High-pressure structural systematics in neodymium up to 302 GPa

Angle-dispersive x-ray powder diffraction experiments have been performed on neodymium metal to a pressure of 302 GPa. Up to 70 GPa we observe the $hP4\to cF4\to hR24\to oI16\to hP3$ transition sequence reported previously. At 71(2) GPa we find a transition to a phase which has an orthorhombic structure ($oF8$) with eight atoms in the unit cell, space group $Fddd$. This structure is the same as that recently observed in samarium above 93 GPa, and is isostructural with high-pressure structures found in the actinides Am, Cf, and Cm. We see a further phase transition at 98(1) GPa to a phase with the orthorhombic $\alpha$-U ($oC4$) structure, which remains stable up to 302 GPa, the highest pressure reached in this study. Electronic structure calculations find the same structural sequence, with calculated transition pressures of 66 and 88 GPa, respectively, for the $hP3\to F8$ and $oF8\to oC4$ transitions. The calculations further predict that $oC4$-Nd loses its magnetism at 100 GPa, in agreement with previous experimental results, and it is the accompanying decrease in enthalpy and volume that results in the transition to this phase. Comparison calculations on the $oF8$ and $oC4$ phases of Sm show that they both retain their magnetism to at least 240 GPa, with the result that $oC4$-Sm is calculated to have the lowest enthalpy over a narrow pressure region near 200 GPa at 0 K.

Figure 1

Diffraction profiles collected from Nd on pressure increase to 97 GPa. The data were collected from the same sample at DLS using a wavelength $\lambda$ = 0.4246 Å. Tick marks beneath profile (a) mark the calculated peak positions in the $hP3$ phase at this pressure. The peaks marked with asterisks are from the W gasket, and the peaks marked with a $+$ are from the Cu calibrant. The two arrows in profile (c) mark the first appearance of peaks from the post-$hP3$ phase. The peak labeled with ‘$\times$’ in profile (d) is a closely spaced doublet which includes the (110) peak from the W gasket and a peak from the new phase. Single-phase patterns from the post-$hP3$ phase are seen in profiles (e) and (f).

Figure 2

Rietveld refinement of the $oF8$ structure to a diffraction profile from Nd at 97 GPa, showing the observed (crosses) and calculated (line) diffraction patterns, the calculated reflection positions, and the difference profile $[R_P$ = 1.8%, $R_{wP}$ = 2.5%, goodness of fit (GoF) = 0.46, $R\left(F^2\right)$ = 6.1%]. The first six peaks of the $oF8$ phase are labeled with their Miller indices.

Figure 3

Diffraction profiles collected from Nd on pressure increase to above 300 GPa. The data were collected from two samples at DLS and PETRA-III using wavelengths of $\lambda$ = 0.4246 Å (DLS) and $\lambda$ = 0.4830 Å (PETRA-III) and so are plotted as a function of wave vector $Q$ so as to take into account the two different wavelengths. Tick marks beneath profile (a) mark the calculated peak positions of the $oF8$ phase. The peaks marked with the asterisks in profiles (a) and (b) are from the W gasket. The two arrows in profile (b) mark the appearance of peaks from the $oC4$ phase, and the arrow in profile (c) marks the almost complete disappearance of a peak from the remainder of the $oF8$ phase. Single-phase patterns are seen in profiles (d), (e), and (f).

Figure 4

Rietveld refinement of the $oC4$ structure to a diffraction profile from Nd at 302 GPa, showing the observed (crosses) and calculated (line) diffraction patterns, the calculated reflection positions, and the difference profile ($R_P$ = 0.7%, $R_{wP}$ = 1.1%, GoF = 0.33, $R\left(F^2\right)$ = 8.2%). The first six observable peaks of the $oC4$ phase are labeled with their Miller indices.

Figure 5

The crystal structures of (a) $oF8$-Nd at 100 GPa and (b) $oC4$-Nd at 105 GPa. Both structures comprise stackings of flat, distorted-hcp atomic layers: the four-layer stacking sequence in $oF8$ is ABCD, while $oC4$ has a two-layer ABAB repeat. The distortion of the layers from hexagonal symmetry can be quantified by the deviation of the $b/c$ axial ratio in $oF8$-Nd, and the $b/a$ axial ratio in $oC4$-Nd, from the “ideal” ortho-hexagonal value of $\sqrt{3}$ = 1.732.

Figure 6

The pressure dependence of the hexagonality of the atomic layers in the $hP3, oF8$, and $oC4$ structures of Nd, as quantified by the $b/a$ ($hP3$ and $oC4$) and $b/c$ ($oF8$) axial ratios (see Fig. 5). Because of the extended $y$ scale, the error bars on the axial ratios are smaller than the symbols used to plot the points, and have therefore been omitted. The experimental data points are shown with filled symbols, while the computed values are shown using unfilled symbols.

Figure 7

The compressibility of Nd up to 302 GPa. The solid line shows the best fitting third-order APL EoS to the full compression curve. The inset shows an enlarged view of the volume near 100 GPa, illustrating the small volume discontinuity ($\mathrm{\Delta }V/V_0$) of 0.4% and change in compressibility at the transition.

Figure 8

Linearization of the compression of Nd shown in the form of an ${\eta }_{\mathrm{APL}}\text{−}{R}_{\mathrm{WS}}/R_{5p}$ plot, where $R_{\mathrm{WS}}$ is the Wigner-Seitz radius in angstroms and $R_{5p}$ is the $5p$ ionic radius [39]. The data from the different phases of Nd are plotted using different symbols, and the phase boundaries are marked with vertical lines. The $hR24$ (Sm) phase, and the $hR24$ and $oI16$ phases (Nd), are labeled as “d-$cF4$”.

Figure 9

The enthalpy gain of the $hP3, oC4$, and $oF16$ phases relative to that of the $oF8$ phase. Notice the range of pressure between 60 and 90 GPa where the $oF8$ phase appears to be most stable. The $oC4$ phase becomes the most stable at pressures above 90 GPa. The $hP3$ phase is most stable below 60 GPa. The kinks on the curves correspond to the loss of magnetization.

Figure 10

The calculated magnetization, in ${\mu }_B/\mathrm{atom}$, of $oF8$-Nd and $oC4$-Nd as a function of pressure. The magnetization in $oC4$-Nd is greatly reduced at 90 GPa, and is zero at 100 GPa—the pressure where it is first observed experimentally. The magnetization of $oF8$-Nd decreases rapidly only above 180 GPa, well beyond the upper pressure at which it is stable.

Figure 11

The calculated volume per atom of $oF8$-Nd and $oC4$-Nd over the pressure range 40–240 GPa. The loss of magnetization in $oC4$-Nd at 90 GPa is accompanied by a volume change ($\mathrm{\Delta }V/V_0$) of 0.9% and a reduction in the compressibility.

Figure 12

The calculated magnetization, in the ${\mu }_B/\mathrm{atom}$, of the $oC4$ and $oF8$ phases of Sm over the pressure range from 100 to 240 GPa. In contrast to the behavior seen in Nd, the magnetization, although decreasing, is nonzero in both phases at all pressures.

Figure 13

The enthalpy gain of $oC4$-Sm relative to that of the $oF8$-Sm over the pressure range 100–240 GPa. The $oC4$ phase is more stable over only a narrow pressure range between 185 and 225 GPa, above which the $oC4$ phase is favored. Note the greatly reduced $y$ scale in comparison to Fig. 9.