The high-pressure, high-temperature phase diagram of cerium

We present an experimental study of the high-pressure, high-temperature behaviour of cerium up to ∼22 GPa and 820 K using angle-dispersive x-ray diffraction and external resistive heating. Studies above 820 K were prevented by chemical reactions between the samples and the diamond anvils of the pressure cells. We unambiguously measure the stability region of the orthorhombic oC4 phase and find it reaches its apex at 7.1 GPa and 650 K. We locate the α-cF4–oC4–tI2 triple point at 6.1 GPa and 640 K, 1 GPa below the location of the apex of the oC4 phase, and 1–2 GPa lower than previously reported. We find the α-cF4 → tI2 phase boundary to have a positive gradient of 280 K (GPa)−1, less steep than the 670 K (GPa)−1 reported previously, and find the oC4 → tI2 phase boundary to lie at higher temperatures than previously found. We also find variations as large as 2–3 GPa in the transition pressures at which the oC4 → tI2 transition takes place at a given temperature, the reasons for which remain unclear. Finally, we find no evidence that the α-cF4 → tI2 is not second order at all temperatures up to 820 K.


Introduction
Cerium (Ce) has long been the focus of both computational and experimental studies of 4f electron behaviour, and is a perfect example of an element displaying a pressure-induced electronic transition [1]. Ce crystallises in either the γ phase 8 Author to whom any correspondence should be addressed.
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(with the fcc structure, denoted cF4 in Pearson notation), or the β phase (with the dhcp structure denoted hP4 in Pearson notation) at ambient conditions [2]. Single-phase hP4 can be made by thermally cycling Ce between room temperature (RT) and 4 K followed by annealing for long periods at 348 K [3].
Ce is best known for its pressure-induced isostructural transition from the γ phase to the α phase (also cF4) at 0.7 GPa and RT, which is accompanied by a large decrease in volume [2]. Since both the γ and α phase have the same structure they will be referred to as γ-cF4 and α-cF4 hereafter. Uniquely in Figure 1. The phase diagram of Ce, based on the present literature, with the different phases identi ed using their Pearson notation. The phase boundaries shown with solid lines are those reported by Schiwek et al [6], while the dashed lines show the forward and reverse transition pressures from and to the α-cF4 phase reported by Antonova et al [31]. The dotted line shows the suggested phase line between the α-cF4 and tI2 phases reported by Tsiok and Khvostantsev [32]. the elements, the γ-cF4 → α-cF4 phase line ends at a critical point [4], most recently estimated to be at 1.5 GPa and 480 K [5], as shown in gure 1 [6], where Ce becomes a solid without compressive strength but with nite shear strength [7]. The mechanisms behind the γ-cF4 → α-cF4 transition have been intensely debated. The 4f electrons are key to the transition, but to what extent electron screening, electron de-localisation and vibrational energy drive this transition, and whether the transition is best described by the Mott transition model [8] or the Kondo volume collapse model [9] is still a subject of ongoing research (see [10], and the extensive review by Nikolaev and Tsvyashchenko [11], and the references therein).
Upon further compression at RT, Ce undergoes a phase transition at ∼4 GPa. Early x-ray diffraction experiments reported that the transition is to a C-centered orthorhombic structure (oC4 in Pearson notation and denoted α ′ in the literature), isostructural with that found in α-uranium at ambient conditions [12,13]. Subsequent x-ray studies [14,15], however, concluded that Ce transforms to a C-centered monoclinic structure (mC4 in Pearson notation and denoted α ′′ in the literature), while others observed both the oC4 and mC4 structures [16,17]. It was later shown that it was possible to transform α-cF4 into either the mC4 or the oC4 structure depending on the prior mechanical treatment of the sample [18]: samples cut from an ingot transform into the oC4 structure [16,17,19], while cold-worked samples or small shavings favour the mC4 structure [14,15,19].
Upon further compression at RT, both the oC4 and mC4 phases transform into a body centred tetragonal (bct) structure (tI2 in Pearson notation, and denoted ǫ in the literature) at ∼12 GPa, which remains stable up to 208 GPa [20], the highest pressure to which Ce has been studied.
There have been many theoretical and computational studies on the stability of the post α-cF4 phase, though different rst-principles techniques (all performed at 0 K, and therefore considering the energetics of the static lattice) yield different results. The linear muf n-tin orbital model favours the oC4 structure [21,22], while applying the full-potential linear muf n-tin orbital (FP-LMTO) model to the same problem nds mC4 to be the only stable phase [23]. Later work using the FP-LMTO model combined with the generalised gradient approximation (GGA) reported that both oC4 and mC4 are meta-stable and α-cF4 transforms directly into the tI2 phase [24]. Local density approximations (LDA), or GGA calculations using the plane wave + pseudopotential method conrmed the metastable nature of both phases [25]. However, when LDA is combined with the Gutzwiller variation approach the result is altered and the mC4 structure is the only stable solution [26]. Despite the large number of theoretical studies a consensus has therefore not been reached as to whether the ground state has the oC4 or mC4 structure.
There is also very little experimental consensus for which of the phases is the most stable between 5 and 12 GPa at RT. Zachariasen and Ellinger [27] reported that upon pressure cycling their oC4 + mC4 mixed-phase sample, it transformed into a pure oC4 phase, which suggested that slow rates of pressure change favour the oC4 phase. Zachariasen and Ellinger also noted that the α-cF4 → mC4 transition requires a very small shift in atomic positions, whereas the α-cF4 → oC4 and mC4 → oC4 transitions require more substantial atomic reorganisation. Most recently, Ma et al have reported that they observed either the oC4 or mC4 phases, depending on whether or not the sample had been precompressed [28] (that is, loaded and then held at 1.5 GPa for three days before the rest of the experiment was performed), and that in the precompressed samples a small amount of the mC4 phase transformed into oC4 on further compression. Upon heating the mC4 phase, Zhao and Holzapfel reported that Ce transforms into the oC4 phase which remains stable on cooling back down to RT [17]. This is consistent with the results of Dmitriev et al [29], who reported that while they observed the mC4 phase on compression at RT, compression of the α-cF4 phase at 473 K resulted in a transition to the oC4 phase.
There have also been a number of high-pressure, hightemperature studies of Ce with the aim of exploring the oC4 + mC4 stability region [6,17,[30][31][32]. The initial studies by King et al [33] and Endo and Fujioka [30] focussed on the α-cF4 → mC4 and mC4 → tI2 phase boundaries, respectively, although King et al presented no evidence that they observed the mC4 phase above 5 GPa rather than the oC4 phase. Both phase boundaries were found to have a negative slope, and were incorporated into a fuller phase diagram determined by Antonova et al using differential thermal analysis and resistivity techniques [31]. By collecting both isothermal and isobaric data, on both pressure and temperature increase and decrease, Antonova et al established the α-cF4 → oC4 + mC4 phase boundary to be curved at high temperature with a large hysteresis between the transition pressures seen on compression and release (see gure 1). By combining their own data with the mC4 → tI2 phase boundary of Endo and Fujioka, Antonova et al suggested that the oC4 + mC4 stability eld was dome shaped, and that the α-cF4-(oC4+mC4)-tI2 triple point was at 8.5 GPa and 630 K. Although they obtained no data on the α-cF4 → tI2 phase boundary, they indicated the likely position and gradient of such a boundary.
Subsequent high-pressure high-temperature diffraction data obtained by Zhao and Holzapfel [17] suggested that the mC4 phase irreversibly disappeared at temperatures above 400 K, and was generally consistent with the phase diagram proposed by Antonova et al. However, while the phase boundary between oC4 + mC4 and tI2 was reported as linear, its slope was steeper than that originally reported by Endo and Fujioka [30]. Zhao and Holzapfel also con rmed the location of the α-cF4-(oC4+mC4)-tI2 triple point at 8.5 GPa and 625 K, but provided no new information on the nature of the α-cF4 → tI2 phase boundary.
Tsiok and Khvostantsev [32] performed an extensive highpressure, high-temperature resistivity study to 15 GPa and 710 K. In contrast to previous studies, they concluded that the tI2 phase was only meta-stable, and that it transformed back to the α-cF4 phase above ∼673 K at pressures above 12 GPa (see gure 1). They also reported that the structure assumed by Ce at any given pressure and temperature was highly dependent on the trajectory in P-T space taken to get to that point. The subsequent diffraction study of Schiwek et al [6], however, con rmed the general phase diagram reported by Zhao and Holzapfel and located the α-cF4 → tI2 phase boundary, which was found to have a steep positive slope, and therefore to be almost perpendicular to that proposed by Tsiok and Khvostantsev.
Schiwek et al also determined the α-cF4-oC4-tI2 triple point to be located around 6.9 GPa and 600 K, coinciding with the apex of the stability region of the oC4 + mC4 phases which was reported as dome-shaped-see gure 1 [6]. While the shape of this stability region is very similar to that originally proposed by Antonova et al, the oC4+mC4 → tI2 phase boundary is slightly different to that reported by Endo and Fujioka [30] and Zhao and Holzapfel [17].
Despite many studies, therefore, the phase diagram of Ce still appears to be uncertain. This is particularly true when phase boundary determinations were made without the identity of the phases concerned (oC4 or mC4) being determined unequivocally using x-ray diffraction.
This uncertainty is further highlighted by our own preliminary diffraction data obtained on isothermal compression at ∼650 K, which showed a α-cF4 → tI2 → oC4 → tI2 transition sequence. This is incompatible with all previously published phase diagrams, and suggests (i) contrary to the report by Tsiok and Khvostantsev, but in agreement with Endo [30], Zhao [17] and Schiwek [6], that the tI2 phase is indeed found at high temperatures, and (ii) that the α-cF4 → tI2 phase line intercepts the dome shaped oC4 + mC4 stability region on the low-pressure side of its apex, contrary to that shown in gure 1. To address these inconsistencies, and to make a de nitive diffraction study of cerium's high-pressure, high-temperature phase diagram, we have performed angledispersive x-ray diffraction experiments using diamond anvil cells (DACs) and synchrotron radiation up to 20 GPa and 820 K.

Experimental details
All of the Ce samples used in this study were cut from a high purity (99.99+%) Ce ingot, provided by Ulrich Schwarz of the MPI für Chemische Physik fester Stoffe in Dresden. As the mC4 phase is reported to irreversibly disappear above 400 K [17], we prepared our samples such that the oC4 phase would be observed at RT, thereby ensuring that the α-cF4 → oC4 and oC4 → tI2 transitions were studied at all temperatures. The samples were therefore cut using sharp scalpel blades in an oxygen-free, water-free glovebox environment (<1 ppm O 2 and < 1 ppm H 2 O), taking care to minimise the mechanical deformation of the sample which induces the transition to the mC4 phase [18].
For RT experiments, the Ce samples were loaded into Merrill-Bassett DACs equipped with tungsten (W) gaskets, and loaded with a small piece of 1 µm thick Ta foil or a small sphere of Cu as a pressure marker. The cells were loaded and sealed in the same oxygen-free, water-free environment used to prepare the samples. No pressure transmitting medium was included to prevent sample contamination, and to minimise any chemical reactions occurring within the sample chamber during sample loading.
The samples studied in the high-pressure, high-temperature experiments were prepared as described above. Samples were loaded into membrane DACs equipped with rhenium gaskets, which were then placed into a custom-built vacuum vessel [34,35]. The samples were heated with Watlow 240 V coiled heaters, which were wrapped around the outside of the DACs. The temperature was measured by using a Ktype thermocouple attached to one of the diamond anvils, close to the gasket. Various pressure markers were used in the high-temperature experiments. Ta, Cu and NaCl were used as pressure markers, with the pressure being determined using the thermal equations of state of Dorogokupets and Oganov [36], Cynn et al [37] and Dorogokupets and Dewaele [38], respectively.
The majority of the x-ray diffraction data used in this study was collected from multiple experiments on the high-pressure beamline I15 at the Diamond Light Source using a monochromated x-ray beam with incident wavelengths of ∼0.4246 Å or 0.3113 Å, collimated to 20 µm in diameter, and a MAR345 area detector. However, other diffraction data were also collected on beamline BL04 at the ALBA synchrotron [43] and on beamline ID09a at the ESRF synchrotron using similar x-ray wavelengths and beamsizes. In total, over 1600 diffraction images were collected from 13 samples in 6 separate synchrotron visits. In all experiments the 2D diffraction images were integrated azimuthally using Fit2D [39] and analysed using Le Bail pro le tting with the Jana software [40]. Apart from the DACs loaded with NaCl, no pressure transmitting medium was included with the sample. As a result, the samples may have experienced non-hydrostatic pressure. The methods of Singh and Takemura were utilized to quantify any non-hydrostatic effects in the cF4 phases [41] and, despite not using a pressure transmitting medium, no non-hydrostatic effects were observed. In addition, no systematic mis ts between the observed and calculated peak positions were observed in the oC4 and tI2 phases, suggesting that nonhydrostatic effects were undetectable.

Room-temperature compression
We performed two RT compression experiments. The two samples were compressed at RT up to 21.8 GPa, one using Ta as the pressure marker, while the other used Cu. After the DACs were closed in the glovebox, the samples were found to be in either the hexagonal hP4 phase, or in the γ-cF4 phase, depending on the pressure in the DACs. At low pressures, mixed-phase hP4/γ-cF4 diffraction pro les were observed, with single-phase γ-cF4 pro les being obtained only above 1.0 GPa. The onset of the γ-cF4 → α-cF4 isostructural transition was observed at 1.1 GPa in both samples, and by 1.8 GPa no trace of γ-cF4 remained.
Regions of the 2D diffraction images obtained from the Tacontaining DAC on compression up to 21.8 GPa are shown in gure 2, and a selection of integrated pro les is shown in gure 3. As the pressure was increased, multiple Bragg spots appeared in the raw 2D images at 4-5 GPa ( gure 2(b)), indicating the growth of a single crystal, which is characteristic of a transition to the oC4 structure [16,18]. Le Bail tting techniques were used to con rm the identity of the oC4 phase. The cell containing the Ta marker indicated the transition started at 4.0(1) GPa, while the Cu-containing DAC showed that the transformation started at 5.2(3) GPa. These transition pressures are in good agreement with previously reported values [16,17,27].
As the pressure was increased further, the diffraction images from the oC4 phase gradually became less singlecrystal-like and more powder-like ( gure 2(c)). The phase transition to the tI2 phase near 12 GPa was identi ed by the appearance of the (101)/(002) peaks from this phase ( gure 2(e)), and diffraction images from tI2 comprised textured Debye-Scherrer rings, with non-uniform intensities around the rings (see gures 2(d) and (e)). The oC4 → tI2 transition occurred at 12.4(2) GPa in the Ta-containing DAC, and at 12.6(2) GPa in the Cu-containing DAC, both in good agreement with previous reports [14,29].
We observed a wide range of co-existence of the oC4 and tI2 phases at RT, such that single-phase diffraction patterns from the tI2 phase were observed only above 21.8 GPa ( gure 3). A large co-existence range of these phases has been reported previously-between 13 and 19 GPa by Gu et al [16], and between 13.3 and 17.6 GPa by Ma et al [42]. We believe that the larger co-existence range observed in the current study arises because of the single-crystal-like nature of our oC4 samples. This resulted in extremely intense re ections from the oC4 phase such that we could still see evidence of the oC4 re ections at higher pressures (21 GPa) than if we had a more powder-like sample. Indeed, it was only in the> 2D images that we could see evidence of the very weak peaks from the oC4  The extended co-existence range of the oC4 and tI2 phases at RT may arise from their very different crystal structures, as a transition between the two requires considerable atomic rearrangement. However, Endo et al [14] and Dmitriev et al [29] both reported co-existence of the monoclinic mC4 phase and the tI2 phase between 12.1 and 17.5 GPa, and 12.5 and 17.7 GPa, respectively, at 300 K. These ranges are similar to those reported for the oC4 and tI2 phases (see above), yet both the mC4 and tI2 structures are only slightly distorted from fcc, and little atomic rearrangement is required to transform between them. The structural changes required at the transition would not therefore seem to be the main reason behind the large co-existence region, and further understanding is needed.

Resistive-heating studies
We used the resistively-heated DACs to determine the phase boundaries between the α-cF4, oC4 and tI2 phases up to ∼820 K and 20 GPa. As expected from the sample-preparation method used, we observe no evidence of the monoclinic mC4 phase in any sample, thus enabling us to locate phase transitions to and from the oC4 phase unambiguously. After loading, the samples were initially compressed into theα-cF4 phase at ∼3 GPa and then heated to the required temperature. They were then compressed isothermally until single-phase tI2 diffraction patterns were obtained. We also attempted to study the oC4 → α-cF4 and tI2 → oC4 reverse phase transitions on decompression, but the piston-cylinder DACs used in this study have a tendency to seize at high temperatures, making controlled pressure release very dif cult. Each isothermal compression was therefore obtained with a different sample. However, in one case, the DAC remained loose enough to enable us to repeatedly compress and decompress the cell. The sample in this DAC was therefore used to study the α-cF4 ↔ tI2 phase boundary, with data being collected on both compression and decompression. Figure 4 shows the phase boundaries that best t our experimental data. We note that there is some scatter in the transition pressures observed for the oC4 → tI2 transitions above 10 GPa, and we return to this later. The α-cF4 → oC4 phase boundary lies within the region of hysteresis observed by Antonova et al [31]. However, the detailed shape of the oC4 stability region at higher pressures is different to what has been reported previously, reaching an apex at ∼7.1 GPa and ∼650 K after which the oC4 → tI2 phase boundary becomes negatively sloped, and increasingly so above ∼11 GPa. We locate the triple point between the α-cF4, oC4 and tI2 phases at 6.1 GPa and 640 K, some 1-2 GPa lower than previous estimates, and nd the α-cF4 → tI2 boundary to have a positive gradient less steep [∼280 K (GPa) −1 versus ∼670 K (GPa) −1 ] than previously estimated.
Attempts to follow the α-cF4 → tI2 phase boundary up to the melting line above 1000 K were unsuccessful. Above ∼550 K weak additional contaminant peaks appeared in the diffraction pro les (as highlighted in gure 5) and above 820 K stronger non-Ce peaks appeared in the diffraction patterns The data were collected along a series of isotherms, and the lled circles mark the highest pressure at which single-phase α-cF4 diffraction patterns were observed at each temperature, while the un lled squares and triangles immediately to their right show the pressures at which the oC4 and tI2 phases, respectively, were rst observed on compressing the same samples. Similarly, at higher pressures, the lled squares mark the highest pressure at which single-phase oC4 diffraction patterns were observed, while the lled triangles to their right show the pressures at which the tI2 phase was rst observed in the same samples. The dashed lines show the phase boundaries reported by Schiwek et al [6], and references therein, while the solid lines show the phase boundaries that best-t the current data. signifying a reaction of the sample with either the gasket or the diamond anvil. The strength of the contaminant peaks suggests that less than 1% of the Ce sample has reacted when they rst appear above 550 K, and that this increases to ∼1% at 770 K and ∼10% at 820 K. At 880 K the contaminant peaks dominated the diffraction pro le, such that no further analysis of the Ce sample was possible. Analysis of the pressure cell after disassembly showed that the culets of both anvils were deeply pitted exactly where the sample had been in contact with them. The hot Ce had therefore reacted with the diamonds above 820 K, and studies to higher temperatures will require that the anvils are protected from the Ce by a chemical barrier. There remains a question as to how the presence of the contaminant phase affected studies of the transition pressures across the α-cF4 → tI2 phase boundary. As said, up to 820 K, a maximum of 10% of the sample had reacted, and the diffraction peaks from the Ce sample remained clearly visible. The reactant was likely to be concentrated in two layers adjacent to the anvil culets with the unreacted sample present in the middle of the gasket hole. As this is the same sample geometry that one would have if the Ce were sandwiched between two layers of a pressure transmitting medium, we believe the presence of the contaminant up to 820 K had no effect on the measurements presented here.
Schiwek et al [6] reported that the α-cF4 → tI2 phase boundary intercepts the oC4 stability eld at its apex. Our data, and the requirement of an α-cF4 → tI2 → oC4 → tI2 phase transition sequence on isothermal compression at ∼650 K seen in our preliminary study, reveal that the α-cF4 → tI2 phase boundary intercepts the oC4 stability eld at lower pressures and temperatures than the position of the apex. Analysis of the diffraction patterns obtained across the α-cF4 → tI2 transition shows a sharp onset of the tI2 phase (as determined by the splitting of the diffraction peaks from α-cF4), with no observable hysteresis (see gure 5) nor co-existence of the two phases. We also see no volume discontinuity, and there is therefore no evidence that the α-cF4 → tI2 is not second order.
Following the analysis of Schiwek et al and Zhao and Holzapfel, the c/a ratio of tI2 was plotted against V/V 0 to determine whether or not the α-cF4 → tI2 transition is continuous. Figure 6 shows the tetragonal distortion of the tI2 phase (denoted c/a − √ 2) plotted against the reduced volume (V/V 0 ) on both pressure increase ( lled symbols) and decrease (un lled symbols) as a function of temperature. The distortion is zero in the α-cF4 phase. There is no evidence of systematic hysteresis in the transition pressure or c/a ratio on pressure increase and decrease. There is also no evidence of any discontinuity in c/a at the α-cF4 → tI2 transition at any temperature other than 643 K, where two data points, one collected on pressure increase (at V/V 0 = 0.7078) and the other on pressure decrease (at V/V 0 = 0.7075) may suggest a discontinuity. However, as it is unlikely that the order of the transition is different at only one temperature, we believe that the apparent discontinuity at 643 K arises from the scatter in the two data points.
The experimental evidence, therefore, is that the α-cF4 → tI2 transition is continuous up to 800 K. While gure 6 suggests that the tetragonal distortion is temperature dependent at a xed volume, this effect arises from the nite slope of the α-cF4 → tI2 phase boundary (see gure 4), such that along an isochore (for example V/V 0 = 0.705 in gure 6) the sample is closer to the phase boundary at higher temperatures, resulting in a smaller tetragonal distortion of the tI2 phase. Indeed, at V/V 0 = 0.705, one can estimate the tetragonal distortion from the data shown at six different temperatures in gure 6 and determine that the distortion decreases linearly with temperature. At V/V 0 = 0.705, the tetragonal distortion reduces to 0 at ∼825 K, and the α-cF4 → tI2 transition would therefore take place at this compression and temperature, in agreement with the α-cF4 → tI2 phase boundary shown in gure 4. Finally, we return to the relatively large scatter seen in the transition pressures and temperatures above 10 GPa ( gure 4). Tsoik et al reported that the structures assumed by Ce at any given P and T were highly dependent on the P-T path taken to get to that point in phase space [32]. As mentioned earlier, all of the diffraction data presented in this study were obtained on isothermal compression, and, with the exception of the data used to determine the α-cF4 → tI2 phase boundary, each isotherm was obtained with a different sample. The compression paths followed to obtain data at each P-T point were therefore as simple as they could be. Also, by using x-ray diffraction, we were able to identify unambiguously the structures involved in the phase transitions, thereby ruling out that the scatter arose from transitions between different structures at each temperature (for example mC4 → tI2 rather than oC4 → tI2). Despite this, we see substantial variations in the pressure at which the oC4 → tI2 transition was observed at each temperature. For example, we found variations of ∼3 GPa in the oC4 → tI2 phase transition pressure in multiple measurements made at ∼575 K (see gure 4). The reasons for this signi cant variation are unclear. The different samples were from the same source, prepared in the same manner, and were loaded with the same pressure marker. We can therefore rule out variations in the transition pressure as arising from sample or pressure calibration issues. And while the rst-order nature of the oC4 → tI2 transition may result in variations in the transition pressure at lower temperatures, one might expect such variations to be reduced at elevated temperatures such as 575 K. Further studies of the oC4 → tI2 transition are required.

Conclusions
Angle-dispersive x-ray powder diffraction experiments have been performed on Ce up to 22 GPa and 820 K, with the aim of determining the stability region of the oC4 phase, and nature of the α-cF4 → tI2 phase boundary. The lowpressure phase boundary between the α-cF4 and oC4 phases is in good agreement with previous studies. The triple point between the α-cF4, oC4 and tI2 phases is found at 6.1 GPa and 640 K, 1-2 GPa lower than previous estimates, and is not at the apex of the oC4 phase stability region, which is located at 7.1 GPa and 650 K. The α-cF4 → tI2 phase boundary is found to have a positive gradient less steep [∼280 K (GPa) −1 versus ∼670 K (GPa) −1 ] than previously estimated. We nd the α-cF4 → tI2 transition to be second order, in contrast to the conclusions reported by Zhao and Holzapfel [17].
Our data suggest that the oC4 → tI2 phase boundary lies at higher temperatures than reported previously, and we observe signi cant scatter in the phase transition pressures observed at any given temperature, the reasons for which are unclear and require further study. In contrast to the claims of Tsiok and Khvostantsev [32], we observed no evidence of the α-cF4 at pressures above the triple point, only the tI2 phase.
Unfortunately, we were unable to study Ce above 820 K due to reactions between the Ce and the diamond anvils. The location of the α-cF4−tI2−liquid triple point thus remains unknown, while the phase behaviour at higher pressures and temperatures remains completely unknown. Given the reaction observed between the Ce and the diamond anvils above 820 K, further studies to investigate the higher pressure/temperature behaviour will need to ensure that the Ce is contained within a non-reactive pressure medium and prevented from contacting the anvils.