Defect properties of vanadium doped barium titanate ceramics

X-ray diffraction (XRD) patterns, electron probe microanalysis (EPMA), electron paramagnetic resonance (EPR) powder spectra (9 and 34 GHz) and the magnetic susceptibility of BaTiO3 + 0.04 BaO + 0.01 V2O5 ceramics were studied to investigate the valence states of V ions and their solubility in the BaTiO3 lattice. In samples sintered at 1400 °C in air, only about 0.1 mol% V is incorporated in the BaTiO3 lattice being in V4+ and V5+ valence state, respectively. 95% of the nominal V dopant content occurs in the secondary phase Ba3(V/Ti)2O8. All BaTiO3 samples investigated are in tetragonal phase at room temperature. In the as-sintered samples V4+ is detected at temperatures T < 20 K by its hyperfine structure (HFS) octet due to the nuclear spin 7/2 of 51V. Samples post-annealed in H2/Ar atmosphere at 1200 °C exhibit a further HFS octet occurring at T > 25 K and vanishing at T > 250 K, which is caused by V2+ ions. This spectrum is characterized by a simultaneous HFS and fine structure splitting constituted by allowed and forbidden transitions. Both V4+ and V2+ ions are incorporated at Ti4+ sites of the BaTiO3 lattice.


Introduction
Barium titanate (BaTiO 3 ) is a material of fundamental importance for a wide range of technical applications (multi-layer ceramic capacitors, ferroelectric random access memories, piezoelectric sensors, actuators, etc) [1-3] and a model system of the theoretical description of ferroelectricity due to the variety of phase transitions. Besides the well-known, temperature-driven phase transitions of the 3 C modification BaTiO 3 shows a further structural phase transition into the hexagonal high temperature 6 H modification. This modification is stable at temperatures >1430°C in air as far as undoped material is concerned. Extrinsic defects, particularly the 3d-, 4d-, 4f-and 5d-ions as well as vacancies, can change the physical properties of this material in a wide range. This distinct ability of tailoring of its physical properties is the basis of the numerous technical applications of BaTiO 3 -based materials. In the past, extensive investigations (permittivity, electrical and thermal conductivity, electromechanical and optical properties, etc) were undertaken to probe in particular the influence of the 3d-ions on the macroscopic properties of barium titanate ceramics. On the other hand, optical and EPR investigations can provide complementary microscopic information on the 3d-ions incorporated in the BaTiO 3 matrix, as e.g. their charge, crystallographic site, and local symmetry of their surrounding. In contrast to the dopants Cr, Mn, Fe, Co, Ni and Cu (see e.g. [4][5][6][7][8][9][10][11]), sparse information on the physical properties of V-doped BaTiO 3 is available in the literature. In 1971 Feltz et al [12] investigated V-doped BaTiO 3 single crystals grown by the flux method in reducing atmosphere. They reported a very low solubility of vanadium in the BaTiO 3 lattice with maximum 1.3 at% V 4+ measured potentiometrically. Later several authors [13,14] found no measureable paramagnetism in air-sintered V-doped BaTiO 3 ceramics. Schwartz et al [15] found no significant EPR spectrum in 0.04 mol% V-doped BaTiO 3 ceramics sintered in air. Liu et al [16] investigated V-doped ceramics with V contents up to 2 mol% sintered in air and reported a solubility of less than 1 mol% V with a maximum sample density at 0.1 mol% V. Their samples are tetragonal at room temperature and exhibit distinct amounts of secondary phases, identified as Ba 3 V 2 O 8 and BaVO 2.8 by XRD. There are few investigations on the influence of vanadium on the dielectric properties and the microstructure of barium titanate and solid solutions with strontium titanate, barium zirconate and barium hafnate ceramics [16][17][18][19][20][21]. In the case of barium titanate, partially inconsistent data are reported on the shift direction of the Curie temperature and on the dielectric/ferroelectric data in general [17,18]. Often it seems that the authors have not noticed the low solubility of vanadium in BaTiO 3 and additionally it is mostly assumed that vanadium is in the V 5+ state without experimental evidence.
The first EPR measurement on V-doped BaTiO 3 ceramics annealed under strongly reducing conditions was made by Schwartz et al [15]. A complex spectrum with a hyperfine pattern spread over ≈650 G and centered around g≈2 was observed in X-band. The authors did not analyse the powder spectrum in detail but they suggest, based on the study of Müller et al on SrTiO 3 :V [22] that the observed EPR specrum is most likely due to V 2+ . Later, to the best of our knowledge, only Shibahara et al [23] reported on EPR investigations of V 4+ in BaTiO 3 -based ceramic multilayer capacitors without giving any details of the measurement. Unlike for BaTiO 3 , there are several studies of vanadium-doped SrTiO 3 single crystals by Kool et al [24,25] and Müller et al [22]. After illumination (λ ≈ 396 nm), an intensive EPR spectrum was observed in this material and characterized as a S=1/2 centre with tetragonal symmetry. On the basis of the hyperfine splittings the spectrum has been attributed to V 4+ substituting for Ti 4+ [24]. The strain-induced effects (by applied uniaxial stress) were interpreted assuming that the SrTiO 3 :V 4+ system has a threefold degenerated vibronic ground state. This vibronic degeneracy is derived from a strong Jahn-Teller effect [25]. After reducing treatment (heating in 6% H 2 /N 2 atmosphere above 1200°C and subsequent quenching) of SrTiO 3 single crystals containing 0.2 mol% vanadium, an EPR spectrum of V 2+ (3d 3 ) with the electronic spin S=3/2 was observed. The g-shift and the hyperfine splitting (HFS) of the central fine structure transition indicate a 40% delocalisation of the spin-density onto Ti conduction band levels. Upon cooling below 130 K the V 2+ intensity decreases due to carrier freeze-out from V 2+ to V 3+ . An exponential line width narrowing is observed with activation energy of 200 meV, which can be accounted for by the thermally activated hopping between V 2+ (double) and V 3+ (single) acceptors [22].
In this paper we present first detailed EPR investigations and EPMA measurements of vanadium doped barium titanate ceramics to gain a deeper insight into the nature of the vanadium defect (incorporation site, valence state) and its solubility into the BaTiO 3 lattice for air-sintered material.

Experimental procedure
A pre-ceramic powder with the nominal composition BaTiO 3 +0.04 BaO+0.01 V 2 O 5 was prepared by the conventional mixed-oxide powder technique. After mixing (agate balls, water) and calcining (1100°C, 2 h) of BaCO 3 (Solvay, VL600, <0.1 mol % Sr), TiO 2 (Merck, no. 808) and V 2 O 3 (Merck, p.a.), the obtained BaTiO 3 powder was fine-milled (agate balls, 2-propanole) and densified to disks with a diameter of 6 mm and a height of about 3 mm. These disks were sintered in air at a temperature of 1400°C for one hour (heating rate 10 K min −1 ). Afterwards, several of them were annealed in a stream of H 2 /Ar (20/20 ml min −1 ) at 1200°C for 120 min.
X-ray powder diffraction on crushed samples was performed with a Bruker D8 Advance Bragg-Brentano diffractometer equipped with a one-dimensional silicon strip detector (LynxEye™) using Cu-K α radiation. The angular range 5 2θ60°was recorded with a step size of 0.0105°and a counting time of 1 s/step. The variable divergence slit was set to illuminate a constant area of 10×6 mm 2 .
Magnetic measurements were carried out using the ACMS magnetometer option of a PPMS 9 (Quantum Design). The temperature-dependent magnetic moments were measured at 9.0 T in the temperature range 5-300 K. The obtained magnetic moments were corrected for the magnetic moment of the sample holder and with respect to the magnetic contribution of the BaTiO 3 matrix.
The microstructure of polished and chemically etched specimens was examined by scanning electron microscopy (SEM) using a FEI (Thermofisher) VERSA 3D (Dual Beam FIB). The vanadium concentration within the BaTiO 3 grains was measured by wavelength-dispersive x-ray EPMA (WDX-EPMA, model CAMEBAX, Cameca), whereas the V-rich secondary phases inside the ceramics were analysed both with EDX system by EDAX attached to the VERSA 3D and with the CAMEBAX WDX system. EPR measurements of pulverized ceramics were carried out in X-(9.4 GHz) and Q-band (34 GHz) with Bruker EMX devices. Temperatures between 5 and 240 K were achieved with Oxford flowing He gas cryostats in connection with an Oxford ITC controller (temperature stability about 0.2 K).
For the determination of the spin-Hamiltonian parameters and the evaluation of the powder EPR spectra the MATLAB 5 toolbox for electron paramagnetic resonance 'Easy Spin 5.2.11' was used [26]. Simulating powder spectra of the standard spin Hamiltonians for electron spin S=1/2 systems (V 4+ ions) and for electron spin S=3/2 systems (V 2+ ions) a satisfactory accuracy in the determination of the respective parameters was achieved. The parameters are the components of the = g tensor and of the hyperfine structure (HFS) tensor = A of the nucleus of 51 V (abundance 100%) with I=7/2 and the axial fine structure parameter D.  B is the magnetic field,  S and  I are the electron and nuclear spin operators, respectively, and μ B is the Bohr magneton. The spectrum of one defect species cannot be modelled by the same parameters = g , = A and D for each grain of the ceramic powder samples since the local symmetry in the surrounding of the paramagnetic defect is weakly distorted by varying strain effects. Therefore, we used distributions of the principal values of the g tensor for the 1/2-spin system (V 4+ ions). In the case of the 3/2-spin system only the distribution of the fine structure parameter D was considered. Assuming random fluctuations in the local lattice parameters in the vicinity of the paramagnetic impurity these distributions can be approximated by a Gaussian function with full widths at halfheight (FWHH) Δg ||, Δg ⟘ and ΔD. Figure 1 shows the room temperature (RT) XRD pattern of an as-sintered sample with 2.0 mol% vanadium.

XRD, microstructure and solubility of vanadium
It consists of tetragonal BaTiO 3 and small traces of a V-containing secondary phase, which was identified as Ba 3 V 2 O 8 . For a quantitative phase analysis a Rietveld refinement was carried out using the Fullprof program suite. The amount of Ba 3 V 2 O 8 accounted to 3 mass% corresponding to 1.1 mol%. The samples annealed in different atmospheres at different temperatures remain tetragonal at RT with one exception, namely the highly reducing treatment in H 2 /Ar at 1400°C for 10 hours. In these samples BaTiO 3 is completely in the hexagonal modification at RT and therefore they are not considered in this work.
An example of the microstructure of a polished and chemically etched as-sintered sample with 2.0 mol% vanadium is shown in figure 2.
Compared with undoped BaTiO 3 ceramics prepared under the same conditions and exhibiting a mean grain size of about 50 μm, the vanadium dopant reduces the grain size to values below 20 μm and increases the porosity distinctly, as visible by the black areas corresponding to holes. On the other hand, we cannot exclude that a part of the holes visible in figure 2 may be caused by grains pulled out during the grinding/polishing process. Figure 2 was taken in back scattered electron (BSE) mode, thus the brightness reflects the mean atomic number of the grains. Therefore, the Ba-rich secondary phase Ba 3 V 2 O 8 can be well recognized by its white color in contrast to the grey BaTiO 3 grains. Because of the rather low solubility of vanadium in the BaTiO 3 lattice [12], WDX-EPMA investigations were performed to determine the V concentration inside the BaTiO 3 particles. Quantitative analysis of the vanadium concentration resulted in a value of 0.10±0.01 mol%, which is the mean value of numerous measurements taken at different points in each of a large number of grains. Hence, 95% of the dopant in a sample doped with nominally 2.0 mol% V is actually incorporated in the secondary phase. A second sample with nominally 10 mol% V was also investigated. The mean value of the vanadium concentration in the grains amounted to 0.15±0.01 mol%, i.e. a similar content as in the sample with a nominal concentration of 2 mol%. These results show that the solubility limit of vanadium in BaTiO 3 prepared in air can be estimated to0.2 mol%. Furthermore, we tried to quantify the V content of the V-rich phase by WDX. Unfortunately, the analysis of several grains gave no clear picture, most likely due to the large excitation volume of the x-ray, which is about 1.5 μm for 20 keV electrons and a sample density of 6 g cm −3 [27]. As a consequence, neighboring BaTiO 3 also contributes to the WDX signal. For this reason, EDX measurements with a lower electron acceleration voltage of 12 keV were performed with the EDAX system attached to the VERSA 3D FIB. They resulted in an atomic ratio Ba:(V+Ti) of nearly 3:2 in the majority of the V-rich grains investigated, confirming that the secondary phase is Ba 3 (V/Ti) 2 O 8 . Obviously, the incorporated Ti atoms (V:Ti≈3:2) change the position of the XRD peaks only slightly compared to pure Ba 3 V 2 O 8 (see figure 1). Figure 3 shows the molar magnetic susceptibility of an as-sintered sample doped with nominally 2.0 mol% vanadium measured in a magnetic field of 9.0 T.

Magnetic susceptibility
At temperatures above ca. 220 K, the measured paramagnetic moment reaches the detection limit of the instrument. Therefore, we restricted the data evaluation to the low temperature region. The molar susceptibility was calculated based on the assumption that the paramagnetic behavior of the sample is caused by 0.1 mol% V. This is a rather rough estimation because of two reasons. First, a part of the vanadium incorporated in the BaTiO 3 grains could be in the diamagnetic V 5+ valence state. Second, since the vanadium in the detected Ba 3 V 2 O 8 phase exhibits a mixed valence of +5 (majority) and +4 [28], the amount of paramagnetic V ions in the secondary phase cannot be neglected. Since the calculated value of n eff close to 2.7 (figure 3) significantly depends on the uncertain molar paramagnetic susceptibility, it unfortunately cannot be used for a rough estimation of the electron configuration of the V ions by the spin-only approximation 6 . The interpretation of the susceptibility data is described in section 4 following the discussion of the EPR data.  6 In the spin-only approximation, n eff =2.8 corresponds to S = 1 pointing to V 3+ ions with two unpaired d electrons.

EPR measurements 3.3.1. As-sintered samples
In room-temperature spectra of our V-doped BaTiO 3 samples only the weak signals of Fe 3+ , Cr 3+ and Mn 2+ ions are observed (see the Q-band spectrum in figure 4).
These impurity ions with concentrations less than 0.02 mol% stem from the source material TiO 2 [8,10]. After cooling down the as-sintered samples (in air) to 6 K, additionally to the impurity lines a very broad line (g≈1.96, ΔB=1600 G) and peaks with low intensitity are observed in the X-band (figure 5), which can be clearly identified as the 51 V hyperfine splitting (HFS) octet of a vanadium spectrum. One of the HFS peaks is overlapping with a strong Fe 3+ line (marked by an asterisk in figure 5).
Both, from the characteristic shape of the HFS peaks and from the different distances between two neighbouring peaks in the X-band spectrum (158 G in the low and 162 G in the high field, respectively), this spectrum can be identified as the parallel component of an axial spectrum. Due to the additional Fe 3+ and Mn 2+ lines in the centre of the spectrum the spectral resolution is rather low and the peaks of its perpendicular part are barely identifiable. This 51 V spectrum can be explained by the spin-Hamiltonian (1) with S=1/2 and I=7/2.  Its parameters were determined by simulation with the 'pepper' function of the Easy Spin packet [26] for MATLAB 1 and are given in table 1. Because of the electron spin S=1/2 corresponding to a d 1 system, we assign this spectrum to V 4+ ions, which is additionally supported by the values of spin-Hamiltonian parameters. Investigations in the Q-band show no improvement in resolution, since the V 4+ signals are broadened by g-strain effects (Δg ||,⟘ ≈ 0.0005). Both the V 4+ spectrum and the broad line are temperature-dependent. Their intensities decrease with temperature and above T=20 K, they are no longer detectable.

Post-annealed samples
In the low-temperature X-band spectrum (T=6 K) of the H 2 /Ar-annealed samples the intensities of the V 4+ spectrum and the broad line (see section 3.2.1) are increased in comparision with the air-sintered samples (see figure 6).
At temperatures higher than 20 K, the V 4+ spectrum and the broad line vanish and a new powder pattern (centre of gravity g=1.97, marked by asterisks) is well visible in the X-band spectrum at T=35 K. To get a better disentanglement of the new pattern from the fine structure transitions of Mn 2+ , Fe 3+ and Cr 3+ ions and to reduce second order effects, all further investigations were performed in the much higher magnetic field of a Q-band spectrometer at temperatures above T=20 K. Figure 7 shows the Q-band spectrum at 35 K with the  characteristic 51 V HFS octet expected for the nuclear spin of 7/2. Each of the eight peaks is split into two main components. The distance Δ between them (marked in the figure at the right-most HFS peak) is dependent on the microwave frequency of the experiment. In the Q-band spectrum, the average distance Δ is about 21.2 G. Furthermore, another feature is observed in this vanadium spectrum. At higher amplification, signals with very low intensity are visible between the pairs of HFS peaks, which are marked in figure 7 by asterisks. These two peculiarities are attributed to the fine structure splitting of the spectrum as described in the following. V 4+ (d 1 , S=1/2) can be easily excluded from the possible paramagnetic vanadium valence states 4+, 3+, 2+corresponding to d 1 (S=1/2), d 2 (S=1) and d 3 (S=3/2), respectively, because of the observed fine structure splitting. The V 3+ ion with integral spin S=1 can also be ruled out for the following reasons. First, the observed good resolution of the HFS octet in a powder spectrum is only possible in the case of a small fine structure parameter D, whereas for V 3+ large D values of about 5 cm −1 have been reported [30, p. 427]. This large D would cause a strong angular dependence in the single-crystal rotation pattern and consequently their powder pattern has a completely other shape as observed in our experiment. Second, an integral spin would yield a considerably larger line width due to the increased spin-lattice coupling [31]. Hence, the observed spectrum is caused by V 2+ with S=3/2 and may be described by the spin-Hamiltonian with a fine structure term according to equation (2). In the spectrum (figure 7 a) only the HFS lines of the central transition are seen.
The feature of the powder pattern for a S=3/2 spin-system (discussed in [7]) corresponds to the splitting Δ of the HFS lines (see  . This is a specific characteristic of EPR spectra of Mn 2+ -, Fe 3+ -and Cr 3+ -doped BaTiO 3 -samples [8]. In the case of divalent vanadium ions with 3d 3 configuration, the hyperfine interaction of the 51 V isotope yields a splitting of the central fine structure peak = -« = + M M S 1 2 S 1 2 in eight allowed peaks (ΔM S =±1, ΔM I =0, M I -nuclear magnetic quantum number) and induces furthermore forbidden transitions with the selection rules ΔM S =±1, ΔM I =±1, lying between the allowed peaks of the central transition [30]. Such kind of transitions become detectable by second-order admixtures arising from the cross products of fine and hyperfine terms in equation (2). The intensity of these doublets In figure 8, the temperature dependence of the V 2+ spectrum of the H 2 /Ar-annealed sample is presented. Above T=20 K, the peaks of V 2+ centers are observed in the powder spectrum besides the lines of Mn 2+ , Fe 3+ and Cr 3+ ions. Up to T=170 K, the line widths and distances of V 2+ peaks are nearly temperature independent. Only at higher temperatures the peaks broaden and their amplitudes decrease. By further increase of temperature the peak splittings are no longer resolved and nearly symmetric lines with small intensities are observed. Above 250 K the V 2+ spectrum is no more detectable. The hyperfine constant A of the V 2+ ion is nearly temperature-independent. The absence of the peaks belonging to the fine structure transitions =  « =  M M S 1 2 S 3 2 prevents the accurate measurement of the temperature dependence of the axial and rhombic fine structure parameters.

Discussion
Dependent on the position of the Fermi level in the band gap of barium titanate the 3d-element vanadium has different oxidation states and can be incorporated as diamagnetic ion V 5+ (electron configuration 3d 0 , free ion ground state 1 S) as well as paramagnetic ions V 4+ (3d 1 , 2 D), V 3+ (3d 2 , 3 F) and V 2+ (3d 3 , 4 F). By incorporation of the impurity ion on the Ti 4+ site vanadium is surrounded by six oxygen ions forming a distorted octahedron in the ferroelectric phases of the 3 C modification of BaTiO 3 . However, in the paraelectric high-temperature phase the octahedron is regular. Owing to the strong local electrical field with octahedral symmetry the orbital degeneracy of the free-ion states is partially lifted [30]  +  + +  + + + + + Only in the case of V 2+ ion, the ground state is a non-degenerate orbital state ( 4 A 2g ) whose spin degeneracy can only be removed by the spin-orbit interaction in combination with the crystalline electrical field of lower symmetry. In contrast to V 2+ , the tetra-and trivalent vanadium ions have triply orbital-degenerate ground states with the symmetries T 2 and T 1 , respectively. According to the Jahn-Teller (JT) theorem such ground states are unstable and their degeneracy is lifted e.g. by small displacements of the neighbouring ions, which lower the symmetry of the crystal field. Since ions with the electronic ground state 3 A 2g have a long spin-lattice relaxation time [30] V 2+ ions should be detected by EPR up to room temperature in contrast to ions with T ground states, which are principally not observable at RT by EPR. On the basis of the observed hyperfine splitting, the resolved vanadium spectrum detected in the as-sintered BaTiO 3 powder samples was attributed to V 4+ ions with S=1/2 substituting for Ti 4+ . The orbital degeneracy of its ground state is lifted by a Jahn-Teller effect between the electronic state T 2g of the V 4+ and a localized vibronic e .g. mode in the linear coupling case. This static Jahn-Teller effect produces an axial distortion of the oxygen octahedron in which the paramagnetic V 4+ is incorporated. This symmetry reduction is reflected in the axially symmetric spin-Hamiltonian for V 4+ . The same situation has been observed for other impurities with 3d 1 electron configuration in BaTiO 3 and SrTiO 3 [24,33,34]. The EPMA measurement revealed that only about 0.1 mol% V is incorporated in the grains. Hence, the concentration of V 4+ is probably even lower, since the presence of V 5+ is very likely (see below). In the as-sintered samples EPR spectra of divalent vanadium were not obseserved.
After post-annealing in H 2 /Ar atmosphere the charge state of the vanadium ions is partially changed and a new EPR spectrum is observed. Based on the distinctive feature of this spectrum it has to be assigned to V 2+ ions with the electron spin S=3/2 located at Ti 4+ sites. In the rhombohedral and orthorhombic modifications of BaTiO 3 the symmetry of the Ti 4+ lattice site is lower than the tetragonal one and a spectrum with orthorhombic symmetry is expected. Due to the lack of outer peaks of the transitions with selection rules =  « =  M M S 3 2 S 1 2 the local symmetry of the V 2+ site cannot be determined unambiguously. The simulation of the V 2+ spectra using the spin-Hamiltonian (2) augmented by the orthorhombic term -( ) E S S x 2 y 2 illustrates additional splittings in the central peaks if E>25·10 −4 cm −1 . Therefore, a small orthorhombic distortion of V 2+ spectrum cannot be excluded. At 35 K, the axial zero field splitting parameter D of V 2+ is in very good accordance with the value of the Cr 3+ ion having the same ground state as V 2+ [35]. The 51 V HFS constant A of 61·10 −4 cm −1 is smaller than the value of V 2+ ions in the ionic crystal MgO (see table 1). This reduction can be attributed to the delocalisation of the unpaired V 2+ electrons onto orbitals of the Ti-O states.
V 2+ ions with the electronic ground state 4 A 2g have a long spin-lattice relaxation time. Their spectra should be easily detected at and above room temperature as observed for other d 3 ions, see e.g. [7,[35][36][37]. However, with increasing temperature, in our samples a line width broadening of the V 2+ spectrum appears above 210 K and finally the spectrum vanishes at T>240 K. Due to the complexity of the observed peak structure it is not possible to determine the individual line width as a function of temperature. It can be assumed that the temperature-dependent line width broadening and finally the complete disappearance of the spectrum is caused by a thermally activated charge carrier transfer process between V 2+ and V 3+ states (see below).
The presence of the other possible valence states V 5+ and V 3+ in the BaTiO 3 grains can be concluded by following consideration. The samples annealed in reducing atmosphere show an increased intensity of the V 4+ spectrum i.e. an increased concentration of V 4+ ions. This indicates that a part of the V 5+ in the as-sintered BaTiO 3 grains is reduced to V 4+ during annealing. Moreover, since the reduced samples include both V 4+ and V 2+ ions, it is possible that also V 3+ ions (d 2 , S=1) occur in those samples, which are not detected by our EPR experiments.
In the spectra of all V-doped BaTiO 3 samples a broad line was observed up to 20 K. Because of the sparse spectral information its interpretation is difficult. We suppose that this line is caused by V 4+ ions in the vanadium-rich secondary phase containing practically the whole V dopant (see section 3.3.1). Due to the higher concentration of the V 4+ ions (see discussion of the magnetic susceptibility below) they are coupled by dipoledipole-interaction and only a single broad line is observed.
The very small paramagnetic susceptibility of the as-sintered samples (figure 3) proves that the majority of vanadium in the secondary phases (95% of the dopant amount) is in the valence state 5+. The measured magnetic moment is a superposition of the contribution of the V 4+ ions both in the BaTiO 3 grains and in the vanadium-rich Ba 3 V 2 O 8 phase, proven by XPS [28]. Since the experimental determined value of the effective Bohr magneton number is very uncertain because of the unknown concentration of V 4+ and since the spin-only formula is not suitable for ions with T 2g ground state as V 4+ , the computer program CONCORD [38] was used for the analysis of the susceptibility data. Simulations of the temperature dependence of the molar magnetic susceptibility showed that the measured data can only be reasonably reproduced if either a lower-symmetric than octahedral or a tetrahedral crystal field is assumed. Both variants occur in the samples, first as tetragonally JT-distorted oxygen octahedra in the BaTiO 3 grains and second as VO 4 -tetrahedra around the vanadium ions in the crystal structure of Ba 3 V 2 O 8 (space group R m 3 ) [39]. Since less than 0.1 mol% of V 4+ is incorporated in the BaTiO 3 grains, we assume that the majority of V 4+ is located in the Ba 3 V 2 O 8 phase and in turn the tetrahedrally oxygen coordinated V 4+ ions dominate the paramagnetic susceptibility. Thus, the susceptibility data were fitted by CONCORD (for details see appendix A of [9]) assuming a crystal field with symmetry T d and including the concentration of the paramagnetic ions as a further fitting parameter. The total concentration of the V 4+ ions was found to be 0.6 mol% confirming our assumption a posteriori. The crystal field fitting parameter 7 B 0 4 amounts to ≈−1000 cm −1 . 7 Wybourne notation [40].

Conclusions
Vanadium exhibits a very low solubility of about 0.1 mol% in the BaTiO 3 grains of nominally 2.0 mol% V doped ceramics sintered in air at 1400°C. The majority of vanadium (95%) forms the secondary phase Ba 3 (V/Ti) 2 O 8 . Up to a nominal doping concentration of 10 mol% V the solubility in BaTiO 3 remains below 0.2 mol%. This low V content is probably the reason that all samples investigated (both as-sintered and post-annealed in reducing atmosphere) are completely in tetragonal phase at RT whereas the other 3d ions Cr-Zn cause at least the partial formation of the hexagonal phase already at nominal doping concentrations of 0.5 mol%.
In the as-sintered samples, V occurs in V 4+ and V 5+ valence state. The former was detected with EPR by its HFS octet due to the nuclear spin of 7/2 of 51 V and was identified as V 4+ ions incorporated at the Ti 4+ site of BaTiO 3 . As a second species V 4+ was found in the V-rich secondary phase Ba 3 (V/Ti) 2 O 8 as a single broad line. In the samples post-annealed in reducing atmosphere, an additional HFS octet occurs, which can be assigned unambiguously to V 2+ ions with a half-integer electron spin of 3/2 by the occurrence of both allowed and forbidden fine structure transitions.