Free energy of bcc iron: Integrated ab initio derivation of vibrational, electronic, and magnetic contributions

We present ab initio derived thermodynamic properties of ferromagnetic bcc iron up to the bcc-fcc phase-transition temperature (1200 K), including vibrational, electronic, and magnetic contributions. The quasiharmonic approximation and finite-temperature density-functional theory are employed to account for vibrational and electronic excitations. The magnetic contribution is derived from the solution of the quantum Heisenberg model within many-body theory using the mean-field and random-phase approximation. The calculated thermodynamic properties show an excellent agreement with available experimental data and reveal the necessity to consider all three types of excitations.

Figure 1

(Color online) Ab initio phonon ( dashed line, left axis, at 300 K) and magnon (solid line, right axis, at 0 K) spectrum of ferromagnetic bcc iron. The results are, respectively, compared with available neutron-scattering data (Refs. 26, 27, 28).

Figure 2

(Color online) Ab initio free energy $F$ at zero pressure as a function of temperature $T$, including various combinations of the vibrational (vib), electronic (el), and magnetic contribution. The latter has been calculated within the MF, iMF, RPA, and iRPA. The CALPHAD data has been obtained with the THERMOCALC program and the SGTE unary database (Ref. 30). Inset. The CALPHAD data are taken as the reference at each temperature.

Figure 3

(Color online) Heat capacity $C_P$ in units of the Boltzmann constant $k_{\text{B}}$ at zero pressure $P$ as a function of temperature $T$, including the various contributions as specified in Fig. 2. The experimental data are from Refs. 31, 32.

Figure 4

(Color online) Comparison of several theoretical approximations for the magnetization $M\left(T\right)=M_{0}m\left(T\right)$ in comparison with experimental data (Ref. 36) and Monte Carlo calculations (Ref. 10). The results are plotted as a function of the reduced temperature $T/T_C$.