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

population of energy level E_i:

thermodynamic sum of states:

free energy:

internal energy:

where: k_B= 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/k_B = 0.67171 K]

• Details of Theory

  • Hamiltonian
  • Fine electronic structure Ei, Γi Ei, Γi(|LSLzSz>)
  • The thermodynamic functions

  Computable properties:

  • entropy S(T)
  • specific heat Cmol(T)
  • magnetic moment and influence of the external magnetic field for it m(B,T)
  • magnetic susceptibility along different crystal directions χi(T)
  • visibility of the energy levels in spectroscopy <Γi|J_|Γj>, <Γi|J+|Γj> , <Γi|JZ|Γj>
  • spin and orbital momenta of the magnetic ion in solid <Γi|L|Γi>, <Γi|S|Γi>