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Calcium-induced cation ordering and large resistivity decrease in Pr0.3CoO2
Journal of Physics and Chemistry of Solids 96-97 (2016) 10–16
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Calcium-induced cation ordering and large resistivity decrease in Pr0.3CoO2 Petr Brázda a,n, Lukáš Palatinus a, Jan Drahokoupil a, Karel Knížek a, Josef Buršík b a b
Institute of Physics AS CR, v.v.i., Na Slovance 1999/2, 182 21 Prague 8, Czech Republic Institute of Inorganic Chemistry AS CR, v.v.i., Husinec-Řež 1001, 25068 Řež, Czech Republic
art ic l e i nf o
a b s t r a c t
Article history: Received 21 December 2015 Received in revised form 4 March 2016 Accepted 29 April 2016 Available online 30 April 2016
Structure of layered cobaltates Pr0.3CoO2 and (PrCa)0.3CoO2 were investigated by electron diffraction tomography and powder X-ray diffraction. The effect of the calcium substitution on thermoelectric properties was evaluated. The structure consists of hexagonal sheets of edge-sharing CoO6 octahedra interleaved by cationic monolayers. The cations form a 2-dimensional a√3 a√3 superstructure in the a–b plane. While Pr0.3CoO2 showed no layer order in the [001] direction, introduction of calcium resulted in the formation of a superstructure spanning over six cationic layers along the [001]. This superstructure model appears to be valid also for the description of the superstructures of CaxCoO2 and SrxCoO2 with x about 1/3. Thanks to the increased number of charge carriers, the substitution of Ca2 þ for Pr3 þ significantly lowers the electric resistivity, while keeping quite high thermopower around 100 μV K 1, though the character of resistivity remained semiconducting. & 2016 Elsevier Ltd. All rights reserved.
Keywords: Thermoelectric cobaltate PrxCoO2 Electron diffraction tomography Powder X-ray diffraction Cobalt oxide
1. Introduction Layered cobaltates with mixed-valent Co3 þ /4 þ atoms are a group of materials with large thermoelectric power [1]. Our group successfully prepared Ln0.3CoO2 (Ln¼ La, Pr, and Nd) by solid state ion exchange reaction from γ-NaxCoO2 (P63/mmc symmetry) [2] and showed that these materials possess large Seebeck coefficient reaching 175 μV K 1 and are thermally stable up to 800 K [3–5]. Application of Ln0.3CoO2 materials for thermoelectric conversion is limited by their high electrical resistivity. The partial substitution of Ca2 þ for Ln3 þ may increase Co valency and thus the chargecarrier concentration. This could eventually lead to a decrease of electrical resistivity and possibly to a change of the semiconducting behaviour of Ln0.3CoO2 to metallic. The substitution of Ca2 þ for Pr3 þ was selected because of the similar ionic radii of these cations. Intercalated cations in Me1/3CoO2 (Me ¼ Ca, Sr, Ba, La, Pr, and Nd) form the a√3 a√3 superstructure (Fig. 1) [3,4,6–9]. The cationic arrangement in the a–b plane is well developed for this superstructure and therefore frequently discussed in the literature. To the best of our knowledge, the order along [001] direction for the a√3 a√3 superstructure has not been discussed in the literature except for our recent works dealing with La0.3CoO2, where we used powder X-ray (PXRD) and neutron diffraction [5] and n
Corresponding author. E-mail address: [email protected] (P. Brázda).
http://dx.doi.org/10.1016/j.jpcs.2016.04.012 0022-3697/& 2016 Elsevier Ltd. All rights reserved.
electron diffraction tomography (EDT) [10]. In the latter work we theoretically deduced some limitations of the layer stacking sequences with respect to the cationic site occupancy (P1 and P2, Fig. 1) [10]. The obtained experimental results for La0.3CoO2 show that there is no order of the cationic layers along the [001] direction in this material. This contrasts with the calcium and strontium analogues, where the maxima of diffracted intensity proving the existence of the order along c may be observed in both PXRD [7,11,12] and selected area electron diffraction (SAED) [6,7,13]. All the published SAEDs are similar and may be interpreted as a result of an R-centred arrangement of cations with periodicity either equal to three CoO2 layers (indicating that the cations would have to occupy the P1 site, which is in disagreement with powder XRD data) [7] or equal to six CoO2 layers assuming presence of a symmetry operation of the structure, which leads to the systematic absences for diffractions with l¼2n þ1 (in this case occupancy of the P2 site would be allowed). In this article, we investigate the cationic arrangement in Pr0.3CoO2 and (PrCa)0.3CoO2 (the ratio Pr:Ca is about 1:1). We show that while the stacking of layers in Pr0.3CoO2 is completely random along [001] in analogy to its lanthanum analogue, substitution of calcium for praseodymium in the structure induces ordering of the cations along the [001] direction. We also show that the published powder X-ray diffractogram of Sr0.35CoO2 [7] can be explained with the same structural model for the stacking order. Further, measurement of conductivity of the Pr0.3CoO2 and (PrCa)0.3CoO2 materials showed that introduction of Ca into the system leads to a significant decrease of resistivity of (PrCa)0.3CoO2
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were transferred onto the Cu TEM grids. Selected area electron diffraction was simulated in the programme JEMS. Electrical resistivity and thermoelectric power were measured using a four-probe method with a parallelepiped sample cut from the sintered pellet. The electrical current density varied depending on the sample resistivity between 10 1 A cm 2 (metallic state) and 10 7 A cm 2 (insulating state). The measurements were performed on sample cooling and warming using a close-cycle cryostat working down to 3 K, see Ref. [18] for details.
3. Results and discussion 3.1. Transmission electron microscopy
Fig. 1. Basic building block of the a√3 a√3 superstructure. It is a three times expanded unit cell of γ-NaCoO2 (P63/mmc symmetry). The superstructure in Me1/3CoO2 (only 1/3 of the P2 (green) cation sites in a layer are occupied) is caused by ordering of the vacancies. The P1 sites (sites between Co atoms) are shown as black hollow spheres. Cobalt atoms are shown with their coordination polyhedron. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
in comparison to Pr0.3CoO2.
2. Experimental The materials were prepared by an ionic exchange between sodium cobaltate and Ca and Pr nitrates (γ-Na0.77CoO2, a ¼2.841 (1) Å, c ¼10.802(5) Å [14]) was mixed with anhydrous Pr(NO3)3 or with a mixture of anhydrous Pr(NO3)3 and Ca(NO3)2 in a dry-box. The molar ratios Na0.77CoO2:Pr(NO3)3:Ca(NO3)2 were 1:0.5:0 (Pr0.3CoO2) and 1:0.7:0.3 ((PrCa)0.3CoO2). Preliminary experiments revealed, that the rate of the ionic exchange of Ca is higher than that of Pr, therefore in order to achieve Pr:Ca¼1:1 stoichiometry in (PrCa)0.3CoO2, the excess of Ca over Pr should be used. The final annealing was done for two days at 340 °C for Pr0.3CoO2 and at 310 °C for (PrCa)0.3CoO2. The unreacted nitrates were washed out repeatedly with large amount of water using an ultrasonic treatment. The products were isolated by sedimentation in water and then dried at 120 °C for 16 h. For the transport measurement experiments, the materials were pressed into pellets and sintered at 300 °C for one day. The density (compactness) of the pellets is affected by the low sintering temperature and it was about 60– 65%. Powder X-ray diffraction was carried out with the Bruker D8 (Cu Kα radiation, λ ¼1.5418 Å, secondary monochromator, BraggBrentano geometry) and PANalytical X’Pert (Co Kα radiation, λ ¼1.790 Å, transmission geometry, Kapton sample support) diffractometers. Rietveld analyses of the PXRD data were performed with Fullprof software package [15]. Partial disorder of the cationic layer stacking was simulated by programme FAULTS [16]. Transmission electron microscopy (TEM) was conducted on a Philips CM120 transmission electron microscope with a LaB6 cathode operating at 120 kV. The microscope is equipped with a CCD Camera Olympus SIS Veleta with 14 bit dynamical range and with an EDAX SSD detector Apollo XLTW for EDS analysis. The electron diffraction tomography [17] was measured in the range from 50° to þ 50° and with the tilt step of 0.7°. The samples were used as they were or only very gently ground and then they
The Pr0.3CoO2 crystals show the a√3 a√3 superstructure. The lack of order along [001] of the superstructure diffractions (Fig. 2) is in accord with PXRD data (see below). Intergrowths with Co3O4 were frequently observed (Fig. S1). The Co3O4 crystals are frequently twinned according to the spinel-law. The observed twinning was perpendicular to only one out of the four possible threefold axes and this particular axis was parallel to the [001] direction of Pr0.3CoO2. For indexing purposes, it was therefore convenient to transform the cubic unit cell of Co3O4 to the hexagonal unit cell setting (H subscript), where the twinning three-fold axis becomes the c-axis. The transformation is then aH ¼ a/2 b/2, bH ¼b/2 c/2 and cH ¼ aþb þc. This situation is completely analogous to the behaviour of the Co3O4/La0.3CoO2 system [10]. Introduction of calcium into the praseodymium cobaltate induced a change of the ordering of the structure. While the a–b superstructure did not change, an appearance of maxima within the rods of diffracted intensity due to cationic superstructure clearly indicate that the stacking sequence is no longer random, but exhibits long-range order, albeit not perfect. The appearance of the diffraction patterns is similar to those published in the literature [6,7,13]. Based on the analysis of the possible ordering with cations in the P2 site we constructed two possible sequences of the cationic layers. The resulting structures have a six-layer periodicity with two interpenetrating R-centred cationic substructures (one substructure is composed of the cations located in the odd layers and the other one in the even layers). These two R-centred substructures may be either both obverse (or both reverse) or they can have the obverse-reverse relationship. These structures are shown in Fig. 3. The symmetry of the obverse-obverse (O–O) structure is C2/c1 and the symmetry of the obverse-reverse (O–R) structure is P6122. The lattice vector transformations from the average (P63/mmc) unit cell is aO–O ¼3a, bO–O ¼a þ2b, cO–O ¼3c for the O–O structure (dimensions of the cell are 3a a√3 3c with respect to the average structure unit cell) and aO–R ¼2aþb, bO–R ¼ a þb, cO–R ¼ 3c (a√3 a√3 3c) for the O–R structure. The simulations of the reciprocal space sections corresponding to h0l, – h–hl, and –hhl (O–O structure) and h0l, 0–kl, and –hhl (O–R structure) are shown in Fig. S2. All three sections are identical for the O–R structure (P6122 symmetry) and the patterns look like the patterns of an obverse-reverse twin, which is an intrinsic feature of the structure. The six-layer periodicity may be directly observed in these sections. Due to the lower symmetry, only the –h–hl and – hhl sections of the O–O structure are identical and show the sixlayer periodicity. The h0l section is different because the diffraction maxima with l ¼2 n þ1 are absent due to the presence of cglide plane. 1 Further details of the crystal structure may be obtained from FIZ Karlsruhe, 76344 Eggenstein-Leopoldshafen, Germany (fax: þ 49 7247-808-666; e-mail: crysdata@fiz-karlsruhe.de) on quoting the deposition number CSD-430226.
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Fig. 2. Reciprocal space sections of a Pr0.3CoO2 crystal: 0kl (a), h–2hl (b), and hk0 (c).
Fig. 3. Possible structures of ordered (PrCa)0.3CoO2 with the six-layer periodicity. Intercalated cations form in odd and even layers two R-centred arrangements, which can have the same orientation (O–O structure, C2/c symmetry) (a) or one is rotated by 180° with respect to the other (O–R structure, P6122 symmetry) (b). Cobalt atoms are shown with their coordination polyhedron.
Three crystals are shown here for illustration of the calcium induced ordering phenomenon in praseodymium calcium layered cobaltate. The crystals differ in the ratio between praseodymium and calcium. The ratio was obtained by EDS. The calcium rich crystal (Pr:Ca ¼3:7) shows well developed maxima within the superstructure diffraction rods, which triple the periodicity along c. The diffraction patterns correspond to the O–O structure (C2/c symmetry) twined by the two-fold axis parallel with [001], thus
creating an O–O/R–R twin (Fig. 4). Simulations of the reciprocal space sections together with their intensity profiles are shown in Fig. S3. The match between the experimental data and the simulations for O–O/R–R twin is good, in particular the difference in the geometry of the sections h0l and –h–hl agrees well with the twinned O–O (C2/c) structure, and cannot be explained by the O–R (P6122) structure. Because the same SAED patterns were observed for the pure Ca and Sr layered cobaltates, it appears that the O–O
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Fig. 4. Reciprocal space sections of a (Pr0.3Ca0.7)0.3CoO2 crystal: (a) h0l, (b) –h–hl, and (c) –hhl and their integrations (d): h0l green, –h–hl red, and –hhl blue. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
structure has the common arrangement with the divalent cations in the layered cobaltates. Increase of praseodymium (Pr:Ca ¼4:6) leads to a further blurring of the maxima causing significant overlap of the neighbouring diffractions, while the systematic absences due to the R-centred arrangement of the cations remain clearly observable (Fig. S4). Finally, the maxima corresponding to the triple periodicity along c vanish when praseodymium content reaches 70 at%. Instead, very weak maxima corresponding to the periodicity of the average structure emerge (Fig. S5). Various cation orderings with a similar level of complexity may be observed in related NaxCoO2 phases simultaneously with charge ordering of Co cations, when x is decreased below 1 [19– 22]. Na þ cations can occupy both P1 and P2 positions (see Fig. 1 for description of P1 and P2). Since the P1 position is less favourable due to the shorter Na-Co distance, the actual occupancies of P1 and P2 are determined by the competition of Coulomb repulsions between Na þ –Na þ within ab-plane and between Na þ –Co3 þ along the c-direction. The ordered distribution of Na þ and vacancies over P1 and P2 positions breaks the uniformity of Co coordination spheres and is the source of the Co charge disproportionation and ordering [23–25]. When x is decreased close to 1/3, the influence of Na þ –Na þ repulsion becomes less important and Na occupies solely the P2 position. In the case of LnxCoO2 the Ln3 þ –Co3 þ repulsion is even stronger, so the occupation of P1 is practically excluded. Since the ordering of Pr3 þ within the ab-plane is strictly regular and the number of vacancies is quite small (x is close to 1/ 3), the coordination sphere of Co remains identical for all Co positions. In the case of (PrCa)xCoO2, we did not detect any cell enlargement in the ab-direction, which would indicate any Pr–Ca ordering, so the distribution of Pr3 þ and Ca2 þ is random and the uniformity of coordination of all Co cations is preserved. Therefore, there is no significant driving force for Co charge ordering in
(PrCa)xCoO2 and actually no charge ordering is observed in our experiments. A spurious phase of cobalt oxide was observed as intergrowth with (PrCa)0.3CoO2 and during the survey of the sample in the TEM we succeeded to find also one grain of pure phase. Surprisingly, the diffraction pattern did not correspond to the trigonal Co3O4, but had a different cell metrics and hexagonal symmetry P63mc. We have attempted to solve the structure and the preliminary composition corresponds to Co5O8 assuming all atomic positions being fully occupied. To the best of our knowledge, a phase of cobalt oxide with this symmetry and lattice parameters (see below) has not been reported yet. We describe its structure in a separate report. Co5O8 forms oriented intergrowths with (PrCa)0.3CoO2 analogous to the intergrowths of Co3O4 with Pr0.3CoO2, thus [001]Co//[001]PrCa and [110]Co//[100]PrCa. It is important to note that we observed only the Co5O8 phase and no Co3O4 in the (PrCa)0.3CoO2 sample (see also powder XRD section). 3.2. Powder X-ray diffraction Powder X-ray diffractogram of Pr0.3CoO2 (Fig. 5, Cu radiation) revealed superstructure diffractions corresponding to the a√3 a√3 superstructure with the lattice parameters a¼ 4.8944 (5) Å and c ¼10.940(1) Å. The strongly asymmetric profile of these diffractions points to the disorder along [001], which was confirmed by TEM (see above). The absence of additional maxima superimposed on the slowly decreasing tail of the 100 diffraction is in agreement with the absence of such maxima in the EDT data. The Rietveld refinement showed that the material contains about 25 mol% of Co3O4. The structural parameters of Pr0.3CoO2 obtained by the Rietveld refinement are presented in Table 1. The diffractogram of (PrCa)0.3CoO2 measured in the Bragg-
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Fig. 5. Powder X-ray diffractogram of Pr0.3CoO2. Positions of the diffraction maxima of Pr0.3CoO2 (without the superstructure diffractions) and Co3O4 are marked by blue and red bars, respectively. Positions of the 100, 200, 210, 310, and 320 diffractions are marked by an asterisk. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Table 1 Structural parameters and selected bond lengths and angles of Pr0.30CoO2 refined by Rietveld method from X-ray diffraction data within the hexagonal space group P63/mmc. Atom coordinates: Pr 2d(2/3,1/3,1/4), Co 2a(0,0,0), O 4f(1/3,2/3,z). Agreement factors: Rwp ¼ 25.1%, χ2 ¼ 1.95.a a (Å)
2.8257(2)
Pr, occupation
0.30(2)
c (Å) Pr, Biso (Å2) Co, Biso (Å2) O, Biso (Å2) O (z)
10.9395(8) 0.39(9) 0.12(6) 0.50(9) 0.0934(5)
Co–O (Å) 6 Pr–O (Å) 6 O–Co–O (deg.) O–Pr–O (deg.) Co–O–Pr (deg.)
1.925(3) 2.366(4) 94.4(2) 73.3(2) 165.7(3)
(PrCa)0.3CoO2 are a ¼4.875(1) Å, and c¼ 32.692(3) Å (b restrained to a√3). Note that the intensity of the diffraction maxima is the same for the O–O and O–R structures, therefore it is not possible to distinguish between these two structures from the powder diffractogram. For Co5O8, we used the preliminary structure model obtained from the EDT data. It described the observed intensities satisfactorily. The obtained lattice parameters are a ¼5.65(2) Å and c¼8.75(5) Å. Introduction of Co3O4 into the fit did not improve the results. The reason of formation of Co5O8 instead of Co3O4 is not clear. The substantial differences in the materials preparation are pelletizing of Pr0.3CoO2 powder, different final annealing temperature and presence of calcium in (PrCa)0.3CoO2. Further, the amount of nitrates in the reaction mixture for preparation of (PrCa)0.3CoO2 was approximately two times higher than for the preparation of Pr0.3CoO2. So far, we were not able to identify what causes such principal change of the phase of cobalt oxide. Due to the strong preferred orientation the evaluation of the stacking disorder could not be done in FAULTS programme [16]. Therefore we chose powder diffraction data published in [7] obtained on Sr1/3CoO2 to estimate the level of Sr layers stacking order and to show that our structure model is valid also for this material. The simulation of the powder diffractogram of Sr1/3CoO2 is shown in Fig. 7 for three different probabilities that the next layer will correspond to the ordered O–O structure: 0.7, 0.8 and 0.9. Increasing disorder in the cationic layer stacking broadens the diffraction maxima associated with the cationic superstructure. The diffractograms obtained with probabilities 0.7 and 0.8 are very similar to the data presented in the work of Yubuta et al., which were obtained on Sr0.35CoO2 [7]. This together with EDT results indicate that our six layer structure model with the R-centred arrangement of the cations is valid not only for the calcium doped Pr0.3CoO2 but also for the strontium and calcium cobaltates. 3.3. Transport properties
a
Regions where the superstructure diffractions have non-zero intensity were excluded.
The resistivity and thermopower of Pr0.3CoO2 and (PrCa)0.3CoO2 are displayed in Fig. 8. Both samples exhibit localized character of resistivity, i.e. increasing resistivity with lowering temperature. The increase of the formal Co valency from 3.1 þ for Pr0.3CoO2 to 3.25 þ for (PrCa)0.3CoO2 (Pr:Ca about 1:1) and the corresponding increase of charge-carrier concentration is manifested by the
Fig. 6. Powder X-ray diffractogram of (PrCa)0.3CoO2. Positions of diffraction maxima of (PrCa)0.3CoO2 and Co5O8 are marked by blue and red bars, respectively. The most intense superstructure diffractions of (PrCa)0.3CoO2 are indexed in the monoclinic O–O cell. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Brentano geometry suffered from a very strong preferred orientation, which led to the observation of nearly only the 00lO–O diffractions. Therefore, we measured the sample in the transmission geometry and focused on the region where the 11lO–O diffractions occur (Fig. 6, Co radiation). The lattice parameters of
Fig. 7. Simulation of the powder X-ray diffractogram of Sr1/3CoO2 in programme FAULTS. A certain level of disorder is introduced into the stacking sequence of the cationic layers. The probabilities p that the next layer will correspond to the ordered structure are 0.7 (green), 0.8 (red), and 0.9 (blue). The probabilities of the other two possible transitions are both equal to (1–p)/2. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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not comparable with the best termoelectric materials, and namely lowering of resistivity by about 2 orders is needed for relevant applications.
4. Conclusion We have analysed in detail the layer stacking in praseodymium cobaltate and praseodymium calcium cobaltate. We observed that the cationic layers in Pr0.3CoO2 do not form any stacking order, similarly to its lanthanum containing analogue. Introduction of divalent calcium induces the ordering of the layers, which eventually leads to the formation of the 3a x a√3 3c superstructure with C2/c symmetry. Though the presence of the ordered structure is obvious from the EDT data, a substantial degree of disorder is still present, as documented by the diffuse diffraction intensity along [001] in the diffraction patterns. The degree of order decreases with increasing ratio Pr:Ca. Our structure model also explains well diffraction data published for pure calcium and strontium cobaltates [6,7,11–13]. Thermoelectric properties of (PrCa)0.3CoO2 are improved compared to Pr0.3CoO2, mainly due to the enhanced electrical conductivity and lower thermal conductivity, while thermoelectric power remains roughly the same.
Acknowledgement
Fig. 8. Resistivity, thermoelectric power and thermal conductivity dependence on temperature of Pr0.3CoO2 and (PrCa)0.3CoO2.
lower absolute value of resistivity for the calcium doped sample. Both dependencies follows the Mott's formula ρ ¼ ρ0 exp(T/T0) 1/2 characteristic for 1-dimensional variable range hopping (VRH). It suggests that conduction paths in the cobalt subsystem are influenced by interactions with magnetic rare earth ions, making the transport effectively 1-dimensional, see Ref. [26] for more details. Whereas the fitted pre-factor ρ0 is similar for both systems (33.4 and 32.0 mΩ cm for Pr0.3CoO2 and (PrCa)0.3CoO2, respectively), the characteristic temperature T0, which is inversely proportional to the density of states near Fermi level [27], has substantially decreased for (PrCa)0.3CoO2 (5580 and 1690 K, respectively). It is in agreement with the presumed increase of charge-carrier concentration in (PrCa)0.3CoO2. For comparison with the conventional activated type of resistivity (Arrhenius type) ρ ¼ ρ0 exp(EA/kBT), the apparent activation energy (EA) is displayed in the inset of the resistivity plot. The activation energy is decreasing with decreasing temperature, which is characteristic for a regime of variablerange hopping. In spite of the substantial decrease of EA for (PrCa)0.3CoO2 compared to Pr0.3CoO2, the activation energy of both samples is above the limit for localized behaviour EA/kB 4T over the whole measured temperature range. Although the character of resistivity is localized, both systems show a quasi-linear (metallic-like) rise of thermopower, with values reaching 140 μV K 1 for Pr0.3CoO2 and 100 μV K 1 for (PrCa)0.3CoO2 at 300 K. The sudden change of Seebeck coefficient to the negative sign observed for Pr0.3CoO2 at 50 K, which is characteristic for all Ln0.3CoO2 samples [4,26], is not present in (PrCa)0.3CoO2. The decrease of thermal conductivity of (PrCa)0.3CoO2 by about 50% compared to Pr0.3CoO2 reflects the higher disorder in the (PrCa) layers caused by a random distribution of the two elements within a layer. Despite the decrease of electrical resistivity and thermal conductivity of (PrCa)0.3CoO2, the termoelectric performance is still
This work was supported by the Czech Science Foundation, Project no. 13-03708S. The authors thank to Mariana Klementová for simulations in programme JEMS.
Appendix A. Supplementary material Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.jpcs.2016.04.012.
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structural modulation in layered hexagonal SrxCoO2 and physical properties of Sr0.35CoO2, Mater. Res. Bull. 42 (2007) 94–101. R. Berthelot, D. Carlier, C. Delmas, Electrochemical investigation of the P2–Nax CoO2 phase diagram, Nat. Mater. 10 (2011) 74–80. J. Rodríguez-Carvajal, Recent advances in magnetic structure determination by neutron powder diffraction, Phys. B 192 (1993) 55–69. M. Casas-Cabanas, J. Rodríguez-Carvajal, M.R. Palacín, FAULTS, a new program for refinement of powder diffraction patterns from layered structures, Z. Krist. (Supplement 23) (2006) S243–S248. U. Kolb, T. Gorelik, C. Kuebel, M.T. Otten, D. Hubert, Towards automated diffraction tomography: Part I—data acquisition, Ultramicroscopy 107 (2007) 507–513. J. Hejtmánek, Z. Jirák, M. Maryško, C. Martin, A. Maignan, M. Hervieu, B. Raveau, Interplay between transport, magnetic, and ordering phenomena in Sm1 xCaxMnO3, Phys. Rev. B 60 (1999) 14057. B. Raveau, M. Seikh, Cobalt Oxides: Crystal Chemistry to Physics, WILEY-VCH, 2012. H.W. Zandbergen, M. Foo, Q. Xu, V. Kumar, R.J. Cava, Sodium ion ordering in Na xCoO2: Electron diffraction study, Phys. Rev. B 70 (2004) 024101.
[21] P. Zhang, R.B. Capaz, M.L. Cohen, S.G. Louie, Theory of sodium ordering in Nax CoO2, Phys. Rev. B 71 (2005) 153102. [22] F.C. Chou, M.-W. Chu, G.J. Shu, F.-T. Huang, W.W. Pai, H.S. Sheu, P.A. Lee, Sodium ion ordering and vacancy cluster formation in NaxCoO2 (x¼ 0.71 and 0.84) single crystals by synchrotron X-ray diffraction, Phys. Rev. Lett. 101 (2008) 127404. [23] I.R. Mukhamedshin, A.V. Dooglav, S.A. Krivenko, H. Alloul, Evolution of Co charge disproportionation with Na order in NaxCoO2, Phys. Rev. B 90 (2014) 115151. [24] I.R. Mukhamedshin, H. Alloul, Co-59 NMR evidence for charge and orbital order in the kagome-like structure of Na2/3CoO2, Phys. Rev. B 84 (2011) 155112. [25] T.A. Platova, I.R. Mukhamedshin, H. Alloul, A.V. Dooglav, G. Collin, Nuclear quadrupole resonance and x-ray investigation of the structure of Na2/3CoO2, Phys. Rev. B 80 (2009) 224106. [26] K. Knížek, P. Novák, Z. Jirák, J. Hejtmánek, M. Maryško, J. Buršík, Magnetism and transport properties of layered rare-earth cobaltates Ln0.3CoO2, J. Appl. Phys. 117 (2015) 17B706. [27] N.F. Mott, J. Non-Cryst. Solids 1 (1968) 1.
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Calcium-induced cation ordering and large resistivity decrease in Pr0.3CoO2 Petr Brázda a,n, Lukáš Palatinus a, Jan Drahokoupil a, Karel Knížek a, Josef Buršík b a b
Institute of Physics AS CR, v.v.i., Na Slovance 1999/2, 182 21 Prague 8, Czech Republic Institute of Inorganic Chemistry AS CR, v.v.i., Husinec-Řež 1001, 25068 Řež, Czech Republic
art ic l e i nf o
a b s t r a c t
Article history: Received 21 December 2015 Received in revised form 4 March 2016 Accepted 29 April 2016 Available online 30 April 2016
Structure of layered cobaltates Pr0.3CoO2 and (PrCa)0.3CoO2 were investigated by electron diffraction tomography and powder X-ray diffraction. The effect of the calcium substitution on thermoelectric properties was evaluated. The structure consists of hexagonal sheets of edge-sharing CoO6 octahedra interleaved by cationic monolayers. The cations form a 2-dimensional a√3 a√3 superstructure in the a–b plane. While Pr0.3CoO2 showed no layer order in the [001] direction, introduction of calcium resulted in the formation of a superstructure spanning over six cationic layers along the [001]. This superstructure model appears to be valid also for the description of the superstructures of CaxCoO2 and SrxCoO2 with x about 1/3. Thanks to the increased number of charge carriers, the substitution of Ca2 þ for Pr3 þ significantly lowers the electric resistivity, while keeping quite high thermopower around 100 μV K 1, though the character of resistivity remained semiconducting. & 2016 Elsevier Ltd. All rights reserved.
Keywords: Thermoelectric cobaltate PrxCoO2 Electron diffraction tomography Powder X-ray diffraction Cobalt oxide
1. Introduction Layered cobaltates with mixed-valent Co3 þ /4 þ atoms are a group of materials with large thermoelectric power [1]. Our group successfully prepared Ln0.3CoO2 (Ln¼ La, Pr, and Nd) by solid state ion exchange reaction from γ-NaxCoO2 (P63/mmc symmetry) [2] and showed that these materials possess large Seebeck coefficient reaching 175 μV K 1 and are thermally stable up to 800 K [3–5]. Application of Ln0.3CoO2 materials for thermoelectric conversion is limited by their high electrical resistivity. The partial substitution of Ca2 þ for Ln3 þ may increase Co valency and thus the chargecarrier concentration. This could eventually lead to a decrease of electrical resistivity and possibly to a change of the semiconducting behaviour of Ln0.3CoO2 to metallic. The substitution of Ca2 þ for Pr3 þ was selected because of the similar ionic radii of these cations. Intercalated cations in Me1/3CoO2 (Me ¼ Ca, Sr, Ba, La, Pr, and Nd) form the a√3 a√3 superstructure (Fig. 1) [3,4,6–9]. The cationic arrangement in the a–b plane is well developed for this superstructure and therefore frequently discussed in the literature. To the best of our knowledge, the order along [001] direction for the a√3 a√3 superstructure has not been discussed in the literature except for our recent works dealing with La0.3CoO2, where we used powder X-ray (PXRD) and neutron diffraction [5] and n
Corresponding author. E-mail address: [email protected] (P. Brázda).
http://dx.doi.org/10.1016/j.jpcs.2016.04.012 0022-3697/& 2016 Elsevier Ltd. All rights reserved.
electron diffraction tomography (EDT) [10]. In the latter work we theoretically deduced some limitations of the layer stacking sequences with respect to the cationic site occupancy (P1 and P2, Fig. 1) [10]. The obtained experimental results for La0.3CoO2 show that there is no order of the cationic layers along the [001] direction in this material. This contrasts with the calcium and strontium analogues, where the maxima of diffracted intensity proving the existence of the order along c may be observed in both PXRD [7,11,12] and selected area electron diffraction (SAED) [6,7,13]. All the published SAEDs are similar and may be interpreted as a result of an R-centred arrangement of cations with periodicity either equal to three CoO2 layers (indicating that the cations would have to occupy the P1 site, which is in disagreement with powder XRD data) [7] or equal to six CoO2 layers assuming presence of a symmetry operation of the structure, which leads to the systematic absences for diffractions with l¼2n þ1 (in this case occupancy of the P2 site would be allowed). In this article, we investigate the cationic arrangement in Pr0.3CoO2 and (PrCa)0.3CoO2 (the ratio Pr:Ca is about 1:1). We show that while the stacking of layers in Pr0.3CoO2 is completely random along [001] in analogy to its lanthanum analogue, substitution of calcium for praseodymium in the structure induces ordering of the cations along the [001] direction. We also show that the published powder X-ray diffractogram of Sr0.35CoO2 [7] can be explained with the same structural model for the stacking order. Further, measurement of conductivity of the Pr0.3CoO2 and (PrCa)0.3CoO2 materials showed that introduction of Ca into the system leads to a significant decrease of resistivity of (PrCa)0.3CoO2
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were transferred onto the Cu TEM grids. Selected area electron diffraction was simulated in the programme JEMS. Electrical resistivity and thermoelectric power were measured using a four-probe method with a parallelepiped sample cut from the sintered pellet. The electrical current density varied depending on the sample resistivity between 10 1 A cm 2 (metallic state) and 10 7 A cm 2 (insulating state). The measurements were performed on sample cooling and warming using a close-cycle cryostat working down to 3 K, see Ref. [18] for details.
3. Results and discussion 3.1. Transmission electron microscopy
Fig. 1. Basic building block of the a√3 a√3 superstructure. It is a three times expanded unit cell of γ-NaCoO2 (P63/mmc symmetry). The superstructure in Me1/3CoO2 (only 1/3 of the P2 (green) cation sites in a layer are occupied) is caused by ordering of the vacancies. The P1 sites (sites between Co atoms) are shown as black hollow spheres. Cobalt atoms are shown with their coordination polyhedron. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
in comparison to Pr0.3CoO2.
2. Experimental The materials were prepared by an ionic exchange between sodium cobaltate and Ca and Pr nitrates (γ-Na0.77CoO2, a ¼2.841 (1) Å, c ¼10.802(5) Å [14]) was mixed with anhydrous Pr(NO3)3 or with a mixture of anhydrous Pr(NO3)3 and Ca(NO3)2 in a dry-box. The molar ratios Na0.77CoO2:Pr(NO3)3:Ca(NO3)2 were 1:0.5:0 (Pr0.3CoO2) and 1:0.7:0.3 ((PrCa)0.3CoO2). Preliminary experiments revealed, that the rate of the ionic exchange of Ca is higher than that of Pr, therefore in order to achieve Pr:Ca¼1:1 stoichiometry in (PrCa)0.3CoO2, the excess of Ca over Pr should be used. The final annealing was done for two days at 340 °C for Pr0.3CoO2 and at 310 °C for (PrCa)0.3CoO2. The unreacted nitrates were washed out repeatedly with large amount of water using an ultrasonic treatment. The products were isolated by sedimentation in water and then dried at 120 °C for 16 h. For the transport measurement experiments, the materials were pressed into pellets and sintered at 300 °C for one day. The density (compactness) of the pellets is affected by the low sintering temperature and it was about 60– 65%. Powder X-ray diffraction was carried out with the Bruker D8 (Cu Kα radiation, λ ¼1.5418 Å, secondary monochromator, BraggBrentano geometry) and PANalytical X’Pert (Co Kα radiation, λ ¼1.790 Å, transmission geometry, Kapton sample support) diffractometers. Rietveld analyses of the PXRD data were performed with Fullprof software package [15]. Partial disorder of the cationic layer stacking was simulated by programme FAULTS [16]. Transmission electron microscopy (TEM) was conducted on a Philips CM120 transmission electron microscope with a LaB6 cathode operating at 120 kV. The microscope is equipped with a CCD Camera Olympus SIS Veleta with 14 bit dynamical range and with an EDAX SSD detector Apollo XLTW for EDS analysis. The electron diffraction tomography [17] was measured in the range from 50° to þ 50° and with the tilt step of 0.7°. The samples were used as they were or only very gently ground and then they
The Pr0.3CoO2 crystals show the a√3 a√3 superstructure. The lack of order along [001] of the superstructure diffractions (Fig. 2) is in accord with PXRD data (see below). Intergrowths with Co3O4 were frequently observed (Fig. S1). The Co3O4 crystals are frequently twinned according to the spinel-law. The observed twinning was perpendicular to only one out of the four possible threefold axes and this particular axis was parallel to the [001] direction of Pr0.3CoO2. For indexing purposes, it was therefore convenient to transform the cubic unit cell of Co3O4 to the hexagonal unit cell setting (H subscript), where the twinning three-fold axis becomes the c-axis. The transformation is then aH ¼ a/2 b/2, bH ¼b/2 c/2 and cH ¼ aþb þc. This situation is completely analogous to the behaviour of the Co3O4/La0.3CoO2 system [10]. Introduction of calcium into the praseodymium cobaltate induced a change of the ordering of the structure. While the a–b superstructure did not change, an appearance of maxima within the rods of diffracted intensity due to cationic superstructure clearly indicate that the stacking sequence is no longer random, but exhibits long-range order, albeit not perfect. The appearance of the diffraction patterns is similar to those published in the literature [6,7,13]. Based on the analysis of the possible ordering with cations in the P2 site we constructed two possible sequences of the cationic layers. The resulting structures have a six-layer periodicity with two interpenetrating R-centred cationic substructures (one substructure is composed of the cations located in the odd layers and the other one in the even layers). These two R-centred substructures may be either both obverse (or both reverse) or they can have the obverse-reverse relationship. These structures are shown in Fig. 3. The symmetry of the obverse-obverse (O–O) structure is C2/c1 and the symmetry of the obverse-reverse (O–R) structure is P6122. The lattice vector transformations from the average (P63/mmc) unit cell is aO–O ¼3a, bO–O ¼a þ2b, cO–O ¼3c for the O–O structure (dimensions of the cell are 3a a√3 3c with respect to the average structure unit cell) and aO–R ¼2aþb, bO–R ¼ a þb, cO–R ¼ 3c (a√3 a√3 3c) for the O–R structure. The simulations of the reciprocal space sections corresponding to h0l, – h–hl, and –hhl (O–O structure) and h0l, 0–kl, and –hhl (O–R structure) are shown in Fig. S2. All three sections are identical for the O–R structure (P6122 symmetry) and the patterns look like the patterns of an obverse-reverse twin, which is an intrinsic feature of the structure. The six-layer periodicity may be directly observed in these sections. Due to the lower symmetry, only the –h–hl and – hhl sections of the O–O structure are identical and show the sixlayer periodicity. The h0l section is different because the diffraction maxima with l ¼2 n þ1 are absent due to the presence of cglide plane. 1 Further details of the crystal structure may be obtained from FIZ Karlsruhe, 76344 Eggenstein-Leopoldshafen, Germany (fax: þ 49 7247-808-666; e-mail: crysdata@fiz-karlsruhe.de) on quoting the deposition number CSD-430226.
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Fig. 2. Reciprocal space sections of a Pr0.3CoO2 crystal: 0kl (a), h–2hl (b), and hk0 (c).
Fig. 3. Possible structures of ordered (PrCa)0.3CoO2 with the six-layer periodicity. Intercalated cations form in odd and even layers two R-centred arrangements, which can have the same orientation (O–O structure, C2/c symmetry) (a) or one is rotated by 180° with respect to the other (O–R structure, P6122 symmetry) (b). Cobalt atoms are shown with their coordination polyhedron.
Three crystals are shown here for illustration of the calcium induced ordering phenomenon in praseodymium calcium layered cobaltate. The crystals differ in the ratio between praseodymium and calcium. The ratio was obtained by EDS. The calcium rich crystal (Pr:Ca ¼3:7) shows well developed maxima within the superstructure diffraction rods, which triple the periodicity along c. The diffraction patterns correspond to the O–O structure (C2/c symmetry) twined by the two-fold axis parallel with [001], thus
creating an O–O/R–R twin (Fig. 4). Simulations of the reciprocal space sections together with their intensity profiles are shown in Fig. S3. The match between the experimental data and the simulations for O–O/R–R twin is good, in particular the difference in the geometry of the sections h0l and –h–hl agrees well with the twinned O–O (C2/c) structure, and cannot be explained by the O–R (P6122) structure. Because the same SAED patterns were observed for the pure Ca and Sr layered cobaltates, it appears that the O–O
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Fig. 4. Reciprocal space sections of a (Pr0.3Ca0.7)0.3CoO2 crystal: (a) h0l, (b) –h–hl, and (c) –hhl and their integrations (d): h0l green, –h–hl red, and –hhl blue. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
structure has the common arrangement with the divalent cations in the layered cobaltates. Increase of praseodymium (Pr:Ca ¼4:6) leads to a further blurring of the maxima causing significant overlap of the neighbouring diffractions, while the systematic absences due to the R-centred arrangement of the cations remain clearly observable (Fig. S4). Finally, the maxima corresponding to the triple periodicity along c vanish when praseodymium content reaches 70 at%. Instead, very weak maxima corresponding to the periodicity of the average structure emerge (Fig. S5). Various cation orderings with a similar level of complexity may be observed in related NaxCoO2 phases simultaneously with charge ordering of Co cations, when x is decreased below 1 [19– 22]. Na þ cations can occupy both P1 and P2 positions (see Fig. 1 for description of P1 and P2). Since the P1 position is less favourable due to the shorter Na-Co distance, the actual occupancies of P1 and P2 are determined by the competition of Coulomb repulsions between Na þ –Na þ within ab-plane and between Na þ –Co3 þ along the c-direction. The ordered distribution of Na þ and vacancies over P1 and P2 positions breaks the uniformity of Co coordination spheres and is the source of the Co charge disproportionation and ordering [23–25]. When x is decreased close to 1/3, the influence of Na þ –Na þ repulsion becomes less important and Na occupies solely the P2 position. In the case of LnxCoO2 the Ln3 þ –Co3 þ repulsion is even stronger, so the occupation of P1 is practically excluded. Since the ordering of Pr3 þ within the ab-plane is strictly regular and the number of vacancies is quite small (x is close to 1/ 3), the coordination sphere of Co remains identical for all Co positions. In the case of (PrCa)xCoO2, we did not detect any cell enlargement in the ab-direction, which would indicate any Pr–Ca ordering, so the distribution of Pr3 þ and Ca2 þ is random and the uniformity of coordination of all Co cations is preserved. Therefore, there is no significant driving force for Co charge ordering in
(PrCa)xCoO2 and actually no charge ordering is observed in our experiments. A spurious phase of cobalt oxide was observed as intergrowth with (PrCa)0.3CoO2 and during the survey of the sample in the TEM we succeeded to find also one grain of pure phase. Surprisingly, the diffraction pattern did not correspond to the trigonal Co3O4, but had a different cell metrics and hexagonal symmetry P63mc. We have attempted to solve the structure and the preliminary composition corresponds to Co5O8 assuming all atomic positions being fully occupied. To the best of our knowledge, a phase of cobalt oxide with this symmetry and lattice parameters (see below) has not been reported yet. We describe its structure in a separate report. Co5O8 forms oriented intergrowths with (PrCa)0.3CoO2 analogous to the intergrowths of Co3O4 with Pr0.3CoO2, thus [001]Co//[001]PrCa and [110]Co//[100]PrCa. It is important to note that we observed only the Co5O8 phase and no Co3O4 in the (PrCa)0.3CoO2 sample (see also powder XRD section). 3.2. Powder X-ray diffraction Powder X-ray diffractogram of Pr0.3CoO2 (Fig. 5, Cu radiation) revealed superstructure diffractions corresponding to the a√3 a√3 superstructure with the lattice parameters a¼ 4.8944 (5) Å and c ¼10.940(1) Å. The strongly asymmetric profile of these diffractions points to the disorder along [001], which was confirmed by TEM (see above). The absence of additional maxima superimposed on the slowly decreasing tail of the 100 diffraction is in agreement with the absence of such maxima in the EDT data. The Rietveld refinement showed that the material contains about 25 mol% of Co3O4. The structural parameters of Pr0.3CoO2 obtained by the Rietveld refinement are presented in Table 1. The diffractogram of (PrCa)0.3CoO2 measured in the Bragg-
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Fig. 5. Powder X-ray diffractogram of Pr0.3CoO2. Positions of the diffraction maxima of Pr0.3CoO2 (without the superstructure diffractions) and Co3O4 are marked by blue and red bars, respectively. Positions of the 100, 200, 210, 310, and 320 diffractions are marked by an asterisk. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Table 1 Structural parameters and selected bond lengths and angles of Pr0.30CoO2 refined by Rietveld method from X-ray diffraction data within the hexagonal space group P63/mmc. Atom coordinates: Pr 2d(2/3,1/3,1/4), Co 2a(0,0,0), O 4f(1/3,2/3,z). Agreement factors: Rwp ¼ 25.1%, χ2 ¼ 1.95.a a (Å)
2.8257(2)
Pr, occupation
0.30(2)
c (Å) Pr, Biso (Å2) Co, Biso (Å2) O, Biso (Å2) O (z)
10.9395(8) 0.39(9) 0.12(6) 0.50(9) 0.0934(5)
Co–O (Å) 6 Pr–O (Å) 6 O–Co–O (deg.) O–Pr–O (deg.) Co–O–Pr (deg.)
1.925(3) 2.366(4) 94.4(2) 73.3(2) 165.7(3)
(PrCa)0.3CoO2 are a ¼4.875(1) Å, and c¼ 32.692(3) Å (b restrained to a√3). Note that the intensity of the diffraction maxima is the same for the O–O and O–R structures, therefore it is not possible to distinguish between these two structures from the powder diffractogram. For Co5O8, we used the preliminary structure model obtained from the EDT data. It described the observed intensities satisfactorily. The obtained lattice parameters are a ¼5.65(2) Å and c¼8.75(5) Å. Introduction of Co3O4 into the fit did not improve the results. The reason of formation of Co5O8 instead of Co3O4 is not clear. The substantial differences in the materials preparation are pelletizing of Pr0.3CoO2 powder, different final annealing temperature and presence of calcium in (PrCa)0.3CoO2. Further, the amount of nitrates in the reaction mixture for preparation of (PrCa)0.3CoO2 was approximately two times higher than for the preparation of Pr0.3CoO2. So far, we were not able to identify what causes such principal change of the phase of cobalt oxide. Due to the strong preferred orientation the evaluation of the stacking disorder could not be done in FAULTS programme [16]. Therefore we chose powder diffraction data published in [7] obtained on Sr1/3CoO2 to estimate the level of Sr layers stacking order and to show that our structure model is valid also for this material. The simulation of the powder diffractogram of Sr1/3CoO2 is shown in Fig. 7 for three different probabilities that the next layer will correspond to the ordered O–O structure: 0.7, 0.8 and 0.9. Increasing disorder in the cationic layer stacking broadens the diffraction maxima associated with the cationic superstructure. The diffractograms obtained with probabilities 0.7 and 0.8 are very similar to the data presented in the work of Yubuta et al., which were obtained on Sr0.35CoO2 [7]. This together with EDT results indicate that our six layer structure model with the R-centred arrangement of the cations is valid not only for the calcium doped Pr0.3CoO2 but also for the strontium and calcium cobaltates. 3.3. Transport properties
a
Regions where the superstructure diffractions have non-zero intensity were excluded.
The resistivity and thermopower of Pr0.3CoO2 and (PrCa)0.3CoO2 are displayed in Fig. 8. Both samples exhibit localized character of resistivity, i.e. increasing resistivity with lowering temperature. The increase of the formal Co valency from 3.1 þ for Pr0.3CoO2 to 3.25 þ for (PrCa)0.3CoO2 (Pr:Ca about 1:1) and the corresponding increase of charge-carrier concentration is manifested by the
Fig. 6. Powder X-ray diffractogram of (PrCa)0.3CoO2. Positions of diffraction maxima of (PrCa)0.3CoO2 and Co5O8 are marked by blue and red bars, respectively. The most intense superstructure diffractions of (PrCa)0.3CoO2 are indexed in the monoclinic O–O cell. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Brentano geometry suffered from a very strong preferred orientation, which led to the observation of nearly only the 00lO–O diffractions. Therefore, we measured the sample in the transmission geometry and focused on the region where the 11lO–O diffractions occur (Fig. 6, Co radiation). The lattice parameters of
Fig. 7. Simulation of the powder X-ray diffractogram of Sr1/3CoO2 in programme FAULTS. A certain level of disorder is introduced into the stacking sequence of the cationic layers. The probabilities p that the next layer will correspond to the ordered structure are 0.7 (green), 0.8 (red), and 0.9 (blue). The probabilities of the other two possible transitions are both equal to (1–p)/2. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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not comparable with the best termoelectric materials, and namely lowering of resistivity by about 2 orders is needed for relevant applications.
4. Conclusion We have analysed in detail the layer stacking in praseodymium cobaltate and praseodymium calcium cobaltate. We observed that the cationic layers in Pr0.3CoO2 do not form any stacking order, similarly to its lanthanum containing analogue. Introduction of divalent calcium induces the ordering of the layers, which eventually leads to the formation of the 3a x a√3 3c superstructure with C2/c symmetry. Though the presence of the ordered structure is obvious from the EDT data, a substantial degree of disorder is still present, as documented by the diffuse diffraction intensity along [001] in the diffraction patterns. The degree of order decreases with increasing ratio Pr:Ca. Our structure model also explains well diffraction data published for pure calcium and strontium cobaltates [6,7,11–13]. Thermoelectric properties of (PrCa)0.3CoO2 are improved compared to Pr0.3CoO2, mainly due to the enhanced electrical conductivity and lower thermal conductivity, while thermoelectric power remains roughly the same.
Acknowledgement
Fig. 8. Resistivity, thermoelectric power and thermal conductivity dependence on temperature of Pr0.3CoO2 and (PrCa)0.3CoO2.
lower absolute value of resistivity for the calcium doped sample. Both dependencies follows the Mott's formula ρ ¼ ρ0 exp(T/T0) 1/2 characteristic for 1-dimensional variable range hopping (VRH). It suggests that conduction paths in the cobalt subsystem are influenced by interactions with magnetic rare earth ions, making the transport effectively 1-dimensional, see Ref. [26] for more details. Whereas the fitted pre-factor ρ0 is similar for both systems (33.4 and 32.0 mΩ cm for Pr0.3CoO2 and (PrCa)0.3CoO2, respectively), the characteristic temperature T0, which is inversely proportional to the density of states near Fermi level [27], has substantially decreased for (PrCa)0.3CoO2 (5580 and 1690 K, respectively). It is in agreement with the presumed increase of charge-carrier concentration in (PrCa)0.3CoO2. For comparison with the conventional activated type of resistivity (Arrhenius type) ρ ¼ ρ0 exp(EA/kBT), the apparent activation energy (EA) is displayed in the inset of the resistivity plot. The activation energy is decreasing with decreasing temperature, which is characteristic for a regime of variablerange hopping. In spite of the substantial decrease of EA for (PrCa)0.3CoO2 compared to Pr0.3CoO2, the activation energy of both samples is above the limit for localized behaviour EA/kB 4T over the whole measured temperature range. Although the character of resistivity is localized, both systems show a quasi-linear (metallic-like) rise of thermopower, with values reaching 140 μV K 1 for Pr0.3CoO2 and 100 μV K 1 for (PrCa)0.3CoO2 at 300 K. The sudden change of Seebeck coefficient to the negative sign observed for Pr0.3CoO2 at 50 K, which is characteristic for all Ln0.3CoO2 samples [4,26], is not present in (PrCa)0.3CoO2. The decrease of thermal conductivity of (PrCa)0.3CoO2 by about 50% compared to Pr0.3CoO2 reflects the higher disorder in the (PrCa) layers caused by a random distribution of the two elements within a layer. Despite the decrease of electrical resistivity and thermal conductivity of (PrCa)0.3CoO2, the termoelectric performance is still
This work was supported by the Czech Science Foundation, Project no. 13-03708S. The authors thank to Mariana Klementová for simulations in programme JEMS.
Appendix A. Supplementary material Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.jpcs.2016.04.012.
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