High-pressure structural study of $\alpha$-Mn: Experiments and calculations

Manganese, in the $\alpha$-Mn structure, has been studied using synchrotron powder x-ray diffraction in a diamond anvil cell up to 220 GPa at room temperature combined with density functional calculations. The experiment reveals an extended pressure stability of the $\alpha$-Mn phase up to the highest pressure of this study, in contrast to previous experimental and theoretical studies. On the other hand, calculations reveal that the previously predicted hcp Mn phase becomes lower in enthalpy than the $\alpha$-Mn phase above 160 GPa. The apparent discrepancy is explained due to a substantial electron transfer between Mn ions, which stabilizes the $\alpha$-Mn phase through the formation of ionic bonding between monatomic ions under pressure.

Figure 1

XRD patterns of $\alpha$-Mn at selected pressures on pressure increase. The red pattern is the calculated pattern of $\alpha$-Mn at 14 GPa. Miller indices of the main peaks are also noted. The asterisks mark Bragg peaks from the rhenium gasket. The inset shows an expanded view of the pattern at 191 GPa. The x-ray wavelength is $\lambda =0.3344\AA$.

Figure 2

(a) Volume-pressure data for $\alpha$-Mn. The solid curve is an unweighted third-order Birch-Murnaghan EOS fit to the experimental data points [19]. The data from Ref. [2] (black dots) are also plotted for comparison.

Figure 3

(a) Comparison between the XRD pattern of Mn at 190 GPa from Ref. [2] (black) and the calculated pattern of hcp Fe at 190 GPa (red) using the EOS of Ref. [23]. Miller indices of hcp Fe are denoted. Miller indices in the experimental pattern are initial indices taken from Ref. [2]. The peaks indexed G100 and G101 are Bragg peaks from the Fe gasket. (b) Comparison between the experimental XRD patten of this study (black) and the calculated pattern of hcp Mn using the calculated EOS of this study (red).

Figure 4

Calculated enthalpy differences for $\alpha$-Mn and hcp Mn phases as a function of pressure. The enthalpy of the $\alpha$-Mn phase is taken as the reference.

Figure 5

The temperature-dependent (a) $H+F_{vib}$ for $\alpha$-Mn and hcp Mn at 180 GPa (see text). The enthalpy of hcp Mn at 0 K was used as the zero-point reference. (b) Vibrational entropies of $\alpha$-Mn and hcp Mn at 180 GPa. The inset shows hcp Mn having slightly lower vibrational entropies below 160 K.

Figure 6

Average per atom Bader charge transfer of Mn ions in the corresponding Wyckoff positions as a function of pressure, as calculated in this study.