High-temperature thermoelectric properties of (1-x)DyBCO − xBNT ceramics

ABSTRACT Dysprosium barium copper oxide – bismuth sodium titanate ((1-x)DyBCO−xBNT) ceramics, where x = 0−0.07 mole fraction, were successfully prepared by a solid-state reaction and sintering method. The DyBa2Cu3O7-δ and (Bi0.5Na0.5)TiO3 powders were separately synthesized by calcining their stoichiometric mixtures at 900°C for 4 h and 800°C for 2 h, respectively. The (1-x)DyBCO−xBNT powders were compacted into pellets and sintered at 930°C for 2 h under normal air atmosphere. Phase identification and morphology of all samples were determined using X-ray diffractometer (XRD). The quantitative phase analysis was analyzed by fitting the XRD pattern using the GSAS-II program. Scanning electron microscopy (SEM) with energy dispersive X-ray spectroscopy (EDS) was used to study microstructure and chemical composition. In all cases, the result of XRD shows that the DyBa2Cu3O7–δ (Dy-123) was identified as the main crystalline phases, due to the good agreement between the observed and calculated patterns after Rietveld refinement. All BNT-doped DyBCO ceramics showed slightly higher density values than the undoped sample, suggesting that BNT helped improve the densification process. The sign of the Seebeck coefficient ( ) was positive for all samples at all measured temperatures, confirming a p-type conduction mechanism. Low BNT doping improved the overall thermoelectric properties of DyBCO ceramics by affecting electrical conductivity ( ), Seebeck coefficient ( ), and thermal conductivity ( ). The dimensionless figure of merit ( ) of all samples increased with increasing temperature. The highest value of 5.67 × 10−2 was observed for the 0.97DyBCO−0.03BNT sample at 863 K.


Introduction
Renewable energy technologies are especially important for the future energy revolution. Thermoelectric (TE) material, which has the ability to directly convert heat to electricity, is one of the potential candidates for future clean energy applications. TE has so far been used mainly in the standalone power-generation technology for biomedical, aerospace, military and remote power applications [1,2]. The efficiency of TE material is evaluated by the dimensionless figure of merit, ZT ¼ σS 2 T=κ T , where σ, S, T, and κ T are the electrical conductivity, Seebeck coefficient, absolute temperature and total thermal conductivity, respectively [1,2]. Therefore, high σ, large S, and low κ T are required for a good TE material. Nowadays, the renewable energy technologies for power harvesting from automobile and industrial waste heat may require oxide materials because of their potential advantages over intermetallic alloys in terms of chemical and thermal stability at high temperature. For examples, SrTiO 3 , ZnO, LaCoO 3 , Na x CoO 2 , Ca 3 Co 4 O 9+δ , and Bi 2 Sr 2 Co 2 O y have been widely studied [3][4][5][6][7][8].
Misfit-layered cobalt-based oxide semiconductors were reported to exhibit large S and considered to be good candidates for thermoelectric materials [5][6][7][8].
Because of the strong electron-electron correlation in these layered Co oxides, there is a possibility for obtaining good thermoelectric properties in these compounds by optimizing the electrical properties and reducing the thermal conductivity. Layered YBa 2 Cu 3 O 7-δ (YBCO or Y-123) material, which is another typical strong electron correlation layered oxide, have been known as a high-T c superconductor. In addition, Y-123 is considered a potential oxide thermoelectric material due to its high σ, moderately high S and low κ T [9][10][11][12][13]. The maximum ZT of YBCO was reported to be around 0.3-0.7 [9][10][11][12][13] and its electrical and thermal transport properties was significantly related to oxygen deficiency (δ) in the lattice. It is well known that Y-123 is an oxide compound whose crystal structure is composed of rocksalt and perovskite units. In these materials, the free charge carriers are confined to the planar Cu-O sheets that are separated by insulating layers. The interaction of the special crystal structure leads to the strong anisotropy of electrical conduction which makes these compounds very interesting for thermoelectric properties investigation. REBa 2 Cu 3 O 7-δ (RE = Nd, Sm, Eu, Gd, Dy, etc.) have better applicability compared to Y-123 system [14][15][16][17][18]. They show a higher metallic-superconducting transition temperature, better surface morphology and also better performance under external magnetic field.
It is well known that the combination of glass-like thermal conductivity and crystal-like electronic properties (i.e. phonon-glass electron-crystal or PGEC) is required for good thermoelectric materials [22]. This approach is most achievable in materials with complex crystal structure, where vacancies and heavy element atoms would act as effective phonon scattering center and reduce the lattice thermal conductivity (κ l ). The combination of two or more compounds in the form of nano-composite or solid solution [23] is one method that seems to support the PGEC concept and provide enhancement in performance of thermoelectric materials.
Bi 0.5 Na 0.5 TiO 3 (BNT) is a non-conducting oxide which is a lead-free perovskite ferroelectric material with reported high S (+375 μV/K) but with very low σ, leading to very low ZT [24]. It is interesting that the BNT contains heavy element atoms which would act as phonon scattering centers, leading to low κ T . Recent research suggests that the κ T of the NCO and YBCO compounds could be reduced by the BNT additions due to more efficient phonon scattering [7,24]. In addition, small amount of BNT was found to enhance the S values of YBCO but larger amount caused the major carrier transport mechanism to transform from p-type to n-type [12]. Due to the high σ of DyBa 2 Cu 3 O 7-δ (Dy-123 or DyBCO) and high S of Bi 0.5 Na 0.5 TiO 3 (BNT) compound, it might be expected that the combination of Dy-123 and BNT at certain composition could lead to thermoelectric efficiency improvement. Therefore, the aim of this study is to fabricate and characterize (1-x) DyBCO−xBNT ceramics. By employing quantitative phase analysis, the relation of phase formation with crystal-structure and microstructural change, composition, density and thermoelectric properties at high temperature were investigated and discussed in details.

Experimental
The samples of (1-x)DyBa 2 Cu 3 O 7-δ −xBi 0.5 Na 0.5 TiO 3 or (1-x)DyBCO−xBNT ceramics were successfully prepared by a solid-state reaction and sintering method. First, the DyBCO powder was prepared by mixing an appropriate amount of Dy 2 O 3 (99.9%, Sigma-Aldrich), BaCO 3 ( � 99%, Sigma-Aldrich) and CuO (98%, Sigma-Aldrich) starting powders. These powders were mixed in a stoichiometric ratio of Dy:Ba:Cu = 1:2:3 and ball milled for 24 h in polyethylene jar with zirconia ball as milling media. The mixed powders were dried and calcined in an opened alumina crucible at 900°C for 4 h under normal atmosphere. Second, the BNT powder was synthesized by mixing the staring compounds of Bi 2 O 3 (99.9%, Aldrich), Na 2 CO 3 (99.5%, Carlo Erba), and TiO 2 (>99%, Sigma-Aldrich) powders in the appropriate ratio and ball milled for 24 h in polyethylene jar with zirconia ball as milling media. The mixed powders were dried and calcined in an alumina crucible at 800°C for 2 h. The powder X-ray diffraction patterns of calcined DyBCO and BNT powder showed single phase with the corresponding orthorhombic and rhombohedral structure, respectively. Finally, the mixed (1-x)DyBCO − xBNT powders, where x = 0, 0.01, 0.03, 0.05, and 0.07 mole fraction, were compacted into disc-shaped pellets and sintered at 930°C for 2 h under normal air atmosphere. The apparent density of the ceramics was measured by the Archimedes method using xylene as the liquid medium. Phase formation of the ceramics was investigated by an X-ray diffractometer (XRD) (Phillips Xpert pro Diffractometer). The relative weight fraction of phases present in DyBCO ceramics was also calculated by using quantitative analysis based on experimental XRD patterns and GSAS-II program [25]. The microstructure was observed in backscattered electron mode using a scanning electron microscope (JSM-5910/JSM-IT300) and chemical composition identification was carried out using energy dispersive X-ray spectroscopy analysis (SEM-EDS). The variation of electrical conductivity and Seebeck coefficient measurement with temperature of bar-shaped (3 mm x 3 mm x 15 mm) ceramic was measured by the Seebeck Coefficient/ Electric Resistance measuring system (ZEM-3, ULVAC-RIKO) from 400-900 K. The variation of thermal conductivity with temperature of disc-shaped pellets (10 mm in diameter and 1 mm in thickness) was observed by a laser flash TC-7000 system (ULVAC SINKU-RIKO) from room temperature to 1000 K. having an orthorhombic structure was present. The result of XRD showed that the diffraction peaks shifted slightly to lower angle when the BNT mole fraction increased as presented in Figure 1. For example, the ceramic with x = 0.01 showed the diffraction peak shift of (112), (005), and (113) reflections from 2θ = 32.71° to 32.43°, 38.56° to 38.39°, and 40.28° to 40.11°, respectively. The change in the unit cell parameters was mainly due to the substitution of Dy-123. There has been some reports suggesting that Cu 2+ (r Cu 2þ = 0.73 Å) site could be substituted by Ti 4+ (r Ti 4þ = 0.605 Å) ions [26][27][28], which produced excess electrons or cation vacancies. The substitution at the Cu site by Ti 4+ was consequently producing free CuO [29]. On the other hand, the ionic radius of Na + (r Na þ = 0.95 Å) is comparable to that of Dy 3+ (r Dy 3þ =1.07 Å) or Ba 2+ (r Ba 2þ =1.35 Å). A number of researchers reported that Na + could occupy both RE 3+ (RE 3+ = Y 3+ , Dy 3+ ) and Ba 2+ [30][31][32] sites, producing hole carriers or anion (i.e. oxygen) vacancies. The effective ionic radius of Bi 3+ (CN =8) was 1.17 Å as reported by R. Shannon [33]. If Ba 2+ was substituted by Bi 3+ , excess electrons or cation vacancies could also be produced, which would not agree with the increase in electrical conductivity observed. Since the ionic radii and valency of Bi 3+ and Dy 3+ are similar, there was a possibility that Dy 3+ would be replaced by Bi 3+ . The substitution at the RE 3+ ion of RE-123 mostly created the RE-211 and BaCuO 2 phase [34][35][36].

Phase formation
Rietveld refinement of the XRD patterns for all ceramic samples was performed using the structural model (COD database) of all possible occurring secondary phases as Dy-123 (Pmmm), Dy-211 (Pnma), CuO (C2/c), BaCuO 2 (Im-3 m), and BNT (R3c). To evaluate quantitatively the best fit of the data, the most accepted factor is the weighted residual minimized in Rietveld refinements (R w ) with the 0% value of R w represents an ideal fit and 10% is acceptable for most cases. The ratio between the two R values defines the goodness-of-fit, where R exp is the expected error [37]. The χ-value of 1.3 or less is empirically considered to be satisfactory. The simulated XRD pattern was obtained using GSAS-II program [25] and the simulated intensity values fit a model to data was presented in Figure 3. The weight fraction of (1-x)DyBCO-xBNT ceramics were summarized in Table 1. The result showed that when the added BNT content increased, the weight fraction of the Dy-123 phase with orthorhombic structure (Pmmm) noticeably decreased while the Dy-211 (Pnma), CuO (C2/c), BaCuO 2 (Im-3c) phases occurred. The presence of BNT phase was not detected in XRD patterns due to the low BNT concentration or    the phase already dissolved in the DyBCO matrix. The results showed that the fraction of CuO of the BNTadded YBCO (0.01 ≤ x ≤ 0.07) samples were detected. CuO was reported to have a band gap of 1.2 eV and p-type semiconducting characteristics [38]. The densification of the RE-123 sample was enhanced by the addition of the CuO content during sintering through the presence of the liquid phase [39]. The high relative density values of BNT-doped DyBCO samples are listed in Table 1. The percentage of non-conducting Dy-211 phase increased with the BNT addition particularly with 0.05 ≤ x ≤ 0.07. Besides, the BaCuO 2 phase is another insulating phase which is frequently observed in the process of preparation of RE-123 [40]. However, the amount of BaCuO 2 for all samples was quite small, i.e. around 0.1-0.3 wt%. Hence, the effect of BaCuO 2 on properties was expected to be negligible compared to Dy-211 (Pnma) and CuO (C2/c).
Phases and structural parameters of the (1-x) DyBCO-xBNT ceramics are listed in Table 2. The result showed that the unit cell volume of the Dy-123 phase expanded with the increase of BNT. It was possible that  the Dy 3+ (r Dy 3þ =1.07 Å) ion was likely substituted by the Bi 3+ (r Bi 3þ = 1.17 Å) ion and Na + ion (r Na þ = 0.95 Å) and then the Dy-211 and BaCuO 2 phases occurred. As can be seen from Table 2, the volume of Dy-123 slightly increased with the increase of BNT addition. It was possible that the Cu +2 ion (r Cu 2þ = 0.73 Å) was replaced by Ti 4+ (r Ti 4þ = 0.605 Å) and also the Na + ion (r Na þ = 0.95 Å) substituted at Dy 3+ /Ba 2+ (r Dy 3þ =1.07 Å and r Ba 2þ =1.35 Å) site. Based on the calculated unit cell volume from Rietveld refinement, the overall effects from BNT addition gave a slight decrease in lattice parameter a while lattice parameter b and c slightly increased, resulting in a small expansion of the unit cell.

Microstructural analysis
The microstructure of undoped DyBCO ceramic samples showed that the grains presented a typical elongated form with a mean size of 3.74 μm as previously reported [41,42]. When the amount of added BNT increased, the morphology exhibited irregular shape.
The measurement of grain size was difficult because the grain boundaries could not be outlined clearly, which partly might be due to the presence of liquid phase (i.e. BaCuO 2 + CuO). The BSE-SEM of fracture surface was presented in Figure 4. From the figure, the porosity and grain boundary were reduced with BNT addition. For RE-123 [39], the CuO phase induced the grain growth and liquid phase sintering. The relative density and shrinkage of samples are listed in Table 1. The results showed that the density of the samples with BNT content were slightly higher than the undoped sample, suggesting that BNT helped improve the densification process. The backscattered electron BSE-SEM images of the polished surface samples are shown in Figure 5. The results showed that the increasing amount of BNT influenced the formation and distribution of Dy-211 phase (white spots) in the Dy-123 matrix (gray regions). As an example, for the sample with x = 0.03, the Dy-123 and Dy-211 phases were obviously confirmed by the BSE-SEM with EDS technique as presented in Figure 6. The evaluated elemental compositions of the ceramics are listed in Table 2. Phases and structural parameters of the (1-x)DyBCO -xBNT ceramics.

Electrical transport
The temperature dependence of electrical conductivity (σ) is shown in Figure 7. At low temperatures, the electrical conductivity of all (1-x)DyBCO−xBNT samples showed an increasing trend with increasing temperature, indicating the semiconducting behavior. At higher temperatures, the σ of all samples reached maximum values and then decreased with increasing temperature, suggesting the transition from semiconducting to metallic conduction behavior. As can be seen from Figure 7, the maximum of σ values for x = 0, 0.01, 0.03, 0.05, and 0.07 samples were found to be 4.08 x 10 2 , 2.8 x 10 3 , 1.42 x 10 4 , 1.32 × 10 3 , and 1.50 × 10 3 Ω À 1 m À 1 , respectively. The substitution level has a pronounced effect on σ. Due to the sign of the S for the Dy-123 sample was positive which confirmed that the conduction mechanism was mainly governed by holes (p-type behavior). For low BNT content doped Dy-123, Bi 3+ , and Na 1+ (overall effective charge = 2+) went to replace some of Dy 3+ , leading to an enhanced hole carrier concentration in the Dy-123 based compound. Similarly, the behaviors of BNT doped YBCO were previously reported by P. Prayoonphokkharat et al [12]. With increasing BNT, the substitutions of RE 3+ by Na 2+ /Bi 3+ also occurred and created hole but the Cu 2+ site of the Dy-123 phase was substituted by Ti 4+ with 0.03 < x ≤ 0.07, which had the effect of reducing hole concentration. The weight percentage of Dy-211 was 1.30%, 0.80%, 6.30%, and 8.60% for x =0.01, 0.03, 0.05, and 0.07, respectively. The weight percentage of BaCuO 2 was 0.30%, 0.20%, 0.20%, and 0.30% for x = 0.01, 0.03, 0.05, and 0.07, respectively. At temperature < 300 K, the σ in the molar ratio of Dy-123:Dy-211 = 100:x was reported to be 8.00 x 10 5 , 7.55 x 10 5 , 7.14 × 10 5 , and 5.88 × 10 5 Ω −1 m −1 for x = 5, 10, 20, and 40, respectively [46]. In addition, the σ in the mass ratio of the Y-123: Y-211 samples was 1.00 x 10 4 , 4.00 x 10 3 , 8.00 × 10 2 , and 3.33 × 10 2 Ω −1 m −1 at 300 K for the Y-123:Y-211 = 90:10, 80:10, 70:30, and 50:50, respectively [47]. These results suggested that the σ of the RE-123 decreased with the increase of the insulating RE-211 fraction. In addition, the resistance of Y-123:BaCuO 2 increased from 0.8 mΩ for the BaCuO 2 = 4 wt.% sample to 0.9 mΩ for the BaCuO 2 = 8 wt.% sample at < 300 K [48]. The decrease of σ was found to be associated with formation of insulating Dy 2 BaCuO 5 (Dy-211) and BaCuO 2 phases for the 0.03 < x ≤ 0.07 sample (Figure 7). On the other hand, CuO phase is a p-type semiconductor (E g = 1.2 eV). The weight percentage of CuO was 2.70%, 6.70%, 5.50%, and 6.40% for x = 0.01, 0.03, 0.05, and 0.07, respectively. The σ of the CuO bulk is ~0.5-3.0 Ω −1 m −1 at 298 K and 30 Ω −1 m −1 at 1000 K [38]. It is suggested that the substitution of the Dy-123 played the important role in the increase of σ, comparing to the effect of secondary phases. The mobile holes for the p-type semiconductor are small polaron hoping conduction (SPHC), and the temperature dependence of σ can be generally expressed as where n, e, a, A, E a , k B , and T are the carrier concentration, electron charge of carrier, intersite distance of hopping, pre-exponential term related to the scattering mechanism, activation energy, Boltzmann constant and absolute temperature, respectively [49]. The E a can be obtained from the slopes of the lnðT=ρÞ versus 1000/T plots [6,49,50] as displayed in Figure 8. Below 673 K, it showed that the activation energy (E a ) decreased with low BNT addition. The sample with x = 0.07 exhibited the lowest E a (35.24 meV). Even though the activation energy for polaron hopping mechanism was lowest, the electrical conductivity was rather low which was similar to that of x = 0.05 sample. We expected that the ionic substitution (e.g. Ti 4+ substituting Cu 2+ , inducing electrons and reducing mobile holes) and the presence of insulating secondary phases played a role in these two compounds. For the x = 0.01 and x = 0.03 samples, the effects of hole carrier production due to Bi 3+ and Na 1+ substituting Dy 3+ may dominate the conduction mechanism. As presented in Figure 4, the 0.01 ≤ x ≤ 0.07 samples have a larger grain size and lower grain boundary than the sample with x = 0. The textures were enhanced, leading to a reduction in the amount of grain boundaries and interfaces, helping to reduce  E a [50]. It suggested that the increase of BNT content play a significant role of E a . At high temperature, the σ decreased when the temperature increased due to the release of the weakly bond oxygen according to Kroger-Vink notation [51], , and e 0 are the O-site substitution with O, oxygen vacancies and electrons, respectively. Due to the fact that the (1-x) DyBCO−xBNT samples exhibited the p-type conduction as will be shown in the next part. Following this behavior, the carrier concentration was decreased by the combination between electron (e 0 ) and hole (h � ) to give a low σ of the samples at high temperature. Similar behavior has been previously reported in oxide like LnBaCuMeO 5+δ (Ln = La, Pr, Nd, Sm; Me = Fe, Cu) [52][53][54], RE-123 (RE = Nd, Sm, Eu, Dy) [55][56][57][58][59], etc. The σ of the Dy-123 and Sm-123 turned up due to the orthorhombic-tetragonal (O/T) transition at high temperature when the oxygen partial pressure was below 10 −2 atm and 10 −5 atm, respectively [56,58]. Hence, with 1 atm flowing He gas, the phase transition from orthorhombic to tetragonal occurred around ~700 K for the RE-123 (RE = La, Nd, Eu, Dy, Ho, Er, Tm) [59]. As shown in Figure 7, at a temperature higher than 800 K, the increase of σ for all samples increased slightly with increasing temperature which was attributed to the phase transformation from Dy-123 (Pmmm) to Dy-123 (P4/mmm).
Seebeck coefficient (S) of (1-x)DyBCO−xBNT ceramic samples was measured as shown in Figure 9. The result showed that the S first decreased at low temperature range and then increased continuously at higher temperature. The sign of the S for all samples was positive which confirmed that the conduction mehanism was mainly governed by holes (p-type behavior). The sample which possessed lower σ also showed higher values of Seebeck coefficient. At low temperature, the S of all samples decreased with when the temperature rose. At low temperature range, the temperature dependence of the S for hole (p) single-band of the non-degenerate semiconductor [60] is explained by  [65] and Bi 2 Sr 2 Ca 1-x Y x Cu 2 O 8+δ [66] compounds were used to express the decrease of S with the increase of temperature. Above 560 K, the S of all samples increased when the temperature increased. This behavior was similar to the S of Y 1−x Pr x Ba 2 Cu 3 O 7−δ [61], YBa 2 Cu 3 O 7−δ [67], YLa x Ba 2-x Cu 3 O 7-δ [62], PrBa 2 Cu 3 O 7 [68] etc. The functional dependence of the S on the variable range hopping regime for an energy dependent density of states can be defined as [69]: and α, k B , and ρ 0 are the decay constant of the localized state, the Boltzmann constant and the density of states at E F , respectively. If the density of states at E F is not a rapidly varying function of the temperature, the S is expected to show a T 1/2 dependence. Another model is the semiclassical model with a single band, the S of RE-123 in the metallic side can be expressed as [69]: expression predicts a linear increase in S with the increasing temperature. As can be seen in Figure 9, the temperature independence of S were observed in the ceramics where x = 0.01 and 0.03 samples, indicating that there was narrow valence band around the Fermi energy E F . In this assumption, the temperature independent of S is dominated by the entropy of distribution of the charge carriers among available sites as provided by the modified Heikes formula [70][71][72][73]. For the thermal energy k B T are smaller than the on-site Coulomb repulsion (U) as S ¼ À ðk B = e j jÞ ln 2 À ðk B = e j jÞ ln ð1 À nÞ=n ½ � where n is number of electrons per Cu site, the conduction process involves hopping of d electrons from one Cu 2+ (d 9 ) ion to a Cu 3+ (d 8 ) ion, then entropy considerations lead to the above formula with n equal to the ratio of Cu 2+ ions to the total number of Cu ions. If all copper atoms can be considered equivalent, then n ¼ 2ð1 þ δÞ=3 for RE-123 [61,62,72]. In case of the Coulomb interaction (U) are smaller than the thermal energy k B T, the S is defined [62,73,74] as S ¼ ðk B = e j jÞ ln n=ð2 À nÞ ½ �, where n is the number of electrons (per unit cell) in the top band as n ¼ 1 þ δ. Following this model, the S related directly with oxygen deficiency or oxygen content of RE-123. At high temperature, the oxygen content of RE-123 tended to reduce when the temperature increased, and thus the increase of the S were observed as shown in Figure 9, corresponding to the narrow band model. Similar behavior of S has been previously reported in YLa x Ba 2-x Cu 3 O 7-δ [62], YBa 2 Cu 3 O 7−δ [63,73,[75][76][77], Pr x Y 1−x Ba 2 Cu 3 O 7−δ [74,78] at high temperature (300 K ≤ T ≤ 1200 K).
The combined effect of electrical conductivity and Seebeck coefficient on the thermoelectric performance is illustrated by the temperature dependence of power factor (PF) as calculated from σS 2 (see Figure 10). The power factor values of the (1-x)DyBCO−xBNT ceramics were found to be weakly dependent on temperature. The maximum power factor values for x = 0, 0.01, 0.03, 0.05, and 0.07 samples are 6.30, 20.91, 36.07, 12.01, and 17.18 µW/mK 2 , respectively. Despite the relatively small S, the power factor of 0.97DyBCO−0.03BNT ceramic showed highest values regardless of temperature which indicated the greater influence of the electrical conductivity upon BNT doping.
The total thermal conductivity (κ T ) of the ceramics was calculated from the measured thermal diffusivity (D), the specific heat capacity (C p ) and density (d) using the relation κ T ¼ DC p d. The values were plotted as a function of temperature from 300 to 1000 K as shown in Figure 11. The results show that low κ T (~2.6-3.8 W/m-K) of the ceramics were observed near room temperature. This may be compared to the κ T of pure Dy-123 annealed under flowing oxygen which was previously reported to be about ~4 W/m-K at 300 K [20] and ~5 W/m-K at 150 K [79]. It is also interesting to note that all ceramic samples without oxygen flowing have a lower κ T at low temperature. The κ T values of all ceramic samples decreased with increasing temperature, indicating that the phonon scattering from lattice vibration became more active. For the ceramic sample with x = 0.05, the κ T is ultra-low to 0.32 W/m-K at 973 K (thermal diffusivity = 0.00142 cm 2 /s and heat specific capacity = 0.36 J/gK). It is well known that the thermal conductivity includes two parts: lattice thermal conductivity (κ l ) and electronic thermal conductivity (κ e ). The κ l corresponds to the propagation of phonons in the three spatial dimensions through the crystal lattice and is defined as where C v is the specific heat per unit volume, v s is the velocity of sound, and l ph is the phonon mean free path. The κ l is governed by the combination of phonon-phonon scattering, point defect scattering or boundary scattering [3], and is expressed as 1 l ph ¼ 1 l defect þ 1 l boundary þ 1 l phonon . Below 573 K, the κ T of the sample with 0.01 ≤ x ≤ 0.07 has higher values than the undoped sample, which was possibly due to the reduction of boundary scattering. If we consider the effect of porosity and use the simplified Maxwell-Eucken model to calculate thermal conductivity of the solid phase (by assuming zero thermal conductivity of pores) according to the equation [80,81], κ m ¼ κ s ð1 À V p Þ=ð1 þ V p =2Þ, where κ m , κ s , and V p are the measured thermal conductivity, the thermal conductivity of the solid phase, and the pore volume fraction, respectively. It could be shown that a higher pore volume fraction decreased the thermal conductivity of the ceramics. Therefore, the ceramic sample with x = 0 has the lowest thermal conductivity with the increase of BNT content. Above 573 K, the presence of secondary phase, heavy element and/or point defects which act as scattering canters, would be another factor for the reinforcement of phonon scattering, resulting in the reduction of the thermal conductivity. These thermal conductivity values are among the lowest known for prospective thermoelectric oxides. However, the thermal conductivity of the samples slightly increased with increasing measuring temperature above 873 K (Figure 11), which corresponded to the phase transition, i.e. from RE-123 (Pmmn) to RE −123 (P4/mmm) [55][56][57][58][59]. Based on several studies on similar material systems, at room temperature, the thermal conductivity of Sm-123 was 4.50, 4.00 and 3.00 W/mK for 7-δ = 6.11, 6.85, and 6.73, respectively [64]. Thermal conductivity of Eu-123 was 4, 3.67, 3.33, and 2.73 W/mK at 300 K for 7-δ = 6.45, 6.97, 6.85, and 6.37, respectively [82]. The phase transitions of RE-123 from orthorhombic to tetragonal phase occurred at 7-δ = 6.45 and 6.5 for RE = Eu and Sm, respectively [56,57]. It suggested that the thermal conductivity of RE-123 not only depended on temperature and oxygen content, but also on the charge carriers and phonons and their interactions, as well as on the oxygen ordering [82].
The lattice thermal conductivity is calculated by subtracting the electrical thermal conductivity from the total thermal conductivity (κ l ¼ κ T À κ e ) as shown in Figure 12(c). Usually, the κ e is calculated from the Wiedemann-Franz law i.e. κ e ¼ σLT where Lorenz number (L) is 2.45 × 10 −8 WΩ K −2 , σ is the electrical conductivity, and T is the absolute temperature. For all the samples, the κ e increases with increasing temperature, as shown in Figure 12(a), and the κ e of the 0.01 ≤ x ≤ 0.07 samples are higher than the un-doped sample. However, it could be noticed that the estimated κ e values for all samples were less than 20% of the κ T except the sample with x = 0.03. This shows that the total thermal conductivity value came mainly from the lattice vibrations as seen from Figure 12(d). The highest κ e value was observed for the sample with x = 0.03 due to its highest σ at 765 K, as shown in Figure 12(b), the κ e =κ T was about ~ 80% at 765 K. This showed the effect of κ e behavior of this sample. Similar phenomena have been reported for thermoelectric material due to its complex structure and/or multiphase [83,84].
The combination of electrical and thermal transport properties allows to estimate the figure of merit, ZT ¼ ðσS 2 =κÞT, as a function of temperature in the (1-x) DyBCO−xBNT ceramics ( Figure 13). The ZT value tended to increase with increasing temperature within the measured temperature range. The addition of BNT was found to improve ZT in DyBCO system. For comparison, the highest ZT values (~5.63 x 10 −2 at 866 K) was observed in the 0.97DyBCO−0.03BNT sample, which was about 4.12 times greater than the ZT value of ~1.38 x 10 −2 for DyBCO at the same temperature range. Comparing to other RE-123 compound, this study was comparable to the previously reported results of PrBCO (ZT = 0.03) and YBCO (ZT = 0.008) at 773 K [80]. It can be obviously seen that the ZT of 0.97DyBCO − 0.03BNT sample was found to be higher than the un-dope RE-123 (RE = Y, Pr and Dy) compounds. However, this compound may not be a suitable candidate for use as thermoelectric material due to their low electrical conductivity and Seebeck coefficient. In order to improve ZT, changing stoichiometry and/or doping [9][10][11][12][13] in order to optimize the carrier concentration may be a viable solution. Following by this process, the thermoelectric properties of Dy-123 compounds would be improved in the future. Compositional and band structure engineering by a more appropriate dopant type and concentration may need to be further explored for the DyBCO compound considering its advantage of very low thermal conductivity at high temperature.

Conclusions
Dysprosium barium copper oxide-bismuth sodium titanate ((1-x)DyBCO−xBNT) ceramics, where x = 0, 0.01, 0.03, 0.05, and 0.07 mole fraction, were successfully synthesized by a solid-state reaction and sintering method. In all cases, the Dy-123 ceramics were identified as the main crystalline phases. The samples with 0.01 ≤ x ≤ 0.07 showed slightly higher density values than the undoped sample, suggesting that BNT helped improve the densification process. Also, the BSE-SEM images of ceramics exhibited the distribution of Dy-211 phase on the Dy-123 matrix due to the BNT doping. The electrical conductivity of the Dy-123 samples was enhanced by the amount BNT content with 0.01 ≤ x ≤ 0.03, and the maximum electrical conductivity (14,200 Ω À 1 m À 1 ) was obtained for the 0.97DyBCO-0.03BNT sample. The values of Seebeck coefficient are positive for all samples, showing that they are p-type conductors. Due to its highest power factor with a low thermal conductivity, the highest figure of merit (ZT) of the sample with x = 0.03 was found to be 5.63 × 10 −2 at 866 K. The ZT was comparatively small for the practical application as the high temperature thermoelectric materials. However, due to its attractively low thermal conductivity, this material can still be further optimized in terms of the power factor by doping and/or changing the stoichiometry.