# Phase diagram of ruthenium characterized In Situ by synchrotron X-ray diffraction and Ab Initio simulations

Simone Anzellini, Anna Herlihy, Serena Dominijanni, Pablo Botella, Annabelle Brooks, Leonid Burakovsky, Anna Pakhomova, Daniel Errandonea

<figure><img src="image_1.png" /></figure>

To cite this version:

Simone Anzellini, Anna Herlihy, Serena Dominijanni, Pablo Botella, Annabelle Brooks, et al.. Phase diagram of ruthenium characterized In Situ by synchrotron X-ray diffraction and Ab Initio simulations. Results in Physics, 2024, 65, pp.107961. 10.1016/j.rinp.2024.107961. hal-05095791

HAL Id: hal-05095791

https://cnrs.hal.science/hal-05095791v1

Submitted on 3 Jun 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_2.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
# Phase diagram of ruthenium characterized *In Situ* by synchrotron X-ray diffraction and *Ab Initio* simulations

Simone Anzellini<sup>a,*</sup>, Anna Herlihy<sup>b</sup>, Serena Dominijanni<sup>c</sup>, Pablo Botella<sup>a</sup>, Annabelle Brooks<sup>b,d</sup>, Leonid Burakovsky<sup>e</sup>, Anna Pakhomova<sup>f</sup>, Daniel Errandonea<sup>a</sup>

<figure><img src="image_3.png" /></figure>

## ARTICLE INFO

**Keywords:**
Phase diagram
Melting line
Laser-heating
X-ray diffraction

## ABSTRACT

In this work, an *in situ* characterization of the high-pressure and high-temperature phase diagram of ruthenium was carried out. This experiment was performed using a combination of laser-heated diamond anvil cell (LH-DAC) and X-ray diffraction (XRD) techniques at the beamline ID27 of the European Synchrotron Radiation Facility (ESRF). XRD patterns were collected in the range of 15 GPa to 110 GPa and from ambient temperature up to 6600 K. While the *hcp-fcc* transition, predicted to occur at elevated temperatures was not observed, this study has produced the first experimental observation of a solid-liquid phase transition of Ru at *HP* conditions. A P-V-T equation of state valid up to 100 GPa and 3000 K is reported.

## Introduction

Transition metals exhibit a series of interesting and useful properties originating from their partially filled *d*-band and the consequent delocalization of their *d*-orbitals. Consequently, they attract significant attention from a range of scientific communities [1–4]. As a result, an extensive amount of research efforts have been dedicated to this group of metals in recent decades. Most studies focused in mapping and interpreting the systematic trends of their properties. For instance, the influence of *d*-band filling on the bulk modulus and cohesive energy [5] as well as on the stability of the crystal structures [6] have all been investigated and quantified. In recent decades, several research group focused their attention in mapping out and understanding the thermodynamic phase diagrams of transition metals under high pressure (*HP*) and high temperature (*HT*) conditions [7]. Despite this fact, surprisingly little is currently known about the behaviour of ruthenium (Ru) under extreme conditions of pressure (*P*) and temperature (*T*) [8]. Ru is a 4*<u>d</u>* transition metal in group 8 of the periodic table, with electron configuration [Kr] 4*<u>d</u>*<sup>7</sup> *s*<sup>1</sup>. It is one of the six components in the platinum-group metals (PGMs) which all share similar physical and chemical properties, such as being inert to most other elements of

the Periodic Table It is for this reason that Ru is usually found in the same mineral deposits as other PGMs [9], and it is easily alloyed with them for industrial applications. For example, Ru can be alloyed with platinum and palladium in order to increase their hardness [10]. There are a few other metals Ru is often alloyed with, including titanium (to increase resistance to corrosion) [11] and molybdenum (to increase the superconducting critical temperature) [12]. Additionally, there have been several studies of ruthenium nitrides at extreme conditions, as these are thought to be promising ultra-hard materials [13–15]. Like many other transition metals, Ru is also frequently used as a chemical catalyst [16–18]. Due to it being very inert, it is also a good candidate for thick-film resistors and low-resistance electrical contacts [19,20]. Pure Ru has a superconducting transition temperature of 0.47 K [21].

At ambient *P* it has a hexagonal close packed (*hcp*) structure and melts at 2607 K [22]. Other than this, not much is currently known about the structural phase diagram of this element under *HP-HT* conditions. Only in 1963, Bucher et al. performed a series of measurements on various metals to investigate how *P* affects superconducting properties [23]. One of these studies focused on the relationship between *P* and the isotope effect for ruthenium and osmium [24]. The samples

<footnote><sup>a</sup> Departamento de Física Aplicada - Instituto de Ciencia de Materiales, Matter at High Pressure (MALTA) Consolider Team, Universidad de Valencia, Edificio de Investigación, C/Dr. Moliner 50, Burjassot, Valencia, 46100, Spain</footnote>

<footnote><sup>b</sup> Diamond Light Source Ltd., Harwell Science & Innovation Campus, Diamond House, Didcot, OX11 ODE, UK</footnote>

<footnote><sup>c</sup> Institut de Minéralogie de Physique des Matériaux et de Cosmochimie (IMPMC), Sorbonne Université, Muséum National d'Histoire Naturelle, CNRS UMR 7590, Paris, 75005, France</footnote>

<footnote><sup>d</sup> H.H. Wills Physics Laboratory, University of Bristol, Bristol, BS8 1TL, UK</footnote>

<footnote><sup>e</sup> Theoretical Division, Los Alamos National Laboratory, Los Alamos, 87545, NM, USA</footnote>

<footnote><sup>f</sup> European Synchrotron Radiation Facility, Avenue des Martyrs, 71, Grenoble, 38043, France</footnote>

<footnote>* Corresponding author.
E-mail address: simone2.anzellini@uv.es (S. Anzellini).</footnote>
were pressurized using the fixed clamp technique [25], and the critical temperatures were recorded as a function of *P* up to 3 GPa. Around the same time, the first *HP* X-ray diffraction (XRD) measurements on Ru were performed. In 1964, Clendenen and Drickamer used powder XRD to measure the volume and lattice parameters of Fe and Ru as a function of *P* up to 40 GPa [26]. In Fe, they observed an *hcp-bcc* (body-centred cubic) transition at ambient *T* and 13 GPa, but for Ru only the *hcp* phase was observed. The following year, Blackburn et al. performed a similar structural characterization study on Fe-Ru alloys [27]. The transitions between *bcc* (body-centred cubic), *fcc* (face-centred cubic) and *hcp* phases were investigated under *P* up to 5 GPa and *T* up to 900 °C. This work was set out to investigate how the percentage of the Ru content in the alloy affects these transitions. After these two studies, it was not until 2002 that another structural characterization study was performed on pure Ru under *P* [28]. In this work, Cynn et al. used diamond anvil cells (DAC) to investigate the compressibility of Ru, Ir, and Os under hydrostatic conditions (using argon as pressure-transmitting medium (PTM)). Energy-dispersive XRD measurements showed experimentally that Ru exists in the *hcp* phase at ambient *T* at least up to 56 GPa.

In addition to the experimental studies described above, there have been a small number of theoretical studies on Ru and its possible phases under high pressure. Zero Kelvin density functional theory (DFT) calculations have predicted that Ru will exist in the *hcp* phase at least up to 400 GPa [29], whereas calculations from first principles of elastic constants showed this value to be as high as 600 GPa [30]. Crucially, when both *HP* and *HT* conditions were accounted for, the first prediction of a phase transition in pure Ru emerged. Using calculations based on DFT and the quasi-harmonic lattice dynamics approximation, Lu et al. predicted that there will be an *hcp-fcc* transition under compression at temperatures above 1750 K [31]. Further theoretical work from Liu et al. produced an alternative, and more detailed, predicted phase diagram through the use of the advanced crystal structure prediction (CSP) algorithm combined with DFT calculations [32]. The *hcp-fcc* transition line in this paper is in agreement with the previous study, however, it vastly extends the data range up to 500 GPa and 10 000 K. In addition, the work by Liu et al. [32] reports the first prediction for the melting curve of Ru.

The only experimental study to date which has investigated the crystal structure of Ru under both *HP* and *HT* conditions was performed by Anzellini et al. [33], using a combination of a resistively-heated (RH)-DAC and synchrotron angle-dispersive XRD. This work set out to characterize a thermal equation of state (EoS) of Ru, and confirmed experimentally that Ru remains in the *hcp* phase up to 150 GPa and 960 K.

From the results summarized above, it becomes clear that the characterization of the phase diagram of Ru at *HP-HT* is far from being completed and that further studies are needed. For this purpose, we herein report a combination of state-of-the-art *in situ* synchrotron XRD studies on Ru up to 110 GPa and 6600 K and density-functional theory (DFT) calculations aiming to characterize the phase diagram, melting curve, and thermal EoS of Ru.

## Methods

### Experiments

Following the same procedure we have described in detail in our previous studies on chromium and cobalt [34,35], for the current study we employed five membrane-type diamond anvil cells (DAC) which were equipped with diamonds with culets ranging from 100 µm to 300 µm. The gaskets used as pressure chamber were prepared from pre-indented and laser-drilled Re foils (200 µm original thickness). The samples (99.999% purity Ru powder from Sigma Aldrich) were initially squeezed between two diamond anvils to obtain a foil of ~ 2 µm thickness. The foil was then cut to the desired size and loaded in

the high-pressure chamber of the DAC between two micron-thickness discs of potassium chloride (KCl) or magnesium oxide (MgO). The discs were previously prepared by laser micro-machining, using femtosecond pulsed laser, at the laboratory of the IPMC of the University of Pierre and Marie Curie in Paris. The obtained discs were oven-dried at 250 °C for a minimum of two hours before being loaded in the DACs. They played three roles in the experiments. They were used as pressure-transmitting medium (PTM), to insulate the sample from the diamond anvils (thermally and chemically), and as pressure gauges.

The experiment was performed at the beamline ID27 of the European Synchrotron Radiation Facility (ESRF) [36]. For the angle-dispersive XRD measurements, the X-ray beam was focused down to $1 \times 1 \ \mu\text{m}^2$ (FWHM) at a monochromatic energy of 33 keV. An EIGER2 X Cadmium Telluride (CdTe) 9M detector was used to ensure fast data collection with a good signal/noise ratio. The sample-to-detector distance and other geometrical parameters of the set up were calibrated following standard procedure from the XRD diffraction rings of a CeO$_2$ standard. This procedure was performed using the DIOPTAS calibration suite [37]. The heating ramps at desired pressure conditions were performed using laser-heating system available for user in the ID27 beamline. Once the sample was brought to the desired pressure, measured from the equation of state of KCl [38] or MgO [39], it was heated from each side of the DAC by two 100 W Nd:YLF lasers. Applying the same methodology described in refs [34,35], the focus and the powers of both lasers, were individually tuned in order to obtain hot spots of similar sizes and *T* at the two surfaces of the sample, so to minimize the axial thermal gradients. Furthermore, as discussed in the review article of Anzellini and Boccato [40], to reduce the radial thermal gradients, both lasers were also slightly de-focused. The thermal radiated signal was collected on a spectrometer via Schwarzschild mirrors and *T* was extracted by spectral radiometry (Planck fitting in the range between 450 nm and 950 nm). However, due to the geometry of the LH-system available at the ID27 beamline, *T* could be measured only from the upstream side of the sample during the heating ramp. For this reason, we ensured that both sides were at the same *T*, within experimental uncertainties, before starting the actual heating ramps. These ramps were performed in a "trigger mode" [34,35], with *T* collected before and after each XRD acquisition. Furthermore, to monitor the status of the sample, XRD data were also collected after each temperature quench. The average of the two temperature determinations was taken as the final *T*. The error in *T* was taken as the maximum difference between the measured *Ts* and the standard deviation obtained from their two-colours pyrometry measurements (Benedetti and Loubeyre [41]). The thermal EoS of KCl [38] (or MgO [39]) was used to determine the *P* on the sample at each data collection. For doing it, we made the assumption that both the sample and the PTM were experiencing the same *T*. Therefore, the maximum error in *P* was calculated as half the difference between the *P* obtained from the KCl (MgO) at the measured *T* and the one obtained at ambient *T* (where the PTM is in contact with the diamonds) as described in Anzellini et al. [34].

Before and after each heating ramp, the alignment between the X-ray beam, the lasers, and the optical system used for *T* reading was checked following the procedure described in Anzellini et al. [42]. During each heating ramp, the power of the lasers was gradually increased until a diffuse signal was detected in the diffraction pattern or it was not possible to further increase *T* (due to changes in the insulating conditions or properties of the sample). Several heating ramps were performed on the same samples at different *P-T* conditions, each time on a different region of the sample. XRD was used to assess the good status, and crystal structure, of the new region of the sample prior heating. During the data analysis, great care was taken to investigate the different aspects of the experiment. The procedure described in Benedetti and Loubeyre [41] was used to assess the reliability of *T* measurements. An accurate analysis of the diffraction patterns was performed to detect the onset of melting and to obtain structural and textural information about the sample and the insulating material. Masks were applied on a
per-image basis and the images were azimuthally integrated using the DIOPTAS suite [37]. To identify crystal structures, a Pawley analysis was performed with the TOPAS suite [43] using previously reported parameters as starting values. In addition, to confirm the presence of liquid Ru, pair distribution functions (PDFs) were extracted from the obtained data using a modified version of the AMORPHEUS software suite [44]. In particular, the PDF signal was extracted using the last solid XRD signal from the sample (prior melting) as background. KCl diffraction peaks were removed from both the background and the sample signal using the RPS software of the AMORPHEUS distribution, following the procedure described in Boccato et al. [44]. Finally, the obtained results were associated with the corresponding *T*, so to obtain a precise structural evolution of the sample as a function of *P* and *T*.

## Calculations

Our theoretical study of the melting curve of Ru was carried out using the Vienna Ab initio Simulation Package (VASP) [45,46]. To describe the electron core-valence structure of Ru the electron configuration was chosen to be [¹⁸Ar 3d¹⁰] 4s² 4p⁶ 4d⁷ 5s¹, i.e. the 16 outermost electrons of Ru were assigned to the valence electrons and the rest were assumed as core electrons. The valence electrons were represented by a plane-wave basis set with a cutoff energy (ENCUT in VASP) of 400 eV, while the core electrons were represented by projector augmented-wave (PAW) pseudopotentials. The generalized gradient approximation (GGA) with the revised Perdew-Burke-Ernzerhof for solids (PBEsol) exchange-correlation functional [47] was chosen for our computer simulations. This choice was made based on the detailed analysis of Ref. [48] of the performance of three exchange-correlation functionals GGA-PBE, GGA-PBEsol and LDA (local density approximation) available in VASP as applied to 3d, 4d and 5d transition metals. It was concluded that 3d transition metals are best described by GGA-PBE while both 4d and 5d ones are best described by GGA-PBEsol except, perhaps, iridium and gold which are both best described by LDA. This conclusion has been confirmed in numerous theoretical studies that followed since then, e.g., PBE for Cu [49], PBEsol for both Ag [50] and Pd [51], and LDA for Au [52], and our present study is no exception. The core radius (the largest value of RCUTs among those for each of the quantum orbitals) of this 16-electron pseudopotential is 2.15 a.u., or 1.14 Å. Since numerical errors in the calculations using VASP remain almost negligible until the nearest neighbour distance reaches 2xRCUT/(1.25 ± 0.05) [53], with this pseudopotential one can study systems with densities up to ~ 55 g/cm³ (a pressure of ~ 15 TPa).

Our quantum molecular dynamics (QMD) melting simulations were carried out using the (direct) Z method implemented with VASP which is described in detail in Refs. [54–56]. We have calculated the melting curves of fcc-Ru, hcp-Ru, and dhcp-Ru, the three solid phases of interest in this study. We used a 490-atom (7×7×5) supercell for hcp-Ru, 512-atom (8×8×2) supercell for dhcp-Ru, and 500-atom (5×5×5) supercell for fcc-Ru with a single Γ-point in either case; with such large supercells, full energy convergence, to ~ 1 meV/atom, was achieved in every case considered. Both the hcp-Ru and dhcp-Ru supercells were first relaxed to obtain the optimized c/a ratio for the hexagonal unit cell that corresponds to the energy minimum at fixed unit cell volume. Such optimized supercells were used for QMD melting simulations. A time step of 1 fs was used in every case. We simulated six melting points of each of hcp-Ru and fcc-Ru, and five melting points of dhcp-Ru, by performing an average of five computer runs per point (for a total of ~ 85 computer runs for the three structures). For each of the three solid phases, the total simulation length was 15 000–25 000 time steps, that is, the average total simulation time was 20 ps in either case.

The results of our melting simulations for the three studied structure are summarized in Tables 1, 2, and 3. The errors in temperature of the calculated melting temperature ($T_m$) are taken as half of the increment of the initial *T* for a series of computer runs at the corresponding density [56]. We chose these increments to be 250 K for the first

<caption>**Table 1**</caption>

The six ab initio melting points of hcp-Ru, ($P_m$, $T_m \pm \Delta T_m$), obtained from the Z method implemented with VASP. The lattice constant values correspond to the ideal hexagonal unit cell.

<table><caption>**Table 2**</caption><thead><tr><th>Lattice constant (Å)</th><th>Density (g/cm³)</th><th>P<sub>m</sub> (GPa)</th><th>T<sub>m</sub> (K)</th><th>ΔT<sub>m</sub> (K)</th></tr></thead><tbody><tr><td>2.800</td><td>10.812</td><td>-20.5</td><td>1510</td><td>125.0</td></tr><tr><td>2.650</td><td>12.754</td><td>47.7</td><td>4190</td><td>250.0</td></tr><tr><td>2.500</td><td>15.190</td><td>166</td><td>6710</td><td>312.5</td></tr><tr><td>2.350</td><td>18.289</td><td>397</td><td>9940</td><td>375.0</td></tr><tr><td>2.250</td><td>20.837</td><td>667</td><td>12750</td><td>500.0</td></tr><tr><td>2.175</td><td>23.068</td><td>970</td><td>15330</td><td>625.0</td></tr></tbody></table>

The five ab initio melting points of dhcp-Ru, ($P_m$, $T_m \pm \Delta T_m$), obtained from the Z method implemented with VASP. The lattice constant values correspond to the ideal hexagonal unit cell.

<table><caption>**Table 3**</caption><thead><tr><th>Lattice constant (Å)</th><th>Density (g/cm³)</th><th>P<sub>m</sub> (GPa)</th><th>T<sub>m</sub> (K)</th><th>ΔT<sub>m</sub> (K)</th></tr></thead><tbody><tr><td>2.800</td><td>10.812</td><td>5.6</td><td>2380</td><td>125.0</td></tr><tr><td>2.650</td><td>12.754</td><td>92.5</td><td>5070</td><td>250.0</td></tr><tr><td>2.500</td><td>15.190</td><td>215</td><td>6720</td><td>312.5</td></tr><tr><td>2.350</td><td>18.289</td><td>446</td><td>8650</td><td>375.0</td></tr><tr><td>2.250</td><td>20.837</td><td>713</td><td>10170</td><td>500.0</td></tr></tbody></table>

The six ab initio melting points of fcc-Ru, ($P_m$, $T_m \pm \Delta T_m$), obtained from the Z method implemented with VASP. The lattice constant values correspond to the fcc unit cell.

<table><thead><tr><th>Lattice constant (Å)</th><th>Density (g/cm³)</th><th>P<sub>m</sub> (GPa)</th><th>T<sub>m</sub> (K)</th><th>ΔT<sub>m</sub> (K)</th></tr></thead><tbody><tr><td>4.00</td><td>10.489</td><td>-22.8</td><td>1320</td><td>125.0</td></tr><tr><td>3.80</td><td>12.234</td><td>27.7</td><td>2910</td><td>250.0</td></tr><tr><td>3.60</td><td>14.389</td><td>125</td><td>5260</td><td>312.5</td></tr><tr><td>3.40</td><td>17.080</td><td>310</td><td>8890</td><td>375.0</td></tr><tr><td>3.25</td><td>19.556</td><td>552</td><td>12880</td><td>500.0</td></tr><tr><td>3.10</td><td>22.535</td><td>949</td><td>18560</td><td>625.0</td></tr></tbody></table>

density, 500 K for the second, 625 K for the third, 750 K for the fourth, 1000 K for the fifth in each of the three cases, and 1250 K for the sixth point of both hcp-Ru and fcc-Ru. The corresponding $T_m$ errors are listed in the tables as $\Delta T_m$. The errors in the pressure at melting conditions ($P_m$) are negligibly small, of order 1–2 GPa in each case.

The QMD melting points calculated for each structure, and summarized in Tables 1, 2, and 3, can be well fitted with an equation of the Simon–Glatzel form $T_m(P) = T_m(0)(1 + P/a)^b$. The equation representing the corresponding melting curves are:

$$T_m^{\text{hcp-Ru}}(P) = 2606 \left(1 + \frac{P}{31.0}\right)^{0.51},$$

$$T_m^{\text{dhcp-Ru}}(P) = 1860 \left(1 + \frac{P}{5.6}\right)^{0.35}, \text{ and}$$

$$T_m^{\text{fcc-Ru}}(P) = 2090 \left(1 + \frac{P}{48.0}\right)^{0.72}.$$

The pair distribution function (PDF) of both liquid Ru and liquid KCl were calculated from the outcomes of the QMD runs at the P-T conditions described in the Results and discussion section. The liquid Ru supercell that we used was obtained from the 490-atom hcp-Ru liquid final states of the QMD melting simulations. The KCl liquid supercell was created by melting a 432-atom (6×6×6) KCl (B2 phase) solid supercell using the following electron core-valence structure: [¹⁰Ne] 3s² 3p⁶ 4s¹ for K and [¹⁰Ne] 3s² 3p⁵ for Cl. The QMD runs of both liquid Ru and liquid KCl were done using the Nosé-Hoover thermostat with a timestep of 1 fs, for a total of 2500 time steps (2.5 ps).

## Results and discussion

### Phase diagram

During the experiment, nine independent LH-ramps were performed following the procedure described in the methods section. The XRD data were collected in a P-T range going from 10 GPa to 110 GPa
<figure><img src="image_4.png" /><figcaption>**Fig. 1.** XRD signal from Ru at around 26 GPa collected on the image plate of the EIGER2 X CdTe 9M detector of ID27 beamline at (a₁, a₂ and a₃) 300 K and (b₁, b₂ and b₃) at 1685 K. All the diffraction reflections have been labelled with different colours to help the reader follow the discussion. The inserts (a₂, a₃) and (b₂, b₃) are zoomed regions to show the peak splitting of the 002 and 102 reflections of Ru *hcp* at the coexistence with the *dhcp* phase. The green continuous lines in the inserts (a₃) and (b₃) have been left from the DIOPTAS suit to help visualize the splitting of the peak.</figcaption></figure>

and from ambient temperature up to 6600 K, respectively. Due to the refractory nature of Ru, two different thermal insulating materials, having very different reported melting temperatures were tested (MgO [57] and KCl [58]). However, during the first ramp performed with MgO a clear chemical reaction between the sample and the diamonds was observed above 2000 K. The reaction was characterized by the formation of RuC [59]. Therefore, all the data obtained in this ramp (but one at 15 GPa) were discarded and, although some of the previously reported melting lines of KCl are close to the one theoretically predicted for Ru [32,58], we decided to swap to this insulating material for the rest of the experiment. In the investigated *P*–*T* range it was possible to index the KCl-B2 and Ru *hcp* solid phases. However, we could not detect any evidence of the previously predicted *HP*–*HT fcc* phase. On the other hand, for some of the performed ramps, at temperature close to the melting temperature, we observed a splitting of the reflections 002 and 102 of *hcp* Ru. An example of the observed evolution is reported in Fig. 1 of the Supporting Materials. The peak splitting was assigned to the formation of the reflections 004 and 104, respectively, of a double-hexagonal-closed-packed structure (*dhcp*) coexisting with the *hcp* phase (see Fig. 1 and Fig. 2 of the Supporting Materials). The *dhcp* phase has been observed not only at 26 GPa, but also at all the pressures below 70 GPa and above 70 GPa, with the only exception of the run performed at 70 GPa. This fact does not exclude the existence of the *dhcp* phase at this pressure. The non observation of *dhcp* at 70 GPa could be related to the development of preferred orientation. The XRD patterns of the *hcp* and *dhcp* phases differ only by the presence of weak peaks in *dhcp* which originate from the splitting of *hcp* peaks where *l* ≠ 0. Therefore, preferred orientations might easily preclude the detection of the *dhcp* phase coexisting with the *hcp* phase. Further experiments, are needed to explore in more detail the HP-HT stability range of *dhcp* Ru.

A similar behaviour, with the appearance of the HP-HT phase, was previously observed in other closed-packed metals [60–63]. As discussed by Errandonea et al. for the case of Mg [61], it is important to notice that *dhcp* and *hcp* structures share the same space group (*P*<sub>63</sub>/mmc). The only difference between both structures is the doubling of the lattice parameter *c* due to a change of the periodic stacking of close-packed layers. Notice that the stacking sequence of *hcp* is ABABABAB and that of *dhcp* is ABACABAC. Thus, a single stacking fault is needed to pass out one structure to the another [64]. It is also very significant to point out that, due to the ductile nature of the transition metals, such stacking faults are formed with relative ease [65], especially, if we take into account the thermal fluctuation induced by the extreme *T* achieved in the present experiment at the conditions where the *dhcp* structure was found. Considering the observation of *hcp* in other close-packed metals and the present observation, the above given

arguments support the possible existence of a *dhcp* phase in Ru under HP-HT conditions.

Similar *T*-induced textural evolutions were detected in each of the performed ramps (Fig. 2). In particular, at ambient *T* both *hcp*-Ru and KCl-B2 show a highly oriented powder signal. While the KCl texture does not change much with the increasing *T*, it is possible to observe an evolution in the signal from Ru. In particular, apart from the expected *T*-induced drifting to lower angles of the diffracted signal, it is possible to observe the progressive *T*-induced growth of Ru grains. This re-crystallization is evidenced by the progressive change of the Ru signal from a highly oriented powder, into a “single-crystal-like” signal. For the ramps where a coexistence of *hcp* and *dhcp* was observed, the two phases showed very similar textures.

As reported for many other transition metals previously studied [34,35,66], Ru shows a *T*-induced “fast re-crystallization” phenomenon before melting. Finally, under further *T*-increase, in six of the performed ramps, it was possible to observe the appearance of a diffuse halo characteristic of a liquid material (see Fig. 3). However, two of the diffuse signals were observed in the ramps performed around 100 GPa and 110 GPa, where the *T*-measurement could not be considered reliable above 2300 K according to the method proposed by Benedetti and Loubeyre [41]. Therefore, data above those *T* are not reported in the present study for those ramps. As the measurement of *T*- were performed using reflective optics, a possible explanation for the observed loss of reliability could be the undetectable (due to the LH-system geometry of ID27) development of a large thermal gradient between the two sides of the sample (probably caused by a misalignment between the two hot spots). This is known to result in erroneous *T*-reading as discussed in Benedetti and Loubeyre [41] and Kantor et al. [67].

According to the literature [58], there are two different reported melting lines of KCl, one (higher melting line) that is well above the experimental melting points we determined for Ru and another one (lower melting line) that passes through the melting points we have experimentally observed for Ru. In order to confirm that the measured melting curve of Ru indeed comes from the Ru sample and not from the PTM, we have extracted the PDF signal of the liquid obtained from our XRD patterns. The structure factors obtained in a Q-range between 0.7–8 Å, as generally obtain for liquid metals in LH-DAC [44], are reported in Fig. 3 of the Supporting Materials. The extracted PDF was then compared with the one obtained from DFT simulations for *hcp*-Ru and KCl-B2 carried out at the same *P*–*T* conditions than experiments. From the obtained results reported in Fig. 4, it is possible to observe how the experimental PDFs are more in agreement with the one simulated for *hcp*-Ru.
<figure><img src="image_5.png" /><figcaption>Fig. 2. 2D XRD signal collected on the image plate of the EIGER2 X CdTe 9M detector showing snapshots of the T-induced textural evolution of the sample and the insulating material during a heating ramp performed around 55 GPa at 300, 1950, 2627, 3262, and 3398 K.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Fig. 3. Integrated XRD patterns for increasing T around 60 GPa. The onset of melting, characterized by the first appearance of the diffuse signal, is observed at 4094 K (purple pattern). The diffuse scattering remains the same with the rising T up to the maximum T measured 4698 K (red pattern). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

In particular, with the only exception of the first peak, all the other simulated peaks of the liquid hcp-Ru (at around 4.54 Å, 6.78 Å, 8.75 Å, and 10.96 Å) match the experimental ones. Furthermore, we need to underline that the exact location of the first peak in the simulated patterns depends on the choice of the pseudopotential (PP) used in VASP and may change slightly if another PP is used. However, the PP selection does not affect very much the position of the other peaks. What is important, is that at the same P-T conditions, the Ru peaks correspond to a slightly shorter distance than that of KCl and, that the PDF of Ru is more structured at longer distances than the KCl one, that becomes flatter around 10 Å.

The Ru phase diagram constructed on the basis of the present experiments is reported in Fig. 5 and compared with results from our calculations and from the literature. From the reported data, it is possible to observe how the present results agree and extend the phase diagram we have previously obtained using a combination of RH-DAC and XRD [33]. We have also reported with a different colour (blue) the points where hcp-dhcp coexistence was observed. Although the

coexistence was not detected in every single ramp, it seems to appear only for T above 1500 K. As previously discussed, we did not detect the presence of the predicted fcc structure. Therefore the present data do not agree with either the prediction of Lu et al. [31] and the solid-solid prediction of Liu et al. [32]. Considering the present solid-liquid phase boundary, in each reported ramp, we have always observed a sudden jump of about 1000 K in the T from the last measured solid to the first liquid. Therefore, differently from similar studies we have previously reported [34,35,66], this time we were not able to perfectly anchor an experimental melting line within the T of the last detected solid and the onset of melting. Therefore, although our measured liquid points (also confirmed by the PDF signals) are well in agreement with the one predicted by the present DFT calculations from both the hcp and the dhcp phases, we are not feeling confident enough to completely exclude any agreement with the melting line predicted by Liu et al. [32].

Thermal equation of state

Fig. 6 shows the unit-cell volumes measured for hcp-Ru at HP-HT conditions and the resulting compression curves along six different isotherms. Following the same procedure reported previously by Anzellini et al. [34], it was possible to establish the P-V-T equation of state (EoS) for hcp-Ru using the EOSfit software suite [68]. In particular, as stated in a previous study on cobalt [34], the P at HT can be described as the sum of the P at ambient T and the thermal P as a function of the increasing T evaluated along isochors:

$$P(V, T) = P(V, 300 \text{ K}) + P_{Th}(T) \quad (1)$$

where the P(V, 300 K) is the isothermal EoS of the material at ambient T and P<sub>Th</sub>(T) represents the thermal pressure. In the present work, P(V, 300 K) was calculated from the data previously reported from one experiment performed using helium as PTM [33], while (P<sub>Th</sub>) was modelled following Holland and Powell definition:

$$P_{Th}(T) = \alpha_0 K_0 \frac{\Theta_E}{\zeta_0} \left( \frac{1}{\exp(\Theta_E/T) - 1} - \frac{1}{\exp(\Theta_E/300) - 1} \right) \quad (2)$$

where Θ<sub>E</sub> is the Einstein T of the material (321.45 K for Ru), K<sub>0</sub> is the bulk modulus at zero pressure obtained from the isothermal EoS at ambient T, α<sub>0</sub> is the volumetric thermal expansion coefficient at 300 K, and ζ<sub>0</sub> is expressed as:

$$\zeta_0 = \frac{(\Theta_E/300)^2 \exp(\Theta_E/300)}{(\exp(\Theta_E/300) - 1)^2} \quad (3)$$

As shown in Fig. 6, data grouped considering T ranges of ± 200 K are well described by a 3rd order Birch-Murnaghan EoS at ambient
<figure><img src="image_7.png" /><figcaption>Fig. 4. PDF signals extracted from the collected XRD patterns (black line) compared to the one obtained from DFT simulation for Ru (blue lines) and KCl-B2 (red line) at the same experimental P-T conditions. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Fig. 5. The phase diagram of Ru as obtained in the present work compared to literature studies. Previously predicted solid-solid phase boundaries [31,32] are reported as purple and black dashed lines. Experimentally observed solid phases are reported as solid points: in black the hcp phase and in blue the hcp-dhcp coexistence phase. The empty purple symbols correspond to the experimentally observed liquid points. The melting curve calculated in the present study from Ru hcp, fcc and dhcp solid phases, are reported as blue, black and green continuous lines, respectively. For reference, the higher and the lower melting lines of KCl reported by Zhou et al. [58] are also shown in the graph as red lines. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

T and a thermal pressure modelled according the Holland and Powell expression with the following parameters: V₀ = 27.13(2) Å³; K₀ = 323(5) GPa; K'₀ = 4.1(1) and α₀ = 1.91(7)×10⁻⁵ K⁻¹. This thermal EoS also reproduces well the data we previously reported for T < 1000 K [33]. To illustrates this fact in Fig. 6 we compare the 800 K isotherm calculated with the present EoS and the 800 K isotherm we published previously from Ru under HP at temperature up to 960 K [33]. From the figure it is possible to observe the good agreement between the two experimental studies. Thus the current P-V-T EoS can be used to describe Ru up to 110 GPa and temperatures from 300 K to 3000 K.

## Conclusions

The P-T phase diagram of Ru was determined *in situ* up to 110 GPa and 6600 K via LH-DAC and synchrotron-based XRD measurements and by *ab initio* calculation. In the investigated P-T range it was not possible to observe the presence of the predicted fcc phase of Ru [31,32]. However, for some of the performed ramps, we observed a coexistence between the hcp and a new dhcp phase of Ru. Such a coexistence is probably due to thermally-induced stacking faults. We were also able to obtain the first *in situ* characterization of the melting curve of Ru, confirmed by the corresponding PDF signal. However,
<figure><img src="image_9.png" /><figcaption>Fig. 6. Compression curves of hcp-Ru along different isotherms. Different colours refer to different T, that are labelled in the legend. The solid lines are the isothermal compression curves obtained from the thermal equation of state established in the present study. The ambient T points and the pink EoS at 800 K are the one obtained in our previous study [66].</figcaption></figure>

although the present *ab initio* results agree with the experimental one, the observed dispersion of around 1000 K between the *T* measured for the last observed solid and the first liquid, does not allow us to rule out the melting line predicted by Liu et al. [32] Unit-cell volumes of the phase measured at *HP-HT* were used to obtain the thermal equation of state of hcp-Ru. From the obtained results, the *P–T*–induced compressibility of Ru, can be expressed by a combination of a 3rd order Birch–Murnaghan EoS with a Holland and Powell expression with the following parameters: $V_0 = 27.13(2) \AA^3$; $K_0 = 323(5)$ GPa; $K'_0 = 4.1(1)$ and $\alpha_0 = 1.91(7) \times 10^{-5} \text{ K}^{-1}$. For pressure below 60 GPa, the present thermal EoS is also in good agreement with the one previously obtained during RH-DAC experiment coupled with XRD technique [33].

### CRediT authorship contribution statement

**Simone Anzellini:** Writing – review & editing, Writing – original draft, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization. **Anna Herlihy:** Writing – review & editing, Writing – original draft, Software, Data curation. **Serena Dominijanni:** Writing – review & editing, Writing – original draft, Investigation. **Pablo Botella:** Writing – review & editing, Investigation. **Annabelle Brooks:** Writing – review & editing, Writing – original draft, Investigation. **Leonid Burakovsky:** Writing – review & editing, Writing – original draft, Methodology, Formal analysis, Data curation. **Anna Pakhomova:** Writing – review & editing, Resources, Methodology, Investigation. **Daniel Errandonea:** Writing – review & editing, Writing – original draft, Funding acquisition.

### Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Data availability

Data will be made available on request.

### Acknowledgements

The authors acknowledge the European Synchrotron Radiation Facility for provisioning of beamtime at the beamlines ID27 (exp. HC 5266). The authors are also grateful to Mohamed Mezouar and Gaston Garbarino for their support during the experiment. We want to thank Daniele Antonangeli for the use of the Femtosecond laser micromachining at IMPMC, developed and realized by the “Cellule Project” with the financial support of ANR 2010-JCJC-604-01. We would like to warmly thank J. Jacobs for his help with the preparation of the diamond anvil cells. S.D. have received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant agreement No. 724690). This work was supported by the Generalitat Valenciana under grants PROMETEO CIPROM/2021/075-GREENMAT and MFA/2022/007, and by the Spanish Ministerio de Ciencia e Innovación, Agencia Estatal de Investigación, and the European Union (MCIN/AEI/10.13039/501100011033) under grants PID2022-138076NB-C41 and RED2022-134388-T (MALTA Consolider Team). This study forms part of the Advanced Materials program and is supported by MCIN with funding from European Union Next Generation EU (PRTR-C17.11) and by the Generalitat Valenciana. S.A. thanks the Generalitat Valenciana for the CIDEGENT grant no. CIDEXG/2022/6.

### Supplementary data

Supplementary material related to this article can be found online at https://doi.org/10.1016/j.rinp.2024.107961.

### References

[1] Wang W-H, Dong C, Shek C. Bulk metallic glasses. Mater Sci Eng R 2004;44(2–3):45–89.

[2] Motta AT, Yilmazbayhan A, da Silva MJG, Comstock RJ, Was GS, Busby JT, Gartner E, Peng Q, Jeong YH, Park JY. Zirconium alloys for supercritical water reactor applications: Challenges and possibilities. J Nucl Mater 2007;371(1–3):61–75.
[3] Liu X, Chu PK, Ding C. Surface modification of titanium, titanium alloys, and related materials for biomedical applications. Mater Sci Eng R 2004;47(3-4):49-121.

[4] Suryanarayana C. Mechanical alloying and milling. Prog Mater Sci 2001;46(1-2):1-184.

[5] Friedel J. In: Ziman J, editor. The physics of metals. Cambridge University Press; 1991.

[6] Pettifor D. Theory of the crystal structures of transition metals. J Phys C: Solid State Phys 1970;3:367.

[7] Parisiades P. A review of the melting curves of transition metals at high pressures using static compression techniques. Crystals 2021;11:416. http://dx.doi.org/10.3390/cryst11040416.

[8] Torchio R, Mathon O, Pascarelli S. XAS and XMCD spectroscopies to study matter at high pressure: probing the correlation between structure and magnetism in the 3d metals. Coord Chem Rev 2014;277:80-94.

[9] Harris DC, Cabri LJ. Nomenclature of platinum-group-element alloys: review and revision. Can Mineral 1991;29(2):231-7.

[10] Raykhtsaum G. PGM Highlights: Platinum alloys: A selective review of the available literature. Johns Matthey Technol Rev 2013;57:202-123.

[11] Sedriks A. Corrosion resistance of titanium-ruthenium alloys. Corrosion 1975;31(2):60-5.

[12] Wei W, Ge M, Wang S, Zhang L, Han Y, Du H, Tian M, Zhang Y. Superconducting properties of molybdenum ruthenium alloy Mo 0.63 Ru 0.37. Eur Phys J B 2018;91:1-7.

[13] Zhang Y, Wu L, Wan B, Lin Y, Hu Q, Zhao Y, Gao R, Li Z, Zhang J, Gou H. Diverse ruthenium nitrides stabilized under pressure: a theoretical prediction. Sci Rep 2016;6(1):33506.

[14] Niwa K, Suzuki K, Muto S, Tatsumi K, Soda K, Kikegawa T, Hasegawa M. Discovery of the last remaining binary platinum-group pernitride RuN2. Chem Eur J 2014;20(43):13885-8.

[15] Sun W, Chakraborty S, Ahuja R. Stabilizing a novel hexagonal ru2c through lifshitz transition under pressure. 2013, arXiv preprint arXiv:1310.0170.

[16] Thirunavukkarasu VS, Kozhushkov SI, Ackermann L. C-H nitrogenation and oxygenation by ruthenium catalysis. Chem Commun 2014;50(1):29-39.

[17] Miao S, Liu Z, Han B, Huang J, Sun Z, Zhang J, Jiang T. Ru nanoparticles immobilized on montmorillonite by ionic liquids: a highly efficient heterogeneous catalyst for the hydrogenation of benzene. Angew Chem 2006;118(2):272-5.

[18] Nguyen ST, Grubbs RH, Ziller JW. Syntheses and activities of new single-component, ruthenium-based olefin metathesis catalysts. J Am Chem Soc 1993;115(21):9858-9.

[19] Hunt L, Lever F. Platinum metals: A survey of productive resources to industrial uses. Platinum Met Rev 1969;13:126.

[20] Rao CR, Trivedi D. Chemical and electrochemical depositions of platinum group metals and their applications. Coord Chem Rev 2005;249(5-6):613-31.

[21] Goodman B. Two new superconducting elements. Nature 1951;167(4238):111.

[22] Oh J-M, Lee B-K, Park H-K, Lim J-W. Preparation and purity evaluation of 5N-grade ruthenium by electron beam melting. Mater Trans 2012;53(9):1680-4.

[23] Olsen J, Bucher E, Levy M, Muller J, Corenzwit E, Geballe T. Superconductivity under pressure. Rev Modern Phys 1964;36(1):168.

[24] Bucher E, Müller J, Olsen J, Palmy C. Superconductivity of osmium and ruthenium under pressure. Cryogenics 1965;5(5):283-4.

[25] Chester P, Jones G. CXXXIV. Superconductivity at very high pressures. Lond Edinb Dublin Philos Mag J Sci 1953;44(358):1281-90.

[26] Clendenen RL, Drickamer H. The effect of pressure on the volume and lattice parameters of ruthenium and iron. J Phys Chem Solids 1964;25(8):865-8.

[27] Blackburn L, Kaufman L, Cohen M. Phase transformations in iron-ruthenium alloys under high pressure. Acta Metall 1965;13(5):533-41.

[28] Cynn H, Klepeis JE, Yoo C-S, Young DA. Osmium has the lowest experimentally determined compressibility. Phys Rev Lett 2002;88(13):135701.

[29] Cazorla C, Alfe D, Gillan M. Zero-temperature generalized phase diagram of the 4 d transition metals under pressure. Phys Rev B 2008;77(22):224103.

[30] Lugovskoy A, Belov M, Krasilnikov O, Yekilov YK. Stability of the hcp Ruthenium at high pressures from first principles. J Appl Phys 2014;116(10).

[31] Lu Z-P, Zhu W-J, Lu T-C, Meng C-M, Xu L, Li X-H. Structural phase transition of Ru at high pressure and temperature. 2013.

[32] Liu Z-L, Zhu C-C, Zhang X-L, Wang H-Y. Phase diagram, shock equation of states, and elasticity of metal ruthenium under high pressure. Physica B 2020;598:412434.

[33] Anzellini S, Errandonea D, Cazorla C, MacLeod S, Monteseguro V, Boccato S, Bandiello E, Anichtchenko DD, Popescu C, Beavers CM. Thermal equation of state of ruthenium characterized by resistively heated diamond anvil cell. Sci Rep 2019;9(1):14459.

[34] Anzellini S, Boccato S, Baty SR, Burakovsky L, Antonangeli D, Errandonea D, Torchio R. Melting line and thermal equation of state of fcc-cobalt: A combined experimental and computational approach. Results Phys 2024;56:107218. http://dx.doi.org/10.1016/j.rinp.2023.107218.

[35] Anzellini S, Errandonea D, Burakovsky L, Proctor JE, Turnbull R, Beavers CM. Characterization of the high-pressure and high-temperature phase diagram and equation of state of chromium. Sci Rep 2022;12(1). http://dx.doi.org/10.1038/s41598-022-10523-2.

[36] Petitgirard S, Salamat A, Beck P, Weck G, Bouvier P. Strategies forin situlaser heating in the diamond anvil cell at an X-ray diffraction beamline. J Synchrotron Radiat 2013;21(1):89-96. http://dx.doi.org/10.1107/s1600577513027434.

[37] Prescher C, Prakapenka VB. DIOPTAS: a program for reduction of two-dimensional X-ray diffraction data and data exploration. High Press Res 2015;35(3):223-30. http://dx.doi.org/10.1080/08957959.2015.1059835.

[38] Dewaele A, Belonoshko AB, Garbarino G, Occelli F, Bouvier P, Hanfland M, Mezouar M. High-pressure-high-temperature equation of state of KCl and KBr. Phys Rev B 2012;85(21):214105.

[39] Dorogokupets P, Dewaele A. Equations of state of MgO, Au, Pt, NaCl-B1, and NaCl-B2: Internally consistent high-temperature pressure scales. High Press Res 2007;27(4):431-46.

[40] Anzellini S, Boccato S. A practical review of the laser-heated diamond anvil cell for university laboratories and synchrotron applications. Crystals 2020;10(6):459.

[41] Benedetti LR, Loubeyre P. Temperature gradients, wavelength-dependent emis-sivity, and accuracy of high and very-high temperatures measured in the laser-heated diamond cell. High Press Res 2004;24(4):423-45. http://dx.doi.org/10.1080/08957950412331331718.

[42] Anzellini S, Kleppe AK, Daisenberger D, Wharmby MT, Giampaoli R, Boccato S, Baron MA, Miozzi F, Keeble DS, Ross A, Gurney S, Thompson J, Knap G, Booth M, Hudson L, Hawkins D, Walter MJ, Wilhelm H. Laser-heating system for high-pressure X-ray diffraction at the Extreme Conditions beamline 115 at Diamond Light Source. J Synchrotron Radiat 2018;25(6):1860-8. http://dx.doi.org/10.1107/s1600577518013383.

[43] Coelho AA. TOPAS and TOPAS-Academic: an optimization program integrating computer algebra and crystallographic objects written in C++. J Appl Crystallogr 2018;51(1):210-8. http://dx.doi.org/10.1107/s1600576718000183.

[44] Boccato S, Garino Y, Morard G, Zhao B, Xu F, Sanloup C, King A, Guignot N, Clark A, Garbarino G, Morand M, Antonangeli D. Amorphous: a Python-based software for the treatment of X-ray scattering data of amorphous and liquid systems. High Press Res 2022;42(1):69-93. http://dx.doi.org/10.1080/08957959.2022.2032032.

[45] Kresse G, Furthmüller J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput Mater Sci 1996;6:15.

[46] Kresse G, Furthmüller J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys Rev B 1996;54:11169.

[47] Perdew JP, Ruzinszky A, Csonka GI, Vydrov OA, Scuseria GE, Constantin LA, Zhou X, Burke K. Restoring the density-gradient expansion for exchange in solids and surfaces. Phys Rev Lett 2008;100:136406.

[48] Dewaele A, Torrent M, Loubeyre P, Mezouar M. Compression curves of transition metals in the Mbar range: Experiments and projector augmented-wave calculations. Phys Rev B 2008;78:104102.

[49] Baty S, Burakovsky L, Errandonea D. Ab initio phase diagram of copper. Crystals 2021;11:537.

[50] Baty S, Burakovsky L, Errandonea D. Ab initio phase diagram of silver. J Phys: Condens Matter 2021;33:485901.

[51] Baty S, Burakovsky L, Luscher D, Anzellini S, Errandonea D. Palladium at high pressure and high temperature: A combined experimental and theoretical study. J Appl Phys 2024;135:075103.

[52] Dubrovinsky L, DubrovinSKaia N, Crichton WA, Mikhaylushkin AS, Simak SI, Abrikosov IA, de Almeida JS, Ahuja R, Luo W, Johansson B. Noblest of all metals is structurally unstable at high pressure. Phys Rev Lett 2007;98:045503.

[53] (Vienna) GK. 2017, private communication.

[54] Belonoshko A, Skorodumova N, Rosengren A, Johansson B. Melting and critical superheating. Phys Rev B 2006;73:012201.

[55] Burakovsky L, Chen S, Preston D, Sheppard D. Z methodology for phase diagram studies: platinum and tantalum as examples. J Phys Conf Ser 2014;500:162001.

[56] Burakovsky L, Burakovsky N, Preston D. Ab initio melting curve of osmium. Phys Rev B 2015;92:174105.

[57] Alfè D. Melting curve of MgO from first-principles simulations. Phys Rev Lett 2005;94(23):235701. http://dx.doi.org/10.1103/physrevlett.94.235701.

[58] Zhou D, Dong J, Si Y, Zhu F, Li J. Melting curve of potassium chloride from in situ ionic conduction measurements. Minerals 2020;10(3):250. http://dx.doi.org/10.3390/min10030250.

[59] Hao J, Tang X, Li W, Li Y. First-principle calculations of high-pressure phase transformations in RuC. Europhys Lett 2014;105(4):46004. http://dx.doi.org/10.1209/0295-5075/105/46004.

[60] Yoo C, Saderlind P, Moriarty J, Cambell A. Dhcp as a possible new epsilon' phase of iron at high pressuresand temperatures. Phys Rev Lett 1996;214:65.

[61] Errandonea D, Meng Y, Häusermann D, Uchida T. Study of the phase transformations and equation of state of magnesium by synchrotron x-ray diffraction. 2003.
[62] Saxena S, Dubrovinsky L, Hdggkvist P, Cerenius Y, Shen G, Mao H. Synchrotron X-ray study of iron at high pressure and temperature. Science 1995;269:1704.

[63] Grosshans W, Holzapfel W, Physik F, Gh-Pad-Erborn U, Postfach, Paderborn, Germany. Atomic volumes of rare-earth metals under pressures to 40 GPa and above. Phys Rev B 1992;45:5171.

[64] Mcmahan A, Young D. Is there a missing rare earth crystal structure? Phys Lett 1984;105A:129.

[65] Gotsis HJ, Papaconstantopoulos DA, Mehl MJ. Tight-binding calculations of the band structure and total energies of the various phases of magnesium. Phys Rev B 2002;65(13):134101. http://dx.doi.org/10.1103/physrevb.65.134101.

[66] Anzellini S, Monteseguro V, Bandiello E, Dewaele A, Burakovsky L, Errandonea D. In situ characterization of the high pressure – high temperature melting curve of platinum. Sci Rep 2019;9(1). http://dx.doi.org/10.1038/s41598-019-49676-y.

[67] Kantor I, Marini C, Mathon O, Pascarelli S. A laser heating facility for energy-dispersive X-ray absorption spectroscopy. Rev Sci Instrum 2018;89(1). http://dx.doi.org/10.1063/1.5010345.

[68] Angel RJ, Mazzucchelli ML, Alvaro M, Nestola F. EosFit-Pinc: A simple GUI for host-inclusion elastic thermobarometry. Am Mineral 2017;102(9):1957–60. http://dx.doi.org/10.2138/am-2017-6190.