A. Synthesis

The Er_0.33Sr_1.67Ni_0.8Cu_0.2O_4−δ (ErSr₅Ni_2.4Cu_0.6O₁₁) sample was prepared in a polycrystalline form using the conventional solid state method. Before use, Er₂O₃ (Aldrich 99.99%) was calcined at 1373 K for 9 h in air to remove any carbonate and bicarbonate impurities. NiO and CuO (Aldrich 99.99%) were used as obtained. Stoichiometric amounts of Er₂O₃, SrCO₃, NiO and CuO were thoroughly ground together and calcined at 1223 K for 36 h. The obtained powder sample was pelleted, then sintered in a tube furnace at 1423 K under flowing oxygen to maximize the oxygen content for 48 h and then cooled slowly to room temperature. The sample is repelletized and reheated several times for the same period until no further changes in the X-ray diffraction pattern were observed.

B. Data collection and electrical measurements

To identify the phase composition and to refine the unit cell parameters, the sample was examined by X-ray diffraction using BRUKER AXS D8 ADVANCE diffractometer with a monochromatic CuKα ₁ radiation (λ = 1.540 56 Å) obtained with an incident-beam curved germanium monochromator. Data were collected at each 0.0078° step width for 1.7 s over a 2θ range from 8.0000° to 120.0063°. Pattern matching and Rietveld refinement were performed using FullProof software (Rodriguez-Carvajal, Reference Rodriguez-Carvajal1990).

Electrical direct current resistivity measurements were performed on sintered pellets using a Lucas Labs 302 four point probe with a Keithley 2400 digital Source Meter (Keithley Instruments Inc., Cleveland, Ohio). Measurements were performed in the temperature range of 320–540 K.

The oxygen content of the compound was indirectly determined at room temperature after calculation of the valence average of the transition metal ions obtained by iodometric titration under flowing nitrogen gas taking into account that Ni³⁺ and Cu³⁺ can be present in the sample with Ni²⁺ and Cu²⁺. In fact, 60 mg sample was dissolved in a solution of 6 M HCl in the presence of an excess KI, leading to reduction of Ni³⁺ to Ni²⁺ and all the copper ions (Cu³⁺ and Cu²⁺), to Cu⁺ ions with the formation of iodine that was titrated with a Na₂S₂O₃ solution using starch as an indicator. The sodium thiosulfate solution was standardized using pure copper wire.

A. Crystal structural and oxygen stoichiometry

The exact temperature, the gas atmosphere, and the reaction time are considered essential to obtain a pure phase containing no traces of the starting materials. In fact the Er_0.33Sr_1.67Ni_0.8Cu_0.2O_4−δ sample was successfully synthesized under flowing oxygen at 1423 K. Inspection of the X-ray patterns at intermediate stages of the synthesis appeared to indicate that an impurity phase identified as Er₂SrO₄ (PDF-00-046-60133) (ICDD, 1994) still persists even after a multitude of sintering. Therefore, a biphasic Rietveld refinement was applied for the Er_0.33Sr_1.67Ni_0.8Cu_0.2O_4−δ sample. Quantitative X-ray analysis of the sample by FULLPROOF program, using Brindley's procedure (Brindley, Reference Brindley1949) indicates a proportion less than 1% of Er₂SrO₄. Hence, this impurity is considered to have a negligible effect on the stoichiometry of the material. The refinement showed a good fit between the observed and the calculated patterns and the cell dimensions obtained from this refinement are given in Table I.

TABLE I. Unit cell for Er_0.33Sr_1.67Ni_0.8Cu_0.2O_4−δ.

Profile analysis of X-ray diffraction pattern for Er_0.33Sr_1.67Ni_0.8Cu_0.2O_4−δ compound was carried out on the basis of a tetragonal system (space group I4/mmm) by analogy with similar phases formed with Ho (Salwa et al., 2011) and Dy (Chaker et al., Reference Chaker, Roisnel, Ceretti and Ben Hassen2007). The background was fitted with a linear interpolation between 100 chosen points. The lattice parameters deduced from the X-ray powder diffraction profile refinement are found to be: a = 3.760 56(4) and c = 12.3889(1) Ǻ.

The stability of the Er_0.33Sr_1.67Ni_0.8Cu_0.2O_4−δ compound having a K₂NiF₄-type structure can be discussed in terms of the tolerance factor value defined by Goldschmidt (Ganguly and Rao, Reference Ganguly and Rao1984), as:

$$t\; =\; \displaystyle{{\displaystyle{{0.33r_{{\rm Er}^{3+} }+1.67r_{{\rm Sr}^{2+} } } \over 2}+r_{{\rm O}^{2 - } } } \over {\sqrt 2 \; \left[{0.8r_{{\rm Ni}^{3+} } 0.2r_{{\rm Cu}^{2+} } r_{{\rm O}^{2 - } } } \right]}}.$$

The K₂NiF₄-type structure is stable over the range 0.866 ≤ t < 1. The T (tetragonal) structure exists for 0.88 ≤ t ≤ 0.99 and the T/O (tetragonal/orthorhombic) structure is present for 0.866 ≤ t < 0.88. Based on Shannon's ionic radii (Shannon, Reference Shannon1976), (r _Er³⁺ = 1.062 Å, r _Sr²⁺ = 1.31 Å in a nine-fold coordination and r _Ni³⁺ = 0. 56 Å, in a low spin case, r _Cu²⁺ = 0. 73 Å and r _O²⁻ = 1. 4 Å in a six-fold coordination), the calculated tolerance factor for Er_0.33Sr_1.67Ni_0.8Cu_0.2O_4−δ is t = 0.9465, this value is included in the tetragonal symmetry stability range.

Consequently, Rietveld refinement of Er_0.33Sr_1.67Ni_0.8Cu_0.2 O_4−δ X-ray data was performed to confirm the K₂NiF₄-type structure. The structural refinement was carried out in the space group I4/mmm starting with atomic positions taken from Ho_0.33Sr_1.67Ni_0.8Cu_0.2O_4−δ (HoSr₅Ni_2.4Cu_0.6O₁₁) (Chaker et al., Reference Chaker, Roisnel, Ceretti and Ben Hassen2007), with Er/Sr and O(2) atoms situated at special positions 4e with coordinates (0, 0, z). The Ni and Cu atoms are located at (0, 0, 0) in the 2a site, and the O(1) atoms at (0, ½, 0) in the 4c site. Atomic positions were refined for all atoms, together with scale factor and profile parameters. It is well known that in Rietveld refinements of heavy-atom structures, using X-ray diffraction data, much problematic intensity may be hidden in the thermal displacement factors of relatively light atoms (Hill, Reference Hill1992; Hamdi et al., Reference Hamdi, Amami, Hlil and Ben Hassen2011a, Reference Hamdi, Ouni, Chaker, Rohlicek and Ben Hassen2011b). That is why we undertook the refinement of oxygen atoms with fixed occupancies at 0.125 and thermal displacement factors fixed to values higher than those of heavy atoms. It was also impossible to refine the Ni/Cu ratio, owing to the similar X-ray scattering powers of these elements. Refinements of the physically sensible isotropic temperature factors were unstable, but good results were obtained by refinement of the overall isotropic displacement factor. Finally, refinement of the preferred orientation correction in the [001]-direction led to a significant decrease of χ ², and a considerable improvement in the visual quality of the fit. A final refinement converged to R _wp = 10.75%, χ ² = 2.51, R _p = 14.80%, R _B = 4.77% and R _F = 2.73%.

To determine the oxygen non-stoichiometry, we carried out an iodometric titration using the Na₂S₂O₃ standard solution. The oxygen non-stoichiometry (δ) is directly correlated with the Ni³⁺ and Cu³⁺ content according to the formulation Er_0.33Sr_1.67(Ni³⁺_1−τ Ni²⁺_τ)_0.8(Cu³⁺_1−τ Cu²⁺_τ)_0.2O_4−δ, with δ = 0.33 + (1/2)τ. The content (1 − τ) of the average of cations transition metals Ni³⁺ and Cu³⁺ was determined by iodometric titration. I⁻ anions reduce Ni³⁺ to Ni²⁺ and all the copper ions (Cu³⁺ and Cu²⁺) to Cu⁺. The titration of the resulting I ₂, by a solution of Na₂S₂O₃ sodium thiosulfate led to determining the value τ = 0.28 and therefore δ = 0.47 after considering the average of cations transition metals Ni³⁺ and Cu³⁺. The obtained results indicate that the compound is oxygen deficient.

B. Structure description

The observed, calculated and difference profiles for the Rietveld refinement of Er_0.33Sr_1.67Ni_0.8Cu_0.2O_4−δ compound are shown in Figure 1. An enlargement of the fit to the 2θ region between 26° and 46° 2θ is also presented in Figure 1. The structural refined parameters for Er_0.33Sr_1.67Ni_0.8Cu_0.2O_4−δ are summarized in Table I.

Figure 1. Observed, calculated and difference profiles for Rietveld refinement of Er_0.33Sr_1.67Ni_0.8Cu_0.2O_4−δ compound.

As shown in Figure 2, the structure can be described as an ordered intergrowth of alternating perovskite (Er/Sr)(Ni/Cu)O₃ and rock salt (Er/Sr)O layers stacked along the tetragonal c-axis. The (Ni/Cu)O₆ octahedra shares corners in the ab-plane forming a two-dimensional array of (Ni/Cu)–O–(Ni/Cu) bonds which is responsible for a variety of interesting physical phenomena, as for example, the anisotropic electrical transport and magnetic exchange interactions (Bassat et al., Reference Bassat, Odier and Gervais1987; Buttrey and Honig, Reference Buttrey and Honig1988).

Figure 2. Crystal structure of the Er_0.33Sr_1.67Ni_0.8Cu_0.2O_4−δ sample with the tetragonal K₂NiF₄-type structure.

C. Electrical conductivity

To obtain dense ceramic pellets for electrical measurements, a powder sample of the material was grounded (in ethanol). A pellet (13 mm in diameter and 1.2 mm thick) was prepared by uniaxial pressing (100 MPa). It was then sintered at 1173 K for 4 h to obtain a disk with high density. The total electrical conductivity σ _e of the sintered ceramic was determined, under air using the four-probe technique, in the temperature range of 320–540 K. The corresponding curve to σ _e vs. 1000/T is reported in Figure 3. First, the conductivity increases with temperature to reach a maximum observed between 425 and 439 K then, above this temperature, the conductivity decreases, owing to the decrease of the oxygen content and correspondingly of the density of Ni³⁺ and Cu³⁺ carriers (Bassat et al., Reference Bassat, Odier and Loup1994; Boehm et al., Reference Boehm, Bassat, Dordor, Mauvy, Grenier and Stevens2005). We focus our study on the conduction mechanism only in the temperature range up to 439 K (where the maximum of conductivity is achieved). Figure 4 shows the relationship of Ln(σT) vs. 1000/T for the temperature range of 320–439 K. The increase of Ln(σT) with increasing temperature indicates that the compound has a p-type semiconductor behaviour over the chosen temperature range. To determine the conduction mechanism, we tried to use the thermally activated adiabatic small polaron hopping as a conduction model (Mott and Davis, Reference Mott and Davis1971; Long et al., Reference Long, Pollak and Shklovskii1991; Iguchi et al., Reference Iguchi, Nakatsugawa and Futakuchi1998; Tan et al., Reference Tan, Chen, Jin, Zhao and Luo2008):

$$\sigma \; =\; \sigma _0 T^{ - 1} {\rm exp}\left({\displaystyle{{ - E_a } \over {k_{{\rm B}\; } T\; \; }}} \right)\comma \;$$

where E _a is the activation energy (polaron formation and hopping energy), σ ₀ is a constant related to polaron concentration and diffusion. In the analysis of the simulated curve: Ln(σT) = f(1000/T), we found that the convergence of curve fitting was achieved in the whole range of temperature. This suggests that the charge transport in Er_0.33Sr_1.67Ni_0.8Cu_0.2O_4−δ ceramic, in the temperature range of 320–439 K, is described by an adiabatic small polaron hopping model, where activation energy, after fitting, is E _a = 0.21 eV.

Figure 3. Thermal variation of electronic conductivity σ_e for the Er_0.33Sr_1.67Ni_0.8Cu_0.2O_4−δ compound (320 ≤ T(K) ≤ 540).

Figure 4. Arrhenius relations of Ln(σT) vs. 1000/T for the Er_0.33Sr_1.67Ni_0.8Cu_0.2O_4−δ.