Fine electronic structure (Ei, Γi) allows to find a thermodynamic functions for the statistical group of N ions. It is usefully, to put N=NA≈6.022.1023 mol-1 (Avogadro constant).

a

 

population of energy level Ei:

thermodynamic sum of states:

free energy:

internal energy:

 

where: kB= 1,38 x 10 -23 J/K (Boltzmann constant)

In temperature T = 0[K] (absolute zero) only the lowest state is occupied. The magnetic moment at 0[K] is equal to the moment of the ground state. It allows evaluate the total, spin and orbital moments.
Taking into consideration the possibility the thermal population of states we automatically achieve a thermal evolution of the single ion properties of the compound.

Useful relationships between units:

ENERGY
[1 K  = 0.0862 meV = 1.38·10 -23 J, ( K - Kelvin)]

MAGNETIC MOMENT
[ μ B -Bohr magnetron]

MAGNETIC SUSCEPTIBILITY
[ μ B /T× ion - Bohr magneton/Tesla×ion ] ( μ B/T × ion = 0.5586 emu/mol)

MAGNETIC MOMENT
M[μ B/ f.u.] ( 1μ B = 9.27 ·10-24 J/T,  J/T = A × m2 ) [μ B× T/kB = 0.67171 K]