Impact of shape and size of particles on the magnetic properties of chromium doped cobalt ferrite

Sm Doped Cu–Ni Spinel Ferrite Nanoparticles for Hyperthermia and Photocatalytic Applications

“…The existence of vacancies together with the mismatch in ionic radii among Ni 2+ , Sm 3+ , and Cu 2+ ions may be responsible for the compressive nature of microstrain in tiny crystals. Such mismatch generates local distortion in the host lattice. − The values of mean crystallite size were noticed to decrease with the increase of Sm ions in the host Cu–Ni ferrite nanoparticles . It is mainly due to the hindrance of crystal growth caused by the incorporation of large sized Sm 3+ ions in the host structure. − Careful observation also revealed that the values of the lattice constant were noted to increase with the increment of Sm dopants in the host ferrite structure.…”

“…After eliminating the instrumental broadening, the overall line-width β (FWHM) of diffracted X-ray peaks contains only the nanocrystallite size (β size ) and microstrain (β strain ) broadening effects and it can be written as , β = false( β size + β strain ) = K λ D ⁡ cos ⁡ θ + 4 ε ⁡ tan ⁡ θ where K denotes the sphericity factor (≈0.89 for the particles owing spherical shape), λ is the wavelength of Cu–K α X-ray radiation (≈1.5406 Å), D specifies the mean crystallite size, ε signifies the microstrain existed inside the crystals and θ represents Bragg’s angle. Furthermore, the Equation is reconfigured to obtain the stated form ,− β ⁡ cos ⁡ θ = ε false( 4 nobreak0em0.25em⁡ sin nobreak0em0.25em⁡ θ false) + K λ D …”

“…Ferrimagnetic 20% Cu doped copper–nickel ferrite (Cu 0.2 Ni 0.8 Fe 2 O 4 ) exhibits an inverse spinel cubic crystal structure where both the Cu 2+ and Ni 2+ ions occupy the octahedral (B) voids and all the Fe 3+ ions are dispensed equally in both the tetrahedral (A) and octahedral (B) voids. − All the Sm 3+ dopant ions prefer to capture the octahedral (B) voids due to their large size in host Cu–Ni ferrite nanoparticles . Theoretically, the average ionic radius per atom ( r A and r B ) of both tetrahedral (A) and octahedral (B) subsites can be estimated by using the stated relationships: ,− r A = false[ C ( Fe 3 + ) r ( Fe 3 + ) false] r B = 1 2 false[ C ( Fe 3 + ) r ( Fe 3 + ) + C ( Cu 2 + ) r ( Cu 2 + ) + C ( Ni 2 + ) r ( Ni...…”

“…It is because of the large size of Sm dopants when compared with the Fe ions. We can also calculate the lattice parameter theoretically for spinel cubic ferrites by using the following equation: ,− a th = 8 3 3 false[ ( r A + R O ) + 3 ( r B + R O ) false] where, R O (1.32 Å) is the radius of oxygen ions and other notations are already indexed. The theoretically obtained values of the lattice constant ( a th ) were also found to be enhanced with the addition of Sm dopants in pristine Cu–Ni ferrite nanoparticles.…”

“…When considering spinel cubic ferrites, the calculated value of ‘ u ’ is minutely higher than the optimum value (0.375). Since the size of tetrahedral voids is less than the octahedral voids, a minor movement of O 2 ions occurs during the incorporation of cations in tetrahedral voids, producing microstrain in the crystal structure. ,− We can estimate the values of the oxygen positional parameter ( u ) of all the ferrites by the stated equation: u = true[ 1 a th √ 3 ( R 0 + r normalA false) + 1 4 ] …”