Influence of the Synthesis Route in Obtaining the Cubic or Tetragonal Copper Ferrite Phases.

In this work, magnetic copper ferrite nanoparticles are synthesized by polymer-assisted sol-gel and coprecipitation methods. The obtained purity and particle size reach values of 96% and 94 nm, respectively. Evident differences in the crystal structure have been found in the synthesized nanoparticles. A tetragonal structure is formed by the sol-gel method, while the cubic form is obtained when the coprecipitation approach is used. This work provides experimental evidence of the formation of both phases by using the same reactants and thermal conditions and only modifying the technical procedure. The formation and stability of each phase are analyzed by temperature-dependent measurements, and the observed crystal structure differences are used to propose a potential fundamental explanation to our observations based on differences in the cations' distribution and Jahn-Teller distortion. Moreover, different copper ferrite purities and particle sizes are found when using each of the methods. The spherical shape of the particles and their tendency to sinter, forming micrometric clusters, are observed by electron microscopy. Finally, the divergence in magnetization between the samples prepared by each method supports our argument about the different cations' distribution and opens the door to a wide range of different technological applications for these materials.


INTRODUCTION 28
Spinel ferrites are a family of ceramic materials with interesting magnetic properties. In addition, 29 the immense capacity to modify ferrites' properties opens the possibility to design materials with 30 novel functionalities. The chemical composition and the crystal structure are the two main aspects 31 that define their characteristics, which can be controlled by an appropriate synthesis and 32 processing route [1][2][3][4] . 33 These materials can be applied in a wide range of technological applications, such as biomedicine 34 5,6 , electronics 7,8 or energy storage 9, 10 . They are increasingly gaining attention for high frequency 35 microwaves applications 11-14 ; their large electrical resistivity makes them unique materials due 36 to the reduced eddy current losses that they experience at elevated frequencies. 37 The spinel structure is chemically represented by the formula AB 2 O 4 . Here, oxygen (O) atoms 38 form a face-centred cubic (FCC) unit cell, meanwhile A are divalent cations occupying tetrahedral 39 lattice sites (S T ), and B represent trivalent cations placed on octahedral sites (S O  (CuFe 2 O 4 ) is known to be a fully inverted spinel, but as the Cu 2+ activation energy is very small 49 when changing its position, the value of x depends on the specific preparation and cooling rate 15 . 50 Moreover, despite the theoretical spinel consists on a cubic structure, CuFe 2 O 4 can be present in 51 two different structures: (i) tetragonal (space group I4 1 /amd) which is stable at low temperatures, 52 and (ii) cubic (space group Fd3m) which appears above 700K (427°C). The formation of the 53 tetragonal phase is attributed to the Jahn-Teller effect 16,17 , which arises from the distortion of one 54 of the axis of the octahedrons (leading to a crystal symmetry reduction) 17-19 caused by the Cu 2+ 55 (3d 9 ) ions migrations to the S T 16, 18,20 . For d 4 and d 9 transition-metal ions, a spontaneous 56 degeneration of the orbits of the neighbouring atoms -leading to a distortion from the regular 57 octahedron -may decrease the electrostatic repulsion and thus increase the stabilization energy 58 18,21 . A Cu 2+ occupancy factor of 0.25 at the S T is a critical value to originate the crystal distortion 59 22 . Nevertheless, it has been proved that both structures can coexist in a temperature range of 60 approximately 40 K 15,23 . The distortion parameter ( ⁄ ) in an ideal tetragonal CuFe 2 O 4 is ~1.06, 61 but it is closely related to the inversion parameter. There is not a clear criterion in literature 62 regarding a possible change in the spinel inversion parameter during the transition. Experimental 63 data suggests that it depends on the synthesis method, as well as the annealing and cooling rates 64 15,24 . 65 There are many different techniques and approaches which have been already used to synthesize 66 ferrites. The oldest and simplest approach is the ceramic method, where the oxide precursors are 67 stoichiometrically mixed and heated up to activate the chemical reaction. The major drawback of 68 this method is the elevated needed temperature (usually above 1000 °C). Apart from the energy 69 consumption problem, there is an important particle growth that limits the production of 70 nanoparticles. Moreover, due to the difficulty to reach a homogeneous mixture of the precursors, 71 the chemical composition of the product is not ideal. If the goal is to produce high-purity 72 nanoparticles, wet chemical methods is an interesting group of processes with many different 73 approaches. Some of these approaches are thermal decomposition 25 , hydrothermal 3,10 , 74 solvothermal 26 , co-precipitation 27-29 , or sol-gel 2,14,20 for instance. 75 In this work, copper ferrite (CuFe 2 O 4 ) nanoparticles are prepared by two different wet chemical 76 methods: polymer-assisted sol-gel and co-precipitation. Both methods are accurately described, 77 and the obtained particles are characterized from a structural and magnetic point of view. The 78 structural difference in the obtained product is discussed, and their formation is analysed by means 79 of temperature dependent measurements.

RESULTS AND DISCUSSION 134
In this work, four combinations of samples have been synthesized: 2 by sol-gel method (denoted 135 with the prefix "SG" in the following plots and discussion), and 2 by co-precipitation (named as 136 "CP"). In both cases one sample has been heated at 800 °C and the other at 900 °C, for 1 hour. 137 Furthermore, three replicates have been done for each of the four combinations. 138 After completing the synthesis, the powder samples have been analysed by XRD. The comparison 139 of the four obtained patterns is shown in Figure 1.

146
Despite the low magnification in this image, it is possible to differentiate two types of traces 147 which are characteristic for each synthesis method. Some differences are the existence of doublets 148 around 30° and 35° in the case of sol-gel samples, meanwhile those prepared by co-precipitation 149 show a single peak in this position, for instance. There are other clear differences at higher angles. 150 The analysis of these patterns reveals an important fact: the predominant phase in all samples is 151 CuFe 2 O 4 , but it has a tetragonal structure (space group I4 1 /amd) in sol-gel samples, whereas it is 152 configured in a cubic structure (space group Fd-3m) when co-precipitation synthesis is used. All 153 samples contain traces of monoclinic CuO, but it is more intense in the co-precipitation ones.

154
Rhombohedral Fe 2 O 3 is only detected in sample SG1. 155 For a clearer qualitative analysis of the presence of each phase, some specific peaks are zoomed 156 in Figure 2. present. It is clear that sol-gel samples follow the tetragonal pattern and co-precipitation ones have 163 the cubic structure. Additionally, we notice that there is a minimum difference in intensity 164 between sol-gel samples, whereas the CuFe 2 O 4 intensity notably increases with temperature in 165 co-precipitation prepared powders. Figure 2.C confirms that the only sample that contains Fe 2 O 3 166 is SG1 -which disappears at higher temperatures -while Figure 2.D verifies that all the samples 167 still contain a small amount of CuO at the end of the process. Additionally, the relative content of 168 CuFe 2 O 4 increases at the higher temperatures for both methods, as could be expected. In this 169 regard, we should comment that co-precipitation samples -which have a cubic structure -have a 170 higher amount of CuO impurities than those samples prepared by sol-gel. 171 Rietveld refinement has then been performed with the goal of obtaining quantitative information 172 about the chemical composition of each sample. In Figure 3 the refined profiles of those samples 173 prepared at 800 °C are shown, while Table 1 summarizes the values obtained for all the 174 synthesized samples.   Table 1. Rietveld refinement compositions obtained for the four samples. "T" refers to the tetragonal structure and 181 "C" to the cubic one. χ 2 represents the quality of the adjustment. it should be noticed that the purity achieved by the sol-gel method is considerably higher than the 190 one obtained by co-precipitation. 191 The Rietveld method has also been used to refine the crystal structure of each of the samples. Recent articles studying the phase transition in sol-gel process 20,34 have obtained a cubic 208 dominant structure just after the gel calcination, which tends to disappear later at higher 209 temperatures. With treatments in the range of 350 °C or 400 °C, the cubic-to-tetragonal phase 210 transition starts, and the tetragonal phase is completely dominant when the CuFe 2 O 4 is processed 211 at or above 800 °C. Furthermore, it has been also reported that traditional ceramic synthesis 212 working in similar temperature conditions also produce the tetragonal phase 23 . In this article we 213 are working at 800 °C and 900 °C, so our results are in perfect accordance with these references. 214 Zhuravlev et al. 34 suggested that the reason why in their sol-gel samples the cubic phase remained 215 stable after burning the gel was the fast cooling rate, which really was a quenching process and 216 stabilized the high temperature structure. Khemthong et al. 35 have recently published an 217 interesting paper where they study the crystallization of the spinel structure during sol-gel 218 combustion by means of in situ X-ray absorption. They conclude that, in the case of sol-gel 219 process, the energy of the combustion may be enough to initiate the CuFe 2 O 4 formation, and the 220 subsequently calcination helps to ensure the crystallinity and phase purity. These conclusions are 221 also in good agreement with Zhuravlev's results. 222 On the other hand, some previous works 24,36,37 have already obtained the cubic phase by using 223 hydrothermal and thermal decomposition routes and applying both, lower and higher 224 temperatures compared with the transition one (427 °C). Furthermore, the cubic structure has 225 also been prepared by means of solid-state reaction under N 2 atmosphere 38 . However, there is not 226 a clear explanation of the reason why the cubic structure is stable at room temperature instead of 227 transforming to the tetragonal one. 228 Overall, in this work we are reporting an experimental evidence of the formation of the two phases 229 by means of the same annealing conditions, cooling rates, and atmosphere conditions. In order to 230 analyse the formation of each structure, one non-calcinated sample prepared by each method has 231 been analysed by temperature dependent XRD. The measurements have been done during both, 232 heating and cooling processes, and between room temperature (28 °C) and 950 °C every 50 °C. 233 Figure 4 shows the obtained diffraction patterns during the heating of the sol-gel sample. It is 234 important to point out that, in the sol-gel sample, the gel has been burned before doing the 235 experiment. This experience, therefore, perfectly simulates the annealing of the sol-gel obtained 236 powder. 237 238

256
It is possible to see, in Figure 5.A, that the (311) peak remains almost invariable until 500 °C, but 257 then starts to increase and shifts to lower 2θ positions. This displacement is due to an increase of 258 the unit cell parameters at high temperatures. Moreover, an additional low-intensity (222) peak 259 appears at around 36.6°. The same happens in Figure 5.B, although in this case the doublet 260 corresponding to the K α1 and K α2 is better defined. 261 peak intensity grows from 500 °C until reaching a maximum at 650 °C due to an improvement of 263 the crystallinity. Then, it decreases -due to the start of the chemical reaction to form the ferrite -264 until completely disappearing at 900 °C. CuO has a similar behaviour: as it is appreciated in 265 Figure 5.D, the resolution of the (111) peak improves above ~ 500 °C, and also starts to reduce at 266 650 °C. The main difference is that, in the case of CuO, it is not completely consumed and there 267 is some remaining intensity at 950 °C. 268 The cubic phase is the dominant phase at high temperatures, as could be expected from literature. 269 However, the tetragonal phase is formed when cooling the sample back to room temperature, as 270 it can be appreciated in Figure 6.

275
During the cooling process the cubic (311) peak shifts to higher 2θ positions due to the cell 276 contraction. However, at approximately 350 °C the cubic peak suddenly reduces, and a doublet 277 appears, which corresponds to the tetragonal phase. The transformation is complete at 300 °C.

278
This transformation temperature range is close to the one expected for the cubic-to-tetragonal 279 transition according to the previously mentioned references. 280 The same experience, with the identical heating and cooling rates has been performed with a 281 powder samples obtained by co-precipitation.

287
In this case, it is observed a poor crystalline structure until 600 °C. The two peaks which are 288 detected in the low-temperature region correspond to CuO and Fe 2 O 3 , indicating that the chemical 289 reaction has not yet started. The cubic phase starts to form at 600 °C and is completely formed at 290 800 °C, when the peaks corresponding to the former oxides are almost null. Furthermore, as it did 291 happen in the previous case, there is some CuO remaining at 950 °C. In order to have more 292 specific information about the cubic ferrite formation, Figure 8 shows some characteristic peaks 293 at higher magnifications at all the measured temperatures.

298
In Figure 8.A and Figure 8.B it is possible to see that the cubic ferrite is not present before starting 299 the annealing process, and starts to be formed between 600 °C and 650 °C. This threshold 300 temperature defining the start of the cubic phase formation is in agreement with the one previously 301 observed with the sol-gel samples. In addition, the crystalline transition and ferrite formation can 302 be clearly detected in this figure. The Fe 2 O 3 peak (Figure 8.C) remains shielded by the background 303 at low temperatures, but it suddenly appears at 500 °C when the crystallinity improves. Then, it 304 starts to reduce its intensity at 650 °C and is completely consumed at 800 °C. CuO follows the 305 same tendency except for the fact that it is not completely consumed, and the peak intensity is 306 still detected at 950 °C. The crystalline transition and ferrite formation temperatures observed in 307 Figure 8.D are in good agreement with those observed for the other two phases. 308 The cubic phase is stable at high temperatures, as could be expected. However, there is a main 309 difference compared with the sol-gel sample: here the cubic phase is continuously formed during 310 the heating process, while in the sol-gel case it was previously formed when burning the gel. 311 As has been seen with the standard XRD measurements presented in Figure 1, co-precipitation 312 method leads to the cubic phase at room temperature. Therefore, the high-temperature structure 313 remains stable when cooling back down, as can be appreciated in Figure 9. There, it can be seen 314 how the only variation is that the (311) peak shifts to higher 2θ positions due to a reduction of 315 cell parameter during contraction. 316

319
Finally, Figure 10 provides a more general comparison of the peaks corresponding to the different 320 phases at different moments of the annealing process. The existence of cubic CuFe 2 O 4 before the 321 annealing process is evident in this image, while it is completely inexistent for the co-precipitation 322 process. However, an important fact that can be noticed from this figure is the difference in the 323 cubic CuFe 2 O 4 peak at 950 °C. The cubic (311) peak in the sol-gel sample is slightly above 35.0°, 324 while it is below this value in the co-precipitation sample. This difference in the peak position 325 indicates a different unit cell parameter in each sample. Consequently, the cubic phase produced 326 by each method at 950 °C seems to have meaningful structural differences. This is an important 327 observation as it may explain the stability of the cubic and tetragonal phase when cooling down 328 for each method. 329

336
Although previous works justified the formation of each phase by means of the cooling rates in 337 the annealing process or the atmospheric conditions, our results demonstrate the formation of the 338 two different crystal structures under the same annealing conditions. The explanation of why the 339 cubic phase produced by co-precipitation is stable when cooling down the sample, but not the one 340 prepared by sol-gel is not a straightforward task. In contrast to previous publications, our results 341 suggest that the stability of one phase or the other is more related to the history of the sample than 342 to the annealing cooling rate. The evidenced structural differences in the cubic phase at 950 °C 343 between each method, as well as the formation of a premature cubic phase in the gel burning 344 process, suggest that the sol-gel method forms a metastable cubic phase that is unstable when 345 cooling down to room temperature after annealing. On the other hand, the cubic phase 346 continuously formed by the co-precipitation method is able to be arranged in a such stable 347 configuration that remains when the sample is cooled down. Considering that high temperature 348 treatments lead to structural and magnetic disorders and that a deficit of Cu 2+ in the S T has been 349 reported for the room-temperature cubic phase 40 , it can be understood that the gel burning process 350 leads to a different cation distribution (i.e. inversion parameter) compared with the continuous 351 ferrite formation during the co-precipitation annealing. This different cation distribution, 352 especially in the case of the Cu 2+ ion, has a direct influence on reducing the crystal symmetry by 353 the Jahn-Teller effect. Therefore, a difference on the system energy due to the different cations 354 distribution may explain the difference in stability between the two cubic phases when cooling 355 down. A deeper crystallographic analysis of these parameters could confirm this hypothesis. 356 In a recent paper, Nikolić et al. 41 proved that an increase on the Fe content favours the cubic 357 phase stabilization. They provide a deep discussion about the Fe 3+ incorporation on the CuO 42 358 structure through the Cu 2+ release to form the CuFe 2 O 4 . Therefore, the oxygen release during the 359 cooling process affects to the cubic or tetragonal stabilization. These conclusions agree with our 360 explanation. Although all of our samples have been prepared with the same Fe 3+ /Cu 2+ ratio 361 (contrary to the experimental procedure presented in 41 ), it is the gel burning process the one that 362 quenches a premature cubic phase with a non-equilibrium cation distribution. This is then the key 363 point, as it affects to the Cu 2+ sides occupancy (i.e. to the Jahn-Teller effect) and to the Fe content 364 on the CuFe 2 O 4 structure. Furthermore, notice that the CuO content (Table 1) is larger for the co-365 precipitation samples than for the sol-gel ones (i.e. a larger Fe content for co-precipitation 366 samples), in good agreement with this argumentation. 367 The effect of the synthesis method on the particle size distribution is analysed by LD 368 measurements. Figure 11 shows the results for each sample.

374
In both cases the number % distribution is under 100 nm, meaning that most of the synthesized 375 particles can be considered as nanoparticles. The small difference that can be found between 376 curves in Figure 11.A is not significant because the device resolution in this range is not sufficient. 377 The average particle size is of 94.0 ± 0.8 nm. On the other hand, Figure 11.B shows the percentage 378 of the volume of the sample that is occupied for each particle size. There, the first remarkable 379 aspect is the difference in particle size between those samples prepared by sol-gel and those 380 prepared by co-precipitation: smaller sizes are achieved by the co-precipitation method, with a 381 difference of one order of magnitude when comparing the centre of their distributions. Moreover, 382 by comparing the two samples prepared by the same approach, it is possible to see how the 383 distributions are displaced to larger diameters in those specimens treated at higher temperatures, 384 especially in the sol-gel case. In order to extract quantitative information about the volume % 385 distributions, a gaussian distribution has been fitted to the experimental data (see Figure 11.C). 386 The mean particle size for each distribution (which are represented in Figure 11.D) clearly show, 387 following the trend previously commented, the dependence of the particle size with the synthesis 388 method and annealing temperature. These results are coherent with what could be expected from 389 a particle growth point of view. 390 There is another remarkable aspect in the volume % distribution: the existence of a smaller 391 population with some hundreds of nanometres in diameter. Considering that each order of 392 magnitude in diameter has 10 3 times less influence in the volume contribution, this population is 393 of immense importance and possibly corresponds to the nanometric population detected in Figure  394 11.A. 395 As it can be observed, the volumetric distributions shown in Figure 11.C are not regular and are 396 formed by the superposition of multiple distributions. We have used the Ulm and Constantinides 397 method 43-46 to deconvolute the individual gaussian distributions that lead to the general profile. 398 The deconvolution for each of the four samples is shown in Figure 12. In addition, a summary of 399 the obtained data is provided in Table 3.   The first aspect that can be observed for the sol-gel samples is that the smaller distribution is 409 centred at ~8.5 μm and ~18 μm for the samples prepared at 800 °C and 900 °C, respectively. 410 Furthermore, this is the most popular distribution for the SG1 sample, while it moves to 54 μm 411 for SG2. These two observations agree with the general tendency observed in Figure 11 and with 412 what could be thermodynamically expected. In addition, the distribution is wider for the sample 413 annealed at 800 °C than the one at 900 °C. On the other hand, the samples prepared by co-414 precipitation mainly consist on one major distribution on the low-size range, and a set of 415 complementary smaller distributions with larger diameters. Again, we see that the main 416 distribution for the sample prepared at 800 °C is smaller than the one for the sample prepared at 417 900 °C. Finally, the main distribution values are smaller for the co-precipitation samples than for 418 the sol-gel ones. 419 SEM images shown in Figure 13 complements the size study of these particles and give 420 information about their shape and distribution. diameter and they are qualitatively bigger for sol-gel samples than for co-precipitation ones. All 427 of these conclusions are in agreement with the results obtained by LD measurements. 428 Furthermore, it is worth to notice that nanometric particles are almost spherical shaped, whereas 429 the aggregates present random shapes. These random shapes can be one of the reasons why in 430 Figure 11.B the curves are formed by the superposition of multiple distributions: LD assumes 431 spherical particles, so the diffraction with non-uniform particles can generate the effect of having 432 multiple distributions. Moreover, the different sintering between nanoparticles also leads to the 433 formation of micrometric clusters of different sizes. The scale of the aggregates' diameters 434 observed in these images agrees with the quantitative approximations shown in Figure 11.D. 435 Additionally, when looking at higher magnification ( Figure 14) it is seen that there is a direct 436 bonding between particles, i.e. sintering has occurred during thermal processes. This effect has 437 been previously reported in other works 20,34,47,48 which synthesize the same kind of materials by 438 the same methods. Thus, the nanometric distribution shown in Figure 11.A may represent the 439 individual small population, meanwhile the micrometric one in Figure 11.B may be representative 440 of the aggregates.

450
It is clear, from Figure 15 Although the reactants and synthesis conditions used in both methods are the same, sol-gel 474 approach produces tetragonal CuFe 2 O 4 meanwhile co-precipitation forms the cubic form of the 475 same material. This is a key conclusion as the existing literature justifies that the formation of one 476 or the other structure is due to a difference on the experimental thermal conditions. Traces of CuO 477 are still present in all the samples (especially in those prepared by co-precipitation) meanwhile 478 Fe 2 O 3 is only present in the sol-gel sample prepared at 800 °C. The XRD profile fitting by Rietveld 479 refinement reveals that the purity of CuFe 2 O 4 increases with temperature for both methods. 480 Purities up to a 96 % and 88 % are achieved, respectively, by the sol-gel and co-precipitation 481 methods. 482 The formation and stability of each crystal structure have been observed by means of temperature 483 dependent XRD measurements. From these measurements it has been proved that, in the sol-gel 484 method, the gel burning process produces a metastable cubic CuFe 2 O 4 phase, which transforms 485 to the tetragonal one after a high-temperature annealing. On the other hand, the co-precipitation 486 cubic phase is continuously formed from 600 °C and remains stable after the annealing process. 487 The structural differences found between the two cubic structures at 950 °C may explain their 488 difference in stability. We propose that the initial gel burning process acts as a quenching process 489 that leads to a metastable cubic phase, whose stability is lower when cooling down. According to 490 the Jahn-Taller principles, we believe that this is due to a different cation distribution (i.e. different 491 spinel inversion parameter) that leads to a different system energy. Furthermore, the clear 492 differences in magnetization between both structures supports this idea. However, a more detailed 493 crystallographic study should be done in order to corroborate this hypothesis. 494 LD particle size analysis has shown that most of the particles have a diameter close to 94 nm, 495 although there are also present micrometre-sized bodies in the samples. SEM microscopy has 496 confirmed the formation of the nanoparticles, and moreover it has proved that the micrometric 497 bodies really consist on sintered nanoparticles. Furthermore, the deconvolution of each of the LD 498 distributions has demonstrated that the size of the sintered bodies clearly depends on the synthesis 499 route and thermal conditions. These results are in excellent agreement with the SEM observations. 500 The novelty in this work comes from the experimental evidence in the preparation of the 501 tetragonal and cubic CuFe 2 O 4 structures by two fast and simple techniques by using exactly the 502 same reagents and temperature conditions. Therefore, the capacity for synthetizing CuFe 2 O 4 via 503 sol-gel or co-precipitation becomes of great importance due to the great technological opportunity 504 it offers to tune the nanoparticles, as the magnetic results show. 505 506 AKNOWLEDGEMENTS 507 J. Calvo-de la Rosa acknowledges Ajuts a la Docència i a la Recerca (ADR) given by the 508 Universitat de Barcelona and the Catalan Government for the quality accreditation given to his 509 research group DIOPMA (2017 SGR 118). Authors would also like to thank Xavier Alcobé for 510 his collaboration on the XRD measurements and results' interpretation. 511 512 513