Ab initio study of the structure and dynamics of bulk liquid Fe

Several static and dynamic properties of bulk liquid Fe at a thermodynamic state near its triple point have been evaluated by ab initio molecular dynamics simulations. The calculated static structure shows very good agreement with the available experimental data, including an asymmetric second peak in the structure factor which underlines a substantial local icosahedral short-range order in the liquid. The dynamical structure reveals propagating density fluctuations, with an associated dispersion relation which closely follows the experimental data. The dynamic structure factors $S(q,\omega )$ show a good agreement with their experimental counterparts which have been recently measured by an inelastic x-ray scattering experiment. The dynamical processes behind the $S(q,\omega )$ have been analyzed by using a model with two decay channels (a fast and a slow) associated with the relaxations of the collective excitations. The recent finding of transverselike excitation modes in the IXS data is analyzed by using the present ab initio simulation results. Several transport coefficients have been evaluated and the results are compared with the available experimental data.

Figure 1

Pair distribution function $g\left(r\right)$ of l-Fe. Continuous (broken) line: AIMD (NM-AIMD) calculations for l-Fe at $T=1873$ K. Open triangles and full circles: experimental XD data at 1843 K from Waseda [9] and Inui [10], respectively. Open circles: experimental ND data at 1873 K from Schenk et al. [11].

Figure 2

Static structure factor $S\left(q\right)$ of liquid Fe. Continuous (broken) line: AIMD (NM-AIMD) calculations for l-Fe at $T=1873$ K. Open circles: experimental ND data at 1873 K from Schenk et al. [11]. Full circles and open triangles: experimental XD data at 1843 K from Inui et al. [10] and Waseda [9], respectively. The inset shows a detailed comparison for the second maximum.

Figure 3

Normalized AIMD calculated velocity autocorrelation function of liquid Fe at 1873 K (full line). The inset represents its power spectrum $Z\left(\omega \right)$. The dashed lines stand for the NM-AIMD calculation.

Figure 4

Normalized AIMD intermediate scattering functions $F(q,t)$ at several $q$ values (in ${\AA }^{-1}$ units), for liquid Fe at $T=1873$ K (full lines). The vertical scales are offset for clarity. The dashed lines are the NM-AIMD results.

Figure 5

Memory function $N(q,t)$ for several $q$ values (full line) along with its two exponential components. The dashed line represents the slow component and the dotted line stands for the fast component.

Figure 6

Generalized specific heat ratio $\gamma \left(q\right)$ as obtained from either the generalized hydrodynamic model (circles) or the generalized viscoelastic model (lozenges). The full circles with error bars are experimental IXS data of Hosokawa et al. [17]. The arrow shows the hydrodynamic value ${\gamma }_0\approx 1.72$.

Figure 7

Dynamic structure factors $S(q,\omega )$ of liquid Fe at several $q$ values. Full circles: experimental IXS data at $T=1843$ K [17]. Full (dashed) line: present AIMD (NM-AIMD) results after convolution with the experimental resolution function.

Figure 8

Same as in the previous figure.

Figure 9

Dispersion relation for l-Fe at $T=1873$ K. Open circles and squares: AIMD results from the positions of the inelastic peaks in the $S(q,\omega )$ and from the maxima in the spectra of the longitudinal current $C_l(q,\omega )$, respectively. Full circles with error bars: IXS data from Hosokawa et al. [17]. Broken line: linear dispersion with the hydrodynamic sound velocity $c_s=3820$ m/s. Full (open) triangles with error bars: experimental (calculated) values for the HWHM $\mathrm{\Gamma }\left(q\right)$ of the inelastic peaks.

Figure 10

(a) Transverse current correlation function $C_t(q,t)$ at several $q$ values for liquid Fe at $T=1873$ K and $q=0.54{\AA }^{-1}$(full curve), $q=1.20{\AA }^{-1}$ (dotted curve), $q=2.00{\AA }^{-1}$ (dashed curve), $q=3.08{\AA }^{-1}$ (dashed-dotted curve), $q=4.05{\AA }^{-1}$ (dashed-double dot curve), and $q=5.03{\AA }^{-1}$ (full circles). The vertical scales are offset for clarity. (b) Same for the spectra $C_t(q,\omega )$. The light red curves are the results of the NM-AIMD simulations.

Figure 11

Transverse dispersion relation for liquid Fe at $T=1873$ K. Open circles: AIMD results from the positions of the peaks in the spectra $C_t(q,\omega )$. Full line: fit to the nonanalytic viscoelastic expression. Dashed line: linear fit. The lozenges with error bars (full circles with error bars) are the positions of the transverselike inelastic modes in the calculated (experimental) dynamic structure factors $S(q,\omega )$.

Figure 12

AIMD calculated dynamic structure factors $S(q,\omega )/S\left(q\right)$ for (top to bottom) $q=0.76$, 0.93, 120, 1.31, and $1.61{\AA }^{-1}$. The vertical scales are offset for clarity. The arrows point to the locations of the transverselike excitations at $q=0.93$, 1.20, and $1.31{\AA }^{-1}$.