Confirm that there are 1.72 Bohr magnetons associated with each cobalt atom, given that the satu

Confirm that there are 1.72 Bohr magnetons associated with...

Key Concepts

Saturation Magnetization

Saturation magnetization is the maximum magnetization a material can achieve under an applied magnetic field when all the magnetic moments are aligned. It provides a measure of the intrinsic magnetic strength of a material and is used in experiments to relate macroscopic magnetic properties to microscopic entities such as atoms or ions.

Bohr Magneton

The Bohr magneton is a fundamental physical constant that represents the natural unit of magnetic moment for an electron due to its orbital or spin angular momentum. It serves as a reference scale when quantifying magnetic moments at the atomic level, enabling the comparison between measured macroscopic magnetization and contributions from individual atoms.

Crystal Structure (HCP)

The crystal structure, specifically the hexagonal close-packed (HCP) arrangement in the context of cobalt, describes the geometric organization of atoms in the solid. Knowledge of the HCP arrangement, including lattice parameters and the c/a ratio, is crucial as it affects the density of atoms in the material and thereby the calculation of properties such as magnetization per atom.

Unit Cell Volume and Atomic Dimensions

The unit cell volume, determined by the crystal structure parameters including the atomic radius and the c/a ratio, provides the basis for calculating the number of atoms per unit volume. This information is essential for connecting the measured macroscopic saturation magnetization to the individual magnetic moments of atoms.

Calculation of Magnetic Moment per Atom

Calculating the magnetic moment per atom involves linking the macroscopic saturation magnetization with the atomic density derived from the crystal structure. By determining the number of atoms in a unit volume and relating it to the total magnetic moment, the magnetic contribution per atom can be evaluated and compared to the Bohr magneton to quantify atomic-level magnetic behavior.

Transcript

00:01 Alright, so here we want to compare that to compound that there are 1 .7 to bohr bha magnetons associated with each cobalt atom right with each cobalt atom so therefore let in prime sub b will be the number of boer magnetons per atom so we will calculate that so this is here and this is m sub s or mu sub b times n and here n is just the number of atoms per cubic meter and the number of items per unit cell six par hexagonal closed peg and this is divided by the unit cell volume so this n is six over v sub c this is unit cell volume right and and substituting these into the past equation par in, so this will be m sub s, v, c over 6 times mu sub b, right? so here the unit cell volume is just the product of the base area times the sill height.

01:23 So this base area is just three times the area of the parallel paved.

01:27 So let which is a parallel paved here right so let this is a parallel paved here right and with the sides of a c d e right and here is this is b this angle is 60 degree right and this angle is 30 degree right and here this is the let this is let this is aside this is two times are right and here so let the area let the area up a cd it is just the length cd times b c but cd is just a cd right and the unnatal edge length bc this bc is a cost 30 degree right and this is a times square root 3 over 2 right and the base area is just let the base area is just uh three times cd side time bc side right so this cd is 3x a square root 3 over 2 and this is 3a square over 2 times square root 3.

03:26 And since we know that c is just 1 .6 to 3 times a and putting this c value, so we will guard that v sub c is area times c, right? and this will be 3a square times c over 2 times square root 3 and this is 3 a square times 1 .6 .23 times a over 2 times square root 3, right? and this v...

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