B-site vacancy induced Raman scattering in BaTiO3-based ferroelectric ceramics

Defects, in particular vacancies, play a crucial role in substituted perovskite systems, influencing the structural features that underpin ferroelectricity. B-site vacancies introduce cation disorder in the perovskite lattice and are in fact one of the main driving forces for relaxor behaviour in barium titanate (BaTiO3, BT) based ferroelectrics. In this work, material systems are carefully selected to qualitatively study the change in B-site vacancy concentration for heterovalent substituted BT-based ferroelectric polycrystals. Raman spectroscopy was used to investigate those systems, and B-site vacancy specific Raman Jo rn al Pr epr oo f


Introduction
Barium titanate (BaTiO3, BT), a prototypical room-temperature ferroelectric (FE) material with ABO3 perovskite form, undergoes a sequence of structural phase transitions before entering into the paraelectric phase above the Curie temperature (125 °C) [1]. Ferroelectricity in BT is due to the long-range correlation of Ti (B-site) cation displacements, and can be modulated by chemical modification upon substitution of alternative chemical species in the equivalent perovskite lattice sites. This has been a common scientific practice to explore the possibilities of finding better performing material systems [2][3][4][5][6], and is an opportunity to tune material properties such as the polarization response, loss mechanisms, electro-mechanical responses, Curie temperature, temperature stability of the permittivity, among others [7][8][9].
For BT based ferroelectric systems, B-site substitution either with homo-or heterovalent cations results first in a characteristic evolution from FE behaviour to diffuse phase transition (DPT) behaviour before entering relaxor state for high substituent contents [10,11]. The onset of relaxor behaviour occurs for lower substituent contents in heterovalent substituted systems, compared to homovalent ones [12,13]. The structural or chemical origin of this difference is not yet fully understood, although the strong local fields determined by the effective charge of the heterovalent dopant and the necessary charge-compensating defect are likely to play a J o u r n a l P r e -p r o o f major role [14]. Especially in heterovalent systems, vacancies (A-, B-site or oxygen) are expected to play a decisive role as charge compensating defects inducing disorder and modifying the functional properties [15].
Raman spectroscopy has been used often in the past to study ferroelectric materials, especially since -having a coherence length as low as few nanometres [16] it can access structural features not visible in laboratory X-ray [11,17,18]. For example, the coexistence of displacive and order-disorder components in BT were first reported from high temperature Raman spectra [19]. For any crystal structure, there is a specific number of Raman active modes that follows the selection rules (purely displacive) and the appearance of broad, disorder-related higher-order components that exist also in (first-order Raman forbidden) centrosymmetric phases at high temperature (above Curie temperature). In addition, there are additional Raman modes in defective or chemically modified systems because of symmetry breaking induced locally by the defects [20]. We show here that these aspects make Raman spectroscopy a useful tool to detect B-site vacancies and their change with composition.
In this work, we identify the Raman modes that are related to B-site defects in BT-based materials. B-site Nb 5+ modified BT (BNbT) and A-site La 3+ modified BT (BLaT) are investigated since they are expected to bear B-site Ti 4+ vacancies (even though substitution occurs at different sites). The results are then compared to B-site (Ga 3+ -Nb 5+ ) co-substituted ceramic samples (BGaNbT) in which the vacancy concentration is expected to be drastically reduced by self-compensation preserving the charge neutrality in the lattice. In other words, we present here a way to qualitatively study the defects in perovskites, which constitutes a relevant input for the design of BT perovskite solid solutions with desired properties [21,22].  Italy; SSA = 3.3 m 2 /g, electronic grade), TiO2 (Electronic grade purity, Toho, Japan; SSA = 6.1 m 2 /g, electronic grade), Nb2O5 (99.9% purity, H.C. Starck, SSA = 6.3 m 2 /g, ceramic grade), La2O3 (+99%, Treibacher Industrie AG, Treibach, Austria) and Ga2O3 (99.99% purity, Aldrich Chemical Co., Milwaukee, WI) were weighed and ball milled using suitable solvent and grinding media for homogenous mixing. In case of BNbT and BLaT, where charge compensation is needed, Ti deficiency was taken in to account to avail the formation of Ti vacancies (VTi '''' , in Kroger-Vink notation). After calcination and subsequent milling, the powders were compacted, pressed and sintered at different temperatures depending on the composition. Organic binders were used before pressing green ceramic bodies and a separate de-binding protocol was followed for the binder burn out process. Table 1 summarizes the compositional details of the investigated barium titanate based systems. Table S1 summarizes the processing parameters used to fabricate the investigated barium titanate based systems. ceramics can as well be found in the literature [23,24].

Experimental procedures
Raman measurements were carried out in a LabRAM 300 spectrometer (Horiba Jobin Yvon, Villeneuve d'Ascq, France) using an excitation wavelength of λ = 532 nm in a backscattering geometry equipped with an edge filter (cut-off: 80 cm -1 ), 1800 gr/mm grating and CCD detector. The laser light was focused on the sample surface by means of a long working distance 100x objective (with NA 0.8, LMPlan FI, Olympus, Tokyo, Japan) and a spot size of 1 m. The effective power at the sample surface was ~2 mW. Temperature-dependent Raman measurements were carried out in a Linkam (THMS600) temperature-controlled stage

Results and discussion
In hard mode Raman spectroscopy, the phase transitions are usually studied by the change in vibrational energy of the crystal lattice that are evident in the observable phonons [18,25].  Figure S3. For tetragonal BT, Raman selection rules predict 13 first-order Raman modes from 100 cm -1 to 900 cm -1 [26]. In ceramics, however, unknown scattering geometries because of random grain orientation makes the mode assignment based on group theory not straightforward even when resolving peak convolutions using asymmetric peak shapes or polarised Raman measurements [27]. For this reason, only dominant modes within peak convolutions can be singled out, as highlighted in both Figure 1 (BT) and Table 2. It is clear that the number of modes decreases with the increase in symmetry. Below the Curie temperature (125 °C), the spectrum can be divided into three parts. Modes associated with part I are related to the A-site, in part II are related to B-O chains and in part III modes are associated to the vibration of oxygen atoms in the BO6 octahedra of ABO3 perovskite [28]. Based on the selection rules, a perfect (i.e. defect-free) perovskite lattice should have permissible modes only within these three zones in the energy landscape (cf. Table 2). Arguments related to selection rules hold validity for a defect-free perfect perovskite but are invalid when it comes to chemically modified systems because of a defective and discontinuous lattice [29]. Before discussing the Raman modes originated by defects in the perovskite lattice, there is one more aspect to consider, related to the structural phase transitions in these materials. In Figure 1, above the Tc of BT, spectral features are visible, although theoretically any Raman activity should be forbidden in a cubic perovskite. These modes are due to second-order spectral components reflecting the phonon density of states, and are related to the intrinsic (dynamic) disorder of BT in the paraelectric phase above Tc [19,30]. Studying the broadening in this case allows estimating the size of these regions [31].
2. Raman mode frequencies shift as a result of a change in bonding environments. In simple terms, a shift to higher frequencies of a Raman mode is the indication of a stronger chemical bond. In ferroelectric based systems, this change in bonding environment is usually from substituents that carry a lone electron pair that facilitates orbital hybridization, ultimately resulting in a change in the bonding nature from prevalently ionic to covalent [27,32,33].
3. Appearance of extra Raman modes due to localised phonon vibrations in the vicinity of a (substitutional) defect, or as a result of the relaxation of Raman selection rules from defectinduced disorder [34].
Only the third aspect is addressed in this work. Extra Raman modes can be categorized widely into the following types [35]: a. Localized vibrational modes (LVM) that are normally seen above the optical branch because of chemical substitution with heavier atoms (i-LVM). c. Modes resulting from the breaking of selection rules induced by disorder in chemically-modified systems. The mechanism is closely related to the phonon confinement described above (which is the source of asymmetric modes) and leads to the appearance of Raman bands at critical points in the Brillouin zone at which the phonon density of states is high (disorder-activated Raman scattering -DARS) [36].
In chemically modified BT, all the three types of extra Raman modes, as demonstrated in this work using three sets of compositions along with pure BT (as described in Table 1). All the dominant Raman modes for the analysed compositions are summarized in Table 2. It is important to note that here all changes in peak positions are related to changes in the chemical environment and the associated atomic-level stresses. Peak shifts related to grain size effects in fact were not detected within the limits of our instrumentation, as evident from the good correspondence between Raman spectra of bulk and powdered BNbT and BLaT ceramics, as shown in Figure S4. A detailed study of ceramic stresses in the present compounds is beyond the scope of this paper. 550-670 530-600 520-600 540-620 *Note: The position of Raman modes corresponds to the maximum of peak intensity. No Raman modes can be assigned with confidence for BGaNbT because of the severely disordered structure resulting from high substitution concentration. The wavenumber of extra modes are approximate values or ranges. All the wavenumbers are in cm -1 .
The charge compensation for BNbT and BLaT are achieved via VTi´´´´ [15,37] and this is valid from the processing point of view since all these samples were fabricated with Ti deficiency.
The charge neutrality is preserved in BGaNbT and no vacancies are expected [11,38]. From Table 1, it is clear that the lattice continuum is broken upon substitution primarily by differences in the ionic radii and defects induced by difference in oxidation states compared to ions in the equivalent crystallographic sites. In this regard, the difference in the oxidation state  compositions FE at RT. BLaT is weakly FE at RT since the Curie temperature is close to RT [21] and BGaNbT is a severely disordered dielectric material [23]. All the chemically J o u r n a l P r e -p r o o f modified BT based systems are disordered as evident from the significant peak broadening (symmetric as well as asymmetric). These convolutions are likely a result of the chemical modification mentioned above. Mode 3appearing in both BT and substituted systems -is a DARS mode that is suggested to originate from lattice defects (such as oxygen vacancies), and thus is present also in pure BT (as evident from the asymmetric shape of the spectral convolution at 550-670 cm -1 . Such DARS modes are more prominent near the modes that are associated to lighter ions (oxygen in case of BT), as is the case of mode 3 in Figure 2.
Interestingly, mode 3 is present also in the purest form of BT single crystals; Wada et al. [39] suggested that even pure BT possesses this type of disorder in its cubic phase, which agrees with the order-disorder model discussed earlier.
As evident from Figure 2, also extra modes (Modes 4, 6 and 7) are visible in the substituted BT spectra. Minor unknown secondary phases (marked in asterisks) were detected in BLaT and BGaNbT from the X-ray diffractogram (cf. Figure S2). These phases, however, do not impact the Raman signature and, consequently, extra modes are only related to heterovalent substitution. Raman peaks from secondary phases in fact appear sharp and will have an inconsistent peak evolution during temperature dependent measurements since the probing spot is constantly changed due to thermal expansion of the samples (for instance: Figure S5).  Raman intensities were adopted from Pokorny et al. [20] Mode 6 (cf. Figure 2) is seen in all substituted systems, which suggests that it is activated by substitution, and not by the presence of vacancies. This mode is assigned as the asymmetric breathing of BO6 and was previously related solely on the ionic radii mismatch caused by Bsite substituents [18,40]. In particular, it was suggested that the shift of this mode is related to the ionic size mismatch between Ti and the foreign B-site substituent. Although ionic size mismatch may play a role in determining this mode's position, our results show that this is not the only responsible factor for the appearance of this mode. In BLaT, in fact, this mode appears although substitution is performed at the A-site and not at the B-site. From the work of Farhi et al. [25]and Pokorny et al. [20], it is clear that both in BNbT and BLaT, mode 6 evolves as a function of substitution concentration. We thus conclude here that mode 6 appears due to either the presence of a foreign atom or a Ti vacancy on the B-site. It is, in essence, due to the vibration of oxygens in perturbed octahedra (i.e. chemical pressure around the B-site). The presence of mode 6 in BGaNbT is associated with the absence of mode 1, BT. These modes can be thus unequivocally assigned as v-LVM modes. In addition, it is important to note that the shoulder that is clearly recorded in BaGaNbT cannot be associated to a vacancy mode because of its peculiar T-dependent evolution. As can clearly be seen in Figure  vacancies in the SrTiO3 system [34,41], and suggest BO6 breathing as vibration scheme.
The ratio of the relative intensities of mode 7 and mode 5 is presented for BNbT series with different Nb concentration along with BLaT for reference purposes (cf. Figure 3). The microstructural information and RT relative permittivity of the BNbT sample series is provided in Table S2 for reference. For more information on the macroscopic properties of BLaT samples, we ask the readers to refer to the available literature [20,21]. Mode 5 is a firstorder Raman scattering mode that obeys the selection rules and is classified as symmetric octahedral breathing mode in the ferroelectric phase of BT. Initially, it is expected that the ratio of intensities should have a linear relationship because of the increase in vacancy concentration as a function of substitution. In Figure 3, however, it can be seen that the relationship is clearly non-linear. It is important to understand that, at RT, FE is gradually lost in BNbT as the substitution concentration increases [25]. This can be due to various reasons, but in essence the material tends to become cubic with substitution concentration because of the discontinuity in the lattice continuum (breaking of O-Ti-O chains on the long range). The breaking of lattice continuity and loss of ferroelectricity in substituted systems can be found in detail in several reports [11,42,43]. The non-linear relationship obtained here is likely due to the gradual loss of polarizability of TiO6 with substitution concentration coupled with the increase in the breathing mode of TiO6 as a result of vacancies at the B-site. Nonlinearity, in fact, starts to be obvious close to the substituent content corresponding to the loss of FE order in BNbT [25]. The same was repeated on BLaT since the two systems have same charge compensation mechanism although the substitution site is A-site in case of BLaT. A similar non-linear behaviour was observed in BLaT with a more pronounced non-linearity when the material is not FE anymore at RT [21]. The difference in the absolute value of relative intensities can be an indication that we have different degree of heterogeneity at the B-site in J o u r n a l P r e -p r o o f BNbT compared to BLaT. BNbT, in fact, may be more heterogeneous at the B-site than the BLaT since both VTi´´´´ and Nb-substitution occur. These heterogeneities play a crucial role in defining phonon modes, so that disorder-related phonon modes become more pronounced in heterogeneous systems (i.e. less intense but broader Raman peaks).

Conclusion:
The appearance of extra Raman modes in perovskites is directly related to lattice disorder and defects. Assigning these extra modes to a specific lattice vibration provides insight on

Declaration of interests
☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
access to Raman equipment. Dr. Maria Teresa Buscaglia and Ms. Theresa Gindel are acknowledged for their support in sample preparation and Raman measurements respectively.
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