In the present work, we synthesized the Cu-doped CoFe₂O₄ (Co_1-xCu_xFe₂O₄) nanoparticles with × = 0.0, 0.2, 0.4 and 0.6, by employing the citrate precursor method. The X-ray Diffraction (XRD) pattern confirmed the pure cubic structure formation with the Fd-3m space group. To know the structural purity of each sample as well as the distribution of cations, Rietveld refinement was carried out. The crystallite size increases from 39.55 nm to 41.80 nm upto x = 0.2 and with further doping of Cu²⁺ ions it decreases to 36.27 nm. Similar variation is observed in the lattice parameter where the value of ‘$a$’ first increases from 8.378 Å to 8.381 Å and then decreases to 8.377 Å. The development of a non-uniform grain is seen using scanning electron microscope (SEM), which reveals the reduction in grain size. Fourier Transform Infrared Spectroscopy (FTIR) showed the two peaks $v_1$ and $v_2$ for all the samples around 541 cm⁻¹ and 408 cm⁻¹, respectively, which further decreases to 532.5 cm⁻¹ and 402.5 cm⁻¹ as the dopant ion concentration increases. The Stiffness constant, and Elastic modulus decrease with doping whereas, the Poisson’s ratio and Pugh’s ratio show a constant value of around 0.249 and 1.660, respectively. Vibrating Sample Magnetometer (VSM) analysis shows a decrease in saturation magnetization (${\sigma }_s$) value from 76.85 emu/g to 43.62 emu/g. The net magnetic moment ($n_B$) decreases from 3.29 ${\mu }_B$ to 1.85 ${\mu }_B$ and the effective anisotropy constant value decreases from 10.672erg/g to 4.461erg/g. Thus, the prepared nanoparticles provide a way forward for their industrial applications.

在本工作中，我们采用柠檬酸盐前驱体法合成了×= 0.0、0.2、0.4和0.6的Cu掺杂CoFe ₂ O ₄ (Co _1-x Cu _x Fe ₂ O _{4 )纳米粒子。}X 射线衍射 (XRD) 图证实了具有Fd-3m空间群的纯立方结构形成。为了了解每个样品的结构纯度以及阳离子的分布，进行了 Rietveld 精修。当 x = 0.2 时，微晶尺寸从 39.55 nm 增加到 41.80 nm，随着 Cu ²⁺离子的进一步掺杂，微晶尺寸减小到 36.27 nm。在晶格参数中观察到类似的变化，其中'$A$' 首先从 8.378 Å 增加到 8.381 Å，然后减小到 8.377 Å。使用扫描电子显微镜 (SEM) 可以看到不均匀晶粒的形成，这揭示了晶粒尺寸的减小。傅里叶变换红外光谱 (FTIR) 显示了两个峰$v_1$和$v_2$对于所有样品，其值分别约为541 cm ^-1和408 cm ^-1，随着掺杂离子浓度的增加，其进一步降低至532.5 cm ^-1和402.5 cm ^{-1 。}刚度常数和弹性模量随着掺杂而降低，而泊松比和皮尤比分别显示出约 0.249 和 1.660 的恒定值。振动样品磁力计 (VSM) 分析显示饱和磁化强度下降 (${\sigma }_s$）值从 76.85 emu/g 到 43.62 emu/g。净磁矩（$n_{乙}$) 从 3.29 减少${\mu }_{乙}$至 1.85${\mu }_{乙}$有效各向异性常数值由10.672erg/g降低至4.461erg/g。因此，制备的纳米颗粒为其工业应用提供了一条前进的道路。