FTT54 Yuzyuk Review Eng

ISSN 1063�7834, Physics of the Solid State, 2012, Vol. 54, No. 5, pp. 1026–1059. © Pleiades Publishing, Ltd., 2012.Original Russian Text © Yu.I. Yuzyuk, 2012, published in Fizika Tverdogo Tela, 2012, Vol. 54, No. 5, pp. 963–993.

1026

Contents1. Introduction2. Selection Rules for Raman Spectra of Some Per�ovskites3. Strontium Titanate4. Lead Titanate

4.1. Single Crystals, Ceramics, and Powders4.2. Lead Titanate Thin Films4.3. (Pb,Sr)TiO3 Solid Solutions4.4. (Pb,Ca)TiO3 Solid Solutions

5. Barium Titanate5.1. Single Crystals, Ceramics, and Powders5.2. Barium Titanate Thin Films5.3. Crystals and Ceramics of (Ba,Sr)TiO3 SolidSolutions5.4. Films of (Ba,Sr)TiO3 Solid Solutions

6. Perovskite Superlattices7. ConclusionsAcknowledgmentsReferences

1. INTRODUCTION

Ferroelectrics are characterized by switchablespontaneous polarization, high permittivity, dielectricnonlinearity, pyroelectric and piezoelectric properties,as well as by linear and quadratic electro�opticaleffects, which has made it possible to design and fabri�cate various functional devices based on these materi�als. Oxides of the perovskite family with the generalformula ABO3 form, most likely, the largest group offerroelectric materials. Solid solutions of different fer�roelectrics and their related materials have usually

been used to optimize physical properties that are nec�essary for specific practical applications. At present,there has been a large amount of experimental dataaccumulated in the literature on the isomorphous sub�stitutions in oxides of the perovskite family and on reg�ular composition–property relationships [1]. Recentadvances made in the growth technology of epitaxialfilms of ferroelectric perovskites have opened up newprospects for the creation of nanoscale heterostruc�tures with a wide range of potential applications inoptoelectronics, microelectromechanics, and micro�wave electronics [2–5]. The structure and propertiesof nanoparticles, films, and superlattices consisting ofnanoscale epitaxial layers of different perovskites differsignificantly from those of bulk ceramics and crystals;hence, the determination of the factors responsible forthese differences is an important and urgent problemof the modern physics of ferroelectrics.

During the proper ferroelectric phase transition,the temperature behavior of the static permittivity ε0

above the phase transition temperature TC (Curie tem�perature) follows, as a rule, the Curie–Weiss law: ε0 ~C/(T – TC), where C is the Curie constant. In crystalsthat undergo displacive phase transitions, the vibra�tional spectrum should significantly change as theCurie temperature TC is approached [6]. According tothe Lyddane–Sachs–Teller relationship, we can writethe following expression for cubic crystals with n opti�cal branches [7–9]:

ωLOi

ωTOi

��⎝ ⎠⎜ ⎟⎛ ⎞

2

i 1=

n

∏ε0

ε∞

��,=

REVIEWS

Raman Scattering Spectra of Ceramics, Films, and Superlatticesof Ferroelectric Perovskites: A Review

Yu. I. Yuzyuk Southern Federal University, ul. Bol’shaya Sadovaya 105/42, Rostov�on�Don, 344006 Russia

e�mail: [email protected] Received August 17, 2011

Abstract—Raman investigations of the crystal lattice dynamics in classical ferroelectric perovskites SrTiO3,PbTiO3, and BaTiO3 have been analyzed. The specific features revealed in the behavior of soft modes duringthe phase transitions occurring in ceramics and powders of these compounds, as well as in several related solidsolutions, have been described. Particular attention has been paid to the investigations of ferroelectric thinfilms and superlattices in which the sequences of structural distortions can be radically different from thoseknown for the initial bulk materials.

DOI: 10.1134/S1063783412050502

PHYSICS OF THE SOLID STATE Vol. 54 No. 5 2012

RAMAN SCATTERING SPECTRA OF CERAMICS, FILMS, AND SUPERLATTICES 1027

where ε∞ is the high�frequency permittivity; and

and are the frequencies of the longitudinal andtransverse vibrations, respectively. Since the frequencyωLO changes in a rather narrow range, the anomalousincrease in the static permittivity ε0 near the Curietemperature is associated with the behavior of the low�

frequency transverse soft mode ~ (T – TC). Thestatic displacements of atoms upon the transition fromthe paraelectric phase to the ferroelectric phase arefrozen shifts of the soft vibrational mode [10, 11].

Investigation of the soft vibrational modes is themain source of information about the microscopicmechanisms of phase transitions in ferroelectrics. Thelattice dynamics of bulk single crystals and ceramicshas been traditionally studied using methods of ther�mal neutron scattering, infrared (IR) absorption orreflection spectroscopy, and combination light scat�tering. It should be noted that the term “combinationlight scattering” has sometimes been used only in theRussian�language scientific literature and was intro�duced by G.S. Landsberg and L.I. Mandelstam, whodiscovered this phenomenon in 1928, almost simulta�neously with C.V. Raman and K.S. Krishnan. How�ever, because C.V. Raman was the first to publish hisresults and describe this phenomenon, then in theEnglish�language scientific literature, this effect iscalled Raman scattering (Raman effect). Details of thehistory of the discovery of the Raman scattering effectcan be found in [12]. It should also be mentioned thatL.I. Mandelstam and G.S. Landsberg searched forlight scattering by phonons of the acoustic branch ofthe crystal, which was predicted by Mandelstam in1918 and by L. Brillouin in 1922, but revealed a lightmodulation by optical vibrations, i.e., Raman scatter�ing. Light scattering by acoustic phonons was discov�ered later and called Mandelstam–Brillouin effect inthe Russian�language literature and Brillouin scatter�ing in the English�language literature.

The Raman scattering technique has been widelyused for studying materials only beginning with themid�1960s of the last century after the advent of per�fect sources of monochromatic radiation—lasers. Thetheory of Raman scattering and the experimentalresults obtained in the 1960s are presented in thereview [13]. With the advent of serial devices equippedwith CCD detectors in the early 1990s of the last cen�tury, it has become possible to significantly increasethe sensitivity of the Raman scattering technique, andthe focusing of the exciting radiation with an opticalmicroscope (micro�Raman scattering) has made itpossible to examine individual domains of single crys�tals, ceramic grains, nanofilms, and nanoparticles.The emergence of the micro�Raman technique,which does not require a large amount of a test mate�rial, as in the case of neutron scattering or IR spectros�copy, has provided significant advantages of Raman

ωLOi

ωTOi

ωTO2

spectroscopy for investigating nanoscale films andsuperlattices. Recently, the surveys have been pub�lished in the foreign literature regarding the applica�tion of micro�Raman spectroscopy to the investiga�tion of phase transitions in crystals, ceramics, andfilms of some ferroelectric perovskites [14, 15].

In the present review, we have considered the mostpopular representatives of the perovskite family,namely, SrTiO3 (ST), PbTiO3 (PT), and BaTiO3 (BT),in which the behavior of the soft modes during phasetransitions had been investigated on single�crystalsamples as early as 1960s–1980s of the last century.This review has been concerned with the effects of ionsubstitution in some solid solutions of the aforemen�tioned compounds, size effects, and comparison of thelattice dynamics of nanoscale thin films and superlat�tices of some ferroelectric perovskites with the latticedynamics of bulk materials.

2. SELECTION RULES FOR RAMAN SPECTRA OF SOME PEROVSKITES

Raman scattering is an inelastic light scattering inwhich the change in the wavelength of scattered lightoccurs as a result of the interaction of incident lightwith long�wavelength optical phonons of the scatter�ing medium. The modulus of the wave vector of anoptical phonon involved in the inelastic light scatter�ing is of the same order of magnitude as the modulusof the wave vector of a photon; consequently, the first�order Raman spectrum provides information on thelong�wavelength phonons with wave vectors |k| ≈ 0[13]. The IR absorption spectra are associated with theelectron transitions between the vibrational levels of amolecule or a crystal, whereas the Raman spectra aredue to the polarization of electron shells by an externalmonochromatic electromagnetic radiation in the visi�ble or UV spectral range. Raman scattering can beconsidered as a result of the modulation of the induceddipole moment by nuclear vibrations. Since the IRand Raman spectra have different origins from thephysical point of view, the corresponding selectionrules are also different. The vibration is active in the IRabsorption spectrum if it is accompanied by a changeof the dipole moment, and this vibration is active inthe Raman spectrum if it is accompanied a change inthe polarizability. Since normal vibrations in crystalsand molecules are determined by their symmetry, theselection rules for the IR and Raman spectra are basedon the group theory. In the study of ferroelectrics,these methods are intercomplementary, because incentrosymmetric crystals, the vibrations are activeeither in the IR spectra or only in the Raman spectra(alternative prohibition rule), whereas in the ferro�electric phase, where there is no inversion center, thevibrations are active both in the IR spectra and in theRaman spectra. It is worth noting that, in some cases,there are vibrations that are inactive both in theRaman spectra and in the IR spectra.

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The perovskite structure can be represented as athree�dimensional network of vertex�shared BO6

octahedra in which voids between the octahedra areoccupied by A cations. The phase transitions occurringin crystals of the perovskite family are provided by twokey mechanisms: (i) displacements of the cations and(ii) rotations of the oxygen octahedra around differentaxes of the high�symmetry parent cubic phase. Duringthe proper ferroelectric phase transition caused by dis�placements of the A cations with respect to the oxygenoctahedra, for example in the PT compound, only onepolar optical mode from the center of the Brillouinzone makes the dominant contribution to the temper�ature behavior of the static permittivity. The ferroelec�tric phase transition in the BT compound is associatedwith displacements of the B cations with respect to theoxygen octahedra. Another type of distortions in per�ovskites is caused by the instability of the crystal latticewith respect to small rotations of the octahedra (rota�tional phase transitions) due to the soft modes corre�sponding to different points at the boundary of theBrillouin zone. The structural changes associated withthe ferroelectric phase transitions in perovskites, as arule, are caused by the condensation of one or severalmodes. The competition between the rotational softmodes, which correspond to the “pure rotations” ofrigid BO6 octahedra around different crystallographicaxes, and the polar soft modes, which correspond tothe displacements of the A and B cations, has often ledto complex sequences of structural distortions in per�ovskites [16].

All the three aforementioned representatives of theperovskite family in the high�symmetry paraelectricphase have a cubic symmetry with space group

. The unit cell of this cubic phase containsone formula unit. The optical vibrational representa�tion of this phase involves three dipole IR�active vibra�tions with the F1u symmetry and one vibration of theF2u type, which is inactive both in IR absorption and inRaman scattering. The sequences of phase transitionsoccurring in the compounds under consideration aredifferent; therefore, we have analyzed the generalprinciples of the formation of Raman spectra in thelow�symmetry phases of the PT, BT, and ST crystals. Adetailed analysis and numerous examples of changesin the selection rules for IR and Raman spectra uponphase transitions in different ferroelectrics can befound in [17].

The PT single crystal undergoes only one phasetransition to the tetragonal ferroelectric phase

(P4mm– ) at the Curie temperature TC, which,according to different data, lies in the range from 763to 766 K. In the tetragonal phase, each of the three F1u

modes is split into the A1 + E modes, and, accordingly,the F2u mode is split into the B1 + E modes. Thus, thefactor group analysis predicts the presence of Γtet =

Pm3m–Oh1

C4v1

3A1 + 4E + B1 phonons in the tetragonal phase of thePT compound. All the A1 and E modes are active bothin the Raman spectra and in the IR spectra, whereasthe B1 mode is allowed only in Raman scattering.Moreover, the long�range electrostatic forces split allthe A1 and E modes into transverse optical (TO) andlongitudinal optical (LO) components.

The BT single crystal undergoes three phase transi�tions to the ferroelectric phases: the tetragonal phase(the Curie temperature TC, according to differentdata, lies in the range from 393 to 403 K), the orthor�hombic phase (TC = 278 K), and the rhombohedralphase (TC = 183 K). The change of the selection rules

during the first transition ( ) is similar tothe case of the PT single crystal. During the subse�

quent transition to the orthorhombic ( –Bmm2)phase, the F1u mode is split into the A1 + B1 + B2

modes, and, accordingly, the F2u mode is split into theA1 + B1 + A2 modes. In this phase, all modes are activein Raman scattering, whereas in IR absorption, allmodes are active, except for the A2 mode. Thus, wehave Γort = 4A1 + 4B1 + 3B2 + A2. It should be notedthat the axes of the orthorhombic unit cell are rotatedthrough an angle of 45° around the pseudocubic axis[010], thus forming the base�centered unit cell con�taining two formula units. In the orthorhombic phase,the perovskite unit cell is monoclinically distorted,and the spontaneous polarization is directed along theelongated diagonal of the face. The axes of the orthor�hombic unit cell are related to the axes of the initialcubic unit cell as follows: a0 = a1 + a3, b0 = a2, and c0 =

a1 – a3. In the rhombohedral ( –R3m) phase, theF1u mode is split into the A1 + E modes, and, accord�ingly, the F2u mode is split into the A2 + E modes.Thus, we have Γromb = 3A1 + 4E + A2. In this phase, allthe A1 and E modes are active both in Raman scatter�ing and in IR absorption, whereas the A2 mode is inac�tive (silent). The spontaneous polarization is directedalong the body diagonal of the face of the initial cubicunit cell.

The ST crystal undergoes a structural phase transi�tion at the temperature Ta = 105 K due to the softeningof the threefold degenerate mode at the boundary ofthe Brillouin zone, which corresponds to antiphaserotations of the oxygen octahedra. This transitionleads to the doubling of the unit cell with a reduction

of the symmetry to tetragonal ( –I4/mcm). Each ofthe three F1u modes is split into the A2u + Eu modes,and the F2u mode is split into the B2u + Eu modes. Allthese modes are inactive in Raman scattering; how�ever, owing to the doubling of the unit cell in the tet�ragonal phase, the phonon branches are folded, andbelow the temperature Ta, in the Raman spectrumthere appear modes that come from the boundary of

Oh1

C4v1

C2v14

C3v5

D4h18



the Brillouin zone: A1g + 2A2g + 2B1g + B2g + 3Eg. Fur�thermore, the IR�active modes A2u + Eu also comefrom the boundary of the Brillouin zone. The afore�mentioned threefold degenerate soft mode is split intotwo components, A1g and Eg, and becomes active inRaman scattering.

Thus, the Raman spectrum of the tetragonal phaseof the ST crystal is caused by the phonons comingfrom the boundary of the Brillouin zone, whereas theRaman spectra of the low�symmetry phases of the BTand PT crystals originate from optical modes at thecenter of the Brillouin zone of the cubic phase. It isobvious that, in ceramics and powders, any symmetrybreaking due to the disorder, vacancies, impurities,pressure, etc., leads to violations of the selection rulesin the Raman spectra. In films and superlattices of fer�roelectric materials, there are not only violations ofthe selection rules, but also, sometimes, a very signifi�cant transformation of the phonon spectrum, whichindicates a change in the symmetry of the phases, aswell as in the sequence of structural distortions as awhole.

3. STRONTIUM TITANATE

Strontium titanate (ST) has been one of the mostpopular objects of investigation since the discovery ofthe polar soft mode in it [18]. The ST crystal under�goes a structural phase transition at the temperatureTa = 105 K due to the softening of the threefold degen�erate mode at the boundary of the Brillouin zone.Below Ta, the soft mode, which is split into two com�ponents, A1g and Eg, becomes active in Raman scatter�ing [19]. With a further decrease in the temperature to2 K, the permittivity steadily increases in accordancewith the Curie–Weiss law, but the peak is not observed.The anomalous increase in the permittivity at lowtemperatures is accompanied by a softening of thelowest frequency threefold degenerate mode F1u at thecenter of the Brillouin zone, which corresponds to thedisplacement of titanium ions with respect to the oxy�gen octahedron. Its frequency decreases to 11 cm–1 at8 K, and the temperature dependence of the frequencyof this soft mode suggests that TC = 32 ± 5 K. However,the transition to the ferroelectric phase does not occurand, despite all the indications that the ferroelectricphase transition approaches, the ST crystal remainsparaelectric.

In contrast to crystals, the lattice dynamics of theST ceramics has been investigated only recently [20],and the observed very significant distinctions havedeserved detailed consideration. It is known [21, 22]that, in ceramics, as well as in crystals, there is noappreciable dispersion of the dielectric susceptibilityat low temperatures and at frequencies of up to1010 Hz. The dielectric susceptibility of the ceramicsamples at liquid�helium temperatures reaches a fewthousands, which is several times less than that in good

single crystals, where this quantity can be as large as25000 [23, 24]. The dielectric loss in the microwaverange of frequencies in the ceramics is significantlyhigher and depends on the grain size [21, 22]. Theceramic samples of the ST compound studied in [20]were prepared using the conventional solid�phase syn�thesis technology. The density of the synthesized sin�gle�phase samples reached 98.8% of theoretical value.The average grain size was determined with a scanningelectron microscope and amounted to 1–2 μm. Thepresence of possible impurities was revealed using theemission spectroscopy methods. The content of Al,Fe, K, Na, and Nb did not exceed 150 ppm. The con�tent of Ba (320 ppm) and Ca (2550 ppm) corre�sponded to their concentration in the initial materials.The inclusion of such impurities as Si (150 ppm), Y(110 ppm), and Zr (2100 ppm) occurred at the stage ofgrinding of the powders. The revealed Ca content canlead to an increase in the dielectric susceptibility atlow temperatures [25, 26], but it does not lead to achange in the phase diagram; i.e., it does not induce aferroelectric state. Previously, it was found that thedielectric properties of the ST single crystals dependon the method used for their surface treatment; more�over, the second harmonic generation was observed inthe surface layer [27]. Therefore, in the study of the STceramics, special attention was drawn to the surfacequality of the samples. The measurements were per�formed both on mechanically polished samples and onthe samples subjected to chemical etching.

The real crystal structure of the ceramic samples atroom temperature was investigated using the X�raydiffraction methods. The parameter of the cubic per�ovskite unit cell in the synthesized ceramic samples(a = 0.390597 nm) was very close to the correspondingparameter in the ST single crystal (a = 0.39050 nm). Adetailed analysis of the diffraction profiles made itpossible to estimate the average size of grains in theceramic samples, which was in good agreement withthe electron microscopy data. Therefore, it was con�cluded that the ceramic samples contained someamount of single�crystal grains. The same sampleswere used in standard dielectric measurements at fre�quencies ranging from 102 to 106 Hz. The dielectricsusceptibility did not reveal any frequency dependenceand, with decreasing temperature, increased to 10000at 10 K.

The reflection spectra in the IR range and theRaman spectra of these ceramic samples were investi�gated over a wide temperature range from 10 to 300 K[20]. All the three F1u IR�active transverse opticalmodes TO1 (soft mode 88 cm–1), TO2 (175 cm–1), andTO4 (566 cm–1) were observed in the cubic phase. Thenotation TOi is commonly used to identify the vibra�tional modes of the cubic phase in order of theirincreasing frequency. The longitudinal optical modescorrespond to the bands LO1 (171 cm–1), LO3

(474 cm–1), and LO4 (792 cm–1). The frequency of the

1030


YUZYUK

IR�inactive mode of the F2u type, according to thehyper�Raman scattering [28], is equal to 266 cm–1 andcorresponds to the LO2 and TO3 components. BelowTa = 105 K, the IR spectra of the ceramic samplesexhibited the Eu mode activated from the R point as aresult of the folding of the Brillouin zone due to theantiferrodistorsive transition. Furthermore, at lowtemperatures, the low�frequency spectra of the STceramics exhibited an additional X�mode with a fre�quency of approximately 40 cm–1, which was notobserved in the IR spectra of single crystals.

As was already noted earlier, in the cubic phase ofthe perovskites, the first�order Raman spectrum is for�bidden by the selection rules, but, at room tempera�ture, the spectrum of the ST ceramic samples containsbroad overlapping bands due to the two�phonon pro�cesses [29]. The temperature dependence of the unpo�larized Raman spectra of the ST ceramic samples isshown in Fig. 1. It can be seen from this figure that, asthe temperature decreases, against the background ofthe second�order bands in the Raman spectra, thereappear narrow lines that correspond to the IR�activemodes; furthermore, below the temperature Ta, themodes from the R point of the Brillouin zone are acti�vated. The frequencies of all lines in the IR and Raman

spectra of the ST ceramic samples and their assign�ment are given in [20]. The behavior of the low�fre�quency modes (below 100 cm–1) with decreasing tem�perature is significantly different from the data avail�able in the literature for single crystals [19]; therefore,we will consider this aspect of the problem in moredetails. The temperature dependences of low�fre�quency modes observed in the IR and Raman spectraof the ST ceramic samples are shown in Fig. 2. TheIR�active TO1 mode appears in the Raman spectrabelow 250 K and exhibits a softening with a furtherdecrease in the temperature. At a temperature of 90 K,the TO1 polar mode intersects with the A1g soft mode,which appears below ~130 K. Then, the TO1 modecontinues softening, and it is reliably identified downto 30 K. At lower temperatures, this mode merges withthe wing of the Rayleigh line; hence, attempts to reli�ably determine its parameters have failed. It should benoted that, in the entire temperature range, the tem�perature behavior of the TO1 mode in the Ramanspectra is in good agreement with the data obtainedfrom the IR spectra. Moreover, below 50 K, theX mode with a frequency of ~40 cm–1 manifests itselfin the Raman scattering. The intensity of the X modesignificantly increases, and it becomes a dominant linein the low�frequency spectra with a further decrease inthe temperature.

As in the single crystal, the frequency of the TO1

mode of the ceramic samples follows the classical law

8006004002000Wave number, cm−1

Inte

nsi

ty,

arb.

un

its

15

25

35

50

60

80

100

120140

160

200

240

292

T, K

X

LO4, A2gTO4

LO2

TO3, LO3

Eg + B1g

B2g

A1g

Eg

+ B

1g

TO

2, L

O1

Fig. 1. Temperature dependence of the Raman spectra ofthe ST ceramics. In all spectra, the intensity is correctedfor thermal occupation factor.

300250200150100500T, K

100

10

90

80

70

60

50

40

30

20

Wav

e n

um

ber,

cm

−1

A1g

TO1

(Eu + A2u)

TO1 (F1u)

Raman

IR

Fig. 2. Temperature dependences of the frequencies of softmodes in the IR and Raman spectra of the ST ceramics.

X



of the soft mode ∝ (T – T0). The extrapolation

of this dependence yields T0 = 31 K, which coincideswith the data on inelastic neutron scattering [30]obtained for the ST single crystals. In the Raman spec�tra of the ST single crystal below the temperature Ta,there appears a pair of soft modes A1g and Eg, with thefrequencies reaching saturation near 49 and 15 cm–1,respectively [19]. In the case of the ceramic samples,the behavior of the A1g component is quite consistentwith the data obtained for the single crystal, and thetemperature dependence of the frequency of this com�ponent obeys the law ∝ (Ta – T)β with the critical

exponent β = 1/3 of the order parameter. The low�fre�quency component Eg is absent in the spectra of theceramics. Most likely, it is this X mode with a fre�quency of 40 cm–1 which is the missing Eg component,whose frequency shift and substantial increase in theintensity are caused by the interaction with the TO1

soft mode. The parameters of the interacting modesare impossible to determine from the unpolarizedspectra because of the strong overlap of the line pro�files of different types of symmetry in the spectra of theceramic samples. The temperature dependence of thetotally symmetric component A1g in the ceramic sam�ples indicates that the primary order parameter (theantiphase rotation of the TiO6 tetrahedra) reaches thesame magnitude as that in the crystal. Since the A1g–Eg splitting, which, in the case of the ceramics reachesonly 9 cm–1, reflects the degree of tetragonal distortion[17], we can conclude that the spontaneous tetragonalstrain in the ceramics is one order of magnitudesmaller than that in the crystal. This can be explainedby the grain clamping in the ceramics by the surround�ing grains, which significantly limits the spontaneoustetragonal strain at temperatures below Ta.

It should be noted that the intensity of the modesthat come from the R point of the Brillouin zone andare activated in the IR and Raman spectra follows thepower law IR ~ (T0 – T)γ, where Ta = 132 K and γ =0.72 ± 0.01, which agrees well both with the dataobtained for single crystals and with theoretical valueγ = 2β [17]. On the other hand, unlike the crystal,where the temperature Ta, according to differentauthors, lies in the range from 105 to 110 K [31], forthe ceramic samples, we have Ta = 132 K. This shift inthe transition temperature is most likely associatedwith the aforementioned internal stresses generated inthe ceramic samples, because, as is known for the STcompound [32], the hydrostatic pressure leads to anincrease in the temperature Ta. Furthermore, even asmall amount of calcium can also lead to an increasein Ta [26].

The polar IR�active vibrations are forbidden in theRaman spectra of the ST cubic crystal; however, theirintensity in the Raman spectra of the ceramic samples

ωTO1

2

ωA1g

is different from zero at temperatures considerablyhigher than Ta. This intensity drastically increasesaccording to the exponential law in the temperaturerange below Ta and is described by the power functionof the frequency of the TO1 soft mode, so that I ∝

, where a = 1.6 ± 0.06 [20]. The appearance of

forbidden polar modes in the Raman spectra indicateslocal violations of the alternative prohibition rule inthe ST ceramic samples. Similar effects of local sym�metry breaking, but at considerably lower tempera�tures, had been observed previously in the calcium�doped ST crystals [26], the ST crystals containing theO18 isotope [33], and even in the nominally pure STcrystals [34], and had been interpreted as ferroelectricfluctuations.

The appearance of the polar phase in the STceramic samples was explained under the assumptionthat the frozen local polarization Pf exists at the grainboundaries of the ceramics where the symmetry is bro�ken, which creates prerequisites for the appearance ofthe dipole moment. Another very probable cause forthe appearance of the local polarization is associatedwith localized point defects, such as oxygen vacanciesand inevitable impurities, for example, calcium impu�rities, whose concentration at the grain boundariescan be considerably higher than the concentrationaveraged over the volume of the ceramic sample. Inthis case, the effective dielectric susceptibility can becalculated as a combination of bulk and surface (grainboundary) layers. The calculations performed in [20]have demonstrated that, in this case, the frequency ofthe soft mode is shifted toward the high�frequencyregion as compared to the position in the spectrum ofthe single crystal. The lowest temperature frequency

in the ceramic sample is equal to 15 cm–1,

whereas in the single�domain crystal, the TO1 mode issplit into the Eu and A2u components with frequenciesof 7.8 and 16.5 cm–1, respectively [35] (the averagevalue is 10.7 cm–1). Such a frequency shift of the softmode is consistent with the low value of the low�tem�perature susceptibility of the ceramic sample as com�pared to the single crystal. The intensity of the polarmodes in the studied ceramics at low temperatures iscomparable to the intensity of these modes in the STcrystals containing approximately 1% Ca, where thefield�induced polarization is of the order of 1 μQ/cm2

[26]. Therefore, if the averaged polarization reachesthis value at low temperatures in the ceramic samples,the frozen local polarization Pf at the grain boundariesshould be substantially higher.

The hybridization of the TO1 mode with the Rg

mode (the X mode in Figs. 1 and 2) due to the loweringof the symmetry is an additional important effect thatacts on the dielectric properties of the ceramic mate�rial. The occurrence of this coupling of the modes sug�gests that the frozen local polarization Pf is directed

ωTO1

α–

ωTO1

1032


YUZYUK

perpendicular to the tetragonal axis c (as in the cal�cium�doped ST crystals [26]). This fact confirms theassumption made by a number of authors that thedipole moment at the grain boundaries is determinedby a specific arrangement of atoms rather than by ran�dom defects [36–38]. Moreover, since the frozen localpolarization Pf exists in the cubic phase and manifestsitself at temperatures substantially higher than thetemperature of the structural phase transition, the tet�ragonal phase is formed in the preferred direction withrespect to the crystal structure of the grain boundaries.The verification of this hypothesis requires detailedinvestigation of the microstructure of the tetragonalphase with a high instrumental resolution.

In recent years, considerable interest has beenexpressed by researchers in the study of thin ST films,whose properties are significantly different from thoseof the bulk crystals. In the ST films, the dielectric sus�ceptibility proves to be substantially lower than that inthe crystal and depends on the thickness of the film.The dielectric susceptibility of the ST films also has atendency toward an increase with decreasing temper�ature, but the curve of the temperature dependence ofthe dielectric susceptibility demonstrates saturation attemperatures below 100 K [39–41]; consequently, thefrequency of the polar soft mode does not reach such alow value as in the crystal and ceases to change at62 cm–1 [42–44]. In this respect, several possible fac�tors responsible for this behavior of the dielectric sus�ceptibility of the ST films have been discussed in theliterature: (a) the influence of an intermediate layer(dead layer) between the film and the electrode [39,40, 45, 46]; (b) mechanical stresses generated by thesubstrate [46]; and (c) disturbance of the stoichiome�try, the porosity, and the presence of grain boundariesin polycrystalline films [45–47]. Investigations of theRaman scattering and IR reflection spectra of severalpolycrystalline ST films have revealed that the pres�ence of polar boundaries in polycrystalline ST filmsleads to a significant increase in the frequency of thesoft mode, and it is this shift of the soft mode whichrepresents a fundamental mechanism responsible forthe significant decrease in the dielectric susceptibilityof the films [48].

In the ST epitaxial films, the sequence of phasetransitions can change rather radically depending onthe character of the influence exerted by the substrate.According to the phenomenological theory for ST epi�taxial films [49–51], in the case of positive strains inthe film (the tensile substrate), there can arise a ferro�electric state with a polarization in the plane of thefilm, and in the case of negative strains (the compres�sive substrate), there can arise ferroelectric phases witha polarization directed perpendicular to the plane ofthe substrate. At low temperatures and small positivestrains in the phase diagram of the ST film, there is amultiphase point at which six phases converge so that,in the low�symmetry phases, the polarization can have

one or two nonzero components in the plane of thesubstrate [51]. Thus, by varying the strain of the STepitaxial film, it is possible to obtain a variety of ferro�electric states. In the ST epitaxial film grown bymolecular beam epitaxy on the DyScO3 tensile sub�strate, the phase transition to the ferroelectric phasewas observed near room temperature [52].

4. LEAD TITANATE

4.1. Single Crystals, Ceramics, and Powders

The lattice dynamics of the PT compound wasinvestigated using the methods of inelastic neutronscattering [53], as well as IR and Raman spectroscopy[54–59]. The first Raman investigations performed byBurns and Scott [55, 56] revealed the soft mode in thePT tetragonal phase, which disappeared at tempera�tures above TC in accordance with the selection rules.A group�theoretical analysis of normal vibrations inthe PT compound was performed somewhat later [57,58]. A detailed assignment of all phonons in the single�domain tetragonal crystal of the PT compound wascarried out by Foster et al. [59]. Below, we will use thenotation of phonon modes used in that work. Theintensities of all Raman�active TO and LO phononshave been recently calculated from first principles[60]. Figure 3 shows the polarized micro�Ramanspectra of the single�domain sample, which wereobtained at room temperature for two scatteringgeometries corresponding to the A1 and E modes.

The assignment of phonons to the LO and TOmodes [55, 56] in the ferroelectric phase is reliableonly in the case where the wave vector is parallel to oneof the principal directions of the crystal symmetry. Forphonons propagating between the principal axes, theA1 and E modes are mixed, so that “quasi�phonons”are observed in the spectra. In the tetragonal phase

with the symmetry, the phonon frequencydepends on the angle θ between the wave vector of theexciting wave and the direction of the polar axis c [59].The phonons observed at θ = 0° and 90° correspond tothe LO and TO modes, respectively. For all intermedi�ate values of the angle θ between these two extremevalues, the lines observed in the Raman spectra have amixed character. The frequency position of the quasi�phonon attributed to the E(TO) and A1(TO) modes isdetermined respectively by the expressions [56–59]

It is obvious that, from the unpolarized Raman spectrameasured on the powders or ceramics consisting of

C4v1

ω2TO( ) ω A1 TO( )( )[ ]2 θsin

2=

+ ω E TO( )( )[ ]2 θ,cos2

ω2LO( ) ω A1 LO( )( )[ ]2 θcos

2=

+ ω E LO( )( )[ ]2 θ.sin2



randomly oriented crystallites, each having a domainstructure, it is impossible to determine accurately thefrequency of the pure TO or LO modes if their fre�quencies are strongly dependent on the angle θ.Detailed investigations of PT single�domain crystals[59] have revealed that not all modes exhibit a strongangular dependence. In particular, the frequencies ofpairs of the modes E(LO3)–A1(LO3), E(TO3)–A1(TO3), and E(TO2)–A1(TO2) differ by more than100 cm–1 and, accordingly, in the spectra of the pow�ders and ceramics, the corresponding lines have anasymmetric shape and are substantially broadened incomparison with the lines in the spectra of the ori�ented single�domain crystals. For the remaining lines,including those for the E(TO1)–E(LO1) soft mode, theangular dependence is insignificant, and the B1 + Eline (289 cm–1) originating from the F2u mode in theparaelectric phase does not exhibit any angular depen�dence. Figure 4 shows the micro�Raman spectra of thePT ceramic samples (in which the average grain sizereaches a few micrometers), which were measured atseveral different points of the sample. The effectivediameter of the focal cylinder was equal to 2 μm. It canbe seen from this figure that the shape of the lines inseveral frequency ranges corresponding to the

E(LO3)–A1(LO3), E(TO3)–A1(TO3), and E(TO2)–A1(TO2) modes depends on the position of the focalcylinder, i.e., on the orientation of the crystallites ofthe ceramics in the scattering volume. When interpret�ing the lines in the spectra of the ceramics and poly�crystalline films, it is necessary to take into accountthat some lines have a mixed character and, therefore,their assignment is somewhat arbitrary.

In the Raman spectrum, the totally symmetriccomponent of the A1(TO1) soft mode with a maximumat 148 cm–1 (Fig. 3) has an asymmetric shape and, ascan be seen from the figure, consists of several overlap�ping bands. The spectral shape of this component isadequately described by a model with an anharmonicdouble�well interatomic potential, which was pro�posed by Foster et al. [59]. More recently, it was shownthat the anomalous scattering intensity at the lowestfrequency soft “subpeak” of the A1(TO1) mode is notdirectly related to the anharmonicity in the double�well potential, but is determined by thermodynami�cally stable lattice defects [61]. It should be noted thatthe inclusion of the double�well potential in the Lan�dau theory made it possible to explain theoretically[62] the temperature dependence of the A1(TO1) softmode, whose frequency does not tend to zero as theCurie temperature TC is approached.

Lead titanate had long been considered as a classi�cal representative of ferroelectrics in the perovskitefamily, which undergoes a displacive phase transitionfrom the cubic phase to the tetragonal phase. However,the presence of the central peak revealed in the spec�trum of the PT compound suggests that, in addition tothe soft�mode behavior, the crystal has a disorder [57,58]. The analysis of the X�ray absorption fine structure(XAFS) spectra [63] has demonstrated that, in the PT


797

A1

(LO

3)

690

E (

LO

3)

647

A1

(TO

3)

504

E (

TO

3)

358

A1

(TO

2)

287

B1

+ E

148

A1

(TO

1)

Inte

nsi

ty,

arb.

un

its

87 E

(T

O1)

218

E (

TO

2)

Fig. 3. Polarized micro�Raman spectra of the a�domainPbTiO3 single crystal at room temperature. The solid lineshows the A1(TO) modes, and the dot�dashed line indi�cates the E(TO) modes. The assignment of the modes isgiven according to [59].


Inte

nsi

ty,

arb.

un

its

qpE

(T

O1)−

E (

LO

1)

qpE

(T

O2)−

A1

(TO

2)

qpE

(T

O3)−

A1

(TO

3)

qpE

(L

O3)−

A1

(LO

3)

Fig. 4. Micro�Raman spectra of the PbTiO3 ceramics inthree different regions of the sample. The arrows indicatethe frequency ranges of quasi�phonons (qp).

1034


YUZYUK

compound, even at temperatures substantially abovethe Curie point TC, the Pb and Ti ions are displacedfrom the centrosymmetric positions, which indicates adisorder in the paraelectric phase. The mechanism ofdisplacement, of course, dominates, and the effects ofdisorder in the PT crystal are less pronounced thanthose in barium titanate.

The investigations of the size effects in PT nanoc�rystalline powders have revealed that, in the Ramanspectra, there occurs a frequency shift of the E(TO1)soft mode toward lower frequencies with a decrease inthe particle size [64, 65]. This behavior suggests thatthe Curie temperature TC decreases with a decrease inthe particle size. The critical size at which ferroelec�tricity disappears in the sample is equal to 12.6 nm.The empirical formula describing the dependence ofthe Curie temperature TC on the particle size D has theform TC = 500 – 588.5/(D – 12.6) [64]. According tomore recent X�ray diffraction data [66], the tetragonaldistortion decreases according to the exponential lawwith a decrease in the particle size and, at room tem�perature, disappears when the critical size reaches7 nm. It should be noted that the size effect becomesvery pronounced for particles smaller than 100 nm andleads to a smoothing of the temperature dependencesin the calorimetric and dielectric measurements [66].In 2000, Fu et al. [67] investigated the temperaturedependence of the Raman spectra of PT nanoparticleswith a size of 7 nm, in which the X�ray diffractionanalysis showed the absence of tetragonal distortion.For particles with a size of 7 nm, the absence of tetrag�onal distortion suggests the existence of the cubicphase and, consequently, the absence of Raman spec�trum. However, the Raman spectrum contained sevenlines, whose positions were fundamentally differentfrom those of the PT tetragonal phase. The investiga�tion of the temperature dependences of the Ramanspectra of PT nanoparticles with a size of 7 nmrevealed the occurrence of the phase transition at atemperature of 166°C, and above this temperature, theRaman spectrum acquired the shape characteristic ofthe PT tetragonal phase. Based on the analysis of thetemperature dependences of the Raman spectra, Fuet al. [67] came to the conclusion that, at temperaturesbelow 166°C, the PT nanoparticles with a size of 7 nmconsist of the low�symmetry phase with the C2V sym�metry, which was not observed in larger particles andcrystals of the PT compound.

4.2. Lead Titanate Thin Films

The lattice dynamics of PT films has been studiedsince the early 1990s of the last century. The behaviorof the soft mode in the IR spectra of the PT films pro�duced by the sol–gel technology on sapphire sub�strates [68] is exactly consistent with the data obtainedby Burns and Scott [55, 56] for single crystals. Theinvestigations of the Raman spectra of the polycrystal�

line PT films prepared by rf cathode sputtering onplatinum�coated silicon substrates have revealed a sig�nificant low�frequency shift in the frequency of thesoft mode in the film with respect to the crystal, whichwas interpreted as the effect of grain clamping of thepolycrystalline films [69]. On the contrary, theobserved increase in the frequency of the soft mode inthe PT epitaxial films on NdGaO3 single�crystal sub�strates was also explained by a two�dimensionalclamping of the film due to the small differencebetween the lattice parameters of the film and the sub�strate [70].

Polycrystalline PT films grown by rf cathode sput�tering on MgO(001) substrates were studied for thefirst time in our earlier work [71]. The micro�Ramanspectra of the PT film and the PT single crystal wereobtained in [71] under identical experimental condi�tions, which allowed a detailed comparison of thetemperature behavior of the soft mode in the film andthe single crystal; hence, the results obtained in thatstudy will be considered in the present review in suffi�cient detail. The X�ray diffraction investigationsrevealed the presence of two types of domains in thesefilms: c�domains with the polar axis normal to the sub�strate and a�domains with the polar axis in the plane ofthe substrate. In the film chosen for the study, the con�centration of c�domains reached 65% at room temper�ature. The averaged (obviously, the unit cell parame�ters in the a� and c�domains can be slightly differentfrom each other) lattice parameters of the film are asfollows: c = 0.411 nm, a = 0.392 nm (c/a = 1.048).The corresponding lattice parameters of the singlecrystal are equal to 0.415 and 0.3904 nm, respectively(c/a = 1.063). The surface and cross section of the filmwere examined using a scanning electron microscope.The thickness of the film was 1 μm, and the grain sizevaried in the range from 0.1 to 0.2 μm.

The Raman spectra of this polycrystalline PT filmare shown in Fig. 5. As was noted above, in the tetrag�

onal phase with the symmetry, the phonon fre�quency depends on the angle θ between the wave vec�tor of the exciting wave and the direction of the polaraxis c. Consequently, the lines observed in the Ramanspectra measured for the polycrystalline PT film withrandom orientations of grains have a mixed LO–TOcharacter. Furthermore, all lines in the Raman spectraof the PT film are considerably broadened in compar�ison with the lines in the Raman spectrum of the PTsingle crystal. The effect of broadening of the Ramanlines is apparently due to the disturbance of the peri�odicity because of the small size of grains in the filmand the large number of grain boundaries. The mostimportant feature of the Raman spectrum of the PTfilm at room temperature is a significant shift of partic�ular lines toward lower frequencies with respect totheir analogs in the Raman spectrum of the PT singlecrystal. By comparing the dependences of the frequen�cies of the lines in the Raman spectra of the PT single

C4v1



crystal on the hydrostatic pressure [72], it is easy tofind that the positions of the lines in the Raman spec�tra of the polycrystalline PT films correspond to fre�quencies in the Raman spectrum of the PT single crys�tal at a pressure of 1.4 GPa [71].

The temperature dependences of the frequencyand full�width at half�maximum (FWHM) of theE(TO1) soft mode in the spectra of the PT single crys�tal and the polycrystalline PT film on the MgO(001)substrate are shown in Fig. 6 in comparison with theresults obtained by Burns and Scott [55, 56]. The dataobtained in our earlier work [71] for the polydomainsingle crystal are in good agreement with the resultsobtained previously in [55–58] for single�domainsamples. The frequency of the E(TO1) soft modedecreases from 89 to 52 cm–1 during heating of thesample from room temperature to the Curie point TC,whereas at temperatures above the transition to thecubic phase, this mode is absent in the spectrum inaccordance with the selection rules. It should be notedthat, above the Curie temperature TC, the Ramanspectra of the PT crystals contain rather weak first�order lines (in [58], these lines were erroneously inter�preted as the second�order Raman spectrum), whichindicates a certain disorder in the PT cubic phase.During further heating of the sample, the Ramanspectrum exhibits only broad bands with maxima at200, 500, and 700 cm–1, which, most likely, reflect thephonon density of states of the optical branches.

It can be seen from Fig. 6 that, at room tempera�ture, the E(TO1) soft mode in the spectrum of the PTfilm has a lower frequency (80 cm–1) and decays morerapidly as compared to the PT single crystal. The tem�perature behavior of this soft mode in the PT film isalso different from the behavior in the PT single crys�tal. In the PT film, this mode softens and reaches aminimum value (52 cm–1) at a temperature ~20 Klower than that in the PT crystal; i.e., the Curie tem�perature of the film TC, f is approximately equal to743 K. The observed decrease in the Curie tempera�ture of the film is apparently due to the grain clampingof the polycrystalline film. The value of this grainclamping gradually decreases during heating of thesample, along with the decrease in the degree of tet�ragonal distortion (c/a), and the shift in the phasetransition temperature by 20 K indicates a decrease inthe pressure from 1.4 GPa at room temperature to0.2 GPa near the temperature of the phase transition.

At room temperature, the full�width at half maxi�mum of the soft mode in the PT film is three timeslarger than that in the PT single crystal and signifi�cantly increases (Fig. 6b) as the phase transition tem�perature is approached. In contrast to the crystal,where the soft mode disappears rather abruptly uponthe phase transition, the intensity of this mode in thefilm is very high even at a temperature of 800 K(Fig. 7). At temperatures above TC, f, the soft mode inthe spectrum of the film is a broad line with the widthapproximately equal to its frequency (50–52 cm–1).The frequency position is almost independent of thetemperature, and the integrated intensity decreasesmonotonically with an increase in the temperature. Itis obvious that the polar regions exist in the studiedfilm at temperatures significantly higher than those inthe single crystal, and the phase transition is diffuse.Among the possible causes for this phenomenon arethe residual mechanical (most likely, inhomogeneous)stresses generated in the film due to the interaction


300

400

500

600

700

800

873

T, KIn

ten

sity

, ar

b. u

nit

s

Fig. 5. Temperature dependence of the micro�Ramanspectra of the PbTiO3 polycrystalline film on theMgO(001) substrate.

800600400T, K

90

50

80

70

60

Wav

e n

um

ber,

cm

−1

(a)

123

800600400T, K

60

10FW

HM

, cm

−1

(b)

12

3

50

40

30

20

Fig. 6. Temperature dependences of the (a) frequency and(b) full�width at half�maximum (FWHM) of the E(TO1)soft mode (1, 2) in the PbTiO3 single crystal according todata taken from (1) [55, 56] and (2) [71] and (3) in thepolycrystalline PbTiO3 film on the MgO(001) substrateaccording to data taken from [71].

1036


YUZYUK

with the substrate, which can lead to activation ofvibrational modes that are forbidden in the cubicphase. Another and, apparently, the most probablecause is the presence of polar regions at the grainboundaries of the polycrystalline films. The gradualdecrease in the intensity of the soft mode at tempera�tures above TC, f is associated with the fact that thermalfluctuations destroy these local polar states.

In the polycrystalline PT films obtained by the sol–gel method on sapphire substrates, the soft mode isalso shifted toward lower frequencies at room temper�ature, and the shift increases with a decrease in thefilm thickness. In the study of the temperature depen�dences of the Raman spectra of the PT films with dif�ferent thicknesses, it was found that the Curie temper�ature TC decreases with a decrease in the film thick�ness from 420 to 20 nm [73]. Almost similar resultswere obtained in the investigation of the Raman spec�tra of the polycrystalline PT films synthesized by thesol–gel method on Pt/Si substrates [74].

Thus, in the polycrystalline PT films, there are sig�nificant shifts in the Curie temperature TC predomi�nantly due to grain clamping in the ferroelectricphase, which is characterized by large spontaneousstrains. Micro�Raman spectroscopy provides a meansfor investigating these effects with a high accuracy anda micron spatial resolution, which makes this tech�nique very promising for the diagnosis of thin films.

4.3. (Pb,Sr)TiO3 Solid Solutions

Solid solutions Pb1 – xSrxTiO3 (PST) can be usedboth in the paraelectric region, because they are prom�ising materials for the design and fabrication of ele�ments intended for microwave devices (resonators, fil�ters, and phase shifters), and in the ferroelectric regionas materials for integrated capacitors and memory ele�ments. In 1955, Nomura and Sawada [75] were thefirst to investigate the phase diagram of PST solid solu�tions. The phase diagram for the PST samples with alow lead content was refined only recently [76]. Thetemperature of the phase transition to the ferroelectricstate lies in the range from 763 to 766 K for lead titan�ate and linearly decreases in the PST solid solutionswith an increase in the strontium content. The ferro�electric phase transition from the cubic phase with the

symmetry to the tetragonal phase with the symmetry occurs at room temperature for a strontiumcontent x ≈ 0.65. Below room temperature, the ferro�electric phase transition in the PST solid solutions isobserved up to xc = 0.998. The compositions with astrontium content in the range 0.7 < x < 0.8 are ofgreatest interest for applications in microwave tech�nology, because, in this case, the required Curie tem�perature can be chosen by varying the strontium con�tent. However, the dielectric susceptibility of ceramicsof these compositions is too high and can be decreasedto the desired level by the dilution of the PST solidsolution with a material characterized by a low permit�tivity and a small dielectric loss, for example, MgO[77]. This technique makes it possible to decrease thepermittivity of the PST : MgO composites to thedesired value. However, in this case, at the grainboundaries of the composite, there can arise bothcompositional and structural inhomogeneities, whichlead to the formation of a local polarization.

Raman spectroscopy is a very effective method forstudying local symmetry breakings, because theyinduce violations of the selection rules and activationof the modes forbidden by the selection rules. The pre�viously published studies of the Raman spectra of PSTnanocrystalline powders [78] have demonstrated that,as in the PT compound, the ferroelectric phase transi�tion in these solid solutions is caused by the instabilityof the low�frequency soft mode, which corresponds tothe displacement of Pb ions with respect to the oxygenoctahedron [55–58]. The transition from the cubicphase to the tetragonal phase at room temperature wasobserved at the strontium content xc = 0.57, which issomewhat different from the data reported in [75].Furthermore, the Raman spectra published in [78] forcompositions with x = 0.8, 0.7, and 0.6 are almostidentical to each other. Moreover, despite the fact that,according to those authors, the Raman spectra forthese compounds correspond to the cubic phase, allthey contain polar modes corresponding to the tetrag�onal phase.

Oh1

C4v1

850800750700650T, K

TC

6

0

5

4

3

2

1

Inte

gral

inte

nsi

ty,

arb.

un

its

Fig. 7. Temperature dependences of integrated intensity ofthe E(TO1) soft mode in the PbTiO3 single crystal (opencircles) and in the polycrystalline film on the MgO(001)substrate (closed circles).



Jain et al. [79] thoroughly investigated the Ramanspectra of the PST solid solutions. Particular attentionwas drawn to the compositions with strontium concen�trations x = 0.8 (PST80) and x = 0.7 (PST70), as wellas to the PST80 composite with MgO (PST80 : MgO);and the role of polar grain boundaries in these materi�als was discussed. The ceramic samples of the PSTsolid solutions studied in [79] were synthesized usingthe conventional solid�phase synthesis technology.The grain size was determined using a scanning elec�tron microscope and varied in the range from 1 to5 μm.

A general view of the unpolarized Raman spectra ofthe ST ceramic samples with different strontium con�centrations is presented in Fig. 8. The concentrationdependence of the position of the lines in the Ramanspectra of the PST solid solutions was previously pub�lished in [78]; however, more recently, somewhat dif�ferent results were obtained in [79]. The significantdifference lies in the fact that the E(TO1) soft mode inthe Raman spectra does not disappear at xc = 0.57 andremains visible up to x = 0.70 at room temperature. Allthe PST solid solutions are characterized by the pres�ence of polar modes in the spectra at temperatures sig�nificantly higher (by approximately 50–80°C) thanthe phase transition temperature. For the PST70 com�position, which, according to the phase diagram [76],has cubic symmetry at room temperature, the intensi�ties of the soft mode and some of the polar modes arevery high, which indicates the presence of polarregions in the sample. A detailed analysis has revealedindications of the polar modes in the spectra of thePST80 sample at room temperature.

Let us dwell in more detail on the study of thePST70 and PST80 compounds and the PST80 : MgOcomposite. According to the X�ray diffraction data[79], the PST80 and PST70 samples have cubic sym�metry with the perovskite unit cell parameters equal to0.3913 and 0.3917 nm, respectively. The X�ray diffrac�tion pattern of the PST80 : MgO composite containsall reflections that are characteristic of the PST80ceramics and a number of additional reflections corre�sponding to MgO. No splitting or shift of the diffrac�tion peaks corresponding to the PST80 compound inthe composite is observed, which confirms the forma�tion of a composite rather than a solid solution of PSTwith MgO.

During cooling, the temperature dependences ofthe dielectric susceptibility of the PST70 and PST80compounds exhibit narrow peaks with maxima at tem�peratures of 283 and 213 K, respectively [79]. Nodependence of the position of the peak on the fre�quency is revealed. For both samples, the Curie con�stant is of the order of ~105, which is typical of first�order phase transitions; however, the dependence of1/ε on the temperature slightly differs from the knowndependence for the PT compound. In the temperaturerange 30–40 K above the dielectric maximum, the

dependence of 1/ε on the temperature deviates fromthe Curie–Weiss law ε = C/(T – TC) and, for bothcompounds, the Curie temperature is 6 K higher thanthe phase transition temperature corresponding to theposition of the dielectric maximum Tm. This behaviorsuggests the presence of local polar regions already inthe paraelectric phase. In the PST80 : MgO compos�ite, the dielectric susceptibility is considerably lowerand the maximum is diffuse. This suggests the pres�ence of polar regions at temperatures above Tm in awider temperature range as compared to the PST80ceramics. The performed X�ray diffraction measure�ments have not revealed disturbances of the long�range order in the composite. The formation of polarregions and the related local symmetry breakings inthe short�range order have been reliably detected bythe Raman scattering methods, because the ferroelec�tric soft mode and other polar modes will be activatedat temperatures higher than Tm.

The Raman spectra of the ST ceramic samples atroom temperature and the Raman spectra of thePST30 ceramic samples at some particular tempera�tures above the peak of the dielectric susceptibility arepresented in Fig. 9. All the spectra were measuredunder identical experimental conditions. As in the


x = 0

x = 0.1

x = 0.2

x = 0.3

x = 0.4

x = 0.5

x = 0.6

x = 0.7

x = 0.8E

(T

O1)

A1

(TO

1)

E (

TO

2)

B1

+ E

A1

(TO

2)

A1

(LO

2);

E (

LO

2)E

(T

O3)

A1

(TO

3)

E (

LO

3)

A1

(LO

3)

E (LO1)

Inte

nsi

ty,

arb.

un

its

Fig. 8. Concentration dependence of the unpolarizedRaman spectra of Pb1 – xSrxTiO3 solid solutions (ceram�ics) at room temperature.

1038


YUZYUK

case of the ST ceramic sample, the Raman spectrumof the PST70 ceramics consists predominantly ofstrongly overlapping bands of the second order in thefrequency ranges 200–450 and 600–800 cm–1. Theband 2TA, which is attributed to the overtone of thetransverse acoustic (TA) phonon in PST70, is shiftedtoward lower frequencies, because, in the PT sample,the frequency of this phonon at the boundary of theBrillouin zone is found to be ~50 cm–1, which is2.5 times lower than that in the ST ceramic sample(~125 cm–1) [80]. These data suggest that, in thePST70 ceramics, the frequency of the TA branch at theboundary is approximately equal to 100 cm–1, whichleads to a shift of the 2TA band from ~250 cm–1 in theST ceramic sample to ~200 cm–1 in the PST70ceramic sample. In the cubic paraelectric phase of thePST70 compound, narrow peaks of the polar modes at~551 cm–1 (TO4), ~500 cm–1 (LO3), ~265 cm–1 (TO3

and LO2 originating from the “silent” F2u mode), and~176 cm–1 (TO2) are clearly seen against the back�ground of the second�order Raman spectrum. Thefrequencies of these lines are consistent with the IRand Raman spectra of the ST ceramic samples.

As was shown above, in the crystal and ceramics ofthe ST compound, the frequency of the TO1 soft modeis equal to 88 cm–1 at room temperature [28], and asthe temperature decreases, it is softened so that the

extrapolation of the temperature dependence suggestsTC = 32 ± 5 K [30]. In the PST70 ceramic sample, thefrequency of the TO1 soft mode is 25 cm–1 at 300 K,and it is softened to 20 cm–1 at the temperature Tm =283 K. The appearance of forbidden polar modes inthe Raman spectra of the PST70 ceramic samples attemperatures above Tm is associated with the presenceof nanoscale polar regions. It should be noted that theintensity of forbidden modes in the PST70 ceramicmaterial is significantly higher than that in the STceramic material (see Section 3), and it increases asthe temperature Tm is approached from above.

The temperature dependence of the frequencies ofthe Raman spectral lines of the PST70 ceramics attemperatures below Tm is shown in Fig. 10. As in thePT compound [55–58], the F1u(TO1) soft mode in thetetragonal phase of the PST70 compound is split intothe E(TO1) and A1(TO1) components. The lowest fre�quency line of the E(TO1) mode, in turn, is also splitinto two components at frequencies of 21 and 34 cm–1;moreover, below Tm, both components exhibit a non�linear temperature dependence as the temperaturedecreases. This removal of the degeneracy of theE(TO1) mode in the A� and B�substituted ABO3 per�ovskites was also observed earlier in [81, 82]. In thecase of the PST solid solutions, the low�frequencyE(TO1) mode has a complex structure in the spectra ofall compounds. Apparently, this is associated with thefact that strontium forms an ionic bond with the sur�rounding oxygen atoms, and the bond of Pb with the

120010008006004002000Wave number, cm–1

Inte

nsi

ty,

arb.

un

its

283 K

300 K

350 K

300 KST

PST70

LO4

TO4

LO2

TO2TO1

LO1

2TALO3; TO3

TO

1

TO

2

LO

1 2TA

Fig. 9. Unpolarized Raman spectra of the ST ceramics at atemperature of 300 K and the PST70 ceramics at temper�atures of 283, 300, and 350 K. Designations: LO and TOare the longitudinal and transverse optical phonons,respectively, and TA stands for the transverse acousticphonons. The intensity is corrected for thermal occupa�tion factor.

300

0

250

200

150

100

50

Wav

e n

um

ber,

cm

−1

30025020015010050T, K

B1 + E (silent)

2TA

A1 (TO2)E(TO2)

A1 (LO1)

A1 (TO1)

E(LO1)

E(TO1)

Fig. 10. Temperature dependence of the frequencies of theRaman spectral lines of the ceramics PST80 (open sym�bols) and PST70 (closed symbols).



environment has a mixed character: along the polaraxis, the Pb–O bond is predominantly covalent,whereas in the plane perpendicular to it, the bond ispredominantly ionic. This feature of the chemicalbonds in the PST solid solutions and the very large dif�ference in the cation masses (m(Pb) = 207m(Sr) =87.6) lead to a splitting of the degenerate E(TO1) softmode.

The complex profile in the frequency range 75–150 cm–1 contains three overlapping lines correspond�ing to the E(LO1), A1(TO1), and A1(LO1) modes. In thePT sample, the A1(TO1) mode has a complex structuredue to the anharmonicity of thermal vibrations [59,61]. It is impossible to establish the existence of a sim�ilar effect in the PST solid solutions from the unpolar�ized Raman spectra, because the profile of the A1(TO1)line cannot be uniquely resolved. The analysis of thetemperature dependence of the frequency and full�width at half maximum of these lines has demon�strated that the frequencies of all lines in the frequencyrange 75–150 cm–1 are weakly dependent on the tem�perature, whereas the full�width at half maximum sig�nificantly decreases with a decrease in the tempera�ture.

A narrow line with a frequency of 170 cm–1 origi�nates from the F1u(TO2) mode of the paraelectricphase; it is a rather hard line and does not reveal a pro�nounced temperature dependence. On the contrary,the position of the A1(TO2) line strongly depends onthe temperature. At temperatures below Tm, the fre�quency of this line is equal to 176 cm–1 and increasessignificantly with a decrease in the temperature, inter�sects the second�order band at 206 cm–1, and reaches243 cm–1 at a temperature of 77 K. The frequencyposition of the narrow line at 265 cm–1 is almost inde�pendent of the temperature. This line is an unresolveddoublet B1 + E, which originates from the F2u (silent)mode of the paraelectric phase. A similar behavior ofthis line was observed in the PT samples. Higher fre�quency lines, which originate from the LO2, TO4, andLO4 modes of the cubic phase, are hard lines andexhibit only a natural narrowing with a decrease in thetemperature. It is important to note that, in the crys�tals and ceramics of the ST compound, the second�order band in the Raman spectra are observed down to10–15 K, whereas in the PST70 ceramics, their inten�sity is very low at temperatures below Tm and rapidlydecreases upon cooling. In contrast to the ST com�pound, the spectra of the PST70 ceramic samples donot contain second�order bands at temperaturesbelow 150 K. The only exception is the 2TA band at afrequency of ~200 cm–1, which was observed as a low�frequency wing of the A1(TO2) line at temperatureslightly below 150 K. The absence of the second�orderspectrum indicates a strong decrease of the anharmo�nicity of thermal vibrations in the tetragonal ferroelec�tric phase of the PST70 compound. In the spectra of

the solid solutions with a high lead content, the sec�ond�order bands are absent altogether, which indi�cates a decrease in the anharmonicity.

During the ferroelectric phase transition in thePST80 ceramics (Tm = 213 K), the behavior of the softmodes is not radically different from that observed inthe PST70 ceramics. As can be seen from Fig. 10, thefrequencies of all the hard modes in the Raman spectraof the PST80 and PST70 ceramic samples have veryclose values. The frequencies of the soft modes in thePST80 ceramics are significantly lower, even thoughthe averaged mass of the A cations is increased. Thismeans that the frequency of the soft mode depends toa greater extent on the force constants rather than onthe mass of the A cations. As in the PST70 ceramics,the forbidden polar modes are also observed in thePST80 paraelectric phase, and their intensity substan�tially decreases with increasing temperature so that, atroom temperature, these modes are weakly pro�nounced against the background of the second�orderRaman spectrum. Since MgO does not exhibitRaman�active lines below 800 cm–1, the spectrum ofthe PST80 : MgO composite is characterized only bythe lines attributing to the PST80 compound. Thetemperature dependence of the Raman spectra of thecomposite is essentially similar to the dependence ofthe spectra of the PST80 ceramics. In the Ramanspectra, as well as in the X�ray diffraction measure�ments, Jain et al. [79] did not reveal any indications ofthe formation of a solid solution of PST and MgO.

As was already noted above, the E(TO1) soft modeis very sensitive to cation substitutions. Therefore, thefact that the splitting of this mode is identical in thePST80 ceramic material and in the PST80�basedcomposite clearly indicates that the composite con�sists of PST80 and MgO grains. However, we cannotexclude a partial diffusion of magnesium into thePST80 grains, and vice versa, the diffusion of lead intothe MgO grains during the formation of the compos�ite. This interdiffusion, if there is, it occurs only withinthe grain boundaries, which, as a rule, tend to accu�mulate vacancies and impurity atoms.

It can be assumed that the size and concentrationof polar regions at the grain boundaries in the compos�ite are considerably greater than those in the ceramicmaterial. Hence, the intensity of forbidden polarmodes in the paraelectric phase of the compositeshould be higher than that in the ceramic material. Acomparison of the Raman spectra of the ceramicmaterial and the composite at room temperature ispresented in Fig. 11. It can be seen from this figure thatthere is a significant difference in the intensities of thepolar modes of the ceramic material and the compos�ite. It should be noted that the forbidden polar modesin the Raman spectra of the PST80 : MgO compositeare observed in a considerably wider temperaturerange as compared to the PST80 ceramics. This can beassociated with inhomogeneous stresses generated as a

1040


YUZYUK

result of clamping (or stretching) of grains in the com�posite. The revealed shifts of some lines in the Ramanspectra [79] clearly indicate the presence of clampingstresses in the PST80 ceramics as compared to thePST80 : MgO composite.

4.4. (Pb,Ca)TiO3 Solid Solutions

Solid solutions Pb1 – xCaxTiO3 exhibit a strongpiezoelectric effect, as well as good ferroelectric andpyroelectric properties [83], both in the bulk and thin�film designs. Moreover, the substitution of calcium forlead significantly decreases the Curie temperature,which makes it possible to vary the operating temper�ature range of functional devices. In this respect,investigation of the properties of these solid solutionsis of interest both from the practical and fundamentalpoints of view. Since at room temperature the CaTiO3

and PbTiO3 compounds belong to different symmetrygroups, the Pb1 – xCaxTiO3 solid solutions undergo acomplex structural evolution for different values of x.

The Raman spectra of single�crystal samples of thePb1 – xCaxTiO3 solid solutions for compositions with acalcium concentration in the range 0 < x < 0.55 havebeen investigated recently in [84]. It has been shownthat the Raman spectra of crystals with calcium con�centrations in the range 0 < x < 0.4 are qualitativelysimilar to the spectrum of tetragonal PbTiO3 and that,in the Pb1 – xCaxTiO3 solid solutions at calcium con�centrations in the range 0.4 < x < 0.5, a new (probably,polar) phase state is formed. This fact contradicts thepreviously drawn conclusions regarding the cubicsymmetry [83, 85] of the Pb1 – xCaxTiO3 solid solutionsin the range of medium concentrations. In terms of theLandau theory of second�order phase transitions, the

admissible topology of the phase diagrams, whichqualitatively correctly reflects the experimental situa�tion in these solid solutions, was discussed in [86].

In the Raman spectra of Pb1 – xCaxTiO3 polycrys�talline films with x ≤ 0.32, the E(TO1) soft mode isshifted toward lower frequencies, as is the case in thePT films, due to the grain clamping [87, 88]. As in thePT crystal [84], the frequency of this mode decreasesonly slightly with the substitution of calcium for leadin the concentration range x ≤ 0.32. The results of X�ray diffraction studies of the films with x = 0.4 suggestscubic symmetry of these compounds [87, 88]; how�ever, the Raman spectra contain clearly defined linesof the first order, which are characteristic of the polarphase. It should be emphasized that the general viewof the Raman spectra for x = 0.4 differs from the spec�tra of the films with x ≤ 0.32; moreover, the soft modeis broadened and significantly shifted toward lowerfrequencies down to 70 cm–1. It is possible that, in thePb1 – xCaxTiO3 films with x = 0.4, there can also arise apolar phase with orthorhombic or tetragonal symme�

try different from , which is observed in the PTcompound and the Pb1 – xCaxTiO3 films with x ≤ 0.32.Obviously, this system of solid solutions has still beenlittle studied and, in this direction, much remains to bedone.

5. BARIUM TITANATE

5.1. Single Crystals, Ceramics, and Powders

Experimental investigations of barium titanatehave revealed a very complex character of structuraltransformations with properties inherent in both dis�placive phase transitions and phase transitions of theorder–disorder type. In the framework of the model ofa displacive phase transition, all atoms initially occupy

positions in a perfect cubic unit cell with the sym�metry at high temperatures. In the tetragonal phase,the Ti ions are displaced along the [001] direction andthe ferroelectric soft mode corresponds to their vibra�tions with respect to the oxygen octahedron [89]. Inthe orthorhombic and rhombohedral phases, the Tiions are displaced along the corresponding directionsof elongation of the unit cell.

According to the model of a phase transition of theorder–disorder type [90–92], the Ti ions in theparaelectric phase are displaced from the centrosym�metric positions at the centers of oxygen octahedraand occupy one of the eight minima along the three�fold axes of the cubic unit cell. The local displace�ments at different temperatures were experimentallydetermined using extended X�ray absorption finestructure (EXAFS) spectroscopy in [93]. In the tetrag�onal ferroelectric phase, only four of these eight posi�tions become energetically favorable; moreover, all thefour aforementioned positions are located in oneplane and related by the fourfold axis, which gives rise

C4v1

Oh1

10008006004002000Wave number, cm−1

Inte

nsi

ty,

arb.

un

its

TO

1 LO

1T

O2

LO

2T

O4

Fig. 11. Raman spectra of the PST80 ceramics (lowercurve) and the PST80 : MgO composite (upper curve) at300 K. The intensity is corrected for thermal occupationfactor.



to a spontaneous polarization along this axis. In theorthorhombic phase, the Ti ions can occupy only twoof the eight positions; and only in the rhombohedralphase, the Ti ions are completely ordered.

Vibrational spectra of BT single crystals were previ�ously investigated in sufficient detail in [94–102]. Itwas established in those works using the data availablein the literature that, both mechanisms, namely, thedisplacement of Ti ions and their ordering, take place.As was noted earlier, in the paraelectric cubic phase of

the BT compound with the symmetry, all opticalmodes are forbidden in Raman scattering. However, aswas shown in [97, 98], the experimental Raman spec�tra of the BT cubic phase always contain two broadbands with maxima at frequencies of 260 and 530 cm–1

(Fig. 12), which is consistent with the eight�minimummodel. On the other hand, according to the IR spec�troscopy data, the lowest frequency transverse modeF1u (170 cm–1 at 1300 K) shows a soft�mode behaviorin the paraelectric phase, which is typical of displacivephase transitions. However, this soft mode is over�damped (the full�width at half�maximum of the line is

more than times greater than the line frequency),apparently, just because of the disorder of the Ti ions.Furthermore, detailed measurements using IR spec�troscopy of the temperature behavior of the soft mode[99] revealed that the frequency of the soft modereaches a value of 60 cm–1 at temperatures consider�ably above TC and then remains constant with adecrease in the temperature down to TC, which dis�agrees with the temperature dependence of the staticpermittivity ε0. This contradiction was resolved in thework by Petzelt et al. [101], who showed using submil�limeter measurements that the unusual behavior of thefrequency of the soft mode in BT single crystals is dueto the interaction of this mode with a low�frequencyrelaxator that exhibits a critical behavior upon thetransition from the cubic phase to the tetragonalphase.

In the Raman spectrum of the ferroelectric tetrag�onal phase, narrow lines appear against the back�ground of broad bands (Fig. 12). The F1u soft mode issplit into two components of different symmetries (A1

and E modes). The A1 component of the soft mode hasa small half�width (less than 50 cm–1) and a frequencyof ~276 cm–1, which slightly increases with a decreasein the temperature and abruptly decreases by 10–15 cm–1 due to the transitions to the orthorhombicand rhombohedral phases [94]. The doubly degenerateE(TO) component of the soft mode is overdamped inthe tetragonal phase and has a frequency, according todifferent sources [97], in the range from 34 to 38 cm–1

at room temperature, whereas its half�width variesfrom 85 to 115 cm–1. In Fig. 12, this mode is seen inthe form of a broad shoulder in the low�frequency regionof the spectrum. A characteristic feature of the Raman

Oh1

2

spectrum of the BT compound is the interference dip ata frequency of 180 cm–1 due to the interaction of theA1 modes [97]. In the orthorhombic phase, the E(TO)soft mode is split into two underdamped components,which exhibit a very weak temperature dependence,whereas in the rhombohedral phase, the frequency ofthe E(TO) soft mode abruptly increases to 250 cm–1

[102]. A detailed assignment of all the optical phononsunder consideration was performed only in a tetragonalsingle�domain crystal of the BT compound [97].Because of the rather complex domain structure in theorthorhombic and rhombohedral phases, the Ramanspectra of the BT crystals are completely depolarized,which makes impossible a detailed assignment of theobserved lines in accordance with the symmetry types.

In the Raman spectra of the BT powders with a par�ticle size of less than 100 nm, the half�widths of alllines are significantly greater than those in the bulkmaterial; moreover, the disappearance of the interfer�ence dip in the frequency region of 180 cm–1 indicatesthat there occurs no interaction between the two low�frequency A1(TO) modes [103–105]. With a decreasein the particle size, the temperature of the ferroelectricphase transition decreases. For samples with a particlesize of less than 100 nm, a diffuse phase transition was


460 K

420 K

380 K

330 K

295 K

275 K

240 K

195 K

160 K

120 K

77 K

BaTiO3C

C

T

T

T

O

O

O

R

R

R

Inte

nsi

ty,

arb.

un

its

Fig. 12. Temperature dependence of the Raman spectra ofthe BaTiO3 ceramics. Arrows indicate the transformationof the E(TO) soft mode. The intensity is corrected for ther�mal occupation factor. Designations: C is the cubic phase,T is the tetragonal phase, O is the orthorhombic phase, andR is the rhombohedral phase.

1042


YUZYUK

observed at the Curie temperature TC = 388 K. All thecharacteristic features of the Raman spectra of the BTcompound were observed only when the particle sizeexceeded 30 nm. The pressures induced in BT individ�ual particles and their aggregates affect both the char�acter and the temperature of the phase transitions[104]. Shiratori et al. [105] carried out an analysis ofthe temperature dependence of the Raman spectra ofthe BT nanoceramics with a particle size of 35 nm anddetermined the Curie temperature TC = 378 K,whereas the Raman spectra and phase transition tem�peratures of the coarse�grained ceramics were foundto coincide with those known for crystals.

5.2. Barium Titanate Thin Films

The Raman spectra of polycrystalline BT films pre�pared by metal�organic chemical vapor deposition(MOCVD) and pulsed laser deposition (PLD) wereinvestigated in detail by Robins et al. [106], who werethe first to perform comparative studies of the BT bulksamples and BT films synthesized under different con�ditions. The synthesized films were inhomogeneous,and the Raman spectra, along with the features typicalof the BT compound, contained lines of impurityphases. Due to the polycrystalline nature of the BTfilms, the polarization measurements have failed toseparate modes according to the symmetry types. Thelow�frequency region has not at all been investigated,and information on the E(TO) soft mode has not beenobtained. Nonetheless, it should be noted that Robinset al. [106] were the first to reveal that the phase tran�sition temperature in BT films is several tens of degreeshigher than the temperature TC of the bulk material,which was explained by a two�dimensional clampingof grains in the polycrystalline film.

Heteroepitaxial BT films grown by rf cathode sput�tering on MgO single�crystal substrates have a rathersimple c�domain structure (the polar axis is perpen�dicular to the substrate), which has made it possible to

obtain the polarized micro�Raman spectra [107]. As isknown from the Raman�activity tensors for the pointgroup C4v (the fourfold axis is directed along thez direction),

modes of only the A1 type have been observed in thescattering geometries related exclusively to the αzz

component. The A1� and B1�type modes are allowedsimultaneously for the αxx and αyy components,whereas the E�type modes are allowed only for the αzx

and αzy components. Therefore, the A1 and E modes inthe c�domain film can be observed separately only inthe side�view backscattering geometry, where the wavevector of the incident beam is parallel to the substrateand the polarization of the incident and scattered lightbeams is parallel or perpendicular to the c axis of thefilm, as is shown in Fig. 13. This scattering geometrymade it possible for the first time to obtain the polar�ized Raman spectra of BT epitaxial films in [107].These spectra are presented in Fig. 14. They are veryclosely similar to the micro�Raman spectra obtainedin [108] for the BT single�domain crystals in 180°scattering geometry.

The Raman spectra of the BT c�domain film atroom temperature are presented in Fig. 14. It is impor�tant to emphasize that the MgO crystal has no Raman�active lines in the frequency range below 800 cm–1;therefore, this crystal is a very suitable substrate forthese purposes. The Raman spectra shown in Fig. 14are well�polarized because of the absence of 90°domains. However, the presence of 180° domains inthe samples brings about a partial depolarization of theincident/scattered light on the domain walls, which,in turn, leads to a partial depolarization of intenselines in the Raman spectra, as is the case in the spec�trum of the BT single crystal [97, 108]. The Ramanspectrum of the film measured in the scattering geom�

etry Y(ZZ) , which corresponds to the A1 modes, hasthe following features: a clear interference dip in thefrequency region of 180 cm–1 and broad lines at fre�quencies of 286, 525, and 725 cm–1. In the Ramanspectrum of the film measured in the scattering geom�

etry Y(XX) , the dip disappears and a narrow peakappears at a frequency of ~180 cm–1, as was observedin the Raman spectrum of the BT single crystal. Thespectrum measured in the scattering geometry

Y(ZX) , which corresponds to the E�symmetrymodes, contains the overdamped E(TO) soft mode,which looks like a shoulder of the Rayleigh line. Nar�row lines of the E mode at frequencies of 180 and

a · ·

· a ·

· · b⎝ ⎠⎜ ⎟⎜ ⎟⎜ ⎟⎛ ⎞

c · ·

· c– ·

· · ·⎝ ⎠⎜ ⎟⎜ ⎟⎜ ⎟⎛ ⎞

· d ·

d · ·

· · ·⎝ ⎠⎜ ⎟⎜ ⎟⎜ ⎟⎛ ⎞

· · e

· · ·

e · ·⎝ ⎠⎜ ⎟⎜ ⎟⎜ ⎟⎛ ⎞

· · ·

· · e

· e ·⎝ ⎠⎜ ⎟⎜ ⎟⎜ ⎟⎛ ⎞

,

A1(z) B1 B2 E(x) E(y)

Y

Y

Y

Normalbackscattering

Side�viewbackscattering

Z

X Y

Y

Z Z

YXFilm

Substrate

Fig. 13. Geometries of normal backscattering and side�view backscattering. The exciting radiation is focused ontothe sample with an optical microscope.



309 cm–1 are clearly seen in the Raman spectrum mea�

sured in the geometry Y(ZX) . The high�frequency Emodes at frequencies of 466 (LO) and 489 (TO) cm–1

are rather weak even in the Raman spectrum of thesingle crystals. In the Raman spectra shown in Fig. 14,these peaks clearly overlap with a broad band in therange of 525 cm–1. Evidently, a rather intense line at525 cm–1, as well as a weak band at 285 cm–1, appearsin the Raman spectrum measured in the geometry

Y(ZX) due to a partial depolarization (leak) ofintense lines of the A1 type.

The Raman spectra of the BT epitaxial film, whichhas the a�domain orientation due to tensile stresses ofthe MgO substrate, exhibit all features typical of theRaman spectra of the BT compound, but the lines thatare characteristic of the E�type symmetry are observed

in the geometry Z(YX) , which indicates the orienta�tion of the polarization in the plane of the substrate[109]. The phase transition to the paraelectric phase isobserved in this film at a temperature of 450 K, i.e.,slightly above the phase transition temperature in thebulk material.

The investigation of the temperature dependencesof the Raman spectra of the BT films on SrTiO3 andLaAlO3 substrates covered by a SrRuO3 buffer layer[110] has demonstrated that, in these films, no phasetransitions typical of the BT compound occur. Overthe entire temperature range from 5 to 325 K, the BTfilms are in the orthorhombic phase with the polariza�tion oriented along the diagonal of the basal plane par�allel to the substrate (the aa phase). In the authors’opinion [110], this orientation of the film is caused bytensile stresses of the buffer layer rather than by theinfluence of the substrate. The experimental resultsagree with the authors' own model calculations [110]and the phase diagram constructed in terms of thephenomenological theory [111].

5.3. Crystals and Ceramics of (Ba,Sr)TiO3 Solid Solutions

As is known [112], in the Ba1 – xSrxTiO3 (BST�x)solid solutions, all phase transitions typical of the BTcompound are observed with an increase in the stron�tium concentration to x ≈ 0.8; in this case, the phasetransition temperatures decrease linearly with anincrease in the concentration x. A detailed concentra�tion dependence of the frequencies of optical modes inthe BST�x ceramics at T = 6 K was published for thefirst time in [113]. The temperature dependence of theRaman spectra of single crystals with strontium con�centrations x = 0.5, 0.65, 0.8, 0.9, and 0.95 has beeninvestigated only recently in [114]. The Raman spectraof the samples with a strontium content above 80% arecharacterized by underdamped soft modes with strongnonlinear temperature dependences that are charac�teristic of second�order displacive phase transitions.

Y

Y

Z

In the concentration range x ≤ 0.8, where there occurtransitions between three ferroelectric phases, the softmodes exhibit weak temperature dependences that arecharacteristic of order–disorder phase transitions.According to the data reported in [114], the soft modesbecome overdamped in the stability regions of not onlythe tetragonal phase but also the orthorhombic phase,which casts some doubt on the existence of the orthor�hombic phase in the BST solid solutions. In accor�dance with the order–disorder model [90–92], thenumber of positions allowed for the Ti ions differs by afactor of two for the tetragonal and orthorhombicphases of the BT compound, which should necessarilyaffect the half�width of the soft modes. As is shown inFig. 12, the low�frequency soft mode in the orthor�hombic phase is obviously underdamped, and its half�width is more than two times smaller than that in thetetragonal phase.

Figure 15 shows the Raman spectra measured forceramic samples of the BST solid solutions at room


Inte

nsi

ty,

arb.

un

its

Y(ZZ)Y

A1 (LO)

A1 (TO)

A1 (TO)

A1 (TO)

E (TO)

A1 (TO)A1 (TO)

A1 (TO)

A1 (LO)E (TO)

B1 Y(XX)Y

Y(XZ)Y

E (TO)

E (TO)E (TO)

E (LO)E (LO)E (LO)

A1 (TO) leak A1 (TO) leak

Fig. 14. Polarized Raman spectra of theBaTiO3/MgO(001) film.

1044


YUZYUK

temperature [4]. The Raman spectrum of the BST�0.3ceramics exhibits all the features inherent in the BTcrystal. The overdamped E(TO) soft mode has almostthe same shape and frequency in the Raman spectra ofceramic samples of the BT and BST�0.3 compositions(the frequency is 40 ± 5 cm–1, and the half�width isapproximately 100 cm–1), whereas the A1(TO) band isshifted toward lower frequencies with an increase inthe strontium content (~276 and ~250 cm–1 in the BTand BST�0.3 samples, respectively). The frequencyshift of the E(TO) component cannot be reliablydetermined because of the large error in the determi�nation of this overdamped mode. The Raman spectraof ceramic samples of the BST�0.5 and BST�0.7 com�positions do not contain polar modes, but exhibitbroad bands induced by disorder, which, unlike thoseof the BT cubic crystal, have a rather complex struc�ture. In the Raman spectra of samples of these compo�sitions, we cannot exclude the activation of second�order bands, which takes place in the spectra of the STsamples.

The temperature dependence of the Raman spectraof the BST�0.3 ceramics is qualitatively similar to the

corresponding dependence of the BT samples. As fol�lows from the T–x phase diagram [112] for the BST�xsolid solutions, the phase transitions between the cubic–tetragonal–orthorhombic–rhombohedral phases in theBST�0.3 ceramics are shifted toward lower tempera�tures with respect to the pure BT compound and occurat temperatures of ~300, 220, and 155 K, respectively.The Raman spectra of the BST�0.3 ceramics, whichare shown in Fig. 16, clearly reflect all the successivephase transitions occurring in this material with varia�tions in the temperature [115].

The Raman spectrum of the BT cubic phase con�tains two broad bands at frequencies of 260 and530 cm–1, whereas in the Raman spectrum of thecubic phase of the BST�0.3 ceramics, similar bands areobserved at frequencies of 240 and 550 cm–1, respec�tively. In the framework of the eight�minimum model,this change in frequencies indicates that the substitu�tion of strontium for barium modifies the potentialrelief of the Ti ions in the cubic phase. As in the BTcompound, the E(TO) soft mode in the tetragonalphase of the BST�0.3 ceramics is overdamped. In theorthorhombic phase, the soft mode acquires an under�damped character and slightly softens during furthercooling. Finally, a radical transformation is observedupon the transition to the rhombohedral phase, wherethe soft mode is abruptly shifted toward higher fre�quencies (140 cm–1). It should be noted that such a

10008006004002000Wave number, cm−1

Inte

nsi

ty,

arb.

un

its x = 0

x = 0.15

x = 0.3

x = 0.35

x = 0.5

x = 0.7

x = 1

E (TO)

A1

(TO

)

A1

(TO

)E

; B

1

E (

TO

); A

1 (L

O)

A1

(TO

)

A1

(LO

); E

(L

O)

Fig. 15. Dependence of the Raman spectra of theBa1 ⎯ xSrxTiO3 ceramics on the composition at room tem�perature. The intensity is corrected for thermal occupationfactor.


Inte

nsi

ty,

arb.

un

its

350 K

330 K

300 K

270 K

230 K

200 K

170 K

150 K

120 K

77 K

C

T

O

R

R

R

O

T

T

C

A

BST�0.3

Fig. 16. Temperature dependence of the Raman spectra ofthe BST�0.3 ceramics [115]. The intensity is corrected forthermal occupation factor.



drastic transformation of the soft mode also occurs inthe BT material upon the transition from the orthor�hombic phase to the rhombohedral phase, where sim�ilar lines are observed at higher frequencies (Fig. 12).

The temperature dependence of the Raman spectraof the BST�0.5 ceramics (Fig. 17) is qualitatively sim�ilar to that described for the BST�0.3 ceramics, but thefrequency of the E(TO) soft mode in the rhombohe�dral phase of the BST�0.5 ceramics is substantiallylower than that in the BST�0.3 sample and is equal to90 cm–1. The frequency of the A1(TO) component sys�tematically decreases with an increase in the Sr con�tent. For the BST�0.3 and BST�0.5 compositions, thefrequencies of this component are equal to 209 and183 cm–1, respectively.

In the Raman spectra of the BST�0.3 and BST�0.5ceramic samples, an additional band is observed in thefrequency range 110–125 cm–1. In Figs. 16 and 17,this band is designated by the letter A. A similar bandwas observed earlier in the Raman spectra of the BST�x ceramics at a temperature of 6 K over a wide concen�tration range 0.2 < x < 0.9 [113]. This band was inter�preted as a disorder�induced phonon density of statesof the transverse acoustic (TA) and longitudinalacoustic (LA) branches, which have a high densitynear the boundary of the Brillouin zone. The experi�mentally observed boundary frequencies of the TA and

LA branches in the BT cubic phase are equal to 115and 140 cm–1, respectively [116], which is in goodagreement with the Raman scattering data.

Thus, according to the Raman scattering data, inthe ceramics of BST�x solid solutions at strontiumconcentrations in the range x ≤ 0.8, there occur tran�sitions between three ferroelectric phases, in which thesoft modes show a behavior typical of the BT com�pound. At high strontium concentrations, the avail�able experimental data are not enough to construct acoherent picture of the lattice dynamics during phasetransitions occurring in these solid solutions.

5.4. Films of (Ba,Sr)TiO3 Solid Solutions

The polarized micro�Raman spectra of the BST�0.3 film (with a thickness of 500 nm) on the MgO(001)substrate at room temperature are shown in Fig. 18.The polarized Raman spectra were measured on asample exactly oriented in accordance with the crys�tallographic axes of the c�domain film: X || [100],

8006004002000

Inte

nsi

ty,

arb.

un

its

Wave number, cm−1

295 K

270 K

240 K

220 K

200 K

170 K

158 K

145 K

130 K

100 K

77 K

C

C

C + T

T

O

O

O + R

R

R

R

A

T

BST�0.5

Fig. 17. Temperature dependence of the Raman spectra ofthe BST�0.5 ceramics. The intensity is corrected for ther�mal occupation factor.


Inte

nsi

ty,

arb.

un

its

Y(ZZ)Y

Y(XX)Y

Y(ZX)Y

E (

LO

)

C D

E (

TO

)

E (LO)B

E (TO)E (LO)

E (TO)E (LO)

A

A1 (LO)DC

A1 (TO)

B

B1

A1 (TO)

A1 (TO)

A

E (TO) soft mode

E (TO) leak

A1 (TO) leak A1 (TO) leak

E (TO) leak

A1 (TO)

A

B

A1

(LO

)

A1 (LO)D

C

A1 (TO)A1 (TO)B1

Fig. 18. Polarized Raman spectra of the BST�0.3 films atroom temperature. The intensity is corrected for thermaloccupation factor. Bands A, B, C, and D are due to localdistortions of the crystal structure (see text).

1046


YUZYUK

Y || [010], and Z || [001]. The Raman spectrum of this

film in the polarization Y(ZZ) has the following fea�tures: a clear interference dip in the frequency regionof 170 cm–1 and broad lines at frequencies of 230 and525 cm–1. In the Raman spectrum measured in the

polarization Y(XX) , the dip disappears and a narrowpeak appears at a frequency of ~170 cm–1, as wasobserved in the spectra of the film and single crystal ofthe BT compound. It should be noted that the A1(TO)component of the soft mode, which has a frequency of276 cm–1 in the Raman spectrum of the BT com�pound, reveals a significant shift toward lower fre�quencies down to 230 cm–1 in the spectrum of theBST�0.3 film; as a result, the interference dip in thefrequency region of 170 cm–1 becomes more pro�nounced. The Raman spectrum, which corresponds tothe E�symmetry modes, contains the underdampedE(TO) soft mode at a frequency of 78 cm–1, which istwice the corresponding value in the spectra of the BTcrystals. Narrow lines of the E mode at frequencies of176 and 300 cm–1 are clearly seen in the Raman spec�

trum measured in the polarization Y(ZX) . The high�frequency E modes observed at frequencies of466 (LO) and 489 (TO) cm–1 are rather weak even inthe spectrum of the single crystals. In Fig. 18, thesepeaks clearly overlap with a broad band at 525 cm–1

[117, 118].

In addition to the polar modes expected from thefactor�group analysis, the Raman spectra of the BST�0.3 film contain four additional bands, which are des�ignated by the letters A, B, C, and D in Fig. 18. Theappearance of these bands is caused by local distor�tions of the crystal structure, which lead to distur�bances of the translational symmetry upon the substi�tution of strontium for barium. Obviously, these bandsshould also be observed in the Raman spectra ofceramic samples; however, in the unpolarized Ramanspectra, they are very difficult to reveal. Only the Aband is reliably observed in the Raman spectra of theBST�x ceramics and has been interpreted as a disor�der�induced phonon density of states of the acousticbranches. Bands B, C, and D are attributed to opticalphonons and exhibit the concentration and polariza�tion dependences, which will be discussed below. Acomparison of the spectra of the BST�0.3 and BST�0.5ceramics suggests the presence of a two�phonon band2TA, 2LA, or LA + TA in the frequency range 230–250 cm–1, which strongly overlaps with the A1(TO)component of the soft mode; therefore, the parame�ters of this band are impossible to determine uniquely.Most likely, it is this circumstance that determines thelarge half�width and intensity of the A1(TO) compo�nent of the soft mode.

The concentration dependences of the polarizedRaman spectra of the BST�x films are shown inFig. 19. It is evident that, upon the substitution of

Y

Y

Y

strontium for barium, the general character of theRaman spectra remains unchanged; furthermore, theRaman spectra of the BST�x films even with x = 0.45correspond to the tetragonal ferroelectric phase. Themajority of the polar modes exhibit a very weak con�centration dependence, whereas the parameters of thesoft modes change rather significantly. As in the spec�trum of the single crystal, the E(TO) soft mode is over�damped in the spectrum measured in the polarization

Y(ZX) for the nominally pure BT film. The fre�quency of the corresponding peak is 35 ± 5 cm–1, andthe half�width is 120 ± 10 cm–1. With an increase in thestrontium concentration, the frequency of the E(TO)soft mode increases; at a strontium concentration x ≥0.3, it becomes underdamped, and the correspondingline of the spectrum is fitted fairly well by the functionof the oscillator with a damping significantly less thanthe frequency of the maximum. The A1(TO) compo�nent of the soft mode in the spectrum of the BT filmhas a frequency of 280 cm–1 and significantly shiftstoward lower frequencies with an increase in the stron�tium content. Moreover, there occurs an enhance�ment of the interaction of this mode with a low�fre�quency mode at 180 cm–1, whose frequency decreasesby only 10 cm–1 for x = 0.45. As a result, the interfer�ence dip in the spectra measured in the polarization

Y(ZZ) becomes more pronounced. In order todetermine the true frequencies of two interacting low�frequency A1(TO) modes, it is necessary to perform asimulation of the spectra according to the proceduredescribed in [97]. As can be seen from Fig. 19, the A1–E splitting of the soft mode, which reflects anisotropyof the short�range interatomic interactions in the tet�ragonal phase, steadily decreases with an increase inthe strontium content.

From the calculations of normal vibrations for theBT compound [89], it is well known that the soft modein BT corresponds to the displacements of titaniumions with respect to the oxygen octahedron, and it isevident that the frequency of this mode depends on theTi–O bond length. In the tetragonal c�domain thinfilm, the E(TO) soft mode corresponds to the dis�placements of titanium ions in the plane parallel to thesubstrate, whereas the A1(TO) soft mode correspondsto the displacements of titanium ions in the plane per�pendicular to the substrate. Obviously, an increase inthe frequency of the E(TO) mode and a decrease in thefrequency of the A1(TO) mode can be associated witha two�dimensional clamping in the heteroepitaxialfilm.

Let us consider the factors responsible for this phe�nomenon. The lattice parameters of the BST�x filmare substantially less than the lattice parameters of theMgO cubic crystal (af < ac). For all values of x, the lat�tice parameter af does not exceed 4 Å, whereas the lat�tice parameter of the MgO cubic crystal is ac = 4.213 Å.Therefore, during the epitaxial growth, the film is sub�

Y

Y



jected to strong tension in the plane of the substrate,which is eliminated through the formation of misfitdislocations. The critical thickness of the film, atwhich the formation of such dislocations begins tooccur, reaches only a few nanometers [119], and a fur�ther increase of the film leads to the normalization ofthe parameters of the crystal lattice. However, thedegree of tetragonality of the BST�x/MgO(001) filmswith a thickness of several hundred nanometers, whichwere studied in [115, 117, 118], is significantly higherthan that for ceramics of similar composition. Thefilms were deposited at a high temperature in the range600–900°C; hence, the cooling of samples resulted inthe appearance of two�dimensional compressivestresses due to the difference between the thermalexpansion coefficients of the materials of the film andthe substrate (αST = 10 × 10–6 K–1, αBT = 10.4 ×10⎯6 K–1, αMgO = 14.8 × 10–6 K–1). During cooling,these thermoelastic compressive stresses make unfa�vorable the formation of a�type domains with thepolarization in the plane of the substrate upon thetransition to the ferroelectric phase; consequently,

only 180° c�type domains with the polarization nor�mal to the substrate are formed in the film. The degreeof tetragonality of this film is higher than that of bulkceramics of similar composition. Therefore, theobserved increase in the frequency of the E(TO) softmode can be unambiguously interpreted as a result ofthe two�dimensional compression due to the differ�ence between the thermal expansion coefficients ofthe materials of the film and the MgO substrate.Despite the relatively large thickness of the films, therole of thermoelastic stresses generated by this sub�strate is fairly significant, and the sequence of phasetransitions occurring in the films changes radically. Itis clear that, in the film released from the substratecompletely or partially, the effects of two�dimensionalmechanical stresses should vanish [120].

The peak of the dielectric susceptibility of thefilms, which corresponds to the phase transition, isusually diffuse, and the temperature dependence ofthe lattice parameters, as a rule, is flattened, so that itis often impossible to determine the phase transitiontemperature with a high accuracy, because the changes


(a)

Y(ZZ)Y Y(XX)Y

Y(XZ)Y

x = 0.45

x = 0.30

x = 0.15

BTMgO

C DA B

A1 (TO) soft mode

Inte

nsi

ty,

arb.

un

its


(b)

x = 0.45

x = 0.30

x = 0.15

BT

C DA B

Inte

nsi

ty,

arb.

un

its

8006004002000Wave number, cm–1

(c)

x = 0.45

x = 0.30

x = 0.15

BT

C D

A

B

E (TO) soft mode

Inte

nsi

ty,

arb.

un

its

100806040200Sr concentration, %

250

0

200

150

100

50

A1−

E s

pli

ttin

g, c

m−

1

(d)

Fig. 19. (a–c) Polarized Raman spectra of the BST�x films and (d) A1–E splitting of the soft mode in films of different composi�tions.

1048


YUZYUK

occur in a rather wide temperature range that, some�times, reaches several tens of degrees. The phase tran�sitions in films, as a rule, have a diffuse character dueto the large number of defects, compositional hetero�geneities, and thermal stresses generated by the inter�action with the substrate. A typical temperaturedependence of the unit cell parameters of one of theBST�0.3/MgO(001) films is shown in Fig. 20. The tet�ragonal unit cell parameters of this film at room tem�

perature are as follows: af = 3.9555 Å and cf = 3.9956 Å(cf/af = 1.010). According to the temperature depen�dence of the unit cell parameters and their ratio (c/a),it can be assumed that, at a temperature of ~365 K,which corresponds to a minimum in the curve of thetemperature dependence of the unit cell parameterc(T), there occurs a phase transition from the ferro�electric phase to the paraelectric phase. The phasetransition in the film is substantially shifted towardhigher temperatures as compared to the ceramic sam�ples, which is consistent with the predictions madefrom the phenomenological theory [111, 121, 122]. Asfollows from the temperature dependences of the unitcell parameters presented in Fig. 20, the unit cellremains tetragonal at temperatures above TC, wherethe degree of tetragonality is even not so high (cf/af =1.006), but is recorded quite reliably.

The temperature dependences of the polarizedRaman spectra of the BST�0.3/MgO are shown inFig. 21. With an increase in the temperature, theintensity of all the polar modes decreases, whereas thefrequency of the E(TO) soft mode increases from60 cm–1 at room temperature to 72 cm–1 at a temper�ature of 365 K. This behavior is typical of the softmode for the BT compound during the transition fromthe ferroelectric to the paraelectric phase. In theRaman spectra of the BST�0.3/MgO film, the polarmodes are observed up to 380 K, which, as can be seenfrom this figure, slightly exceeds the Curie tempera�

800700600500400300T, K

0.400

0.398

0.396

0.394

Lat

tice

par

amet

ers,

nm

1.011

1.005

1.010

1.009

1.008

1.007

1.006

c/a

c/a

c

a

Fig. 20. Temperature dependences of the unit cell param�eters a and c of the BST�0.3/MgO film.

8006004002000

Inte

nsi

ty,

arb.

un

its

Y(ZZ)Y Y(XX)Y Y(ZX)Y

300 K

320 K

350 K

360 K

370 K

380 K

400 K

600 K

900 K

1200 K

8006004002000

300 K

320 K

350 K

360 K

370 K

380 K

400 K

600 K

900 K

1200 K

8006004002000

300 K

320 K

350 K

360 K

370 K

380 K

400 K

600 K

900 K

1200 K

Wave number, cm–1

Fig. 21. Temperature dependences of the polarized Raman spectra of the BST�0.3/MgO film. The intensity is corrected for ther�mal occupation factor.



ture TC determined from the temperature dependenceof the lattice parameters.

This discrepancy can be explained as follows. X�raydiffraction has made it possible to investigate fairlyaccurately the behavior of the unit cell parameters ofthe film during the ferroelectric phase transition. Polarnanoregions can exist in the film in a specific range oftemperatures above the Curie point TC (which wasdetermined from the diffraction experiment) becauseof the compositional heterogeneity, as well as differentdefects and dislocations. Since the phase transition ina thin film occurs not to the cubic phase, but to the tet�ragonal phase, it is impossible using the X�ray diffrac�tion technique to determine whether a new phase ispolar or not. The Raman spectra in this case provideinformation about the presence (or absence) of just thepolar vibrations, which allows one to identify the polarregions formed in the film at temperatures above TC. Itis the presence of such polar regions in the materialwhich leads to a smearing of the phase transition in thefilms. At temperatures above 380 K, only the bandsinduced by disorder are observed in the Raman spec�tra. The absence of polar modes in the Raman spectra

suggests the nonpolar symmetry of the paraelec�tric phase, in which the first�order Raman spectrum isforbidden. Obviously, the two�dimensional stressesreduce the symmetry of the paraelectric phase fromcubic to tetragonal [121–123]. It is important to note

D4h1

that the value of two�dimensional stresses in the filmsdepends on the growth mechanism during the filmdeposition, which makes it possible within particularlimits to vary the temperature of the ferroelectric tran�sition [124].

Below room temperature, the sequence of phasetransitions in the film under consideration is radicallydifferent from the well�known sequence of phase tran�sitions in ceramic samples of the same composition[115, 125, 126]. The polarized Raman spectra of theBST�0.3/MgO film at low temperatures are shown inFig. 22. In contrast to the samples of bulk ceramics,the temperature dependence of the Raman spectra ofthe film is monotonic down to 30 K. At temperaturesin the range 150–160 K, a partial depolarization of thespectra begins to occur, which then gradually increaseswith decreasing temperature of the sample.

The depolarization of the lines in the Raman spec�tra indicates that the selection rules change upon thediffuse phase transition occurring in the temperaturerange from 120 to 150 K. The frequency of the E(TO)soft mode steadily decreases during cooling of thesample to ~120 K and then again slightly increases(Fig. 23). On the contrary, the frequency of the A1(TO)component of the soft mode increases and reaches sat�uration at ~150 K. Furthermore, an additional com�ponent of the soft mode with a strong temperaturedependence arises in the Raman spectra measured in

8006004002000

Inte

nsi

ty,

arb.

un

its

Y(ZZ)Y Y(XX)Y Y(ZX)Y

295 K

240 K

220 K

190 K

160 K

140 K

110 K

70 K

30 K

8006004002000

295 K

240 K

220 K

190 K

160 K

140 K

110 K

70 K

30 K

6004002000

295 K

240 K

220 K

190 K

160 K

140 K

110 K

70 K

30 K

Wave number, cm−1

Fig. 22. Polarized Raman spectra of the BST�0.3/MgO film at low temperatures. The intensity is corrected for thermal occupa�tion factor.

1050


YUZYUK

the polarization Y(XX) at temperatures below~150 K. The E(TO) soft mode is split into two compo�nents, which are well separated at 30 K and observedin different scattering geometries corresponding to thedifferent components of the polarizability tensor,

namely, Y(XX) and Y(ZZ) [115]. The temperaturedependence of the components of the soft mode sug�gests a reduction in the symmetry of this film at tem�peratures in the region of ~150 K; in this case, thephase transition is diffuse and a rather weak depolar�ization of the spectra during cooling indicates the for�mation of a specific domain structure that has no ana�log in bulk ceramics. It is known from the investigationof BT single crystals that a very complex domain struc�ture is formed in the orthorhombic and rhombohedralferroelectric phases, which leads to a complete depo�larization of the Raman spectra. In the BST�0.3/MgO(001) heteroepitaxial films, there arise two�dimensional stresses, which bring about the formationof a 180° c�domain structure in the tetragonal phaseand, apparently, play an important role in the low�temperature phase transitions. The observed splittingof the E(TO) soft mode and the appearance of one of

its components in the polarization Y(XX) at temper�atures below ~150 K indicate monoclinic symmetry ofthe low�temperature phase. Moreover, the characterof the polarized Raman spectra suggests that thereoccurs no transition to the rhombohedral phase in the

Y

Y Y

Y

BST�0.3/MgO(001) heteroepitaxial films. Accordingto the phenomenological theory [111, 121–123], therhombohedral phase with spontaneous polarizationalong the body diagonal of the initial cubic cell (P1 =P2 = P3 ≠ 0) is not realized in epitaxial films on cubicsubstrates.

The analysis of the influence of the thickness of theBST�0.2/MgO(001) ferroelectric films on thesequence of phase transitions has been established thatthere is a critical film thickness (50–100 nm) aboveand below which the films are subjected to compres�sive and tensile stresses, respectively [127]. In the pres�ence of tensile stresses in the films (the parameteralong the normal to the substrate is less than theparameter in the substrate plane), there occur phasetransitions from the paraelectric tetragonal phase tothe ferroelectric aa�phase and then to the r�phase.Under compressive stresses in the films (the parameteralong the normal to the substrate is larger than theparameter in the substrate plane), there occur phasetransitions from the paraelectric tetragonal phase tothe ferroelectric c�phase and then to the r�phase. Theobserved change of the phase states in films of differentthicknesses is in qualitative agreement with the theo�retical phase diagram [121]. At a critical film thicknessof ~80 nm, the frequency of the E(TO) soft modechanges abruptly [128]. For a film thickness of largerthan the critical value, the frequency of the E(TO) softmode is equal to 78 cm–1, and when the thickness ofthe film is less than the critical value, the frequency ofthe soft mode is 56 cm–1. This indicates that the filmsundergo structural transformations when mechanicalstresses reverse sign.

The Raman spectra of BST�x films (x = 0.50, 0.65,0.80, 0.90, and 0.95) on ST and LaAlO3 single�crystalsubstrates, which have their own Raman spectra, wereinvestigated during the phase transitions in these filmsby Tenne et al. [129, 130]. For the screening of theRaman spectrum of the substrate, the substrate surfacewas preliminarily covered by a SrRuO3 conductinglayer with a thickness of 300 nm. The thickness of theBST�x films was 1 μm. As compared to the single crys�tals of the same compositions [129], the Raman spec�tra of the BST�x films are characterized by shifts of thelines toward higher frequencies and a significantextension of the temperature interval in which the softmode has an overdamped character. Relating thesefeatures of the Raman spectra to the presence ofnanoscale polar regions in the BST�x films, Tenneet al. [129, 130] found similarities between the behav�ior of these films and the behavior of thePb(Mg1/3Nb2/3)O3 relaxor ferroelectrics.

In an external electric field applied perpendicularto the direction of the spontaneous polarization of theBST�0.2 c�domain film on a MgO substrate, theRaman spectra exhibit a partial depolarization, whichindicates a reduction of the symmetry of the crystallattice to monoclinic [131].

~~

4003002001000

260

240

220

90

80

70

60

50

Fre

quen

cy,

cm−

1

A1 (TO)

E (TO)

zz

xx

zx

~~

T, K

Fig. 23. Temperature dependences of the frequencies of allcomponents of the soft mode in the Raman spectra of theBST�0.3/MgO film.



Thus, the results of the lattice dynamics studiesperformed over the last ten years with BST�x epitaxialfilms indicate that there are significant differences inthe behavior of soft modes in these films as comparedto their bulk analogs. Changes have been observed notonly in the phase transition temperatures, but also inthe sequence of phases.

6. PEROVSKITE SUPERLATTICES

Ferroelectric superlattices consisting of alternatinglayers of both polar and nonpolar perovskites were syn�thesized for the first time by the Japanese scientists[132, 133] using molecular beam epitaxy and pulsedlaser deposition. The use of perovskites that are differ�ent both in the chemical composition and in the thick�ness of layers in superlattices has made it possible toachieve very significant advantages in the performancecharacteristics as compared to single�component fer�roelectric films. By varying the periodicity of the epi�taxial layers forming the corresponding superlattices,it is also possible to obtain a significant spontaneouspolarization and to change substantially the Curietemperature or the permittivity of the materials [133].The possibility of designing and fabricating superlat�tices with specified functional parameters has madethese objects very promising for practical applications.The use of layers of different compositions provides ameans for controlling the strains of the layers and,thus, purposefully varying the ferroelectric propertiesof these structures. Since the stresses induced by mis�matches in lattice parameters of adjacent layers lead tochanges in the ion positions, some of the lattice vibra�tions, in particular the ferroelectric soft modeobserved in the Raman spectra, are usually very sensi�tive to the presence of strains in thin layers.

The superlattices formed by alternating layers oftwo classical ferroelectrics, namely, BT and PT, wereprepared by pulsed laser deposition on MgO substratesso that the number of unit cells n in each layer of theBTn/PTn superlattice varied from 6 to 45 and the totalthickness of the synthesized films was equal to 380 nm[134]. Based on the study of the Raman spectra for allperiods of modulation, it was demonstrated that thePT layers have an a�domain orientation with sponta�neous polarization in the plane of the substrate,whereas the BT layers, on the contrary, have a c�domain orientation; i.e., the spontaneous polarizationin the latter layers is perpendicular to the substrate. Itwas also found that the polarized Raman spectra mea�sured in the geometry of backscattering normal to thesubstrate contain lines that are characteristic of PT a�domain layers; in this case, the A1(TO) and E(TO)modes undergo significant shifts toward lower fre�quencies due to the internal compression of the PTlayers in superlattices, which decreases with anincrease in the modulation period.

The most studied to date are BTn/STn superlatticesin which the ferroelectric state can be induced in theST layers by means of their strains caused by the mis�match between the lattice parameters of the BT andST layers [133]. The cubic unit cell parameter of theST layer is equal to 3.905 Å, which is considerablysmaller than the unit cell parameters of the BT com�pound both in the cubic phase (3.996 Å) and in the tet�ragonal phase (c = 4.036 Å, a = 3.992 Å). The distor�tions of the layers and the directions of polarization inthe superlattice can be varied by properly choosing thecompressing or stretching substrate, growth condi�tions, and thicknesses of the layers forming the super�lattice.

The polarized Raman spectra of the BTn/STn

superlattice (n = 10) synthesized by pulsed laser depo�sition on MgO substrates [135–137] are shown inFig. 24. The Raman spectra of this superlattice exhibitall features that are characteristic of the BT com�pound. In accordance with the previously discussedselection rules for the BST c�domain films, no linesare observed in the Raman spectra measured in the

scattering geometry Z(YX) , which is in agreementZ

8006004002000Wave number, cm–1

Inte

nsi

ty,

arb.

un

its

Y(ZZ)Y

Y(XX)Y

Z(YY)Z

Y(ZX)Y

Y(XZ)Y

E (TO4)

E (TO4)

E (TO3)E (LO3)

E (TO2)E (LO2)

E (TO1)

A1

(LO

3)A1

(TO

3)

A1

(LO

2)A1

(TO

2)

A1

(TO

1)A

1 (L

O1)

FA

MZ(YX)Z

Fig. 24. Polarized Raman spectra of the BT10/ST10 super�lattices at room temperature. The intensity is corrected forthermal occupation factor.

1052


YUZYUK

with the tetragonal symmetry of the unit cell of thesuperlattice. The Raman spectra measured in theother two off�diagonal scattering geometry, namely,

Y(ZX) and Y(XZ) , contain the E�type modes, aswell as the totally symmetric A1(TO2) and A1(TO3) leaklines due to the polarization disturbances. The Ramanspectra measured in the diagonal scattering geometriescontain the A1(TO2) line at a frequency of 270 cm–1,which reveals a considerably more pronounced inter�action with the low�frequency A1(TO1) mode, whereasthe interference dip is shifted toward lower frequenciesand is much more pronounced in the polarizations

Y(XX) and Y(ZZ) , as well as in the spectra of thesuperlattice, as compared to the case in the BT crystal.The narrow line, which corresponds to the E(TO3) andE(LO3) modes, has almost the same frequency as inthe spectra of the BT compound, i.e., 308 cm–1,whereas the peak corresponding to the E(TO2) andE(LO2) modes is slightly shifted toward lower frequen�cies and has a frequency of 173 cm–1. The largest dif�ference as compared to the BT compound is observedfor the E(TO1) soft mode, which, in the spectrum ofthe superlattice, becomes an underdamped line with afrequency of 106 cm–1 and a half�width of ~70 cm–1.

Y Y

Y Y

It should be noted that, in the Raman spectra of the STcrystal, the lowest frequency F1u mode is also under�damped and has a frequency of 88 cm–1 at room tem�perature. However, in the Raman spectra of the BTcrystal, this mode is overdamped and characterized bya half�width of more than 100 cm–1. Thus, the major�ity of the vibrational modes of the BT10/ST10 superlat�tice have frequencies close to the correspondingmodes of the BT and ST crystals, whereas the E(TO1)soft mode is significantly different. Most likely, this isassociated with the two�dimensional clamping of theBT layers by the ST layers, which have smaller latticeparameters. As a result of the layer clamping, in theplane parallel to the substrate, the BT layers have ahigher degree of tetragonality than the BT crystal. TheST layers, in turn, are distorted by the BT layers andbecome tetragonal, which leads to a splitting of thethreefold degenerate ST modes into Raman�active A1

and E components with frequencies close to the corre�sponding BT modes. Consequently, both types of lay�ers acquire a vibrational spectrum that is typical of tet�ragonal BT.

An increase in the thickness of the layers formingthe superlattice results in a weakening of the clampingof each of the layers. Figure 25 shows the spectra mea�

sured in the scattering geometry Y(ZX) for severalsuperlattices at room temperature [136, 137]. The fre�quency of the E(TO1) soft mode decreases with anincrease in the periodicity from 115 cm–1 (n = 6) to100 cm–1 (n = 25), whereas its half�width increases. Alinear extrapolation of the square of the frequency sug�gests a complete relaxation of the two�dimensionalclamping, when the thickness of each layer of thesuperlattice exceeds 320 nm.

An important feature of the Raman spectra of peri�odic multilayer structures is the appearance of foldedacoustic modes (FAM), which manifest themselves inthe low�frequency Raman spectra due to the folding ofthe Brillouin zone. It is known that, in the vicinity ofthe center of the Brillouin zone, where k = 0.1(2π/a),the acoustic branches can be considered to be almostlinear and their slope is determined by the correspond�ing velocity of sound. In the superlattices, there occursa folding of the Brillouin zone; as a result, new bound�aries of the Brillouin zone arise at kz = π/d, where d =d1 + d2 is the period of the superlattice. A multiplefolding of phonon branches leads to the appearance ofnumerous optical and acoustic phonons in the Ramanspectra, so that now these phonons are located at thecenter of the Brillouin zone. The polarized low�fre�quency Raman spectra for several BTn/STn superlat�tices are shown in Fig. 26. As a result of repulsion ofthe modes, the activated acoustic modes appear alwaysin the form of doublets with frequencies ω± =v±(2πm/d), where v+ and v– are the velocities ofsound waves in the ST and BT crystals, respectively.Since the intensity of higher order modes is relatively

Y


Inte

nsi

ty,

arb.

un

its

n = 25

n = 20

n = 14

n = 10

n = 6

SuperlatticesBTn/STn

Fig. 25. Dependence of the E(TO) soft mode on the mod�ulation period in the spectra of the BTn/STn superlatticesat room temperature. The intensity is corrected for ther�mal occupation factor.



low, only the first doublet with m = 1 is reliablyrecorded in the spectra. The observed frequencies ofthe doublets are in good agreement with the acousticbranches calculated in the linear approximation. Forthese systems, Raman spectroscopy is a rather simpleand reliable method for determining the periodicity ofthe superlattices. It should be noted that the quantity(ω– + ω+)/2 is linearly dependent on the superlatticeperiod d and, thus, determines the effective velocity ofsound in the multilayer medium of the superlattice. Asimilar folding should also take place for opticalphonon branches. However, because of the large half�width of the lines of the corresponding opticalphonons, additional peaks that arise from the foldingof the branches cannot be observed at room tempera�ture. Nonetheless, a few additional lines, i.e., foldedoptical modes (FOM), were revealed in the Ramanspectra of the superlattices at low temperatures, [135].

The Raman spectra of the BTn/STn superlatticesare well polarized over the entire temperature rangefrom 77 to 1123 K. In contrast to the Raman spectra ofthe bulk crystals of the BT and ST compounds, thespectra of the superlattices exhibit a monotonic tem�perature dependence (Fig. 27), whereas the low�fre�quency lines that arise as a result of the folding of theacoustic branches do not depend on the temperature.Below room temperature, no indications of phasetransitions have been revealed. The frequency of theE(TO1) soft mode slightly decreases, while the othermodes do not depend on the temperature. It is obviousthat, in the superlattice, the ST and BT layers stronglyinteract with each other; consequently, in the BT lay�ers, no reduction of the symmetry occurs upon thetransition to the orthorhombic and rhombohedral

phases with the rotation of the polar axis. On the con�trary, the BT layers lead to a stretching of the ST layers,so that the latter layers do not undergo a structuralphase transition due to the rotation of the octahedra.As the temperature increases, the frequency of theE(TO1) component of the soft mode increases from106 to 140 cm–1 at a temperature of 600 K. As in theBST films, the intensity of the polar modes steadilydecreases as the temperature of the transition to theparaelectric phase is approached, which, in this sam�ple, is very diffuse and occurs in the temperature rangefrom 650 to 700 K. This temperature is substantiallyhigher than the temperature of the ferroelectric phasetransition in the BT crystal. Such a significant shift inthe Curie temperature TC in the superlattices takesplace not only as a result of thermoelastic stressescaused by the MgO substrate but also, apparently, to agreater extent, due to the very large deformation of theepitaxial layers forming the superlattice. This makes itpossible to stabilize the tetragonal ferroelectric phaseover an unusually wide temperature range, which, ofcourse, is very important for practical applications.

The use of ultraviolet light (351.1 nm) for excita�tion of Raman spectra has made it possible to investi�gate the BT/ST superlattices grown by molecularbeam epitaxy on ST substrates [138]. Since the sec�ond�order Raman spectrum is observed for the STcompound, the spectrum of the thin film cannot bedistinguished against its background under excitationwith laser radiation in the visible range. Owing to thesmall depth of penetration of ultraviolet radiation into


Inte

nsi

ty,

arb.

un

its

ω−

ω+

BT6/ST6

BT7/ST7

BT8/ST8

BT9/ST9

BT10/ST10

Fig. 26. Activated acoustic modes in the Raman spectra ofthe BTn/STn superlattices at room temperature.

9006003000 9006003000Wave number, cm−1

Y(ZZ)Y Y(ZX)Y

77 K150 K

200 K

250 K

295 K350 K400 K

450 K

500 K

550 K

600 K

700 K

900 K1123 K

FA

M

FO

M

FO

M

Inte

nsi

ty,

arb.

un

its

Fig. 27. Temperature dependence of the polarized Ramanspectra of the BT10/ST10 superlattice. The intensity is cor�rected for thermal occupation factor.

1054


YUZYUK

the sample, the desired signal is predominantlyobtained from the film, whereas the contribution fromthe substrate to the desired signal in this case is mini�mal. The technique proposed by Tenne et al. [138]enables one to work with the films whose thicknessvaries in the range from 100 to 200 nm. The investiga�tion of the asymmetric superlattices BTn/STm with dif�ferent numbers of unit cells of the BT and ST com�pounds in alternating layers has demonstrated animportant role played by epitaxial distortions in thesuperlattices [138]. For example, it was shown that thetetragonally distorted BT layers polarize the ST layersadjacent to them, which leads to the formation of theferroelectric phase with the Curie temperature thatcan be varied over a wide range from 150 K forBT2/ST13 to 640 K for BT8/ST4. According to theauthors’ opinion [138], the BT layers in these superlat�tices are ferroelectric even when their thickness isequal to only one unit cell.

The physical properties of artificial superlatticescan be controlled not only by varying the thickness ofthe layers but also by changing the chemical composi�tion of one of the layers. In recent works [139, 140], itwas found that the BaTiO3/(Ba,Sr)TiO3 (BT/BST)superlattices grown by pulsed laser deposition on MgOsubstrates with a constant periodicity of the BTn/BSTn

(n = 10) layers and a variable Ba/Sr composition in theBST layers are characterized by a systematic change inthe frequency of the soft mode (by a factor of morethan three) depending on the Ba/Sr ratio. This

approach to constructing superlattices has made itpossible to change the static permittivity by one orderof magnitude without a change in the periodicity ofthe superlattice and a change in the total thickness ofits layers.

In the superlattices of BaTiO3 ferroelectrics andBaZrO3 (BTn/BZn) paraelectrics, which were grownby pulsed laser deposition on MgO substrates [141], aquite different situation takes place, because theparameter of the cubic unit cell of the paraelectriccompound BZ (a = 4.192 Å) exceeds the unit cellparameters of the BT compound. The period of mod�ulation of the BT and BZ layers was varies from 16 to1056 Å, and the total thickness of each of the superlat�tices was approximately equal to 400 nm. The layersforming the BTn/BZn superlattices studied in [141]contained from 2 to 132 unit cells, which made it pos�sible to trace the transformation of the structural dis�tortions and vibrational spectra of these superlatticesin comparison with single�component films of the ini�tial compounds. The Raman spectra of the BTn/BZn

superlattices measured in the side�view scatteringgeometry are shown in Fig. 28.

According to the X�ray diffraction data [141], theBZ film is distorted so that the parameter along thenormal to the substrate is larger than that of the singlecrystal. The absence of the Raman spectrum for this

film is consistent with the symmetry, which waspredicted theoretically in [142]. In the BT film, the

D4h1

Y(ZX)Y Y(XX)YY(ZZ)Y

BT�film

n = 132

n = 63

n = 32

n = 15

n = 8

n = 4

n = 2

BZ film

80060040020008006004002000Wave number, cm−1

8006004002000

Inte

nsi

ty,

arb.

un

its

Fig. 28. Polarized Raman spectra of the BTn/BZn superlattices as a function of the modulation period and the spectra of the BTand BZ films. The intensity is corrected for thermal occupation factor.



parameter along the normal to the substrate is smallercompared to that of the single crystal; therefore, thisfilm contains the monoclinic phase r or the orthor�hombic phase aa, which are predicted both from firstprinciples and from the phenomenological theory[123, 142].

The Raman spectra of the superlattices with a smallperiod Λ = 16 Å (n = 2) are very similar to the Ramanspectra of Ba(Ti,Zr)O3 (BTZ) solid solutions [143].The Ti–O–Zr bonds are formed at the interfaces ofthe adjacent layers; as a result, the Raman spectraexhibit all features that are well known for the spectraof the BTZ solid solutions, for example, two interfer�ence dips at frequencies of 140 and 180 cm–1. There�fore, the superlattices with the period Λ = 16 Å repre�sent a mesoscopically modulated BT–BZ solid solu�tion. The polarization characteristics of the Ramanspectra abruptly change with an increase in the layerthickness. For the superlattices with 4 ≤ n ≤ 32, theRaman spectra measured in the scattering geometries

Y(ZX) , Y(ZZ) , and Y(XX) differ from each otherand from the Raman spectra of the superlattices withn = 2. In the superlattice, the BZ layers are clamped bythe BT layers adjacent to them, and the parameteralong the normal to the substrate is increased as com�pared to that of the bulk material. As a result of thisdistortion, the threefold degenerate modes of the BZcubic crystal are split and become active in the Ramanscattering. The frequencies of the observed lines in theRaman spectra of the superlattices are close to the fre�quencies of the lines in the spectra of the BZ com�pound under hydrostatic pressures [144]. It is impor�tant to emphasize, however, that the Raman spectra ofthe BTn/BZn superlattices are not a simple superposi�tion of the spectra of the BT and BZ compounds. Thehalf�widths of all lines in the Raman spectra of theBTn/BZn superlattices with 4 ≤ n ≤ 32 are considerablyless than those in the spectra of the superlattice withn = 2. It is evidence that their structure is ordered as aresult of the interaction of alternating epitaxial layers.The E(TO1) soft mode is significantly shifted towardthe high�frequency region and manifests itself as theunderdamped peak at a frequency of 200 cm–1 in the

geometry Y(ZX) . Epitaxial strains in the layers sub�stantially reduce the disorder of the Ti ions, and thehalf�width of the soft mode drastically decreases.Moreover, it seems likely that the degeneracy of thissoft mode is removed, because the observed line has anasymmetric shape, and, quite possibly, it consists oftwo components. Such a high frequency of the softmode is characteristic of the completely orderedrhombohedral phase of the BT compound. Since thisphase cannot exist in epitaxial films on cubic sub�strates, the monoclinic phase r, most likely, is formedin the superlattices with 4 ≤ n ≤ 32, because the polar�ization characteristics of the Raman spectra are con�sistent with this symmetry [141].

Y Y Y

Y

In the superlattices with periodicities of 500 Å(n = 63) and 1056 Å (n = 132), there occurs a broad�ening of the lines in the Raman spectra, which acquireall features that are characteristic of the BT com�pound. This change is caused by the relaxation of epi�taxial stresses due to the formation of misfit disloca�tions in the layers whose thickness is already quite sig�nificant. As a result, the BZ layers are distorted onlynear the interfaces, whereas in the central part of thelayers, distortions are either negligible or absent alto�gether. It can be seen from Fig. 29 that, with anincrease in the modulation period, the frequency ofthe E(TO1) soft mode decreases from 200 cm–1 (n =15) to 118 cm–1 (n = 132), while its half�widthincreases. This figure also presents the frequencies ofthe soft mode in the BTn/BTZn superlattices [143]. Amore significant shift of the soft mode in the Ramanspectra of the BTn/BZn superlattices, as compared tothe spectra of the BTn/BTZn superlattices, is appar�ently caused by a larger mismatch between the latticeparameters of the BT and BZ layers (3.72%) as com�pared to the mismatch between the lattice parametersof the BT and BTZ layers (0.47%).

Thus, the first investigations of the Raman spectraof ferroelectric perovskite superlattices have made itpossible to determine the important features of thestructural distortions that occur in alternating layers.Raman spectroscopy provides important informationabout the lattice dynamics of multilayer structures; inview of the large variety of possible superlattice vari�ants, this method of investigation is obviously pro�mising.

10008006004002000Modulation period, Å

200

40

160

120

80

Fre

quen

cy,

cm−

1

BT/BZ

BT/BTZ

BaTiO3 film

BaTiO3 crystal

Fig. 29. Frequency of the E(TO1) soft mode as a functionof the modulation period of the BTn/BZn and BTn/BTZnsuperlattices.

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7. CONCLUSIONS

Investigation of the lattice dynamics is necessaryfor a deeper understanding of the nature of the ferro�electricity in materials. Raman spectroscopy has beentraditionally used to investigate ferroelectric materialsand to establish composition–property relationshipsin numerous solid solutions. Recent advances made bymicro�Raman spectroscopy in the study of phase tran�sitions and size effects in powders, ceramics, and filmsof ferroelectrics have demonstrated that this method ishighly informative in elucidating the factors responsi�ble for significant differences in the physical propertiesof nanoscale ferroelectrics and their macroscopic ana�logs. Raman spectroscopy provides a means for diag�nosing polar boundaries in grains of ceramics andpolycrystalline films, because the formation of polarregions and the subsequent local symmetry breaking inthe short�range order lead to relaxation of selectionrules. Micro�Raman spectroscopy has made it possi�ble to investigate the effects of grain clamping in poly�crystalline films, ceramics, and composites with a highaccuracy and a micron spatial resolution, which ren�ders this technique very promising for the use in thediagnosis of such objects. The determination of thesequences of phase transitions in epitaxial films, wherethe applicability of X�ray diffraction analysis methodsis very limited, has required an integrated approachinvolving a number of intercomplementary methods.Raman spectroscopy provides a means for refiningsymmetry of phases and is a very important techniquein addition to X�ray diffraction methods.

The use of layers of different compositions insuperlattices has made it possible to control the defor�mation of the layers and, thus, to specify and vary theferroelectric properties of these heterostructures.Since the stresses and induced lattice mismatch inadjacent layers bring about changes in the ion posi�tions, the ferroelectric soft mode observed in theRaman spectra is usually very sensitive to strains gen�erated in thin layers. Recent studies of the Ramanspectra of ferroelectric perovskite superlattices haverevealed important features of the structural distor�tions that arise in alternating layers. Research in thelattice dynamics of ferroelectric perovskite superlat�tices is only at the initial stage, and in view of the widevariety of possible combinations of layers in ferroelec�tric superlattices, much remains to be investigated.

ACKNOWLEDGMENTS

This study was supported by the Russian Founda�tion for Basic Research (project nos. 06�02�16271�a,09�02�00666�a, and 10�02�91158�GFEN�a).

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Translated by O. Borovik�Romanova

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