Question

Gadolinium element exhibits as ferromagnetic below 16° C with 7.1 Bohrmagneton per atom. Calculate the magnetic moment per gram. Calculate saturation magnetization when Atomic weight of Gadolinium is 157. 26 and its density is 7.8 X 10 3 kg /m3. I. What does magnetic moment per gram mean? II. In this scenario, how saturation magnetization could be increased or decreased? III. How this increase or decrease affects the response of the Gadolinium?

Answer 1

157.26 gm of Gadolinium has Avogadro number of atoms, i. e. 6.023 X 10²³ atoms.

157.26 gm of Gadolinium has magnetic moment of 7.1 X 6.023 X 10²³ Bohrmagneton.

The magnetic moment per gram of Gadolinium = (7.1 X 6.023 X 10²³) / 157.26 = 0.2719 X 10²³ Bohrmagneton

Let N is the number of atoms per unit volume of the magnet.

N= ρN_A / A = 7. 8X 6.023 X 10²³ / 157.26 =0.298 X 10²³ atom/cm³
Here ρ is density, N_A is Avogadro Number and A is the atomic weight.

Magnetic moment per atom, i. e.

μ_atom=7 .1μ_B=7 .1X9 .27 X 10⁻²⁴ A−m ²=65 . 817 X 10⁻²⁴ A−m ²=65.817 X10⁻²⁰ A−cm ²  

Saturation magnetization, μ_s=Nμ_atom=0.298 X10²³X 65.817 X 10⁻²⁰=19.61 X 10³=1961 A /cm.

The saturation magnetization value of a material decreases with increase of temperature. And it increases with increase in particle size as temperature increases crystallite size increases.