Dalou et al.
Progress in Earth and Planetary Science(2024) 11:27
https://doi.org/10.1186/s40645-024-00629-8

Progress in Earth andPlanetary Science

Open Access

REVIEW

Review of experimental and analyticaltechniques to determine H, C, N, and S solubility
and metal–silicate partitioning during planetarydifferentiation
Celia Dalou1*, Terry‑Ann Suer2, Laurent Tissandier1, Weronika L. Ofierska3, Alice Girani3 and Paolo A. Sossi3

Abstract
During their formation, terrestrial planets underwent a magma ocean phase during which their metallic cores segre‑
gated from their silicate mantles and their early atmospheres formed. These planetary formation processes resulted
in a redistribution of the abundances of highly volatile elements (HVEs, such as H, C, N, and S) between the plan‑ets’ metallic cores, silicate mantles, and atmospheres. This review presents the numerous experimental techniques
used to simulate the conditions and identify the parameters that influenced the behavior of HVEs during planetary
formation. We also review the analytical techniques used to characterize the different types of experimental sam‑ples and quantify the distribution of HVEs between metallic and silicate phases, as well as their solubilities in silicate
glasses. This exhaustive review targets students and young researchers beginning their work on the subject, or, moregenerally, scientists seeking a better understanding of this field of research.
Keywords Differentiation, Magma ocean, Core formation, Evaporation, Experimental techniques, Low-pressure, Highpressure, Oxygen fugacity, Analytical techniques, Partition coefficients
1 Introduction
The development of life-supporting molecules depends
on the availability of volatile elements (H, C, N, O, S) at
a planet’s surface, which, alongside other critical parameters, has allowed the development and maintenance of astable biosphere on Earth (Kasting and Siefert 2002). The
prevailing surface conditions on terrestrial planets weremainly determined by the composition of their atmospheres and the existence (or lack) of a magnetic field
protecting their surfaces from solar winds. Furthermore,*Correspondence:
Celia Dalou
celia.dalou@univ-lorraine.fr
1
Université de Lorraine, CNRS, CRPG, 54000 Nancy, France
2
Laboratory for Laser Energetics, University of Rochester, Rochester, NY,USA
3
Institute of Geochemistry and Petrology, ETH Zürich, 8092 Zurich,
Switzerland

the long-term stability of these surface conditions hinges
upon the prevalence and rates of plate tectonics, which
recycles volatile elements between a planet’s interior andits surface (e.g., Dehant et al. 2007; Foley and Driscoll
2016). However, these present-day conditions are notrepresentative of the entire history of a rocky planet,
which, at times, was partially to completely molten, i.e.,characterized by a magma ocean stage(s). Magma oceans
are thought to have facilitated metallic core segregation,
as well as the formation of early atmospheres, via solidification and degassing. Thus, the magma ocean stage likely
set the initial volatile element distributions between theinteriors and surfaces of rocky planets (Elkins-Tanton2008).
The current composition of a terrestrial planet’s
core depends not only on the bulk composition of theplanet, but also on the solubility of volatile elementsin the magma ocean and the metal–silicate partition© The Author(s) 2024. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which
permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to theoriginal author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images orother third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line
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Dalou et al. Progress in Earth and Planetary Science(2024) 11:27

coefficients of H, C, N, O, and S, which vary with pressure, temperature, and oxygen fugacity. Over the last two
decades, the effects of these conditions on the redistribution of highly volatile elements (HVEs; here, H, C, N, andS) have been investigated experimentally by simulating
magma ocean degassing and core formation on different
rocky planets. Such experiments are used to determine
HVE solubilities and metal–silicate partition coefficients,
respectively.
Large-volume apparatuses have been used in most ofthese experimental studies, achieving pressures from 0.5
to 24 GPa and temperatures up to 2400 °C (e.g., Roskosz
et al. 2013; Boujibar et al. 2014; Chi et al. 2014; Li et al.
2016; Dalou et al. 2017; Clesi et al. 2018; Malavergne
et al. 2019; Grewal et al. 2019, 2021; Fichtner et al. 2021).
Recently, superliquidus (i.e., melting) experiments performed in laser-heated diamond anvil cells (LHDACs)
have extended the range of these measurements to conditions considered relevant to core formation on Earth(i.e., ≥ 45–55 GPa, ≥ 4000 °C; e.g., Suer et al. 2017; Mahan
et al. 2018; Fischer et al. 2020; Tagawa et al. 2021; Blanchard et al. 2022). HVE solubility measurements in silicate liquids complement these metal–silicate partitioning
measurements and have enhanced our knowledge of volatile outgassing and cycling between Earth’s early mantle
and atmosphere (e.g., Libourel et al. 2003; Hirschmann
et al. 2012; Ardia et al. 2013; Armstrong et al. 2015; Newcombe et al. 2017; Boulliung et al. 2020; Bernadou et al.
2021; Dalou et al. 2022; Sossi et al. 2023). The choice ofanalytical techniques (bulk or local mass spectrometry,nuclear microprobe, or vibrational spectroscopy) to characterize HVE concentrations in both metal and silicate
phases depends on several criteria, including the sizes
and textures of experimental samples and anticipated
HVE concentrations in different phases.
Oxygen comprises ~ 44 wt.% of Earth’s mantle and,by extension, a similar fraction of the silicate mantles ofother terrestrial planets; it therefore plays a key role indetermining the speciation of volatile elements in atmospheres and mantles or magma oceans. The abundance ofO relative to the other rock-forming elements, together
with the pressure–temperature conditions at the surface of a magma ocean, determines the oxygen fugacity (fO2) at the surface. Because O is far in excess of theother major atmosphere-forming elements (the HVEs) inmagma oceans, the fO2 dictates their relative fugacities(e.g., the CO/CO2 and ­H2/H2O ratios) in the atmosphere(Hirschmann 2012; Sossi et al. 2020a). Moreover, because
different gaseous molecules have different solubilities
in silicate liquids (e.g., Yoshioka et al. 2019; Bower et al.
2022), the HVE distributions between planetary interiors
and atmospheres depend on fO2. On Earth, iron is by far
the most abundant redox-sensitive element, and, because

Page 2 of 33

the oxygen abundance in geologically relevant phases israrely measured directly (if ever), the redox state of iron­(Fe3+/Fe2+) is a key proxy for the fO2 of a system, be it
rock, fluid, or gas.
In this review, we summarize the above-mentioned
experimental and analytical techniques, as well as thelimitations and challenges associated with each experimental technique and chemical analyses of experimental charges.

2 Defining partitioning and solubility
2.1 Partitioning

In terrestrial planets, core formation represents thelargest mass transfer event in their history. The partitioning of elements between silicate and metallic
phases can be generally described as:

E n+ O n n−

2 silicate melt0
= Emolten
metal +

n
O2 ,
4 gas

(1)

where n is the oxidation state of element E dissolved in
the silicate melt. By definition, in its metallic form, element E has zero net charge. Hence, at equilibrium:K =a E 0 · f (O2 )n/4
a E n+ On−n= Dimetal−silicate ·2

γ E 0 · f (O2 )n/4
γ E n+ On−
n

,

2

(2)
where K is the equilibrium constant, a the activity, γ theactivity coefficient, and f the fugacity. The partition coefficient of an element of interest i between metallic andsilicate phases, Dimetal−silicate, is defined as Ximetal /Xisilicate,
where X denotes the mole fraction concentration of thatelement in each phase. Hence, the quantity Dimetal−silicate
in Eq. 2 is proportional to the molar ratio of element iin the silicate and metallic phases. Were core formation
to have occurred at equilibrium (or incomplete equilibrium; Zube et al. 2019), elements would have distributed between the Fe-rich metallic phase and the silicate
mantle according to their thermodynamically governed
partition coefficients. Consequently, elements with highDimetal−silicate values are siderophile and strongly depleted
in the mantle, whereas those with low Dimetal−silicate values are lithophile and should theoretically remain inchondritic proportions in the mantle (Wade and Wood2005).
The equilibrium constant, K, is related to the Gibbs
Free Energy change of the reaction (ΔGrxn) through:Grxn = −RT lnK .

(3)

Because both phases involved in the reaction are
liquids, to a first order, the entropy terms of the freeDalou et al. Progress in Earth and Planetary Science(2024) 11:27

Page 3 of 33

energy reaction are likely to be small, and partitioning
can be approximated as:

lnDimetal−silicate ≈ �H /RT ,lnDimetal−silicate = a +(4)where ΔH is related to the enthalpy of the reaction terms.
Importantly, because ΔH is nearly independent of temperature, the partition coefficient D tends to unity at infinite temperature.
Pressure changes are more difficult to predict, as they
depend upon the partial molar volumes and compressibilities of the volatile species in both the silicate liquid
and the metal. This is governed by:
dlnDimetal−silicate
V 0
=
,
(5)
dP
RT

γ metal
P
IW
b
+c −d
− ln  E n/2 ,
T
T
2
metal
γFe

(10)

where IW is the iron–wüstite redox buffer:

IW = −2log10

aFe
γFe XFe= −2log10.
aFeO
γFeO XFeO(11)

The constants a, b, c, and d are determined using multivariate least-squares linear regression of the measured Dimetal−silicate, P, T, and phase compositions (e.g.,
Wade and Wood 2005; Chidester et al. 2022; Suer et al.
2023). In other words, Eq. (10) allows us to constrain thedependence of the partition coefficients on P, T, and fO2.

T

which, when integrated, gives:
 metal−silicate 
Di,1
�V 0
ln
=−
(P2 − P1 ),metal−silicate
R
Di,2
T

2.2 Solubility(6)where V 0 is the molar volume change in the massaction equation, showing that lnDimetal−silicate is proportional to P (e.g., by taking P1 as 1 bar). Under the conditions of core formation, HVEs are expected to be at least
partially dissolved in the magma ocean (see Sect. 2.2,
below), and the system does not contain a gas phase; inthis case, it is seldom important to consider the pressure
dependence. The volume change of the reaction, even if
V 0 is constant, only plays a significant role when thepressure integral is large enough (e.g., the pressure range
relevant to core formation).
Alternatively, metal–silicate partitioning can be
expressed using the exchange coefficient with Fe (thedominant component of planetary cores), KD, such as:

EO n2 +nn
Fe ⇔ FeO + E,22n/2
and, KD = Dimetal−silicate /DFe .

(7)
(8)

where KD is related to the equilibrium constant K ofreaction (2), which can be defined in terms of KD andthe activity coefficients (γ) of the metal and silicate
phases by combining with Eq. 2 as:n/2
silicate
γFeO
γEmetalbP =a+ +c .
ln K = ln KD + ln n/2 + ln silicate
T
T
metal
γ
γFe
EOn/2

(9)
Then, lnDimetal−silicate can also be expressed in terms of
the above variables and constants as:

The solubility of a given species describes its capacity todissolve into a condensed phase. Determining the solubilities of major atmosphere-forming elements in silicate
liquids is therefore central to understanding the composition of the primitive atmosphere. The most abundant
molecule in Earth’s atmosphere, ­N2, dissolves in silicate
liquids at high oxygen fugacities as (Libourel et al. 2003):

N2gas = N2liquid ,(12)

implying an equilibrium relationship of the kind:

K = a(N2 )/f (N2 ).

(13)

Therefore, solubility laws require that the fugacity of therelevant gaseous species and the mole fraction of the dissolved species in the melt be defined. In such scenarios,
and if the quantity of the dissolved species is sufficiently
dilute so as not to perturb the structure of the solvent (silicate liquid), the solubilities can be fit to Henry’s Law as:

X(N2 ) = αf (N2 )β .

(14)

where X is the mole fraction, α is proportional to thequotient of K and the activity coefficient of ­N2, and β isthe stoichiometric coefficient. Some species show departures from Henry’s Law: notably, the dissolution reactionof ­H2O defines β = 0.5 at low fH2O (Hamilton et al. 1964;
Newcombe et al. 2017; Sossi et al. 2023). Therefore, controlling fugacity in experiments is invaluable for defining solubility laws. Moreover, the equilibrium constant K(and hence α) changes with temperature owing to the freeenergy change of the reaction, which can be determinedby varying T while keeping other variables constant.
Many homogeneous gas-phase reactions between
major atmosphere-forming species are, in turn, dependent on fO2. For example:

Dalou et al. Progress in Earth and Planetary Science(2024) 11:27

1
H2gas + O2gas = H2 Ogas ,
2

(15)

1
1
COgas + O2gas = CO2gas ,
2
2

(16)

1
COgas + H2gas + O2gas = CH4gas + 2OHgas.
2(17)

Consequently, varying fO2 at constant P and T in the
C–O system will control the CO/CO2 ratio of the gas
phase. Hence, a change of the Henrian solubility constants upon a change in fO2 may indicate a change in gasphase speciation.

3 Experimental techniques
The diversity of conditions to be tested to simulate different planetary environments implies the use of a wide
range of experimental setups. They mainly differ in termsof the P–T conditions they can attain. Each high-pressuretechnique can be used to assess the unique thermodynamic states of planet-forming materials at P–T ranges
relevant to core–mantle differentiation in bodies of sizes
ranging from asteroids to large terrestrial planets. In contrast, 1-atm devices used for solubility experiments differ
mainly in terms of sample mass, quench speed, and fO2
control. Compositional analyses of these samples are typically performed ex situ, and solubility data and partition
coefficients are determined by the concentration ratiosof elements of interest between the metal and silicate
phases. Among the parameters to be evaluated before
experimentation, the size of the sample is critical because
it constrains the type of analyses that can be performed.
3.1 Large‑volume apparatuses
3.1.1 Low‑pressure devices for solubility experiments

In contrast to high-pressure experiments, low-pressurestudies can be performed under open-system conditions(that is, mass can be lost from the experimental charge)at (near-)ambient pressures, as is the case for levitationand vertical-furnace experiments. Both techniques are
performed in large reacting chambers (from tens of cubic
centimeters to several liters), meaning that evaporated
species are able to leave the immediate vicinity of theheated sample (e.g., Donaldson 1979). Furthermore, fO2(and the fugacities of other gaseous species) can be set bycontinuously flowing gas mixtures, the nature of which
depend on the conditions to be tested. This is the key
advantage of low-pressure conditions: because high-temperature vapors behave essentially ideally at 1 bar, their
thermodynamic quantities are precisely known (e.g.,
from the JANAF tables; Chase 1998) and their fugacities
for a given bulk gas composition are easily defined (toPage 4 of 33

within a few percent relative). Because HVEs have stablegas species at standard temperature and pressure (STP),
such as N­ 2, ­CO2, CO, H­ 2, ­SO2, and O­ 2, the gas flow rates
can be precisely controlled to accurately fix fN2, fCO2,
fCO, and so on.
In contrast, sealed silica tubes are closed systems, andmetallic buffers or reducing/oxidizing species must be
added within the tube to control the fO2.
3.1.1.1 Aerodynamic levitation furnaces This kind of
furnace is mainly composed of a conical nozzle, with acentral hole from which a gas or gas mixture flows. The
gas flows at typical velocities of the order of ~ 10 m/s(hundreds of cubic centimeters per minute, depending on
the nozzle diameter) and is used to stably levitate the sample (e.g., Nordine and Atkins 1982; Pack et al. 2010). Additionally, the gas can also be used to control the fO2, orindeed the fugacity of the desired gaseous species, since
the gas compositions can be changed by mixing ­H2, ­CO2,
and Ar gases using multiple gas flow controllers (Badroet al. 2021).
In most of these devices, the sample is heated by
a ~ 100 W continuous-wave C­ O2 laser with a wavelengthof 10.6 µm that is focused to a spot diameter of 1–5 mm
depending on the size of the sample (Fig. 1). Other heating sources (solar furnaces, mirror furnaces) have also
been used for specific applications, but are more difficult
to implement (Oran and Berge 1982). Temperatures canbe very high (e.g., > 3000 °C using laser heating), but caneasily be adapted according to the process of interest (seereviews by Hennet et al. 2006 and Pack et al. 2010).
The main benefit of this technique is the absence ofcontact with the sample container during the experiment,
preventing chemical interactions with the container (e.g.,
Fe is not lost into Pt wires or crucibles, and samples are
not contaminated with ­Al2O3 or its impurities, as in vertical tube furnaces). Moreover, crystallization is unaffected by heterogeneous nucleation along the container
surface. Other advantages include (1) the possibility ofreaching very high temperatures (> 3000 °C) and (2) very
short experimental durations owing to the low sample mass, which allows rapid heating/cooling cycles andresults in quench rates of ~ 850 °C/s for ~ 2-mm-diameter
spheres (Badro et al. 2021). These specificities have been
exploited to make peridotitic glasses as analogs of magma
oceans (e.g., Sossi et al. 2020b). Otherwise, homogeneous
peridotitic samples have been prepared by a sol–gel process, which often contains a moderate amount of water(Auzende et al. 2011).
However, the small volume of the heated sample complicates temperature measurements, accomplishedusing an optical pyrometer rather than thermocouples. Although such pyrometers have precision on theDalou et al. Progress in Earth and Planetary Science(2024) 11:27

Page 5 of 33

Fig. 1 Aerodynamic levitation furnace. a Schematic of the setup modified from Ni et al. (2021). b Photograph of the setup at the Eidgenössische
Technische Hochschule (ETH, Zürich, Switzerland), and c zoom of the levitated sphere (modified from Badro et al. 2021)

order of a few degrees, instability in the laser heating
can result in fluctuations of ~ 50 °C (Sossi et al. 2023).
Moreover, the unknown emissivities of some liquids
at the wavelength(s) of the pyrometer means that additional calibration is required to derive absolute temperatures (e.g., Sarou-Kanian et al. 2005; Taguchi et al. 2023).
Depending on the geometry of the furnace (especiallyfor single-laser devices), the combination of laser heating and the cooler gas stream on the sample may inducea thermal gradient despite the rotation of the sample during the run (as observed in Hennet et al. 2006). To remedy this, dual laser setups are common, and a third laser
can even be added to offset cooling induced by the gas(Hennet et al. 2006). The relatively high gas flow rates
required to stably levitate a sample (several hundreds ofstandard cubic centimeters per minute; Landron et al.
2000; Pack et al. 2010) promote mixing and hence a constant fO2. However, such high flow rates increase theadvection of evaporated species from the surface (seeCharnoz et al. 2021 and Young et al. 2022 for theoreticaltreatments), promoting further evaporation. Because thesystem is open to mass transport and the sample has afinite mass, this evaporation (unless congruent) changes
the composition of the residual sample. Indeed, this environment can result in the evaporation of volatile andmoderately volatile elements (mainly the alkalis, S, F, andCl, but also Mn, Cr, and Zn; Sossi et al. 2019), which arethen carried away from, and thus depleted in, the sample(Pack et al. 2010; Badro et al. 2021; Ni et al. 2021).
Consequently, levitation furnaces are best suited tothe study of high-temperature materials or those withlow volatile abundances, although they can also be
gainfully used to investigate thermodynamically unequilibrated processes such as evaporation.

3.1.1.2 Vertical drop‑quench furnaces This furnace
design has long been employed in petrological studies
to examine phase relations, evaporation, crystallization,
textural relationships, and partition coefficients between
phases. High temperatures up to ~ 1700 °C are reachedat 1 atm using metallic heating elements (usually ­MoSi2,
but graphite is also feasible). Experiments are performed
within a refractory tube (mainly ­Al2O3, but sometimes­SiO2 or SiC for lower or higher T experiments, respectively) in which gas mixtures can be pumped to control
the fugacities of oxygen and other elements. Samples
are held in the hot zone of the furnace (typically ~ 3 cmlong) by metallic wires (often Pt, but also Ir, W, and Re formore reduced atmospheres) or metallic/refractory crucibles (such as Pt or ­Al2O3) and are efficiently quenched(> 700 °C/s, as estimated from the decrease in sample
brightness within ~ 1 s) by dropping them into the lower,
cold part of the furnace, sometimes directly into a water
bath (Fig. 2).
The main advantage of vertical drop-quench furnaces
is that the experimental temperature is precisely andaccurately controlled. Absolute temperatures are calibrated using metals whose melting points are known towithin ~ 1–2 °C (usually Au at 1064 °C and Pd at 1555 °C).
Moreover, these furnaces can often be programmed tofollow complex thermal histories, which is more relevant
to natural samples than simple isothermal experiments.
Another benefit is the possibility of varying the sample
size: small samples (~ 10 mg) can be useful to quickly
reach equilibrium with the gas phases (i.e., in a few minutes), and different surface/volume ratios can be tested,
for example, to obtain information about evaporation
processes (e.g., Mathieu et al. 2008). Gas flow rates may
also be precisely controlled, varied over a relatively wide

Dalou et al. Progress in Earth and Planetary Science(2024) 11:27

Page 6 of 33

Fig. 2 Photographs and a schematic of the vertical drop-quench furnace at the Centre de Recherches Pétrographiques et Géochimiques (CRPG,
Nancy, France)

range (typically tens to hundreds of standard cubic centimeters per minute), or varied systematically with time
to simulate changing fugacity conditions (e.g., PrabhaMohan et al. 2023). Oxygen fugacities are typically independently measured by means of the electromotive force(emf ) via an oxygen probe ­(SIRO2; Badwal et al. 1987;
Mendybaev et al. 1998) composed of an yttria-stabilized
zirconia (YSZ) solid electrolyte and Pt electrode.
One of the limitations of 1-atm furnaces is the necessity of using sample containers. Generally, samples
should not contain elements that readily alloy with thesample container at the conditions of the experiment;
for example, the use of Pt in the well-known wire-loop
method (Presnall and Brenner 1974; Donaldson et al.
1975) is problematic if the silicate melt contains iron.
Indeed, if the mass of the container is large enough,alloying can modify the composition of the sample andthe thermal resistance of the wire (Presnall and Brenner 1974; Corrigan and Gibb 1979). One approach toovercome this issue is to use a pre-alloyed container,
although this adds to the experimental preparation
time (Grove 1982).

Another limitation, as with other open-system devices,
is the evolution of the sample composition due to evaporation of the most volatile species (e.g., O’Neill 2005;
Sossi et al. 2019), although this process is slower than in
a levitation furnace due to the lack of advection. If undesired, this effect can be mitigated by adding the volatilesof interest to the atmosphere in the furnace (Amalberti
et al. 2018; Boulliung et al. 2020; Boulliung and Wood2022) or by adding a supplementary volatile source, suchas a bucket containing the volatile compound of interest(e.g., Georges et al. 2000; O’Neill 2005; Borisov 2008).
However, experiments using a supplementary volatilesource are difficult to undertake and typically only reacha steady state rather than true equilibrium.
In summary, vertical furnaces are very thermally stable
and thus suitable for solubility and evaporation experiments. However, they are prone to evolving sample
compositions that may preclude their use for naturally
relevant studies.
3.1.1.3 Sealed silica tubes Sealed silica tubes are intermediate between the open-system protocols previously

Dalou et al. Progress in Earth and Planetary Science(2024) 11:27

described and the closed-system high-pressure devices
described in the next subsections. These devices areclosed systems that are run at low pressures (~ 0.1 to a
few bars for experiments at temperatures relevant tomagmatic systems). They contain the sample(s) and, if
needed, a metallic buffer (Fig. 3a) or a graphite crucible(Fig. 3b) to control fO2 and a ‘source’ of the element tobe tested (Fig. 3). The tubes are prepared at room temperature and must be evacuated (to ~ ­10−2 mbar) before
sealing to accommodate the overpressure upon heating.
Once closed, the tubes are inserted into a furnace (usuallymuffle furnaces, sometimes vertical furnaces).

a)evacuated sealed
silicat tube

Page 7 of 33

The sizes (diameter and length) of the tubes can beadapted to a given study depending on the materials
necessary, potentially varying the tube volume from ~ 1
to ~ 100 ­cm3. Other factors controlling tube size are theease of shaping the tubes (it becomes difficult to seal
small bulbs with a torch) and the size of the furnacechamber.
In contrast to open-system devices, sample compositions will be only moderately affected by evaporation insealed tubes; indeed, the most volatile elements will start
to volatilize, but will eventually reach their vapor saturation pressure, preventing further loss from the sample

evacuated sealed
silicat tube

Platinum cap
glass sample
C or S reservoircplatinum crucible

graphite cap

alumina orsilica crucible

graphite crucibles
C or S reservoir

solid metal/ oxide

glass sampleb)sealed silicate tubes
alumina crucible
carbon crucible

5 cm
Fig. 3 a Schematics of two different sealed silica tube experimental designs (modified from Chevreux et al. 2021). b Photograph of two sealed silica
tube experiments in a muffle furnace, standing in alumina crucibles (courtesy of Mahaud Chavanieu, CRPG)

Dalou et al. Progress in Earth and Planetary Science(2024) 11:27(Khedim et al. 2008; Chevreux et al. 2021; Cartier et al.
2023). That said, a volatile source can be added to thetube to, at high temperature, produce a gas that will interact with the sample, allowing the “ingassing” of various
elements (Mathieu et al. 2008, 2011). The closed-systemnature of these experiments also constrains the conditions that can be tested. First, the fO2 must be imposedby metallic buffers or by adding oxidizing or reducing elements to the samples, making it difficult to test alarge fO2 range. Moreover, the use of metallic buffers canpreclude some applications; for example, in S solubility
experiments, S reacts with metallic buffers to produce
sulfides.
Due to the pressure differential between the inside andthe outside of the tube (i.e., the atmosphere), the tubes
can deform or even be punctured in high-temperatureruns. Consequently, temperatures as high as 1450 °C are
difficult to test, even in short runs of a few hours, andtemperatures should not exceed 1400 °C for longer runs(> 24 h). Thus, sealed silica tubes are a good protocol for
performing solubility and controlled evaporation experiments for volatile or moderately volatile elements (S,alkalis, etc.) because they can last from a few minutes toseveral days. Although experimental limitations (temperature, testable elements, etc.) can limit their applications,sealed silica tubes are a good compromise for low-pressure, closed-system experiments.
3.1.2 Large‑volume moderate‑ to high‑pressure devices (LVP)

Internally heated pressure vessels (IHPVs) are designed
for experimental studies at medium to high temperatures (up to 1400 °C) and pressures up to 1 GPa, whereas

Page 8 of 33

piston-cylinder apparatuses can reach temperatures
up to 2000 °C and pressures of 0.5–4 GPa (or, rarely, 6GPa). These two apparatuses are therefore limited toexperiments investigating the first hundreds of kilometers of terrestrial magma oceans, but are appropriate forstudying core–mantle equilibration on smaller planetary
bodies like the Moon or Mercury (≤ 5 GPa; Rai and vanWestrenen 2014; Cartier and Wood 2019). In contrast,
multi-anvil presses are used to attain pressures of 5–25
GPa and temperatures up to 3000 °C, conditions more
relevant to core–mantle segregation on larger planets (Bouhifd and Jephcoat 2011; Rai and van Westrenen2013).
3.1.2.1 Internally heated pressure vessels (IHPVs) IHPVs
consist of a thick-walled metallic pressure vessel sealed
by closure plugs at both ends, in which the pressure isapplied by a gas. The pressure medium is injected in gaseous form using two multipliers and piston systems capable of reaching pressures up to 1 GPa. The injected gas
is most often Ar, but can also be a mix of Ar and H in
variable proportions, making it possible to simulate more
reducing environments. The sample is heated by an internal-resistance two-loop tube furnace heater (Mo wiring,
17 mm internal diameter), which can reach temperatures
up to 1400 °C. The vessel is cooled using a coil in whichwater circulates. A plug and shutter system guarantees thewatertightness of the internal part under pressure, whichcontains the furnace and the sample. The quenching system comprises two Pt rods which allow the sample(s) tobe held in the hot part of the autoclave (Fig. 4). The sample hangs from an alumina nacelle using a fine (0.2 mm)

Fig. 4 Schematic diagram of an internally heated pressure vessel with rapid quench device (left) and a rapid quench IHPV at Bayerisches
Geoinstitute (right, modified from Yoshioka 2018)

Dalou et al. Progress in Earth and Planetary Science(2024) 11:27

wire (Pt or PtRh). Quenching is performed by sending anelectrical discharge into the rods to explosively fuse thewire, allowing the nacelle and the capsule(s) to fall fromthe hot zone of the furnace (+ 1000 °C) to the cold zone(− 100 °C), achieving quench rates of about 500 °C/s (Holloway et al. 1992). Two to three thermocouples (e.g., S
type; ­Pt90Rh10–Pt]) can be used at different heights in the
hot zone to monitor temperature (Fig. 4); temperature
gradients can vary from 0 to 20 °C over 1 cm within the
hot zone.
Because Ar gas is used as the main pressure medium,pressure is known more accurately in IHPV experiments
than in other large-volume apparatuses, hence the common use of IHPVs to study volatile element behaviors
during magma ocean degassing (Yoshioka et al. 2019;
Bernadou et al. 2021). Moreover, by adding various proportions of hydrogen to the Ar pressure medium, theoxygen fugacity can be controlled following the reaction:­H2 + 1/2 ­O2 = ­H2O (Gaillard et al. 2003).
3.1.2.2 Piston‑cylinder apparatuses Both piston-cylinder and multi-anvil apparatuses are based on hydraulicPage 9 of 33

pressure systems that drive one or two vertical hydraulic rams to compress a cylindrical cavity. Relatively large
sample sizes are employed in the piston cylinder apparatus (~ 200 ­mm3 in a 1/2″ assembly) compared to themulti-anvil type LVP. The piston-cylinder apparatus consists of a “bomb” with a centered cylindrical hole either
3/4″ (≤ 1.2 GPa) or 1/2″ (≥ 1 GPa) in diameter. The pressure on the sample chamber within the cavity is generated
by pushing a piston into the cylindrical cavity. Whereas
the bomb is made of pre-stressed steel rings, both thepiston(s) and the core of the bomb are made of tungsten
carbide (Fig. 5a). The lower ram transfers the pressure to
the sample through the piston, while the upper hydraulicram provides the end-load pressure during an experimentto support the pressure vessel from the opposite side of
the master ram (Fig. 5a). In general, pressure is appliedand maintained using two hand-pumps, but recently,
pressure controller systems have allowed programmed
pressure profiles to be executed using automatic pumps.
A fraction of the hydraulic pressure is not transmitted tothe sample, as evidenced by the heterogeneous pressure
distribution and frictional strain between the carbide coreFig. 5 a Schematic of the end-loaded piston-cylinder apparatus. b Photograph of the bridge, the bomb, the top plates and the assemblies, and cschematic of a 1/2″ assembly (modified from Condamine et al. 2022)

Dalou et al. Progress in Earth and Planetary Science(2024) 11:27

and the cell assembly, which cause pressure losses (e.g.,
Condamine et al. 2022) that vary with experimental pressure, temperature, and duration. Therefore, depending on
the conditions of interest, a variety of piston-cylinder cell
assemblies are available to transform the uniaxial pressure
into hydrostatic isotropic pressure. At high temperatures(> 1600 °C), talc (Fig. 5b) or ­BaCO3 cells should be favored
over NaCl salt cells as the electrical insulator, althoughtalc produces too much frictional strain on the carbide
core and must be avoided in experiments at very highpressures (> 3 GPa, < 1600 °C; Condamine et al. 2022).
Hence, special attention is required in the choice of materials used. Capsules are contained in a MgO ring sleevesandwiched between top and bottom MgO plugs (Fig. 5c).
The alumina sleeve is placed in an assemblage composedof, from innermost to outermost, graphite, pyrex, andelectrical insulator cell cylinders. Finally, samples areheated electrically via copper electrodes on the top plate
and the bridge, creating an electrical circuit through theresistive graphite heater (Fig. 5a). During high temperature experiments, the pressure vessel is cooled using circulating water. The electrical connection to the graphite
heater is maintained through the steel plug on the top anda graphite and steel disk at the bottom of the assembly.
The temperature distribution within assemblies depends
on the assembly material, as described in Schilling and
Wunder (2004). The experimental temperature is monitored using a thermocouple, inserted axially such that thewelded junction is in close contact with the top of the capsule. Dunn and Luth (1993) reviewed the different types
and best uses of thermocouples. Type-C thermocouples­( W95Re5–W74Re26) are the most adapted to very hightemperatures (up to ~ 2300 °C) for metal–silicate partitioning or magma ocean degassing experiments. At theend of the experiment, before decompression, the power
to the furnace is cut and the experiment is quenched “rapidly”, i.e., at ~ 130 °C/s (Ezad et al. 2023), although recent
developments on new “rapid quench” piston-cylinders
have improved quench rates to 160 °C/s (Ezad et al. 2023).
Both IHPVs and piston-cylinder apparatuses can beequiped with a pressure controller, allowing controlled
isothermal decompression experiments. We note, however, that isothermal decompression experiments are
more commonly run in the context of volcanic degassing
to simulate magmas ascending through volcanic conduits(e.g., Gardner et al. 1999; Nicholis and Rutherford 2009)
than to simulate the degassing of a fully molten surface ina magma ocean context.
3.1.2.3 Multi‑anvil presses Multi-anvil presses arecapable of generating pressures and temperatures relevant to shallow depths within Earth’s lower mantle (≥ 25
GPa, 2300 °C) while maintaining a relatively large sam-Page 10 of 33

ple volume on the order of ~ 10 ­mm3. Multi-anvil presses
differ from piston-cylinders because the pressure isapplied using a hydraulically driven ram that compresses
two opposite outer guide blocks, each containing threehardened-steel primary-stage anvils that, in turn, compress eight tungsten carbide secondary anvils in multiple
directions (Fig. 6a). This approach can reach 25 GPa, oreven higher pressures if the anvils are made of sintereddiamonds (Zhai and Ito 2011) or newer tungsten carbide
anvils (TF05 and TJS01), which can reach over 30 GPa(e.g., Kunimoto et al. 2016; Ishii et al. 2017, 2022). The
secondary anvils have truncated corners such that theassembly of the eight cubes into a larger single cube leaves
an octahedral shaped cavity at the center (Fig. 6b), wherean octahedral high-pressure ceramic cell containing
the sample is placed. Samples are placed into this outer
MgO + ­Cr2O3 octahedral ceramic pressure medium, a­ZrO2 thermal insulator, a resistance graphite or L
­ aCrO3
heater, and MgO or A
­ l2O3 spacers (Fig. 6b). The addition
of 5% C
­ r2O3 to the MgO pressure medium lowers its thermal conductivity. The upper component encloses a MgO
tube used to accommodate the thermocouple, and a solid
MgO cylindrical spacer is placed at the bottom (Fig. 6b).
The middle part contains the sample capsule inside a thin
MgO sleeve. In the sample area, the heater has a thicker
wall to create a smaller axial thermal gradient. A molybdenum ring and disk are also used to improve electricalcontact (Fig. 6b). As in the piston cylinder, current ispassed through a graphite or lanthanum chromite furnace to heat the sample. For a given uniaxial load generated by the hydraulically powered guide blocks, the size ofthe octahedral cell assemblies (hence the truncation edge
length of the WC anvils) controls the pressure generated
on the sample.
As with the piston cylinder, quenching is required to“freeze” the samples to keep HVEs within the structure ofhigh-pressure melts. For this reason, recent works havefocused on improving quench rates in LVPs. Bondar et al.
(2021) showed increasing the quench rate of traditional
multi-anvil presses from 650 to 6700–8200 °C/s; thisstate-of-the-art technique currently works to pressures
up to 9 GPa and temperatures up to 2200 K.
3.1.3 The critical choice of capsule materials

In general, capsules consist of welded noble metals or
metallic alloys. The choice of sample capsule depends
on the pressure, temperature, and oxygen fugacity ofthe experiments. In studies applied to planetary magma
oceans, reducing conditions require the use of AuPd, Pt,
or graphite capsules (e.g., Bernadou et al. 2021; Dalou
et al. 2017; Grewal et al. 2019). In IHPVs, double capsules with external AuPd or Au capsules and internal Pt
capsules have been developed to control and monitor

Dalou et al. Progress in Earth and Planetary Science(2024) 11:27

Page 11 of 33

Fig. 6 a Photograph of the multi-anvil press installed at the Vrije Universiteit (Amsterdam, Netherlands), modified from Knibbe et al. (2018). b
Schematic of the multi-anvil press secondary anvils, and a schematic and photographs of the assembly (courtesy of Pierre Condamine). Notethat at the interface between the pressure medium and the pyrophyllite gasket, the copper coil around the thermocouple may significantly affectthe electromotive force (EMF) of the thermocouple. Specifically, the nominal temperature is estimated to be ~ 150 K lower than the nominal
temperature without a copper coil (Nishihara et al. 2006)

hydrogen and oxygen fugacities during experiments(e.g., Wilke and Behrens 1999). In piston cylinder andmulti-anvil press experiments, graphite capsules or double Pt-graphite capsules (i.e., inner graphite and outerPt; e.g., Armstrong et al. 2015) are often used to prevent Fe loss to the metal containers, ensure reducing
conditions, and achieve high temperatures approachingplanetary magma ocean conditions. However, graphite
capsules are a source of C and lead to graphite-saturated

conditions that yield C-saturated metal alloys. They arealso more or less porous depending on their density,
which often results in volatile losses (e.g., Grewal et al.
2019; Dalou et al. 2019a). Single-crystal olivine, pure
forsterite, or MgO capsules can be used as alternatives,
but the increasing dissolution of MgO with increasing
experimental temperature (Fichtner et al. 2021; Dalou
et al. 2022) must be considered when selecting starting
materials.

Dalou et al. Progress in Earth and Planetary Science(2024) 11:27

3.1.4 Experimental designs

To study the metal–silicate partitioning of volatile elements, starting materials are silicate gels or mixtures ofoxide powders considered analogous to a magma ocean
composition and a core-forming metallic alloy composition. As magma ocean analogs, tholeiitic, primitive
basaltic, or magnesian basaltic compositions are generally chosen (e.g., Kuwahara et al. 2019a; Grewal et al.
2019; Fichtner et al. 2021; Blanchard et al. 2022). In thecase of multi-anvil presses, the high quench rate allows
the use of chondritic and/or peridotitic compositions
that are closer analogs to magma oceans (Roskosz et al.
2013; Boujibar et al. 2014), although it remains difficult
to quench those compositions without forming olivine
dendrites unless modifications to the standard design
are made (see Bondar et al. 2021). Core-forming alloys
are generally either solely iron or an iron–nickel mixture(Roskosz et al. 2013; Grewal et al. 2019) that may include,
as discussed in the following section, a mix of iron carbide, sulfide, or nitride and iron monosilicide (e.g., Boujibar et al. 2014; Grewal et al. 2019). However, the choiceof experimental design implies certain assumptions
about Earth’s accretion and core formation, as summarized in the following.
One procedure is to load a capsule with two separate
phases: an iron alloy (Fe ± Ni, Si) containing the volatileelements of interest and a volatile-free (sometimes ironfree) silicate powder (e.g., Ballhaus et al. 2017; Grewal
et al. 2021; Blanchard et al. 2022). The alloys are preparedby mixing pure metal alloys (Fe, FeS, F­ e83Si17, Ni, F­ e4N,­Fe7N3, etc.; e.g., Kilburn and Wood 1997; Dasgupta et al.
2013; Boujibar et al. 2014; Grewal et al. 2019; Jackson
et al. 2021). A step to melt this mixture can be included;

Page 12 of 33

for instance, Blanchard et al. (2022) alloyed pure Fe with
13
C powder in a piston cylinder melting experiment at
2 GPa and 1873 K for 10 min in a MgO capsule. Oncethe metallic alloys are loaded into the capsule with thesilicate powder and brought to the desired high-pressureand high-temperature (HP–HT) conditions, volatile elements equilibrate by diffusion from the metal alloy to thesilicate phase, producing a large metallic pool (> 400 µm
in diameter) on one side of the capsule and a large pool ofsilicate glass on the other (Fig. 7a). This procedure is ideal
for physically and chemically separating fragments of silicate glass from the metal for bulk analyses by inductively
coupled plasma mass spectrometry (ICP-MS) or gas
mass spectrometry (see below). This design assumes thatthe core formed from large metal fragments that resulted
from the accretion of large differentiated planetesimals
and planetary embryos (Kleine and Rudge 2011). In thiscase, HVEs are already partitioned into the metal fragments and partially re-equilibrate with the surrounding
silicate (magma ocean).
Alternatively, following the continuous accretion
model (e.g., pebble accretion), the accreting metals form
droplets small enough to equilibrate with the surrounding magma ocean (Kleine and Rudge 2011). To experimentally simulate the processes approximated in thismodel, volatile elements and a Fe-bearing silicate powder
representing the magma ocean are loaded into the capsule with a reducer (e.g., Si or Fe metal). For instance,hydrogen can be added to the starting silicate powder as Mg(OH)2 (e.g., Iizuka-Oku et al. 2017), Al(OH)3(Clesi et al. 2018), or synthesized water-bearing silicate
glass (e.g., Tagawa et al. 2021). For carbon, graphite capsules have been widely used as the carbon source (e.g.,

Fig. 7 Equilibrated metal–silicate samples produced in piston cylinder experiments. a Sample from Li et al. (2015) produced at 3 GPa, 1600 °C,
and IW–4.8, by loading a volatile-bearing metal and a volatile-free silicate into the capsule (the single-stage core formation approach). b and c
Samples from Dalou et al. (2017) synthetized at 3 GPa, 1600 °C, and IW–2.3, and from Speelmanns et al. (2018) synthetized at 1 GPa, 1250 °C,
and IW–3.0, respectively, both produced by loading volatiles, Fe-bearing silicate powder, and a reducing metal into the capsule (the continuous
accretion approach). See text for full descriptions of the two approaches

Dalou et al. Progress in Earth and Planetary Science(2024) 11:27

Dasgupta et al. 2013; Li et al. 2016; Dalou et al. 2017). To
avoid C saturation in the metal phase, other types of capsules can be used (see previous section) and either graphite powder or vitreous carbon spheres added as the C
source. For nitrogen, S­ i3N4 can be used both as a sourceof N and as a reducing agent (e.g., Roskosz et al. 2013;
Speelmanns et al. 2019; Dalou et al. 2017, 2019a). Since
its reduction potential is high, other sources of N, such as­NH4NO3, have also been used (e.g., Li et al. 2016; 2023).
In these experiments, because reduction occurs during
heating, the metal segregates from the silicate at HP–HT.
Hence, the equilibration of volatile elements between
the metal and the silicate is controlled first by the reduction reaction and then by diffusion between the silicate
melt and the metal alloy. This experimental procedure
produces small metal blobs (10–80 µm in diameter) randomly distributed throughout the silicate glass (Fig. 7b,c; e.g., Speelmanns et al. 2019; Dalou et al. 2017, 2019a),
unless the experiments are sufficiently long (≥ 6–12 h) toallow metal blobs to sink and coalesce into larger blobs(> 150 µm). However, such long experiments are often
affected by volatile losses through the capsule (e.g., Dalou
et al. 2019a).
In both cases, metal–silicate experiments are run atleast 50 °C above the silicate liquidus (e.g., Dalou et al.
2017; Grewal et al. 2019), and experiments of both protocols are performed at similar temperatures. Assumingthat chemical equilibrium is attained during the experiment, both of the above experimental approaches produce equivalent results. For instance, similar nitrogenpartition coefficients between metal and silicate phases
were reported by Grewal et al. (2019, 2021) using the first
protocol and by Dalou et al. (2017) and Speelmanns et al.
(2019) using the second protocol.
3.1.5 Attainment of chemical equilibrium

Chemical equilibrium must be assessed before publishing solubility or metal–silicate partitioning data. The firstargument to support chemical equilibrium for an experimental sample is the compositional homogeneity of thephases (glass and metal) with respect to major elements
and the investigated volatile(s) (H, C, N, and/or S) whenmeasured by local analyses (see analytical section). The
second argument is to perform time series experiments(i.e., experiments of variable durations): partition coefficients correlate with run duration below a certain run
duration but remain stable over longer durations, suggesting a steady state has been reached. If independent
tests yield similar results, this steady state can be equatedwith the attainment of equilibrium. Owing to the differences in diffusivities, the characteristic equilibration timediffers for each element and varies with experimental
conditions, such as P–T, fO2, and phase compositions.

Page 13 of 33

However, elements may not necessarily diffuse in theirelemental (monatomic) form, but rather as moieties (seeRichter et al. 2009); diffusivities thus also reflect speciation, which is itself a function of P–T–X (e.g., Boulliung
et al. 2021). Despite the relative ease with which timeseries can be performed, few are reported for metal–silicate experiments involving the equilibration of highly
volatile elements (e.g., Shi et al. 2022 for N). Instead, thediffusivities, expressed in ­cm2/s, of larger, heavier elements (mainly Si, Mg, and O in silicates or Fe and C inmetals) are often used to calculate characteristic diffusion distances in comparison to the sizes of the samples
or the phases (e.g., Malavergne et al. 2019). The argument
here is that if larger and heavier elements (i.e., with theoretically slower diffusivities) are equilibrated in a sample synthesized at a certain duration, so must be smaller
and lighter elements. Nonetheless, reversal experiments
remain the most robust test of equilibrium; they are
typically performed by varying the form in which starting materials are added to the experimental charge andascertaining whether the same experimental product is
produced. Finally, when partitioning or solubility data
already exist in the literature at similar conditions tothose being investigated, chemical equilibrium can beassessed by comparison with previous studies.
3.2 Laser‑heated diamond anvil cell (LHDAC) experiments

LVPs produce samples large enough to be analyzed bybulk or local analytical methods, allowing for numerous
and various types of structural, chemical, and vibrational
analyses (see Sect. 5). As summarized above, thermodynamical parameters such as pressure, temperature, andoxygen fugacity can be controlled with relative precisionusing those experimental techniques. However, none ofthose methods can achieve the average P–T conditions
relevant to metal–silicate equilibration during Earth’s
core formation (i.e., ≥ 45–55 GPa and ≥ 4000 °C; Bouhifd
and Jephcoat 2011).
To determine metal–silicate partition coefficients at
conditions relevant to core–mantle segregation in a
deep magma ocean, experiments are also performed in
LHDACs, in which materials are compressed between thetruncated tips of two diamonds to pressures of 30–100
GPa and heated by an infrared (IR) laser to temperaturesof 3000–6000 °C (Siebert et al. 2012; Fischer et al. 2015;
Bouhifd and Jephcoat 2011). Starting materials are usually thin foils of iron alloyed with trace elements of interest and a pellet of powdered silicate/oxide mixture (e.g.,basalt, peridotite, pyrolite compositions). Using a needle
or other micromanipulator, these are placed in a preindented gasket sample chamber that is, in turn, placed
between the two diamonds, and the pressure is increasedby squeezing the diamonds’ tips together via tightening

Dalou et al. Progress in Earth and Planetary Science(2024) 11:27

screws (Fig. 8a). Although rhenium or stainless steel
are commonly used, various gasket materials have been
employed, such as diamond, beryllium, boron (Lin et al.
2003), or a combination of Kapton, amorphous boron,and epoxy (Merkel and Yagi 2005). The choice of gasket
is important because it determines the maximum attainable pressure, sample thickness, and the stress conditions
within the sample (Merkel and Yagi 2005).
Many factors control the ability of DACs to generatepressure, but the simplest parameter is the diameter (d)of the diamonds’ culets. O’Bannon et al. (2018) foundthat the maximum pressure a DAC can reach varies

Page 14 of 33

linearly with d−0.54. For more details on the relationshipbetween anvil geometry and achievable pressure, thereader is referred to O’Bannon et al. (2018). Pressurein the experimental chamber is determined before andafter the experiments based on either the fluorescence ofa small ruby placed near the edge of the chamber (Maoet al. 1978; Eggert et al. 1989; Dewaele et al. 2004) or thehigh-wavenumber edge of the diamond band in Raman
spectra (Eremets et al. 2023). Uncertainties on these pressure measurements range between 5 and 10 GPa (Eremets et al. 2023). A thermal pressure correction is applied
to the pressures measured after heating (Yen et al. 2020).

Fig. 8 a Photograph of a diamond anvil cell (DAC) with a cross section of the region hosting the experimental sample, modified from Yang
and Zhaohui (2011). b Simplified schematic of a two-sided laser-heated system. Laser is directed by mirrors (M) to the two sides of the DAC.
Thermal emission is directed via beam splitters (bs) to spectrometers to determine temperature. An objective collects an image which is focusedby lenses (L) onto a camera. The DAC is usually illuminated by a white light source (not shown). Filters (F) are used to block unwanted wavelengths
or reduce intensity. c Top-down view through diamond of a metal–silicate partitioning experiment after laser heating (the dark region indicateswhere the sample was molten) and a 4-color temperature map of the sample collected during laser heating (courtesy of T.A. Suer). d Small metal
grains in the quenched silicate of the same sample, from Suer et al. (2017)

Dalou et al. Progress in Earth and Planetary Science(2024) 11:27

The optical transparency of the diamond anvils allows
lasers to be used to heat the samples to high temperatures (Fig. 8b; Boehler 2000; Anzellini and Boccato 2020).
Laser heating systems vary in design and capabilities,
but generally consist of one or two IR lasers applying
controlled heating to the material held between the two
diamonds. ­CO2 or YAG lasers with powers ranging from50 to 200 W and peak wavelengths of 1064–1094 nm are
typically used. The beams are collimated, directed, andfocused into the sample chamber using suitable mirrors
and lenses (e.g., Fig. 8b). Laser spot sizes can vary from10 to 50 μm in diameter, and the temperature of the sample is raised by increasing the laser power. Images of thesample (typically magnified 10–20 times) and its thermalradiation are collected by a CCD camera and spectrometer, respectively. Thermal emission spectra from theheated region are recorded from one or both sides of theexperiment and temperatures are extracted by fitting to a
Wien or Planck function (Benedetti and Loubeyre 2004;
Heinz and Jeanloz 1987; Walter and Koga 2004). Thermal
emissions are collected by monochronometers in somestudies, but multi-wavelength 2-D images can also be
obtained from the heated region (Fig. 8c; Du et al. 2013;
Campbell 2008; Lord et al. 2014).
Two major sources of uncertainty in laser heating
studies are chromatic dispersion from refractive opticalcomponents and strong temperature gradients. Detailed
discussions of how chromatic dispersion affects extracted
temperatures and recommendations for reducing theseeffects are available in Walter and Koga (2004) and
Benedetti and Loubeyre (2004). Through careful characterization of the experimental components and using
consistent calibration standards, temperature uncertainties can be reduced to a few percent. Characterizing
the wavelength dependent emission and absorption ofmaterials used in the experiments under pressure canfurther help to ensure accurate temperature determination (Deng et al. 2017). A source of further uncertainty intemperature determinations, particularly for polyphasesamples, is Mie scattering of the thermal emissions when
passing between grains and phase boundaries (Lobanov
et al. 2021). This effect can lead to uncertainties as largeas ≥ 1000 K and should be considered when extracting
temperatures in future partitioning studies.
The sample region at the focus of the laser heats up
by absorbing laser energy until molten. If the sample issimultaneously probed by X-ray diffraction during heating, melting can be detected by disappearance of diffraction peaks or diffuse scattering (Yang 2016). For off-line
experiments, changes in sample appearance from the
motion of the melt or plateauing/leveling off of temperature have been used to detect melting although thesemethods can be imprecise (Andrault et al. 1998; Fiquet

Page 15 of 33

et al. 2010; Yang 2016; Yang and Li 2016). In metal–silicate experiments, the IR laser couples with the metallic
part of the sample. Prolonged exposure to the IR laser
anneals the silicate and metal phases into well-defined
regions, as reflected by the morphologies produced
in many metal–silicate partitioning experiments (e.g.,
Bouhifd and Jephcoat 2011; Siebert et al. 2012; Fischer
et al. 2015; Suer et al. 2017; Blanchard et al. 2022). Shutting off the laser power rapidly quenches the experiments
within microseconds, such rapid quench rates typicallylead to glass formation which is thought to lock in equilibrium composition attained during melting. However,large amounts of H cannot be retained in the metal phaseupon quenching and thus exsolve as bubbles, forming particular metallic quench textures (Okuchi 1997;
Okuchi and Takahashi 1998).
During the laser heating partitioning experiments,
samples can be heated continuously for a few to several
tens of seconds. According to Fick’s laws of diffusion,these timescales are long enough for chemical equilibration to occur for most species across the length scale ofthe molten hotspot (Corgne et al. 2008). Although thesample is completely molten under the focus of the laser,
its outer regions remain solid and steep temperature
gradients can occur during heating (Deng et al. 2017).
Therefore, the size of the sample is of critical importance.
The temperature in the middle of the hotspot can be considered to be homogenous, although thermal gradients
become large away from the center. Temperature gradients drive chemical diffusion through the Soret effect,
which can cause chemical zoning in experiments onmolten silicates (Prescher et al. 2014; Sinmyo and Hirose
2010). The ratio of a specie’s charge to its ionic radiusdetermines its behavior along a thermal gradient. Therefore, the spatial distribution of major and trace species
can be used to assess the degree of diffusion in metal–
silicate partitioning experiments. Many studies havereported compositional homogeneity of major and trace
species in both the metal and silicate phases of experiments as an indication of minimal thermal gradients.
However, ascertaining such chemical homogeneity on
the small spatial scale of the samples (tens of microns) is
challenging, and further investigations by microanalyticaltechniques such as nanoscale secondary-ion mass spectrometry (NanoSIMS), transmission electron microscopy (TEM), and/or atom probe tomography (ATP) areneeded.
3.3 Controversies surrounding partitioning measurements

Despite recent advances, measurements of volatile element partition coefficients remain controversial. Quench
textures in both LVP and DAC experiments have beendifficult to interpret, potentially resulting in inaccurately

Dalou et al. Progress in Earth and Planetary Science(2024) 11:27

reported trace element compositions and partition coefficients. Dendritic and quenched rim-overgrowth textures in LVP samples make it difficult to determine theequilibrium composition of the quenched liquid. Microscale and nanoscale metal-rich inclusions in the silicate
have been difficult to assess with volumetric techniquessuch as electron probe microanalysis (EPMA) and cantherefore complicate the interpretation of silicate traceelement compositions. Analyses at higher spatial resolution, such as TEM imaging (Blanchard et al. 2022), haveprovided evidence of two distinct populations of metallic
inclusions in the silicate glass: (1) large, irregularly dispersed inclusions up to several hundred nanometers indiameter (Fig. 8d), and (2) much smaller, uniformly dispersed inclusions a few tens of nanometers across. The
larger population can be observed by scanning electron
microscopy (SEM) and Blanchard et al. (2022) reported
compositions similar to the largest metallic blobs intheir samples, suggesting that they formed at high temperature, contrary to previous assumptions (Fischer et al.
2020). The presence of these larger metallic inclusions isa critical problem for determining HVE contents in silicate glasses because they may lead to overestimated contents of those siderophile elements in the silicate melt.
For instance, Fischer et al. (2020) analyzed large areas ofsilicate glass including such “large” metallic inclusions
because they considered the inclusions to have resulted
from the quench, and thus that they would have been
dissolved in the silicate at high P–T. However, Blanchard et al. (2022) avoided such “large” inclusions whenanalyzing their silicate glasses and obtained C partition
coefficients one order of magnitude higher than those of
Fischer et al. (2020) at comparable P–T conditions.
Although peridotitic or pyrolytic glasses are often usedas magma ocean analogs, their high magnesium contents promote the growth of dendrites during quenching. In comparison, the use of basaltic or andesitic melts
improves the homogeneity of the glass because they are
more easily quenchable (e.g., Blanchard et al. 2022).
The loss of volatile elements from quenched experimental samples is another factor that can affect thesemeasurements. Hydrogen has been particularly difficult
to measure in experiments because its small atoms tend
to escape the sample during quenching. Indeed, hydrogen may escape from samples prior to measurements
upon decompression; F­ eHx is known to decompose intobody-centered cubic Fe and molecular ­H2 (Iizuka-Oku
et al. 2017). In addition, Clesi et al. (2018) and Malavergne et al. (2019) conducted carbon-saturated experiments, leading to carbon enrichment of the metal, which
may hinder hydrogen incorporation (Tagawa et al. 2021).
The presence of quench minerals in silicate glasses produced in LVP experiments (Clesi et al. 2018; Malavergne

Page 16 of 33

et al. 2019) are also problematic because of the structuraldifference between melt and mineral, which likely causesa loss of incompatible volatile elements from the melt.
Therefore, reported hydrogen partition coefficients varyby more than an order of magnitude at the same conditions (Okuchi 1997; Clesi et al. 2018; Malavergne et al.
2019; Tagawa et al. 2021). Nevertheless, recent analyses
combining EPMA, nuclear magnetic resonance spectroscopy, and elastic recoil detection analysis (ERDA) provided valuable data for hydrogen partition coefficients(Clesi et al. 2018; Malavergne et al. 2019).
Volatile concentrations added to the starting materials of some experiments can be much higher than thosemeasured in natural samples. Such high concentrations violate Henry’s law, leading to large uncertainties
on reported partition coefficients for C (Kuwahara et al.
2019b; Grewal et al. 2021) and N (Shi et al. 2022; Grewal
et al. 2022). Indeed, some elements are even saturated in
the quenched silicate.
Finally, differences in the results of regression models used to fit measured HVE partition coefficients havebeen observed between the P–T ranges of LVP and DAC
experiments. Evolving chemical tendencies in these distinct thermodynamic regimes may be responsible forthese varied trends, and single linear functions are probably not sufficient over such large P–T ranges. Moreover,although fO2 can also strongly affect these measurements, it is not always accurately accounted for.

4 Controlling and determining fO2
during experiments
The oxygen fugacity of a magma ocean is a fundamental parameter for understanding the early evolution of aterrestrial planet because it controls the speciations andsolubilities of volatile elements, their partitioning during core formation (siderophile versus lithophile), andtheir degassing into the primitive atmosphere (lithophileversus atmophile). Therefore, it is essential to accurately
control and/or determine fO2 in experimental petrology.
Several techniques have been developed to control fO2 in
HP–HT experiments depending on the type of apparatus
used. This section describes the ex situ determination offO2 in experimental samples containing metal, or, in theabsence of any metallic phase, using Mössbauer or X-ray
Absorption Near-Edge Structure (XANES) spectroscopy.
4.1 From metal–silicate equilibrium

The effect of fO2 on the solubilities of volatile elements
in reduced silicate melts can be investigated in a vertical furnace at atmospheric pressure by controlling the
mixture of CO-CO2 or ­N2-CO-CO2 gases supplied toDalou et al. Progress in Earth and Planetary Science(2024) 11:27

the atmosphere during the experiment (e.g., Boulliung
et al. 2020). To reach very low oxygen fugacities, graphite
crucibles can be used to reach fO2 conditions at or more
reduced than the C/CO buffer (i.e., IW − 6.6 at 1 atm and1425 °C, reported in log units relative to iron–wüstite,i.e., Fe–FeO, equilibrium, IW) according to the reaction­Cgraphite + 1/2 ­O2gas = ­COgas. The C/CO buffer is reachedwhen pCO is ~ 1 bar at total pressure Ptotal = 1 bar, which
is usually the case in vertical furnaces. To lower this fO2,
it is possible to add an inert gas (rare gases, ­N2, or others depending on the study) to decrease pCO by diluting
the CO gas (Libourel et al. 2003). For instance, Libourel
et al. (2003) performed experiments at different fO2 while
using graphite crucibles under variable nitrogen partialpressures of 0.05 < pN2 < 0.95 atm.
Under most conditions, fO2 can be monitored during
the experiment using a zirconia oxygen probe ­(SIRO2
C700 + solid zirconia electrolyte oxygen sensor) withan uncertainty of ± 0.1 log units. In IHPVs, fO2 can be
flexibly controlled by admixing ­C H4 or ­H2 with the Ar
pressure medium to impose the desired fH2, and hence
also fO2 in hydrous experimental charges (Gaetani andGrove 1997; Moore and Carmichael 1998; Cottrell et al.
1999; Zajacz et al. 2010, 2011, 2012; Pichavant et al.
2014). Under anhydrous conditions, graphite capsulesor sintered forsterite capsules can also be used to reach
low fO2 (Namur et al. 2016).
The most common method to vary (not control) oxygen fugacity in piston cylinder and multi-anvil apparatuses is to use metal buffers in addition to graphite,olivine, or forsterite capsules; this approach allows themaintenance of low fO2 conditions during experiments
and prevents the loss of iron, contrary to metallic alloy
capsules such as Pt (e.g., Grove 1982). Graphite capsules are commonly used to buffer the fO2 near the C/
CO buffer via the reaction:

2FeOsilicate + Cgraphite capsule = 2Femetal + CO2gas .
(18)
Fichtner et al. (2021) used both San Carlos olivine
and pure single-crystal forsterite (Fo) as capsules.
Whereas Fo capsules can be considered as inert (to thefirst order), olivine capsules buffer fO2 via the reaction:
Fe2 SiO4olivine capsule ↔ 2 FeOsilicate melt + SiO2silicate melt ,(19)
by maintaining the FeO content of the silicate melt,thus preventing the sample from reaching very low fO2
conditions.
The coexistence of a metal and its oxide at equilibrium constitutes an oxygen buffer, and can be used tocontrol fO2 during HP experiments, or to determine
fO2 in quenched samples (e.g., Cottrell et al. 2009;

Page 17 of 33

Burkemper et al. 2012; Dalou et al. 2017; Grewal et al.
2019; Blanchard et al. 2022). The common oxygen
buffer relevant to early terrestrial planets is IW, which
is often used to control and measure fO2 in Fe‑bearing experiments, including metal–silicate partitioning
experiments. Iron or silicon metal are most often used
to lower oxygen fugacities via the equilibria:

Fealloy + 1/2 O2 = FeOsilicate melt

(20)

Sialloy + O2 = SiO2silicate melt

(21)

whereas specific capsules can be used in LVPs to target a range of fO2 conditions, in DAC experiments, thediamonds impose the fO2 within the chamber. Fe and/or Si metal can be added to DAC experiments, but theychange the composition of the system (e.g., Fischer et al.
2015). In both LVPs and DACs, carbides (Fichtner et al.
2021), nitrides (Dalou et al. 2017; Speelmanns et al. 2019;
Jackson et al. 2021), or sulfides (Namur et al. 2016; Labidi
et al. 2016; Suer et al. 2017) are also commonly usedbecause they act both as a source of volatile elements andreducers via reactions such as:
6 FeOsilicate melt + Si3 N4nitride = 6 Fealloy + 3 SiO2silicate melt
+ 2 N2silicate melt or alloy .

(22)
After experiments, the intrinsic oxygen fugacities ofquenched samples are calculated from thermodynamic
modeling of Fe–FeO equilibrium (Eq. 20) between metallic and silicate glasses based on electron microprobe
analyses and expressed relative to IW. Following thisequilibrium, fO2 can be calculated from the Fe and FeO
concentrations of coexisting alloy and silicate melt via therelation (Médard et al. 2008):
log10 f O2 =



 




melt
XFeO
2
alloy
melt
−
ln
γ
+
ln
γ
−
lnK
ln
Fe
Fe
alloy
ln(10)
XFe(23)
melt and X alloy are the mole fractions of FeO
where XFeOFe
and Fe in the silicate melt and the metal alloy, respecmelt and γ alloy are
tively, calculated on a cation basis, γFeO
Fe
their respective activity coefficients, and K is the equilibrium constant of the reaction calibrated by Médard et al.
melt is assumed to be unity in an ideal solution(2008). γFeO
model, but values up to 1.7 have been used to model
non-ideal solutions (Holzheid et al. 1997). This difference would shift the ΔIW value by ± 0.46 log units (Speelmanns et al. 2019). The effects of other components (e.g.,alloy
C, N, Si, P, S, or Ni) on γFe are accounted for using aderived version of the “Wagner ε formalism” (Wagner
1962; Ma 2001) for non-ideal interactions in liquid Fe
alloys, following the approach and formulation of Wade

Dalou et al. Progress in Earth and Planetary Science(2024) 11:27

and Wood (2005) and utilizing the calculator provided
at http://​www.​earth.​ox.​ac.​uk/​~expet/​metal​act/. To allow
direct comparison to the IW buffer, the activity of Fe canbe adjusted following the method of Stanley et al. (2014).
Whereas the stable liquidus phase of solid Fe is δ-Fe athigh pressure, the IW buffer is calibrated for γ-Fe (seereferences in Stanley et al. 2014). Therefore, the activity ofalloy
Fe in the alloy, aFe , must be correct for both (1) the difference in the entropy of fusion (S ) of the stable phaseof Fe at experimental conditions (γ-Fe; extrapolated from
Desai 1986) and that of the stable liquidus phase (δ-Fe),and (2) the temperature difference between experimental temperatures (T ) and the extrapolated fusion curve of
gamma-Fe (TL; Andrault et al. 2009) to obtain the activityof Fe in HP–HT liquid alloys as:�S(T − TL )
alloy
γ-Fe
,
aFe = aFe + exp(24)
RT
where R is the ideal gas constant and temperatures are in
kelvin. The resulting fO2 value calculated from Eqs. (23)and (24) is then compared to the IW buffer corrected forpressure effects following Zhang et al. (2016).
Under very reduced conditions (< IW–4), FeO is nolonger present in silicate melts at weight percent concentrations. In this case, fO2 is also calculated from Si–SiO2
equilibrium as described by Cartier et al. (2014).
However, in some cases, metal blobs are too small tobe analyzed. In samples loaded in AuPd and Pt capsules,
palladium and iridium powders can also be mixed withthe starting products to create Fe–Pd and Fe–Ir alloys
as fO2 sensors in the capsules (Bernadou et al. 2021). In
such cases, the activity coefficients of iron (γFe) for the
Fe–Ir and Fe–Pd alloys are determined using Woodland
and O’Neill’s (1997) equation and taken from Aukrustand Muan (1962), respectively. Bernadou et al. (2021) calculated fO2 using both methods (i.e., the capsule alloys
vs. the activity coefficients of FeO in the silicate melt and
Fe in the metal alloy) and compared the results to checkfor internal consistency and validate their attainment ofequilibrium; they obtained differences between 0.1 and
0.4 log units.
4.2 In the absence of metal

In samples with no metallic phase, it is fundamental to
the redox state of multivalent elements to probe the samples’ fO2. Because Fe is the most abundant multi-valenceelement in the mantles of terrestrial planets, knowledgeof its valence state is important for understanding oxygen fugacity in the absence of metals. Nonetheless, someexperiments can be performed with Fe-free compositions to study the evaporation or solubility of siderophileelements (e.g., Dalou et al. 2022). In that case, the redox

Page 18 of 33

state of other transition metals such as Ti, Eu, V, Cr, or Ni
can be used as a proxy to determine a sample’s fO2.
4.2.1 Mössbauer spectroscopy

Mössbauer spectroscopy is a well-established, nondestructive technique mostly used in the Earth sciences
to investigate the redox states of elements with Mössbauer-sensitive isotopes in solid media. It provides information on the electronic environment around the nucleiof those isotopes, through which it is possible to determine their valence (i.e., redox state), site occupancy, distortion of the coordination environment, spin state, andmagnetic properties (Bancroft et al. 1967; Gütlich et al.
1978; Burns and Solberg 1990).
Samples amenable to the collection of Mössbauer and
XANES (described below) spectra can be produced byexperimental techniques including, but not limited to,those mentioned above. The quantity of 57Fe is a limiting variable for Mössbauer spectroscopy given its low
natural abundance; therefore, experimental samples areoften doped with 57Fe. In contrast, the quality of XANES
spectra is insensitive to the proportions of the isotopesof iron. For both methods, different sample preparation
techniques (polished surface, sample thickness, or bulk
powder) are possible and depend on the beamline.
The Mössbauer effect is based on the recoilless emission and absorption of γ-rays during nuclear transitions
between the ground and excited states of certain nuclei
in a solid (Mössbauer 1958). Despite H, C, N, and S nothaving any Mössbauer-active isotopes, the redox stateof silicate glasses can be determined by investigating
the 14.4 keV transition of 57Fe. Studies of 57Fe represent
more than 95% of all Mössbauer applications (McCammon 2003), with the remainder being limited to othercommon Mössbauer-active isotopes such as 119Sn (e.g.,
Gütlich et al. 1978; Roskosz et al. 2020).
Today, Mössbauer spectroscopy, alongside wet chemistry and XANES spectroscopy, is one of the most widelyused techniques for determining F­ e3+/∑Fe in solids (Dyaret al. 2006). Its quantification is based on the deconvolution of the Mössbauer spectrum into one or more subspectra (McCammon and Kopylova 2004), from which
the relative areas and hyperfine parameters (i.e., central shift, quadrupole splitting, and hyperfine magnetic
splitting) of each subspectra can be obtained. Beyond
the Curie or Néel temperature, the Mössbauer spectraof paramagnetic materials, such as silicate glasses, arecharacterized only by the central shift and quadrupole
splitting, resulting in Mössbauer spectra comprising
two absorption lines (i.e., doublets; Fig. 9a). The range
within which the central shift and quadrupole splitting
occur enables the identification of the valence and spin(2024) 11:27

a)Mössbauer spectrab)

XANES spectra

QFM = 11.2

QFM = 3.3

Normalised intensity

state (Bancroft et al. 1967). Moreover, in a crystalline
solid, information on the coordination environment andsite distortion are also obtained (Bancroft et al. 1967;
McCammon and Kopylova 2004). However, below theCurie or Néel temperature, magnetic splitting is observedand Mössbauer spectra are characterized by six absorption lines (i.e., sextets) (McCammon 2000). The relative
amount of each subspectrum (i.e., site) is determined by
its area compared to the total Mössbauer spectrum area.
Hence, high spectral resolution is crucial, especially forsilicate glasses, which are characterized by (1) the symmetrical broadening of initially Lorentzian line shapes
into Gaussian distributions that reflect the occupationof Fe in a variety of different sites, and (2) their lack oflong-range order (Jayasuriya et al. 2004; Virgo and Mysen
1985; Yaroslavtsev and Chumakov 2022). The relative
amounts of each oxidation state (i.e., F­ e2+ and ­Fe3+), as
quantified by the areas of their corresponding doublets,
also depend on the absorber-thickness effect (which
depends on the number of Fe nuclei and the cross section of the sample) and the recoil-free fraction of eachoxidation state (McCammon and Kopylova 2004). Variations in sample thickness or its thickness variability canalter the intensities of the absorption lines, potentiallycompromising accurate identification of existing species,
especially when F­ e3+ is present in minimal amounts inhighly reduced materials. The recoil-free fraction of eachoxidation state is a temperature-dependent parameterand differs between ­Fe2+ and ­Fe3+ (De Grave and Van
Alboom 1991). Because the recoil-free fractions of both
­Fe2+ and ­Fe3+ approach 1 at low temperatures, several
studies have performed analyses under liquid He (4 K)or liquid N­ 2 (77 K) to maximize the recoil-free fraction(e.g.Roskosz et al. 2020; Zhang et al. 2017), thereby avoiding overestimating the ferric iron content (De Grave and
Van Alboom 1991).
Mössbauer spectroscopy can be conducted both atambient and HP conditions, but not at high temperature owing to its effect on the recoil-free fraction. Compared to laboratory-based Mössbauer sources, thegreater brilliance (and hence more rapid data collection)of synchrotron sources are crucial for precisely characterizing the redox states of silicate glasses, should thesamples be limited by low 57Fe abundance or small spatial extents (Potapkin et al. 2012). The spectrum collection time depends on the amount of 57Fe, velocity range(mm/s), and temperature (McCammon 2021), typicallytaking ~ 1–4 h, compared to a few days using a conventional Mössbauer source for similar quality spectra.
Additionally, the F­ e3+/ΣFe ratios from XANES spectra
are quantified by comparing the spectra of unknowns(i.e., samples) to those of well-known standards, established via Mössbauer spectroscopy or wet chemistry (e.g.,

Page 19 of 33

Relative intensity

Dalou et al. Progress in Earth and Planetary Science

QFM = – 4.6

Fig. 9 Comparison between 57Fe-enriched Mössbauer spectra(left) and the pre-edge region of the Fe K-edge XANES spectrum(right) of MORB glasses (synthesized and equilibrated at 1400 °C
and indicated ­fO2 conditions relative to the QFM buffer) analyzed
at room temperature and pressure (modified from Berry et al.
2018). For theses glasses, ΔQFM + 11.2 corresponds to ­Fe3+/ΣFe = 1,
ΔQFM + 3.3 to ­Fe3+/ΣFe ≈ 0.4, and ΔQFM –4.6 to ­Fe3+/ΣFe = 0

Berry et al. 2018; Cottrell et al. 2009). Indeed, Mössbauer
calibrations show that the intensities of XANES spectralfeatures, such as the centroid or edge energies, are notsimple linear functions of F
­ e3+/ΣFe in silicate glasses orother isotropic phases such as garnet (Berry et al. 2003;
Wilke et al. 2004; Zhang et al. 2017), emphasizing therole of Mössbauer spectroscopy in determining the absolute ­Fe3+/ΣFe ratios of solids.
4.2.2 X‑ray absorption near‑edge structure (XANES)
spectroscopy

XANES is a non-destructive element-selective techniqueutilizing synchrotron radiation to generate X-ray photons of a specific energy (i.e., monochromatic) that arethen absorbed by the material of interest to excite a coreelectron from an initial ground state to an unoccupiedor continuum state above the Fermi level. The energy of
the absorption edge corresponds to the core-level energy,
which is characteristic for each element. Because of thecapacity to characterize the electronic environment
around any element, it has become widely popular in the
Earth Sciences over the past ~ 30 years.
XANES spectra can be divided into three characteristic
regions in order of increasing energy: the pre-edge, edge,
and post-edge. Each region is used to determine a material property. The spectral shape in the pre-edge regionof transition metals (e.g., Fe K-edge, Fig. 9b) is related
to the transition from the 1 s core state to a bound statein the 3d shell (1 s → 3d, the quadrupole transition). The
strength of this transition is only 0.1% that of the dipole

Dalou et al. Progress in Earth and Planetary Science(2024) 11:27

transition, but, because of the high density of state for the
3d-band, small peaks (usually 1–3% intensity) are visible
in most octahedral transition metal systems (Henderson
et al. 2014). These peaks provide information about theelectronic properties and local geometry of the absorbing atom, through which it is possible to determine its
valence. In most instances (i.e., unless forbidden by selection rules), the edge region reflects the binding energy ofa core level. The shift of the edge to higher energies withhigher valence can be used to determine (but rarely toquantify) the valence of 3d transition metals in unknown
systems. The extended X-ray absorption fine structure(EXAFS) region occurs at higher energies (post-edge)
and provides information on the local geometric structure around the absorbing site. In this section, we focus
only on the pre-edge and edge regions of XANES spectra.
By far the most widely used application of XANESin the Earth Sciences involves 1 s X-ray absorption(K-edges) of 3d transition metals, especially Fe in glasses
and minerals (Bajt et al. 1994; Berry et al. 2003, 2018;
Wilke et al. 2004; Cottrell et al. 2009). XANES spectra are
not readily predicted via ab-initio simulations (althoughdensity functional theory simulations are becoming moresophisticated; see Jahn and Kowalski 2014), meaning thatthe redox state of iron (and those of other elements) are
typically quantified by empirical means. Of these, themost widely used is to determine the relative intensities of the two pre-edge features, one at ~ 7112 eV andthe other at ~ 7113.5 eV, by integrating the areas under
the two curves (typically assuming either Gaussian or
pseudo-Voigt functions) to yield the centroid energy (e.g.,
Wilke et al. 2001; Fig. 9b). The centroid energy can thenbe compared with those of standards with known ­Fe3+/
Fe2+ to determine that in the unknown. In most cases,
the centroid energy varies in a non-linear fashion with
­Fe3+/Fe2+ because the intensities of the peaks at 7112
and 7113.5 eV differ according to the symmetry of thesite(s) in which Fe resides; lower symmetry sites (e.g., tetrahedral) induce higher intensity pre-edge features thancentrosymmetric (e.g., octahedral) sites. Nevertheless,the merit of this approach is that the energies of the endmembers remain fixed and are thus independent of coordination or composition (Wilke et al. 2001; Fiege et al.
2017). The reader is referred to Berry et al. (2003), Wilke
et al. (2004), Cottrell et al. (2009), and Hawthorne andWaychunas (1988) for detailed discussions of peak andbackground fitting methods. This approach can achieve a
precision of ± 0.02 on the ­Fe3+/ΣFe ratio. Other methods
involve using the shift in edge energy in tandem with thecentroid (Berry et al. 2018), linear combination fitting, orwhole-spectrum treatments that yield comparable results(± 0.036; Dyar et al. 2016). One point of warning is thatthe pre-edge intensity of K-XANES has a self-absorption

Page 20 of 33

issue, which affects the XANES spectrum (e.g., Berryet al. 2010). The effect of self-absorption leads to spurious attenuation of peak intensities (particularly that of
the white line) and can be ameliorated by decreasing theeffective thickness of the sample containing the element
in question. This may be achieved by decreasing the path
length of the X-rays interacting with the sample by collecting only fluoresced X-rays with detector(s) placed at
an acute angle, or, if possible, diluting the sample throughadmixture with other, non-absorbing compounds, suchas boron nitride or cellulose.
Other transition metals relevant to geological systems
that have been measured in glasses by XANES are Ti(e.g., Cormier et al. 2011), Eu (e.g., Burnham et al. 2015),
V (e.g., Sutton et al. 2005), Cr (e.g., Berry and O’Neill
2004), Co (e.g., Choy et al. 2001), Ni (e.g., Essilfie-Dughan
et al. 2012), Cu (e.g., Berry et al. 2006), and Zn (e.g., Waychunas et al. 2003).
Because the treatment of XANES spectra does notyield absolute amounts of the species (largely redox state)in question, a set of standards with oxidation states precisely quantified by Mössbauer spectroscopy or wet
chemistry is required to accurately quantify the proportions of redox pairs. Furthermore, because XANES spectra are sensitive to all aspects of the electronic structureof the target element, quantifying redox state requiresthat the element of interest in both the samples andstandards be in the same coordination environment(Galoisy et al. 2001; Berry et al. 2003; Wilke et al. 2001;
Cottrell et al. 2009). Moreover, as the photon fluxes of
3rd-generation and later synchrotron setups increase,spurious changes in oxidation state induced by interactions with the incident beam via electron transfer (‘beam
damage’) have become prevalent. Both increases anddecreases in mean valences have been reported (e.g., Ferreira et al. 2013), particularly for glasses with high watercontents (e.g., Gaborieau et al. 2020). Because the probability for this transformation increases with time (i.e.,with increasing integrated flux), the occurrence of beam
damage can be ascertained by performing rapid scans(e.g., energy-dispersive) or sampling various points in a
homogeneous sample at the energy at which the change
in intensity is expected to occur. Finally, because theincident synchrotron radiation is polarized, the absorption intensities of anisotropic phases vary according totheir orientation. Therefore, accurate determination of
the bulk redox state of an anisotropic material requires
characterization of redox state as a function of crystallographic axis (e.g., Steven et al. 2022).
Unlike Mössbauer spectroscopy, XANES is applicable
to all natural states of matter, is relatively insensitive totemperature (often performed at high temperature; Neuville et al. 2014), and can be applied to a broader range ofDalou et al. Progress in Earth and Planetary Science(2024) 11:27

elements including S (e.g., Métrich et al. 2009; Brounce
et al. 2019; Lerner et al. 2021). These strengths enable
XANES to provide a more comprehensive constraint on
the fO2 of a sample by comparing multiple redox-sensitive elements in the same phase. Consequently, XANES is
the preferable choice for routine redox measurements inwell-characterized systems given an element- and phasespecific calibration to prior determinations. Additionally, in systems with multiple redox-sensitive elements,
electron exchange between two redox couples can occur
upon quenching, the most well-studied example beingthat between Cr and Fe: C­ r2+ + ­Fe3+ = ­Cr3+ + ­Fe2+ (Berryet al. 2006; Cicconi et al. 2015).

5 Compositional analyses
The choice of analytical method is more often limited by
the size or mass of the experimental sample than by thevolatile element abundances in the phases. Indeed, starting materials for HP–HT experiments are often enrichedin volatile elements at the wt.% level, and, despite variations of their partition coefficients and volatile losses
through capsules, the concentrations of volatile elements
in phases easily reach tens to hundreds of parts per
million.
5.1 Bulk analyses

From IHPVs to DACs, the size of the sample chamberdecreases from 60 mm to ≤ 100 µm in diameter, withassociated consequences on the applicability of analyticalmethods. For instance, IHPV and piston cylinder samples are > 20 mg, allowing the metal and silicate phases
to be separated manually and individually analyzed using
bulk methods. After quenching and decompression, capsules are carefully opened or cut in half with a diamondwire saw. Metal and glassy silicate phases are then separated by hand under a binocular microscope, washed,
and crushed to a fine grain size (50–150 µm). Nitrogenconcentrations in silicate and metallic phases have beenmeasured using elemental analyzers (Speelmanns et al.
2018, 2019) and by noble gas mass spectrometry (NGMS;
Li et al. 2016; Mosenfelder et al. 2019; Dalou et al. 2019a;
Boulliung et al. 2020). Both IRMS and NGMS requirechemical separation followed my mass spectrometricanalysis carried out with gas via magnetic sector mass
spectrometry. Extraction and chemical separation techniques vary depending on the nature of the material andthe targeted elements. Both analytical techniques requirea filament-based source to ionize the gas, a vacuum system to maintain the ions, an analyzer for dispersing theions according to their masses and charges, and a detection system (faraday cups or electron multipliers). The
main difference between the two techniques lies in thevacuum system, which can be dynamic (IRMS) or static

Page 21 of 33(NGMS). For IRMS, the sample and reference gases are
introduced through a dual inlet to allow rapid comparison and normalization; hence, the gases are continuously leaked into the spectrometer and the system mustbe pumped dynamically. In contrast, for NGMS, the gas
mass spectrometer is isolated from the vacuum pumping
system and the gas is consumed during analysis. In addition, the gas is isolated cryogenically and introduced via a
simple inlet. Another difference is that IRMS can measure the abundances of H, C, N, and S, whereas NGMS
can only measure N abundances.
Those bulk absolute methods are advantageous
because they do not require reference materials withsimilar matrices for calibration and they have reproducibilities < 2% (1σ) for samples with abundances exceeding 100 ppm (as in doped experimental samples). Several
studies have measured N contents by NGMS in small
pieces of both metal and silicate heated individually witha continuous-mode infrared C­ O2 laser mounted on an
x–y stage (Li et al. 2016; Dalou et al. 2019a), or within afurnace equipped with a tungsten wire (Shi et al. 2022).
Repeated heating stages are used to verify that all N was
extracted. The extracted gas is then purified to chemicallyremove active volatile species such as ­H2, ­CH4, ­H2O, CO,and ­CO2 before analysis by NGMS.
Sulfur concentrations in metallic and silicate phases
have been analyzed by IRMS (Labidi et al. 2016), but thismethod requires a wet chemistry step to transform the S
dissolved in phases into ­SF6 gas for IRMS analysis. The
advantage of this bulk method for S-bearing experimental samples is that it averages heterogeneities within themetallic phases that are present due to the immiscibilityof C-rich and S-rich iron alloys. Although both NGSM
and IRMS are very precise methods, NGSM can measure N concentrations at the ppm level to better than 10%
precision in glass fragments of 0.4–2 mg or metal beads
of a few micrograms (Dalou et al. 2019a; Boulliung et al.
2020), whereas IRMS requires hundreds to thousands ofmilligrams of material to measure C, N, or S concentrations with such precision. In addition, if sufficient molesof an element are present in the sample, such methods
can also provide isotopic compositions.
5.2 Local analyses

Small experimental samples or multiphase samples withphases smaller than 50 µm require local analytical methods(Table 1). In such cases, recovered capsules from large-volume apparatuses are often cut in half using a diamond wire
saw and one half is mounted into epoxy/resin, attached toa base using crystal bond or ethyl 2-cyanoacrylate (“superglue”), and polished with ­Al2O3 powder and ethanol.

Dalou et al. Progress in Earth and Planetary Science(2024) 11:27

Page 22 of 33

Table 1 Comparison of the different analytical techniques used to perform chemical analyses of experimental run productsTechnique

Spatial resolution

Detection limits

Uses

EPMA

≥ 1 µm

100 s of ppm

C, N, S

SIMS

≥ 10 µm

A few to 10 s of ppm

H, C, N, S

NanoSIMS

100 s of nm

A few to 10 s of ppm

H, C, N, S

LA-ICP-MS

10 s of µm

700 ppm

S

ERDA

10–100 s of µm

90 ppmH, C

IR spectroscopy

10 s of µm

A few to 10 s of ppm

H, C

Raman spectroscopy

100 s of nm to a few µm> 1000 ppm

H, C

5.2.1 Electron probe microanalysis (EPMA)

EPMA has been used to determine C, N, and S concentrations in experimental samples. This method has been
applied to both LVP and DAC samples (e.g., Roskosz et al.
2013; Fisher et al. 2020), but is more commonly used for
LVP samples. EPMA measures the characteristic X-ray
intensities emitted by elements present in a sample when
its surface is bombarded with a focused electron beam.
For each element, the characteristic X-ray intensity emitted from the sample is normalized to that of a standardof known composition, and this normalization is referredas the k-ratio. The measured k-ratios are transformed
into concentrations via analytical algorithms. Dependingon the density of the material, the analytical area can besmaller than 1 µm by applying small accelerating voltage(e.g., 10 kV), although this remains difficult by EPMA.
The compositions of 1-μm to submicron phases often
have larger analytical uncertainties, suggesting contamination by adjacent phases (e.g., Ishii et al. 2023).
Because the detection limits are high for N and S (0.03
and 0.01 wt.%, respectively; von der Handt and Dalou
2016; Labidi et al. 2016), EPMA can only be used forhighly doped samples. Carbon contents in metal alloys
are often calculated by difference, but can be also measured by EPMA if the samples are not carbon coated(Boujibar et al. 2014). For instance, Dasgupta et al. (2013)
coated their polished experimental samples with aluminum as a conductive coating, using stoichiometric­Fe3C and F­ e7C3 as primary and second standards, respectively, to measure C in metallic melts. This method shows
good agreement with C contents measured by SIMS
(Dasgupta et al. 2013).
The advantage of EPMA is that it is not very sensitive
to matrix effects; thus, reference materials do not needto have compositions extremely similar to those of theanalyzed phases. For instance, stoichiometric cementite­(Fe3C, Boujibar et al. 2014), silicon nitride ­(Si3N4, Dalou
et al. 2017) or iron nitride ­(Fe2N or ­Fe4N, Roskosz et al.
2013), and pyrite ­(FeS2, Labidi et al. 2016) have been used
to measure C, N, and S, respectively. In addition, C, N,

and S can be analyzed alongside other major elements.
In studies presenting metal–silicate partitioning data on
C, N, and S, these elements are often measured in thesilicate phase either by SIMS (or NanoSIMS) or EPMA,
but the metal phases are most commonly measured by
EPMA (e.g., Dalou et al. 2017; Suer et al. 2017). The main
reasons are that (1) there are currently no metallic reference materials available to calibrate these measurements
by SIMS, and (2) C, N, and S are often present at levels of
thousands of parts per million or a few weight percent in
the metal phases and are therefore easily measurable byEPMA. In contrast, as C, N, and S are siderophile overan extended range of experimental conditions, they arepresent at hundreds of parts per million in the silicate
glasses, making them difficult to analyze by EPMA.
The main advantages of EPMA are (1) the ease of accessin many laboratories, (2) high spatial resolution, (3) low
analytical costs compared to other analytical methods,
and, as mentioned before, (4) simultaneous determination of C, N, and S alongside other major elements.
5.2.1.1 Secondary‑ion mass spectrometry (SIMS) The
abundances of H, C, N, and S in silicate glasses are commonly determined by SIMS with detection limits at the
ppm level and internal precision better than 5%, which is
generally well below the standard deviation of the number of analyses performed in experimental samples (e.g.,
Dalou et al. 2017; Nash et al. 2019; Boulliung et al. 2020;
Fichtner et al. 2021). This method can be applied to both
LVP and LHDAC samples, but the large beam spot size
(generally > 10 µm in diameter) have limited its use for
LHDAC samples. It is therefore more suitable for LVP
samples.
For SIMS analyses of H, C, N, and S, a focused primary
ion beam of ­Cs+ (an ­O− beam would generate positive
secondary ions) is used to ablate (or ‘sputter’) the surface
of a polished sample, and the resulting secondary ionsare extracted and transferred to a mass spectrometer for
analysis. Whereas IRMS and NGMS require simple mass
spectrometers with only a section magnet to separate

Dalou et al. Progress in Earth and Planetary Science(2024) 11:27

masses at high mass resolution because of the chemical
separation procedures performed beforehand, there is no
chemical separation procedure performed before SIMS
analyses, so a high mass resolution is necessary to reduce
interferences and separate molecular and atomic isobaric species. For instance, Füri et al. (2018) used a mass
resolution ≥ 10,725 to separate the 15N16O− peak from29
SiH2− in N- and H-bearing silicate glasses, whereas amass resolution of 600 was used in recent NGMS analyses of N, regardless of the detector (Boulliung et al. 2020).
The key features of SIMS that allow the local measurement of ppm levels of H, C, N, and S in silicate glasses are(1) its high secondary ion yields, and (2) the extremely
low background signals, facilitating high signal-to-noise
ratios.
Measurements of volatile elements by SIMS require acertain sample preparation protocol to lower the background noise and increase the precision of the measurements, as follows. Samples must be removed from theirresin mount, pressed into high-purity indium metal
mounts, and gold-coated. Then, samples are generally
left in an oven and/or a degassing bench for at least 24 h,and then in the instrument airlock for at least another24 h to ensure the thorough removal of any adsorbed
water before introduction into the sample chamber. In
addition, prior to analysis, the surfaces of glasses andmetals are pre-sputtered for 180 s over a minimum areaof 10 μm × 10 μm to minimize any surface contamination. Because volatile abundances are determined using
the calibrated relationship between the secondary-ion
intensity ratios 16OH−/29Si−,16OH−/17O−, 16OH−/18O−,
12
C/18O−, 14N16O−/16O2−, and/or 32S−/30Si− and the
known equivalent H­ 2O, ­CO2, N, or S abundances in silicate glass reference materials, the reference materials
must have major element compositions similar to thoseof the experimental silicate glasses. This method is welldeveloped and calibrated, and many laboratories aroundthe world have analyzed H, C, and S for decades (e.g.,
Delaney and Karsten 1981; Pan et al. 1991; Hervig 1992;
Deloule et al. 1995; Hauri 2002; Hauri et al. 2002). In contrast, nitrogen analyses were only recently developed,
and reference materials remain scarce (Regier et al. 2016;
Füri et al. 2018; Mosenfelder et al. 2019). Nonetheless,the agreement between N analyses via SIMS and NGMS
is very promising (Fig. 10a).
5.2.2 NanoSIMS

NanoSIMS can be used to analyze LVP samples (e.g., Gaoet al. 2022), but remains the most common method foranalyzing HVEs in DAC samples (e.g., Suer et al. 2017;
Blanchard et al. 2022). Indeed, DAC experimental sample
volumes (~ 0.0001 ­mm3) are orders of magnitude smaller

Page 23 of 33

than those from multi-anvil experiments (~ 1 m­ m3 for thesmallest multi-anvil samples). Therefore, DAC samples
require special preparation for analysis. After quenching and decompression, a cross section of the quenchedmelted region is recovered using a focused ion beam
(FIB) instrument (Fig. 11a, b). These 1–5-µm-thick lamellae, usually of a 20 µm × 30 µm region, are polished by ion
milling and placed on a suitable substrate for chemical
analysis. More details on DAC sample preparation can befound in Jennings (2020). Recently, NanoSIMS has beenused to image the relative abundances of C (Fischer et al.
2020; Blanchard et al. 2022) and S (Suer et al. 2017) inmetal and silicate phases.
Although its fundamental principle is similar to SIMS,
NanoSIMS has the ability to refocus a ­Cs+ primary beam
to ~ 50 nm in diameter, thereby combining fine spatial
resolution with a sector mass spectrometer capable ofisotopic analyses like SIMS. The advantage of NanoSIMS
relative to standard SIMS analyses is the submicron lateral resolution, which is achieved by positioning the
primary probe-forming lens parallel and very close to
the sample, focusing the beam to a very small diameter.
NanoSIMS analyses are performed in two steps: first, thesample is chemically imaged using a controlled raster ofthe primary beam across the sample surface to produce
high-resolution ion maps for selecting a region of interest(1–5 µm2); then, analyses are performed while avoiding
cracks, grain boundaries, graphite inclusions, etc. However, using such a finely focused primary beam (of a few
picoamperes) to sputter the sample surface results in secondary ion signals that are commensurately low, leading
to lower precision than in conventional SIMS analyses.
Yet, this method is widely used to visualize elemental distributions because it employs multiple detectors and canchemically (and sometimes isotopically) map up to sevenelements. Although, NanoSIMS neither has the flexibility to easily analyze several volatile elements at the sametime (detectors—i.e., electron multipliers and faradaycups—cannot be switched as easily as on a SIMS) nor themass resolution power (MRP) to measure isotopic compositions of non-doped phases, its MRP and detection
limits are sufficient to distinguish 12C−, 14N16O−, and 32S−
from interferences by neighboring mass peaks (Suer et al.
2017; Blanchard et al. 2022; Gao et al. 2022). Similar to
SIMS analyses, C, N, and S abundances are determinedfrom 12C, 14N16O, and 32S, respectively, normalized to 29Si
or 28Si (Fig. 11c, d); therefore, this method also requires
reference materials with compositions/matrices similar
to those of the experimental samples. Hydrogen contents,as ­H−, can be quantified by NanoSIMS in experimental
silicate glasses, but these analyses are more common for
natural materials (e.g., Shilobreeva 2017).

Dalou et al. Progress in Earth and Planetary Science

b)

6000

1
1:

Model
Prediction interval 99%

R2 = 0.99

4000

2

3000

1
1:

1.5

2000

1

S/28Si – nanoSIMS

N (ppm) – SIMS

5000

0.5

1000

0

0

Page 24 of 33

32a)(2024) 11:27

0

1000

2000

3000

0

0.5

4000

N (ppm) – NGMS

1

5000

1.5

2

6000

S (ppm) – LA-ICP-MS

Fig. 10 a Comparison of N abundances measured by SIMS and NGMS in synthetic glasses (modified from Boulliung et al. 2020). (Inset) Low
concentration data (< 2 ppm N) are shown on an enlarged scale. b NanoSIMS calibration curve for S analyses, with 32S/28Si determined by NanoSIMS
reported as a function of S contents independently determined by laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS,
modified from Suer et al. 2017)

Fig. 11 LHDAC sample (modified from Suer et al. 2017) showing a and b LHDAC sample preparation for analysis, c a backscattered SEM imageof a metal–silicate sample synthesized at 66 GPa and 3500 K, and d NanoSIMS chemical maps illustrating that most S is partitioned into the metal
blob of that same sample, modified from Suer et al. (2017)

Dalou et al. Progress in Earth and Planetary Science(2024) 11:27

5.2.3 Laser ablation inductively coupled plasma mass
spectrometry (LA‑ICP‑MS)

Sulfur contents in silicate and metallic phases can be also
determined by LA-ICP-MS, although this technique ismore destructive than SIMS (Table 1). Rather than a liquid introduction system found on a standard ICP-MS,
the sample is directly ablated by a pulsed laser beam
generally a few tens of µm in diameter. Therefore, thismethod is only adapted to LVP samples.
When the sample is fragmented to atomic levels within
the ablation cell, a certain amount of matter is extracted
from the surface of the sample by vaporization, generating aerosols of nanoparticles (a mixture of excited atoms,
ions, molecules, and solid particles). The amount of material and the size of the particles removed depends on thenature of the sample analyzed and the energy of the laser,which can be regulated. To reduce thermal alteration of
the sample, and thus lower the elemental fractionation
during ablation, a flat-top-type homogeneous energy
distribution and short-wavelength ultraviolet laser must
be used. The aerosol is then transported by a helium gas
flow to the plasma of the ICP-MS. The ions are electrostatically directed into a mass spectrometer, separated
according to their mass-to-charge ratio, and eventuallysent to a detector. As with SIMS or EPMA, quantitative analyses require calibration using external standard
materials of known composition and with matrices similar to that of the analyzed sample. Few S concentrations
determined by LA-ICP-MS have been reported in the literature because S measurements are challenging due to:(1) spectral interferences; (2) the lack of well-calibrated
reference materials, particularly for silicates; and (3)problems with blank contamination, which become significant at low sulfur concentrations (Ripley et al. 2011).
Yet, compared to SIMS analyses, the key feature of LAICP-MS is the ability to ablate a relatively large volume
of material quickly, enabling a high signal-to-noise ratio.
With this method, sulfur contents have been determined in silicate glasses (Rottier and Audédat 2019)
down to concentrations of 700 ppm. Rottier and Audédat (2019) tested the feasibility of S measurements by
LA-ICP-MS in silicate glasses using a routine spot size of
40 µm, but also managed to analyze phases as small as
13 µm. Using a double correction method to account fora systematic drift between calculated and true sulfur concentrations, they quantified sulfur in silicate glasses down
to several hundreds of parts per million; after correction, the difference between S concentrations obtained by
EPMA and LA-ICP-MS was less than 5%.
5.2.4 Nuclear microprobe techniques

Hydrogen and carbon contents in experimental samples from metal–silicate equilibration experiments

Page 25 of 33

have been measured by nuclear microprobe techniques
in LVP samples (e.g., Clesi et al. 2018; Malavergne et al.
2019). This technique is only suitable for LVP samples
because of its low spatial resolution. In these methods,
the interaction of an energetic ion beam with the target
produces spectra from the reaction products (X-rays,
charged particles). Hydrogen abundances in phases
have been determined by elastic recoil detection analysis (ERDA; Bureau et al. 2009; Withers et al. 2012; Clesi
et al. 2018), in which an incident 4He+ beam is focused
onto a large area (50 × 200 µm2) of the polished sample and interacts with hydrogen. This interaction causes
elastic recoil, ejecting the H nucleus from the sample
surface for detection. ERDA does not require calibration (Bureau et al. 2009). As with SIMS, the analytical depth is limited to several micrometers beneaththe surface. This method allows H determination at
the micrometric scale with 5–15% relative uncertainties and a detection limit of 94 ppm H­ 2O (Bureau et al.
2009). Carbon abundances have been measured using
nuclear reaction analysis (NRA), which employs adeuteron microbeam to produce the nuclear reaction
12
C(d,p)13C upon interaction with the sample (Wanget al. 2010). The accuracy on such C determinations
is 4–8% for metallic phases and 15–17% for silicate
glasses (Malavergne et al. 2014).
Despite the numerous advantages of these methods,
especially the fact that they are quasi absolute, spectral
analyses require two-step processing using two distinct
programs (RISMIN, Daudin et al. 2003; and SIMNRA,
Mayer 1999) and perfect knowledge of the beam parameters and the major element compositions of the phases
determined by EPMA. Sample preparation is not very
different from that for SIMS volatile analyses: samples
must be mirror-polished on one side, pressed into an
indium mount, and stored both before and after gold
coating in a furnace and/or desiccator to prevent volatile adsorption onto the sample surface. The main difference compared to SIMS mounts is that samples must bealigned across the mount because analyses are performed
with a grazing angle of 75°.
5.2.5 Vibrational spectroscopy

IR and Raman spectroscopy are both vibrational techniques used to determine the speciation, and sometimes
the abundances, of HVEs. IR spectroscopy is the resultof light absorption by vibrating molecules, whereas
the Raman effect is due to the scattering of light by thevibrating molecules. In both cases, the peak positions are
determined by the vibrational energies associated withthe bonds within the molecules of the sample. Hence,
Raman and Fourier-transform IR (FTIR) spectra areoften used and can be interpreted similarly. However, IR

Dalou et al. Progress in Earth and Planetary Science(2024) 11:27

Page 26 of 33

concentration. Therefore, doubly polished sections can be
repeatedly measured and thinned to decrease a spectrum’s
signal-to-noise ratio and peak absorbances to less than 2 inboth the near-infrared and mid-infrared regions (Mosenfelder et al. 2019). Notably, the measurement of the sample thickness often represents the largest source of error intransmission IR analyses.
The IR method is based on Beer’s law:A = ε · c · ℓ,Fig. 12 Comparison of peaks associated with C–O–N–H species in a
Raman spectra and b FTIR spectra of the same experimental silicate
glasses produced at 3 GPa, 1800 °C, and IW–1.1 (blue) and IW–1.8(orange) (modified from Grewal et al. 2020). a Background corrected
Raman spectra, and b background corrected, thickness normalized
FTIR spectra. The dashed curves show the broad asymmetric peakof O–H vibrations post-deconvolution from N–H stretching frequency
in the similar range

is more sensitive to hetero-functional groups, i.e., polarfunctional groups such as molecules formed from H
bonds, whereas Raman is more sensitive to homo-nuclear
bonds such as ­O2 or ­N2. Therefore, polar bonds with highdipole moments such as N
­ H4+ and ­H2O are emphasized
in FTIR spectra but appear very weak in Raman spectra. Conversely, highly polarizable bonds such as triplebonded ­N2, CN, ­O2, or ­CO2 are commonly emphasized in
Raman spectra but appear very weak or inactive in FTIR
spectra (Fig. 12). Nonetheless, the vibrations of numerous HVE-bearing molecules, particularly H-bonded molecules, are active in both IR and Raman spectra.
5.2.5.1 Infrared spectroscopy IR spectroscopy is oneof the most popular methods for determining the abundance and speciation of the H-bearing moieties O­ H− andmolecular water in silicate phases because this technique
is non-destructive, yet highly sensitive. Generally, the analyzed area can vary from a few square microns to 100 × 100µm2 depending on the HVE species and concentrations, aswell as the sample’s texture. Therefore, this method is only
adapted to LVP samples. Analyses are most commonly performed in transmission mode, requiring that samples betransparent and doubly polished; this can present a challenge for small multiphase experimental samples. The sample thickness required generally varies from several hundreds of micrometers to < 10 µm, but depends on the HVE(25)

where A is the absorbance, ε the molar absorption coefficient ­(M−1 ­cm−1), c the molar concentration (M), and ℓthe optical path length (cm). This law describes the linear relationship between the number of infrared active
bonds in a matrix and the quantity of absorption andallows the determination of the concentration of a species as c = (WM · A)/(d · ρ · ε), where WM is the molar
weight (g/mol), d the sample thickness (equivalent toℓ),and ρ the density of the sample. Therefore, this method
requires a specific calibration of the absorption coefficient,ε, for a given matrix composition and volatile species. Nonetheless, numerous studies of H in both naturaland synthetic silicate glasses by IR analysis have demonstrated very good sensitivities and accuracies (down to afew ppm H; see review by Bureau et al. 2009).
5.2.5.2 Raman spectroscopy Because Raman spectroscopy employs visible wavelengths, it provides better spatial resolution (hundreds of nanometers to a few
micrometers) than IR spectroscopy. Nevertheless, Raman
spectroscopy has been essentially used for LVP samples(see references below).
Relatively recent studies determining H contents by
micro-Raman spectroscopy (e.g., Mercier et al. 2009;
Le Losq et al. 2012; Schiavi et al. 2018) have employed
two methods called “external” and “internal” calibrations. “External” calibrations compare the intensity or
integrated intensity of the water band (i.e., the height ofthe peak or the area under the peak, respectively) in an
unknown sample to those of well-characterized standard glasses. Therefore, this method requires calibration
curves as with SIMS, but in this case, the slopes of thecurves must vary as a function of silicate glass composition. In contrast, “internal” calibrations normalize theintensity of the water band to those of bands in the silicate spectral region (e.g., Mercier et al. 2009; Le Losq
et al. 2012), which tends to correct for or decrease theeffects of instrumental and analytical conditions suchas laser power fluctuations, focusing errors, and differences in confocal volume size, as well as differencesin light absorption and reflectance that depend on theglass structure and composition. By combining thesetwo calibration methods, Schiavi et al. (2018) improved

Dalou et al. Progress in Earth and Planetary Science(2024) 11:27

Page 27 of 33

the accuracy of Raman H measurements to a relative
standard deviation of ~ 4% (1σ) on average, though thisreaches ~ 12% (1σ) for water contents of ~ 0.1 wt. %.
Although the detection limits are relatively high forsome natural samples, both Raman and FTIR analyses
are useful for experimental samples, which are usuallyenriched in H. The main advantages of Raman spectroscopy are that it requires minimal sample preparation (only a relatively flat surface), is non-destructive,
and allows rapid analysis (within minutes) at high spatial
resolution (Schiavi et al. 2018). Another advantage is that
Raman signals can be gathered below the sample surface,which allowed Dalou et al. (2022) to determine C and N
speciation in bubbles degassed from a reduced silicate
melt analogous to a magma ocean.
Carbon can also be quantified by FTIR and microRaman spectroscopy with accuracies on the order of 0.2–
0.4 wt.% (Amalberti et al. 2011, 2021; Morizet et al. 2013;
Schanofski et al. 2023). However, all analytical developments for FTIR and Raman have focused on measuring C as C
­ O2 or C­ O32− dissolved in silicate glasses. In
reduced silicate glasses analogous to a magma ocean, C
is dissolved as C
­ H4 or C­ N−, or can even occur as graphite(Armstrong et al. 2015; Dalou et al. 2019b; Mosenfelder
et al. 2019). Therefore, it is not yet possible to quantify
the abundances of multiple C species in such reduced
glasses (Armstrong et al. 2015), although their relative
abundances can be investigated depending on P, T, fO2,
and composition (see Armstrong et al. 2015 for C; Dalou
et al. 2019b and Mosenfelder et al. 2019 for N; Wilke et al.
2011 and Namur et al. 2016 for S).

Finally, whereas LVP studies show that oxygen fugacity is a key parameter controlling the solubility, and thus
the degassing and metal–silicate partitioning, of HVEs
(Suer et al. 2023), the specific effects of variable oxygen
fugacities on metal–silicate partitioning of HVEs remains
untested at > 25 GPa, i.e., in DAC experiments, due totechnical challenges (e.g., Kulka 2021).
More generally, the complementary techniques
reviewed herein have promoted large improvements
in our understanding of the behaviors of HVEs during
planetary formation processes. Nonetheless, an important gap remains: metallic reference materials are needed
for the application of local analytical techniques such as
SIMS or NanoSIMS to HVE analyses of metal blobs inexperimental samples.

6 Conclusions
The last two decades of advances in analytical methods
have provided the experimental petrology community
with methods for analyzing challenging, multiphase experimental samples comprising silicate glass, metal beadsof various sizes, and bubbles. The achievement of DAC
experiments coupled with the development of NanoSIMS
has allowed laboratory simulations of conditions relevant
to core formation and associated analyses. These very HP
experiments have shown results in first-order agreementwith results from experiments using large-volume apparatuses (Suer et al. 2023). Yet, partition coefficients obtained
over a large range of temperature or pressure conditions
show discrepancies that are not straightforward to understand (e.g., Rose-Weston et al. 2009; Suer et al. 2017, 2023).
They may be related to changes in chemical behaviors
across the large range of P–T conditions probed by largevolume apparatuses and DACs. Still, this implies partition
coefficients should not be extrapolated beyond the P–T
ranges in which they were measured (Suer et al. 2023).

Availability of data and materials
Not applicable.

Acknowledgements
The authors thank Evelyn Füri and Laurette Piani for their support and fruitful
discussions on analytical techniques. We are particularly grateful to Sumith
Abeykoon and Pierre Condamine for providing unpublished figures and help‑
ing with references. We also thank Damanveer Grewal for providing original
figures that helped make Fig. 12 and we warmly thank Robert Dennen for his
English editing and his great help to improve Fig. 1, 5, 6 and 8. We are very
grateful to two anonymous reviewers for their very helpful and constructive
reviews and to associate editor Ohfuji san for managing our submission. This is
CRPG contribution number 2856.
Author contributions
CD conceived, designed, and wrote the review. TAS wrote the LHDAC section
and supervised the NanoSIMS section; LT wrote the low-pressure apparatuses
sections, AG wrote the Mössbauer section, and WO wrote the XANES section,
supervised by PS, who also contributed to the introduction, defining partition‑
ing and solubility sections and the low-pressure apparatuses sections. All
authors read and approved the final manuscript.
Funding
This work was supported by ANR CSI Planet.

Declarations
Competing interests
The authors declare no competing interests.
Received: 10 November 2023 Accepted: 23 April 2024

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