The impact of rare earth Nd³⁺ cations on structural, spectral, magnetic and dielectric parameters of NiFe₂O₄ nanoparticles

Figures & data

Figure 1. Synthesis scheme of Nd-substituted NiFe₂O₄ nanocrystallites.

Figure 2. (a) XRD pattern of Nd-substituted NiFe₂O₄ and (b) shifting in XRD peaks (311).

Figure 3. A relation between Nd concentration, cell constant and crystallite size.

Table 1. Various XRD parameters of Nd-substituted NiFe₂O₄ nanocrystallites.

Compositions	Cell constant α (Å)	Cell volume (Å^3)	Crystallite size (nm)	X-ray density ρx (g cm^−3)
NiFe2O4	8.3501	582.20	14.25	5.35
NiNd0.0125Fe1.9875O4	8.3534	582.89	15.21	5.37
NiNd0.025Fe1.975O4	8.3549	583.20	15.84	5.39
NiNd0.05Fe1.95O4	8.3521	582.62	14.70	5.44

Figure 4. FTIR spectra of Nd-substituted NiFe₂O₄ nanocrystallites.

Table 2. FTIR modes (υ₁ and υ₂) and force constants (F_t and F_o) for Nd-substituted NiFe₂O₄ nanocrystallites.

Compositions	Wavenumber υ1 (cm^−1)	Wavenumber υ2 (cm^−1)	Ft × 10^5 (dynes/cm)	Fo × 10^5 (dynes/cm)
NiFe2O4	429	597	3.91	3.97
NiNd0.0125Fe1.9875O4	410	600	3.95	3.81
NiNd0.025Fe1.975O4	428	602	3.97	3.99
NiNd0.05Fe1.95O4	419	597	3.91	3.88

Figure 5. Magnetic-Hysteresis curves of Nd-substituted NiFe₂O₄ nanocrystallites at room temperature.

Table 3. Hysteresis parameters values derived from room temperature hysteresis loops for Nd-substituted NiFe₂O₄ nanocrystallites.

Compositions	Ms (emu/g)	Mr (emu/g)	Hc (Oe)	k × 10^3 (erg/g)	R = Mr/Ms (squareness ratio)	nB µB (Bohr Magneton)
NiFe2O4	41.67	2.12	0.027	1.1719	0.0509	1.7497
NiGd0.0125Fe1.9875O4	31.27	4.45	0.040	1.3029	0.1423	1.3193
NiGd0.025Fe1.975O4	20.34	2.05	0.070	1.4831	0.1007	0.8622
NiGd0.05Fe1.95O4	12.31	0.82	0.066	0.8463	0.0666	0.5267

Figure 6. (a) Real part of dielectric permittivity, (b) imaginary part of dielectric permittivity, and (c) tan loss vs frequency (GHz) of NiNd_xFe_2-xO₄ nanocrystallites.