Abstract
This study presents a novel contribution to the chromite literature by simulating and analyzing, for the first time, the contributions from the ferrimagnetic, paramagnetic, and superparamagnetic phases to the observed magnetization as a function of applied field, π΄βββ (
π0
π―βββ ), of Co(1βx)NixCr2O4 (
x
=
0, 0.15, 0.20) nanoparticles. The modified Langevin function, incorporating a particle size distribution term, was also used to simulate the π΄βββ (π0π―βββ ) curves for the samples exhibiting superparamagnetism. An innovative deconvolution technique, implemented using customized and self-developed Wolfram Mathematica programs, provided a detailed breakdown of the contributions to the various phases, delivering unique insights into the importance of each magnetic phase. As not to have a loose-standing theoretical approach, this study focused on a dual approach in which real samples were synthesized and characterized first, and the actual experimental results were compared with the simulated data to evaluate the validity of the deconvolution technique used in the set-up of the Mathematica programs.
In order to obtain nanoparticle samples with the needed characteristics that were to be probed theoretically, Co(1βx)NixCr2O4 (0 β€ x Λ 1) nanoparticles were synthesized, as this system has in the past showed the desirable qualities such as magnetic phase transitions, and superparamagnetism. Both the sol-gel and co-precipitation methods were used in the preparation of the samples, where the particles were calcined at two distinct temperatures, 773 K and 1173 K, to achieve the particular particle sizes critical for this study. This calcination approach provides insights into how the particle size affects the material's morphological, structural and magnetic properties. Initial results probing purely the effect of calcination temperatures on the samples indicated that those calcined at 773 K had average particle sizes below 10 nm and exhibit pronounced superparamagnetic behaviour near the Curie temperature,
iv
TC, characterized by negligible coercivity and remanence. Conversely, samples calcined at 1173 K, with particle sizes around 100 nm, revealed a complex interplay of superparamagnetic and ferrimagnetic properties, evidenced by the shape of the experimentally obtained hysteresis loops.
The characteristics of the Co(1βx)NixCr2O4 nanoparticles were systematically explored in the compositional range of 0 β€ x Λ 1, in order to understand the intricate modifications in magnetic and structural properties induced by nickel doping. This comprehensive analysis reveals significant insights into how nickel substitution tailors the material's properties for potential applications requiring precise magnetic behaviour control. Key findings include the identification of 773 K as the threshold for crystalline phase formation, with amorphous materials forming at lower calcination temperatures and Cr2O3 emerging as a secondary phase at 773 K. Calcination up to 1173 K was optimized to control nanoparticle size, preventing growth beyond the nanoscale. Early studies during the initial stages of this work probed the effect of the ramping rate during the calcination process and its impact on the various properties was evident β thus, a constant ramping rate was used further during this study.
The structural and morphological characteristics of Co(1βx)NixCr2O4 (0 β€ x Λ 1) nanoparticles, synthesized by co-precipitation and sol-gel techniques, were thoroughly analyzed. X-ray diffraction confirmed the Co(1βx)NixCr2O4 nanoparticles are of the cubic phase with a space group of Fd-3m, with Rietveld refinement validating phase purity at 1173 K. In contrast, samples calcined at 773 K showed the formation of a secondary Cr2O3 phase. The materials prepared through co-precipitation exhibit a lower concentration of impurities and demonstrate superior quality compared to sol-gel synthesis methods. As a result, most of the samples used in this study were synthesized using the co-precipitation method, ensuring high purity and consistency. This approach not only enhances the overall material properties but also provides a more reliable foundation for investigating the structural and magnetic characteristics of the
v
nanoparticles. This method improves the material properties and offers a more consistent basis for studying the structural and magnetic features of the nanoparticles.
Transmission electron microscopy revealed significant size variations influenced by calcination temperature, with energy-dispersive X-ray spectroscopy confirming the theoretical composition and absence of contamination. Fourier transform infrared spectroscopy validated structural integrity by identifying characteristic vibrational modes of Co(1βx)NixCr2O4 nanoparticles.
Magnetic properties were studied using a vibrating sample magnetometer. Field and temperature-dependent magnetization measurements showed a distinct decrease in coercivity with increasing temperature across all samples. For Co(1βx)NixCr2O4 nanoparticles with x = 0, 0.15, 0.20, and 0.25, calcined at 773 K, superparamagnetic behaviour was evident in a temperature range near TC, with negligible hysteresis, attributed to the small particle size. In contrast, samples calcined at 1173 K exhibited a mix of ferrimagnetic and superparamagnetic phases, with saturation magnetization and coercivity diminishing above TC. Notably, a critical observation was the disappearance of spin spiral magnetic order (at temperature TS) for samples with x > 0.50.
A creative simulation methodology was developed to analyze the π΄βββ (π0π―βββ ) curves by combining ferrimagnetic, paramagnetic, and superparamagnetic contributions. For nanoparticles below 10 nm, a modified Langevin function incorporating a particle size distribution provided a remarkably accurate fit to the experimental data, showcasing the strength of the model and the quality of the simulation software developed.
Neutron diffraction studies were done to probe the structure and phases present in the material. In addition, this part of the investigation into the properties of the Co(1βx)NixCr2O4 nanoparticles allowed for a better understanding of the secondary Cr2O3 phase and permitted the
vi
determination of the various transitions more accurately. The analysis of the neutron diffraction data revealed ferromagnetic ordering contributions superimposed on the (111) nuclear reflection for all samples, with magnetic satellite peaks (220)* indicating non-collinear spin-spiral ordering below TS in most samples. For x = 0.85, structural transformations were observed as the (220) peak transitioned to (202) at lower temperatures, highlighting a unique interaction between structural and magnetic properties.
Thus, this study reports on a systematic and innovative analysis of the effect of nickel doping on the morphological, structural and magnetic properties of CoCr2O4, through the synthetization of Co(1βx)NixCr2O4 (0 β€ x Λ 1) and their characterization using various experimental techniques. The obtained data was further analysed through simulations, leading to significant contributions to understanding the complex properties of Co(1βx)NixCr2O4 nanoparticles. The integration of advanced synthesis and characterization techniques with cutting-edge magnetic simulation methods, demonstrates the novelty of this research. The present studyβs findings pave the way for designing materials with tailored magnetic behaviours for diverse technological application.