See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/257328184 High-temperature thermoelectric properties of Ca1−xPrxMnO3−δ (0⩽x 0:15) leads to an increase of the resistivity again There are several concepts used for the interpretation of conducting phenomenon in perovskites The temperature dependence can be described using the small polaron model given by Mott [8] According to this theory, the resistivity is expressed by, r Ea ¼ C exp ; T kB T where C is given by C¼ kB expð2gRÞ: Ne2 a2 xð1 À xÞnph Here, e is the absolute value of the electron charge, N is the number of ion sites per unit cell volume (Mn sites), a is an average intersite distance for polaron hopping obtained from the relation a=(1/N)1/3, g is the electron wave function decay constant, nph is the optical phonon frequency, x is the fraction of available sites occupied by small polarons (assumed equal to the Mn3+ concentration), and Ea is an activation energy for hopping conduction By plotting log(r/T) as a function of 1/T, one can determine the activation energy, Ea, in the temperature range from 300 to 700 K, as seen in Fig 3a Fig 3b shows the activation energy of doped samples as a function of x in the Ca1Àx Prx MnO2:98 solid solutions A tendency of the activation energy to increase with increasing doping Pr concentration (x) is seen in Fig 3b This increase indicates that an increase of the Mn3+ concentration is favorable for the formation of polarons in this temperature interval The well-observed jump of Ea at xB0:2 indicates that the small polaron is more stabilized for xX0:2: Fig shows the temperature dependence of the Seebeck coefficient for Ca1Àx Prx MnO2:98 (x ¼ À 0:67), and reveals that the dominating electrical carriers at room temperature are electrons for all samples except for x ¼ 0:67: At high temperatures, the conducting character is n-type for the whole system (including both electron- and hole-doping samples) This is an interesting feature of HT behavior in comparison with the symmetric property at temperatures below room temperature [6], where n- (or p-) conducting type prevails in the case of xo0:5 (or x > 0:5) The dominating electron conducting character shows that the carrier mobility rather than their concentration governs HT transport ARTICLE IN PRESS B.T Cong et al / Physica B 352 (2004) 18–23 21 -2.5 Ca1-xPrxMnO2.98 -3.5 x=0 x=0.05 x=0.10 x=0.15 x=0.20 x=0.40 x=0.67 -50 α (µVK-1) log[ρ/T (K-1Ω cm)] -3.0 -100 Ca1-xPrxMnO2.98 -4.0 -200 -4.5 -250 200 -5.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 600 800 1000 T (K) 1200 1400 Fig Temperature dependence of the Seebeck coefficient, a, for Ca1Àx Prx MnO2:98 (x ¼ À 0:67) sintered bodies the HT limit, assuming that the energies of the Jahn–Teller (DJT ) and the Coulomb interaction (U) are smaller than the thermal energy ðDJT ; U5kB TÞ: kB À r0 À x a ¼ À ln : r0 À þ x e 0.15 Ea (eV) 400 103/T (K-1) (a) 0.10 0.05 0.1 (b) x=0 x=0.05 x=0.10 x=0.15 x=0.20 x=0.40 x=0.67 -150 0.2 0.3 0.4 x 0.5 0.6 0.7 Fig (a) log(r/T) vs TÀ1 for Ca1Àx Prx MnO2:98 (x ¼ À 0:67) (b) Activation energy, Ea, as a function of doping Pr concentration for Ca1Àx Prx MnO2:98 (x ¼ À 0:67) in the temperature range from 300 to 700 K behavior The Seebeck coefficients of the small polaron conduction system at HT can be interpreted by Marsh and Parris’s theory [9], developed for a strong coupling system This theory is applied for the case that the B-site transition metal of perovskite ABO3 has the number of electron, n, in the 3d manifold, 3pnp5: We used the following formula for the Seebeck coefficient in Here, r0 is the number of eg electrons per Mn3+ site, and x is the doping concentration The comparison between theoretical and experimental values for the concentration dependence of Seebeck coefficient is shown in Fig A good agreement is observed for r0 ¼ 1:3: The HT theory [9] appears to describe our experiments well Fig demonstrates the temperature dependence of the thermal conductivity, l The contribution from the electronic thermal conductivity, le, is calculated by using Wiedemann–Franz’s law as given in Ref [3] For all samples the phonon contribution lph=lÀle is much more important than the electronic one Fig shows the temperature dependence of the power factor, sa2 ; calculated from the measured Seebeck coefficient and the electrical conductivity s ¼ rÀ1 : The power factor increases as the temperature increases, and reaches the value of 2.43 Â 10À4 WmÀ1 KÀ2 for the electron-doping compound (xo0:5) with x ¼ 0:15 at 1200 K This quantity is sufficiently small for the hole-doping samples with x > 0:5 (for x ¼ 0:67; power factor is near zero) ARTICLE IN PRESS B.T Cong et al / Physica B 352 (2004) 18–23 22 ρ0 = 1.3 2.5 -100 Ca1-xPrxMnO2.98 -200 2.0 (x 10-4 W m-1K-2) α (µVK-1) ρ0 = 1.05 573 K 873 K 1073 K 1273 K -300 1.0 0=1.3 1.5 Ca1-xPrxMnO2.98 x=0 x=0.05 x=0.10 x=0.15 x=0.20 x=0.40 x=0.67 0=1.05 0.5 -400 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 x 0.0 Fig The concentration dependence of the Seebeck coefficient for Ca1Àx Prx MnO2:98 (x ¼ À 0:67) Ca1-xPrxMnO2.98 3.5 200 400 600 800 1000 1200 1400 T (K) Fig Temperature dependence of the power factor, sa2, obtained from the measured Seebeck coefficient and electrical conductivity data e x=0 x=0.05 x=0.10 x=0.15 x=0.20 x=0.40 x=0.67 2.5 2.0 1.5 1.2 1.5 Z (x 10-4 K-1) (W m-1 K-1) 3.0 1.0 0.5 0.0 200 0.9 0.6 0.3 400 Fig Thermal (x ¼ À 0:67) 600 800 1000 T (K) conductivity, l, 1200 1400 0.0 of Ca1Àx Prx MnO2:98 200 400 600 800 1000 1200 1400 T (K) Fig Figure of merit, Z, of Ca1Àx Prx MnO2:98 as a function of temperature The temperature dependence of the figure of merit, Z, in this system is plotted in Fig Z increases with increasing praseodymium fraction from to 0.15 A doping level x > 0:15 leads to a strong reduction of Z This quantity is near zero for x ¼ 0:6: room temperature In view of application as a high-temperature thermoelectric material, the large figure of merit of Z ¼ 1:5 Â 10À4 K À1 for x ¼ 0:15 at T ¼ 1100 K indicates good possibilities Conclusions Acknowledgements Ca1Àx Prx MnO3Àd perovskite compounds were prepared and their thermoelectric properties were investigated in the high-temperature region It was shown that the observed HT transport properties are much different from those in the region below The author (B.T Cong) thanks the JAIST-HUS collaboration program for supporting his short visit at JAIST, where a part of this work was done The help of the VNU Asia Research Center is also acknowledged ARTICLE IN PRESS B.T Cong et al / Physica B 352 (2004) 18–23 References [1] C.N.R Rao, B Raveau (Eds.), Colossal Magnetoresistance, Charge Ordering and Related Properties of Manganese Oxides, World Scientific, Singapore, 1998 [2] M Ohtaki, H Koga, T Tokunaga, K Eguchi, H Arai, J Solid State Chem 120 (1995) 105 [3] P.X Thao, T Tsuji, M Hashida, Y Yamamura, J Ceram Soc Japan 111 (2003) 544 [4] C Martin, A Maignan, M Hervieu, B Raveau, Phys Rev B 60 (1999) 12191 23 [5] E Pollert, S Krupicka, E Kuzmicova, J Phys Chem Solids 43 (1982) 1137 [6] Z Jirak, S Krupicka, Z Simsa, M Dlouha, S Vratislav, J Magn Magn Mater 53 (1985) 153 [7] D Vega, G Polla, A.G Leyva, P Konig, H Lanza, A Esteban, J Solid State Chem 156 (2001) 458 [8] N.F Mott, E.A Davis, Electronic Processes in Non-crystalline Materials, Clarendon Press, Oxford, 1971 [9] D.B Marsh, P.E Parris, Phys Rev B 54 (1996) 16602