Equation of state and high-pressure/high-temperature phase diagram of magnesium

The phase diagram of magnesium has been investigated to 211 GPa at 300 K, and to 105 GPa at 4500 K, by using a combination of x-ray diffraction and resistive and laser heating. The ambient pressure hcp structure is found to start transforming to the bcc structure at $\sim 45$ GPa, with a large region of phase-coexistence that becomes smaller at higher temperatures. The bcc phase is stable to the highest pressures reached. The hcp-bcc phase boundary has been studied on both compression and decompression, and its slope is found to be negative and steeper than calculations have previously predicted. The laser-heating studies extend the melting curve of magnesium to 105 GPa and suggest that, at the highest pressures, the melting temperature increases more rapidly with pressure than previously reported. Finally, we observe some evidence of a new phase in the region of 10 GPa and 1200 K, where previous studies have reported a double-hexagonal-close-packed (dhcp) phase. However, the additional diffraction peaks we observe cannot be accounted for by the dhcp phase alone.

Figure 1

The atomic volume of Mg as a function of pressure to 211 GPa at 300 K, as obtained from cells 1 and 2 (see main text for descriptions of each). Data points from the hcp phase are shown using solid symbols, while data from the bcc phase are shown using open symbols. Data from cells 1 and 2 are plotted using diamonds and squares, respectively. The data of Nishimura et al. [10], plotted with filled and open circles, are shown for comparison. The solid and dashed lines show the Vinet equations of state for the hcp and bcc phases, as determined from the current data, using the parameters given in Table 1. All error bars are smaller than the symbols used to plot the data. The inset shows an enlarged view of the atomic volume at pressures between 30 and 70 GPa, and highlights the volume change at the hcp-to-bcc transition.

Figure 2

Diffraction profiles collected on pressure increase from 41.1 to 56.2 GPa, and then back down to 31.3 GPa, at 700 K. The diffraction peaks from the Mg sample, MgO PTM, and Cu pressure marker are identified with tick marks beneath the bottom profile. Indices are given for the most intense diffraction peaks from each of the three materials. All diffraction patterns have had a smoothly varying background removed for clarity.

Figure 3

The temperature dependence of the hcp-to-bcc phase transition pressure in Mg on compression. The $P\text{−}T$ conditions at which single-phase hcp, mixed-phase hcp-bcc, and single-phase bcc profiles are observed are shown using filled, half-filled, and unfilled symbols, respectively. Data collected on pressure increase are plotted with squares, while data collected on pressure decrease are plotted using diamonds. The data collected on pressure decrease have been offset vertically by +10 K (at 300 K and 700 K) and +15 K (at 780 K) for clarity. The dot-dashed and dashed lines highlight the phase boundaries calculated by Moriarty and Althoff [4] and Mehta et al. [6], respectively. The two hatched areas shows the mixed-phase regions determined in the current study on pressure increase and decrease.

Figure 4

Integrated diffraction patterns obtained on laser heating Mg from 300 to 1315 K at 3.6 to 5.6 GPa. Two diffraction peaks, which can be indexed as the (103) and (105) peaks from a dhcp structure, appear at 1246 (77) K and are indexed in the highest-temperature profile. Two additional reflections, not fit by the dhcp structure, appear at $15.9^{\circ }$ (2.24 Å) and $25.6^{\circ }$ (1.40 Å), and the lowest-angle of the two peaks is highlighted with a $+$ symbol. The inset shows part of the two-dimensional diffraction image collected at 1315 K, illustrating the spotty texture of the sample peaks.

Figure 5

The $P\text{−}T$ phase diagram of Mg to 105 GPa and 4500 K. hcp-phase points are shown in black, bcc-phase points are shown using unfilled symbols and mixed-phase points are shown using half-filled symbols. Points where melting is observed are plotted with gray-filled symbols. Data plotted with square symbols are from the laser-heating portion of this study, and diamond symbols plot the resistive-heating data. The circular symbols with crosses around 15 GPa and 1300 K are those labeled dhcp in Errandonea et al. [19]; points where extra diffraction peaks were observed in this study are shown as open circles. The data plotted with stars near 50 GPa and 3500 K show the melt points from Urtiew and Grover [39]. Gray, downward-pointing triangles show the melting points from Errandonea et al. [16], with the gray dot-dash line showing the fit to these data from the same work. The gray dashed line at higher temperature is an extension to the Errandonea et al. melt line above 50 GPa, extrapolated to give the best agreement with the present data. The black lines at lower pressures show the hcp-bcc phase boundaries of Moriarty and Althoff [4] (dotted) and Mehta et al. [6] (dashed), with the solid black line showing the phase boundary determined in the current study.