Estelle Glais
email: estelle.glais@cnrs-imn.fr

Florian Massuyeau

Romain Gautier
email: romain.gautier@cnrs-imn.fr

Tuning the Emission Color and Temperature Range of Dual-mode Luminescent Thermometer by Dopant Valence States Control

Keywords: Luminescent sensors, dopant valence state, Mn luminescent centers, dual-mode thermometer

Dual emitting materials are of great interest for luminescence thermometry. The operating temperature range, the thermal sensitivity as well as the emission color are crucial parameters, which define the competitiveness of the thermal sensor. In this work, we propose a new and convenient method for the modulation of emission color range and sensitivity through the control of the dopant oxidation states and crystal field variations. To this end, we investigated inorganic phosphors in which two valence states of Mn luminescent centers can be stabilized. When inserted in octahedral environment, Mn 4+ ions present a red luminescence ( 2 E → 4 A 2 transition), whereas Mn 2+ ions exhibit a green luminescence in tetrahedral environment ( 4 T 1 → 6 A 1 transition). Due to the different behavior of Mn 4+ and Mn 2+ luminescence properties according to the temperature, the resulting emission color vary from red to green and can be exploited for visual temperature detection. We demonstrate the proportion of Mn 4+ and Mn 2+ ions can be finely tuned, owing to a thermally driven Mn 4+ to Mn 2+ reduction, which allow to modulate color change at a specific temperature. Two isostructural materials were investigated SrMgAl 10 O 17 :Mn 4+ ,Mn 2+ and BaMgAl 10 O 17 :Mn 4+ ,Mn 2+ and can be envisioned as competitive ratiometric and colorimetric luminescent thermometer, with tunable properties.

Introduction

Luminescence thermometry is a promising method that have been extensively studied over the past decade [START_REF] Dramićanin | Trends in luminescence thermometry[END_REF], which allows a precise, real time, and contactless measurement of the temperature.

Thermometry based on luminescence properties changes of materials is relevant in various fields as medicine, aeronautic, microfluidic or catalysis [START_REF] Vetrone | Temperature Sensing Using Fluorescent Nanothermometers[END_REF][START_REF] Brites | Thermometry at the nanoscale[END_REF][START_REF] Geitenbeek | Luminescence thermometry for in situ temperature measurements in microfluidic devices[END_REF]. The accuracy as well as the temperature range, on which the luminescent sensor should be efficient, vary according to the selected application.

Numerous inorganic materials doped with luminescent ions have been developed and are very promising [START_REF] Mclaurin | Dual-Emitting Nanoscale Temperature Sensors[END_REF][START_REF] Dramićanin | Sensing temperature via downshifting emissions of lanthanide-doped metal oxides and salts. A review[END_REF][START_REF] Marciniak | Luminescence lifetime thermometry with Mn 3+ -Mn 4+ co-doped nanocrystals[END_REF]. The robustness and the competitiveness of a specific luminescent sensor can be defined thanks to its thermal sensitivity. However, the tuning of the temperature ranges in which the material sensitivity reaches the maximal value, as well as the modulation of the resulting emission color at a given temperature remains challenging. The lack of properties flexibility of specific materials with remarkable performances for thermal sensing limit their development to other applications. As a consequence, a variety of materials with targeted features is needed. In this work, we propose a new and simple method for the thermal response modulation of a single luminescent material. More specifically, we focus on the stabilization of several valence states of the same element, namely Mn 4+ and Mn 2+ (the two main existing forms of Mn ions studied for their luminescence properties), in a single matrix. Manganese is an abundant resource, and can be considered as an efficient alternative to rare earth elements for luminescence applications. The local coordination as well as the distribution in the host lattice determines the luminescence properties of divalent or tetravalent Mn ions [START_REF] Zhou | Mn 2+ and Mn 4+ red phosphors: synthesis, luminescence and applications in WLEDs. A review[END_REF]. The photoluminescence color of Mn 2+ ion varies from green to red according to the local environment in which it is inserted whereas Mn 4+ ion exhibits a red emission [START_REF] Brik | Influence of Covalency on the Mn 4+ 2E g → 4 A 2g Emission Energy in Crystals[END_REF][START_REF] Zhou | Research progress and application prospects of transition metal Mn 4+ -activated luminescent materials[END_REF][START_REF] Li | Research progress of Mn doped phosphors[END_REF].

Moreover, Mn 4+ doped-materials have been of interest for luminescence thermometry application [START_REF] Yang | Thermometry of red nanoflaked SrAl 12 O 19 :Mn 4+ synthesized with boric acid flux[END_REF][START_REF] Glais | MgTiO 3 :Mn 4+ a multi-reading temperature nanoprobe[END_REF][START_REF] Dramićanin | Li 2 TiO 3 :Mn 4+ Deep-Red Phosphor for the Lifetime-Based Luminescence Thermometry[END_REF][START_REF] Trejgis | Highly sensitive multiparametric luminescent thermometer for biologically-relevant temperatures based on Mn 4+ , Ln 3+ co-doped SrTiO 3 nanocrystals[END_REF]. The difference in the luminescence thermal sensitivity between Mn 4+ and Mn 2+ ions has recently been reported in some inorganic materials [START_REF] Dong | ZnGa 2-y Al y O 4 :Mn 2+ ,Mn 4+ Thermochromic Phosphors: Valence State Control and Optical Temperature Sensing[END_REF][START_REF] Zhu | A highsensitivity dual-mode optical thermometry based on one-step synthesis of Mn2+:BaAl12O19-Mn 4+ :SrAl 12 O 19 solid solution phosphors[END_REF]. The co-stabilization of Mn 2+ and Mn 4+ ions in two isostructural materials, namely SrMgAl 10 O 17 :Mn 4+ ,Mn 2+ (SMA:Mn) and BaMgAl 10 O 17 : Mn 4+ ,Mn 2+ (BMA:Mn) has been discussed. In such matrices, Mn 2+ and Mn 4+ ions are stabilized in tetrahedral and octahedral sites respectively leading to two distinct emission bands [START_REF] Ju | Photoluminescence properties of color-tunable SrMgAl 10 O 17 :Eu 2+ ,Mn 2+ phosphors for UV LEDs[END_REF][START_REF] Cao | Luminescence Properties and Synthesis of SrMgAl 10 O 17 :Mn 4+ Red Phosphor for White Light-Emitting Diodes[END_REF][START_REF] Singh | Eu 2+ and Mn 2+ Co-doped BaMgAl 10 O 17 Blue-and Green-Emitting Phosphor: A Luminescence and EPR Study[END_REF][START_REF] Wang | Non-Rare-Earth BaMgAl 10-2x O 17 :xMn 4+ ,xMg 2+ : A Narrow-Band Red Phosphor for Use as a High-Power Warm w-LED[END_REF][START_REF] Cao | Luminescence properties and charge compensation of BaMgAl 10 O 17 :Mn 4+ , K red emitting phosphor[END_REF][START_REF] Xu | The role of co-dopants on the luminescent properties of α-Al 2 O 3 :Mn 4+ and BaMgAl 10 O 17 :Mn 4+[END_REF][START_REF] Hu | Non-stoichiometric defectcontrolled reduction toward mixed-valence Mn-doped hexaaluminates and their optical applications[END_REF][START_REF] Kang | Narrow-Band SrMgAl 10 O 17 :Eu 2+ , Mn 2+ Green Phosphors for Wide-Color-Gamut Backlight for LCD Displays[END_REF]. Using an approach similar to the one previously implemented for Eu 3+ /Eu 2+ doped oxides in solid state lighting applications [START_REF] Behrh | A Chemical Route Towards Single-Phase Materials with Controllable Photoluminescence[END_REF][START_REF] Yuan | Tuning the oxidation states of dopants in Li2SrSiO4:Eu,Ce and control of the photoemission color[END_REF], we selected SMA and BMA materials to precisely control the reduction process of Mn 4+ to Mn 2+ and the corresponding luminescence properties. SMA:Mn and BMA:Mn are investigated as colorimetric and ratiometric dual-mode luminescent thermometer. The dopant valence state is demonstrated as efficient parameter for the modulation of the color range as well as the associated temperature.

Material & Methods

SrMgAl 10 O 17 :Mn and BaMgAl 10 O 17 :Mn materials were prepared through a solid state synthesis. SrCO 3 , BaCO 3 , MgO, Al 2 O 3 , MnCO 3 were used as starting materials. Precursors were weighted according to stoichiometric proportions and grounded in agate mortar during 30 min. Only MgO precursor was incorporated in excess to improve Mn 4+ stabilization (charge compensation) and to prevent the formation of the parasitic phases SrAl 2 O 4 and BaAl 2 O 4 . The as prepared powder was transferred to alumina crucible and heated at 1500 °C during 15 h. This sintering process was performed under air using a muffle furnace and repeated in order to reduce the proportion of secondary phases. The crystallized materials were then placed in a home-made machined stumatite sample holder where several isolated crucibles are continuously distributed along the temperature gradient axis. This sample holder was placed in a thermal gradient oven under ultra-high vacuum (≈ 10 -6 mbar) for the reductive thermal treatment (temperature range from 400 °C to 800 °C, SI -3). Xray diffraction patterns were obtained by powder X-ray diffraction using a Bruker D8 diffractometer with Cu-Kα radiation (λ = 1.5406 Å). Diffraction data were recorded in a 2θ range from 10° to 90° in 0.02° steps. Excitation and emission photoluminescence spectra were recorded with a Jobin-Yvon Fluorolog 3 spectrophotometer using a xenon light source (450 W). Liquid nitrogen cryostat Oxford OptistatDN-V was used for temperature dependent photoluminescence spectra.

Results and discussion

3.1. Crystal structure and phase identification SMA:Mn and BMA:Mn materials both present isostructural crystal structures (P6 3 /mmc space group). SMA:Mn and BMA:Mn exhibit an orderly layered structure in which spinel blocks of SI -2, and the absence of Mn 4+ luminescence signal originating from these secondary phases, it is assumed that no change in the luminescence properties is induced by the presence of these impurities.

Optical characterizations

Emission spectra of SMA:Mn and BMA:Mn are reported in Figure 2a. Two emission bands can be identified. The first band centered at 514 nm can be attributed to the 4 T 1 →6 A 1 transition of Mn 2+ ion.

The second one centered around 660 nm corresponds to the 2 E → 4 A 2 (Mn 4+ ) transition. Excitation spectra monitored at 514 nm and 658/660 nm are characteristic of Mn 2+ and Mn 4+ signatures respectively (Figure 2b). Four bands can be highlighted in Mn 2+ excitation spectra, the corresponding transitions

3.3.Modulation of Mn 4+ /Mn 2+ ratio

The co-stabilisation of Mn 4+ and Mn 2+ ions in SMA and BMA hosts after synthesis in air atmosphere has been highlighted through the analysis of photoluminescence properties. The Mn 4+ /Mn 2+ ratio can be modulated owing to a reductive thermal treatment (RTT) of samples after synthesis. To this end, a thermal gradient oven is used, which allows to perform the reductive To accelerate the characterization process, we designed a set up to collect photoluminescence properties directly on the stumatite sample holder, without further sample handling (SI -3). The sample holder is fixed on a X-Y table in which the movement along two axes is computer-controlled.

Optical fibers are coupled to the spectrofluorimeter. Each sample is characterized by automatically moving the sample holder along X and Y axes. The recorded photoluminescence spectra are presented in Figure 3a. The intensity of Mn 2+ emission increases relatively to Mn 4+ emission when the temperature of the RTT increases. Thus the RTT allows the increase of Mn 2+ concentration due to the progressive reduction of Mn 4+ into Mn 2+ . As the Mn 2+ emission band is characteristic of Mn 2+ ion in tetrahedral site, we assume that the reduction process is associated with cation diffusion from Oh site to Td site. The charge balance would be preserved owing to the formation of oxygen vacancies. The resulting emission color associated to each photoluminescence spectra are presented on CIE diagram Figure 3b. The color emission shifts from red to green with the increase of RTT temperature. After a RTT at 800 °C under ultra-high vacuum, the Mn 4+ emission band is still detected as the reduction of Mn 4+ → Mn 2+ is not complete. However, since the human eyes are more sensitive to green light, the proportion of Mn 2+ is sufficient to shift the resulting emission color in the green region. The same phenomenon is obtained for BMA material (SI -4). This method, based on the thermally-driven reduction of dopant, enables the fast synthesis of a large number of compounds. It allows the fine tuning of the oxidation state of dopants and the modulation of the luminescence properties. The same approach can be transposed to many other systems for the discovery of new materials with competitive and flexible properties.

Luminescence thermometry

The luminescence behavior according to the temperature is then investigated on samples with fixed Mn 4+ and Mn 2+ concentrations. The photoluminescence spectra of SrMgAl 10 O 17 :Mn 4+ ,Mn 2+ after reductive thermal treatment with resulting yellow-orange emission (T RTT ≃ 750 °C) are recorded from 0 °C to 200 °C (Figure 4a). The selected sample is labeled as SMA-RTT. In the investigated temperature range, the intensity of Mn 2+ band only slightly decreases compared to the Mn 4+ contribution. To this end, Mn 2+ will be considered as the reference. As reported in Figure 4b, the Mn 4+ 2 E → 4 A 2 transition exhibits a huge temperature dependence. The evolution of Mn 4+ /Mn 2+ intensity ratio according to the temperature is reported Figure 5 and can be modeled by a sigmoidal curve as the emission arises from two distinct emitting centers. The investigated temperature range is smaller than the temperature required for Mn 4+ reduction into Mn 2+ . We assume that concentrations of both ions remain constant on this whole range. Consequently, this parameter is not responsible of the luminescence properties variation according to the temperature.

The competition between radiative and non-radiative deexcitation process can be modelled by Mott-Seitz function (Equation 1), where k B is the Boltzmann constant, ∆E the activation energies of thermal quenching process, I 0 the intensity emission at T = 0 K, and a a fitting parameter corresponding to the ratio between radiative and non-radiative transition probabilities [START_REF] Brites | Chapter 281 -Lanthanides in Luminescent Thermometry[END_REF]. In this general equation, all deactivation channels that can be induced by the temperature increase are taken into account. (1)

However, in the case of SrMgAl 10 O 17 :Mn 4+ ,Mn 2+ -RTT sample, Mn 4+ exhibits a greater temperature dependence than Mn 2+ in the investigated temperature range, thus the Mn 2+ contribution can be neglected. In addition, only one quenching process is identified, therefore one deexcitation channel (indexed channel 1) can be considered. Thus, the fitting equation is simplified (see Equation 2) and the associated fitting curve can be plotted (dashed line in Figure 5) with the following fitting parameters I 0 = 8.22 ± 0.11, a 1 =2.96 10 6 ± 1.58 10 6 , and ΔE 1 = 3696 ± 139 cm -1 .

≃

The thermal sensitivity, defined by Equation 3, is represented in solid blue line on Figure 5. In the case of SMA-RTT material, the thermal sensitivity value increases from RT to 130°C to reach 2.77 %/°C, and then slowly decreases when the temperature is further stepped up. The sensitivity is competitive compared to other luminescent thermometer reported in the literature [START_REF] Brites | Thermometry at the nanoscale[END_REF][START_REF] Wang | Luminescent probes and sensors for temperature[END_REF][START_REF] Dramićanin | Luminescence Thermometry: Methods, Materials, and Applications[END_REF], which confirm the ability of SMA:Mn material as effective ratiometric thermometer.

Figure 5 : Mn 4+ /Mn 2+ intensity ratios of SMA:Mn -RTT and BMA:Mn -RTT (dots), the dashed lines correspond to the fitting curves and the solid lines are the associated thermal sensitivities.

(

The evolution of Mn 4+ /Mn 2+ ratio according to the temperature is also investigated for SMA:Mn samples without RTT or with a higher temperature of RTT namely 800 °C (Figure SI -5). The absolute value of the ratio changes according to the RTT temperature but the variation remains similar, as represented by the sensitivity curves. The maximal sensitivity occurs in the same temperature range (between 125 and 130 °C) and the maximal value is around 2.5 and 3 %/°C for the three samples. One interesting change is the difference in emission color range of the phosphor. The emission color obtained from CIE coordinates are represented in Figure 6. The horizontal bars represent the color evolution from RT (left) to high temperature (right). Whereas the SMA:Mn sample without RTT (Figure 6a) displays a color change from red to green with temperature increase up to 200 °C, the color range for SMA:Mn sample with a 750 °C RTT (Figure 6b) and 800 °C RTT (Figure 6c) present a different behavior. The temperature of color variation (i.e. temperature threshold) can also be tuned according to the temperature of the RTT. The resulting emission color changes from yellow to green around 125°C for SMA:Mn sample without RT, while the same phenomenon occurs at 90 °C and 70 °C for SMA:Mn sample with a 750°C and 800 °C RTT respectively (dashed lines Figure 6). This remarkable property can then be explored for temperature variation detection. Unlike the absolute and self-referenced determination of the temperature, which can be achieved thanks to Mn 4+ /Mn 2+ intensity ratio, the color change tracking will allow an accessible and simply-to-implement temperature identification around a temperature threshold. The color range as well as the temperature threshold can much higher for the deexcitation channel with ΔE 2 = 3825 ± 143 cm -1 . To this end, we assume that the deexcitation channel 2 can be considered as predominant. The maximal sensitivity of BMA:Mn-RTT arise at higher temperatures than SMA:Mn-RTT sample and reaches 1.9 %/°C at 200 °C.

The difference in activation energies of thermal quenching process between SrMgAl 10 O 17 :Mn 4+ ,Mn 2+ -RTT (ΔE 1 ) and BaMgAl 10 O 17 :Mn 4+ ,Mn 2+ -RTT (ΔE 2 ) is directly linked to the crystal field energy. To illustrate this statement, the energy level diagram is reported in Figure 7. In both materials, 2 E → 4 A 2 transition is responsible of Mn 4+ red luminescence. Excitations at 426 and 450 nm for SMA:Mn and BMA:Mn materials respectively allow the promotion of electron from the 4 A 2 ground state to the 4 T 2 excited state. The presence of an intersection between parabolas of the ground state and excited states induces a non-radiative deexcitation channel. Thus ΔE value calculated using the Mott-Seitz model, can be defined as the energy difference between the 2 E emitting level and the cross-intersection point.

With temperature increase, the probability of non-radiative deexcitation through this channel increases, and above a certain temperature, this deexcitation path prevails. As illustrated by the Tanabe-Sugano diagram, no change occurs in the relative position between the 4 A 2 ground state and the 2 E excited level according to the crystal field. However, the position of the 4 T 2 level shifts toward higher energy with crystal field increase. Thus, the crossover responsible for the non-radiative deexcitation process occurs between the parabolas of the 4 A 2 ground state and the 4 T 2 excited state. As a consequence, the activation energies of thermal quenching process increase in BMA:Mn-RTT (ΔE 2 = 3825 ± 143 cm -1 ) relatively to SMA:Mn-RTT material (ΔE 1 = 3696 ± 139 cm -1 ). Thus the crystal field splitting drastically influences the luminescence thermal stability of Mn 4+ -doped material and shifts the maximal thermal sensitivity to higher temperature. By modulating the environment of the activator, the temperature range on which the thermal sensor is efficient can then be adjusted.

Conclusion

In summary, the co-stabilization of Mn ions with two different valence states have been highlighted from the analysis of photoluminescence properties. The proportion of each valence states of dopant have been finely controlled according to the temperature variation of the reductive posttreatment. We developed a strategy, allowing to synthesize and analyze the properties of multiple samples in a combinatorial approach and demonstrate the possibility of a fast and thorough tuning of the luminescence properties. Furthermore, we also evidenced the ability of SMA:Mn and BMA:Mn materials doped with Mn 4+ and Mn 2+ activators as competitive and reliable dual-mode luminescent thermometers (colorimetric and ratiometric). The valence state of dopant as well as the crystal field of the host have been demonstrated as critical parameters, that can be simply tuned in order to optimize the thermal response of the sensor and control the temperature range on which the thermometer is efficient. This strategy can then be adapted to other thermometers in order to accelerate their luminescence properties optimization, and can be generalized to other applications as LEDs, imaging or anticounterfeiting.

MgAl 10 OFigure 1 :

 101 Figure 1 : XRD patterns of SrMgAl 10 O 17 :Mn 0.2%at (blue) and BaMgAl 10 O 17 :Mn 0.2%at (orange)

Figure 2

 2 Figure 2 : a) Emission spectra of SrMgAl 10 O 17 :Mn 4+ ,Mn 2+ (blue) and BaMgAl 10 O 17 :Mn 4+ ,Mn 2+ (orange) b) Excitation spectra of SrMgAl 10 O 17 :Mn 4+ ,Mn 2+ (blue) and BaMgAl 10 O 17 :Mn 4+ ,Mn 2+ (orange), the dashed lines (resp. solid lines) correspond to Mn 4+ (resp. Mn 2+ ) excitation spectra c) schematic representation of Mn 2+ and Mn 4+ energy levels and the corresponding transitions observed in photoluminescence spectra d) Tanabe-Sugano diagram of d 3 ion in octahedral environment; the blue (resp. orange) dashed line corresponds to the crystal field strength of SrMgAl 10 O 17 (resp. of BaMgAl 10 O 17 ) host matrix.

Figure 3 :

 3 Figure 3 : a) Photoluminescence spectra of SrMgAl 10 O 17 :Mn 4+ ,Mn 2+ after reductive thermal treatment at different temperatures from 400 °C (dark green) to 800 °C (red) -λ exc = 426 nm b) associated CIE coordinates.

Figure 4 :

 4 Figure 4 : a) Photoluminescence spectra of SrMgAl 10 O 17 :Mn 4+ ,Mn 2+ -RTT from 0 to 200 °C b) associated integrated intensity of Mn 4+ (red) and Mn 2+ (green) bands.

Figure 6 :

 6 Figure 6 : Evolution of the resulting emitting color according to the temperature of a) SMA:Mn without RTT samples b) SMA:Mn-RTT 750 °C c) SMA:Mn-RTT 800 °C, threshold temperatures are reported in dashed lines.

Figure 7 :

 7 Figure 7 : Energy levels diagram of Mn 4+ ion inserted in SrMgAl 10 O 17 and BaMgAl 10 O 17 hosts.

A 1 → 4 T 2 ( 4 G),[START_REF] Dramićanin | Sensing temperature via downshifting emissions of lanthanide-doped metal oxides and salts. A review[END_REF] A 1 → 4 E,[START_REF] Geitenbeek | Luminescence thermometry for in situ temperature measurements in microfluidic devices[END_REF] A 1 ( 4 G),[START_REF] Dramićanin | Sensing temperature via downshifting emissions of lanthanide-doped metal oxides and salts. A review[END_REF] A 1 → 4 T 2 ( 4 D), and[START_REF] Dramićanin | Sensing temperature via downshifting emissions of lanthanide-doped metal oxides and salts. A review[END_REF] A 1 → 4 E ( 4 D) are reported in the schematic scheme of energy level (Figure2c). Both activators can be excited in the blue and in the UV regions.Similarly, three bands can be identified on Mn 4+ excitation spectra. They can be attributed to the[START_REF] Geitenbeek | Luminescence thermometry for in situ temperature measurements in microfluidic devices[END_REF] A 2 → 4 T 1 , 4 A 2 → 2 T 2 and 4 A 2 → 4 T 2 transitions. In addition, the excitation spectrum of Mn 4+ inserted in BaMgAl 10 O 17 host matrix is blue shifted compared to excitation spectrum of Mn 4+ inserted in SrMgAl 10 O 17 . As a d 3 ion, the position of Mn 4+ energy levels depends on the environment in which it is inserted. The corresponding Tanabe Sugano diagram is reported in Figure2d. The relative position of energy levels involved in the photoluminescence process is drastically dependant on the crystal field strength (Dq) and on the interelectronic interaction represented by the Racah parameter B. The Dq/B value of both SMA:Mn and BMA hosts are reported on the Tanabe-Sugano diagram[START_REF] Adachi | Photoluminescence properties of Mn 4+ -activated oxide phosphors for use in white-LED applications: A review[END_REF][START_REF] Adachi | Crystal-field and Racah parameters of Mn 4+ ion in red and deep red-emitting phosphors: Fluoride versus oxide phosphor[END_REF]. It can clearly be highlighted that a Sr 2+ by Ba 2+ substitution in isostructural host leads to an important variation of the energy of the 4 T 1 and 4 T 2 levels compared to the 2 E and 4 A 2 levels. Such a difference can be directly observed on excitation spectra, the energy increase between levels involved in radiative transition leads to a blue shift of the associated bands. As a consequence, the spectral overlap between Mn 2+ emission spectrum and Mn 4+ excitation spectrum is smaller in BMA compared to SMA host. Excitation wavelengths are selected in order to optimize Mn 4+ and Mn 2+ emissions and are fixed at 426 nm for SMA:Mn samples and 450 nm for BMA:Mn samples for this work.

Acknowledgments

This work was supported by the National Agency for Research (ANR JCJC Combi-SSL, ANR-16-CE08-003-01).

be tuned for a single material according to the Mn 4+ /Mn 2+ ratio, and can be relevant for many applications as electronics or microfluidics, where critical temperature should not be exceeded for performances sustainability. Thus, after calibration, the same material can be used as dual mode thermometer, namely colorimetric and ratiometric.

The luminescence thermal stability is also investigated for BaMgAl 10 O 17 :Mn 4+ ,Mn 2+ -RTT sample (SI -6). As reported in Figure 5, the Mn 4+ /Mn 2+ intensity ratio also decreases with temperature increase (orange dots). Nevertheless, the luminescence behavior of BaMgAl 10 O 17 :Mn 4+ ,Mn 2+ -RTT sample deviates from SMA:Mn-RTT one. It is important to notice that for both samples no irreversible change in the luminescence properties occurs with the temperature increase. Cyclic processes are performed between two temperatures (40 °C and 100 °C), showing the reversibility of the luminescence properties as well as the robustness of the thermal sensor (SI -7). Following the Shannon and Prewitt table, the ionic radius of Sr 2+ (resp. Ba 2+ ) inserted in a 6-coordinated site is about 126 pm (resp. 142 pm). This difference in ionic radius leads to a change in crystal lattice parameters, the values obtained from Rietveld refinement are reported in SI -2. Hence a remarkable change in luminescence properties is observed between SMA:Mn-RTT and BMA:Mn-RTT materials. Besides the blue shift of photoluminescence excitation spectrum of BMA:Mn reported in the previous part, the luminescence thermal stability is also influenced. Whereas only 31 % of initial Mn 4+ intensity is detected at 100 °C for SMA:Mn-RTT, 66 % of initial Mn 4+ intensity remains in BMA:Mn-RTT at the same temperature (Table 1). However, in the case of BMA:Mn, two different contributions should be taken into account in order to understand the intensity ratio evolution according to the temperature, identified as channel 2 and 3, indicating that unlike SAM:Mn-RTT, more than one quenching process occurs in BMA:Mn-RTT.

The fitting curve of Mn 4+ /Mn 2+ ratio in BMA-RTT material is plotted in dashed line in Figure 5 with the fitting parameters I 0 = 10.73 ± 0.02, a 2 = 560462 ± 256072, ΔE 2 = 3825 ± 143 cm -1 , a 3 = 9.7 ± 2.9 cm -1 and ΔE 3 = 917 ± 64 cm -1 . The new deexcitation channel (channel 3) exhibits a lower activation energy of thermal quenching process (ΔE 3 ), and consequently occurs at lower temperature.

Nevertheless, a 2 >> a 3 , meaning that the ratio of non-radiative vs. radiative transition probabilities is

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.

Appendix A : Supplementary material

Supplementary Material.


Simon Ayrinhac
email: simon.ayrinhac@sorbonne-universite.fr

Michel Gauthier

Marc Morand

Yiuri Garino

Silvia Boccato

Frédéric Decremps

Paraskevas Parisiades

Philippe Rosier

Nicki C Siersch

Abderraouf Seghour

Daniele Antonangeli

Determination of indium melting curve at high pressure by picosecond acoustics

Keywords: Picosecond Acoustics, Equation of State, Phase Diagram, High Pressure, Melting Curve, Sound velocity, Indium

teaching and research institutions in France or abroad, or from public or private research centers.

I. INTRODUCTION

Determination of the thermoelastic properties of liquids at extreme conditions of pressure and temperature is fundamental for understanding the properties of condensed matter (e.g. [1,2]), with direct implications in geophysics and planetary sciences (e.g. [3][4][5][6]). Even though it is an experimentally challenging task, many previous studies dealt with the determination of phase diagrams, including melting curves, equations of state or sound velocities measurements in the liquid phase, in addition with other thermodynamic properties determination such as bulk modulus or thermal expansion. In particular, many techniques were developed to measure the melting curves (see [7,8] for a review). Early methods were based on visual observations [9,10], existence of a temperature plateau [11], or on changes in electrical resistivity [12]. More recent in situ diagnostics include the appearance of diffuse signal in X-ray diffraction [13,14], characteristic changes in the X-ray absorption spectroscopy [15] and detection by Synchrotron Mossbauer Spectroscopy experiments [16].

During the last decades, picosecond acoustics (PA) combined with diamond anvil cell (DAC) has been increasingly used to measure the thermoelastic properties of liquids and solids as well as their phase diagram. Nowadays, the combination of these two techniques appears to be a powerful and versatile laboratory tool [17] used to accurately measure both the melting curve and the sound velocities under high temperature and pressure conditions [18][19][20]. So far, PA has been successfully applied to study various solids (e.g. ice [21,22], Ar [23], H [24]) and liquids (e.g. Hg [25,26], Ga [18], Rb [20], Cs [19]).

To further explore the detection and metrology capabilities of PA, liquid indium can be considered a very interesting case study. First of all, its properties are very well known at ambient pressure [27,28], making In a standard calibration substance [29,30]. In particular, its melting temperature is a secondary reference point of the international temperature scale (ITS) [31]. Secondly, due to its low melting temperature, its ductility and low chemical reactivity [32], In can be routinely handled in the laboratory. Thirdly, although there are many papers on the measurements of sound velocities in liquid indium at high temperatures and ambient pressure (see for example the review of Blairs [33]), experimental data at gigapascal pressures are very scarce. To the best of our knowledge, the sound velocities at high pressure were measured only by Coppens et al. [34] up to around 0.01 GPa, and by Alatas et al. [35] and Komabayashi et al. [36] up to 6.7 GPa. Finally, the phase diagram of solid indium appears to be unusual compared to other III-A group elements (Al, Ga, Tl) and has attracted interest over time [37][38][39][40][41]. At ambient conditions, indium crystallizes in a tetragonal distortion of the compact cubic FCC system. This face-centered tetragonal structure (FCT) is stable at ambient temperature up to 50 GPa [41]. The c/a ratio is observed to reach a maximum value around 20 GPa [37,41], which is related to an increased distortion of the FCT structure with respect to FCC. Above 50 GPa a solid-solid transition occurs and the In structure changes from FCT to a face-centered orthorombic (FCO) arrangement, stable up to ≈150 GPa [41]. The In phase diagram was also explored by ab initio electronic structure calculations at T=0 K [42], and at high temperatures by XRD (T>500 K) [43], but no other transitions were reported in the solid phase up to 247 GPa [41]. From all the above, we can conclude that In is particularly stable at high pressure and temperature compared to other metallic elements [44].

Regarding the liquid phase, although the melting point is well known at ambient pressure, the melting curve measured by several authors with different techniques shows significant discrepancies above 4 GPa [45]. The knowledge of the melting curve is actually crucial as it is used as a calibration curve at high p and high T (see for example reference [36]). This calls for a new set of experimental data obtained using a state of the art technique, with a particular attention dedicated to both the detection criteria of the solid-liquid transition, and the accurate pressure and temperature metrology.

Sound velocities in solids and liquids are markedly different and changes in sound velocities are a very sensitive probe to detect a solid-liquid phase transition [18,46,[START_REF] Xu | Phase diagram of tin determined by sound velocity measurements on multi-anvil apparatus up to 5 GPa and 800 K[END_REF] or subtle transformations in the liquid phase [19,20]. Furthermore, accurate velocity measurements allow to derive useful thermodynamical quantities and to obtain the equation of state of the liquid [START_REF] Su | Equation of state of liquid bismuth and its melting curve from ultrasonic investigation at high pressure[END_REF][START_REF] Ayrinhac | Heat capacity ratio in liquids at high pressure[END_REF]. We have thus reexamined the properties of liquid indium in the temperature range 420-680 K and from ambient pressure to 6 GPa by PA technique combined with an externally heated diamond anvil cell (hDAC).

II. EXPERIMENTAL METHODS AND SET-UP

A. Picosecond acoustics set-up

Picosecond acoustics is a time-resolved, pump-probe, optical technique that generates and detects propagating strain waves in solids or liquids [START_REF] Maris | Picosecond ultrasonics[END_REF][START_REF] Matsuda | Fundamentals of picosecond laser ultrasonics[END_REF].

In our set-up, the infrared beam from a mode-locked Ti:sapphire laser (λ = 800 nm, pulse width 100 fs, repetition rate ≈80 MHz i.e. 12.548(4) ns) is divided into a pump and a probe beam (see Fig. 1).

The pump beam passes through an acousto-optic modulator (AOM), which modulates the intensity of the pump beam around 1 MHz, to improve the signal-to-noise ratio through lock-in detection (HF2LI from Zurich Instruments). Then the pump beam is focused onto one of the surfaces of the sample (beam waist ≈ 1.5 µm), and, for metallic samples as the case of present interest, directly absorbed. The so-generated thermal stress relaxes and an acoustic wave propagates into the sample.

The probe beam is delayed with respect to the pump by a mechanical delay line (optical length 4 m, maximum delay time 13.33 ns) and focused on the opposite surface of the sample to detect its reflectivity changes due to the arrival of the acoustic wave.

These changes in reflectivity can be detected on the variation either in the intensity or in the phase of the reflectivity signal. The intensity variation ρ = Re (∆R/R) is related to the photoeleastic properties of the sample. Unfortunately, the photoelastic variation induced in indium is very small and a reflectivity measurement set-up is not efficient enough in this case. An interferometric system should be used instead.

By means of a beam splitter, the probe beam is divided in two. One part is focused on the sample with the use of an objective mounted on a XY piezoelectric stage (P-517.2CL from Physik Instrumente) exploited to scan the sample surface over a 100×100 µm 2 area and collect surface phonon imaging data [START_REF] Sugawara | Watching ripples on crystals[END_REF]. The remaining part of the probe beam is reflected on a reference mirror mounted on a piezoactuator with a feedback loop to stabilize the Michelson interferometer [START_REF] Perrin | Interferometric detection of hypersound waves in modulated structures[END_REF][START_REF] Zhang | Three-dimensional acoustic wavefront imaging in anisotropic systems by picosecond acoustics[END_REF]. The two beams reflected by the sample and the reference mirror are then mixed to obtain interferences before being collected by two amplified photodetectors. The voltage difference V A -V B between the two photodetectors (PDA and PDB in Fig. 1) is proportional to the phase change of the relative reflectivity variation φ = Im (∆R/R). The obtained signal shown in Fig. 1 (bottom) is thus affected by both the sample surface displacement and its refractive index variations through photoelastic effect [START_REF] Matsuda | Fundamentals of picosecond laser ultrasonics[END_REF].

B. Metrology : determination of pressure and temperature

Measurements are performed in a restively-heated diamond anvil cell, equipped with a pair of diamonds with culets of 600 µm and a pre-indented rhenium gasket. The large culets are chosen to facilitate surface phonon imaging as a sample with a diameter larger than 100 µm and thickness of tens of microns is needed. Heating is achieved by an external resistive heater ring, whose power is controlled by the target temperature measured by a K-type thermocouple located between the DAC and the resistive heater, and tuned by a PID controller. A second thermocouple is glued in contact with one of the diamonds.

The indium sample (127 µm thick foil from Sigma-Aldrich Chemie GmbH, purity 99.99% metal basis) is loaded at ambient conditions in a hole drilled in the rhenium gasket with a diameter of 340 µm and a thickness around 50 µm (a scheme of the sample chamber can be visualized in Fig. 1). The indium sample entirely fills the hole and plays both the role of metallic transducer and pressure transmitting medium when in the liquid state. Even when solid, being a soft metal, it does not sustain strong uniaxial stress and this deviatoric stress vanishes each time the sample melts.

Sm-doped strontium tetraborate (SrB 4 O 7 :Sm 2+ ) optical sensor is used as in situ pressure gauge [START_REF] Datchi | Optical pressure sensors for high-pressure-high-temperature studies in a diamond anvil cell[END_REF], as the shift of the 7 D 0 -5 F 0 fluorescence line depends on the applied pressure but is almost independent of temperature. In addition, a ruby sphere (3000 ppm Cr-doped corundum: Al 2 O 3 :Cr 3+ ) [START_REF] Chervin | Ruby-spheres as pressure gauge for optically transparent high pressure cells[END_REF] is placed inside the sample chamber and, in this case, the shift of the luminescence signal is sensitive to both p and T [START_REF] Syassen | Ruby under pressure[END_REF].

The fluorescence signal of the two calibrants is excited by a CW Sapphire Laser from Coherent Inc operating at λ = 488 nm.

The combined use of the two in-situ sensors allows not only to probe pressure, but as well to perform an independent check of the T-values measured by the thermocouple. In practice, being almost insensitive to T , the shift in the signal of the Sm-doped strontium tetraborate directly provides the pressure. The temperature can then be determined by the ruby calibrant by imposing in the signal analysis the pressure determined from the Sm-doped strontium tetraborate (see [58], section I).

As shown in Fig. 2, there is an excellent agreement between the temperature provided by the thermocouple glued to the diamond and the temperature estimated from the in-situ sensors according the two models. Unfortunately the ruby sphere disappeared inside the liquid before performing measurements at the highest isotherm (680 K). However, since the value of temperature given by the thermocouple was proven reliable for all other temperatures, this has been used for all the p -T measurements.

The uncertainty on temperature measurements from the thermocouple is evaluated to be ±2K and on pres- sure measurements determined from Sm-doped strontium tetraborate calibrant to be 0.1 -0.2 GPa.

III. EXPERIMENTAL RESULTS

A. Sound velocity measurements

Sound velocity measurements are performed through the analysis of the patterns detected by surface imaging and their evolution as a function of the delay time (i.e. producing a "movie") [18]. In liquid state, as in any elastically isotropic medium, phonon imaging patterns are circles, growing as a function of time, due to the arrivals of the spherical wavefronts generated by the focused pump beam at the opposite side of the sample (see the set-up at Fig. 1).

An integrated profile is obtained from each image and then all the profiles are stacked as a function of time to produce a figure showing growing circles as a function of time (see Fig. 3). The theoretical expression of the radius as a function of time R(t) is obtained by the following set of equations [18]

z(t) = v (t + mT laser -τ ) , e 0 = v(t 0 + mT laser -τ ), R(t) = (z -e 0 ) ((2 C(z) -z) + e 0 ) (1)
where

C(z) = z 1 + zR z 2
, v is the compressional sound velocity, T laser = 12.548(4) ns is the period between two subsequent pump laser shots, m is an integer which accounts of the number of shots between generation and detection, τ = 0.329 ns is the pump-probe coincidence time that depends on the optical path difference between probe and pump beams, e 0 is the sample thickness, t 0 is the emergence time of the wave, and z R is the acoustic Rayleigh length. A typical value of z R is 15 µm but it depends on the quality of the pump beam focusing on the sample surface. In the case where the thickness of the sample e 0 is larger than z R , Eq. 1 greatly simplifies as [26]

R(t) = v z(t) 2 -e 2 0 . (2)
Parameters to be determined by the fitting process are then v, t 0 and z R . These are fixed or left free, depending on the features of each movie. The evolution of the radius of the second (n=2) and third (n=3) waves are not fitted, but calculated replacing e 0 by (2n -1) e 0 . With this method, the thickness e 0 and the sound velocity v are independently determined. The sound velocity data here obtained as a function of p and T are shown in Fig. 4 ([58], section II.A) . Uncertainty on sound velocity is evaluated to be around 25 m/s.

Sound velocity data at ambient pressure as a function of temperature are numerous in literature and are reviewed by Blairs [33] (compiling refs. [34,[START_REF] Kleppa | Ultrasonic velocities of sound in some metallic liquids. adiabatic and isothermal compressibilities of liquid metals at their melting points[END_REF][START_REF] Turner | A new technique for measuring the velocity of sound in liquid metals[END_REF][START_REF] Berthou | The compressibilities of liquid Sn-Tl, In-Bi, Sn-In, Bi-Sb, and Bi-Cd-Tl alloys[END_REF][START_REF] Almond | Ultrasonic speed, compressibility, and structure factor of liquid cadmium and indium[END_REF][START_REF] Bek | Röntgen-Beugungsuntersuchungen an Bi-In-Schmelzen (in german) : X-Ray diffraction experiments with Bi-In-melts[END_REF][START_REF] Pashuk | Temperature dependence of superround velocity and related volumetric dependence of the young modulus of some metals[END_REF] and Fig. S3 in [58]).

On the contrary, sound velocity measurements as a function of pressure are scarce. Coppens [34] performed pioneering measurements but only up to 1500 psi, i.e. around 0.01 GPa. More recently, Alatas et al. [35] and Komabayashi et al. [36] measured the sound velocities by inelastic X-ray scattering through the fit of the phonon dispersion curve ω(Q) [START_REF] Antonangeli | Elastic anisotropy in textured hcpiron to 112 GPa from sound wave propagation measurements[END_REF]. Alatas et al. [35] measured sound velocity for only 3 data points up to 4.0 GPa and 633 K. Komabayashi et al. [36] extended the p -T range up to 923 K and 6.7 GPa. These data are however scattered, with large error bars, and, for clarity are not shown in Fig. 4 where our data set is compared to the velocities obtained from the EOS [36]. The sound velocity is linked to the adiabatic bulk modulus B S and the density ρ via the relation

v = B S /ρ, (3)
then our measurements can be compared with values derived using the Komabayashi density-pressure-temperature relation [36] which requires only 6 thermoelastic parameters to calculate sound velocity: the density at ambient pressure ρ 0 , the isothermal bulk modulus B T,0 , the pressure derivative of the isothermal bulk modulus B ′ T,0 = (∂B T /∂p) p=0 , the thermal expansion α 0 , the Anderson-Grüneisen parameter δ T [START_REF] Birch | Thermal expansion at high pressures[END_REF] and the Grüneisen parameter γ G .

The density ρ is obtained from the isothermal Vinet equation of state (EOS) [START_REF] Vinet | A universal equation of state for solids[END_REF]

p = 3B T,0 1 -x x 2 e η(1-x) with η = 3 2 (B ′ T,0 -1) (4)
where x = (ρ/ρ 0 ) -1/3 . The thermal expansion α is calculated at any p and T using the Anderson-Grüneisen parameter δ T α = α 0 x 3δT

(5) leading to the thermal EOS ρ(p, T )

ρ = ρ 0 e -α(T -TM ) (6)
from which the bulk modulus is derived as

B T = ρ ∂p ∂ρ T (7)
and finally the adiabatic bulk modulus is obtained as

B S = B T (1 + αγ G T ) . (8)
Despite its simplicity, this model based on simpler assumptions than other thermal EOS formalisms (see for example Ref. [START_REF] Litasov | Thermal equation of state and thermodynamic properties of molybdenum at high pressures[END_REF]) well accounts for the thermodynamic quantities at ambient pressure when using parameters given in Ref. [36] from the seminal work of Kamioka [46] : ρ 0 = 7031.11 kg/m 3 , B T,0 = 32.8 GPa, B ′ T,0 = 5.5, α 0 = 12 10 -5 K -1 , δ T = 5.5, and γ G = 2.5.

As shown in Fig. 4 this EOS, associated with previous inelastic X-ray scattering data [35,36], provide a good test of our experimental determination of the sound velocity at high pressure.

Previous authors provided a data review and an accurate evaluation of thermodynamic quantities at ambient pressure: v(T ) [33], ρ(T ) [27] and C p (T ) [START_REF] Chapman | The heat capacity of liquid metals[END_REF] (fitted by a third order polynomial in Ref. [START_REF] Ayrinhac | Heat capacity ratio in liquids at high pressure[END_REF]).

Following the seminal work of Shaw and Caldwell [START_REF] Shaw | Device for measuring sound speeds in reactive liquids at high pressure and temperature[END_REF], these data combined with the present accurate determination of (dv/dP ) T,p=0 = 121(6) m.s -1 .GPa -1 , considered independent of the temperature, offer the opportunity to accurately calculate B T,0 (T ) and B ′ T,0 (T ) and to revise the equation of state up to ≈ 10 GPa. All the thermodynamic equations used are detailed in [58], section II.C. The calculated data are shown in Table I and are in very good agreement with Kamioka [46], with the notable exception for α 0 and B T which must be be revised by approximately -10% and +4% respectively ([58], Fig. S4).

Finally the equation of state of liquid In is calculated from the thermodynamic parameters given in Table I and the isothermal Vinet EOS for each temperature. The results shown in Fig. 5 are close to Komabayashi [36].

FIG. 5. Equation of state in liquid

In calculated from the Vinet EOS and thermodynamic parameters given in table I (solid lines) compared to the EOS of Komabayashi (dashed lines). The experimental data are from Shen [START_REF] Shen | Molar volumes of molten indium at high pressures measured in a diamond anvil cell[END_REF] and Takubo [START_REF] Takubo | Development of density measurement for metals at high pressures and high temperatures using x-ray absorption imaging combined with externally heated diamond anvil cell[END_REF].

B. Determination of the melting curve

In this work, the melting of In was determined using two different methods. The first method is the detection of the isothermal solid-liquid phase transition through a large difference in the delay time of the arrival of the first echo, direct consequence of the changes in the sample thickness and mainly in the sound velocity upon transition [18], (see Fig. 6). The melting line was crossed along isotherms for increasing and decreasing pressures. This method is very accurate since the sound velocity is very sensitive to modifications in long-range order and consequently in the thermodynamic properties of the material. Noteworthy, the liquid-solid transition is always accompanied by a "plateau" in the curve of the sample pressure p as a function of membrane pressure p m likely consequence of the volume variation at the transition ([58], Fig. S5).

The second method is the tracking of pressure and temperature for which liquid and solid phases coexist in equilibrium, and follow this along the melting line [START_REF] Datchi | Extended and accurate determination of the melting curves of argon, helium, ice (H2O), and hydrogen (H2)[END_REF][START_REF] Giordano | Melting curve and fluid equation of state of carbon dioxide at high pressure and high temperature[END_REF]. Here, we remember that according to the Gibbs phase rule, for a single component system, T and p are not independent when two phases are in coexistence, as along the melting line (only one degree of freedom). The experimental protocol starts with measurements in the liquid, and then the temperature is continuously decreased (at a rate around 1 K/s). When the melting temperature is reached, the pressure in the sample chamber decreases due to volume reduction of the sample due to partial solidification. Further volume reduction in both coexisting solid and liquid is expected due to the temperature decrease. These aspects favor the decrease in p concomitant to the imposed decrease in T along the melting line. However, due to the non transparency of the sample, the visual observation of the solid-fluid equilibrium is impossible. The full transition of the sample into the solid is thus checked by three ways ([58], Fig. S7). Firstly, the pressure stops to decrease although the temperature continues to decrease. Secondly, the transition from liquid to solid is observed by phonon imaging of the surface, with the apparition of non circular patterns due to the elastic anisotropy of solid indium. Thirdly, a large shift of the delay time of the echo peak is observed at the transition (similarly to what shown in Fig. 6 as travel time modification upon phase transition is quite higher than the variations due only to the temperature or the pressure in the liquid phase, see also Fig. S7 in [58]).

The compilation of the measurements done by the two methods are presented in Fig. 7. The melting line is fitted by the widely used Simon-Glatzel equation [START_REF] Simon | Remarks on fusion pressure curve[END_REF]

T M (p) = T ref p -p ref a + 1 1/c , (9)
where p ref = 0 GPa, T ref = T 0 M = 429.74850(34) K are the well known values used as secondary point of the international temperature scale (ITS) [30,31] and the two adjustable parameters a and c have been found to be a = 4.61 (11) GPa and c = 1.792 (34).

In order to check the consistency of our data, we can compare the slopes of the meting line at ambient pressure κ obtained by the Simon-Glatzel relation (see Eq. 10) and by the Clausius-Clapeyron relation (see Eq. 11).

From the Simon-Glatzel relation we obtain

κ = dT M dp p=0 = T 0 M ac = 52.0(16) K/GPa. ( 10
)
This value is higher than the values given by Jayaraman et al. (Table 3 in Ref. [START_REF] Jayaraman | Fusion curves and polymorphic transitions of the group iii elements aluminum, gallium, indium and thallium at high pressures[END_REF]) ranging from 43 to 50 K/GPa.

The Clausius-Clapeyron relation gives the slope of the melting line at ambient pressure as

κ ref = T 0 M (V m,liq -V m,sol ) ∆H m,M . (11)
where V m are molar volumes in liquid and solid, and ∆H m,M is the molar enthalpy of fusion (or melting). The quantities entering this relation measured at T M and ambient pressure are carefully reviewed ([58], section III.B).Here we emphasize that the largest source of uncertainty in κ ref comes from the value of ∆V m , which is crucial to evaluate the consistency of the data [START_REF] Kulyamina | Titanium melting curve: data consistency assessment, problems and achievements[END_REF]. Resulting κ ref = 53.1(48) K/GPa is in agreement with κ determined from the Simon-Glatzel relation.

To summarize, our determination of κ is in agreement with previous published values and gives further confidence in the reliability of our temperature measurements. As explained in the text, experimental (p,T ) points are obtained in two ways. Method 1) large and sharp shift of the arrival time of the first acoustic echo upon pressure increase (blue solid triangles) and upon pressure decrease (blue empty triangles) along isothermal paths; Method 2) through monitoring the liquid-solid equilibrium (empty black squares). All the data are fitted by a Simon-Glatzel equation (dash-dotted red line, see text and Eq. 9). In addition, an extrapolation of the Clausius Clapeyron relationship at ambient pressure is shown (Eq. 11, green line), as well as the polynomial function given by Richter extrapolated above 3.5 GPa (black dotted line, see Table 1 in ref. [START_REF] Richter | Asymmetrical friction in a piston-cylinder device and the effect on the melting curves of indium and bismuth[END_REF]).

IV. DISCUSSION

The melting curve obtained in the present study and extrapolated up to 12 GPa, pressure up to which no anomaly is expected in the liquid, is compared to literature data in Fig. 8.

The disagreement between our data and the melting curve recently proposed by Errandonea [45] is evident for pressures above 3 GPa. In this work a Bridgmantype cell was employed up to 12 GPa and melting was identified as a drop in the resistance, measured with the 4-point technique, which is a well proven melting criterion. Concerning metrology, the pressure scale used in their work relies on a calibration curve relating loading pressure and sample pressure, which is linear and well constrained by many reference points [START_REF] Errandonea | High-pressure electrical transport measurements on p-type GaSe and InSe[END_REF]. On the contrary, in the Bridgman pressure apparatus used, the temperature was measured by a thermocouple located 500 µm away from the center. Therefore temperature gradients could explain an underestimated temperature, to a larger extent to what claimed by the authors (less than 25 K [45]). In further support of these remarks, the slope at ambient pressure of melting curve determined by Errandonea is κ = 45.2 K/GPa, is much lower than the expected reference value κ ref = 53.1(48) K/GPa and lower than our determination (κ = 52.0(16) K/GPa). [START_REF] Jayaraman | Fusion curves and polymorphic transitions of the group iii elements aluminum, gallium, indium and thallium at high pressures[END_REF] and their correction of the Dudley data, Millet (1968) [START_REF] Millet | Experimental Melting Curves of Cadmium, Indium, Lead, Tin, and Zinc and Mössbauer Measurements in Iron to 90 Kilobars[END_REF] (data points are taken from [START_REF] Cannon | Behavior of the elements at high pressures[END_REF] [START_REF] Cannon | Behavior of the elements at high pressures[END_REF]), [START_REF] Richter | Asymmetrical friction in a piston-cylinder device and the effect on the melting curves of indium and bismuth[END_REF] [START_REF] Richter | Asymmetrical friction in a piston-cylinder device and the effect on the melting curves of indium and bismuth[END_REF], Höhne (1996) [START_REF] Höhne | On the pressure dependence of the heat of fusion and melting temperature of indium[END_REF], Shen (2002) [START_REF] Shen | Melting studies of indium: determination of the structure and density of melts at high pres-sures and high temperatures[END_REF] (red filled squares: solid, red empty squares: liquid), and Errandonea (2010) [45]. The inset shows the low pressure region.

Recently, Ma et al. [START_REF] Ma | Modeling the pressuredependent melting temperature of metals[END_REF] propose an agreement with the measurements of Errandonea. However this model is based on two experimental (p,T ) data of the melting curve, which were directly taken from the measurements of Errandonea. Such a low melting temperature is also supported by the values of Dudley [32]. However this work used an outdated pressure scale, subsequently proven to be inaccurate. Specifically, the Ba I-II transition pressure was assumed according to Bridgman [START_REF] Bridgman | The resistance of 72 elements, alloys and compounds to 100000 Kg/cm 2[END_REF], with p Ba I-II = 77.4 katm = 7.843 GPa, while the revised value p Ba I-II = 5.50(5) GPa at 295.15 K was established in the subsequent work of Haygarth et al. [START_REF] Haygarth | Determination of the pressure of the barium i-ii transition with single-stage piston-cylinder apparatus[END_REF]. In addition, Decker made a careful review (see Table 7 in the Ref. [START_REF] Decker | High-pressure calibration: A critical review[END_REF] and related discussion) including the data of Haygarth and some other studies resulting in p Ba I-II = 5.53 (12) GPa at 298.15 K. Based on this revised value, the calibration curve of Dudley can be corrected ([58], section III.C). The melting curve of Dudley before and after the correction is shown in Fig. 8. The so-corrected melting curve is in agreement with our data.

Richter [START_REF] Richter | Asymmetrical friction in a piston-cylinder device and the effect on the melting curves of indium and bismuth[END_REF] performed measurements in pistoncylinder up to 3.5 GPa and determined the melting curve by the differential thermal analysis (DTA) technique, carefully corrected for asymmetrical friction, and by the volumetric technique. The results obtained by the two techniques are consistent and yield to a melting curve modelled according to a least-square fit as T M = 156.0 + 52.6p -2.25p 2 where p is in GPa, and T M is in Celsius. Our data at low pressure are in excel-lent agreement with these measurements, as well as with results of McDaniel et al. [START_REF] Mcdaniel | Melting curves of five metals under high pressure[END_REF], and Höhne et al. [START_REF] Höhne | On the pressure dependence of the heat of fusion and melting temperature of indium[END_REF].

Our data are extrapolated at pressures above 6 GPa according to the Eq. 9. This extrapolation is in agreement with the melting temperatures of Shen measured by X-ray diffraction (XRD) [START_REF] Shen | Melting studies of indium: determination of the structure and density of melts at high pres-sures and high temperatures[END_REF], and in good agreement with Millet [START_REF] Millet | Experimental Melting Curves of Cadmium, Indium, Lead, Tin, and Zinc and Mössbauer Measurements in Iron to 90 Kilobars[END_REF], despite the uncertainties of these measurements highlighted by Cannon [START_REF] Cannon | Behavior of the elements at high pressures[END_REF].

V. CONCLUSION

In this work the phase diagram and the thermoelastic properties of liquid indium have been accurately investigated over an extended pressure and temperature range by picosecond acoustics measurements in combination with resistively-heated diamond anvil cells. Particular care was devoted to the associated metrology. Indium was observed to be a very stable metallic compound at high pressure and high temperature, both in its solid and liquid phases. The thermodynamic properties of the liquid phase, well documented at ambient pressure as a function of temperature, have been here implemented to simultaneous high pressure and high temperature conditions, according to well established thermodynamic formulations built on precise sound velocity measurements performed along selected isotherms. A p-ρ-T EOS for the liquid has been also derived.

The liquid-solid transition was determined through a clear and unambiguous criterium: the jump in time-offlight measurements that directly relates to the changes of thermoelastic properties between the two phases. We have also constrained the melting curve by monitoring the liquid-solid equilibrium along several experimental runs. Results obtained by the two methods are consis-tent, and the measurements are in good agreement with the thermoelastic references values of indium at ambient pressure.

Thanks to the careful metrology of pressure and temperature, our data offer an accurate determination of the melting curve, and the T M (p) line could be used as a calibration curve for future investigations.

Besides the specific interest of the case of indium, our study shows the reliability and versatility of picosecond acoustic technique and associated methods, opening to the study of more complex or reactive liquid systems such as the alkali metals, sulfur or phosphorus. Furthermore, since sound velocity is highly sensitive to the changes of the thermoelastic parameters, a similar approach can be used to probe first-order transitions other than melting, as well as more subtle transitions related to progressive changes in structure. Finally, studies can be extended over a larger pressure and temperature range using more performing resistive-heating systems rather than the simple external heater employed in this study. Experiments exploiting local or internal heaters for example can reach temperatures up to 1100-1300 K (e.g. [START_REF] Antonangeli | Simultaneous sound velocity and density measurements of hcp iron up to 93 GPa and 1100 K: An experimental test of the Birch's law at high temperature[END_REF][START_REF] Du | Efficient graphite ring heater suitable for diamond-anvil cells to 1300 K[END_REF]). Moreover, temperatures higher than 1000 K can be achieved by laser heating.

At first, pressure is determined using the SmSTB calibrant. The experimental lineshift of the ruby sensor is then corrected for the pressure effects by shifting it according to the determined pressure value. Temperature is finally obtained by analysis of the so-corrected lineshift.

The two lines R 1 and R 2 are fitted to Voigt profiles as a function of energy (cm -1 ), with a linear background. Following Dorogokupets et al. [18] and revue in ref [43], pressure and wavelength λ R1 are related, being:

p = A 4 ǫ (1 + B 4 ǫ) with ǫ = λ R1 (p, T 0 ) -λ R1 (p 0 , T 0 ) λ R1 (p 0 , T 0 ) (5)
where A 4 = 1884 GPa, B 4 = 5.5 and λ R1 (p 0 , T 0 ) = 694.336 nm is our reference value at ambient condition. This relation is generally used to derive pressure from ruby measurements. Here we use to re-scale lineshift for pressure effects.

As discussed in the main text, we used two methods to analyse the temperature dependence of the lineshift ∆λ R1 :

1. The first method is based on a phenomenological model [15] in which only the position of the maximum of the luminescence signal is determined, after data smoothing. At low temperatures, the R 1 and R 2 lines are well separated and the maximum is obvious equal to the position of the R 1 line. However at high temperatures the R 1 and R 2 lines get close and progressively merge. The temperature dependence of the ruby line is then described assuming 3 distinct regions, "low", "medium" and "high" temperatures, each one having a specific expression relating temperature to lineshift. In the present case our data belong to the "high" temperature region, where the dependence of the maximum position as a function of temperature is given by a polynomial function (Eq.( 2) in Ref. [15])

∆λ R1 (T ) = A 3 ∆T + B 3 ∆T 2 + C 3 ∆T 3 , with ∆T = (T -T 0 ) × 10 -3 (6)
with T 0 =296 K, A 3 = 7.46(4) nm/K, B 3 = -3.01(25) nm/K 2 and C 3 = 8.76 (33) nm/K 3 .

2. The second method is based on the ruby properties as described by McCumber et al. [33] treated according to the simplified approach proposed by Syassen [43].

Temperatures estimated according the two methods are within mutual uncertainties. Supplementary Figure S1. (left) SmSTB luminescence signal fitted to a single Voigt profile (red line). According to Eq. (1-2) p=4.45 GPa. (right) Ruby luminescence signal fitted to two Voigt profiles (green lines), whose addition is shown as red line, and analysed according to McCumber model [33] with pressure imposed from the SmSTB determination, yielding to T calib =612.5 K. Both measurements are performed on calibrants embedded in liquid indium at high pressure and T th =619.95 K as determinated using a thermocouple glued on one of the diamonds of the high pressure cell. TABLE I. Raw data collected by the phonon imaging method in liquid state, from fit of R(t) (depending on the run, some values, written in bold, have been fixed). Pressure p is determined by the SmSTB optical sensor and temperature T by a thermocouple glued in contact with one of the diamonds of the DAC ; m is an integer which accounts of the number of shots between generation and detection, v is adiabatic sound velocity, t0 is the emergence time of the wave, e0 is the sample thickness, and zR is the acoustic Rayleigh length. Note that serie 1 was performed with λ0 = 950 nm and serie 2 with λ0 = 800 nm. serie run no p (GPa) T (K) m v (m/s) t0 (ns) e0 (µm) zR (µm) The adiabatic bulk modulus B S is derived from B S = ρv 2 and from Blairs [9] the adiabatic sound velocity in m/s at ambient pressure is expressed versus temperature in K as v(T ) = 2442 -0.298T. (7) According to Assael [4] the density in kg/m 3 obeys ρ(T ) = 7349.468 -0.762T.

!!! "!!! #!!! $!!! %!!! &!!! '!!! ( ) *
From the classical relation between isothermal and adiabatic stiffness [34] s

T ijkl = s S ijkl + T α ij α kl /ρC p (9)
where C p (T ) is the isobaric specific heat in J/mol/K, we obtain the expression between the isothermal and adiabatic bulk modulus

B S B T = 1 + B S T α 2 ρC p = 1 + T α 2 v 2 C p = γ = 1 + γ G αT, ( 10
)
where γ is the heat capacity ratio and γ G = αv 2 /C p the Grüneisen parameter. Numerical values for B S are then extracted from the C p (T ) publication of Chapman [11] and modelled as in Ref.

The thermal expansion

α(T ) = - 1
To fully determine the EOS, the two derivatives of the bulk modulus versus pressure

∂B T ∂p T = 1 + 2B T v ∂v ∂p T - B T γ ∂γ ∂p T , (13)
and temperature

∂B T ∂T p = -αB T + 2B T v ∂v ∂T p - B T γ ∂γ ∂T p , (14)
are required and then the following set of equations is needed [41,45]:

∂γ ∂p T = (γ -1) 2 α ∂α ∂p T + 2 v ∂v ∂p T - 1 C p ∂C p ∂p T . ( 15
) ∂γ ∂T p = (γ -1) 1 T + 2 v ∂v ∂p T + 2 α ∂α ∂T p - 1 C p ∂C p ∂T p , (16)
∂C p ∂p T = - T ρ ∂α ∂T p + α 2 , ( 17
) ∂α ∂p T = 1 B 2 T ∂B T ∂T p , (18)
Finally the Anderson-Grüneisen parameter involved in the thermal expansion modeling is derived as

δ T = - 1 αB T ∂B T ∂T p . (19)

B. Slope of the melting curve from the Clausius-Clapeyron relation

This section presents the details of the calculation of κ ref , the slope of the melting curve at ambient pressure from the Clausius-Clapeyron relation [37], where

κ ref = dT M dp p=0 = T 0 M (V m,liq -V m,sol ) ∆H m,M . (20)
The terms appearing in this Equation are defined below.

Physical and thermodynamical data

The melting temperature at ambient pressure is [1,38] T 0 M = 429.748500(341) K.

The molar mass of indium is M = 114.818 g/mol [13]. Measurement of Archer et al [3] are considered the most accurate and are the most used value among the documented standards [1] for the the molar enthalpy of fusion (or melting) ∆H m,M . This value, with an uncertainty at 2σ, is ∆H m,M = 28.6624(76) J/g i. e. ∆H m = 3290.96(44) J/mol (22) with an uncertainty this time at 1σ.

Liquid state

The density in liquid indium at ambient pressure as a function of temperature is carefully reviewed by Assael [4], and it is described by the equation

Difference of the molar volumes

The difference of the molar volumes between the solid and the liquid at the melting temperature T 0 M is ∆V m = V m,liq -V m,sol with uncertainties estimated from error propagation δ∆V m = (δV m,liq )

2 + (δV m,sol ) 2 , so that ∆V m = 406(36) 10 -9 m 3 /mol. Supplementary Figure S8. Solid indium density at ambient pressure versus temperature. Data are from Roth [39], Gamertsfelder [20], Hidnert & Blair [25] obtained from a 250-mm rod sample of cast In (black plus) and from a 200-mm rod (black crosses), Williams [46], Schneider [40] and Iida [29]. The red dashed line is a instrumental weighted linear regression through the experimental points. The density of the solid phase at room temperature (20 C or 293.15 K) is 7295(4) kg/m 3 . The principal contribution to this uncertainty comes from the δ∆V m /∆V m term, which represents the small difference in density between solid and liquid phases at melting with respect to the uncertainty of the density measurements.

The Clausius-Clapeyron relation at ambient pressure

To conclude, the resulting value is

κ ref = 53.1(48) K/GP a.
The comparison of this result to the value provided by Höhne et al [28], κ = 50.7(30) K/GPa, shows a good agreement within the mutual uncertainties. In addition, as a byproduct of this study, the density of solid In at ambient temperature (298.15 K) is revised to ρ(298.15 K) = 7292(4) kg/m 3 .

1 FIG. 1 .

 11 FIG. 1. (Top) Schematic view of the set-up. PBS: polarizing beamsplitter, λ/2: half-wave plate, λ/4: quarter-wave plate, PD: amplified photodetector, A.O.M. stands for acousto-optic modulator, and ref. mirror for reference mirror as a part of a Michelson interferometer. Blue ellipses represents optical objectives. (Bottom) Interferometric signal as a function of delay time obtained in liquid In at high pressure and temperature with collinear pump and probe beams. Numbers identify consecutive echoes corresponding to the n th wave arriving at the sample surface on the probe side. (Inset) Magnification of the third echo.

FIG. 2 .

 2 FIG.2. Temperature estimated from the in-situ optical sensors T calib (see text and [58], section I) as a function of the temperature value T th provided by the thermocouple glued to one of the diamonds of the DAC. The analysis of the ruby fluorescence line shift is performed according to two models, Datchi[START_REF] Datchi | Optical pressure sensors for high-pressure-high-temperature studies in a diamond anvil cell[END_REF] (red empty circles) and McCumber[START_REF] Mccumber | Linewidth and temperature shift of the r lines in ruby[END_REF] (blue crosses). The equality relation is indicated by the dashed line.

FIG. 3

 3 FIG.3. a) Phonon imaging pattern of the acoustic wavefront at the liquid-diamond interface in liquid indium at 3 GPa and 682 K with collinear pump and probe at circular pattern center for 11.9606 ns a pump-probe delay. b) Integrated profile. c) Integrated profiles stacked versus time. For clarity, the final image between 0 and T laser is duplicated 3 times. The colored ripples and the lines show the radius of the circles detected at the sample surface versus time. The nonlinear R(t) curves are linked to the volume waves propagating inside the sample and appearing at the surface, whereas the linear R(t) curves are due to the pure surface waves (possibly surface skimming bulk waves propagating in the diamond at the interface diamond-sample[START_REF] Chigarev | Analysis of ultrasonic echoes induced by pulsed laser action on an iron film in a dia-mond anvil cell[END_REF]). Only the first nonlinear curve is fitted by the function R(t), and the calculation with the obtained results is shown as the blue dotted line. The red and green dotted lines are calculations corresponding to multiple reflections in the sample (n = 2 and n = 3 respectively) and demonstrate the quality of the fit procedure.

FIG. 4 .

 4 FIG.4. Sound velocity in liquid indium as a function of pressure and temperature, measured by the phonon imaging method. The data are compared with velocities derived from the thermal EOS of Komabayashi[36] calculated along three reference isotherms. (Inset) Sound velocity as a function of temperature at ambient pressure, measured by the phonon imaging method (average thickness e0 = 68.3(12) µm, with imposed parameter zR = 16.2(4) µm) above melting temperature (TM ). The data are compared with the average linear relation of Blairs[33] (blue dotted line) and its dispersion (grey area, see Fig.S3in [58]), and with the sound velocity calculated from the thermal EOS.

FIG. 7 .

 7 FIG.7. Indium melting line measured by picosecond acoustics. As explained in the text, experimental (p,T ) points are obtained in two ways. Method 1) large and sharp shift of the arrival time of the first acoustic echo upon pressure increase (blue solid triangles) and upon pressure decrease (blue empty triangles) along isothermal paths; Method 2) through monitoring the liquid-solid equilibrium (empty black squares). All the data are fitted by a Simon-Glatzel equation (dash-dotted red line, see text and Eq. 9). In addition, an extrapolation of the Clausius Clapeyron relationship at ambient pressure is shown (Eq. 11, green line), as well as the polynomial function given by Richter extrapolated above 3.5 GPa (black dotted line, see Table1in ref.[START_REF] Richter | Asymmetrical friction in a piston-cylinder device and the effect on the melting curves of indium and bismuth[END_REF]).

FIG. 8 .

 8 FIG.8. The melting curve obtained in this work by picosecond acoustics (red line) and extrapolated above 6 GPa (red dotted line) is compared with the literature data: Dudley (1960)[32], Dudley corrected in this work,[START_REF] Mcdaniel | Melting curves of five metals under high pressure[END_REF] [START_REF] Mcdaniel | Melting curves of five metals under high pressure[END_REF],[START_REF] Jayaraman | Fusion curves and polymorphic transitions of the group iii elements aluminum, gallium, indium and thallium at high pressures[END_REF] [START_REF] Jayaraman | Fusion curves and polymorphic transitions of the group iii elements aluminum, gallium, indium and thallium at high pressures[END_REF] and their correction of the Dudley data,[START_REF] Millet | Experimental Melting Curves of Cadmium, Indium, Lead, Tin, and Zinc and Mössbauer Measurements in Iron to 90 Kilobars[END_REF] [START_REF] Millet | Experimental Melting Curves of Cadmium, Indium, Lead, Tin, and Zinc and Mössbauer Measurements in Iron to 90 Kilobars[END_REF] (data points are taken from[START_REF] Cannon | Behavior of the elements at high pressures[END_REF] [START_REF] Cannon | Behavior of the elements at high pressures[END_REF]),[START_REF] Richter | Asymmetrical friction in a piston-cylinder device and the effect on the melting curves of indium and bismuth[END_REF] [START_REF] Richter | Asymmetrical friction in a piston-cylinder device and the effect on the melting curves of indium and bismuth[END_REF],Höhne (1996) [START_REF] Höhne | On the pressure dependence of the heat of fusion and melting temperature of indium[END_REF],Shen (2002) [START_REF] Shen | Melting studies of indium: determination of the structure and density of melts at high pres-sures and high temperatures[END_REF] (red filled squares: solid, red empty squares: liquid), and Errandonea (2010)[45]. The inset shows the low pressure region.

  [5] in a polynomial form C p (T ) = 32.513 -1.033 10 -2 T + 9.8459 10 -6 T 2 -33.463 10 -10 T 3 ,

  Supplementary FigureS5. Example of the "plateau" observed in the pressure membrane of the DAC as a function of the sample's pressure observed at the solid-liquid phase transition. This "plateau" is always observed at the phase transition, although with a variable extension. . Ensemble of the experimental runs performed to determine the melting curve in indium based on the liquid-solid equilibrium, with a zoom (inset) in the p -T range where several data superimpose.

  Supplementary FigureS7. p -T data obtained in run 7 (upper right) compared to the melting curve determined by a Simon-Glatzel (dashed black line). The transition from liquid to solid at 544.4 K and 2.43 GPa is associated with a shift of the echo peak (upper left vs. T and bottom right vs. P). At the end of the run, the solid phase is confirmed by a non-circular pattern observed at the surface for a delay time of 13.299 ns (colored picture at the bottom left, the color scale goes from low values in blue to high values of the signal in red).

ρ

  liq (T ) = 7022 -0.762 (T -429.748) with an uncertainty of 0.5% at the 95% confidence level (2 σ) and T in K, ρ in kg/m 3 . With a 1 σ uncertaincy, we get ρ liq (T 0 M ) = 7022(18) kg/m 3 i.e. V m,liq = M ρ liq = 16.35 10 -6 m 3 /mol and δV m,liq = V m,liq δρ liq ρ liq = 40.88 10 -9 m 3 /mol.

3 .

 3 Solid stateTo determine the density at T 0 M in the solid In at ambient pressure as a function of temperature, a linear fit ρ sol (T ) = aT + b is performed to the literature data obtained in the solid phase (see Fig.S8), yielding to b = 7308.9(39) kg/m 3 and a = -0.69(4) kg/m 3 /C.The density at T 0 M is thenρ sol (T 0 M ) = aT 0 M + b = 7201 kg/m 3 ,with the uncertaintyδρ sol (T 0 M ) = (T 0 M δa) 2 + (aδT 0 M ) 2 + δb 2 =7 kg/m 3 , and finally V m,sol = M ρ sol = 15.94 10 -6 m 3 /mol, δV m,sol = V m,sol δρ sol ρ sol = 16.20 10 -9 m 3 /mol.

Finally

  κ ref is obtained asκ ref = T 0 M ∆V m ∆H m,M = 53.1 K/GP a.with a relative uncertainty δκ ref given by

TABLE I .

 I Thermodynamic data of liquid In calculated from reference data v(T ), ρ(T ), Cp(T ), and the value of (dv/dp)T,p=0 determined in this work.

	T K		v m/s	ρ kg/m 3	Cp J/kg.K	α0 10 -5 K -1	BT GPa	dBT /dT MPa/K	B -′ T	δT -	γG -
	T 0 M	2313.93	7022.00	258.0		10.85	34.02	-20.26	5.25	5.49	2.25
	450	2307.90	7006.57	257.4		10.88	33.62	-20.01	5.25	5.47	2.25
	500	2293.00	6968.47	256.0		10.93	32.63	-19.40	5.24	5.44	2.25
	550	2278.10	6930.37	254.8		11.00	31.68	-18.81	5.23	5.40	2.24
	600	2263.20	6892.27	253.8		11.06	30.75	-18.23	5.22	5.36	2.23
	650	2248.30	6854.17	252.9		11.12	29.85	-17.66	5.21	5.32	2.22
	700	2233.40	6816.07	252.2		11.18	28.98	-17.11	5.20	5.28	2.21
	750	2218.50	6777.97	251.6		11.24	28.14	-16.58	5.19	5.24	2.20
	800	2203.60	6739.87	251.2		11.31	27.33	-16.07	5.18	5.20	2.19
	850	2188.70	6701.77	250.8		11.37	26.53	-15.59	5.16	5.17	2.17
	900	2173.80	6663.67	250.4		11.44	25.77	-15.12	5.15	5.13	2.16
	950	2158.90	6625.57	250.1		11.50	25.02	-14.68	5.14	5.10	2.14
	1000	2144.00	6587.47	249.8		11.57	24.30	-14.26	5.13	5.07	2.13
		1
					liquid			solid
		0
	(ns)		T=510 K
	peak t	1
		0
					1.70	0.05 GPa
			1.4	1.5	1.6	1.7	1.8
				P (GPa)

FIG.

6

. Transition between liquid and solid indium (grey region) as recorded by the large and sharp variation of the arrival time of the first acoustic echo at T=510 K. The transition pressure, measured both for increasing p (top panel) and decreasing p (bottom panel), is in this case 1.70(5) GPa.

This coefficients are different than those written in Ref.[15] because of a typo.

VI. ACKNOWLEDGMENTS

This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation Programme (grant agreement No. 724690). Femtosecond laser micromachining at IMPMC has been developed and realized by the "Cellule Project" with the financial support of ANR 2010-JCJC-604-01. Authors wish to thank also Yoann Guarnelli for his help in DAC preparation.

Supplementary Information

In this work, pressure and temperature are accurately determined in-situ. Pressure is measured by analysis of the luminescence signal of the Sm-doped strontium tetraborate calibrant (noted SmSTB thereafter), while temperature is obtained by analysis of Cr-doped corundum (ruby) calibrant, both loaded inside the sample chamber of a diamond anvil cell (actually embedded in the liquid sample). An independent determination of the temperature is provided by a thermocouple glued on the side of one of the two diamonds in the DAC. The accuracy of the temperature reading of the thermocouple is confirmed by the temperature obtained in-situ.

A. SmSTB : a pressure sensor

The pressure determination via the shift of a luminescence signal is used since 1975 [36]. Syassen [43] made a review for ruby and shown that the more accurate expression can be written as a function of ǫ = ∆λ/λ(p 0 , T 0 ). Accordingly, pressure can be derived from the 7 D 0 -5 F 0 luminescence line of SmSTB (samarium-doped strontium tetraborate SrB 4 O 7 :Sm 2+ ) fitted to a single Voigt function. Following Datchi et al. [15,16] the corresponding pressure p is derived according the following analytical form

where λ(p, T 0 ) is the actual luminescence peak position at pressure p and temperature T 0 and λ(p 0 , T 0 ) = 685.437 nm is our reference value of the luminescence line measured at ambient conditions (p 0 = 0 GPa, T 0 = 296 K) [15]. The 3 parameters, A 1 = 3.989(6) GPa/nm, B 1 = 6.915(74) 10 -3 nm -1 and C 1 = 16.6(10) 10 -3 nm -1 , extracted from Ref. [15] p. 454, have been determined using the "DO2007 ruby scale" [18] (see Eq. ( 6) in Ref. [15]).

Using

4 with those of ruby (see next section) A ruby = 1884 GPa, B ruby = 5.5 and C ruby = 0, we note that the pressure sensitivity of SmSTB is close to those of ruby. Moreover, the 7 D 0 -5 F 0 luminescence line is a singlet and should be less sensitive to pressure gradients and temperature than the 2 E -4 A 2 R 1 line used for ruby calibrant.

In fact, at ambient pressure, the shift of the luminescence line of the SmSTB is basically temperature independent. To estimate the error due to neglecting the temperature, the Eq.( 2) is modified as ∆λ(p, T ) = ∆λ p0,T0 (p) + ∆λ P0,T0 (T ) = λ(p, T 0 ) -λ(p 0 , T 0 ) + λ(p 0 , T ) -λ(p 0 , T 0 ).

(

Following Datchi et al. [15] we assume a quadratic form for ∆λ p0,T0 (T )

where A 2 = -87(12) 10 -3 nm/K, B 2 = 462(60) 10 -3 nm/K 2 , C 2 = -238(70) 10 -3 nm/K 3 have been determined( 1 ) at p = p 0 and are supposed to be pressure independent.

In our temperature range the maximum pressure deviation is then around 0.05 GPa i.e. of the same order of magnitude of the experimental uncertainty on our pressure measurement.

In practice, for our purposes, the effect of temperature variation on λ and hence on the estimation of pressure from the above presented analysis of luminescence signal of the SmSTB calibrant can be considered negligible. The ruby calibrant, commonly used for pressure determination and in this paper, is a chromium-doped corundum (α-Al 2 O 3 :Cr 3+ ) with 3000 ppm Cr concentration. The pressure effects of the chromium concentration can be found in Ref [12], and a nice revue of ruby properties useful for high pressure community can be found in ref [43].

Differently from SmSTB, the lineshift of the 2 E -4 A 2 ruby luminescence signal depends both on pressure and temperature. Accordingly, from the combined use of the two calibrants we can get both pressure and temperature. liquid In Supplementary Figure S3. Sound velocity in liquid In at ambient pressure and as a function of temperature, from melting temperature up to 1300 K. The selected references are from the review paper of Blairs [9], as well as the average trend described as v(T ) = 2442 -0.289T , where T is in K and v is in m/s. The grey area represents the dispersion of the literature data (Kleppa [31], Hill [26,27], Gitis [22], Coppens [14], Turner [44], Berthou [8], Almond [2], Bek [7], Kamioka [30] and Pashuk [35]). Note: in the Table 24 of Blairs [9] the value "2448" (associated to Ref. [27] on first line) should be replaced by "2441". Supplementary Figure S4. Comparison between the thermodynamic data obtained by the EOS of Komabayashi [32] (red lines), the data from Assael [4], Blairs [9] and Kamioka [30] (blue dashed lines) and the data calculated from exact thermodynamical relations (green lines, see part II C). ρ is the density, BT 0 the isothermal bulk modulus, α the thermal expansion, v the adiabatic sound velocity, B ′ 0 the pressure derivative of the isothermal bulk modulus and γG is the Grüneisen parameter.

C. Correction of the melting curve from Dudley et al

The original calibration curve used by Dudley [19] is shown in Fig. S9 below. They used a pressure value of 24.8 katm for the solid-solid phase transition Bi I-II at ambient temperature, and 77.4 katm for Ba I-II, from the work of Bridgman [10]. Their calibration curve is linear p(katm) = a p(psi), with a = 12.89(9) 10 -3 psi/katm. However, this calibration curve has to be corrected as the pressure value of the Ba I-II transition given by Bridgman was discussed and revised in following studies. The seminal work of Haygarth et al [24] gives p Ba I-II = 5.50(5) GPa at 295.15 K. Decker made a careful review (see Table 7 in [17] and the associated discussion) including the data of Haygarth and some other works, and he gives p Ba I-II = 5.53 (12) GPa at 298.15 K. Concerning the transition Bi I-II, Getting [21] gives a reference value of p Bi I-II = 2.520(5) GPa at 298.15 K.

The calibration curve between press load and sample pressure is in most cases nonlinear, as seen in Fig. 5 from Ref [23], or in Fig. 4 from ref [42] and the curve depends on the tetrahedron size (see Fig. 8 in ref. [6]).

Based on these features, we propose the following ad hoc non linear functional form p (GPa) = (1.4 + 0.053 p (katm)) 1 -e -p (katm)/10 ,

which is shown in Fig. S10.