz1000 Hz100 Hz100 HzE-field induced phase transition .21.8.6.4.2.2.411,111,and 111-oriented polar domains are equallychanged in energy by a (001)-oriented E-field,so there is no driving force to move the domain walls.Since the single-domain permittivity along the (111)domain polar axis is modest,it is natural to suggest that field-induced rotation of the domain vectors (as in Fig.5.16c)is the intrinsic strain mech-anism,with a field-induced switch over to a tetragonal form at a very high field as observed (Fig.5.16d).Now,it is natural also to question whether,on the basis of the observed polarization changes,the tilt would be adequate to generate the observed strain levels and if so,what would be the required tilt of P s from (111)to produce the strain level observed before the switchover.Early phenomenolog-ical analysis [27]using strain measured in the tetragonal state to characterizeFig.5.16.Sequence of states in an(001)-oriented PZN:4.5PT single crystal.In virgin,poled,under modest(001)Efield,and after high switchingfieldQ11show that the induced strain is more than adequate.More recent calcu-lation[28]using total strain measured for the tetragonal state after switching to determine Q11agrees closely with the observed S3and S1values,and the calculated tilt of P s from(111)before switchover is similar to that measured in the tilt of the optical indicatrix under(001)-oriented E-field in a rhombo-hedral single domain[29].With support also from ab initio calculation[30], there is now little doubt that the driving mechanism for high d33and large S3 under(001)-oriented E-field is rotation of the polarization vector away from the(111)direction in the rhombohedral domain towards the orientation of the driving E-field.The basic explanation is quite clear;however,there is much complexity in the detail.In a relaxor ferroelectric,a poling operation is required to put the low-temperature form into the ferroelectric phase with long-range order.The resulting phase may depend on the magnitude,orientation,and temperature of the poling operation.The original phase diagram is oversimplified,and in some compositions close to the MPB there is evidence of stable monoclinic and orthorhombic forms.Unfortunately,much confusion has also been gener-ated by overemphasis on the role of the monoclinic phase in these crystals.It is absolutely true that under high(001)E-field the P vector in the domain is tilted more than20◦away from the rhombohedral(111)and the symmetry is unquestionably monoclinic,but of critical importance is the fact that the monoclinic form is metastable so that when thefield is removed the domain reverts back to its equilibrium rhombohedral form giving the recoverable an-hysteretic quasi-linear actuation strain under the E-field.It is perfectly true that in the monoclinic state P s may lie anywhere in the mirror plane between rhombohedral and tetragonal orientation,but it is absolutely untrue that it is free to rotate in this plane in that for any given composition,temperature, and pressure,the vector will always occur at the same orientation in one of the family of24permitted orientation states.What is unusual is that the P s vector will change its orientation in the mirror as a function of temperature, giving an unusual component of pyroelectricity orthogonal to the direction of P s in the single domain.Clearly,for the type of actuation achieved in the (001)-poled rhombohedral form of both PMN:PT and PZN:PT,in rhombo-hedral compositions close to the MPB the last thing one would want is a stable intervening monoclinic form between tetragonal and rhombohedral,as this would necessarily introduce massive hysteresis in the strain because the P s vector drops into and has then to be pulled out from the stable tilted orientation.A key basic unresolved problem in the PMN:PT and PZN:PT systems is why the tilting mechanism is so astoundingly successful in raising piezoelectric response.Other simpler perovskites such as BaTiO3and KNbO3 have ferroelectric/ferroelectric phase boundaries,and at temperature close to the boundary exhibit appropriate high dielectric anisotropy[31,32].For sim-ple domain-average-engineered structures,however,both measured and cal-culated properties,although significantly enhanced,are almost an order of magnitude less than in the relaxor ferroelectrics.For future development based on the relaxor single crystals,it would ap-pear that a very important question is how the residual disorder and random fields soften both the dielectric and elastic properties without destroying the high-temperature reach and the strong remanent polarization in the poled ferroelectric forms,as discussed further in Sect.5.5.4.2Tungsten-Bronze Structure Relaxor FerroelectricsA substantial number of corner-linked-octahedron-type complex ferroelectric oxides that crystallize in the tetragonal tungsten-bronze crystal structure exhibit the relaxor ferroelectric character.A cross-section of the structure nor-mal to the fourfold axis(Fig.5.17)illustrates the corner linking of octahedra, which is much less regular than in the perovskite,leading tofive-,four-,and threefold tunnels for the A-sites running parallel to the fourfold symmetry axis.The general chemical formula is of the form(A1)4(A2)2C4B10O30,where A1are15-fold coordinated sites in thefivefold tunnels,A2are12-fold coor-dinated in the fourfold tunnels,C are ninefold coordinated in the threefold tunnels,andB are the sixfold coordinated B-site cation as in the perovskite.Fig.5.17.Cross-section of a ferroelectric tetragonal tungsten-bronze taken normal to the fourfold axis.Identifyingfivefold(A1),fourfold(A2),and threefold tunnels and the15-,12-,and9-fold coordinated sites in these tunnelsTable5.1.Ferroelectric species that could occur from the4/mmm prototypic point symmetry in Shuvalov notation.Non-zero components of P s delineated for each species14/mmm(1)D4F4mm p2Z=0,p2X=p2Y=024/mmm(2)D2F mm2p2X=p2Y=0,p2Z=034/mmm(4)A2F m p2X=p2Y=0,p2Z=044/mmm(4)A.4F m p2X=p2Y=0,p2Z=054/mmm(8)A1F1p2X=p2Y=p2Z=0An example of a ferroelectric(non-relaxor)bronze in which all sites are occu-pied is(K4)A1(K2)A2Li4(Nb)10O30.Very frequently,however,the structure is quite stable when not all cites arefilled as,for example,in the solid solution (Sr x Ba1−x)5Nb10O30,in which the A-sites are only5/6filled,there is charge unbalance,disorder,and strong relaxor behavior.All bronze structured ferroelectrics and relaxor ferroelectrics have high-temperature paraelectric point symmetry4/mmm,which by Aizu/Shuvalov symmetry considerations limits possible ferroelectric species and polar direc-tion to those given in Table5.1.That the setting is with the fourfold axis along z,P i2=0,means that for the i th direction±P s i occurs with equal proba-bility in the domain structure.To date,only ferroelectrics in4mm and mm2 point symmetries have been found;however,there is mounting evidence that in several relaxor compositions nanopolar regions may have lower symmetry involving a small tilting of the P vector away from the four-or twofold axis.5.4.2.1Barium Strontium Niobate (Sr 1−X Ba x )Nb 2O 6Neither pure barium niobate nor pure strontium niobate will form in the bronze structure;however,in the solid solution they form 0.25Ba/0.75Sr to 0.75Ba/0.25Sr stable tungsten-bronze structure forms.The most widely studied is (Sr 0.61Ba 0.39)Nb 2O 6,which is pseudo-congruently melting so that excellent-quality,large,and striation-free single crystals can be grown.It has been shown from X-ray analysis by Abrahams [33]that the large Ba 2+ions are exclusively in the 15-fold A 2-sites,while the strontium ions are mixed between A 1and A 2sites and the smaller C site is completely empty.Massive dispersion in the weak-field dielectric permittivity (Fig.5.18)im-mediately suggests relaxor ferroelectric behavior,which is supported by the Vogel–Fulcher analysis (Fig.5.19),and there is clear evidence from both op-tical birefringence and thermal contraction studies of the presence of c -axis micropolar regions up to a Burns temperature some 200◦C above the dielectric maximum at T m .The uniaxial character of the polar behavior permits a very simple macroscopic demonstration that the polar nanoregions between T m(a)(b)00000000000000000000000。