Ju rgen Ro

del,**,w Wook Jo,Klaus T.P.Seifert,Eva-Maria Anton,and Torsten Granzow Institute of Materials Science,Technische Universita t Darmstadt,287Darmstadt,Germany

Dragan Damjanovic

Ceramics Laboratory,EPFL,1015Lausanne,Switzerland

A large body of work has been reported in the last 5years on the

development of lead-free piezoceramics in the quest to replace lead–zirconate–titanate (PZT)as the main material for elect-romechanical devices such as actuators,sensors,and transduc-ers.In specific but narrow application ranges the new materials appear adequate,but are not yet suited to replace PZT on a broader basis.In this paper,general guidelines for the develop-ment of lead-free piezoelectric ceramics are presented.Suitable chemical elements are selected first on the basis of cost and toxicity as well as ionic polarizability.Different crystal struc-tures with these elements are then considered based on simple concepts,and a variety of phase diagrams are described with attractive morphotropic phase boundaries,yielding good piezo-electric properties.Finally,lessons from density functional the-ory are reviewed and used to adjust our understanding based on the simpler concepts.Equipped with these guidelines ranging from atom to phase diagram,the current development stage in lead-free piezoceramics is then critically assessed.

I.Introduction

A

LTHOUGH

piezoceramics have been in commercial use for a

long time,1–4they have witnessed a tremendous growth rate over the last decade.This is in part connected to the successful transfer of the multilayer capacitor technology to manufactur-ing multilayer actuators.5Now,displacements of tens of mi-crometers are available in microseconds and actuators are able to support stresses in the order of tens of megapascals.6Appli-cation opportunities now abound in the areas of piezoelectric fuel injection,piezoelectric motors,piezoelectric printing ma-chines,piezoelectrically controlled thread guides,microposition-ing systems,and many others.2,3

For a long time the dominant piezoceramic has been lead–zirconate–titanate (Pb(Zr 1Àx Ti x )O 3or PZT).1It is commonly

used with a composition close to the morphotropic phase bound-ary (MPB;a phase boundary,where a change of composition only changes the phase)around x 50.48,where properties such as piezoelectric coefficients,dielectric permittivity,and coupling factors are maximized.1,4It has a coercive field of about 1kV/mm and a remanent polarization of about 35m C/cm 2.Hence,the poling field is much below the dielectric breakdown strength,and poling at an elevated temperature gives it directional properties and transfers it into the piezoelectric state.7Unipolar electric field excursions typically from zero electric field to 2–3kV/mm,corresponding to a potential of about 200V at a typical layer thickness of 80m m,provide a strain of 0.1%–0.2%.A large-signal piezoelectric coefficient as large as 779pm/V has been re-ported for doped PZT.8Some of the large-volume applications require strain over an extended temperature regime,which PZT can provide up to about 1751C with little temperature depen-dence.9Usage at higher temperature is limited by the danger of thermal depoling,associated with a Curie temperature of 3001–4001C and a significant increase in conductivity.Finally,doping PZT with acceptors and donors allows manufacture of hard and soft PZTs with the associated width of accessible properties.1

These very attractive properties come with some drawbacks,some of which are due to the very nature of being a good pi-ezoelectric that can provide electric field-induced strain.Among ceramics,PZT has one of the lowest elastic moduli.10A Young’s modulus of about 70GPa puts PZT in one class with ordinary window glass,sodium–potassium silicate.Similarly,a low elastic modulus translates into a low cohesive stress at the crack tip 11and provides PZT with an intrinsic toughness or crack tip toughness of 0.7MPa Ám 1/2,12,13which is,again,very similar to the ordinary window glass.10Further,the remanent strain of 0.1%–0.2%9associated with the poling procedure translates into a strain incompatibility between active and inactive regions in a multilayer actuator 14and is a driving force for crack initi-ation followed by crack propagation.15

The increasing success of PZT releases more and more lead,mainly in the form of either lead oxide or lead zirconate titanate into the environment.This occurs during calcination and sinte-ring,where PbO evaporates,during hard machining of compo-nents,and after usage with attendant problems of recycling and waste disposal.As a consequence,the European Union (EU)in 2003included PZT in its legislature to be substituted as a haz-ardous substances by safe materials 16,17;see also Section II.This directive gave a boost to the search for lead-free piezoceramics,

D.J.Green—contributing editor

This work was supported by the Deutsche Forschungsgemeinschaft under SFB 595(Electric fatigue of functional materials)and by the state center ADRIA on adaptronics.

**Fellow,The American Ceramic Society.w

Author to whom correspondence should be addressed.e-mail:roedel@ceramics.tu-darmstadt.de

Manuscript No.256.Received December 19,2008;approved February 24,2009.J ournal

J.Am.Ceram.Soc.,92[6]1153–1177(2009)

DOI:10.1111/j.1551-2916.2009.03061.x r 2009The American Ceramic Society

which had started just before the year 2000,as witnessed by Fig.1providing statistics for refereed publications on lead-free piezoceramics from 1950up to now.In fact,there were very early considerations in the 1950s and 1970s to replace lead in piezoceramics.18Thus,it comes as no surprise that the search for lead-free piezoceramics is described as one of the pillars in to-day’s roadmap for ceramics.19The recent discovery of very high piezoelectric response in relaxor-ferroelectric single crystals,20Pb(Mg 1/3Nb 2/3)O 3–PbTiO 3and Pb(Zn 1/3Nb 2/3)O 3–PbTiO 3,which exhibit coupling coefficients as high as 94%and piezo-electric coefficients of 2500pC/N (or five times higher than commercial PZT)have triggered a parallel search for high-per-formance lead-free single crystals.21,22

There are excellent publications available reviewing the on-going effort for the search of lead-free piezoceramics.28–30This contribution has a somewhat different focus in that it attempts to provide a perspective on this development by introducing guidelines and concepts for this search.These are related to po-tentially promising chemical elements,electronic structures,crystal structures,and phase diagrams to be utilized in this search.Also,we include the current understanding from atom-istic modeling.A review on the current material development is also provided.However,the parallel effort in processing tech-nology in texturing lead-free piezoceramics to optimize proper-ties 31is not covered.We continue with detailing the legal situation throughout a large part of the countries involved in this research effort.

II.Legal Situation

The amount of waste electrical and electronic equipment gener-ated in the EU is growing rapidly.The hazardous substances contained in these wastes are a major concern for their safe dis-posal.As of July 1,2006,the European Parliament has adopted the directives Waste Electrical and Electronic Equipment (WEEE)and Restriction of the use of certain Hazardous Sub-stances in electrical and electronic equipment (RoHS)in order to prevent,reuse,or recycle waste electrical and electronic equip-ment and to protect human health and environment by the sub-stitution of hazardous substances by safe or safer materials.16,17

The RoHS applies to the specified categories of electrical and electronic equipment used in households and industries.Medical devices,monitoring and control instruments,and spare parts for older devices are excluded.For the listed devices,the maximum allowed concentration is set to 0.1wt%in homogeneous mate-rials for lead,mercury,hexavalent chromium,polybrominated biphenyls,and polybrominated diphenyl ethers,and to 0.01%

for cadmium.Some defined applications containing hazardous substances are exempt from the directive if the elimination is technically or scientifically impracticable.The list of exempted applications,which will be reviewed at least every 4years,in-cludes the use of lead in electronic ceramic parts,e.g.,piezo-electric devices.Hence,the use of PZT in piezoelectric devices is still allowed in the EU,but will be prohibited as soon as there is a practicable substitution available.

There are activities to establish similar regulations in coun-tries all over the world.In Switzerland,Norway,the U.S.state of California,and Turkey,the EU legislation was adopted into the respective national or state laws and is already enforced 32–35or is due in June 2009.36In California restrictions only affect the four metals;the two flame retardants are excluded.Each U.S.state has established its own regulations,but so far laws similar to the EU-RoHS only exist in California.In Norway the ex-pansion of the regulations to 18hazardous substances and to all consumer products is planned.

There are different approaches to establishing RoHS-like reg-ulations in Asia.In South Korea regulations equivalent to the EU legislation with respect to the restricted substances,maxi-mum concentration values,and exemptions are already en-forced.37In China and Japan labeling of electronic devices is required if the values for the six EU-defined hazardous sub-stances exceed the corresponding EU maximum concentra-tions.38–40China intends to prohibit the manufacturing and import of listed electronic devices containing more than the max-imum concentration values for hazardous substances,although the date of the enforcement is not yet clear.The list includes piezoelectric ceramic parts;exemptions are not provided.40

RoHS legislation in Australia,New Zealand,and Thailand is still in progress.It is expected that similar regulations like the EU-RoHS will be established.41

III.Required Properties

In the following,we introduce some key material properties and fundamental relationships as a basis to discuss the salient ma-terial properties for actuators,sensors,and transducers in an exemplary fashion.We then conclude this section with general remarks applicable to a variety of applications.

(1)Actuators

Actuators and high-precision positioning systems require high strain with high force,e.g.to drive motors,control fuel injection,etc.2This strain is provided through electromechanical coupling using either piezoelectricity or electrostriction.

In tensor notation the electric field-induced strain,S ij ,can be written as a power series either in electric field,E k ,or in polar-ization,P k .Here,d kij and g kij denote the piezoelectric coeffi-cients,whereas M ijkl and Q ijkl denote the electrostrictive coefficients.To distinguish the d and g coefficients,they are also termed piezoelectric charge constant d and piezoelectric voltage constant g 42:

S ij ¼d kij E k þM ijkl E k E l þÁÁÁði ;j ;k ;l Þ¼1;2;3

(1)S ij ¼g kij P k þQ ijkl P k P l þÁÁÁ

(2)

The first term in either equation represents the contribution of the converse piezoelectric effect,and the second term electro-striction.

For a material development,a consideration of longitudinal and transverse displacements is often sufficient.For the converse piezoelectric effect,Eq.(1)can be simplified to 43

S i ¼d ij E j

(3)

The linearity of strain and applied electric field,however,holds true only for small electric field,with the piezoelectric co-efficient,d ij ,being termed a small-signal property.

44

Fig.1.Publications on lead-free piezoceramics in refereed journals for the time range from 1950to November 2008.The statistic was created by counting the relevant papers citing Saito et al .,23Takenaka et al .,24,25Elkechai et al .,26Sasaki et al .,27and Shrout et al .28Beyond that,a search was conducted in ‘‘ISI Web of Science’’and ‘‘Sciencedirect’’with key-words such as ‘‘lead-free,’’‘‘piezoelectric,’’‘‘ferroelectric,’’‘‘KNN,’’‘‘BNT,’’and similar.The collected papers were again searched for rel-evant references.

1154Journal of the American Ceramic Society—Ro ¨del et al.Vol.92,No.6

In a similar fashion,electrostrictive materials can be catego-rized in a simplified version 43:

S i ¼Q ij P 2j

(4)

The electrostriction coefficient,Q ij ,exhibits a well-defined correlation with the thermal expansion coefficient of the mate-rial 45and has been found to have very weak temperature de-pendence.46

Actuators are primarily designed for maximum strain at min-imum coaxial electric field.This leads to a quantity S 3,max /E 3,max as an important figure of merit,which has resemblance to the piezoelectric coefficient d 33in Eq.(3),with the difference,that S 3,max /E 3,max is a large-signal quantity and hence in ferroelectrics includes strain contributions by domain switching.It is therefore termed large-signal d 33value.The distinction between the small-and large-signal piezoelectric coefficient is an important one,as the values differ by a factor of about 2for the case of soft PZT.47It should be noted,however,that domain walls may also con-tribute to the small-signal piezoelectric coefficient through do-main wall bending or local switching of domain wall segments.48All these so-called extrinsic contributions (as opposed to intrin-sic or lattice response)are evidenced through nonlinearity,hys-teresis,and frequency dependence of the strain.Note that nonlinear piezoelectric strain is fundamentally different from the electrostrictive strain.In electrostriction,the strain is a qua-dratic function of the field and strain has the same sign for the negative and positive field.The nonlinear piezoelectric strain may have a complex field dependence but the nonlinear contri-bution changes with the sign of the field.Figure 2shows the unipolar strain hysteresis for different cycling amplitudes in ex-emplary fashion for a commercial PZT material.Note that the strain response as function of applied electric field is almost lin-ear up to 2kV/mm (a typical driving field)with little hysteresis.At higher driving fields,hysteresis is still small,but the piezo-electric effect begins to saturate and the curves start to flatten out.The obtainable strain at given electric field also depends on electric field interval,49frequency,50pressure,51and tempera-ture.9Examples for obtainable strain as a function of the max-imum electric field for a PZT disk (a)and as a function of pressure for a multilayer actuator (b)are provided in Fig.3.Figure 3is a different presentation of the curves from Fig.2,highlighting a reduced strain increment at about 2–3kV/mm.In applications,multilayer actuators are utilized under a small compressive stress of 10–20MPa to reduce the tendency to cracking at electrode edges.The magnitude of the compressive stress has only a small effect on the obtainable strain,as dem-onstrated in Fig.3(b).For technological reasons,the dielectric displacement of the actuator is also crucial,as it determines the current required per actuator stroke.Further,the blocking force,defined as uniaxial force on the actuator,which can be applied to exactly compensate for the electric field-induced ex-

tension,assesses the mechanical capabilities of the actuator.As actuators heat up during service and run after a cold start,the temperature dependence of properties like obtainable strain and dielectric displacement is also important.

(2)Sensors

Piezoelectric sensors are widely used to detect stresses,s j ,by monitoring the dielectric displacement,based on the following relation:

D i ¼d ij s j

(5)

The coefficient d 33is most often used in applications and of-ten referred to as just ‘‘the’’piezoelectric coefficient.In accor-dance to the obtainable strain,S 3,max ,the piezoelectric coefficient is a complex function of magnitude of the mechan-ical or electric driving field,52bias electric field,50frequency,50,52temperature,53and pressure.47As in the previous section on ac-tuators,we illustrate the field dependence on a commercial bulk material and the stress dependence on a multilayer actuator.In the application regime of unipolar loading,the piezoelectric co-efficient exhibits a noticeable linear decrease with increasing field (Fig.4(a)).An increasing uniaxial stress generates a decrease in piezoelectric coefficient at zero electric field,and first an in-crease,and then a decrease in piezoelectric coefficient at high electric field (Fig.4(b)).47

For comparison,typical d 33coefficients are on the order of 2pm/V in SiO 2,20pm/V in bismuth titanate-based Aurivillius structures,4200pm/V in PZT,and 42000pm/V in relaxor-ferroelectric single crystals (e.g.,Pb(Zn 1/3Nb 2/3)O 3).Among listed materials only PZT has a significant contribution from domain wall displacements.

Next to the magnitude of the piezoelectric coefficient,its low temperature dependence,a high electric resistivity,and a low permittivity are among the key requirements for a successful development of piezoceramic

sensors.

Fig.2.Unipolar strain hysteresis curves for soft lead–zirconate–titan-ate (PZT)bulk ceramic for different amplitudes of the cycling field.Note that the zero-field value is chosen arbitrarily to facilitate the display of four curves in one

graph.

Fig.3.(a)Strain amplitude during unipolar cycling as a function of field amplitude for soft bulk lead–zirconate–titanate (PZT).(b)Unipolar macroscopic strain at 2.3kV/mm dc field as a function of the uniaxial mechanical load for soft PZT multilayer.47

June 2009Development of Lead-free Piezoceramics 1155

(3)Transducers

For the purpose of this text,transducers can be defined as pi-ezoelectric elements operating at elevated frequencies or under resonance conditions,at frequencies from tens of kilohertz to tens of megahertz.They are used for ultrasonic imaging in med-icine,underwater listening and ranging (sonars),nondestructive materials’testing,medical therapy,high-frequency filters,sur-face acoustic wave devices,and other applications.The driving voltages can be high so that extrinsic effects mentioned for sen-sors and actuators cannot be neglected in transducers.From the device point of view,the most important properties are the cou-pling coefficient,dielectric permittivity,acoustic velocity,and acoustic impedance.Machinability is important to obtain small elements (tens of micrometers)needed for high-frequency oper-ation.Requirements vary from one type of transducers to an-other.Single-element transducers (thin disks with high geometrical capacitance)require materials with a low permit-tivity and large thickness coupling coefficient k t while array transducers (long rods with low geometrical capacitance)require large longitudinal coupling coefficient k 33and large permittivity.Together with a requirement for low temperature dependence of the resonant frequency,the medical transducers must exhibit high Curie temperature to resist depoling at sterilization tem-perature (about 1301C).The largest k t (0.69)is measured along a nonpolar direction of single crystals of KNbO 3,54while the largest k 33(40.9)is exhibited along nonpolar directions of re-laxor-ferroelectric single crystals.20,55

(4)Secondary Requirements

The development of lead-free piezoceramics with some excep-tions has not advanced yet to the state to consider a set of sec-ondary requirements.However,a developmental effort may be advised to keep some of these in mind.Multilayer actuators with a separation of electrically active and inactive regimes will de-velop strain incompatibilities and stresses,14leading to the threat

of crack initiation and crack propagation.56Similarly,pressure sensors may experience complex stress situations and are re-quired to have sufficient resilience against mechanical loading.Lead-free piezoceramics with possibilities of either bridge-toughening or process-zone toughening 57are therefore pre-ferred.Further,the successful application of new materials should be tested on the basis of costs against other technolog-ical competitors.Here it is advantageous to develop materials with low sintering temperatures,so that electrode materials 58with low melting temperature such as high Ag-content alloys or copper can be utilized.

Finally,it is interesting to remark that the PZT family in practice appears in some dozen varieties that cover nearly the whole spectrum of applications.z At the moment,at least,lead-free materials are most often developed with a specific applica-tion in mind.For example,KNbO 3single crystals with the highest known k t of about 0.69and small permittivity of about 100are perfectly suitable for single-element transducers operat-ing at high frequencies (tens of megahertz),59,60but not for other types of transducers,sensors,or actuators.Similarly,bismuth titanate-based layered structures are best known for their high Curie temperature and temperature stability.Their piezoelectric properties are rather inferior to those of PZT so that these ce-ramics have little use outside the high temperature range.This narrow specialization is a serious limiting factor for presently used lead-free materials as it increases development and pro-duction costs.One of the greatest challenges in developing new lead-free materials will be to find a family with properties that are as diverse as those in PZT.And,if this turns out to be im-possible,as the present state-of-the art seems to suggest,then it will be necessary to develop several materials that will replace PZT in specific applications.

IV.General Considerations

(1)Cost and Toxicity

Although the toxicity of lead and lead-based compounds has been well acknowledged,lead-containing piezoceramics,for ex-ample PZT,are still in dominant use for most of the practical applications.This is mainly due to the absence of alternatives whose properties are competitive to those of the lead-containing counterparts.However,it is quite evident that a heavy restric-tion on the use of lead-containing piezoceramics is impending worldwide due to the following facts.The amount of lead in the usual lead-containing piezoceramics is more than 60wt%,and once the lead comes into the human body,it accumulates in various organs,leading potentially to fatal effects to fetus,in-fertility,cancer,and so forth.61,62Note that not only the lead in lead-based compounds such as PZT but also the lead oxide as a starting material are known to dissolve when they are exposed to an aqueous environment.63It follows that for the development of the next-generation piezoceramics the replacement of toxic substances is of paramount importance.Hence,a complete list of toxicity of substances and a complete classification of these substances should guide future investigations.

Figure 5shows the toxicity of the elements classified into three distinctive categories depending on the degree of toxicity,when they are prepared as a compound in the form either of a carbonate or of an oxide.Because the toxicity of the compounds is closely related to that of the individual components,this di-agram could also serve as guideline for toxicity of the final products of our interest.For example,the high level of toxicity of PZT is mainly due to that of Pb or PbO.The nontoxic cat-egory denoted by the green color and slightly toxic one denoted by the yellow color in Fig.5represent the substances whose toxic level is at most irritant and harmful mostly in the case of a direct contact.On the other hand,the toxic category denoted by the orange color indicates the substances that can cause

acute

Fig.4.(a)Small-signal piezoelectric coefficient for soft lead–zirconate–titanate (PZT)bulk ceramic as a function of the electric bias field.(b)Small-signal piezoelectric coefficient at zero field (triangles)and at 2.3kV/mm dc field (squares)as a function of the uniaxial mechanical load for soft PZT multilayer.47

z

For example,Ferroperm (http://www.ferroperm-piezo.com)offers 15products,one of which is a lead-free high-temperature material,two are based on lead titanate and lead metaniobate,and the rest are different varieties of PZT.

1156Journal of the American Ceramic Society—Ro ¨del et al.Vol.92,No.6

effects on the living organisms and are dangerous for the envi-ronment.Figure 5justifies why potassium sodium niobate-based and bismuth-based materials are the most common choices as alternative to PZT.28–30It is interesting to note that bismuth is a nontoxic heavy metal.In fact,several studies have demon-strated that bismuth has practically no harmful effect on the living organisms.65–67

The exclusive dominance of lead-based piezoceramics,repre-sentatively PZT,over the piezoelectric market for more than half a century is not solely due to their excellent properties but also due to considerations of cost.This stems from the fact that most commercially available lead-based piezoceramics such as PZT,PMN-PT,PLZT,etc.,are all based on relatively inexpen-sive raw materials,as shown in Fig.5.In addition,the consol-idation of raw materials with a density of more than 96%is easily achieved even by conventional pressureless sintering tech-niques.68Hence,economical considerations are as important as excellent functional properties in the development of lead-free piezoceramics.Relative prices for the commercially available raw materials either in the form of carbonates or oxides are provided in Fig.5.The price of each substance in euro/kg refers to the online catalogue of a major supplier and is evaluated for the metal-based powders whose purity is 99.5%or higher.

(2)Crystal Structure

In the following,we consider the most common crystal struc-tures found in piezoelectric applications.For a more detailed presentation,the reader should refer to classical textbooks.1,69Although the properties of single-crystal ceramics are often su-perior to those of polycrystalline materials,they are generally difficult,if not impossible,to produce.From a commercial point of view,only polycrystalline ferroelectrics are viable for mass-production.Because the orientation of the crystallites in a ceramic is arbitrary,a symmetry-breaking element has to be in-troduced externally in order to get a piezoelectric response.As a result,only ferroelectric materials can be used in piezoelectric ceramics.They can be poled,i.e.,their polar axis can be aligned

by an external electric field,resulting in the required break in inversion symmetry.Thus,of the 20noncentrosymmetric crys-tallographic point groups that have the potential to display pi-ezoelectric properties,only the 10‘‘polar’’groups need to be considered for piezoelectric ceramic materials:1(triclinic),2,m (monoclinic),2mm (orthorhombic),3,3m (rhombohedral),4,4mm (tetragonal),6,and 6mm (hexagonal).Among all possible crystal structures,the perovskite structure is probably the most versatile and technologically relevant.70,71Perovskites are of the chemical composition ABO 3.The structure may be described as a simple cubic unit cell with a large cation on the corners (A site),a smaller cation in the body center (B site),and oxygen in the centers of the faces.A schematic sketch can be seen in Fig.6.The structure is a network of corner-linked oxygen octahedra,with the smaller cation filling the octahedral holes and the larger cation filling the dodecahedral holes.If one assumes the ions

to

Fig.5.Diagram showing relative cost and toxicity of the elements of

interest.

Fig.6.Cubic perovskite unit cell.A-site cations are gray,B-site cations green,oxygen red.

June 2009Development of Lead-free Piezoceramics 1157

t¼

R AþR o

ffiffiffi

2

p

ðR BþR oÞ

¼1(6)

Here,t is the Goldschmidt tolerance factor.72As a rule of thumb,a perovskite structure is stable only if the tolerance fac-tor is in the range0.9o t o1.1;larger deviations of t from unity generally prevent crystallization of a compound with the com-position ABO3in the perovskite structure.Perovskite structures can tolerate A-site and O-site vacancies,but there are only very few reports on perovskite structures with B-site vacancies.73 The versatility of the perovskite structure is in part based on the many different distortions of the unit cell.It can be distorted

(a)along the cubic[100]direction(i.e.,the edges of the cube),resulting in a tetragonal cell,

(b)along the[110]direction(i.e.,the face diagonal of the cube),giving an orthorhombic cell,

(c)along the[111]direction(volume diagonal of the cube), creating a rhombohedral cell,or

(d)along arbitrary[hk0]or[hkl]directions(monoclinic and triclinic cell,respectively).

This distortion is often accompanied by tilting of the oxygen octahedra,creating glide mirror planes in the structure.As there are three equivalent[100]directions in the cube,a spontaneous polarization can develop in six directions:7[1,0,0],7[0,1,0], and7[0,0,1].Correspondingly,there are12possible domain variants in the orthorhombic structure,8in the rhombohedral, 24in the monoclinic,and48in the triclinic structures.

There have been attempts to predict the crystal system at room temperature based on the tolerance factor.Generally, structures with t close to unity show lower distortion and low Curie temperature.For t41,geometric considerations favor a tetragonal distortion,although a large number of perovskites with t41are cubic and therefore not ferroelectric at room temperature.A tolerance factor t o1favors lower symmetries; structures containing rare-earth elements are most often orthorhombic,otherwise,rhombohedral structures are more common.74However,this concept has to be used with caution: the ionic radii depend on the coordination number of the ions, which in turn depends on the structure.Furthermore,many materials with perovskite structure have several phases and change from one crystal system to another with changing tem-perature.As a rough guideline,the tolerance factor can be used to estimate crystal systems,but for a more reliable estimation, more in-depth considerations of crystal chemistry are necessary.

A variation of the perovskite structure is the so-called bis-muth layer structure(BLS)that is often encountered in piezo-electric materials75with the chemical formula Bi2A xÀ1

B x O3x13. This structure can be considered as a layer of perovskite unit cells,infinite in two dimensions,separated by(Bi2O2)21layers. The perovskite layer can have a thickness of one or more unit cells,denoted by the parameter x in the chemical formula.Fig-ure7shows a BLS ferroelectric;to keep thefigure simple,a structure with x52is selected.A typical representative of the BLS type is Bi4Ti3O12,where A5Bi,B5Ti,and x53.Mate-rials with BLS have a tetragonal symmetry in the high-temper-ature phase,limiting the number of domain orientations that can arise during the phase transition into the low-temperature ferroelectric phase,which can still be tetragonal,but more often is orthorhombic or monoclinic.

While the cubic unit cell of the perovskite is easily pictured, the structure of important ferroelectrics like lithium niobate is more complex.77–79Despite the chemical formula,LiNbO3does not crystallize in the perovskite structure:the tolerance factor is too low due to the small size of the Li ion.Its structure is de-picted in Fig.8.The basic unit is still the oxygen octahedron with a Nb ion in the center.The octahedra are again corner linked.In the ideal structure all octahedra are identical and reg-ular;three,related by the lattice operator,are in parallel orien-tation,and the other three are rotated,relative to thefirst,by 1801about the triad axis.Each octahedron shares each corner of its upper face with a corner of the lower face of an octahedron of the next layer.The Li ions are situated in the interstitial sites among the corner-linked octahedra.In the paraelectric phase this structure belongs to the symmetry group 3m.During the phase transitions,the cations are shifted along the axis or rota-tion,destroying the inversion symmetry and leaving the sym-metry group3m.As a result,materials of this type are uniaxial ferroelectrics that can only develop1801domain walls.

A fourth important class of ferroelectrics based on oxygen octahedra is formed by compounds with potassium tungsten bronze structure.80Their chemical formula is A x B2O6.However, in contrast to the simple structures described above,they have5 formula units per crystallographic unit cell.The structure con-sists of a framework of BO6octahedra,where

B is commonly occupied by Ti,Nb,Ta,or W.They share corners in such a way that three types of interstitial sites result.Each unit cell contains two large pentagonal A sites,each coordinated by15oxygen ions,four somewhat smaller tetragonal B sites,coordinated by 12oxygen ions,and four very small trigonal

C sites,coordinated by nine oxygen ions.The C sites are too small except the small-est ions such as Li1.Therefore,they are generally vacant in most tungsten bronze-type ferroelectrics.In contrast,A and B

sites Fig.7.Bismuth layered structure ferroelectric with the example of Bi2Àx Pb x Sr1.5Ca1.5Mn2O9Àdelta76(x52).The perovskite layers sepa-rated by Bi2O2layers are clearly

visible.

Fig.8.Crystal structure of LiNbO3derived from X-ray diffraction. Lithium ions are depicted gray,niobium blue,and oxygen red.The oct-ahedra faces are displayed in light blue.The viewing direction is per-pendicular to the crystallographic c-axis.

1158Journal of the American Ceramic Society—Ro¨del et al.Vol.92,No.6

can accommodate a large number of different ions.As a result, there are a large number of compounds and solid solutions that crystallize in the tungsten bronze structure.Depending on the distortion of the octahedra,the paraelectric high-temperature phase is of tetragonal or lower symmetry.As a result,the num-ber of possible polarization directions in the ferroelectric phase is not as high as in the perovskite structure;hence,tungsten bronze-type ferroelectrics are usually uniaxial.

(3)Electronic Structure

To emulate the piezoelectric properties of lead-containing ma-terials such as PZT,one has to understand the physics behind this extraordinary behavior.Most noteworthy is the large dis-tortion of the crystallographic unit cell of lead-containing per-ovskites.It will be shown in Section IV(4)that this alone does not make PZT as successful as it is.This is related to difficulties of reorienting the polarization direction in highly distorted ma-terials,lowering their usefulness in actual piezoelectric applica-tions.For now,however,we will focus on the‘‘perfect’’ferroelectric perovskite:pure tetragonal lead titanate(PbTiO3, PT).It is characterized by a c/a ratio of1.06381at room tem-perature,compared with,e.g.1.011in BaTiO3,with the distor-tion being stable against high temperatures up to the Curie temperature of4901C.To quote a textbook verbatim:‘‘From the microscopic point of view,ferroelectricity arises from a combined action of two opposing factors:a static instability of the symmetric state of the crystal lattice and thermalfluctuations which account for the dynamic stabilization of this state.’’82 There are a large number of studies that describe the interaction between the dipole moments in different unit cells based on the polarizability of the unit cell.There are,however,far less pub-lications on the question why one unit cell is more or less po-larizable than another.Simple calculation of the distortion based on ionic radii is not enough to explain the differences be-tween PT and BT.83Instead,one has to take at least two differ-ent factors into account that both depend on the electronic structure of the ions involved:the polarizability of the ions(not to be confused with the ionic polarizability of the material84) and their tendency to form chemical bonds by hybridization of electronic orbitals.

Purvis and Taylor85have shown how the presence of polariz-able point dipoles influences the piezoelectric and pyroelectric coefficients of a material.Although they based their discussion on the presence of polarizable molecules,it also holds for other types of point dipoles such as ions with a dipole moment.While the ions in a perovskite structure are usually depicted as spheres, i.e.electric monopoles,higher electrostatic moments in general and dipole moments in particular cannot be neglected if the ion occupies a lattice site with a symmetry that allows a nonvanish-ing electricfield to cause a polarization.86Detailed computa-tions agree with the intuitive assumption that the induced ionic dipole moment is large if the polarizability of the ion is large.As a result,the‘‘ionic radius’’is replaced by a‘‘crystal radius of the ion’’:it can no longer be considered spherical,but is of rather elongated shape.87Thus,the unit cell is distorted by the non-spherical ions even in the absence of an external electricfield. The distortion tends to be larger if the ions involved have higher polarizability.Furthermore,a highly anisotropic polarizability leads to changes in the phononic spectrum of the crystal that favor large vibrations and in turn high piezoelectric coeffi-cients.88,Figure9shows possible candidates for A,B,and ox-ygen sites in perovskite-type structures;Fig.10provides the periodic table with the elements in oxidation state as occurring in the perovskite structure and compares the polarizability90of a large number of ions.Elements with high,intermediate,and low polarizability arefilled with green,yellow,and orange color,re-spectively.Lead ions rank comparably high,although not ex-cessively so.This has been traced to the large effective crystal radius of the ion as well as the comparably high‘‘effective num-ber of electrons.’’91In addition,the special electronic structure of the Pb21ion comes into play.Its electronic configuration is [Xe]4f145d106s2.The remarkable feature here is the two elec-trons in the outermostfilled6s2subshell.They form a so-called lone pair,a name derived from the chemistry of polar molecules like NH3or H2O,where these configurations are more com-monly encountered.Lone pairs,i.e.two electrons paired by their antiparallel spin in afilled subshell and not involved in chemical bonding,form a dumbbell-like extrusion of the electron density on one side of the ion,increasing the polarizability and the dis-tortion of the unit cell.Additionally,they lend themselves very easily to hybridization with the orbitals of other ions.The im-portance of this hybridization has been shown by Cohen.92He found that in both BaTiO3and PbTiO3the Ti3d states are strongly hybridized with the O2p,and that the hybridization is enhanced by the ferroelectric distortion.The A-site Ba ion, however,is largely isolated;there is no hybridization of the Ba 5p orbitals.In contrast to this,the Pb6s orbitals are strongly hybridized with the O2p states,reducing the distance between the lead ion and one oxygen ion.This effect enhances the dis-tortion of the unit cell.

If one considers to replace the Pb ion while retaining the good ferro-and piezoelectric properties,one should contemplate ions that have both high polarizability,i.e.a large radius and a high effective number of electrons,91and possess a lone electron pair in an outer shell.Sb31and Te41fulfill the second requirement; their polarizabilities,however,are significantly smaller than that of Pb2190(Fig.10).Only Tl1and Bi31meet both the require-ments.Of the two,Tl is quite expensive,prohibiting its use on an industrial scale(see Section IV(1)),and,even more importantly, its toxicity dwarfs even that of lead.From the atomistic point of view,bismuth-containing compounds thus seem to be the most likely successors to lead-based piezoelectrics.93

(4)Phase Diagrams

Having discussed suitable elements(Sections IV(1)and IV(3)) and crystal structures(Section IV(2)),we now consider suitable phase diagrams in our search for high-performance lead-free piezoceramics.From the extensive body of work on PZT,1it is known that the MPB between rhombohedral and tetragonal PZT maximizes dielectric permittivity,piezoelectric coefficient, and coupling factor.Landau–Devonshire–Ginzburg theory pro-vides that the Gibbs free energy profile for the rhombohedral and the tetragonal PZT exhibits anisotropicflattening at the MPB.94This enhances domain wall mobility.Further,a high transverse dielectric permittivity,w11,is associated with facili-tated polarization rotation for the case of off-polar-axis-oriented ceramic grains.95These grains contribute to a large macroscopic piezoelectric response through a high piezoelectric shear coeffi-cient,d15.A tendency toward a monoclinic distortion results from theflat Gibbs free energy function and,in the extreme case,may lead to a monoclinic phase.96This polarization rota-tion has been verified experimentally using high-energy X-rays97 and theoretically rationalized using an ab initio approach.98A very similar Gibbs free energy function pertains also to a poly-morphic phase transition(PPT).94Hence,both phase transi-tions,one with changes in composition only(MPB)and the other one involving temperature change(PPT),can lead to good piezoelectric properties.Naturally,materials exhibiting an MPB are more attractive as the good properties are not restricted to a narrow temperature range.

Before discussing MPB in lead-free materials,it is perhaps useful to state that the view of MPB in PZT is today much more complex than it appeared just a decade earlier.There are four different,even somewhat opposing,views of what an MPB is in ferroelectrics,and in PZT in particular.Thefirst view is that the MPB region in PZT consists of a monoclinic phase,which bridges Zr-rich rhombohedral and Ti-rich tetragonal phases.99 The second view is that monoclinic distortion observed in X-ray diffraction experiments is only apparent and due to the coexis-tence of tetragonal microdomains and rhombohedral nanodo-mains.100The third view proposes a model where there is no sharp boundary across the MPB in the PZT phase diagram.All

three phases (tetragonal,monoclinic,and rhombohedral)can be considered as monoclinically distorted,with progression from short-range to long-range to short-range order across the MPB region.101The fourth view claims that presence of PbTiO 3is

crucial for appearance of an MPB in all lead-based systems.Lead titanate exhibits a pressure-induced transition from tetrag-onal to monoclinic to rhombohedral phases at 0K.The other end member (e.g.,PZrO 3)simply tunes this phase transition

to

Fig.9.Possible candidates for A,B,and oxygen sites in perovskite-type

structures.

Fig.10.Polarizability of typical cations in A

3in their most common valence state.

In the following,we suggest design guidelines using promising end members in constructing phase diagrams suitable for MPBs with lead-free piezoceramics.Feasible end members can be found with orthorhombic,tetragonal,and rhombohedral crys-tal structures,examples of which are provided in Table I.

The tolerance factor concept72outlined in Section IV(2)is useful in considering further compounds for tetragonal and rho-mbohedral crystal structures based on the size of A,B,and ox-ygen ions.Tetragonal and cubic perovskite structures are typically found for a tolerance factor t41.0,while lower sym-metries,such as rhombohedral,orthorhombic,and monoclinic perovskite structures are found for t o1.0.74The ionic radii are provided by Shannon.104In a similar fashion to the investi-gation of the MPB between BNT and BT,24many other systems have been explored in the search for MPBs.Table II provides examples for phase diagrams formed by end members from two different crystal structures from above.Some guidelines could possibly be found from the concepts proposed by Eitel et al.105for lead-based materials in their search for high Curie temperature.

The concept of the MPB between two crystal structures may be further extended to reachingflat Gibbs free energy curves by combining solid solutions among end members of three different crystal structures.This concept is visualized in Fig.11,where a quasi-ternary phase diagram between BNT–BT and KNN is constructed.A number of MPBs are marked for further exploration.This concept using the phase diagram provided has been exploited by Zhang et al.115–117with compositions on the line(full line in Fig.11)connecting the MPBs between BNT–BT24and KNN–BT.106In a similar manner,other connecting lines between MPBs(e.g.,from0.94BNT–0.6KNN to0.94BNT–0.06BT)appear as attractive candidates for further consideration(dotted line in Fig.11).A further varia-tion on this approach has been demonstrated by Wu et al.118 and Li et al.,119who explored the systems BNT–BT–NN118and BNT–BKT–NN,119respectively.In their approaches,they also added sodium niobate with the view to adding an antiferro-electric material to mimic the case of PZT where one of the end members PZ has the antiferroelectric order.A combination of MPBs between same crystal structures has also been demon-strated to provide useful results.Specifically,Makiuchi et al.120 combined the tetragonal/rhombohedral system BNT–BT with another tetragonal/rhombohedral system BNT–BKT and ob-tained improved properties(see also Section V(2)).(5)Guidance from Theory

Guidance in developing lead-free piezoceramics can be envis-aged from computer simulation and modeling including meth-ods of continuum mechanics,122from phenomenological Ginzburg–Landau–Devonshire models94,95and from ab initio modeling.123,124Following the prior sections,methods based on quantum mechanics should have the strongest impact,because they allow predicting the role of particular elements in the context of ferroelectricity,as well as the suitability of certain phase compounds,in analogy to Sections IV(1)–IV(4).We address these issues specifically for lead-free piezoceramics in the following,but begin with general guidelines obtained on piezoceramics.

A seminal paper from199292emphasized the relevance of charge distortion and covalency.Hybridization between the ti-tanium3d states and the oxygen2p states was described as es-sential for ferroelectricity.The author also found strong hybridization between lead and oxygen states,resulting in large strain,which then stabilizes the tetragonal state in PbTiO3.In comparison,the interaction of barium with oxygen is completely ionic and a rhombohedral structure is favored for BaTiO3.A-site and B-site activities are further considered by Ghita et al.125 Greater B-site activity,for example,is described as enhancing the size of the rhombohedral region in phase diagrams for fer-roelectric perovskites,thus determining the position of the MP

B between rhombohedral and tetragonal crystal structures.This is governed by the interaction of the A site to oxygen and the B site to oxygen bonds mediating the A-site to B-site repulsion.126This interplay is then studied to predict the MPB between PbTiO3 and a Bi-based perovskite.

While a number of very insightful publications on Pb-based ferroelectrics could benefit from structural data on the materials of interest and on the availability of polarization and strain val-ues,the theoretical work on lead-free piezoceramics could be related to the benchmarking on PZT and other materials.It now has in part overtaken the experimental effort in the search for lead-free piezoceramics.

In contrast to lead titanate,92where the tetragonal ground state is stabilized by strain,off-centering of an A ion(in this case lithium)can alone provide strong A site-driven ferroelectricity and a tetragonal ferroelectric ground state.This is augmented by frustration of tilt disorders of the oxygen octahedra,which destabilizes the inversion symmetry.127As a result,the presence of an MPB between tetragonal and orthorhombic structures is suggested in KNbO3–LiNbO3.Similar to lithium,silver has the potential to off-center on the A site in the perovskite structure,128enabling an internal polarization similar to PbTiO3. Large rotations of the oxygen octahedra,however,seem to pre-vent ferroelectricity in AgNbO3.One possible approach,alloy-ing AgNbO3with BaTiO3,is predicted to provide a good

Table I.Examples of Compounds of Different Crystal Structures for the Construction of Phase Diagrams Containing

a Morphotropic Phase Boundary

Orthorhombic Tetragonal Rhombohedral KNbO3(KN)BaTiO3(BT)Bi1/2Na1/2TiO3

(BNT) NaNbO3(NN)Bi1/2K1/2TiO3

(BKT)

BiFeO3(BF)

AgNbO3(AN)BaCu1/2W1/2O3

(BCuW)BiMg1/2Ti1/2O3 (BMT)

Table II.Examples for Phase Diagrams Based on End Members from Two Different Crystal Structures Orthorhombic/tetragonal Orthorhombic/rhombohedral Tetragonal/rhomboedral KNN/BT106,107BNT–NN108BNT/BT24

KNN/BKT109BNT–BCuW110BNT/BKT26,111

BNT–KNN112,113BF/BT

114Fig.11.Quasi-ternary phase diagram between BNT–BT and KNN ex-hibits a number of MPBs useful for further exploration,which have been reported.24,106,112,113,121piezoelectric material with two MPBs.Although good proper-ties in this system have not been reported,the potential of AgNbO3has been demonstrated recently,where large electric fields of22kV/mm produced very high polarization(52m C/ cm2).At low electricfields,however,the reported ferroelectricity was very weak129as predicted.128In a related study,Kagi-mura130found that the small ion(in comparison with Ba21) La31shifts off-center and initiates ferroelectricity in the nonfer-roelectric host material BaZrO3.

Although BiAlO3according to its tolerance factor of1.01is expected to be tetragonal,density functional calculations83,131 predict it to be rhombohedral.Moreover,its internal polar-ization is suggested to be larger than that of PbTiO3.Indeed, its rhombohedral structure has been confirmed on BiAlO3 synthesized by a high-pressure high-temperature technique.132 Its properties are characterized by a low room-temperature piezoelectric coefficient,but a high Curie temperature (T c45201C).133,134

Finally,Burton and Nishimatsu135computed the phase dia-gram of KNN and predicted a miscibility gap.This could be accessible by slow cooling and provide chemical clustering and relaxor characteristics in KNN.

V.Sodium Potassium Niobate and Related Materials

K1Àx Na x NbO3(KNN)is the most investigated lead-free ferro-electric system of the last5years following work of Saito and colleagues23,136,surpassing bismuth alkali titanate-based mate-rials.In2004,this group at Toyota Central Research Labora-tory reported on KNN materials modified by Li,Ta,and Sb, with piezoelectric constants comparable to those of PZT at room temperature.While this report has triggered much of the subsequent activities in lead-free materials all over the world,it should be mentioned that the same family of materials has at-tracted the interest of industry earlier.Thus,Murata Manufac-turing Co.hasfiled patents in1998and1999on KNN ceramics modified by Li and Ta and additional elements.137In Europe, thefirst large-scale European projects on KNN-based materials started in2001138and projects dedicated to the development of lead-free piezoelectrics have beenfinanced since then either on a European or national level.

(1)Structure and Properties of Pure K1Àx Na x NbO3

K1Àx Na x NbO3is a solid solution of potassium niobate(KNbO3 or KN)and sodium niobate(NaNbO3or NN).Both are or-thorhombic at room temperature.KN displays the same se-quence of phases as barium titanate,but all phase transitions appear at higher temperatures than in BT.18,139NN was origi-nally reported as ferroelectric140but is in fact antiferroelectric.141 For typical properties of pure KNN and its end members KN and NN,see Table III.

Pure KN ceramics are more difficult to prepare1than KNN, but large crystals are now routinely produced.Crystals are mostly of interest for their outstanding nonlinear optical prop-erties.151Only recently it has been discovered that KN crystals exhibit interesting piezoelectric properties along special crystal directions.54,152Of most interest are unusually large coupling coefficients for horizontal shear surface acoustic waves and thickness extensional mode,k t.The latter exhibit a maximum value of0.69along a direction that is40.51away from the polar axis as shown in Fig.12,and is the largest k t reported in any material.For comparison,a typical value for PZT is about0.5.For this special crystal orientation k t exhibits remarkable tem-perature stability from room temperature up to1601C.60Com-bined with a low relative dielectric permittivity(about100) along the same direction,these properties are very attractive for single-element medical ultrasonic transducers operating at high frequencies.59Because they are mostly produced for optical applications requiring extensive polishing and a perfect mono-domain state,KN crystals are prohibitively expensive.However, as reported by Davis et al.,60the high electromechanical prop-erties can also be obtained in[001]C-oriented crystals,Fig.12, rotated by451away from the polar axis.Because this orienta-tion can be domain engineered153(i.e.,polydomain)and optical quality polishing is not needed for crystals to exhibit excellent electromechanical properties,the price of crystals can be re-duced significantly.Further KN is noted for exhibiting surface acoustic waves based on pure horizontal shear.152Other than that pure KN has generated little interest as a piezoelectric ma-terial.Pure NN is antiferroelectric and thus nonpiezoelectric and will not be discussed here.

First reported as ferroelectric by Shirane et al.,18KNN was investigated in detail by Egerton and Dillon142who reported piezoelectric data and identified enhanced ferroelectric proper-ties at the47.5%potassium niobate composition.The phase diagram of K1Àx Na x NbO3is much more complex than that of PZT28with several thermally induced phase transitions(PPTs) and MPBs summarized by Ahtee and colleagues154,155as dis-played in Fig.13.

At room temperature,phase transitions lie at17.5%,32.5%, and47.5%NN content,the latter commonly taken as50/50 analogous to PZT.Notable is the almost composition-indepen-dent PPT between ferroelectric phases at B2001C and between ferroelectric and paraelectric phases at B4001C.On the sodium-rich side only small substitutions of sodium by potassium cause a transition to ferroelectric(region Q)from the pure antiferro-electric sodium niobate(region P).

The properties of KNN are inferior to those of PZT(Table III)and this fact together with difficult processing(see next sec-tion)made these materials of little interest for applications.This changed at the end of the1990s when environmental and health concerns required a radical approach in developing new piezo-electric materials.

(2)Processing of KNN-Based Materials

(A)Processing of Polycrystalline KNN and its Deriva-tives:In conventional mixed oxide processing of KNN-based materials,desirable for industrial applications,four critical is-sues are currently known.They are volatility of alkali ox-ides,156,157compositional inhomogeneity,for example,when tantalum is introduced,158phase stability at high tempera-tures,159and most significantly poor densification.145The vola-tility can be addressed by introducing excess alkali metal oxides160and calcination and sintering in atmospheric pow-der161in sealed crucibles,where mass loss is negligible.159Mec-hanochemical activation or synthesis by high-energy ball milling can reduce calcination temperatures or replace the calcination step entirely and further reduce loss of alkali metal oxides.162,163 Compositional inhomogeneity of Ta-modified KNN is attenu-ated by forming precursors of predetermined compositions of materials with similar reactivity.158The phase instability of the perovskite phase at high temperatures is closely related to vol-atility of the alkali metal oxides.Just above11001C,alkali-de-ficient secondary phases of tungsten bronze structure can appear and are accompanied by abnormal grain growth.1This limited

Table III.Typical Properties of KNN and its End Members

T C(1C)e r k p(%)d33(pC/N) KNN40018,142230–475143,14423–40142,143,145,14680–160142,143,145 KN416–434140,147410001481514957149

NN48014020–200144,150——

temperature range for sintering results in poorly densified ce-ramics with at most 93%–95%of theoretical density when the conventional sintering technique is practiced.142,146,165The dens-ification can be improved through manipulation of heating rates to within 2K/min.Variations of sintering temperatures of 20K lead to a three percentage point change of relative density lead-ing in turn to a drop in coupling coefficient to 50%of the achieved maximum value.While it is widely assumed that there is an MPB at 47.5%NN,there are some who suggest that the improved behavior is due to better sintering around this NN concentration.28,166Densification can be improved by hot press-ing leading to 99%–99.8%relative density and in turn to a 20%higher coupling coefficient (0.48)compared with the highest re-ported in conventionally sintered samples as well as almost dou-bling d 33values.167–169

While there are few reports on spark plasma sintering of KNN-based materials,170,171achieved relative densities of 98%are lower than for hot pressed materials.Sintering of sodium-rich compositions proves difficult.Increased coercive field and an almost halved remnant polarization are discouraging.High-temperature annealing is always required to reduce conductivity due to oxygen deficiency.Nevertheless,a d 33value of 148pC/N and dielectric constants at room temperature of 550compared with 275–470for hot pressed and conventionally sintered sam-ples should be noted.

(B)Single Crystals and Thin Films:Single crystals of pure NN and NN with low concentrations of potassium are relatively easily prepared from the flux method with Na 2O,K 2O,Nb 2O 5,and NaF 18,140,172or NaBO 2173as solvents.KN crystals

are grown from a melt of K 2O and Nb 2O 5by spontaneous nu-cleation.174However,these methods were reported unsuitable for growing K 0.5Na 0.5NbO 3crystals of reasonable quality.154Recently,KNN crystals with sodium/potassium ratios near 1:1have been grown via a self-flux method from KNN powder us-ing eutectic NaF/KF flux.175KNN 176and Li-and Ta-modified KNN 177single crystals were grown by solid-state crystal growth using KTaO 3seed crystals with K 4CuNb 8O 23as a sintering aid.This method overcomes difficulties in fabricating crystals with precisely controlled compositions.These crystals,while with controlled composition,are not of full density.Hot pressing in-stead of conventional sintering can reduce the porosity of the grown crystals.178KNN crystals with 2%Li with good proper-ties have been grown by top-seeded solution growth (TSSG).60

Thin films of piezoelectric materials are attractive for MEMS and ultrasonic transducers providing lower operating voltages and higher frequencies than what can be expected in bulk ce-ramics.Radio-frequency (RF)magnetron sputtering with K 1/2Na 1/2NbO 3targets onto a Pt 0.8Ir 0.2substrate yielded single-phase perovskite films with about 30%deficiency in the alkali metal oxides.Processing under reduced pressure and tempera-ture suggested that the deficiency is not a result of the heat treatment but the sputtering process.179Dielectric constants of about 500are reported.180Films of KNN without deficiency of alkali elements can be achieved by adjusting the ratio K:Na:Nb in the target material to 1.5:1.5:1.181As a drawback of alkali compensation,however,long-term stability and resistance to humidity are adversely affected.Pulsed laser deposition,on the other hand,can give thin films of KNN with near stoichiometric composition.182Cho and Grishin 183in fact reported that apply-ing high pressure during the deposition is one of the key pa-rameters in achieving a good stoichiometry,which is guaranteed only when all the elements are thermalized simultaneously dur-ing deposition.They also report a remnant and spontaneous polarization of 10and 17.5m C/cm 2,respectively,a loss tangent of 2.5%,coercive field of 2kV/mm,and a resistivity of about 1012O Ám 183equal to the bulk resistivity.142Conductivity of (Li,Ta,Sb)-modified KNN thin films can be reduced by three orders of magnitude with manganese doping.184Early attempts to pre-pare KNN via three different sol–gel routes,alkoxide route,ox-alate,and Pechini method,did not result in single-phase perovskite films even at sintering temperatures of 9001C.Sta-bility of the precursor solutions and porosity were also an is-sue.185Tanaka et al .186further investigated the alkoxide route and fabricated single-phase perovskite films.Films by chemical solution deposition needed 15%–50%excess alkali metals to form single-phase material and gave dielectric constants up to 900.187Chemical vapor deposition is also known to produce single-phase films,but avoiding niobium deficiency is still a challenge.188

(3)Chemical Modifications of KNN

The chemical modifications of KNN can generally be divided into two groups.The first group attempts to improve properties by preparing compositions close to an MPB or by shifting the orthorhombic to tetragonal (O –T )phase transition found in pure KNN at 2001C 154,155to near or below room temperature.The second group attempts to improve the sintering behavior of KNN while keeping its inherent structure and phase diagram aiming to improve specific properties like piezoelectric or cou-pling constants.While the latter was the intention of many studies,e.g.,work of Saito et al .,23the former was often accom-plished.28Some common values for different chemical modifi-cations of KNN can be found in Table IV.We next discuss both issues in some detail.

(A)Modifications to the Phase Diagram:Enhancement of electromechanical properties can be achieved in a material by inducing structural instabilities.These can have different origins:compositional (MPB),1thermal (PPTs),203or can be induced by external electric 98or stress 204fields.94MPB is a preferred route because unlike temperature,the composition does not

change

Fig.12.The thickness-coupling coefficient in KNbO 3single crystals.The angle y indicates rotation away from the polar axis ([110]C in pseu-docubic system).The k t is largest for y 540.51,but nearly as high values are obtained at y 5451(i.e.,[001]C in pseudocubic direction).The latter cut can be domain engineered (poled into sets of equivalent domain states 153

).

Fig.13.Phase diagram of K x Na (1Àx )NbO 3.Regions labeled with Q,K,and L are monoclinic,although angular distortions are such that they are commonly regarded as orthorhombic ferroelectric;M and G are or-thorhombic ferroelectric;F,H,and J are tetragonal ferroelectric.Region P is orthorhombic antiferroelectric.154,155Taken from ACerS-NIST Phase Equilibria Diagram Database.

during exploitation.Stress-induced instabilities are impractical as in many cases they require separate devices to maintain ex-ternal field;however,it may be interesting to explore composite solutions in which one phase provides the pressure.Ideally,an MPB should exhibit little temperature dependence,i.e.,it should be close to vertical in the temperature–composition phase dia-gram.This is nearly the case in PZT,where the MPB only slightly depends on temperature.

For compositions close to a vertical MPB this means that temperature variations always keep the material close to the MPB,i.e.close to the instability condition;see Fig.14(a).If the MPB is temperature dependent,then properties will be en-hanced close to the temperature of the phase transition and the MPB.As temperature changes the material is brought away from both MPB and PPT instabilities,and properties decrease (see Fig.14(b)).This is the case for the Li-and Ta-modified KNN,as illustrated by phase diagrams shown in Matsubara et al .205and Klein et al .,206and is probably the case for most of the modified KNN compositions presently being investigated.

In ferroelectric materials crossing a phase transition line also leads to changes in domain wall structure and thus depolariza-tion of ceramics.To avoid depoling,it is often preferable to use compositions with PPT below room temperature.The perovs-kite mineral,CaTiO 3is known as an effective phase transition shifter in KNN-based materials.In Li-and Sb-modified KNN it can lower the O –T phase transition temperature well below room temperature leading to a material with somewhat lower properties than when CaTiO 3is not used but with a better thermal stability over a temperature range from À501to 2001C.207,208

Despite highly temperature-sensitive properties,the chemical modifications of KNN exploiting the enhancement of the prop-erties at the O –T phase transition have seen considerable inter-

est.193,194,209–219In their paper on the discovery of large piezo-electric coefficients in KNN modified with Li,Ta,and Sb (d 334300pC/N (untextured),d 334400pC/N (textured),Curie temperature of 2531C)Saito et al .23interpreted the enhanced properties as a consequence of an MPB between the ortho-rhombic and tetragonal phases.The position of this phase tran-sition has now been asserted to lie at 6%–7%LT.192,220Subsequent studies have shown that in the Li-modified mate-rial the phase boundary between orthorhombic and tetragonal phases is temperature dependent and is situated near room tem-perature for compositions with maximum d 33.28Thus,the en-hanced piezoelectric response in Li-,Ta-,Sb-modified KNN is most likely due to the effects of the PPT.It is worth mentioning that a vertical MPB has been reported below À1001C in Li-modified KNN.206Following the work of Saito et al .23,the enhancement of the piezoelectric properties was attempted either by moving the O –T PPT to ambient temperature,accomplished by minor changes in original composition,or by optimizing processing conditions.Commonly d 33values of around 200pC/N and Curie temperatures of about 3501C are reported with a few studies reaching values of d 33of 300pC/N.210A gain of 100pC/N normally comes with a 100K penalty in Curie temperature.Related subsystems with variations in Li and Ta,158,159,161,192,220–226Li and Sb,227–235Li alone,161,1–192,205,224,236–242or just Ta 243–245have been in-vestigated in great detail regarding microstructure,sintering conditions and phase transition temperature.Generally speak-ing,the effects of the constituents are as follows:tantalum doping hinders abnormal grain growth and decreases T C and the O –T transition temperature.243–245Lithium decreases the O –T transition temperature to room temperature at about 6at.%A-site substitution and increases T C while also improving densification.The effect of LiSbO 3is similar to that of LiNbO 3,except 1%less is required to shift the O –T transition to room temperature.227,229It has become apparent that other issues such as temperature stability of polarization and piezoelectric prop-erties,190,191processing difficulties,and the cost of tantalum would impede large-scale industrial application.SrTiO 3doping of KNN produces relaxor behavior 197,198,220,246,247with dielectric constants reaching 3000and with SrZrO 35000at the same time providing better cycling stability than lanthanum-doped PZT.248This effect occurs to a lesser degree when using CaTiO 3,249where e r is only about 1000.CaTiO 3,however,improves the resistance to humidity when used in small quantities.BNT gives relaxor behavior with a less temperature-stable dielectric constant.199

It was reported that BaTiO 3forms an MPB 106with KNN,at approximately 6%BT;however,a closer inspection of the di-electric data in this report suggests that in this solid solution

6%

Fig.14.A vertical MPB as schematically shown in (a)provides tem-perature-independent properties,while a curved MPB does not (b).

Table IV.Typical Properties of Materials Derived from KNN

System

e 33T /e 0

k p

(%)d 33(pC/N)P r

(m C/cm 2)E c

(kV/mm)S max /E max (pm/V)T d /T 2(1C)T c (1C)

References

KNN 16%Li

38235

B RT 475Guo et al .1

20

2.0

15

Higashide et al .190480Hollenstein et al .191500

45250175450Hollenstein et al .192KNN 1Li,Ta,Sb

300400

253Saito et al .23

6.4(10)35.68.7B 0.2338

Zhao and Zhang 1931282

49.4274 4.37

B 1.550

Yoo et al .194

KNN 1SrTiO 30–10%412–144816–32.530–96Guo et al .19537195

Wang et al .19615%3000Kosec et al .197333075

Bobnar et al .198

KNN–BNT 43195B 1.4

375

Zuo and colleagues 113,199KNN–5BT 105836225Ahn and colleagues 200,201KNN–2BT 1003291047.5 1.2358Guo et al .106

KNN 1Cu

B 200

39

180

20

1.3

225

170

402

Matsubara et al .202

BT shifts O–T transition(PPT)closer to room temperature. Sintering of Ba-modified KNN was improved by formation of a liquid phase above10601C200also causing abnormal grain growth.201Mixtures with other ferroelectric systems in low concentrations like BiFeO3,250Bi1/2K1/2TiO3,109BNT,113 or BNT–BT251also exhibited dominant effects from PPT rather than MPB.

(B)Modifications Targeting Sintering Behavior:Copper has been discovered as an effective sintering aid in the form of K4Cu(Nb/Ta)8O23,202giving97.5%relative density and unipo-lar strain of0.09%at4kV/mm252as well as d33values of180 pC/N.The percentage of sintering aid should,however,remain below0.5%,otherwise piezoelectric properties degrade.253Sinte-ring temperatures as low as9501C were possible for KNN-rich systems.254,255Copper sintering aids have since been added to various more complex KNN-based systems256,257with equiva-lent effect.In required concentrations,both T C and the O–T transition were reported to decrease slightly.258

Some effects of single-element doping can be summarized as follows:silver oxide,or Ag(Nb/Ta)O3,increases the Curie tem-perature of Li-,Ta-,and Sb-modified KNN more strongly than LiNbO3while decreasing the O–T transition tempera-ture.219,259,260Replacing niobium with30at.%tantalum gives increased electrostrictive effects and0.11%unipolar strain at4 kV/mm.Manganese lowers losses and e r107and improves the mechanical quality factor Q m and k p.261A study of0.5%alkali-earth doping showed that strontium and calcium improve sinte-ring and magnesium oxide hinders it.All these elements de-creased phase transition temperatures.Barium oxide leads to formation of secondary phases.262ZnO and SnO2improve sinte-ring.WO3,SnO2,Sc2O3,and CeO2hinder grain growth,and all but SnO2also hinder densification.263Zirconia impedes grain growth.2Bi2O3appears to improve phase stability of KNN at high temperatures,265but raises sintering temperatures as well.

PZT is used as hard or soft material1and any‘‘universal’’lead-free alternative to PZT would also have to be made in soft and hard variants.Another option is to develop several lead-free materials,some of which would have hard and some soft characteristics.In a recent study,Hagh et al.266showed that Ba-doped(K,Li,Na)(Nb,Sb)O3exhibits softening with Ba concentrations below1.5mol%.The authors propose compen-sation of naturally formed V K vacancies by Ba K donor defects. Once the1.5mol%limit is passed,the compensation is elec-tronic.A similar limit is believed to exist in donor-doped PZT1 where softening is possible only below certain concentrations of donor dopants.Interestingly,other studies on unmodified (K,Na)NbO3claim that A-site doping with Sr did not lead to softening.267A possible explanation for the absence of softening in that study was that the material was simultaneously doped with Ti for Nb,creating acceptor Ti Nb defects,which could have neutralized Sr-donor charges;thus,there was no need to create A-site vacancies as a compensating effect and the softening effect was absent.

In summary,so far there are no methods for raising the O–T transition to higher temperatures,all dopants had the opposite effect.Few,in particular LiNbO3and AgNbO3,increased T C allowing for purely tetragonal material from room temperature to beyond4001C but with the inherently lower piezoelectric properties of the tetragonal phase.The main mechanism of en-hancement of the piezoelectric properties appears to be the proximity of the O–T PPT to room temperature rather than compositional(MPB)effects.

VI.Bismuth Sodium Titanate and Related Materials Similar to KNN,Bi-based materials like bismuth sodium titan-ate Bi1/2Na1/2TiO3(BNT)and bismuth potassium titanate Bi1/2 K1/2TiO3(BKT)have attracted wide interest as a possible alternative to lead-containing piezoceramics.Solid solutions of these ceramics,either among each other or together with BaTiO3,were found to form MPBs with enhanced piezoelectric properties compared with those of their end members.24,27While the MPB concept was very successful in PZT,1there are some drawbacks for lead-free systems.These are the presence of a depolarization temperature below T C and a poor temper-ature stability of the properties due to a curved MPB.28How-ever,several patents already have beenfiled indicating the benefit of Bi-based lead-free materials for industrial applica-tion.268,269

(1)Structure and Properties of Selected Bi-Based Materials

(A)BNT and BKT:Bismuth sodium titanate Bi1/2Na1/2TiO3 (BNT)and bismuth potassium titanate Bi1/2K1/2TiO3(BKT)are important as end members for a variety of solid solutions,al-though the properties of the pure materials themselves are not sufficiently good for applications.In1960Smolenskii et al.270 found BNT to be a perovskite-type ferroelectric at room tem-perature.BNT is a relaxor ferroelectric with a diffuse phase transition from rhombohedral to tetragonal phase between2001 and3201C and from tetragonal to cubic phase at5401C.271–274 The region between2001and3201C has been discussed contro-versially as either being antiferroelectric275or exhibiting a coex-istence of rhombohedral and tetragonal phases with polar regions.272–274Recently,in situ temperature TEM studies sug-gested that there is a phase transition from ferroelectric rho-mbohedral to antiferroelectric orthorhombic phase proceeded via an antiferroelectric modulated phase consisting of ortho-rhombic sheets in a rhombohedral matrix in the temperature range from2001to3001C.A second phase transition from O–T phase occurs near3201C,which corresponds to the antiferro-electric/paraelectric phase transition.276,277

Properties of BNT are summarized in Table V.Here and in the following the dielectric constant e33T/e0was taken from poled samples and is usually higher than the dielectric constant e r from unpoled samples.1High leakage currents together with the high coercivefield make it difficult to pole BNT;thus,for conven-tionally produced samples saturation could not be reached.1The sintering temperature is higher than12001C,which might be the reason for high conductivity due to vaporization of Bi ions.278 However,dense ceramics have also been obtained at tempera-tures as low as9801C.112With normal sintering at12251C and 0.3wt%Bi excess or hot pressing at11001C without Bi excess, saturated hysteresis loops were obtained.30,278BNT has a tem-perature of maximum permittivity of about T m53201C;never-theless,the depolarization temperature T d associated with the ferroelectric–nonferoelectric phase transition of about2001C is rather low.

BKT was synthesized by Popper et al.282in1957,but its fer-roelectricity wasfirst proven by Buhrer,283who found a high Curie temperature of3701C.BKT is a tetragonal lead-free fer-roelectric with a second phase transition at a temperature just above3001C.Similar to BNT,BKT is difficult to sinter284and also difficult to pole due to a high E c.With hot pressing methods densities higher than97%and d33582pC/N were ob-tained.279,280The poling process was improved byfield cooling, and together with Bi as a sintering aid d33was raised up to100 pC/N.However,these measures decreased the temperature of second phase transition and Curie temperature.280Properties of BKT are summarized in Table V.

(B)Binary Bi-Based Systems BNT–BT,BKT–BT,and BNT–BKT:Among the BNT solid solutions(1Àx)Bi1/2Na1/ 2

TiO3–x BaTiO3(BNT–BT)found by Takenaka et al.24stands out.Figure15shows the phase diagram of BNT–BT proposed by Takenaka.24There is an MPB between rhombohedral and tetragonal phases at x50.06with highly enhanced dielectric and piezoelectric properties.The piezoelectric constant d33was found to be125pC/N,e33T/e05580,k33555.0%,and tan d51.3%.However,T c dropped significantly at the MPB to values as low as2881C,and more importantly,T d became very low at the MPB due to the formation of an antiferroelectric phase.As mentioned above,in contrast to PZT the MPB is strongly curved,thus leading to low-temperature stability of the properties.In contrast to BNT and BKT,BNT–BT is easily sintered at temperatures between11001and12001C.Many researchers have since investigated BNT–BT synthe-sized by different methods near the MPB composition.285–291 The overall achieved properties of BNT–BT and of Bi-based solid solutions are summarized in Table VI.Studies on compo-sitions on the BT side of BNT–BT revealed inferior piezoelectric and dielectric properties with low T d,T c,P r,and high E c and tan d.292–294

Like in the case of pure BNT,there is still a controversy about the phase transformations of BNT–BT.Takenaka et al.24pro-posed the existence of an antiferroelectric phase at temperatures higher than T d based on dielectric and piezoelectric measure-ments.Suchanicz et al.294suggested instead a coexistence of po-lar tetragonal regions in a nonpolar cubic matrix.Qu and colleagues306,307explained the deformed hysteresis loops above T d with the coexistence of trigonal and tetragonal states with alternating polar microdomains.

Bi1/2K1/2TiO3–BaTiO3(BKT–BT)ceramics in contrast re-vealed relatively low piezoelectric properties with d33%60pC/ N,k33%37%,and a comparable T c%2901C.305

Bi1/2Na1/2TiO3–Bi1/2K1/2TiO3(BNT–x BKT)was synthesized in1996by Elkechai et al.26and enhanced piezoelectric proper-ties were discovered in the composition being close to the rho-mbohedral–tetragonal phase boundary.Later the existence of an MPB between rhombohedral BNT and tetragonal BKT be-tween x50.16and0.2was proposed by Sasaki et al.27However, there is still a controversy about the existence of an MPB in BNT–BKT.308As expected from the high Curie temperature of BKT,BNT–BKT possesses higher T c and T d with respect to BNT–BT.The piezoelectric constant d33and e33T/e0are also slightly higher while other properties are comparable(see Table VI).BNT–BKT reveals relaxor behavior possibly due to cation disorder of Na and K at the A site.297,309In analogy with BNT–BT ceramics,BNT–BKT exhibits the lowest T d at the proposed MPB,where best piezoelectric properties are observed.298With increasing BKT content above30mol%,ceramics are less dense and more difficult to pole because of increasing leakage cur-rents.298,299Bi excess as compensation of Bi-volatilization and optimized sintering temperature could improve densification and piezoelectric properties.300,310,311

(C)Ternary Systems BNT–BT–BKT and BNT–BT–KNN:The ternary system BNT–BKT–BT was investigated intensively due to high piezoelectric properties combined with a relatively high Curie temperature near the MPB between rho-mbohedral and tetragonal phases(see Fig.16).120,303,312–316Typ-ical values for MPB compositions are shown in Table VI on the basis of a selected example.303In general,properties are com-parable to the binary systems discussed earlier.Like in the sys-tems above,there is an inverse relation between d33and T d with the highest d33and lowest T d at the MPB.317Properties of BNT–BKT–BT were suggested to be good enough to replace PZT in certain applications such as ultrasonic wirebonding transduc-ers318and accelerometers.319

Another approach to producing high-strain BNT-based ma-terial was to combine an MPB between a rhombohedral(BNT) and a tetragonal structure(BT)with an orthorhombic material (KNN)to ease domain wall movement and polarization rota-tion.Peak strains under unipolar loading of0.45%were ob-tained.115Although the polarization–field curves point to a perfectly ferroelectric material,the crystal structure appears to be close to cubic115and domain structures cannot be imaged.116 Albeit nominally far into the antiferroelectric or nonpolar re-gime,strains of0.2%with little temperature dependence can be obtained up to2001C.117Recent work suggests that a strong lattice distortion only occurs under the electricfield,which then allows the development of high strains.320Similar effects as KNN in BNT–BT were obtained in Ta-doped BNT–BT.321

(2)Processing

(A)Polycrystalline Bi-Based Materials:Bi-based binary and ternary systems are usually obtained by conventional ceramic processing.As mentioned above,in the pure BNT and BKT systems sintering temperatures are high and dense ceramics can-not be obtained easily.With hot pressing full densification could be achieved,but this method is too expensive for most applica-

Table V.Properties of BNT and BKT w

e33T/e0 (1kHz,RT)k33

(%)

d33

(pC/N)

S max/E max

(pm/V)

P r

(m C/cm2)

E c

(kV/mm)

T d

(1C)

T c/T m

(1C)References

BNT422(HP)48(HP)98(HP)38w7.3w200315–337

(Bi)Jaffe and colleagues1,270,275,278

406(Bi)47(Bi)94(Bi)

BKT769(HP)34(HP)k p

15(CS)82(HP)–101

(HP1Bi)

133

(HP)

22.2

(HP)

5.25

(HP)

310

(HP)

370–410

(HP)

Hiruma and

colleagues279–281

w Saturation not reached.HP,hot pressing;Bi,0.3wt%bismuth excess;CS,conventional

sintering.

Fig.15.Phase diagram of BNT–BT.F a,ferroelectric rhombohedral phase;F b,ferroelectric tetragonal phase;AF,antiferroelectric phase;P, paraelectric phase.

24Fig.16.Phase diagram of BNT–BKT–BT system includes the morpho-tropic phase boundary between rhombohedral and tetragonal phases.120tions.Chemical processes like the solution/sol–gel,322hydrother-mal,323stearic acid gel,324or aqueous citrate gel325method have several advantages,namely controlled grain size and shape,mo-lecular-level homogeneity,high purity,low sintering tempera-tures,and easy processing of thinfilms.These methods were successfully used to prepare high-quality BNT or BNT–BT powder.

Wang et al.326investigated the effects of TiO2-nonstochiome-try with conventional sintering at the MPB of BNT–BT.They found that a deficiency in TiO2generally enhances k p and d33, but decreases T d and P r.TiO2excess on the other hand has the opposite effect,but still decreases P r.Therefore,it is important to control TiO2fluctuation in the production process.

Textured materials could enhance piezoelectric properties due to their anisotropy.Texturing has the advantage that there are no negative effects like lowered T d in comparison with engi-neering due to compositional changes.As stated in the intro-duction,we will not discuss processing of textured materials in detail,but will only give a short overview.In the following ex-amples,the reactive templated grain growth method(RTGG)or templated grain growth combined with hot pressing(TGG/HP) are discussed.

With the aid of37.5%plate-like Bi4Ti3O12templates with respect to Ti content,327excess Bi2O3328or Na2CO3329promotes preferential grain growth via RTGG in BNT and k p as well as d31are enhanced.Textured BNT–BKT by RTGG330–333or BNT–BT by RTGG334or TGG/HP335also show significantly enhanced d31and coupling factors compared with their nontex-tured counterparts.Degrees of orientation from F50.6–0.9and an increase of piezoelectric constants and electromechanical coupling factors between20%and200%were also achieved.

(B)Single Crystals and Thin Films:BNT-based single crystals were obtained by theflux,336–341Czochralski,21,339 TSSG,342,343Bridgman,336,344and metal strip heated zone melt-ing method.338High strain values of0.87%or0.85%were ob-served in BNT–BKT–BT single crystals whose composition was 7at.%K,34at.%Na,and6at.%Ba or in BNT–5.5BT crystals, respectively.21,341Mn doping in BNT crystals doubled d33to 120–145pC/N while decreasing T d only from1951to1871C.342 Generally properties of single crystals seem to depend highly on synthesis procedure.A performance in the range from no pi-ezoelectric properties336to highly improved properties com-pared with polycrystalline ceramics with respect to d33and T c values were observed.21,340

There are only few reports on lead-free BNT-based thinfilms. Generally,thinfilms are difficult to pole due to high leakage currents.345,346BNT thinfilms with thicknesses of several hun-dred nanometers and grain sizes of about100nm were synthe-sized by sol–gel345,347,348and an RF magnetron sputtering method.346

For pure BNT synthesized by the sol–gel method,the dielec-tric constant was280–300,tan d52%,P r58.3m C/cm2,and E c520kV/mm.P r was lower than in BNT bulk material be-cause full poling could not be achieved.345In BNT–x BKT thin films an MPB was found at x50.15with P r513.8m C/cm2,di-electric constant of360,and tan d55.9%.348

For BNT thinfilms synthesized by the RF magnetron sput-tering method and subsequent annealing at7001C for1h in Bi-rich atmosphere,P r511.9m C/cm2,E c53.79kV/mm and dielectric constant between650and470were obtained.346 (3)Chemical Modifications of Bi-Based Materials

BNT was doped in order to decrease sintering temperature,to achieve full poling and to enhance electromechanical properties as well as to increase T c.The addition of Fe349increased the density of BNT samples and allowed preparation of dense sam-ples even at temperatures below9001C.It was proposed that Fe31-acceptor ions induced oxygen vacancies and thus improved atomic diffusion during sintering.Li,350Mn,351Ce,307BaCu1/ 2

W1/2O3,110and Bi2O3352were found to decrease conductivity, making poling easier and improving d33,k p,and P r.At the same time,a decrease in phase transition temperatures was found.

BiScO3and BiFeO3raise T c of BNT up to4001C together with an improvement of P r.Temperature curves of dielectric permittivity become broader with reduced maximum indicating a more pronounced relaxor behavior.However,E c is raised to values as high as4kV/mm,making poling difficult.353,354In BNT–BT,BiFeO3is also found to shift T c to higher values.355 In BNT the addition of dopants generally induces local in-homogeneities and local cation disordering,which results in re-laxor-ferroelectric behavior.356

BNT was also doped with La,357Sr,275,358–360Ta,361 NiNbO3,362NaNbO3,108,281,304,356,363or K1/2Na1/2NbO3,113 BNT–6BT with La,3–366Nb,288,3Mn,367–369Ag,370 Li,295,296or Ce,371–373BNT–BKT with Ce,374Sr,375or Sr/La,376 and BNT–BKT–BT with Li.377,378Generally,these dopants enhance properties like P r,k p,d33,and the temperature of maximum dielectric constant T m,mostly considered as T c.E c and T d are lower than in undoped materials.In contrast to the dopants above,cobalt lowers the piezoelectric properties, but enhances T d by about201C,thus allowing usage of the BNT–6BT piezoceramics in a wider temperature range.How-ever,due to the significant reduction in d33and increase of E c, the usefulness of doping with Co for practical applications is doubtful.288,379

Exact values of T d vary among different reports due to differ-ent measurement techniques and a high compositional depen-dence.Nevertheless,the minimum value for T d was always found at the composition with the highest piezoelectric proper-

Table VI.Properties of Some Bi-Based Lead-Free Ceramics w

System

e33T/e0

(1kHz,RT)

k p

(%)

d33

(pC/N)

S max/E max

(pm/V)

P r

(m C/cm2)

E c

(kV/mm)

T d/T2

(1C)

T c/T m

(1C)References

BNT–x BT MPB

x56%–8%601–82621.2–36.7122–17637.8–40 2.72–3.4190–105225–288Chen and

colleagues285–290

BNT–6BT17.5Li99036.820839.2 3.2785260Lin and

colleagues295,296 BNT–6BT–2KNN——3056716 1.3—B260Zhang and

colleagues116,117

BNT–20BKT MPB 884–94527–35140–19024020–38 2.0–4.0130–170280–300Sasaki and

colleagues27,297–302

88BNT–8BKT–4BT

MPB

8103617027040 2.9162262Zhang et al.303 BNT–2NN624188827.8 5.67B100B300Takenaka and

colleagues108,304 BKT–40BT379k33376125 6.55291Hiruma et al.305 w Component–x Component,x:mol%.ties.T d is an indication for the stability of ferroelectric domains. Less stable domains are easy to switch;thus piezoelectric prop-erties are enhanced for less stable ferroelectric domains that co-incides with a low depolarization temperature.288This tradeoff was found in all Bi-based systems.

BNT–BT at the MPB was studied with additional Zr,380but poor properties were obtained due to the formation of a cubic phase.Other researchers reported comparable values for d33 (B120pC/N),k p(B15%),T d(1201C),and e33T/e0(845)for BNT–BaZr x Ti(1Àx)with x50.06–0.07with respect to BNT–6BT(see Table VI).381,382Additional CuO as a sintering aid could enhance d33up to157pC/N and T d up to B1501C.382 In the case of Li doping in BNT–BKT,d33and k p increased together with T d,383but for higher dopant concentrations poor piezoelectric properties were observed together with low phase transition temperatures and a stabilization of the rhombohedral phase.111,375,383In detail,Li doping of4at.%revealed high k33560%,d335176pC/N,and T d51711C.383The enhance-ment of T d was explained by the small ionic radius of Li leading to a lattice distortion that increased phase transition tempera-

tures.383Other researchers found similar properties in Li-doped BNT–BKT ceramics.384,385

In summary,dielectric and piezoelectric properties of Bi-based piezoceramics can be engineered through doping,but effects are quite small and improvement of piezoelectric prop-erties is mostly at the expense of a decrease in T d or vice versa.

VII.Properties of Today’s Lead-Free Piezoceramics This chapter summarizes some of the key properties of recently developed lead-free piezoceramics and compares them in a set of figures.Almost all of the best properties stem from materials introduced in the last two chapters,which are derivatives of KNN(Section V)or derivatives from BNT–BT or BNT–BKT (Section VI).Some other developments outside of these regimes, however,should be mentioned.Among the electrostrictive ma-terials,a lead-free ferroelectric relaxor(Sr0.35Na0.25Bi0.35TiO3or SBNT)386was reported to have a unipolar strain of0.1%at8 kV/mm,which translates into an effective large–signal d33value of125pm/V.This strain is related to a polarization of22m C/ cm2and an electrostrictive coefficient Q33of0.02m4/C2(see Eq.

(4)).Electrostrictive materials can be attractive due to the ab-sence of a poling strain,which causes internal stresses and the absence of hysteresis,albeit only if the obtainable strain is com-petitive.Further,flexoelectricity387should be mentioned,as it is able to generate an elastic strain by an electricfield gradient and therefore,in principle,can provide piezoelectric composites con-taining no piezoelectric element.

For actuators,the achievable strain in the required tem-perature regime is the key material property.Figure17com-pares three recently developed lead-free piezoceramics with a commercial PZT(PIC151,Physik Instrumente,Lederhose, Germany).The textured modified KNN according to Saito et al.23is optimized for high-room-temperature properties and is able to provide a similar strain of about0.15%at2kV/mm as the commercial PZT.In contrast,the best BNT–BKT mate-rials30deliver a lower strain reaching0.18%at8kV/mm.The BNT–BT–KNN material developed by Zhang et al.115demon-strates that as yet unexplored mechanisms exist in lead-free piezoceramics capable of delivering strain in excess of0.4%at 8kV/mm.

Normalized strain(S max/E max),piezoelectric coefficient(d33), and planar coupling factor(k p)are compared for some of the most advanced lead-free piezoceramics in Figs.18–20.These are a set of typical material parameters used in quantitative com-parison.28Often these properties are plotted as a function of Curie temperature,which gives a good correlation for the case of the piezoelectric coefficient for PZT,but not for the lead-free piezoceramics.28Here,we compare the different material prop-erties by plotting them as a function of the phase transition lying closest to room temperature.In the case of KNN materials,this allows immediate assessment of the contribution of the O–T phase transition to the obtainable strain.For the case of the Bi-based system,the depolarization temperature may limit the us-age at higher temperatures.Further,materials at temperatures close to the ferroelectric/antiferroelectric phase transition have been reported to exhibit enhanced obtainable strain.301On the other hand,the depolarization temperature(T d)describes the phase transition at zero electricfield.In reality,this may be shifted to higher temperatures with the application of the electric field and may enhance the useful temperature regime as sug-gested by high obtainable strains far beyond the nominal T d.

Large-signal d33values higher than300pm/V have been reported28for KNN materials with the O–T phase transition close to room temperature(Fig.18).The respective values drop to o200pm/V for O–T phase transitions approaching2001C.In comparison,BNT–BKT28,301materials have been developed with large-signal piezoelectric coefficients in the range around 200pm/V exhibiting depolarization temperatures around2001C. BNT–BLT301materials exhibit decreasing large-signal d33values from about150pm/V at a T d of501C to100pm/V at T d of 2001C.The BNT–BT–KNN116,117compositions display the highest obtainable strains for polycrystalline piezoceramics (see also Fig.17).

Naturally,the small-signal d33values are lower than the large-signal piezoelectric coefficients by the extrinsic piezoelectric effect and any possible effects byfield-induced phase transfor-mations.Akin to Fig.19,the d33values for the KNN-based materials28are very high for O–T transitions close to room tem-perature and drop to values of about100pC/N for transition temperatures of about2001C.BNT–BKT materials28,301with depolarization temperatures between1601and2301C exhibit pi-ezoelectric coefficients between100and170pC/N.Only a

small Fig.17.Unipolar strain as function of electricfield for lead-free pie-zoceramics(textured KNN,23BNT–BT–KNN,115BNT–BKT–BT,30 and PIC151115)as compared with commercial lead–zirconate–titanate

(PZT).

Fig.18.Normalized strain S max/E max as function of respective phase transition temperature for lead-free piezoceramics(T O–T for KNN-based,T d for BNT-based materials;reference:KNN-based,28BNT–BT–KNN,116,117BNT–BKT,28,301and BNT–BLT301).

decrease in d 33values starting with 100pC/N at T d of 501C to higher T d is noted with the BNT–BLT ceramics.301BNT–BT–KNN materials 116,117display high strains only at increased elec-tric fields and exhibit very low d 33values of no more than 100pC/N.

Trends for the planar coupling factors (Fig.20)for KNN-based materials 28and BNT–BKT materials 28are similar as for the large-signal piezoelectric coefficient and the small-signal pi-ezoelectric coefficient.High values of 35%–60%are obtained for KNN-based materials with low O –T transition temperatures and intermediate values can be found for BNT–BKT materials with 30%–40%.

These charts only provide some of the relevant material prop-erties (see Section III).To evaluate if a new material is feasible for industrial application,it would also be interesting to assess blocking stress,hysteresis,and losses.Unfortunately,these properties are usually not reported.Within this restriction,they can be used in two different ways.If a material develop-ment is contemplated with the hope to replace PZT with one material alone,then all these properties and more require opti-mization.An alternative approach may also be feasible of searching for lead-free piezoceramics,which are useful for ac-tuators having high strain and general requirements as stated in Section III and at the same time look for a different PZT re-placement for the application as sensors and transducers,re-spectively.

In summary,the development of lead-free piezoceramics has made great strides in the last 5–10years.Some materials are available for smaller market segments and temperature regimes and may require the next step of optimization,e.g.for mechan-ical properties and general reliability.For a replacement of PZT,

the guidelines on possible chemical elements (Sections IV (1)and IV (3)),crystal structures (Section IV (2)),and phase dia-grams (Section IV (4)),as well as ab initio modeling (Section IV (5))suggest the following:

(1)Replacing lead by bismuth allows access to MPBs with attendant properties with little dependence on temperature.(2)Several bismuth containing phase diagrams between te-tragonal and rhombohedral elements warrant full exploration.(3)A search routine with measuring piezoelectric coefficient and crystal structure at zero electric field alone may be limiting as it neglects the opportunity of field-enforced phase transition.On the side of fundamental understanding of piezoceramics,research should also be directed toward a better understanding of the various mechanisms to obtain high electrically induced strain including field-dependent phase transitions and polariza-tion rotation next to the intrinsic piezoelectric effect and domain wall motion.Finally,the effect of dopants on the new lead-free piezoceramics is only marginally understood.

VIII.Conclusions

While our understanding in the search for lead-free piezoceram-ics has been improved significantly over the last years,the cur-rent research appears directed toward incremental improvements of a limited number of material systems.These exhibit apparent shortcomings mainly related to the temperature dependence of piezoelectric properties.It is thus recommended to use the peri-odic table and guidelines with respect to choice of atom,crystal structure,and phase diagram to a broader degree.Specifically,the following suggestions can be provided for development and scientific understanding of new piezoelectric materials:

(1)Explore a broader materials base than attempted recently.(2)Pay due attention to temperature dependence of piezo-electric properties.

(3)Explore nature of ferroelectric/antiferroelectric transi-tions and electric field-dependent phase transitions.

(4)Establish fruitful interactions between the areas of at-omistic modeling,synthesis,and characterization of lead-free piezoceramics.

For complex situations,an additional characterization of mechanical domain switching may prove helpful,while more advanced materials may require better understanding of mechanical properties.

Acknowledgments

We are indebted to a number of colleagues for valuable discussions on various aspects of this work,in particular Karsten Albe,Michael Hoffmann,Ingo Kerkamm,Achim Kleebe,Alain Kounga,Hans Kungl,Jacob Jones,and Xiaoli Tan,and to Emil Aulbach for excellent technical support.We also thank both reviewers for their very helpful comments.

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Ju rgen Ro

del is a Professor in the department for Earth and Materials Science at Technische Universita t Darmstadt.He received a Diploma in Materials Science from Universi-ta t Erlangen-Nu rnberg and a Ph.D.from the University of California at Berkeley.During his postdoc peri-ods at NIST,Gaithersburg,and TU Hamburg-Harburg he investigated crack propagation in ceramics and composites and completed a Habili-tation at TU Hamburg-Harburg.At TU Darmstadt part of his research is focussed on processing of lead-free piezocera-mics and high-temperature piezoelectrics as well as toughened piezoceramics.In addition to the ceramics group,he also leads the center of electric fatigue at TU Darmstadt.He is a fellow of the American Ceramic Society and was a past Chairman of the Gordon Research Conference on Ceramics.In Germany he served the Deutsche Forschungsgemeinschaft (DFG)a four-year term as speaker of the review board for Materials Science and received the DFG research award for young scientists (Heinz-Maier-Leibnitz-Preis)in 1992and the DFG research award for senior scientists (Gottfried Wilhelm Leib-niz-Preis)in 2009.He authored/co-authored about 160refer-eed publications and 2patents.

Wook Jo is the group leader for the development of the next-generation lead-free and high-temperature piezoelectric ceramics at the insti-tute of materials science,Tech-nische Universita t Darmstadt,Germany.He received his Ph.D.in 2005from Seoul National Uni-versity on the theoretical modeling on the equilibrium crystal shape (ECS)and its relation to micro-structure evolution of materials

during sintering processes.After his Ph.D.,he joined the Center for Microstructure Science of Materials (CMSM)at Seoul National University as a postdoctoral research associ-ate.During his stay at CMSM,he mainly focused on reinfor-cing the theoretical model with experimental evidences,and he published a feature article in the Journal of the American Ceramic Society [Vol.,pp.2369(2006)]with Professor Doh-Yeon Kim and Nong-Moon Hwang,which discusses the experimental and theoretical aspects on sintering phenom-enon.Later,he joined the current work group as a postdoc-toral research associate in 2007.Since then,he has been working with Professor Ju rgen Ro

del on the processing and electrical characterizations of lead-free piezoelectric ma-terials.

Klaus T.P.Seifert is a Ph.D.candi-date in Materials Science at the Technische Universita t Darmstadt,where he does research on new lead-free piezoceramics in the group of Prof.Ro del.He received his Mas-ter of Physics from Oxford Univer-sity,Great Britain in 2005.

Eva-Maria Anton is currently a Ph.D.candidate in Materials Science at the Technische Univer-sita t Darmstadt,Germany.Her research is about the development of new lead-free piezoceramics under the supervision of Prof.Ju r-gen Ro del.Ms.Anton got her diploma in Materials Science in 2008at the same University.As a part of her studies she stayed at Purdue University,Indiana,and published her work about domain switching mechanisms in polycrys-talline ferroelectrics together with Professor R.Edwin Garcıa,John E.Blendell,and Keith J.Bowman.

Torsten Granzow obtained a di-ploma in physics and a Ph.D.in crystallography from the University of Cologne,Germany,in 1999and 2003,respectively.In 2004,he joined the Department of Earth and Materials Science of the Tech-nische Universita t Darmstadt as a postdoctoral researcher,where he is heading a group responsible for the characterization of ferroelectric ma-terials.After a brief stay as a Visit-ing Associate at the California Institute of Technology,he is currently finishing his habilitation at the TU Darmstadt.His main research interest lies in the domain structure,phase transition and the electrical,mechanical and optical properties of polar single crystals and polycrystalline ceramics.He has co-authored about 45scientific papers and received the Heinz Maier-Leibnitz Prize of the German Research Foundation (DFG)in

2008.

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Vol.92,No.6

Dragan Damjanovic received his B.Sc.diploma in physics from the University of Sarajevo,in1980, and Ph.D.in Ceramics Science from the Pennsylvania State Uni-versity(PSU)in1987.From1988 to1991he was a research associ-ate in the Materials Research La-boratory at the PSU.He joined the Ceramics Laboratory,Insti-tute of Materials,at the Swiss Federal Institute of Technology in Lausanne(EPFL)in 1991.He is currently an adjunct professor and teaches under-graduate and graduate courses on electrical properties of materials.His research interests include dielectric,piezoelectric and ferroelectric properties of crystals,films,and ceramics as well as application of ferroelectric and piezoelectric materials in actuators,sensors,and high frequency transducers.He has published more than150articles.In the last ten years he has participated in or led more than a dozen European and Swiss projects in thefield of piezoelectric materials.He is an IEEE

Fellow.

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