Pharmaceutical Sciences Claire Jarry and Matthew S. Shive
11.2 Oxides as Potential
11.2.4 Large Thermopower in Metallic Oxides: The Misfi t Layer Oxides
NaxCoO2 is at the origin of the search for new thermoelectric oxides. NaxCoO2 is a layered material with CoO2 layers of tilted edge-shared octahedra separated by randomly fi lled Na layers.
Two models have been proposed to explain the large S value.
Th e fi rst one takes into account the spin and orbital degeneracies associated to a mixture of low spin Co3+ and low spin Co4+, which is responsible for a large entropy and therefore a large S [8]. Th is
model should be applied only for localized systems and cannot explain the metallicity of NaxCoO2. Th e second one has been proposed by Singh who calculated the band structure of NaxCoO2
[16]. Due to the rhombohedral symmetry of the CoO2 layers, the t2g orbitals are split in two sublevels. Th ere would therefore be two types of carriers, light ones in the eg′ band responsible for metallicity, and heavy ones in the a1g band responsible for a large thermopower.
Th e misfi t layered oxides have been discovered in our labora- tory a decade ago [3]. Th eir structure has the same CoO2 layers of tilted edge-shared octahedra, separated in this case by NaCl-like layers (Figure 11.8). Th ere can be three or four separating layers.
Recently, new misfi ts with two separating layers have been reported [17,18]. Th e structure can be described with two monoclinic sublattices, with common a, c, and b parameters but 100
0 200 400 600 800 1000 1200
150 200
x= 0.0 x= 0.05 x= 0.3
T (K) Pr1−xCaxCrO3
S (μV/K)
250 300 350
FIGURE 11.5 S(T) of the Pr1−xCaxCrO3 series.
400 350 300 250 200 150 100
300 350 400 450 500 T (K)
550 600 650 700 Pr0.95Ca0.05CrO3
Pr0.7Ca0.3CrO3
S (μV/K)
FIGURE 11.6 S(T) measured up to 700 K of Pr1−xCaxCrO3 (x = 0.05 and 0.3).
0.0
−100 0 100 200 300 400 500 600 700 800 900 1000
0.1 0.2 0.3
x (Ca concentration)
0.4 0.5
Pr1−xCaxCrO3
Calculated value taking orbital degeneracy Calculated value from Heikes formula
S (μV/K)
FIGURE 11.7 S as a function of the Ca2+ concentration. Th e solid line corresponds to the Heikes formula (Equation 11.1), and the dotted line to the Marsh and Parris model, which takes into account the spin and orbital degeneracies (Equation 11.2).
CoO2 S2
b2
b1
S1
CaO CoO
CaO
CoO2
FIGURE 11.8 Schematic description of the misfi t structure of [Ca2CoO3][CoO2]1.62, with the CoO2 layers and the NaCl-like layers.
incommensurate b parameters, with the ratio b1/b2∼ 1.6–2 (b1 for NaCl-like layer and b2 for CoO2 layer).
Th e misfi t oxides possess common features with NaxCoO2: they are metallic, with a large thermopower at room tempera- ture [4]. Th e aim of our work was to dope the CoO2 layers and understand the evolution of S (and r) with doping.
11.2.4.1 Infl uence of Doping
Substitutions take place most of the times in the NaCl-like layers, except for the case of Rh, as detailed in the following discussion. The doping of the CoO2 layers is therefore induced by the charge balance between the two sublattices: the NaCl- like layers are positively charged (a, which is unknown), while the CoO2 layers is negatively charged, the two sublat- tices being electrostatically bounded. Taking into account this charge balance, the following equations can be written for the Co valency:
= + = − α +
Co
1 2
3 4
v x b b/
where x is the Co4+ concentration.
x depends both on a and on the b1/b2 ratio, where b1 and b2 are the b parameters of the NaCl-like layers and CoO2 layers, respec- tively. Another important parameter is the oxygen stoichiome- try, which directly aff ects a.
Th e investigation of the diff erent families of misfi ts has shown a general trend. First, the thermopower does not change much, from +90 μV/K for [Tl0.81Co0.2Sr1.99O3]RS[CoO2]1.79 [19] to 170 μV/K for [Ca2Co0.6Ti0.4O3][CoO2]1.62 [20]. Second, two diff erent fami- lies of behaviors are observed. Some misfi ts show a metallic behavior down to low T (2 K), and a small positive magne-
toresistance (MR), as for [Tl0.81Co0.2Sr1.99O3]RS[CoO2]1.79 and [Bi2Ba1.8Co0.2O4][CoO2]2 [21]. On the other hand, most of them show a strong increase of resistivity at low T, with a strong nega- tive MR. Th e thermopower is always smaller in the fi rst family.
Due to the large number of unknown parameters (oxygen stoichiometry in the two sublattices, cobalt valency in the NaCl- like layer, among others), it is very diffi cult to precisely know the Co valency in the CoO2 layer and check the validity of the Koshibae’s formula [8]. We have nevertheless found that, for a given family of misfi t, S always increases when b1/b2 decreases (Figure 11.9).
Th e same trend is observed in the [Pb0.7Sr2−xCaxCo0.3O3] [CoO2]b1/b2 system (Figure 11.10) where S increases from S = 120 μV/K for x = 0 (b1/b2 = 1.79) to S = 165 μV/K for x = 2 (b1/b2 = 1.62) [22]. Also, this evolution is observed from 110 μV/K for [Sr2CoO3][CoO2]1.80 (b1/b2 = 1.80) to 120 μV/K for [Ca2CoO3] [CoO2]1.62 (b1/b2 = 1.62) [23].
Following the vCo equation, vCo = x + 3 = −(a/(b1/b2)) + 4, x theoretically decreases when b1/b2 decreases. From the Koshibae’s formula, S increases when x decreases. Th e results presented here can therefore qualitatively be understood in this frame- work: S should increase when b1/b2 decreases.
For a constant b1/b2, it is also possible to modify a, and thus vCo. By doping [Ca2CoO3][CoO2]1.62 with Ti4+ [20], or Pb3+, b1/b2
is unchanged (1.62), but S is equal to 165 μVK with Ti4+ or 160 μV/K for Pb3+, instead of 120 μV/K. If the oxygen content is unchanged, a is increased by the substitution, and vCo decreases, consistently with an increase of S through the Koshibae’s formula.
Recent experiments of annealing and titration by Karppinen et al. have shown that doping indeed modifi es the S value and that the smaller content of Co4+ corresponds to the larger S [24].
0
−20 0 20 40 60 80 100 120 140 160
50 100 150
1.7 90 100 110 120 130 140
1.8 1.9 2.0
b1/b2
T (K)
200 250 300
BiPb/Ca/Co/O
Bi/Ca/Co/O
Bi/Sr/Co/O Bi/Ba/Co/O
BiCa BiPbCa
BiSr
BiBa
S (μV/K) S300k (μV/K)
FIGURE 11.9 S(T) of the Bi-based family of misfi t. Inset: S at 300 K as a function of b1/b2.
Th e quantitative analysis of S as a function of doping can unfortunately not be made here due to the number of unknown quantities. Other techniques are now needed to evaluate the Co4+ concentration and make a more quantitative analysis.
11.2.4.2 Importance of Low Spin State
Following the generalized Heikes formula, the large entropy associated to the low spin states of Co3+ and Co4+ in the CoO2
layers would be at the origin of the large thermopower.
Interestingly, rhodium can partially [25] or totally be substituted to cobalt in the CoO2 layer [26]. Rhodium is isoelectronic to cobalt, and always low spin, with Rh3+ (t2g6) and Rh4+ (t2g5) electronic confi guration. We have thus investigated the magne- totransport properties of [Bi1.95Ba1.95Rh0.1O4][RhO2]1.8, knowing that le Rh species are in the low spin states, to compare them to the cobalt misfi ts [27].
Th e material is metallic and shows a large S of +90 μV/K at 300 K (Figures 11.11 and 11.12). Th ese properties are very close to
the ones measured in BiBaCoO [21], and this similarity is indi- rect proof of the low spin states proposed in the case of cobalt misfi ts. Also, a small positive MR of +5% is observed at low tem- perature in a magnetic fi eld of 7 T. Th is is, to our knowledge, a unique case of MR in the rhodium oxides, and this emphasizes the peculiarity of the transport properties observed in these CdI2-like layers.
11.2.4.3 Electrical Resistivity and Thermal Conductivity
Two different kinds of behaviors are observed in the misfits.
At low temperature, only two misfits measured so far are metallic down to 2 K [19], or with a small increase of resistiv- ity at low temperature [21], associated with a small positive MR. All the others present a transition to a more resistive behavior below 100 K, associated to a strong negative MR (−90% at 2.5 K in 7 T for BiCaCo [28]). In most of them, an increase of Seebeck coefficient is associated to an increase of
0 0 40 80 120 160 200
0 50 10−2 10−1 100 101 102 103 104 105 106
50
(a) (b)
100 150 200 250 300 350 100 150 200
T (K) T (K)
x= 0.0 x= 0.5
x= 1.5 x= 2.0
x= 0 x= 0.5 x= 1.5
x= 2
250 300 350 S (μV K−1)
r (Ω cm)
FIGURE 11.10 (a) r(T) of the Pb/Sr/Ca/Co/O misfi ts; (b) S(T) of the Pb/Sr/Ca/Co/O misfi ts.
100 200
T (K)
300 400
00 5 10 15 20
r (mΩ cm)
FIGURE 11.11 r(T) of the Bi/Ba/Rh/O samples.
00 20 40 60 80 100
50 100 150
T (K)
200 250 300
S (μV K−1)
FIGURE 11.12 S(T) of Bi/Ba/Rh/O.
the resistivity and a transition to a more localized behavior, in the whole temperature range, as shown in Figure 11.10a for the PbSrCaCoO series. Nevertheless, in all these materials, the resistivity remains in the same range at room temperature with r ∼ 10–100 mΩ cm.
Th e thermal conductivity measured in polycrystals is always small with k ∼ 2–3 W/m/K at 300 K (Figure 11.13). Following the Wiedemann-Franz law, it can be shown that the electronic part of the thermal conductivity is very small, with kel ∼ 0.03 W/m/K at 300 K. Th ese small values are close to the ones reported in disordered materials [29] and show that these materials could be good example of phonon glasses and electron crystals (PGEC) [30].
Combining all these values, maximum power factors close to 2 × 10−4 W/m/K2 can be obtained at 300 K. By optimizing the texturation process in these materials, ZT values close to 1 have been reported [5].
11.2.5 SrRuO3: A Metallic Perovskite