# Semi-quantitative µLIBS mapping of germanium diffusion between metal and silicate during planetary core-mantle segregation

Baptiste Le Bellego, Vincent Motto-Ros, Béatrice Luais, Cécile Fabre, Célia Dalou, Pierre Condamine, Laurent Tissandier

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## To cite this version:

Baptiste Le Bellego, Vincent Motto-Ros, Béatrice Luais, Cécile Fabre, Célia Dalou, et al.. Semi-quantitative µLIBS mapping of germanium diffusion between metal and silicate during planetary core-mantle segregation. Spectrochimica Acta Part B: Atomic Spectroscopy, 2024, 222, pp.107059. 10.1016/j.sab.2024.107059. hal-05204335

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Semi-quantitative µLIBS mapping of germanium diffusion between metal and silicate during planetary core-mantle segregation

Baptiste le Bellego, Vincent Motto-Ros, Béatrice Luais, Cécile Fabre, Célia Dalou, Pierre Condamine, Laurent Tissandier

PII: S0584-8547(24)00204-0

DOI: https://doi.org/10.1016/j.sab.2024.107059

Reference: SAB 107059

To appear in: *Spectrochimica Acta Part B: Atomic Spectroscopy*

Received date: 14 August 2024

Revised date: 18 October 2024

Accepted date: 20 October 2024

Please cite this article as: B. le Bellego, V. Motto-Ros, B. Luais, et al., Semi-quantitative µLIBS mapping of germanium diffusion between metal and silicate during planetary core-mantle segregation, *Spectrochimica Acta Part B: Atomic Spectroscopy* (2024), https://doi.org/10.1016/j.sab.2024.107059

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# Semi-quantitative µLIBS mapping of germanium diffusion between metal and silicate during planetary core–mantle segregation

Baptiste Le Bellego<sup>a, b, *</sup>, Vincent Motto-Ros<sup>c</sup>, Béatrice Luais<sup>b</sup>, Cécile Fabre<sup>d</sup>, Célia Dalou<sup>b</sup>, Pierre Condamine<sup>e</sup> and Laurent Tissandier<sup>b</sup>

<footnote><sup>a</sup> Université de Lorraine, CNRS, CRPG, F-54000 Nancy, France</footnote>

<footnote><sup>b</sup> Centre de Recherches Pétrographiques et Géochimiques (CRPG), Université de Lorraine, CNRS, UMR 7358, 15 Rue Notre Dame des Pauvres, BP 20, CEDEX, F-54501 Vandœuvre-lès-Nancy, France;
beatrice.luais@univ-lorraine.fr,celia.dalou@univ-lorraine.fr,laurent.tissandier@univ-lorraine.fr</footnote>

<footnote><sup>c</sup> Institut Lumière Matière UMR 5306, Université Lyon 1 – CNRS, Université de Lyon, Villeurbanne,
France; vincent.motto-ros@univ-lyon1.fr</footnote>

<footnote><sup>d</sup> GeoRessources, UMR7359, CNRS, Université de Lorraine, F54000 Nancy, France; cecile.fabre@univ-lorraine.fr</footnote>

<footnote><sup>e</sup> Laboratoire Magmas et Volcans – CNRS, Clermont-Ferrand, France; pierre.condamine@uca.fr</footnote>

<footnote>* Corresponding author. Phone number: +33 3 83 59 42 09, E-mail address: baptiste.le-bellego@univ-lorraine.fr, 15 Rue Notre Dame des Pauvres, BP 20, CEDEX, F-54501 Vandœuvre-lès-Nancy, France</footnote>
**Abstract**

Understanding the distribution of elements between the cores and mantles of planetary bodies is essential for elucidating the geological and geochemical processes operating during their formation. Because the semi-metallic element Ge shows complex siderophile, chalcophile, and lithophile properties, it is particularly significant for investigating core–mantle segregation and ore deposit formation. Recent advancements in *in situ* microanalysis techniques, such as µLIBS, have enabled high-resolution elemental mapping of Ge and other trace elements.

This study explores the application of µLIBS imaging to investigate the high-
temperature/high-pressure distribution of Ge between metallic and silicate matrices
analogous to planetary cores and mantles. By cross-calibrating the µLIBS intensities with
electron microprobe profile analyses carried out on piston cylinder experimental samples,
we produced semi-quantitative Ge maps from which we extracted Ge concentration profiles
to assess Ge diffusion from the silicate to the metal. We determined, for the first time, the
diffusion coefficient of Ge between metal and silicate to be D(Ge)metal = 4.03E-13 ± 3.6E-14
m²/s at 1 GPa and 1350 °C. Our results demonstrate the capability and efficiency of µLIBS for
providing detailed, high-resolution (15 µm) trace element concentration data at few ppm
levels, offering a time- and cost-effective alternative to conventional techniques.

These findings bring insights on planetesimal differentiation and on chemical
exchanges between metal and silicate phases in a magma ocean and between two different
metal phases occurring at the bottom of the magma ocean during planetesimal formation.

**Keywords**

Micro LIBS, Elemental imaging, Germanium, Diffusion, Quantification, Metal-silicate

**Highlights**

* Germanium diffusion fronts in metal and silicate phases can be imaged by µLIBS.

* We conducted a study on HP-HT sample under planetesimal formation conditions.

* 2 concentration models are proposed to quantify Ge diffusion in metal and silicate.

* We constructed high-resolution (15 µm) semi-quantitative Ge images at ppm levels.

* Metal-silicate Ge diffusion coefficients were calculated for the first time.
# 1. Introduction

The formation of the Earth and other rocky planets involved the segregation of a metallic core from the overlying silicate mantle (and, eventually, the crust). Precise, high-resolution identification of elemental distributions between the core and mantle is required to have a clear understanding of the geological and geochemical processes of the formation of the Earth. Qualitative and quantitative analyses of metal elements in particular are crucial for identifying the mechanisms and thermodynamic conditions of their incorporation into these metal and silicate matrices. Specifically, the semi-metallic element germanium shows complex siderophile (iron affinity), chalcophile (sulfur affinity), and lithophile (silicate affinity) behaviors and is thus key to constraining the physicochemical processes not only of planetary core–mantle segregation [1–3], but also of ore deposit formation [4,5].

In recent years, the improved detection of micrometer-scale chemical heterogeneities of Ge and other trace metals in geological and extra-terrestrial samples [4–12] has been facilitated by the development of *in situ* microanalytical techniques such as synchrotron X-ray fluorescence (μXRF), electron microprobe, laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS), secondary ion mass spectrometry, and laser-induced breakdown spectroscopy (LIBS). Among those techniques, *in situ* μLIBS is used to qualitatively map/image the distributions of elements, especially Ge [9,13], in complex materials prior to any quantitative analysis. Because μLIBS is a completely optical approach, it is compatible with optical microscopy at ambient conditions and, despite its relatively simple implementation, can detect ppm-level elemental concentrations at spatial resolutions of around ten micrometers. Moreover, the fast acquisition rates of μLIBS are limited only by the laser frequency and detector speed, which can reach kHz rates [14–16], making μLIBS particularly suitable for applications requiring rapid imaging and large-scale analysis [17–20].

Quantitative analyses of geological materials have been achieved by calibrating μLIBS with other techniques [21,22]. However, due to the destructive nature of laser ablation, multiple measurements at the same sample position cannot be averaged; each pixel must be captured in a single laser shot without any statistical information available. The challenge of applying a quantitative approach to heterogeneous samples with varying matrices and Ge gradient concentrations has been addressed only sparingly in the literature.
Cugerone et al. [9] coupled µLIBS trace element chemical maps with microprobe analyses to identify the redistribution of Ge between microminerals containing tens of percent Ge within larger, Ge-poor quartz grains (hundreds of ppm Ge) in Zn-S ore deposits. Fabre et al. [22] coupled µLIBS imaging of an entire thin section with spot microprobe analyses to obtain quantitative elemental images consistent with µXRF imaging results. Both studies produced mineralogical and quantitative elemental maps useful for investigating mineralogy and the natural occurrence of rare elements such as Ge in ore deposits. This approach thus offers a faster and cost-effective alternative to more common techniques (microprobe, LA-ICP-MS) used to map trace element concentrations in complex samples. Despite these advantages, it remains challenging to obtain quantitative µLIBS results due to the uniqueness of each plasma measurement and the heterogeneous nature of geological samples and their matrices, both in terms of atomic structure and elemental contents. Reliable quantitative µLIBS imaging thus requires that issues such as matrix effects, linearity of the detector response, calibration strategies, and expected uncertainties be addressed [17,20,23–26].

In this study, we explore the potential of µLIBS imaging for investigating the distribution of Ge at high spatial resolution in drastically different matrices (metal alloy and silicate glass). We specifically focus on laboratory experimental samples comprising metallic capsules filled with Ge-doped silicate, which serve as proxies for planetary metallic cores and silicate mantles. These experiments aimed to simulate the segregation of solid metal fragments [27] from a planetary magma ocean and their gradual equilibration. We cross-calibrated microprobe analyses of Ge and modeled the concentrations as a function of LIBS emission line intensities to produce semi-quantitative Ge concentration maps and average concentration (diffusion) profiles in both the metal and silicate matrices. We also focused on determining uncertainties in a single-shot configuration, which have not yet been reported. The results of this study will facilitate the quantification of the diffusion processes leading to the distribution of Ge between the primary metal and silicate reservoirs during planetary formation, particularly regarding the formation of metallic cores in planetary embryos and asteroids.

## 2. Material and methods

### 2.1. *Samples*
One synthetic calcium magnesium aluminosilicate (CMAS) glass of anorthite-diopside eutectic composition was prepared by mixing pre-dried, spectroscopically pure SiO₂, Al₂O₃, MgO, and CaCO₃ reagents. The mixture was then decarbonated by slow heating (3 °C/min) and fused in air twice for 4 h at 1400 °C in platinum crucibles within a 1 atm muffle furnace. The melt was quenched to glass in water, then crushed and ground in an automatic agate mortar for 30 min. The powder was doped with 10,000 ppm Ge Aldrich standard solution to obtain a nominal composition of 3200 ppm Ge, then fused again in air for 15 min at 1400 °C in the same muffle furnace, quenched, and crushed for 15 min. This starting silicate composition (Table 1) was then loaded in Fe₉₀Ni₁₀ alloy (γ-like structure) sealed capsules, described below.

<table><caption>**Table 1.** Compositions of the starting materials (wt.%, except for Ge in ppm). Both the major element and Ge concentrations of the metal phase were measured by microprobe (LMV, Clermont-Ferrand). Bulk major element and Ge concentrations in the silicate glass were measured using ICP-MS and ICP-OES (SARM, Nancy).</caption><thead><tr><th rowspan="2"></th><th colspan="2">Metal phase</th><th colspan="7">Silicate phase</th></tr><tr><th>Fe<br>wt.%</th><th>Ni<br>wt.%</th><th>SiO<sub>2</sub><br>wt.%</th><th>CaO<br>wt.%</th><th>Al<sub>2</sub>O<sub>3</sub><br>wt.%</th><th>MgO<br>wt.%</th><th>FeO<sup>a</sup><br>wt.%</th><th>Na<sub>2</sub>O<br>wt.%</th><th>Ge<br>ppm</th><th>Total</th></tr></thead><tbody><tr><td>CMAS-02</td><td>—</td><td>—</td><td>51.28</td><td>23.40</td><td>14.42</td><td>11.04</td><td>&lt;D.L.</td><td>0.17</td><td>3147</td><td>100.31</td></tr><tr><td>Relative error</td><td></td><td></td><td>&lt;2%</td><td>&lt;2%</td><td>&lt;2%</td><td>&lt;2%</td><td></td><td>&lt;25%</td><td>&lt;5%</td><td></td></tr><tr><td>Fe<sub>90</sub>Ni<sub>10</sub></td><td>89.98</td><td>9.87</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>99.92</td></tr><tr><td>2σSD</td><td>0.72</td><td>0.24</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr></tbody></table>

The metallic capsules were synthetized using the “vacuum pulling” method in an inductively heated water-cooled crucible system at the Institute Jean Lamour (Nancy, France) metallurgy lab. A 40 g mix of 90% pure Fe pellets (99.95% purity) and 10% Ni pellets (99.995% purity) was first completely melted at 1500 °C under a continuous Ar flux. The metallic melt was then very rapidly “vacuum pulled” into a silica tube. This process allows the synthesis of long, homogeneous Fe-Ni cylinders. The homogeneity along the cylinders was verified by energy dispersive X-ray spectroscopy in a scanning electron microscope at Centre de Recherches Pétrographiques et Géochimiques (CRPG, Nancy, France). The cylinders were homogenous to within 0.72 wt.% error (2σ SD) for Fe and 0.24 wt.% (2σ SD) for Ni. The cylinders were cut and machined into capsules 5 mm long with external and internal diameters of 3.9 and 3.3 mm, respectively (i.e. capsule walls 0.3 mm thick).

<footnote>ᵃ Concentrations below 0.015 wt.% were considered to be below the detection limit (D.L.).</footnote>
The Fe-Ni capsules were filled with the starting silicate powder, welded shut, and loaded in a ¾-inch piston cylinder assembly (Fig. 1.A) as described by Condamine et al. [28] and summarized here: the sample was placed in a graphite furnace, itself placed within multiple layers of different materials to maintain the sample assembly, prevent temperature gradients, and convert the unidirectional pressure applied at the top and bottom of the assembly into isotropic pressure. The experiments were performed at 1 GPa and 1350 °C (CRPG, Nancy, France). Run temperatures were controlled to within ± 1 °C of the set point using C-type (W<sub>95</sub>Re<sub>5</sub>/W<sub>74</sub>Re<sub>26</sub>) thermocouples. Experimental durations were varied between 20 min and 48 h to vary the Ge content via diffusion from the silicate glass into the metallic capsule. Each experiment produced a different sample, named for its duration: MS-20M, MS-3HA, MS-3H-B, MS-6H, MS-12H and MS-48H (with MS-3H-A and MS-3H-B being duplicates from two different experiments with the same duration). Before decompression, the experiment was rapidly quenched (~175 °C/s) by cutting power to the furnace to obtain a homogeneous quenched glass.

The final experimental products were cut in half using a wire saw, individually mounted in epoxy (Fig. 1.B), and polished to 0.25 µm with ethanol and anhydrous diamond pastes. To ensure the accuracy of µLIBS analyses, special consideration was given to the flatness of the sample surfaces; the regularity of each sample's surface was verified under an optical microscope. For microprobe analysis, the samples were carbon-coated (15–20 nm thickness).

## 2.2. Electron microprobe analysis

The major element compositions and Ge concentrations in the metallic capsules were determined using a CAMECA SxFive Tactics electron microprobe at the Laboratoire Magmas et Volcans (LMV, Clermont-Ferrand, France). Fe, Ni, and Si measurements in the metallic phases were conducted using a 15 kV accelerating voltage, a 15 nA beam current, a focused beam (~1 µm diameter), and on-peak of 10 s and background counting times of 10s (5s before the spike and 5s after the spike). Ge concentrations in the metal were analyzed using a focused 15 kV beam operating at 200 nA and respective on-peak and background counting times of 10s and 30s (15s before the spike and 15s after the spike) on three spectrometers (TAP crystals) to achieve a mean detection limit of 110 ± 42 ppm, and a mean standard deviation of 72 ppm over an acquisition time of approximately 4 min per point.
Metallic Fe, Ni, Si, and Ge standards were used for calibration. Concentration profiles were acquired across the entire width of the metallic capsule to the right of and below the experimental load (i.e. two roughly orthogonal profiles per sample) at 15 µm increments to mitigate the effects of any thermal gradients induced by the piston cylinder. The average acquisition time for each profile was approximately 2.5 hours. The first measurement point of each profile was at the interface between the silicate and metallic phases (red lines on Fig. 1.B).

<figure><img src="image_4.png" /><figcaption>**Fig. 1.** (A) Schematic (not to scale) of the piston cylinder assembly used herein. The sample, assembly, and piston have been enlarged for visibility. (B) A halved sample after a piston cylinder experiment viewed under binocular microscope. The apparent heterogeneities in the transparent silicate glass are reflections of the metal capsule behind the glass. Red lines represent the location of the 2 profiles that were made for each sample.</figcaption></figure>

### 2.3. MicroLIBS imaging

To achieve precise µLIBS imaging, we employed a Nd:YAG laser (Centurion GRM, Lumibird) emitting a fundamental wavelength of 1064 nm with a pulse duration of 7 ns and a repetition rate of 100 Hz. We focused the laser beam onto the sample surface using a 15x magnification lens (LMM-15X-P01, Thorlabs). In all analyses, the pulse energy was set to 0.6 mJ. In this configuration, a single laser shot ablated a crater approximately 7 µm in diameter for an estimated spatial resolution of 15 µm. All µLIBS analyses were conducted at room temperature and ambient pressure. An argon flow of 1.0 L/min was blown through the plasma, both to prevent surface contamination by deposition of previously ablated material
and to enhance the plasma emission. The plasma emission was collected by two lens-fiber
systems coupled to three spectrometers to simultaneously detect emission lines from all
elements of interest. The first spectrometer was a Shamrock 500 (Andor, Oxford
Instruments) equipped with a 1200 lines/mm grating (blazed at 300 nm) centered at 265 nm
to cover the 256-276 nm spectral range with a resolution of around 0.08 nm. This range was
specifically selected to detecting Ge, Fe, Si, Ni, and Al. The second and third spectrometers
were two Shamrock 303 spectrometers (Andor, Oxford Instruments), the first with a 1200
lines/mm grating centered at 305 nm to cover the 275-335 nm spectral range and the
second with an 800 lines/mm grating centered at 790 nm to cover the 740-840 nm spectral
range; these additional spectral ranges were chosen to detect Na, K, Sr, O, C, S, and Cl (not
presented in this study). Shamrock spectrometers were equipped with an ICCD camera
(Istar, Andor, Oxford Instruments) synchronized to the Q-switch of the laser. The spectra
were recorded with a delay of 700 ns, a gate of 5000 ns, a gain of 1000. The optimal spectral
ranges and the most suitable Ge emission lines to mitigate potential interference from Fe
were informed by previous Ge analyses performed on the same iLM platform [9,26,29,30].

Samples were moved line-by-line in the x-y plane orthogonal to the laser beam via a
motorized translation stage to achieve a spacing of 20 µm between the centers of
consecutive ablation spots. Emission spectra were recorded at each sampling position. The
laser pulse energy and focus on the sample were strictly controlled by using real-time
imaging of the plasma to precisely align the optical fiber used to collect the plasma
emission; thus, LIBS measurements were stable during all our µLIBS analyses [31]. Software
developed in the LabVIEW environment was used to control all system components,
allowing for automated sequencing to scan regions of interest at a specified resolution.
Once scanning was completed, elemental maps were created for each element of interest
by selecting their specific emission lines following a previously described protocol [20,31].
Relative elemental abundances were displayed in false-color images with an arbitrary color
assigned to each element. Finally, we used the open-source ImageJ software to display and
further analyze the elemental images.

**3. Results**

3.1. *Elemental images*
The elemental maps of the six samples are identical in size, each being 500 × 1250 pixels (625,000 pixels in total) (Fig. 2.A). The full µLIBS recording (analysis) time was 1 h and 40 min for each sample. Single laser shots were used for each pixel to limit phase mixing, avoid altering the sample surface, reduce potential matrix effects, and accurately map the sample surface. For our analysis, we selected emission lines at 265.1 nm (Ge I), 288.1 nm (Si I), 302.1 nm (Fe II), 273.7 nm (Ni I), and 265.2 nm (Al I) for their high signal/background ratios and to avoid dramatic self-absorption or interference from other emission lines [20]. Consideration of the entire sample section facilitates a better understanding of Ge concentration variations between the silicate and iron phases, thereby allowing the Ge migration rate to be estimated more accurately than by conventional analysis of a single 1D profile.

Because the interaction between the laser and the sample material differs in the silicate and metallic phases, we cannot show compositional differences between the phases meaningfully in the same image using the same intensity scale. Thus, we segmented the µLIBS images into separate masks for the silicate and metallic phases (Supplementary Fig.S1) based on the Ni and Si signals, respectively. We report elemental µLIBS imaging of Ge, Si, and Al in the silicate glass and Fe and Ni in the metal (Fig. 2.A).

The Ge measurements show varied intensity levels (Fig. 2.B). Experiment MS-20M showed higher intensities in the center of the silicate phase that decreased towards the metal-silicate interface. At the interface, the µLIBS image displays a narrow band of very high intensity, with local Ge-rich spots (Fig. 2.B); characterization revealed that these spots were associated with the occurrence of Fe-Ge-rich metal beads smaller than 5 µm in the silicate phase. MS-3H-A, MS-3H-B, and MS-6H exhibited moderate intensities with increasing width of the Ge-rich zone in the metal surrounding the silicate phase. We note that although MS-3H-A and MS-3H-B are duplicates, they exhibited different intensities in the center of the silicate phase due to the concentration of an Fe-Ge-rich quench phase [32] in the center and bottom of MS-3H-A. Nonetheless, bulk measurements of Ge in the metal phase (ICP-MS) and major elements in the silicate phase (EPMA) showed no significant differences in the two samples. This consistency in the duplicates validates the reproducibility of the experiments.
<figure><img src="image_5.png" /><figcaption>**Fig. 2 (A)** First and second columns: Ge intensity images (265.1 nm) of the metal and silicate phases respectively, with the masks applied (see **Supplementary Fig. S1**) for six distinct experiments. Third and fourth columns: Fe (302.1 nm) and Ni (273.7 nm) intensity images, respectively, in the metal phase with mask applied. Note that the silicate phase is not represented for these two elements due to the presence of measurement artefacts. Fifth and sixth columns: Si (288.1 nm) and Al (265.2 nm) intensity images, respectively, of both phases (raw images without masks) used to determine phase homogeneities. **(B)** (Left) Ge intensity image (265.1 nm) of the silicate phase with the mask applied (**Supplementary Fig. S1**) for sample MS-20M. (Right) Enlarged view (4x zoom) of the region indicated by the black box in the left image. White arrows denote the presence of Fe-Ge-rich metal beads.</figcaption></figure>

MS-12H and MS-48H showed low Ge intensities in the silicate and more diffuse intensities throughout the capsule. The Ge-rich band is even broader, reaching the edge of the metallic capsule for MS-48H. The Fe and Ni images of the capsules (**Fig. 2.A**) showed highly homogenous intensities for all samples that are consistent with the starting composition (90 wt.% Fe, 10 wt.% Ni). Therefore, we were able to image Ge diffusion from the silicate to the metallic capsule, including the progressive advance of the Ge diffusion front in the metal phase. Ca (318.1 nm) (**Supplementary Fig. S1**) was also analyzed to check
for the presence of different silicate phases because Ge partitioning can vary depending on
silicate composition and structure [33,34]. All experiments in which other phases than glass
was observed are not included in the study.

3.2. *Elemental calibration methods*

The µLIBS maps offer valuable qualitative insights into elemental diffusion during
these experiments. However, diffusion rates in the two phases can only be calculated from
precisely measured concentrations (Ge, Ni, Al, etc.). Because each pixel in the µLIBS maps
corresponds to an individual LIBS spectrum, the net optical emission intensities can be
correlated with known concentrations in ppm or wt.%. Here, we used individual quantitative
spot measurements to convert the µLIBS intensity maps into semi-quantitative data based
on separate correlations for the silicate and metallic phases. µLIBS measurements of both
the metal and silicate phases were calibrated by combining image-overlay techniques with
cross-calibration of microprobe Ge concentration profiles and µLIBS Ge intensity profiles.
We exploited the matching 15 µm resolution of the microprobe profiles and µLIBS images to
overlay backscattered electron images with corresponding microprobe Ge concentration
profiles and µLIBS intensity images. In this way, we constructed pixel-by-pixel µLIBS Ge
intensity profiles (Fig. 3) using ImageJ.

To further demonstrate the calibration process, we present an example of the Ge
distribution at the metal–silicate interface and within the metal for sample MS-3H-A (Fig. 3).
The Ge concentration (Fig. 3.A) decreases from approximately 25,000 ppm at the metal–
silicate interface to 110 ppm (the detection limit) over a distance of 200 µm. These values
show a mean relative standard deviation (RSD) of 3.8%, with individual RSD values varying
from 0.16% at the highest Ge concentrations to 23% at the lowest. Compared to the
concentration profile (Fig. 3.A), the LIBS intensity profile (Fig. 3.B) shows a similar trend,
decreasing from almost 5000 to near 0 (arbitrary units) over the same distance. The mean
RSD for LIBS intensities was estimated to be approximately 10% for each pixel during the
extraction of Ge intensities from each spectrum.
<figure><img src="image_6.png" /><figcaption>**Fig. 3.** Comparison of Ge profiles obtained by microprobe and µLIBS analyses of the metal phase in sample MS-3H-A. The metal and silicate phase distribution are indicated by the two distinct red and blue colors on either side of the metal-silicate interface. (A) Ge concentration profile (ppm) in the metal determined by microprobe; error bars are 2σ (= 49 ppm). (B) Reconstructed Ge µLIBS intensity profiles (arbitrary units) determined for the Ge emission line at 265.1 nm; 10% error bars were estimated for each pixel when extracting Ge intensities from individual spectra.</figcaption></figure>

a. Metal phase

For each sample, two profiles (see Section 2.2 and Fig.1.B) were treated with the
same approach demonstrated in Fig. 3, providing us a dataset of 164 pairs of known Ge
concentrations and corresponding Ge µLIBS intensities at the same position. This dataset
spans intensities of 0–4900, corresponding to Ge concentrations of 0–25,000 ppm. From
these concentration–intensity pairs, we constructed a calibration (Fig. 4) using quadratic
regression to account for the large variations of Ge concentrations between the different
experiments. The model shows a strong correlation (R² = 0.9674) and a standard error of the regression S<sub>y/x</sub> = 138.3. Some points (7 of 164) plot along a line below the regression; these points are from the same profile in sample MS-3H-A and are thus considered as a whole with the other profiles.

<figure><img src="image_7.png" /><figcaption>**Fig. 4.** Calibration curve for Ge in the metal phase, obtained from the intensity of the Ge LIBS emission line at 265.1 nm (arbitrary units) and Ge concentrations (ppm) measured by microprobe (LMV, Clermont-Ferrand). Upper and lower confidence limits indicate the 70% confidence level.</figcaption></figure>

Cross-validation of the model indicates that a linear model should be used for low to
moderate concentrations (<5000 ppm Ge in our case) because the Ge emission line (265.14
nm) is remarkably intense and primarily involves the fundamental state (NIST
https://www.nist.gov/pml/atomic-spectra-database). However, at higher concentrations, a
photon emitted by one Ge atom and propagating towards the detector can be absorbed by
another Ge atom in its fundamental state (self-absorption), resulting in a reduction of the
peak intensity of the spectral line. Small instances of self-absorption can be adequately
modeled using a quadratic model and can therefore be considered at high elemental
concentrations. In our case, we prefer the quadratic model for constructing our semi-
quantitative images because Ge concentrations in the metal reached up to 2.5 wt.% (i.e.
25,000 ppm). The quantification is limited by the 110 ppm (2σ) detection limit of the EPMA.
With a mean Ge concentration of 13,426 ppm in the metal and the standard error of the regression (S<sub>y/x</sub>) of 138.3 ppm, this results in a relative error of approximately 1% at the 70% confidence level (1σ). The high R<sup>2</sup> value demonstrates the robustness of the calibration. Both of these factors indicate that the model predictions are precise and well within the acceptable range of measurement errors, making LIBS imaging a reliable tool for reconstructing semi-quantitative images from punctual EPMA.

b. Silicate phase

We applied the same approach to establish a Ge calibration for the silicate phase.
Due to the heterogeneities in this phase, i.e. the presence of metal beads (see Section 3.1.),
only 1-mm-long one profile at the bottom-center of sample MS-20M (Fig. 6) was used to fit
the μLIBS intensities. Because this sample had the highest Ge concentration in the silicate
phase, this calibration covers the entire range of Ge concentrations measured in all samples.

Because the Ge concentrations in the silicate phases did not exceed 6000 ppm in any
sample, we employed least-squares linear regression to construct our model (Fig. 5). The
determination coefficient (R² = 0.9316) and standard error (S<sub>y/x</sub> of 57.7) are robust despite
the multiple heterogeneities observed in the sample. We note that the y-intercept of the
calibration curve for silicate glass is much higher compared to that for the metal matrices.
<figure><img src="image_8.png" /><figcaption>**Fig. 5.** Calibration curve for Ge in the silicate phase, obtained from the intensity of the Ge LIBS emission line at 265.1 nm (arbitrary units) and Ge concentrations (ppm) measured by microprobe. Upper and lower confidence limits indicate the 70% confidence level.</figcaption></figure>

### 3.3. Semi-quantitative maps

The variations of Ge, Ni, Si, Fe, and Al concentrations in our samples are clearly visible in the qualitative µLIBS elemental maps. The relationships between the intensities of the elemental peaks and the Ge concentrations at individual points demonstrate that it is possible to transform the intensity maps into quantitative concentration maps [17]. We tested both the linear and quadratic calibration models for the metal phase but, given the large range of Ge concentrations (from hundreds of ppm to several wt.%), selected the quadratic model to account for potential self-absorption. For the silicate phase, we selected the linear calibration model to produce semi-quantitative images (Fig. 6). We present for the first time semi-quantitative Ge maps of three experimental samples with distinct run times: MS-20M (20 min), MS-3H-B (3 h), and MS-12H (12 h). These maps are colorized from dark red (0 ppm) to yellow/white for the highest concentrations (18,000 ppm) in the metal and from dark blue (0 ppm) to light blue/white for the highest concentrations in the silicate (21,000 ppm). We note that the highest concentrations are not representative of the entire samples because the highest concentrations in the metal were measured at the metal–
silicate interface, whereas those in the silicate were measured in the small metal beads (appearing as white dots within the silicate in Fig. 6). The metal-silicate interface and the exterior of the capsule are indicated by white outlines one pixel thick, although the metal-silicate interface overlaps the high Ge concentrations at the interface.

These three samples show the same characteristics identified from the intensity images (Fig. 2) concerning the Ge distribution within the different phases. Here, though, the calibrated color scales emphasize the contrast between areas rich in Ge and those where Ge concentrations are below the microprobe detection limit. This ensures better definition of the Ge diffusion front in the metal.

<figure><img src="image_9.png" /><figcaption>**Fig. 6.** Semi-quantitative Ge maps of three samples: MS-20M (20 min), MS-3H-B (3 h), and MS-12H (12 h). These maps were obtained by applying our silicate (Fig. 5) and metal (Fig. 4) calibrations to the Ge µLIBS intensity images (Fig. 2). Orange lines correspond to the location of metal profiles (MP) that were used to construct the metal model. The green line corresponds to the location of the silicate profile used to construct the silicate model. Unique Ge concentration scales are shown for</figcaption></figure>
both phases. The white rectangle on sample MS-12H approximates the area from which average profiles were extracted.

### 3.4. Average profiles

The high resolution and semi-quantitative concentrations of our Ge maps allowed us to produce average concentration profiles for the three samples shown in **Fig. 6**. The purpose of making average profiles for these large samples with extensive areas of interest is to mitigate sample heterogeneities and thereby increase precision in the calculation of Ge diffusion coefficients *D*(Ge). In the metal, we averaged hundreds of profiles throughout the same side of an entire capsule. These profiles begin at the metal-silicate interface ($x_0 = 0 \mu m$) and progress toward the exterior edge of the metal capsules. To define $x_0$ for each profile, we used the Ni mask that was used to distinguish between the metal and silicate phases. The profile step was chosen to be 15 $\mu m$ to match the resolution of our µLIBS intensity images. For each value of x ($x = 0, x = 15 \mu m, ...$), the µLIBS Ge intensities were averaged and converted to Ge concentrations using the quadratic calibration model (**Fig. 4**).

For instance, in the averaged profile of MS-3H-B, the value for line 1 (at $x = 0 \mu m$) was derived from 20 individual pixels, each representing one Ge (265.1 nm) intensity value per pixel. In comparison, the value for line 2 (at $x = 15 \mu m$) was obtained from 34 pixels (**Supplementary Fig. S2**). Since the distribution of Ge is not uniform across the entire width of the metal capsule, particularly in the outermost parts at the top and bottom and at the metal-silicate interface, the number of pixels considered in the average for each line may differ, represented by the white rectangle in **Supplementary Fig. S2**. After all average intensities were extracted, we applied our model to quantify Ge concentrations in ppm, allowing us to quantify Ge to the ppm level.

Using the 70% confidence limits calculated for our metal calibration, we determined the minimum and maximum errors on the averaged Ge concentrations and the mean relative standard error for each sample: $1\sigma$ RSE = 8.7% and 4.2% for MS-3H-B and MS-12H, respectively. These propagated errors include the initial standard deviation of the microprobe measurements, the 10% variability in the LIBS signal, and the resulting errors introduced by the quadratic fit at the 70% confidence level. Although, they are notably higher than the mean relative standard deviation of microprobe measurements (1.9% at the same confidence level), we stress that here, each Ge concentration value is averaged from
approximately 200 profiles, mitigating all sample heterogeneities. We also constructed an average profile for the MS-20M sample. However, the profile is only 60 µm long and, with a step size of 15µm, the resulting profile could not be utilized to calculate a diffusion coefficient. Therefore, it will not be presented here. Furthermore, because our approach employing average profiles to study Ge diffusion is both novel and exploratory, only two samples were selected for the following discussion. It is beyond the scope of this study to present all the diffusion profiles; a more comprehensive investigation of the diffusion processes will be presented in a future contribution.

To calculate $D(\text{Ge})_{\text{metal}}$ for samples MS-3H-B and MS-12H, we considered diffusion at 1 GPa and 1350 °C in a semi-infinite medium [35] from molten silicate to solid Fe-Ni metal with respective starting Ge concentrations of 3147 ppm and 0 ppm. For these samples, we obtained $D(\text{Ge})_{\text{metal}} = 2.02\text{E-13} \pm 2.5\text{E-14 m}^2/\text{s}$ (MS-3H-B) and $4.03\text{E-13} \pm 3.6\text{E-14 m}^2/\text{s}$ (MS-12H).

## 4. Discussion

Our semi-quantitative Ge maps are a novel approach to studying experimental samples that simulate the thermodynamic conditions controlling core formation and planetary differentiation. Our results demonstrate that we can now image the progressive diffusion of Ge in Fe<sub>90</sub>Ni<sub>10</sub> metal as analogous to iron meteorites and, more broadly, metallic planetary reservoirs.

### 4.1. *Time efficiency and high-resolution of µLIBS imaging*

We estimate the µLIBS acquisition time over three spectral ranges for a single sample, and the associated processing to produce the elemental images, to be a few hours; 2h of scan per image and a few hours of processing (note that 6 images are processed at the same time in a single file). In contrast, traditional methods, particularly microprobe, require an average of 2.5 h to acquire a single concentration profile. Moreover, our LIBS imaging method, calibration of intensities to known concentrations, and averaging of diffusion profiles from hundreds of individual profiles significantly reduces acquisition time and uncertainties on concentration measurements by mitigating the impacts of sample
heterogeneities on profile analysis. For example, acquiring 100 profiles by microprobe
would take approximately 250 hours, but only a few hours with µLIBS.

Another powerful advantage of the µLIBS is the high resolution (15 µm) when
measuring trace element concentrations. Usually LA-ICP-MS technique is used to map trace
elements with a very low detection limit. In our case, several LA-ICP-MS measurements on
our samples show that the spot size should be between 73 µm with 5 Hz frequency and 133
µm and 10 Hz for the lowest concentrations, resulting in a deep ablation of the sample
surface and very large spot sizes for a poor resolution compared to the LIBS'. Using µLIBS to
map and quantify trace elements (especially Ge) allows us to combine all the benefit of the
high-resolution of the electron microprobe with the low detection limits of the LA-ICP-MS,
at the ppm level in our case.

## 4.2. *Calibration curve distinctions*

The calibration curves derived for the metal and silicate models show significant
differences. These variations between the two calibration models arise from their distinct
data distribution. Specifically, the metal model is built on an uneven data distribution, with
many more data points at lower Ge concentrations, whereas the silicate model is built on a
much more balanced data distribution. This suggests that greater precision is achieved at
lower Ge concentrations in the metal phase, whereas the silicate model is optimized only
within the specific concentration range addressed herein. The use of distinct calibration
curves reinforces the need to use separate masks when generating intensity images.

## 4.3. *Average profiles and Ge diffusion*

Our Ge concentration profiles reflect Ge diffusion from the silicate to the metal, and
represent the first attempt to study and quantify the chemical kinetics of Ge by calculating
diffusion coefficients between metal and silicate. We obtained two different Ge diffusion
coefficients for two different experiments (MS-3H-B and MS-12H). The two values show
important variations outside the 2σ SE, with a factor 2 between samples at the same P and
T. As the diffusivity is characteristic of the materials and conditions, it shouldn't change with
time if held at the same conditions. We can easily explain these differences by the fact that
the experiment at 3 hours is not fully chemically equilibrated compared to the one at 12
hours. For the further interpretations, only the value of Ge diffusion coefficient of the sample MS-12H will be used.

Nevertheless, only a few studies currently provide Ge diffusion coefficients in metals at different thermodynamic conditions (P, T) and for different diffusion modes: "volume diffusion" (lattice diffusion and self-diffusion) of Ge at 1 bar and 550-860 °C [36], and "grain boundary diffusion" between high-purity Fe metal and Fe-Ni metal in the IIA iron meteorite Coahuila (single crystal kamacite, a Ni-poor Fe-Ni metal phase) or in the metal phase the Springwater pallasite (olivine + polycrystalline kamacite) at 1 bar or 1 GPa and 1150-1400 °C [37]. Ge self-diffusion coefficients at 1 bar (1E-22 to 1E-16 m²/s) [36] are lower than Ge grain-boundary diffusion coefficients at 1 GPa in iron meteorites (1E-14 to 1E-13 m²/s) [37] due to the different diffusion mechanisms. Consequently, our calculated Ge diffusion coefficients (2E-13 to 4E-13 m²/s) are most comparable to those in iron meteorites and pallasites. Indeed, the mode of diffusion in our experiments resembles grain-boundary diffusion, implying that Ge diffusion is faster in cases where it diffuses between two distinct phases. Consequently, in the context of planetesimal formation [38,39], chemical equilibration of Ge between a silicate magma ocean and droplets of segregated liquid metal should be faster than between large ponds of metal at the base of the magma and the liquid core of a planetesimal.

Moreover, previously determined Ge diffusion coefficients in silica glass are strongly temperature dependent, with D(Ge)_{silicate} varying between 6E-14 and 1E-16 m²/s between 1400°C and 1150°C respectively [40], which are comparable to Ge volume diffusion in metal. In that case, Ge diffusion between a liquid silicate phase and a solid metal phase would also be faster than "Pure" diffusion of Ge in an amorphous silicate phase.

This study should be regarded as a preliminary exploration of the potential of combining semi-quantitative μLIBS with diffusion modeling. Further applications of this method will enable the determination of cooling rates of solidifying metals from Ge data, as previously done by comparing analyzed Ni profiles across taenite (Fe-Ni) lamellae with modeled Ni diffusion profiles in kamacite [41] to determine metallographic cooling rates for pallasites. We also expect that our approach could be extended to different phases (diffusion within a silicate phase and within a metal phase [37]) and different chemical exchange mechanisms other than pure diffusion (e.g., evaporation, crystallization dynamics,
metal solidification, etc.). We will further extend this approach to experimental metal-
silicate samples that will be performed under different P, T, fO₂ conditions to constrain
processes of Ge distribution in reservoirs during planetesimal formation. Hence, this will
also highlight the thermodynamic dependency of the Ge diffusion coefficient.

**5. Conclusions**

We developed a semi-quantitative µLIBS technique for the rapid, high-resolution characterization of elemental distributions in equilibrating, heterogeneous silicate–metal systems, here focusing on Ge diffusion from a silicate phase to a metallic phase in high temperature/high pressure experimental samples. The implementation of this method does not require extensive sample preparation, has a high analytical frequency (100 Hz), and this method is highly complementary to punctual spot analyses, while also providing a true 2D view of diffusion processes in centimeter-sized samples.

We cross-calibrated µLIBS analyses against punctual electron microprobe analyses to obtain quantitative, high-resolution Ge concentration maps capable of detecting concentrations down to a few hundred ppm. The µLIBS maps were quantified using phase-specific calibrations to avoid any bias resulting from differences in laser-matter interactions (similar to matrix effects). Because the Ge concentrations can be accurately quantified, this technique overcomes some limitations due to the time and analytical costs of traditional analytical methods. Indeed, we acquired detailed images and concentration profiles significantly faster (here, by ~2 orders of magnitude) than by microprobe alone, offering a substantial advantage over conventional methods. This time efficiency, as well as the ability to visualize diffusion fronts in materials analogous to those in planetary reservoirs under the conditions of planetesimal formation, represent significant advancements in the analysis of experimental petrology samples, as well as more complex geological or extraterrestrial samples.

The experimental metal–silicate setup used herein aimed to simulate the processes
of metal–silicate differentiation in planetary bodies. The silicate phase represents a
compositionally simplified shallow magma ocean of a planetesimal in its early stage of
differentiation. Additionally, by using sealed metal capsules to prevent any evaporation, we
simulated chemical exchanges at the core–mantle boundary deep beneath the surface of a planetesimal during its differentiation. Based on our Ge maps and averaged concentration profiles, we determined new metal–silicate Ge diffusivities at high pressure/high temperature.

Our sample-averaged profiles enabled us to quantify the migration of germanium from Ge-bearing silicate to metal. This approach allows for a more precise determination of Ge diffusion parameters than individual profiles. These parameters can then be used to identify time-constrained processes that ultimately shape the Ge concentrations in planetary metal and silicate reservoirs. Our method and results can be applied to different matrices (metal alloys and silicate glasses) in extraterrestrial samples to determine cooling rates, parent body sizes, and gain further understanding of chemical exchanges between metal and silicate phases, and between two different metal phases at the bottom of the magma ocean during planetesimal formation.

## Acknowledgments

We thank Delphine Lequin for the assistance on the experiments (CoMaX platform at CRPG), Jean-Luc Devidal (LMV – Clermont-Ferrand) for electron microprobe and LA-ICP-MS measurements and Julien Zollinger, Jacob Kennedy (IJL – Nancy) for metal rods manufacturing. Robert Dennen is thanked for his careful English editing of the manuscript. The authors acknowledge the ANR – France (French National Research Agency) for its financial support of the PlanetGEM project (Grant#ANR-21-CE49-0011 to B.L.) and the Lorraine Earth and Environment Observatory (OTELo) 2021 program. This is CRPG contribution 2861.

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

**Data availability**

The original spectral LIBS datacubes can be shared upon request to the corresponding author.

**Declaration of generative AI and AI-assisted technologies in the writing process.**

During the preparation of this work the author(s) used ChatGPT and DeepL in the writing process in order to improve the readability and language of the manuscript. After using this tool/service, the author(s) reviewed and edited the content as needed and take(s) full responsibility for the content of the published article.

**Appendix A. Supplementary data**

Additional supporting information in Supplementary material.
References

[1] B. Luais, Isotopic fractionation of germanium in iron meteorites: Significance for nebular condensation, core formation and impact processes, Earth Planet. Sc. Lett. 262 (2007) 21–36. https://doi.org/10.1016/j.epsl.2007.06.031.

[2] B. Luais, Germanium chemistry and MC-ICPMS isotopic measurements of Fe–Ni, Zn alloys and silicate matrices: Insights into deep Earth processes, Chem. Geol. 334 (2012) 295–311. https://doi.org/10.1016/j.chemgeo.2012.10.017.

[3] O.J. Rouxel, B. Luais, Germanium Isotope Geochemistry, Rev. Mineral Geochem. 82 (2017) 601–656. https://doi.org/10.2138/rmg.2017.82.14.

[4] R. Belissont, M.-C. Boiron, B. Luais, M. Cathelineau, LA-ICP-MS analyses of minor and trace elements and bulk Ge isotopes in zoned Ge-rich sphalerites from the Noailhac – Saint-Salvy deposit (France): Insights into incorporation mechanisms and ore deposition processes, Geochim. Cosmochim. Ac. 126 (2014) 518–540. https://doi.org/10.1016/j.gca.2013.10.052.

[5] A. Cugerone, B. Cenki-Tok, A. Chauvet, E. Le Goff, L. Bailly, O. Alard, M. Allard, Relationships between the occurrence of accessory Ge-minerals and sphalerite in Variscan Pb-Zn deposits of the Bossost anticlinorium, French Pyrenean Axial Zone: Chemistry, microstructures and ore-deposit setting, Ore Geol. Rev. 95 (2018) 1–19. https://doi.org/10.1016/j.oregeorev.2018.02.016.

[6] A.J. Campbell, M. Humayun, Compositions of group IVB iron meteorites and their parent melt, Geochim. Cosmochim. Ac. 69 (2005) 4733–4744. https://doi.org/10.1016/j.gca.2005.06.004.

[7] R. Belissont, M. Muñoz, M.-C. Boiron, B. Luais, O. Mathon, Distribution and oxidation state of Ge, Cu and Fe in sphalerite by µ-XRF and K-edge µ-XANES: insights into Ge incorporation, partitioning and isotopic fractionation, Geochim. Cosmochim. Ac. 177 (2016) 298–314. https://doi.org/10.1016/j.gca.2016.01.001.

[8] R. Belissont, M. Munoz, M.-C. Boiron, B. Luais, O. Mathon, Germanium Crystal Chemistry in Cu-Bearing Sulfides from Micro-XRF Mapping and Micro-XANES Spectroscopy, Minerals 9 (2019) 227. https://doi.org/10.3390/min9040227.

[9] A. Cugerone, B. Cenki-Tok, E. Oliot, M. Muñoz, F. Barou, V. Motto-Ros, E. Le Goff, Redistribution of germanium during dynamic recrystallization of sphalerite, Geology 48 (2020) 236–241. https://doi.org/10.1130/G46791.1.

[10] G. Florin, B. Luais, T. Rushmer, O. Alard, Influence of redox processes on the germanium isotopic composition of ordinary chondrites, Geochim. Cosmochim. Ac. 269 (2020) 270–291. https://doi.org/10.1016/j.gca.2019.10.038.

[11] A. El Korh, B. Luais, M.-C. Boiron, E. Deloule, D. Cividini, Investigation of Ge and Ga exchange behaviour and Ge isotopic fractionation during subduction zone metamorphism, Chem. Geol. 449 (2017) 165–181. https://doi.org/10.1016/j.chemgeo.2016.11.017.
[12] G. Florin, O. Alard, B. Luais, T. Rushmer, Abundances of siderophile elements in H-chondrite metal grains: Implications for the origin of metal in unequilibrated ordinary chondrites, *Geochim. Cosmochim.* Ac. 341 (2023) 1–15. https://doi.org/10.1016/j.gca.2022.11.014.

[13] J. Coron, S. Papier, S. Decrée, V. Ferreira, L. Duponchel, J.M. Baele, Investigating critical metals Ge and Ga in complex sulphide mineral assemblages using LIBS mapping, *Spectrochim. Acta B* 219 (2024) 107004. https://doi.org/10.1016/j.sab.2024.107004.

[14] D. Menut, P. Fichet, J.-L. Lacour, A. Rivoallan, P. Mauchien, Micro-laser-induced breakdown spectroscopy technique: a powerful method for performing quantitative surface mapping on conductive and nonconductive samples, *Appl. Opt.* 42 (2003) 6063. https://doi.org/10.1364/AO.42.006063.

[15] H. Bette, R. Noll, High speed laser-induced breakdown spectrometry for scanning microanalysis, *J. Phys. D: Appl. Phys.* 37 (2004) 1281–1288. https://doi.org/10.1088/0022-3727/37/8/018.

[16] R. Noll, Laser-Induced Breakdown Spectroscopy: Fundamentals and Applications, Springer Berlin Heidelberg, Berlin, Heidelberg, 2012. https://doi.org/10.1007/978-3-642-20668-9.

[17] F. Trichard, L. Sorbier, S. Moncayo, Y. Blouët, C.-P. Lienemann, V. Motto-Ros, Quantitative elemental imaging of heterogeneous catalysts using laser-induced breakdown spectroscopy, *Spectrochim. Acta B* 133 (2017) 45–51. https://doi.org/10.1016/j.sab.2017.04.008.

[18] C. Fabre, D. Devismes, S. Moncayo, F. Pelascini, F. Trichard, A. Lecomte, B. Bousquet, J. Cauzid, V. Motto-Ros, Elemental imaging by laser-induced breakdown spectroscopy for the geological characterization of minerals, *J. Anal. At. Spectrom.* 33 (2018) 1345–1353. https://doi.org/10.1039/C8JA00048D.

[19] C. Fabre, L. Marulier, B. Monfaredi, V. Motto-Ros, B. Bousquet, A. Eglinger, A. Tarantola, Exploring Rare Earth Elements in complex microscopic mineral phases: Inputs from µLIBS imaging, *Spectrochim. Acta B* 216 (2024) 106954. https://doi.org/10.1016/j.sab.2024.106954.

[20] V. Motto-Ros, S. Moncayo, F. Trichard, F. Pelascini, Investigation of signal extraction in the frame of laser induced breakdown spectroscopy imaging, *Spectrochim. Acta B* 155 (2019) 127–133. https://doi.org/10.1016/j.sab.2019.04.004.

[21] L. Jolivet, M. Leprince, S. Moncayo, L. Sorbier, C.-P. Lienemann, V. Motto-Ros, Review of the recent advances and applications of LIBS-based imaging, *Spectrochim. Acta B* 151 (2019) 41–53. https://doi.org/10.1016/j.sab.2018.11.008.

[22] C. Fabre, K. Trebus, A. Tarantola, J. Cauzid, V. Motto-Ros, P. Voudouris, Advances on microLIBS and microXRF mineralogical and elemental quantitative imaging, *Spectrochim. Acta B* 194 (2022) 106470. https://doi.org/10.1016/j.sab.2022.106470.
[23] T. Takahashi, B. Thornton, Quantitative methods for compensation of matrix effects and self-absorption in Laser Induced Breakdown Spectroscopy signals of solids, Spectrochim. Acta B 138 (2017) 31–42. https://doi.org/10.1016/j.sab.2017.09.010.

[24] J. El Haddad, E.S. de Lima Filho, F. Vanier, A. Harhira, C. Padioleau, M. Sabsabi, G. Wilkie, A. Blouin, Multiphase mineral identification and quantification by laser-induced breakdown spectroscopy, Miner. Eng. 134 (2019) 281–290. https://doi.org/10.1016/j.mineng.2019.02.025.

[25] A. Nardecchia, V. Motto-Ros, L. Duponchel, Saturated signals in spectroscopic imaging: why and how should we deal with this regularly observed phenomenon?, Anal. Chim. Acta 1157 (2021) 338389. https://doi.org/10.1016/j.aca.2021.338389.

[26] L. Duponchel, A. Cugerone, M. Muñoz, V. Motto-Ros, Diagnosis and correction methods for spectral interference in the framework of LIBS imaging, Spectrochim. Acta B 207 (2023) 106758. https://doi.org/10.1016/j.sab.2023.106758.

[27] D.C. Rubie, F. Nimmo, H.J. Melosh, Formation of the Earth's Core, in: Treatise on Geophysics, Elsevier, 2015: pp. 43–79. https://doi.org/10.1016/B978-0-444-53802-4.00154-8.

[28] P. Condamine, S. Tournier, B. Charlier, E. Médard, A. Triantafyllou, C. Dalou, L. Tissandier, D. Lequin, C. Cartier, E. Füri, P.G. Burnard, S. Demouchy, Y. Marrocchi, Influence of intensive parameters and assemblies on friction evolution during piston-cylinder experiments, Am. Mineral. 107 (2022) 1575–1581. https://doi.org/10.2138/am-2022-7958.

[29] D. Fougerouse, A. Cugerone, S.M. Reddy, K. Luo, V. Motto-Ros, Nanoscale distribution of Ge in Cu-rich sphalerite, Geochim. Cosmochim. Ac. 346 (2023) 223–230. https://doi.org/10.1016/j.gca.2023.02.011.

[30] A. Cugerone, B. Cenki-Tok, M. Muñoz, K. Kouzmanov, E. Oliot, V. Motto-Ros, E. Le Goff, Behavior of critical metals in metamorphosed Pb-Zn ore deposits: example from the Pyrenean Axial Zone, Miner. Deposita 56 (2021) 685–705. https://doi.org/10.1007/s00126-020-01000-9.

[31] V. Motto-Ros, E. Negre, F. Pelascini, G. Panczer, J. Yu, Precise alignment of the collection fiber assisted by real-time plasma imaging in laser-induced breakdown spectroscopy, Spectrochim. Acta B 92 (2014) 60–69. https://doi.org/10.1016/j.sab.2013.12.008.

[32] A.C. Simon, T. Pettke, P.A. Candela, P.M. Piccoli, C.A. Heinrich, The partitioning behavior of As and Au in S-free and S-bearing magmatic assemblages, Geochim. Cosmochim. Ac. 71 (2007) 1764–1782. https://doi.org/10.1016/j.gca.2007.01.005.

[33] K. Righter, C. King, L. Danielson, K. Pando, C.T. Lee, Experimental determination of the metal/silicate partition coefficient of Germanium: Implications for core and mantle differentiation, Earth Planet. Sc. Lett. 304 (2011) 379–388. https://doi.org/10.1016/j.epsl.2011.02.015.
[34] J. Siebert, A. Corgne, F.J. Ryerson, Systematics of metal-silicate partitioning for many siderophile elements applied to Earth's core formation, Geochim. Cosmochim. Ac. 75 (2011) 1451-1489. https://doi.org/10.1016/j.gca.2010.12.013.

[35] J. Crank, The mathematics of diffusion, second ed., Oxford University Press, Oxford, 1975.

[36] G. Vogel, G. Hettich, H. Mehrer, Self-diffusion in intrinsic germanium and effects of doping on self-diffusion in germanium, J. Phys. C: Solid State Phys. 16 (1983) 6197-6204. https://doi.org/10.1088/0022-3719/16/32/012.

[37] K. Righter, A.J. Campbell, M. Humayun, Diffusion of trace elements in FeNi metal: Application to zoned metal grains in chondrites, Geochim. Cosmochim. Ac. 69 (2005) 3145-3158. https://doi.org/10.1016/j.gca.2005.01.010.

[38] M. Roskosz, B. Luais, H.C. Watson, M.J. Toplis, C.M.O. Alexander, B.O. Mysen, Experimental quantification of the fractionation of Fe isotopes during metal segregation from a silicate melt, Earth Planet. Sc. Lett. 248 (2006) 851-867. https://doi.org/10.1016/j.epsl.2006.06.037.

[39] D.C. Rubie, D.J. Frost, U. Mann, Y. Asahara, F. Nimmo, K. Tsuno, P. Kegler, A. Holzheid, H. Palme, Heterogeneous accretion, composition and core-mantle differentiation of the Earth, Earth Planet. Sc. Lett. 301 (2011) 31-42. https://doi.org/10.1016/j.epsl.2010.11.030.

[40] M.V. Minke, K.A. Jackson, Diffusion of germanium in silica glass, J. Non-Cryst. Solids 351 (2005) 2310-2316. https://doi.org/10.1016/j.jnoncrysol.2005.04.052.

[41] J. Yang, J.I. Goldstein, E.R.D. Scott, Main-group pallasites: Thermal history, relationship to IIIAB irons, and origin, Geochim. Cosmochim. Ac. 74 (2010) 4471-4492. https://doi.org/10.1016/j.gca.2010.04.016.
Author statement: CRediT

Semi-quantitative µLIBS mapping of germanium diffusion between
metal and silicate during planetary core–mantle segregation

Baptiste Le Bellego<sup>a, b, *</sup>, Vincent Motto-Ros<sup>c</sup>, Béatrice Luais<sup>b</sup>, Cécile Fabre<sup>d</sup>, Célia Dalou<sup>b</sup>, Pierre Condamine<sup>e</sup> and Laurent Tissandier<sup>b</sup>

<sup>a</sup> Université de Lorraine, CNRS, CRPG, F-54000 Nancy, France

<sup>b</sup> Centre de Recherches Pétrographiques et Géochimiques (CRPG), Université de Lorraine, CNRS, UMR 7358, 15 Rue Notre Dame des Pauvres, BP 20, CEDEX, F-54501 Vandœuvre-lès-Nancy, France

<sup>c</sup> Institut Lumière Matière UMR 5306, Université Lyon 1 – CNRS, Université de Lyon, Villeurbanne, France

<sup>d</sup> GeoRessources, UMR7359, CNRS, Université de Lorraine, F54000 Nancy, France

<sup>e</sup> Laboratoire Magmas et Volcans – CNRS, Clermont-Ferrand, France

* Corresponding author. E-mail address: baptiste.le-bellego@univ-lorraine.fr, 15 Rue Notre Dame des Pauvres, BP 20, CEDEX, F-54501 Vandœuvre-lès-Nancy, France

**Baptiste Le Bellego:** Methodology, Validation, Formal analysis, Investigation, Data curation, Writing – original draft, Writing – review & editing, Visualization. **Vincent Motto-Ros:** Methodology, Software, Formal analysis, Investigation, Resources, Data curation, Visualization. **Béatrice Luais:** Conceptualization, Methodology, Validation, Resources, Writing – Review & Editing, Supervision, Project administration, Funding acquisition. **Cécile Fabre:** Validation, Writing – Review & Editing, Visualization. **Célia Dalou:** Conceptualization, Methodology, Validation, Writing – Review & Editing. **Pierre Condamine:** Methodology, Validation, Investigation. **Laurent Tissandier:** Conceptualization, Methodology.
**Declaration of interests**

[x] 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.

[ ] The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

<figure><img src="image_10.png" /></figure>
Planet differentiation (metal-silicate segregation)

<figure><img src="image_11.png" /></figure>

Piston cylinder HP-HT experiments

<figure><img src="image_12.png" /></figure>

μLIBS Imaging

<figure><img src="image_13.png" /></figure>

High-resolution semi-quantitative Images

<figure><img src="image_14.png" /></figure>

<figure><img src="image_15.png" /></figure>

Modelling

EPMA measurments

Ge diffusion quantification

Ge metal-silicate diffusion coefficients

<figure><img src="image_16.png" /></figure>
Highlights

Semi-quantitative µLIBS mapping of germanium diffusion between
metal and silicate during planetary core–mantle segregation

Baptiste Le Bellego a, b, *, Vincent Motto-Ros c, Béatrice Luais b, Cécile Fabre d, Célia Dalou b, Pierre Condamine e and Laurent Tissandier b

* Germanium diffusion fronts in metal and silicate phases can be imaged by µLIBS.

* We conducted a study on HP-HT sample under planetesimal formation conditions.

* 2 concentration models are proposed to quantify Ge diffusion in metal and silicate.

* We constructed high-resolution (15 µm) semi-quantitative Ge images at ppm levels.

* Metal-silicate Ge diffusion coefficients were calculated for the first time.

<footnote>a Université de Lorraine, CNRS, CRPG, F-54000 Nancy, France</footnote>

<footnote>b Centre de Recherches Pétrographiques et Géochimiques (CRPG), Université de Lorraine, CNRS, UMR 7358, 15 Rue Notre Dame des Pauvres, BP 20, CEDEX, F-54501 Vandœuvre-lès-Nancy, France</footnote>

<footnote>c Institut Lumière Matière UMR 5306, Université Lyon 1 – CNRS, Université de Lyon, Villeurbanne, France</footnote>

<footnote>d GeoRessources, UMR7359, CNRS, Université de Lorraine, F54000 Nancy, France</footnote>

<footnote>e Laboratoire Magmas et Volcans – CNRS, Clermont-Ferrand, France</footnote>

<footnote>* Corresponding author. E-mail address: baptiste.le-bellego@univ-lorraine.fr, 15 Rue Notre Dame des Pauvres, BP 20, CEDEX, F-54501 Vandœuvre-lès-Nancy, France</footnote>