Question: Magnetite (Fe 3 O 4 ) has a spinel structure whose unit cell composition of magnetite (Fe 3 O 4 ) can be represented by

Magnetite (Fe₃O₄) has a spinel structure whose unit cell composition of magnetite (Fe₃O₄) can be represented by the formula [Fe²⁺Fe 3 and 2+O 2- and 4]₈. The Magnetite has a cubic unit cell edge length of 0.837nm. Suppose we replace 10% (atomic fraction) of the Fe²⁺ cations in magnetite with Cu²⁺ cations while the dimensions of the unit cell are almost identical. Bohr Magnetons of a Fe²⁺cation and a Cu²⁺ cation are 4 and 1, respectively. Bohr Magneton B is equal to 9.2710^-24 Am^2. It is assumed that trivalents Fe³⁺ions distribute equally in tetrahedral and octahedral positions, leading to no net contribution of Fe³⁺ ions to the magnetization of the material. Please estimate

a) The saturation magnetization of the copper ferrite [Fe²⁺(Cu²⁺)Fe 3 and 2+O 2- and 4]8 ! (5 points)

b) The saturation flux density of the copper ferrite. Vacuum permeability 0=410^-7 H/m! (3 points)

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