Introduction

It has long been established that most of the composition of Earth’s main reservoirs (i.e. the core and the bulk silicate Earth) is the result of thermodynamic equilibrium at high pressures (P) and temperatures (T) during the accretion and differentiation of the planet, about 4.5 billion years ago (see a review by Rubie et al. 2015b). During the accretion stage, collisions between Mars-sized embryos and proto-planets are sufficiently energetic to partially or fully melt the planet. This resulted in a succession of deep magma oceans that led to the chemical fractionation of siderophile elements (iron-loving elements) and lithophile elements (silicate-loving elements) between the different reservoirs. The major element compositions of the mantle and the core of the planet were fixed once the accretion and differentiation of the planet were finished, about 200 million years after the beginning of solar system history. The chemical compositions of Earth’s reservoirs have direct implications for countless properties of the Earth, such as its internal dynamics, through its magnetic field produced in the core, and mantle convection, or habitability at the surface. To understand the observables that we have today, it is necessary to simulate in the laboratory the conditions of Earth’s formation.

The most commonly-used static tool to generate the pressure and temperature conditions of Earth’s differentiation (P > 40 GPa, T > 3500 K) simultaneously is the laser-heated diamond anvil cell apparatus (LH-DAC), although recent developments have enabled high P–T conditions to be achieved using internal resistive heating in the diamond anvil cell (Heinen et al. 2021), which minimizes the thermal gradient in such experiment. The LH-DAC can be combined with different in situ techniques to monitor the changes in structure or composition that are induced by elevated P–T compositions. Among other techniques, the most prominent ones include X-ray diffraction, X-ray fluorescence and absorption spectroscopy and X-ray imaging, which can be performed in situ under high P–T conditions using synchrotron radiation, as reviewed by Shen and Mao (2017). In addition to, or apart from, in situ measurements performed whilst the sample is at high P (and sometimes high T), it is also possible to perform ex situ analysis of the sample after high temperature and pressure conditions are released. Analyzing quenched samples ex situ has been performed previously after preparation by the Focused Ion Beam (FIB) technique (e.g. Irifune et al. 2005; Miyahara et al. 2008; Ricolleau et al. 2008; Fiquet et al. 2010; Siebert et al. 2012; Blanchard et al. 2017; Jackson et al. 2018). The FIB has thus become the most commonly used technique to extract a lamella of a sample synthetized in a LH-DAC. Further chemical characterization can then be performed using electron microprobe (EPMA), and after further thinning, transmission electron microscopy (TEM). Those techniques present different advantages and disadvantages, but most importantly they are only suitable to quantify element concentrations in excess of the several hundred ppm level, and only if appropriate standards are available.

Understanding the distribution of trace elements between Earth’s reservoirs is essential to place constraints on the different steps of the accretion. Siderophile elements present in trace concentrations in the Earth’s mantle can provide important information on the conditions of Earth’s differentiation. For example, the redox environment of the early Earth can be constrained using vanadium (e.g. Siebert et al. 2013) or the depth of the magma ocean using nickel and cobalt (Li and Agee 1996; Bouhifd and Jephcoat 2011; Siebert et al. 2012). Ultimately, the results of such experiments with multiple elements can be combined to build self-consistent models of Earth’s accretion and differentiation (e.g. Rubie et al. 2015a).

In high P–T experiments, the elements of interest are usually doped at higher level in the starting material compared to their natural abundances to ensure concentrations that are detectable by EPMA in both the metallic and the silicate phase. Highly siderophile elements (HSE) are present in the Bulk Silicate Earth (BSE) in chondritic proportions (Kimura et al. 1974; Chou et al. 1983). This is at odds with their strong affinity for iron, which should have led to a complete segregation of these elements into the core during Earth’s accretion. This observation has been the basis of a late stage of meteoritic bombardment on Earth after the core formation ceased, to explain HSEs abundances in the mantle. Up to about 0.5% of Earth’s mass would have been accreted during this episode (Walker 2009; Rubie et al. 2016) to explain the abundances of these element in the mantle. Studying the partitioning of these siderophile elements between metal and silicate at the possible conditions of core formation (P > 40 GPa and T > 3500 K) is of fundamental importance, but analyzing trace element concentrations in quenched silicate melts produced in the LH-DAC is far from easy. For LH-DAC experiments, the sample is contained in a sample chamber of a metallic gasket of about 100 µm in diameter, and 25 µm thickness (both depending greatly on the pressure), and the final heated area is about 20 µm in diameter. As described above, the samples are usually extracted using FIB, which results in sample dimensions of about 20 \(\times\) 20 \(\times\) 3 microns (length \(\times\) width \(\times\) thickness). In that case, classical techniques used for samples synthesized with large volume presses such as laser ablation ICPMS cannot be used to detect trace element abundances (e.g. Mann et al. 2012; Laurenz et al. 2016). Therefore, the use of special techniques that include microfabrication using a FIB to extract a lamella of the sample at a very precise location has become of great importance and is described later in this manuscript.

In this report, we will describe and compare two different methods that allow the determination of elemental concentrations in standard samples and elemental ratios in recovered samples from high-pressure experiments, namely Nanoscale secondary ion mass spectrometry (NanoSIMS) and synchrotron radiation nano X-ray fluorescence (nano-XRF). Both methods have been used already by the high P–T Earth science community. Badro et al. (2007) proposed to use NanoSIMS to study the partitioning of elements (strontium, scandium and yttrium) between the different phases of Earth’s lower mantle present at very low concentration (few tens of ppm). Recently, NanoSIMS was used to investigate the metal–silicate partitioning of carbon and platinum (Fischer et al. 2020; Suer et al. 2021; Blanchard et al. 2022) in the context of Earth’s core-mantle differentiation. XRF has also been used previously with LH-DAC techniques (Andrault et al. 2012; Petitgirard et al. 2012), but only in situ, and not with a nanometer-sized beam as discussed here, but with a micrometer-sized beam. NanoSIMS and nano-XRF techniques are very different in various aspects, the most important being that nano-XRF is a deeply penetrative but nondestructive method, whereas NanoSIMS is a surface sensitive and destructive method. The second major difference between the two techniques is that NanoSIMS can probe isotopes, whereas nano-XRF cannot. We will especially focus on the use of these techniques to measure various siderophile elements (from moderately to highly siderophile, hereafter MSE and HSE, respectively) present in trace amounts in quenched silicate melts, and at a few wt% level in metallic alloys. We will first present our results on several kinds of standards, before moving on to samples synthetized at high P–T conditions in a LH-DAC.

Methods and results for standards

Synthesis and preparation of standards

Before measuring actual samples from LH-DAC, it is necessary to have appropriate standards, with known composition in both major and trace elements. Suitable standards are a key for both nanoprobe techniques presented here. We have synthesized standards using an aerodynamic levitation furnace (Auzende et al. 2011) for MSEs. We also used a glass synthesized with a piston cylinder press and described elsewhere (Chen et al. 2020) for HSEs. An aerodynamic levitation furnace enables homogeneous glasses to be synthesized that are doped in the element(s) of interest, and has already been used and presented in previous publications related to high P–T experiments (e.g. Blanchard et al. 2017). Here, we have used this technique to synthetize silicate glasses and metals doped in molybdenum and tungsten (Mo and W) at the CEMHTI laboratory in Orléans, France. For the silicate, we started by mixing high purity oxide and carbonate powders in an agate mortar to reproduce the composition of the primitive upper mantle in major elements as determined by Palme and O’Neill (2014). We added WO3 and MoO3 in different proportions (see Table 1). The powder samples were subsequently decarbonated, pressed into small pellets of about 25 mg and placed in the nozzle of the aerodynamic levitation furnace. A CO2 laser is then focused on the sample and, as it melts, the gas flow is increased to maintain the levitation of the liquid in the conical nozzle. The melting is detected via a temperature plateau using a pyrometer, and a stable levitation is monitored through a video system. After few seconds of melting, the power of the laser is cut off to immediately quench the sample into a glass. The synthesized spheres were then cut in half and polished to perform chemical analysis. We analyzed major elements using EPMA, and trace elements by both LA-ICP-MS and EPMA at the Bayerisches Geoinstitut (BGI, Bayreuth, Germany). Both methods show similar results for standards containing up to 1000 ppm of Mo or W, but diverge for standards containing 100 ppm, with LA-ICP-MS values much closer to the expected concentrations. Using those methods, we could demonstrate that the standards were homogeneous over their entire volume. We report in Table 1 the compositions of the standards synthesized by this method. During levitation, the gas composition can be changed, which influences the redox environment of the sample. For silicate standards, we used an argon flux, allowing to maintain reducing conditions. Likewise, spheres of metal Fe doped in W and Mo were synthesized by aerodynamic levitation in purified argon to be used as standards. We synthesized three different metallic standards with various concentrations of W and Mo to establish calibration curves of the nanoprobes against the reference analysis using the microprobe and LA-ICP-MS. The compositions of the metallic spheres were checked using EPMA at BGI and are reported in Table 2.

Table 1 Compositions of the silicate standards and starting material along with their respective uncertainties used in this study reported in wt% except when indicated differently
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Table 2 Metal spheres used as standards with different concentrations of Mo and W, in wt%
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For HSEs, we have used a standard synthesized in a piston cylinder apparatus to create homogeneous glasses doped in siderophile elements by Chen et al. (2020). A complication with HSEs in silicate glasses that was noted previously (Brenan et al. 2003; Ertel et al. 2008; Médard et al. 2015) is the occurrence of metallic nanonuggets. The problem is to consider those nuggets as either quench products, or a stable equilibrium phase at the experimental conditions. Médard et al. (2015) demonstrated that nanonuggets were experimental artifacts formed during the quench, and hence should be avoided when analysing HSE concentrations in silicate glass in order not to overestimate their abundances. The glass used here contained several HSEs and was carefully checked at high resolution by Chen et al. (2020). Their analysis did not reveal any metal nanonuggets within a resolution of about 10 nm. We report in Table 1 the composition of this standard (IZ-01) for which the details of preparation can be found in Chen et al. (2020). This standard offers a wide diversity of siderophile elements (Ag, Pd, Rh, Ru, Pt, Ir, Au and Re) at different concentrations, from tens to thousands of ppm. In the following, we have especially worked on the elements Ag, Rh, Ru and Re using this standard.

Since nano-XRF is a penetrative method, we wanted to assess the importance of the geometry of the experimental set-up on the measurements, so we have performed several tests. We have tested keeping the standards as a bulk (few millimeters) and also extracted lamellae with different thicknesses using a Ga+ beam FIB at the BGI and at the GFZ (Potsdam, Germany). Details of the FIB procedure are described in the supplementary information and are also discussed in length in Lemelle et al. (2017).

Nano-XRF measurements

Nano-XRF measurements were performed on the ID16B beamline at the European Synchrotron Radiation Facility (ESRF, France). This beamline is dedicated to hard X-ray nano-analysis with a spatial resolution of 59 \(\times\) 44 nm2 and can reach very high flux (1012 photons s−1) using a pink beam (ΔE/E = 10–2) mode (quasi-monochromatic), considerably reducing the acquisition time per analyzed points. The X-ray beam was set at 29.5 keV, and the brilliance was very high with a maximum photon flux of 1.4 \(\times\) 1012 photons s−1 at the sample location. During the experiment, X-ray photons shine on the samples ejecting core electrons from atomic orbitals. The created holes are then filled by electrons from higher orbitals. During this relaxation process, X-ray photons (fluorescence photons) are re-emitted with characteristic energies for each element in the periodic table and are detected by solid state detectors to infer the elemental composition in the illuminated specimen area. The instrument is equipped with two multi-element Si-drift detectors with 3 and 7 elements, respectively (of 50 mm2 active area each) positioned in a back-scattered geometry at approximately 15° from the sample plane that can work simultaneously to collect the maximum signal. Using this technique, it is possible to map a large area (up to 30 \(\times\) 20 microns in our case) of our standards and samples with a high sensitivity for the heavy elements studied here. Using an excitation energy of 29.5 keV, we could reach the K-emission lines of Mo, Ag, Rh, Ru and the L-lines of W and Re. Attenuators in the incoming beam are used if needed, to avoid the saturation of the detectors and keep dead time below 30% (usually even below 15%), meaning that the fluorescence-photon events are counted as real and not electronically generated due to an excess photon that would saturate the detector. This low detector dead time can be accurately compensated by a simple linear correction. At such high energy the X-ray incident beam can penetrate millimeters of material and the XRF signal for different elements will be affected by the thickness of the sample. High energy fluorescence (i.e., Mo K alpha, at 17.48 keV) can be generated at depth in the sample and find their way out, while lower energies fluorescence signals (i.e., Fe at 6.4 keV, Ca at 3.6 keV) will be strongly affected by self-absorption effect within the sample. Standards and samples extracted by FIB were mounted on Cu-grids during the FIB preparation, and each grid was subsequently taped to a Si3N4 membrane using double sided tape. The membrane itself was attached to a PEEK holder using Kapton tape. As developed in the following, we also tested the nano-XRF technique on bulk samples (i.e., not extracted by FIB).

Using the nano-XRF, we acquired high precision chemical distribution maps of the standards (500–1000 ms exposure time per pixel) with step sizes on the order of 100 nm from which we could extract Regions of Interest (ROIs). Each pixel represents one data point containing a full energy dispersive XRF-spectrum, so by summing up a large area, or ROI, the statistics of the sum spectrum is highly improved. In Fig. 1, we illustrate the effect of different geometries on nano-XRF measurements. Figure 1a and b highlight the differences in XRF intensities for Mo-line peak and Mo/Fe ratio, respectively as a function of the thickness of the FIB cut silicate standard. We compare 1-, 3- and 5- micron thick samples along with a large half sphere of the different materials synthetized with aerodynamic levitation. One can see on Fig. 1a that using the XRF peak intensity of Mo, the intensity is significantly lower for the 1-micron thick sample compared to the 5-micron thick one and also the estimated concentration of Mo in the standard increases with increasing thickness. Figure 1b highlights the importance of using XRF intensity ratios instead to establish calibration curves that are trustworthy, since in this case it circumvents the effect of thickness and we see no more difference between the different thicknesses for FIB extracted lamellae. We also compare in Fig. 1b the XRF intensity ratios of Mo/Fe for both the large spheres (“infinite thickness”) and the FIB foils, and it is clear that there is a strong difference in the intensity of the signal between the two. Thus, the sample and standard should have the same thickness within a few microns. This figure highlights the importance of having standards that have a geometry close to that of the sample itself to define the calibration curve. It also shows that using the aerodynamic levitation furnace is a great option to synthesize standards, since even at extremely small scales (well below 1 micron), the sample is homogeneous. A close up of the FIB-extracted samples presented in Fig. 1b is provided in Fig. S2c. In the two lower panels of Fig. 1, we compare the spectra obtained in the case of a FIB lamella (3-micron thickness) with the one obtained with a large sphere. One can see again that the counts are much higher in the second case. The difference in background in Fig. 1c and d is due to the presence of Cu and Pt contributions in Fig. 1c that changes the intensity in the range between 8 and 12 keV. Additionally, the thickness also affects the noise level at high energy when comparing the Mo peak between the two samples. We present in Fig. S2 nano-XRF maps obtained for the different FIB thicknesses and for the sphere. The difference thicknesses were estimated from views form the top of the FIB lamellae during the FIB process.

Fig. 1
figure 1

Effect of thickness on the Mo intensity with a 1-, 3- and 5-microns thickness. b Effect of thickness on the XRF intensities of Mo/Fe measured from FIB lamellae and large spheres. Impact of thickness on number of counts for c a FIB lamella of 3 microns thickness and d a large sphere, in both cases for the sample PO100

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Because the composition of the sample is known from our previous EPMA and/or LA-ICP-MS measurements, we could also retrieve the concentrations of several siderophile elements. To do so, we used the software PyMca developed at the ESRF (Solé et al. 2007). We defined one ROI in standard IZ-01 at the center of the FIB lamella and we defined the major elements that are known for the matrix, which includes also the light elements that are not detected in the XRF spectra (i.e., elements with Z lower than that of Na). With this information and using calcium as internal standard, a matrix correction could be performed (Beckhoff et al. 2007) and we could access the trace-element composition of the sample. We note that PyMca also accounts for secondary fluorescence by the matrix correction. It also takes into account the re-absorption of the XRF from the sample and of the air between sample and detector when all these parameters are known, i.e. sample thickness, distance between sample and detector and geometry of the sample and detector.

It is possible to calculate the uncertainty (minimum detection limit, MDL) on each measurement i (\({C}_{\mathrm{MDL},i}\)) following Petitgirard et al. (2009) such that:

$$C_{{{\text{MDL}},i}} = \frac{{3 \times \sqrt {I_{{\text{B}}} } }}{{I_{i} }} \times \frac{\sqrt t }{{\sqrt {1000} }} \times C_{i}$$
(1)

with IB the intensity of the background, Ii the intensity of the peak of the element i integrated over the 3 \(\sigma\) zone, t the collection time, and Ci the actual concentration of element i. Some chemical elements in our standards were present at low concentrations (i.e., 70 ppm of Mo in PO100 for instance). As seen with Fig. 1, it is possible to derive precise calibration curves, that are applicable from very low concentrations to orders of magnitude higher. From this and Eq. 1, we can estimate that the detection limit is a few ppm for elements that can be detected with K-alpha lines, and few tens of ppm for elements with L-lines, which makes nano-XRF an excellent method for resolving low concentrations of elements in FIB-extracted samples. Of course, this depends on the complexity of the sample (textural complexity or non-homogeneous element concentrations for instance), and can vary if the sample is more complex than what we used here. As also discussed below, ideally, the major elements composition of the standard and the sample should be close to increase accuracy.

Additionally, if the thickness of the sample of interest is known, the main parameter that can be tuned and can influence the output is the density of the sample when using PyMca software. This parameter is not always easily accessible, especially for experimental samples. To estimate the importance of the chosen density on the output results, we changed the estimated density of our FIB lamellae of standard IZ-01 from 2.5 to 3.5 g cm−3 while keeping the other parameters constant. The choice of these densities is justified because the composition of this standard approximates the eutectic composition of the anorthite-diopside system at 1-bar that have respective densities of ~ 2.7 and ~ 3.2 g/cm3. We plot in Fig. 2 the result of changing the density compared to the concentrations reported in Chen et al. (2020) for IZ-01. One can see that there is an excellent agreement between what is expected and the concentrations derived using nano-XRF technique, with a maximum difference of 20%. For all elements, using a density of 3.5 g cm−3 results in concentrations closest to the expected ones, since there are 10% or less of difference between our results and that provided by Chen et al. (2020). In this case, we used calcium as internal standard because it is one of the major elements of this standard (see Table 1), but Ca can be affected by reabsorption, which may explain the deviation of about 10% from the expected values. Ideally, it would be better to use another element closer to the one of interest, like iron, but in this particular standard, the amount of iron is quite low (~ 0.2 wt%), precluding its usage as reliable internal calibrant.

Fig. 2
figure 2

Percentage of similarity between the values derived from our nano-XRF measurement and the values provided by Chen et al. (2020) for the standard IZ-01 as a function of the density chosen. We calculated the abundances of each element using the software PyMca. A value of 100 on the Y axis means that our calculation from nano-XRF measurements reproduce exactly the value proposed by Chen et al., 2020

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Further, we could identify several limitations related to the use of nano-XRF with FIB lamellae. First, because of the use of FIB, we could always detect Ga implantation on our standards (and samples), along with Pt signal coming from the welding, and copper from the TEM grid. Hence, if one wants to study one of these three elements, some adjustment has to be made, for example the use of another element than Pt during the FIB procedure. Otherwise, we suspect that no useful information can be extracted from the analysis. We also noted that the way the sample is attached to the Cu grid is of great importance. Indeed, the sample should ideally be welded from both sides, and be aligned with the surface of the Cu grid, to maximize the signal coming out and avoid shadow effect on the detector. But regardless of the welding, the fluorescence coming from the Cu-grid will be visible on the spectra, which can be an issue, depending on the elements of interest. We illustrate these effects on Fig. 3 where one can see the intensity of the peaks for Cu, Ga and Pt on our FIB extracted material. Those spectra are from the standard IZ-01, and one can see that there are some overlaps between the peaks of the elements of interest and Cu, Pt and Ga. Welding the sample to a Si-wafer (instead of a Cu-grid and a silicon nitride membrane as we did) has been done in previous studies (Suer et al. 2021) but not tested here. While it sounds like a good alternative, Si-wafer are thick and this might result in scattering that could blind the detectors.

Fig. 3
figure 3

Intensity spectra from standard IZ-01 obtained by Nano-XRF. Intensity of a the Cu Ga and Pt peaks coming from the TEM grid and the FIB procedure, b Ru, Rh, Ag and Re

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Finally, it is worth noting that the standards should ideally be very close (in composition, structure, density) to the samples. This is important to limit the matrix effect when establishing the calibration lines. In our case, the standards were not synthetized at high pressure, and the composition is not exactly that of the samples. Nonetheless, the use of our standards is justified as these were the most reliable standards available to us. In the future, it would be interesting to test the potential differences that arise from using standards synthesized at high P–T.

NanoSIMS measurements

NanoSIMS relies on using a highly focused primary ion beam (O− or Cs+) to bombard the sample and by doing so sputters ionized material from the surface layers. The ejected secondary ions are subsequently analyzed by a mass spectrometer. This technique is optimized for nanoscopic scale spatial resolutions. NanoSIMS measurements are sensitive to matrix effects, so we took particular care in synthesizing and using relevant standards. NanoSIMS analyses were performed using the CAMECA NanoSIMS 50L at the Open University (Milton Keynes, UK). Prior to analysis, an area of each sample was pre-sputtered using a focused primary beam of 16 keV O− ions with a probe current of ~ 100 pA to remove surface contamination and achieve a constant count rate. The sizes of the pre-sputtered areas varied from 15 \(\times\) 15 to 20 \(\times\) 20 microns. Analyses were then carried out in imaging mode by rastering a 50 pA O− beam onto the inner 10 \(\times\) 10 to 15 \(\times\) 15 microns areas. With this probe, a spatial resolution of ~ 300 nm was achieved. The mass resolving power was set at > 5000 (Cameca definition) and secondary ions of 95Mo16O+, 186W16O +, 30Si+, and 54Fe+ (sometimes 56Fe+) collected in electron multipliers simultaneously. The oxide ions were measured as they offered enhanced secondary ion yields over the atomic ions, especially for W. Final isotope maps are generated by aligning and summing stacks of 100 images, with each image composed of 128 × 128 pixels with a dwell time of 2 ms per pixel. Total analysis time for each map is therefore approximately 60 min. The data were processed with L’Image software (Larry Nittler, Carnegie Institute Washington D.C.), correcting for detector deadtime and stage drift, after which we extracted from the region of interest the ratios 95Mo/30Si and 186W/30Si for the silicate standard, and 95Mo/54Fe and 186W/54Fe for the metallic one. We performed five analyses on each standard to test the reproducibility of the measurements. From these measurements, we derived calibration curves for 95Mo/30Si and 186 W/30Si ratios in the silicate matrix and 95Mo/54Fe and 186W/54Fe, see Fig. 4. On those figures, each point is the mean of the five analyses performed on each sample. One can see that for the metallic standards, the calibration curve is slightly less good than for the silicate one. This is probably due to the presence of a dendritic quench texture that developed upon quench for the spheres synthesized using the aerodynamic levitation device.

Fig. 4
figure 4

Calibration curves obtained at the NanoSIMS for a W/Si and b Mo/Si in silicate melts and for c W/Fe and d Mo/Fe in metallic melts

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We display in Fig. 5 the NanoSIMS maps that were established for the standards PO1000 for 30Si, 56Fe, 95Mo and 186W16O. One can see that at the scale of the measurements, no heterogeneity can be detected in the material, such as nanonuggets. The counts are of course much higher for Si and Fe, but Mo and W are still detectable with this technique. It must be noted that, contrary to the measurements we did using nano-XRF, the standards were bulk and not extracted by FIB. We did so because NanoSIMS is a technique that is especially sensitive to the surface of the analyzed sample, so it allowed us to save a lot of preparation time.

Fig. 5
figure 5

NanoSIMS chemical maps of standard PO1000 for several isotopes (30Si, 56Fe, 186W16O and 95Mo16O)

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Application to high P–T samples

High P–T experiments

We applied both nano-XRF and NanoSIMS techniques on samples synthesized using a LH-DAC for which the objective was to evaluate the evolution of the metal-silicate partition coefficient (D, with \(D={X}_{\mathrm{M}}^{\mathrm{metal}}/{X}_{{\mathrm{MO}}_{n/2}}^{\mathrm{silicate}}\) in molar fraction, with n the valence state of the element M) of tungsten and molybdenum with pressure and temperature. To do so, it is necessary to measure trace concentrations of siderophile elements in quenched silicate melt equilibrated at high P–T with a quenched molten metallic alloy doped in siderophile elements. In our case, we studied the siderophile elements Mo and W. Those two elements are vertically adjacent in the periodic table, and they are the only two MSEs that are cosmochemically refractory. As such, they can be used as tracers of core–mantle differentiation, because they should be present in chondritic proportions in the bulk Earth. In addition, W is part of the Hf-W isotopic system that is used to constrain the timing of core formation (e.g., Kleine et al. 2002).

As starting materials, we used sample PO1 synthesized by aerodynamic levitation as described previously for the silicate part (see also composition in Table 1), and iron-nickel (Fe95Ni5) or FeNiS (Fe80Ni10S10) thin foils for the metallic part. The choice of the FeNiS alloy was made to test the effect of sulfur on the metal-silicate partitioning of W and Mo. A rhenium gasket with an initial thickness of 250 µm was pre-indented down to 40 µm using diamonds with 200-to-300-micron culets. Subsequently, a hole of about 100 µm diameter was machined in the center of the indentation, using a laser drill, to serve as a sample chamber. A thin foil of metal alloy sandwiched between two layers of silicate glass starting material was loaded in the sample chamber (Fig. 6). The pressure was slowly increased and monitored using the diamond Raman edge method (Akahama and Kawamura 2004) until the target pressure was reached. The loaded and pressurized diamond anvil cells were then heated to the target temperature using a double-sided YAG laser at BGI and at the GeoForschung Zentrum (GFZ, Potsdam). Details of both heating systems are provided in Lobanov et al. (2020) and Blanchard et al. (2022), respectively. The temperature was monitored using the spectro-radiometric analysis of the thermal emission spectrum of the sample under the gray body assumption (Benedetti and Loubeyre 2004). The peak temperature was maintained for a few seconds, which is enough to closely approach thermodynamic equilibrium given the size of the samples (few tens of microns, see Fig. 6c) and the high temperatures, above the peridotite liquidus (Fiquet et al. 2010). The target peak temperature was chosen at each pressure point so that both the metal and the silicate were molten. Temperatures given in Table 3 are the averages of three to six measurements taken at the peak temperature. Following Lobanov et al. (2021), we estimate that the uncertainties on the temperature measurement is about 20% relative, and is an upper bound on the error in temperature associated with non-graybody effects. The laser power was then shut down to ensure a fast quench of the sample and, because the diamonds are excellent thermal conductors, the heat is very quickly dissipated out of the sample, so that the quench is quasi-instantaneous. The samples were recovered at ambient pressure, after slowly decompressing the load on the diamond anvils, to perform ex situ measurements. Given the geometry and very small size of the samples in such experiments, the samples are not directly accessible since the zone that reacted and equilibrated at high P–T is buried below the surface (see Fig. 6c). To extract the region of interest where the peak temperature was reached and the sample had melted, we used the FIB facility at the BGI and at the GFZ, that allowed us to extract 3-micron thick lamellae from each of our experiments (see procedure described in the supplementary information, and Fig. S1). Care was taken to extract lamellae that had parallel surfaces on both sides of the samples for the metal and the silicate phases. The extracted samples had the same thickness as the standards that were used to establish the calibration (3 microns). We present in Table 3 the experimental conditions of the high P–T runs of this study. For these samples, electron microprobe analysis was not performed.

Fig. 6
figure 6

a Schematic drawing of a diamond anvil cell apparatus. b Optical picture taken through the diamonds of a loaded diamond anvil cell experiment. c Schematic drawing showing the geometry of the sample embedded inside the rhenium gasket, seen from the side

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Table 3 Summary of experimental conditions and metal–silicate partition coefficients (and their associated uncertainties in brackets) retrieved from nano-XRF and NanoSIMS measurements
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Nano-XRF measurements of high P–T samples

FIB lamellae from the samples were attached to PEEK holders, the same way we fixed standards (see above), to perform nano-XRF analysis. We could produce high resolution maps of the samples using a nanobeam at ID16B as described above. We show in Fig. S3 a nano-XRF intensity map of such a sample that was obtained with an acquisition time of 1000 ms per pixel, the longest that we have performed in this study. One can see the level of detail that can be obtained using such a probe. The spatial resolution that is reached allows us to observe small features such as the calcium perovskite around the quenched metal that was molten at high P–T. Note that this particular sample does not contain Mo or W, so it was not used to calculate DMo and DW.

We show in Fig. 7 another typical map that can be obtained using this technique from which we extracted chemical information. Since those samples have two phases present (metal and silicate) as opposed to the standards described above, we had to select the ROIs for each of the phases of sample × 8 synthesized at 35 GPa and 2900 K (see Fig. 7). We could integrate over a large area of sample to have better statistic using the software PyMca. This procedure was performed on each phase of each sample and we could extract Mo/Fe and W/Fe ratios that could be compared with the calibration curve obtained for the standards (see Fig. 1). By doing so, we could calculate the metal-silicate partition coefficients of W (DW) and Mo (DMo) for our experiments, as presented in Table 3.

Fig. 7
figure 7

a Backscattered electron image of sample × 8 recovered by FIB from LH-DAC experiments. b Total intensity map obtained by nano-XRF measurements along with integrated spectra of the delimited area for the silicate and c for the metal

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We present in Fig. 9, a comparison between a recent determination of DW and DMo by Huang et al. (2021) and the results derived in this study. Unlike us, the partition coefficients of Huang et al. (2021) were retrieved from electron microprobe analysis. In our case, no electron microprobe analysis was carried on the samples. Our quantification merely relies on the calibration curves presented above. This allows for a direct assessment of the validity of our method, and one can see that the magnitudes of DW and DMo derived by both studies are comparable. Our study extends the P–T range of metal-silicate partition coefficients for those elements, and it also agrees with the conclusions of Huang et al. (2021) that pressure makes both W and Mo less lithophile (decrease of D with pressure). Nevertheless, the temperature effect seems more controversial, with a decrease of both DMo and DW with temperature. For Mo, this has already been proposed by Siebert et al. (2011), whereas such an effect was not proposed for W in previous studies (Siebert et al. 2011; Wade et al. 2012; Huang et al. 2021; Jennings et al. 2021). It must be noted that for previous studies deriving thermodynamic parameterization of evolution of the metal–silicate partition coefficients are not used at face value, but normalized to the metal-silicate partitioning of Fe (DFe) at the power n/2 with n being the valence of the element considered. By doing so, the dependence on oxygen fugacity of the experiment is removed, and this is especially important for high valence elements, such as W and Mo (6 + and 4 + respectively). In this study, we have not attempted to calculate DFe or to proceed with thermodynamic modeling, but we were rather interested in testing the two analytical techniques on a suite of standards and high P–T samples.

For the standards, we had EPMA analysis that allowed us to use a known matrix correction to estimate the concentration of the elements of interest. In the case of our high P–T samples, this can also be done, but several difficulties have to be overcome. To perform EPMA analysis on FIB-recovered samples, it is necessary to have phases that are large enough to accommodate the interaction volume produced by the electron beam (about 1 micron3 with operating conditions of 15–20 keV). Hence, it is mandatory to have phases of at least several microns thick to perform accurate EPMA analysis. Another complexity is to move high P–T samples from one holder to another without losing them, since those samples are extremely small, fragile and easy to lose, even when attached to a TEM Cu grid. If these difficulties can be overcome, then it is possible to analyze trace elements, as we did for standards in addition to the major elements using conventional probes. Here, we did not perform EPMA measurements on our high P–T samples.

Another potential limiting factor in our case is the difference in the composition of our standards compared to our experimental samples, especially in terms of the iron concentration in the silicate (and to a lesser extend in the metal). Metal-silicate partitioning samples synthetized by LH-DAC have usually up to 20 wt% FeO in the silicate phase (e.g. Siebert et al. 2012; Blanchard et al. 2017; Jackson et al. 2018). This is about twice of what we have in our standards. This ultimately is a source of uncertainties in the values of DW and DMo that we calculated. Hence, we have estimated a maximum value by directly using the calibration curve, and a minimum value that is half of it to incorporate the factor two difference in FeO between the standards and the sample. The values and their uncertainties reported in Table 3 and Fig. 9 are the result of this treatment.

NanoSIMS measurements of high P–T samples

Two of the high P–T samples were measured using the NanoSIMS: samples × 8 and × 9 synthetized at 35 GPa and 2900 K and 68 GPa and 3850 K, respectively. They were mounted on electrically conductive carbon tape to provide a uniform electric field over the sample. In Fig. 8, the NanoSIMS maps for different isotopic ratios are reported for sample × 8 synthesized at 35 GPa and 2900 K that was already presented in Fig. 7. We first sputtered away the upper layer of each sample to get rid of the oxide layer present at the surface. The O− anions beam was then scanned across the sample to obtain an overview of the whole samples before selecting specific ROIs for both metal and silicate parts. As for the standards, we could define ROIs in both the metal and the silicate and extract 95Mo/30Si and 186W/30Si for the silicate part (excluding the Ni/Si rich area to avoid nanonuggets), and 95Mo/54Fe and 186W/54Fe for the metallic part.

Fig. 8
figure 8

NanoSIMS chemical maps of sample × 8 for several isotopes (28Si, 54Fe, 186W16O and 95Mo16O)

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Using those ratios and the calibration lines defined earlier, we calculated DMo and DW for these two samples. The values are given in Table 3, and also reported in Fig. 9. One can see that they compare well with data obtained with nano-XRF and EPMA from Huang et al. (2021). The standards used to calculate DMo and DW from NanoSIMS measurements are the same as the ones used for nano-XRF. Hence, the same problem arose regarding the difference in composition (mostly in FeO) between our samples and the standards. The uncertainties reported in Table 3 and Fig. 9 are due to this matrix effect.

Fig. 9
figure 9

Comparison between our metal–silicate partitioning coefficient of Mo and W obtained by nano-XRF measurements (in green), and with NanoSIMS measurements (in black) with published data from Huang et al. (2021) obtained by electron microprobe measurements. The uncertainties on P and T are estimated to be 5 GPa and 20% of each temperature measurement, respectively

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Conclusions

We have shown that using nanoprobes on samples retrieved using FIB, such as high pressure and high temperature samples synthesized in a LH-DAC, trace element mapping and quantification can be successfully performed. We have compared two nano probes, namely nano-XRF and NanoSIMS, that present some similitudes but also several differences, as summarized in Table 4, that must be taken into account depending on the type of measurements one wants to perform. The spatial resolution of both nano-XRF and NanoSIMS enables analyzing very small structures present in FIB-extracted samples. In this work, we have used both NanoSIMS and nano-XRF to estimate metal-silicate partition coefficients of Mo and W in samples synthesized in laser-heated diamond anvil cells and retrieved by FIB. We obtained results that are comparable to those obtained independently using EPMA. This highlights that these methods are robust, and are suitable for such kind of samples. The elemental sensitivity of those instruments can be used to infer very low concentrations of elements (down to few ppm), as evidenced the detection limits established from the study of our standards. Further, the spatial resolutions of 300 nm for the nanoSIMS down to 50 nm (even 10 nm in some cases) for the XRF are promising for the analysis of extremely small samples. Such features are greatly superior to the detection limits and spatial resolution of the microprobe for example. Hence, those methods have a high potential to investigate the behavior of highly siderophile elements in silicate melts, for instance in the frame of Earth’s core-mantle differentiation. More generally, elemental diffusion between grain boundaries of minerals or the partitioning of trace elements between solid–solid or solid–liquid phases can be explored, for example to understand their behavior in the frame of magma ocean solidification.

Table 4 Comparison of nano-XRF and NanoSIMS analytical techniques
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