2.1.Synthesis

Starting materials (Cu, Al, Ta, and Se) with nominal purity of 99.99 wt. % in the stoichiometric ratio were mixed in an evacuated (10^-4 Torr) and sealed quartz tube with the inner walls previously carbonized to prevent the chemical reaction of the elements with quartz Polycrystalline ingots of about 1 g were prepared by the melting and annealing technique. The quartz ampoule is heated until 493 K (melting point of Se), keeping this temperature for 48 h and shaking all the time using an electromechanical motor. This procedure guarantees the formation of binary species at low temperatures avoiding the existence of Se free gas at high temperature, which could produce explosions or Se deficiency in the ingot. Then the temperature was slowly increased until 1423 K, with the mechanical shaker always connected for better mixing of the components. After 24 h, the cooling cycle begins until the anneal temperature (800 K) with the mechanical shaker is disconnected. The ampoule is keeping at the annealing temperature for 1 month to assure the thermal equilibrium. Then the furnace is switching off. This preparation method has proven to give good results ^6,12.

2.2.Scanning Electron Microscopy (SEM)

Stoichiometric relations of the samples were investigated by scanning electron microscopy (SEM) technique, using a Hitachi S2500 equipment. The microchemical composition was found by an energy-dispersive X-ray spectrometer (EDS) coupled with a computer-based multichannel analyzer (MCA, Delta III analysis, and Quantex software, Kevex). For the EDS analysis, K α lines were used. The accelerating voltage was 15 kV. The samples were tilted 35 degrees. A standardless EDS analysis was made with a relative error of ±5-10% and detection limits of the order of 0.3 wt %, where the k-ratios are based on theoretical standards. Table IIshows the experimental stoichiometry of the sample Cu₂FeIn₂Se₅.

2.3.Differential Thermal Analysis (DTA)

Differential Thermal Analysis (DTA) measurements were carried out in a fully automatic Perkin-Elmer apparatus, which consists of a Khantal resistance furnace (T_max = 1650 K) equipped with Pt/Pt-Rh thermocouples and an informatics system for the automatic acquisition data. The internal standard used was a high purity (99.99 wt. %) piece of gold. The temperature runs have been performed from ambient temperature to 1400-1500 K, which is the recommended operative limit. The heating rate is controlled electronically to 20 Kh^-1; the cooling rate was given by the natural cooling of the furnace after switching off. From the thermogram, transition temperatures are manually obtained from the ΔT vs. T graph with the criteria that the transition occurs at the intersection of the baseline with the slope of the thermal transition peak, as usual. The maximum error committed in the determination of transition temperatures by this method is estimated to be ±10 K.

2.4.X-ray powder diffraction

The X-ray powder diffraction data were collected at room temperature, in a θ/ θ reflection mode using a Siemens D5005 diffractometer equipped with an X-ray tube (CuK α1 radiation: λ=1.54056 Å; 40 kV, 30 mA) and a diffracted beam graphite monochromator. A 1 mm aperture slit, a 1 mm divergence slit, a 0.1 mm monochromator slit, and a 0.6 mm detector slit were used. The specimen was scanned in the 2θ range of 10-110^o, the scan step was 0.02^o, and the time of counting in every step was 10 s. Quartz was used as an external standard. The instrument analytical software was used to establish the positions of the peaks.

3.1.Differential thermal analysis

In Fig. 1, the thermogram for sample Cu₂FeIn₂Se₅is displayed.

Figure 1 DTA response of sample Cu₂FeIn₂Se₅. 

In the heating cycle, it can be observed two thermal transitions at 1017 and 964 K. The shape of the peak is typical of an incongruent melting point where the solid phase transits to a solid + liquid region at 964 K and then to a liquid phase (melting) at 1017 K. However, in the cooling cycle, up to five thermal transitions are observed. The fact that only two thermal transitions are observed in the heating cycle and five in the cooling is probably due to the difference between the heating and cooling rates in competition with the velocity of the thermal transitions. The heating rate is electronically fixed at 10 K/min, whereas the cooling rate is variable, given by the natural cooling of the furnace after switching off. Transitions solid-to-liquid (and viceversa) are faster than solid-to-solid and involve higher energies (variation in the enthalpy, ΔH), for these reasons, solid-to-solid transitions are better observed in the cooling cycle.

The high-temperature transition at 1366 K in the cooling, coincides with the melting point of FeSe reported as 1348 K ²² suggesting that, at this temperature, the liquid phase undergoes to a liquid + FeSe region. The liquid + FeSe region is wide, from 1366 K to 1109 K (257 degrees). At 1109 K, the liquid phase solidifies, possibly in the disordered sphalerite β- phase accompanied by FeSe-phase. At 1013 K, the semi-ordered α'- phase coexists with the β'- phase and FeSe, at 953 K, the region is a´ + β and finally, at 923 K, the region is only a´. In Fig. 2, a schematic representation of the successive phase transitions is given.

Figure 2 Schematic illustration of thermal transitions for the sample Cu₂FeIn₂Se₅ in the cooling cycle. 

3.2.X-ray powder diffraction analysis

Figure 3 shows the resulting X-ray powder pattern for the Cu₂FeIn₂Se₅’ compound. When the 2θ positions of the 20 first peaks in the diffraction pattern are introduced into the auto-indexing program Dicvol04 ²³, a tetragonal cell of dimensions a = 5.780(1) Å, c = 11.610(2) Å is obtained. These parameters are similar in magnitude to the parent’s chalcopyrite structure CuInSe₂²¹ and P-chalcopyrite structure CuFeInSe₃¹⁰. The systematic absence condition in the general reflections of the type hkl indicating a P-type cell, and the hhl:l = 2n and 00l:l = 2n conditions suggests the extension symbol P4¯2c. To find the atomic positions to adjust the diffraction pattern was employed a similar analysis to that used in the structural determination of the quaternary alloy CuFeInSe₃, which crystallize in the same space group ¹⁰. It should be noted that this analysis was carried out starting from the prototype of the P-chalcopyrite structure, which was the structure of the Cu-poor Cu-In-Se compound β -Cu_0.39In_1.2Se₂²⁴.

Table IIIshows the 6 better models used in the cation distribution analysis on the available Wyckoff positions. In this Table the Rietveld refinement ²⁵ results are shown. Many other tests were performed where the Cu⁺ cations were moved from the origin (2e), and Wyckoff positions (2a) and (2c) were used for the cations distribution, but only with poor results. The final model was confirmed by checking the chemical sense of the structure in terms of its distances and bond angles.

The program Fullprof ²⁶ was employed for the Rietveld refinement analyzes. In each case, the angular dependence was described by the usual constrain imposed by the Cagliotti’s formula ²⁷, and the peak shapes were described by the Thompson-Cox-Hastings pseudo-Voigt profile function ²⁸. The background was described by the automatic interpolation of 67 points throughout the whole pattern. One overall isotropic temperature factor was refined to describe the thermal motion of the atoms. Model 3 showed the best fit and the Rietveld refinement results are shown in Table IV. Figure 3 shows the Rietveld refinement plot for the quaternary compound Cu₂FeIn₂Se₅. Table V shows the atomic coordinates, isotropic temperature factor, bond distances, and angles for the new compound.

Figure 3 A plot illustrating the final Rietveld refinement of Cu₂FeIn₂Se₅. The bars in the graphic symbolize the Bragg peak positions. The lower trace is the difference curve between observed and calculated patterns. 

Cu₂FeIn₂Se₅is a normal adamantane structure compound ⁵, and consists of a three-dimensional arrangement of distorted CuSe₄, FeSe₄ and InSe₄ tetrahedral connected by common faces (Fig. 4b). In this compound, as in the related CuFeInSe₃, occurs a degradation of symmetry from the chalcopyrite structure I4¯2d to a related structure P4¯2c ¹⁰. In this adamantane model, each cation is tetrahedrally bonded to four anions and at the same time, each Se anion is coordinated by four cations [one Cu1, one Fe, one In1, and one M cation (either Cu2 or In2)] located at the corners of a lightly distorted tetrahedron.

Figure 4 a) CuInSe₂ (I 4 2d), b) Cu2FeIn₂Se₅ (P 4 2c) c) CuFeInSe₃ (P¹42c) d) CuFe₂InSe₄ (I 4 2m) Unit cell diagram, in the ca plane, for the chalcopyrite a) CuInSe₂ (I 4 2d) (x = 0), compared with the P-chalcopyrite structures (P 4 2c) b) Cu₂FeIn₂Se₅ (x = 1=3) and c) CuFeInSe₃ (x = 1=2), and the stannite structure d) CuFe₂InSe₄ (I 4 2m)) (x = 2=3). 

The tetrahedra containing the Cu1 atoms [mean Se...Se distance 3.970(6) Å] are lightly smaller than those containing the M (Cu2 or In2) [means Se...Se distance 4.108(6) Å], Fe atoms [mean Se...Se distance 4.012(6) Å], and In1 atoms [mean Se...Se distance 4.294(6) Å] respectively.

The interatomic distances are shorter than the sum of the respective ionic radii for structures tetrahedrally bonded ²⁹. The Cu-Se [2.431(5) Å], Fe-Se [2.458(5) Å] and In-Se [2.630(5) Å], bond distances compare well to those observed in some other adamantane structure compounds such as CuInSe2 (2.432-2.591Å) ²¹, Cu₂SnSe₃ (2.415 Å) ³⁰, CuFeInSe₃ (2.421-2.520 Å) ₍₁₀₎, CuFe₂InSe₄ (2.417-2.50 Å) ¹¹, CuMn₂InSe4 (2.447-2.594 Å) ³¹, CuMnInSe₃ (2.428 -2.614 Å) ¹³, CuVInSe₃ (2.518−2.530 Å) ³² and Cu₃In₇Se₁₂ (2.419−2.523 Å) ³³.

The chemical structural model was checked by the analysis of the interatomic distances using the BVS formula based on the bond-strength examination ^34,35. The atomic valence of an atom is assumed to be distributed between the bonds that it forms. BVS of atom 𝑖, denoted 𝑉 𝑖 , is then Vi=∑jSj=∑jexp[Ro-Rijb], where S_j is the valence of one bond, and the sum is over all neighbors j. The constant b =0.37 was empirically determined ³⁴. R_o represents the length of a bond of a unit valence, and R_ij is the experimentally determined distance between atoms i and j. The values for the reference distance R_o for Cu-Se, Fe-Se, and In-Se are 2.02, 2.28 and 2.47 Å, respectively ³⁵. Table VI shows the BVS results for Cu₂FeIn₂Se₅, indicating that the oxidation state for each ion is in good agreement with the expected formal oxidation state of Cu⁺, Fe²⁺, In³⁺, and Se^2- ions.

Figure 4 shows the crystal structure evolution of (CuInSe₂)_1-x (FeSe)_xalloys, which confirms the phase diagram proposed for this system ¹². Starting from the chalcopyrite structure (Fig. 4a) CuInSe₂ with space group I4¯2d, when introducing a transition metal (Fe) into the chalcopyrite matrix, a first effect is the disorder of the cationic network. This effect is observed in the P-chalcopyrite structures with (Fig. 4b) x = 1/3 Cu₂FeIn₂Se₅(this work) and (Fig. 4c) x = 1/2 CuFeInSe₃, both crystallize in space group P4¯2c, where a cationic disorder resulting from the occupation of several cations in the same Wyckoff site is observed. By increasing the amount of the transition metal to x = 2/3, the cationic network is reordered in a tetragonal space group I4¯2m CuFe₂InSe₄ (Fig. 4d), which crystallize with a stannite-type structure.

From the magnetic point of view, these materials -due to their cationic ordering- are diamagnetic, ferromagnetic, and ferromagnetic, respectively ^6,12.