## 1 Introduction
(1958) [11] reported the first data for iron to \(P\) of several Mbar, essentially in excess of \(P\) in the center of the Earth. Since that time, the EOSs of virtually hundreds or even thousands of condensed materials have been studied, including elements, compounds, alloys, rocks and minerals, polymers, fluids, and porous media. These studies have employed both conventional and nuclear explosive sources, as well as impactors launched with a range of guns to speeds of order of 10 km/s. Recently, with the establishment of the NIF Gigabar platform at the Lawrence Livermore National Laboratory [12], pressures of order of 1 Gbar (10\({}^{5}\) GPa, or 100 TPa), deep into the atomic pressure regime, have been routinely achieved in their experiments [13] (in this regime, \(P\) exceeds \(P_{a}\), the so-called atomic pressure required to significantly distort core electron orbitals and estimated as \(P_{a}=E_{\rm H}/r_{\rm Bohr}^{3}=294\) Mbar, where \(E_{\rm H}\) is the Hartree energy and \(r_{\rm Bohr}\) is the Bohr radius). The lanthanides series includes lanthanum (La) and the 14 following elements in which the 4\(f\)-electron shell gets progressively filled. This shell is half-filled for europium (Eu) and fully filled for ytterbium (Yb), which is responsible for both of them being divalent, in contrast to the remaining lanthanides, which are all trivalent, similar to their transition metal counterparts, scandium (Sc) and yttrium (Y). Because the 4\(f\)-electrons are localized deep in the lanthanide atoms (specifically, in their Xe-cores), they do not participate in metallic bonding [14], which is dominated by the 5\(p\), 5\(d\), and 6\(s\) valence electrons. The typical electron structure of a lanthanide atom is [Xe] 4\({}^{m}\) 5\(d^{0}\) 5\(d^{0}\) 6\(s^{2}\) or [Xe] 4\({}^{m-1}\) 5\(d^{1}\) 6\(s^{2}\). The dominance of the \(spd\)-valence electrons in the bonding is responsible for the lanthanides' phase diagrams to vary slowly across the series so that their relations to one another is clearly seen [15]. The well established fact about the lanthanides is that, with increasing \(P\), virtually all of them undergo the same sequence of phase transformations from one hexagonal polytype to the next; it is characterized by the varying hexagonal layer stacking of the corresponding crystal structure: hexagonal close-packed (hcp, AB) \(\rightarrow\) a-Sm (9R, ABCBCACAB) \(\rightarrow\) double-hcp (dhcp, ABAC) \(\rightarrow\) face-centered cubic (fcc, ABC) \(\rightarrow\) distorted fcc (dfcc) \(\rightarrow\ldots\) [PERSON] et al. [16] showed that the dfcc phase of praseodymium (Pr) is \(hR24\), another hexagonal polytype with 24 atoms per unit cell, i.e., with a stacking of 24 ABC-layers. \(hR24\), along with two alternative crystal structures, namely, orthorhombic \(o\)16, and \(o\)S8, were identified as dfcc for other lanthanides. Recently, a possible extension of the above phase transition sequence to include post-dfcc phases was suggested in Ref. [17]. The actinides form a similar series, from Ac to lawrencium (Lr), in which the 5/6-electron shell gets progressively filled. In this respect, a comparison of the phase diagrams of the two series is useful and informative, but in contrast to the lanthanides, the structural systematics for the actinides, in terms of a sequence of phase transformations on increasing \(P\), is much less obvious for the light actinides, but becomes more obvious for the heavier actinies, starting with americium (Am) [18]: dhcp \(\rightarrow\) fcc \(\rightarrow\)\(\alpha\)-U \(\rightarrow\ldots\) Note that, again, in contrast to the lanthanides, \(\alpha\)-U is not one of the hexagonal polytypes. The principal Hugoniots of lanthanides have been experimentally investigated in several studies, e.g., refs. [7; 19], but only a few substances at a time. The systematic study of the Hugoniots for the lanthanide series as a whole was carried out in Refs. [8; 20]. Specifically, 13 lanthanides out of 15 were studied in [8] (in addition to Sc and Y), and 9 in [20] (in addition to Sc, Y, and hafnium (Hf)).