Peculiar Properties of Phase Transitions in Na0.5Bi0.5TiO3-xBaTiO3 (0<x<6) Lead-free Relaxor Ferroelectrics Seen Via Acoustic Emission

Na0.5Bi0.5TiO3-xBaTiO3 (0<x<6) relaxor ferroelectrics crystals were investigated by means of dielectric and acoustic emission methods. Dielectric curves exhibit the slightly visible small maxima near the depolarization temperatures, Td, and the wide maxima at the temperatures of Tm, whereas the acoustic emission exhibits the sharp bursts, corresponding to Td, Tlm, which is known to be a temperature exhibiting a strong frequency dispersion, TRE, which is known to be a temperature above which a frequency dispersion vanishes, and the Tm and the Tp manifesting a transition to the paraelectric phase. Based on the AE data it was established that all these characteristic temperatures shift down as x increases, but with different slopes. A mechanism of such the differences is discussed.


Introduction
Relaxor ferroelectrics (RFEs) include a large group of solid solutions and complex compounds (mostly oxides) with ABO 3 perovskite structure, and their properties are known to be in contrast to the ordered ferroelectrics (FEs). Both Pb-based and Pb-free A(B' 1/2 B'' 1/2 )O 3 and A(B' 1/3 B'' 2/3 ) O 3 relaxors attract a great attention due to their intrinsic chemical inhomogeneity and related local structural distortions due to the difference in ionic charges and radii between the different kinds of B-or A-site cations in the former (Pb-based) 1 , or on both A-and B-sites in the latter (Pb-free compounds) 2 , which is a reason of the existence of polar nanoregions (PNRs) resulting in the giant and smeared maxima of dielectric permittivity, ɛ', at temperature referred as T m , which depends on the measuring frequency. Being mobile the PNRs nucleate at high enough Burns temperature, T B , on cooling, below so-called intermediate temperature, T*, they begin to couple and merge into larger ones, become a long-lived and so the deviation from a Curie-Weiss law and a frequency dispersion starts 3 , and on further cooling the PNRs become frozen into a nonergodic dipole glass state below Vogel-Fulcher temperature, ascribed as freezing temperature, T f , some degrees below the T m [1][2][3] . While all these characteristic points: T B , T* and T m , were detected in Pb-based RFEs 4-7 as well as in some Pb-free RFEs 8,9 , in Pb-free relaxors of Na 0.5 Bi 0.5 TiO 3 -xBaTiO 3 (NBT-xBT) they have been established recently using an acoustic emission (AE) method 10 . Moreover, in the latter paper it was shown that the temperature T lm , corresponding to local dielectric maxima of ɛ', or so-called "hump", low temperature and frequency dependent one, plays a role of T m in the Pb-based RFEs and is caused by interaction between PNRs only, whereas the high temperature maximum of ɛ', ascribed as to be corresponding to T m , is caused of coexisting of some phases with which NBT-xBT is known to be rich.
In accordance with the structural studies a sequence of the phase transitions when heating the pure unpoled NBT crystals and ceramics is following:  13 . While the high-temperature data of two latter works coincides well, the data of former work is inconsistent with them due to presence of low-temperature Trigonal I → Trigonal II phase transition near 200°C 11 . Later it was shown 12 , that there is not any phase transition between room temperature and 250°C, and the observed steep drop of piezomodulus higher than the so-called depolarization temperature, T d ≈ 190°C 14 , is presumably caused by percolation of disordered P4bm nano-scale platelets 15 , embedded in the R3c matrix in pure NBT 16 . Along with the piezomodulus, on heating the dielectric constant exhibits anomalies around of 200°C, slightly above T d [17][18][19][20][21] , accompanied by strong frequency dispersion as well as marks out the AFE P4bm to PE Pm3m phase transition around the T m of 320°C [17][18][19][20][21] . Also these two dielectric anomalies usually accompanied by jumps of the thermal expansion coefficient 17 , peaks of differential scanning calorimetry curve 22 , electrostrictive strain 23 and elastic compliance 24 . In addition, on heating the domain twins appear near 260°C and disappear near 295°C, whereas on cooling they appear near 240°C and disappear near 205°C, exhibiting a hysteresis of about 55°C 22,25 and disappear above approximately 540°C 25,26 .
When incorporating the Ba ions in A-site of NBT-xBT the dielectric anomalies smear and shift by the temperature, but the direction of such the shifts is not clearly seen due to smearing of dielectric curves as well as contradictory sometimes, especially concerning the T m [19][20][21][27][28][29] . Moreover, in pure NBT the maximum of ɛ' there is a clearly seen to be not symmetric: jump of ɛ' on some tens of degrees below T m , shifting to lower temperatures and gradually vanishing as the content of Ba increases 20,21 . Note, that this jump of ɛ' approximately coincides with disappearance of the domain twins near 295°C 22,25 .
Scrupulous observations of domain morphology, performed with NBT-xBT, allowed the authors [30][31][32] to establish an existence of two-phase mixture (complex domains) with volumes of R3c FE domains (~100nm) embedded in the matrix of P4bm AFE nanodomains (<20nm), PNRs, in NBT-6BT ceramics (core-shell grain structure) at room temperature, that does provide the excellent piezoelectric properties. In particularly, in NBT-6BT particularly, lying in the middle of morphotropic phase boundary, around 40% of the grains display such complex domains with R3c-P4bm structure, while the rest ones display P4bm PNRs only. On heating the volume fraction, containing these complex FE domains, starts to shrink at around T d ≈ 120°C and this process continues until ~160°C when the whole grain is completely occupied by PNRs with P4bm symmetry. The R3c → P4bm structural phase transition undergoes through the finite temperature interval of about 40°C: the volume with P4bm PNRs expands at the expense of the volume with the R3c complex domains and finally occupies the whole grain. During further heating the major part of P4bm PNRs transform to P4bm long-range phase near T RE ≈ 220-230°C though their small amount exists far above the T m 32 , and above of 335°C the tetragonal -cubic structural phase transition takes place at T p .
Previously the dielectric constant, measured on heating in NBT-6BT crystals, clearly shows the low temperature "hump" of ɛ' 19,[27][28][29][30] between of 140 and 220°C, accompanied by AE bursts between of 127 and 225°C, which also exhibits the bursts corresponding to T m ≈ 290°C and T p ≈ 390°C, respectively 33 . Recently, using the AE, it was confirmed that the temperature of this "hump", ascribed as the T lm , exhibits the strong frequency dispersion, whereas the T d exhibits no dispersion, and all these characteristic temperatures of NBT-6BT: T d ≈ 123°C, T lm ≈ 150÷180°C, T RE ≈ 225°C, T m ≈ 300÷310°C and T p ≈ 327°C have been successfully detected by AE 10 , in good agreement with the early detected data 33 .
Because AE has proven itself to be a reliable method to detect all the characteristic temperatures in NBT-6BT relaxors ferroelectrics more precisely in comparing with the smeared maximum of dielectric permittivity, we have applied it to detect of these temperatures in NBT-xBT compounds and to study their shift in dependence on the Ba content.

Experimental Details
Na 0.5 Bi 0.5 TiO 3 -xBaTiO 3 (x = 0; 2; 2,5; 3,25 and 6) crystals were grown using a Czochralski method. Powder reagents of Na 2 CO 3 , BaCO 3 , Bi 2 O 3 and TiO 2 were used as the starting materials. Stoichiometric amounts were weighed and homogenized in agate vessel in alcohol for 2 h. The obtained mixture was then calcined at 800ºC for 4 h. The crystal growths were carried out at concentration dependent temperatures from the range 1300-1360ºC. The obtained crystals with dimensions about 1.5 mm × 1.5 mm × 2.5 mm were homogeneous, transparent and slightly yellowish. No cracks and inclusions were observed. The silver contacts were fired at 650°C for 30 min. We used the unpoled samples in order to avoid the changing in phase structure that can be completely altered after applying an electric field 17 .
AE is known to be a nondestructive method, based on detection of the mechanical elastic waves, radiated by the different structural defects in the solid states under some external loadings: stress, temperature, electric field, as well as by arising of the mechanical twins during the martensite phase transitions in metals and their alloys. The waves are detected using a piezoelectric sensor, fairly often connected with the sample through a dielectric acoustic waveguide to avoid of its overheating 34 . Traditionally in FEs the AE is well proven in detection of the structural phase transitions, T c , due to arising of the domains and their mechanical interaction [35][36][37][38] as well as recently it is well proven in a study of all the characteristic temperatures in RFEs: T m , T* and T B due to arising of the PNRs and their mechanical interaction [4][5][6][7][8][9][10]33 . AE technique has been described previously elsewhere 11 . A sample was pasted with a silver epoxy on the polished side of a fused silica acoustic rod waveguide. A PZT-19 disk piezoelectric sensor was attached to the rear end of the waveguide. A sensor was electrically coupled to a 500 kHz bandpass low noise variable (up to 40 dB) preamplifier connected to a detector-amplifier (40 dB). A Ch-Al thermocouple junction was glued to the waveguide near the sample. A waveguide with the pasted sample is vertically mounted from below into resistance element furnace. The dielectric data were measured using a HP4263A LCR meter wired to the sample. All the thermocouple, amplifier, and LCR meter outputs were interfaced with a PC for a coupled readout. The measurement of the dielectric constant real part ɛ' and AE count rate (s -1 ) were performed in the temperature range of 20-400°C with a rate of about 1-3°C/min at the measuring frequency of 1 kHz on heating. Figure 1 presents the temperature dependences of the real part of dielectric constant ɛ' and AE count rate for all the compounds. The ɛ' (T) curves exhibit two groups of smeared (diffused) humps and maxima: the low temperature humps corresponds to T lm , in the range of 150-200ºC and the high temperature maxima corresponds to T m in the range of 300-350ºC. These results are in good agreement with previous studies 10,19,21,[27][28][29][30][31]33 . For pure NBT the form of the ɛ' curve is not symmetric around T m : from the low temperature side it is steeper in comparison with the high temperature side, as observed previously 21 . With an increase in the Ba content the dielectric constant ɛ' around T m becomes symmetric and gradually rises in both the T d and T m when they shift towards the lower temperature in good coincidence with the previously observed data, too 19,20,22 .
Although the AE bursts exhibits some scattering in the values, some trends of distribution are still visible (Table 1). Indeed, it is well seen that the values of , corresponding to both T d and T m , are stronger than the one, corresponding to T RE . Such the distribution of values of is similar that previously observed when transforming through the R3m rhombohedral -Amm2 orthorhombic -P4mm tetragonal -Pm3m cubic phase transitions in BaTiO 3 ceramics 35 . Moreover, it is clearly seen, too, that the becomes stronger when transforming through the AFE P4bm -FEl P4/mbm -PE Pm3m phases in good coincides with one previously observed in some well-known perovskite FEs, undergoing through the AFE -FE -PE phases 37 . Thus, one can conclude the AE method rightly reflects the sequence of the phase transitions in RFEs and so could be to apply for express identification of their phase transitions types by the quantities of , as it was revealed in Ref. 37 .
All the AE bursts point out the phase transitions, taking place in NBT-xBT compounds, except of T lm . AE bursts, accompanying the T lm was recently shown to correspond the interaction between the PNRs only 10 . Concerning the phase transitions they can be qualified based on the structural data [11][12][13][14][15][16] and scrupulous studies of domain structure 22,25,26,[30][31][32] . On heating at T d the R3c → P4bm phase transition starts and this temperature is even ascribed to be the Curie temperature, T c 26 , and such the statement closes a row of the characteristic points in NBT-xBT family: T d ≡ T c , T lm ≡ T m of Pb-based RFEs, T RE ≡T* 10 , and the T B ≈ 420÷450ºC 40 . During this phase transition the frequency dispersion of a dielectric constant exists up to T RE , where the long-range P4bm phase arises. So, the relaxor property of NBT-xBT continues from T d to T RE . Presumably, at T m the P4bm phase transforms to the tetragonal centrosymmetric P4/mbm nonpolar ferroelastic phase 16 , which further transforms to Pm3m phase at T p . AE points out the T p ≈ 330°C only for NBT-6BT compound, for other compositions the T p lies upper of a heating possibility of our furnace. Figure 2 presents the temperatures of all the characteristic points, detected by AE, as a function of Ba content x. All the temperatures decrease linearly with ecreasing x. Similar linear down of T c was earlier observed in BaTiO 3 crystals when substituting the Ba ion by its heavier isotope 41 . So, a decrease in the phase transitions temperatures with enhancement of x leads us to conclude that the Ba ion mainly substitutes the light Na ion rather than the heavy Bi ion, especially since both radii of Na and Bi are nearly equal to each other: 1.18Å ≈ 1.17Å (CN = 8).
On the other hand, the slopes of these linear dependencies are essentially different. Indeed, while the slopes of T m , T lm and T d are found to be approximately the same order of magnitude: -7.3, -6.6, and -4.2, respectively, the slope of T RE is found to be -16,6 as well. Taking into account that both the FE R3c and AFE P4bm phases coexist between T d and T RE , we tend to think that such the steep slope of the T RE (x) dependence is caused by a chemical pressure contributed by the incorporated Ba ions as their content increases. Recently based on both the theoretical and experimental data it was shown that a pressure downs the temperature of FE-AFE phase transition steeper than the temperature of AFE-PE phase transition 42 , in good agreement with our present data. And, thus, we have confirmed that P4bm phase is really the AFE one.

Conclusion
In summary, we have investigated the Na 0.5 Bi 0.5 TiO 3 -xBaTiO 3 (0<x<6) relaxor ferroelectrics crystals by means of dielectric and acoustic emission methods. We have detected all the phase transitions: ferroelectric-rhombohedral →antiferroelectric-tetragonal, starting above T d and finishing above T RE ; antiferroelectric-tetragonal → ferroelastictetragonal at T m ; and ferroelastic-tetragonal → paraelectriccubic at T p . We have plotted the shifts of these temperatures with dependence on Ba content and established that all the temperatures decrease as Ba content increases. Also we have found out that the T RE decreases steeper in comparing with the others and have shown that such the steeper decrease of T RE is characterisitc for ferroelectric-rhombohedral → antiferroelectric-tetragonal phase transition when enhancing an intrinsic pressure as Ba content increases.