Determination of phase boundaries and diffusion coefﬁcients of copper in spinel CuCr 2 Se 4 and delafossite CuCrSe 2 by galvanostatic intermittent titration technique (GITT)

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Introduction
Multiferroic magnetoelectric materials exhibit ferroelectric and ferromagnetic properties, providing technological prospects in new multifunctional devices [1][2][3].For example, multiferroics are used in memory devices [4].It is known [5,6], that various alloys with magnetic properties are widely used in various microdevices, however layered dichalcogenides like CuCrSe 2 also exhibit interesting magnetic properties and memory elements can be developed based on such materials [1][2][3].In layered materials like CuCrSe 2 with R3m structure, Cu atoms are distributed only in one tetrahedral plane [7].As a result, the crystal lattice is non-centrosymmetric, allowing for electric polarization of the crystal along the c axis [1].The temperature of spontaneous polarization coincides with the temperature of magnetic ordering in the Cr sublattice.It is known [8] that the main interaction in the Cr sublattice is ferromagnetic.However, the regular triangular sublattice prohibits ferromagnetic ordering and leads to frustrations.It seems that frustrations are highly dependent on the level of defectivity in the Cu sublattice.This is because the asymmetric environment in the chromium sublattice causes the material to be multiferroic.Therefore, it is crucial to investigate the level of defectiveness in this material.Studying defectiveness in spinel is significant as it helps to understand the impact of the lattice structure on the permissible level of defectiveness.
CuCrSe 2 has a crystal structure [9] similar to that of delafossite ( CuCrO 2 ) [10], which is shown in Figure 1a.The compound CuCr 2 Se 4 (or Cu 0.5 CrSe 2 ) is known for its spinel structure [11] (Figure 1b).The delafossite lattice of CuCrSe 2 can be described as a lattice of CrSe 2 layers intercalated with copper.While there is literature available on spinel CuCr 2 Se 4 , there is a need for data on phase diagrams in the Cu x CrSe 2 system needs to be present [12].The similarity with intercalation compounds suggests a possible region of homogeneity for both CuCrSe 2 and Cu 0.5 CrSe 2 .The density of Cr 3d states in CrSe 2 was theoretically predicted to be halfmetallic with 100% spin polarization [13].The possibility of obtaining CrSe 2 from K x CrSe 2 was demonstrate in [14,15] according to the following reaction: CrSe 2 layered and spinel structures can be obtained using this approach.
CrSe 2 material should be obtained without heating since it is unstable and decomposes at a temperature of 600 K according to reaction (2) [15]: The aim of this study was to investigate phase equilibria in the CrSe 2 -Cu x CrSe 2 (delafossite) and CrSe 2 -Cu x Cr 2 Se 4 (spinel) systems at room temperature.

Methods
Samples of Cu x CrSe 2 and Cu x Cr 2 Se 4 were synthesized using precise weighed amounts (0.0001 g) of elements in evacuated quartz ampoules via the solid-phase method.This approach ensures purer products free of chloride impurities during syntheses from solutions [16].The synthesis was carried out in several stages with repeated homogenization.Based on the experience of the authors [14,15], CrSe 2 from CuCrSe 2 was obtained using a similar method through the following reactions: 1 st stage Cu + 2Cr + 4Se → CuCr 2 Se 4 (space group Fd 3 m), Single-phase finely dispersed CuCrSe 2 and CuCr 2 Se 4 powders, crystalline iodine I 2 , and acetonitrile CH3CN were used for synthesis.Prior to synthesis, residual water was removed from acetonitrile using molecular sieves (4A NaA).A stoichiometric amount of compounds and iodine was taken and 10 wt.% excess of iodine was added.Being the synthesis medium, acetonitrile was taken in excess.The synthesis was carried out for one week with periodic stirring of the samples in an ultrasonic bath once a day for 30 minutes.After 7 days, the resulting products were filtered and washed with acetonitrile to remove CuI, then dried to remove acetonitrile vapor.
The homogeneity of the synthesized samples was checked using X-ray powder diffraction (XRD) on a Shimadzu XRD 7000 Maxima diffractometer (monochromatic CuKα radiation, λ =1.5406 Å, scanning 2 θ angle range of 10 • -90 • , Bragg-Brentano geometry) in the Collective Use Center "Ural-M" of the Institute of Metallurgy, Russian Academy of Sciences, Ural Division.
Copper was removed from CuCrSe 2 and CuCr 2 Se 4 electrochemically using the galvanostatic intermittent titration method (GITT) for coulometric titration.The electrochemical cells used were Cu|Cu + |Cu x CrSe 2 and Cu|Cu + |Cu x Cr 2 Se 4 for the Cu x CrSe 2 and Cu x Cr 2 Se 4 systems, respectively.Metallic copper was used as the counter and negative electrode.The cathode material consisted of Cu x Cr y Se 2 :C45 Carbon Black:Polyvinylidene fluoride at 80:10:10 wt.%, respectively.A 0.1M solution of CuI in acetonitrile was used as an electrolyte.The search for phase boundaries was conducted through coulometric titration with a titration step of dx=0.025mol (2.5 mol%).Electrochemical measurements were conducted at room temperature using a BTS-4000 (5V, 10mA) potentiostat.The principles of determining phase boundaries through the electromotive force (EMF) method and the GITT method are described in [17][18][19][20].

Results and discussion
The results of coulometric titration are presented in Figure 2.  The experimental data analysis enabled us to determine the diffusion coefficient order.In this case, we used the technique described in [21][22][23], which involves analyzing the dependence of ∆E ∼ f (t) after turning the titration current on and off and solving equation (8): where t is the duration of the current pulse; L -diffusion length (electrode thickness); ∆E s -potential difference when the current is turned off; ∆E t is the potential difference when passing current excluding iR .Figure 2c and Figure 2d show the Cu concentration dependences of the diffusion coefficients for CuCr 2 Se 4 and CuCrSe 2 , respectively.The maximum diffusion mobility for CuCr 2 Se 4 ( D =10 −8.5 cm 2 /s) and CuCrSe 2 ( D =10 −8.5 cm 2 /s) corresponds to the stoichiometric compositions.Deviation from stoichiometry may result in a deficiency of mobile Cu ions or vacancies available for filling.
The diffusion coefficients decrease when defects occur with increasing and decreasing Cu content, as in the case of CuCr 2 Se 4 spinel.The diffusion coefficient reaches a minimum value at x=0.3 and remains almost constant with a further decrease in Cu content (Figure 2c).This Cu concentration is in good agreement with the percolation threshold for a cubic lattice (0.31 for the problem of cubic lattice nodes with interaction between nearest neighbors [24]).Forming of Cu 1.75−1.82Se is possible when moving towards compositions with high Cu content.The decrease of D at x>0.7 may be associated with the work to destroy the structure.
Figure 2d shows the dependence of the diffusion coefficient on the Cu content for the CuCrSe 2 system.The maximum value of D corresponds to the composition Cu 0.95 CrSe 2 .Increasing or decreasing the Cu content results in a decrease in D values, which may be attributed to the hindered movement of Cu ions due to defects along its sublattice.
It is worth noting that the boundary of the region with a sharp increase in the scatter of the Cu diffusion coefficient in CuCr 2 Se 4 (0<x<0.3 in Figure 2c) coincides with the boundary of the single-phase region according to electrochemical data.This may be due to the material's inhomogeneity ( CrSe 2 ), which complicates the diffusion process.However, in the case of CuCrSe 2 , such an increase in scatter when crossing the boundary of the single-phase region is not observed (Figure 2d).The difference between copper's role in the lattice of layered CrSe 2 and spinel CuCr 2 Se 4 is evident.In the former, copper acts as an intercalated impurity, while in the latter, it is an essential part of the crystal structure.In the regions corresponding to cubic CrSe 2 , copper's mobility is negligible.
To determine the chemical composition of the samples obtained by chemical extraction of Cu, an energy-dispersive X-ray (EDX) analysis was used.The averaging of the chemical composition was conducted over at least 10 points.Scanning electronic microscope (SEM) images were obtained on a Quanta-200 microscope.Figure 3 shows SEM images of CrSe 2 , Cu 0.5 CrSe 2 and CuCr 2 Se 4 at the same magnification.SEM images of CrSe 2 , Cu 0.5 CrSe 2 , and CuCr 2 Se 4 were processed using the ImageJ software package [25].The resulting distribution of the number of grains by their area is shown in Figure 4.
The chemical compositions of the obtained samples are listed in Table 1.The initial CuCr 2 Se 4 crystal structure is described by cubic ordering Fd3m with a lattice parameter of a =10.326Å, which agrees with the literature data [12].
The diffraction pattern's general profile remained unchanged after copper was chemically extracted from CuCr 2 Se 4 .An additional low-intensity peak at 46 degrees, corresponding to elemental copper, appeared.This peak was most likely formed during the decomposition of the CuI reaction product.The lattice parameter of a =10.323Åremains unchanged within the calculation error.Table 2 presents the results of a full-profile analysis of the diffraction patterns performed using the GSAS II software package [26].A copper defectivity of 6% in the CuCr 2 Se 4 phase is observed.
A full-profile analysis of an XRD pattern of CrSe 2 obtained from CuCrSe 2 (Figure 5) shows that even after chemical extraction of Cu, it remains within the lattice to some extent.This may be due to the presence of both large and small particles in the starting substance powder, as shown in Figure 3, which causes non-uniform reaction.A lattice copper concentration according to full-profile analysis is of x=0.24, which is consistent with the EDX findings presented in Table 1.[14].This composition coincides with the composition of spinel -CuCr 2 S 4 ; however, it retains a layered structure with trigonal symmetry.The EMF of the electrochemical cell's "plateau" region indicates that it is composed solely of a mixture of CrSe 2 and CuCrSe 2 .This suggests that there is no layered compound with the composition of Cu 0.5 CrSe 2 present in this system.It can be assumed that the defectiveness of the resulting sample is associated with a blocking effect.This means that copper is extracted from the surface of crystals [27].

Conclusions
The current study has established for the first time the copper homogeneity regions for CuCrSe 2 with a delafossite structure and CuCr 2 Se 4 with a spinel structure and assessed their width.In thermodynamic analysis of phase relationships, it is important to consider the presence of noticeable regions of homogeneity in these materials.
Chemical and electrochemical methods were used to partially extract copper from the CuCrSe 2 and CuCr 2 Se 4 compounds.It was found that chemical extraction is gentler and does not damage the matrix.The maximum value of diffusion coefficients D =10 −8.5 cm 2 /s was achieved at compositions close to stoichiometric for both CuCrSe 2 and CuCr 2 Se 4 systems.An increase in the number of defects results in a decrease in the values of diffusion coefficients.

Figure 2
Figure 2 shows a large homogeneity region of approximately 15 mol.% and wide two-phase regions for both Cu x CrSe 2 (spinel and delafossite) systems.Homogeneity regions were found to be in the Cu concentration range of 0.9<x<1.2(0.45 <x<0.6 in terms of Cu 0.5 CrSe 2 ) for spinel Cu x Cr 2 Se 4 and of 0.9<x<1.05for delafossite Cu x CrSe 2 .The Cu concentration range of x>0.8 for Cu x Cr 2 Se 4 corresponds to the precipitation of Cu or to the formation of Cu dendrites in the

Figure 4 .
Figure 4. Distribution of the number of grains by their area for CrSe 2 , Cu 0.5 CrSe 2 and CuCr 2 Se 4 .

Table 1 .
Chemical composition of Cu x CrSe 2 compounds before and after copper extraction.