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\DOI{10.5802/crphys.150}
\datereceived{2022-11-07}
\daterevised{2023-01-05}
\dateaccepted{2023-02-23}
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\dateposted{2023-04-20}
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\begin{document}



\begin{noXML}
%
%\TopicEF{From everyday glass to disordered solids}{Du verre quotidien
%aux solides d\'esordonn\'es}

\title{From nanoscale heterogeneities to nanolites: cation clustering
in glasses}

\alttitle{Des h\'{e}t\'{e}rog\'{e}n\'{e}it\'{e}s nanom\'{e}triques aux
nanolites : les~agr\'{e}gats cationiques dans les verres}

\author{\firstname{Laurent} \lastname{Cormier}\CDRorcid{0000-0002-3554-0707}\IsCorresp}
\address{Institut de Min\'{e}ralogie, de Physique des Mat\'{e}riaux et
de Cosmochimie (IMPMC) (Sorbonne Universit\'{e}, CNRS UMR 7590,
Mus\'{e}um national d'Histoire naturelle, IRD UMR 206), 4 place
Jussieu, 75005 Paris, France}
\email[L. Cormier]{laurent.cormier@sorbonne-universite.fr}

\author{\firstname{Laurence} \lastname{Galoisy}\CDRorcid{0000-0001-5244-5851}}
\addressSameAs{1}{Institut de Min\'{e}ralogie, de Physique des
Mat\'{e}riaux et de Cosmochimie (IMPMC) (Sorbonne Universit\'{e}, CNRS
UMR 7590, Mus\'{e}um national d'Histoire naturelle, IRD UMR 206), 4
place Jussieu, 75005 Paris, France}
\email[L. Galoisy]{laurence.galoisy@upmc.fr}

\author{\firstname{G\'{e}rald} \lastname{Lelong}\CDRorcid{0000-0002-3561-8228}}
\addressSameAs{1}{Institut de Min\'{e}ralogie, de Physique des
Mat\'{e}riaux et de Cosmochimie (IMPMC) (Sorbonne Universit\'{e}, CNRS
UMR 7590, Mus\'{e}um national d'Histoire naturelle, IRD UMR 206), 4
place Jussieu, 75005 Paris, France}
\email[G. Lelong]{gerald.lelong@sorbonne-universite.fr}

\author{\firstname{Georges} \lastname{Calas}\CDRorcid{0000-0003-0525-5734}}
\addressSameAs{1}{Institut de Min\'{e}ralogie, de Physique des
Mat\'{e}riaux et de Cosmochimie (IMPMC) (Sorbonne Universit\'{e}, CNRS
UMR 7590, Mus\'{e}um national d'Histoire naturelle, IRD UMR 206), 4
place Jussieu, 75005 Paris, France}
\email[G. Calas]{georges.calas@upmc.fr}


\shortrunauthors

\keywords{\kwd{Glass} 
\kwd{Structure}
\kwd{Heterogeneities}
\kwd{Nucleation}
\kwd{Spectrocopy}}


\altkeywords{\kwd{Verre} 
\kwd{Structure} 
\kwd{H\'{e}t\'{e}rog\'{e}n\'{e}it\'{e}s}
\kwd{Nucl\'{e}ation}
\kwd{Spectroscopie}}


\begin{abstract}
The structural behavior of cations in multicomponent oxide glasses
cannot be described within a random network model, due to the presence
of cation clusters that provide original properties. These clustering
processes are even observed for cations that may occur at a percent
level concentration, which makes it all the more spectacular. In
particular, the structural and chemical characteristics of
Zr$^{4+}$- and
Fe$^{2+}$/Fe$^{3+}$-based clusters in
(alumino)silicate glasses illustrate the link between the short-range
order around cations and the formation of nanoscale heterogeneities.
The structural characteristics of these Zr- or Fe-rich clusters are
similar, as both are based on edge-sharing cation polyhedra. Cations
may also occur in a network-forming position. In that case, cation
sites are corner-linked with the silicate network. In such positioning,
Pauling rules and local charge balance requirements will favor cations
be diluted at a nanoscale. The topological constraints of these two
types of local structure are stronger for the former than for the
latter, as disorder effects are smaller for edge-sharing than for
corner-sharing polyhedra. This may explain crystal nucleation during
the growth of such ordered heterogeneities, giving rise to original
properties that are illustrated in a large diversity of glassy
materials encompassing high-tech glass-ceramics and volcanic glasses.
\end{abstract}


\begin{altabstract}
Le comportement structural des cations dans les verres d'oxydes
multicomposants ne peut pas \^{e}tre d\'{e}crit dans un mod\`{e}le de
r\'{e}seau al\'{e}atoire, en raison de la pr\'{e}sence d'agr\'{e}gats
de cations \`{a} l'origine de propri\'{e}t\'{e}s originales. Ces
processus de regroupement sont m\^{e}me observ\'{e}s pour les cations
en faible concentration, ce qui le rend d'autant plus spectaculaire. En
particulier, les caract\'{e}ristiques structurales et chimiques des
agr\'{e}gats \`{a} base de Zr$^{4+}$- et de Fe$^{2+}$/Fe$^{3+}$ dans
des verres (alumino)silicates illustrent le lien entre l'ordre \`{a}
courte port\'{e}e autour des cations et la formation
dh\'{e}t\'{e}rog\'{e}n\'{e}it\'{e}s nanom\'{e}triques. Les
caract\'{e}ristiques structurales de ces amas riches en Zr ou en Fe
sont similaires, car les deux sont bas\'{e}es sur des poly\`{e}dres
cationiques partageant des ar\^{e}tes. Les cations peuvent
\'{e}galement se trouver en position de formateur de r\'{e}seau. Dans
ce cas, les sites cationiques sont reli\'{e}s au r\'{e}seau
silicat\'{e}. Dans un tel positionnement, les r\`{e}gles de Pauling et
les exigences locales d'\'{e}quilibrage des charges favoriseront la
dilution des cations \`{a} l'\'{e}chelle nanom\'{e}trique. Les
contraintes topologiques de ces deux types de structure locale sont
plus fortes pour le premier que pour le second, car les effets de
d\'{e}sordre sont plus faibles pour le partage des poly\`{e}dres par
ar\^{e}tes que pour le partage par sommets. Cela peut expliquer la
nucl\'{e}ation du cristal pendant la croissance de ces
h\'{e}t\'{e}rog\'{e}n\'{e}it\'{e}s ordonn\'{e}es, donnant lieu \`{a}
des propri\'{e}t\'{e}s originales qui sont illustr\'{e}es dans une
grande diversit\'{e} de mat\'{e}riaux vitreux englobant les
vitroc\'{e}ramiques de haute technologie et les verres volcaniques.
\end{altabstract}


\maketitle

\end{noXML}

\vspace*{-10pt}


\section{Introduction}

A glass is defined by a lack of periodicity and long-range order and a
specific thermodynamic behavior with the existence of the glass
transition. Information about the structure of oxide glasses and melts
at a molecular-scale helps rationalize and understand their properties
\cite{1,2}. In multicomponent glasses, network-forming cations
occur in tetrahedral sites or similar network position, the
network-forming role arising from well-defined topological
relationships within the polymeric network. Cations occur either as
modifiers, playing a depolymerizing role of the polymeric framework, or
as charge compensators, in the vicinity of charge-defective sites in
the glassy network. These structural properties govern most glass
properties. However, cation clustering is not predicted in such a
simplified model of glass structure, despite increasing evidence of its
importance. 




Glass structure remains a challenge, because glasses possess no
long-range structural periodicity or symmetry. Information about short-
and medium-range organization around most cations is limited, due to
the non-directional and partly ionic nature of the bonds between
cations and oxygen atoms. The use of specific structural techniques and
modeling codes has demonstrated that the structure of glasses does not
obey a random distribution and cannot be described as a homogeneous
atomic distribution \cite{2}. In the modified random network (MRN)
model proposed by Greaves \cite{3}, the structure of multicomponent
glasses is no more described as being homogeneously random (continuous
random network model \cite{4}) in contrast to silica and other
network glasses. This model proposes that non-framework cations
(alkalis and alkaline-earths, transition elements{\ldots}) are not
distributed at random throughout the silicate framework. These cations
rather occur within domains percolating through the polymerized network
constituted by SiO$_{4}$ tetrahedra and forming less polymerized and
more ionic regions. The polyhedral units characterize the short-range
order (SRO). The structure beyond the first shell of nearest neighbors
corresponds to the medium range order (MRO), usually observed up to
1--2~nm~\cite{5}, which obeys the basic crystal chemical principles
(e.g., Pauling rules). Such a model has been successful to rationalize
spectroscopic, structural and macroscopic properties of glasses
\cite{6,7}.


Direct evidence of cation clustering and structural heterogeneity of
glasses was provided by neutron diffraction experiments with isotopic
substitution. This original approach has demonstrated the existence of
Ca--Ca, Ni--Ni and Ti--Ti pairs in Ca-, Ni- and Ti-bearing glasses,
respectively \cite{8}. The geometry of these atomic pairs is based
on edge-sharing sites, corresponding to 5-coordination for
Ni$^{2+}$ and Ti$^{4+}$ or 6-coordination
for Ca$^{2+}$. In addition, a spectacular cation
clustering, at least up to 0.6~nm diameter, has been observed by X-ray
absorption spectroscopy (XAS) in low-alkali borate glasses containing
minor M$^{2+}$ cations (M $=$ Ni, Co, Zn)~\cite{9}.


The importance of these structural heterogeneities appears in the glass
transition phenomenon itself. In fact, dynamical heterogeneities are
considered as an important concept with regions of slow and high
mobility, the importance of which increases as the glass transition
temperature ($T_g$) is approached by the system. These domains are
associated with chemical or structural fluctuations. In Molecular
Dynamics simulations of CaO--Al$_{2}$O$_{3}$--SiO$_{2}$ glasses,
dynamical heterogeneities have been identified with compositional and
structural fluctuations associated with regions enriched with CaO and
Al$_{2}$O$_{3}$ (high mobility) or SiO$_{2}$ (low
mobility)~\cite{10}. Over the last 10~years, the importance of
nanoscale heterogeneities has been increasingly recognized due to the
emergence of new techniques, notably by directly imaging the spatial
and chemical fluctuations using Transmission Electron Microscopy
(TEM)~\cite{11,12,13}. These techniques allow a visualization
of the nanoscale glass structure, especially as extended phase
separation occurs~\cite{14}.


A deeper knowledge of the MRO is critical for an understanding of a
wide range of macroscopic properties, including mechanical and optical
properties or crystallization processes \cite{12,15,16,17}.
For instance, the clustering of rare earth ions in silica glass
degrades the performance of optical devices, as it favors non-radiative
energy transfers causing in turn a quench of fluorescence. Addition of
a codopant, such as Al, improves the spatial distribution of rare earth
ions R, forming R--O--Al bonds (with rare-earth compensating the charge
deficit of AlO$_{4}$ tetrahedra) at the expense of R--O--R linkages,
leading to the disappearance of these rare-earth clusters~\cite{2}.

In this paper, we analyze recent results that have been obtained on
cluster-containing glasses trough a multi-technique approach, using
diffraction and spectroscopic techniques complemented by numerical
modeling. These  data show that the structural behavior of cations
cannot be predicted by considering a random network model of
multicomponent oxide glasses. The structural heterogeneities are
observed for the case of Zr (part 2) and the influence of this
organization on the crystallization properties is considered (part 3).
We then focus the discussion on the case of Fe, showing experimental
proofs of Fe segregation even at dilute Fe concentration (part 4) and
in natural glasses (part 5). In these latter materials, Fe
heterogeneities are likely related to the presence of nanolites that
strongly impact viscosity properties. In part 6, we discuss how both
Zr- and Fe-clusters are based on edge-sharing cation polyhedra in which
cations are segregated. By contrast, cations in a network-forming or
network-modifying position show only corner-sharing linkages with the
(alumino)silicate network. The topological constraints of these two
types of local structure are stronger for the former than for the
latter. Indeed, degrees of freedom and hence disorder effects are
smaller for edge-sharing than for corner-sharing polyhedra. The
structural and chemical characteristics of Zr- and Fe-clusters help
rationalize the role of these elements on the properties of glasses and
glass-ceramics, including volcanic glasses and high-tech glasses. These
structure-property relationships are observed even in diluted glasses,
which makes these clustering processes all the more spectacular.


\section{Heterogeneities in glasses: a typical case with Zr$^{4+}$}


Because chemical selectivity is needed when investigating
multicomponent glasses, XAS, associating Extended X-ray Absorption Fine
Structure (EXAFS) and X-ray Absorption Near Edge Structure (XANES)
spectroscopies, has been extensively used, giving detailed information
on MRO~\cite{18}. Among transition elements, Zr$^{4+}$ is
particularly attractive due to its stability in a large diversity of
coordinated sites. In silicate glasses, Zr$^{4+}$ {is known to play a
stabilizing or nucleating role, depending on the coexisting cations}
\cite{19,20,21}. We have investigated the Zr$^{4+}$
{environment in different aluminosilicate glasses with monovalent and
divalent cations using XAS} \cite{22}. A combination of K- and
L-edge XANES spectra unambiguously revealed that the Zr$^{4+}$
environment differs between glasses containing alkalis (Li and Na
aluminosilicate glasses) or divalent cations (Mg, Ca, Zn). Zirconium
coordination does not appear to influence its nucleating role
(Figure~\ref{fig1}). Indeed, in alkali aluminosilicate glasses,
Zr$^{4+}$ dramatically favors the nucleation rate in Li-bearing
glasses and, by contrast, does not enhance crystallization in
Na-bearing glasses. Therefore, Zr coordination is not the only relevant
parameter to determine the ability for Zr$^{4+}$ to act as a
nucleating agent. By and large, for the main nucleating agents in
glasses (i.e. Zr$^{4+}$ {or Ti$^{4+}$), there is no evidence that
specific sites or coordination numbers can be proposed to favor
nucleation} \cite{23}. The key factor governing
nucleation/crystallization lies instead in the medium range
organization.

\begin{figure}
\includegraphics{fig01}
\caption{XANES spectra at L$_{2}$-edge (left) and K-edge (right) for
zirconium in various aluminosilicate glasses showing more or less high
degree of nucleation, as determined by Differential Scanning
Calorimetry (adapted from~\cite{22}). Two groups of spectra can be
distinguished: spectra for monovalent cations (Na$^{+}$ and Li$^{+}$)
and divalent cations (Ca$^{2+}$, Mg$^{2+}$, Zn$^{2+}$) corresponding to
different Zr environments.\label{fig1}}
\end{figure}

Interestingly, XAS is able to probe MRO (Figure~\ref{fig2}). For
instance, EXAFS data on Mg aluminosi{\hubreak}licate glasses (MgAS) containing
4~mol\% ZrO$_{2}$ show the contribution of the next-nearest neighbors
(Si and Zr) and provide constraints to model Zr environment. This
approach demonstrates the presence of strong, edge-sharing linkages
between 7-coordinated Zr sites, a local structure that mimics that
encountered in m-ZrO$_{2}$. Conversely, in most Zr-bearing alkali
glasses, Zr is 6-coordinated and is only corner-linked to Si/Al-sites
(and charge-compensating cations).


\begin{figure}
\includegraphics{fig02}
\caption{EXAFS spectra at Zr K-edge in a Mg-aluminosilicate glass and
is decomposition in different shells of neighbors allowing proposing a
structural model for Zr environment (adapted from
\cite{20}).\label{fig2}}
\end{figure}

The close proximity between Zr atoms inferred from EXAFS in the initial
MgAS glass can be directly visualized using HAADF-STEM (High Angle
Annular Dark Field---Scanning Transmission Electron Microscope) imaging
(Figure~\ref{fig3}). Due to the chemical contrast of the HAADF
technique, it is possible to ascribe the bright regions to a greater
local concentration of Zr atoms having a diffuse interface with the
remaining glass (dark regions in Figure~\ref{fig3}). The amorphous
Zr-rich heterogeneities have a size larger than the diameter of
critical nuclei, usually observed with a size of 2--5~nm
\cite{20,21,22,23,24}. Therefore, these structural fluctuations cannot be
considered as pre-critical nuclei but as intrinsic components of the
structural organization of the glass matrix. Figure~\ref{fig3}
corresponds to a typical MRN topology: the cations such as Zr form
channels within the depolymerized network structure, resulting in a
nanosegregation of network-forming (silicate groups) and modifying
components (Zr and Mg).


\begin{figure}
\vspace*{2pt}
\includegraphics{fig03}
\vspace*{2pt}
\caption{HAADF-STEM images of Mg-aluminosilicate glass containing 
4~mol\% ZrO$_{2}$. The bright regions correspond to Zr-rich regions.
With heat treatment and nucleation, these regions become brighter and
are the preferential location for ZrO$_{2}$ crystallization (adapted
from \cite{25}).\label{fig3}}
\vspace*{2pt}
\end{figure}

The formation of nanoscale heterogeneities is confirmed by Small Angle
Neutron Scattering data (SANS) (Figure~\ref{fig4}), obtained at the
Center for Neutron Research (NIST, USA).  
In fact, the \mbox{Zr-free} MgAS glass already exhibits small fluctuations in
the SANS signal, though these fluctuations cannot be observed in
HAADF-STEM imaging due to the lack of chemical contrast between the
components of this glass. This reflects inherent fluctuations within
the structure of aluminosilicate glasses. Tentatively, these
fluctuations can be associated to a non-random distribution of Al
species around Si. As the MgAS glass contains important fraction of
five- and six-fold coordinated Al ($^{[5]}$Al and $^{[6]}$Al,
respectively)~\cite{26}, we can speculate that AlO$_{5}$ and
AlO$_{6}$ polyhedra have important edge-sharing linkages, resulting in
denser regions formed by $^{[5]}$Al--$^{[6]}$Al-rich domains. As a
support to this hypothesis, a heterogeneous distribution of Al has been
observed in a phase-separated Al$_{2}$O$_{3}$--SiO$_{2}$ glass, where
the fraction of highly coordinated Al species are more abundant in
regions having a large Al$_{2}$O$_{3}$ content~\cite{27}. 

\begin{figure}
\includegraphics{fig04}
\vspace*{-10pt}
\caption{SANS data for a Mg-aluminosilicate glass without and with Zr,
showing a feature characteristic of fluctuations with size of 2 to
3.9~nm.\label{fig4}}
\end{figure}

\break
As a consequence of the introduction of ZrO$_{2}$, the size of
inhomogeneities detected by SANS increases. Addition of ZrO$_{2}$
impacts the mesoscopic organization of the glass structure. The
presence of Zr-rich regions can be explained by Zr$^{4+}$ sites being
either in 6- or 7-fold coordination and competing less favorably than
Al$^{3+}$ cations for charge-balancing cations~\cite{28,29}.
They tend to segregate by edge-sharing linkages. Edge-sharing of
Zr$^{4+}$ sites is consistent with the short \mbox{Zr--Zr} distances
(${\sim}$3.1~\AA{}) extracted from EXAFS data
(Figure~\ref{fig2}) and characteristic of edge-sharing linkages
\cite{20}. EXAFS cannot distinguish the nature of the other
next-nearest neighbors since Mg, Al and Si have close X-ray scattering
amplitudes. However, ZrO$_{7}$ polyhedra are more likely edge-shared
with AlO$_{5}$ or AlO$_{6}$ units than with a tetrahedral unit because
the latter case yields to strong distortion to accommodate polyhedra
with large different sizes. Pauling rules also favor the presence of
high-coordinated sites to avoid the overbonding of the O ligands.


These amorphous nanoscale chemical heterogeneities appear unavoidable
and inherent to the glass structure. Even a fast-quenched glass,
showing no sign of macroscopic phase separation such as opalescence,
exhibits Zr segregation~\cite{11}. However, at a slow quench rate,
a clear glass-in-glass immiscibility associated with a macroscopic
opalescence, can be identified. This result suggests that
heterogeneities as those displayed in Figure~\ref{fig3} are likely the
first step in the phase separation process occurring above $T_g$. An
unknown and crucial issue would be to determine whether such
heterogeneities appear during cooling in the supercooled liquid state,
near $T_g$, or if they are already present at high temperatures in the
molten state. A recent study on the solubility of Zr in peraluminous
glasses has concluded that segregation is related to the presence of a
sub-liquidus immiscibility field in MgAS glasses, as heterogeneities
increase in size at high Al/Si ratios~\cite{30}. This study also
emphasizes the role of Al$^{3+}$ cations and the preferential
association of Zr and Al in the same demixed regions.


Since the pioneering work of Dargaud and co-workers
\cite{11,25}, further HAADF-STEM investigations have confirmed
the presence of heterogeneities in several glass systems, often close
to an amorphous-amorphous separation: Ta-bearing Li aluminosilicate
glasses~\cite{31}, Ca aluminosilicate~\cite{16}, basaltic
\cite{32} or metallic glasses~\cite{17,33}. Though this
technique requires a good chemical contrast between glass constituents,
it has been recently demonstrated that it is possible to distinguish
Al-rich and Si-rich regions in a phase separated
Al$_{2}$O$_{3}$--SiO$_{2}$ glass~\cite{27,34}.


\section{From heterogeneities to nucleation}\label{sec3}


These static structural fluctuations play a crucial role in the
crystallization process, as they are often the first step evoked during
crystalline nucleation~\cite{14,35,36,37,38}. During
heat treatment, Zr-rich regions tend to merge: the bright regions in
Figure~\ref{fig3} become brighter with sharper boundaries than in the
starting glass after a heating treatment at 920~\textdegree C. We
observe that nucleation forms, at first, tetragonal ZrO$_{2}$
nanocrystals preferentially at the diffuse connections between the
Zr-rich domains, showing the direct relationships between
inhomogeneities and nucleation pathways~\cite{25}. The static
fluctuations induce variations in the local barriers to nucleation for
the different regions of the system, which can facilitate the formation
of the primary nanocrystals \cite{39}. The segregation of Zr$^{4+}$
ions acts as an activated mechanism favoring the local reorganization
of the structure towards a crystalline order. At further heating
treatment of 975~\textdegree C, these ZrO$_{2}$ nanoparticules only
slightly grow in size. The glassy matrix surrounding the crystals shows
weak contrast fluctuations suggesting that Zr$^{4+}$ ions are almost
completely incorporated within the crystalline regions.


In SiO$_{2}$--Al$_{2}$O$_{3}$--MgO--ZrO$_{2}$ glasses, the nucleation
of ZrO$_{2}$ occurs prior to the formation of $\rmbeta$-quartz solid-solution
\cite{20,35,38}. This first step is also associated with an
increase of the SAXS signal indicating critical nuclei sizes of
${\sim}$2~nm~\cite{40}. During this initial step, $^{[5]}$Al and
$^{[6]}$Al may diffuse within crystalline ZrO$_{2}$, since doping of
ZrO$_{2}$ is often encountered, particularly by trivalent
elements~\cite{41}. We have characterized by $^{27}$Al NMR the Al
environment in a glass heat treated at the temperature of ZrO$_{2}$
nucleation (spectrum not shown). No increase in the proportion of
AlO$_{6}$ units and no narrow peak characteristic of crystalline
phases, are detectable. This result rules out the possibility of
significant doping of Al$^{3+}$ in initial nano-zirconia. An
alternative explanation is that Al$^{3+}$ ions are expelled at the
boundary of the ZrO$_{2}$ nano-crystals. This behavior was indeed
observed in an aluminosilicate glass containing TiO$_{2}$ and
ZrO$_{2}$, in which the first crystallizing phase is ZrTiO$_{4}$
\cite{24}. An Al rich layer was detected by electron energy-loss
spectroscopy and a specific interaction was proposed between
ZrTiO$_{4}$ and Al$^{3+}$, in good agreement with the present results.
This scenario has attractive advantages. It provides a diffusion
barrier preventing particle growth and Ostwald ripening. Furthermore,
the remaining glass corresponding to Si-rich regions associated with
AlO$_{4}$ units can favor the formation of $\rmbeta$-quartz.


The experimental evidence of heterogeneities supports recent
simulation studies showing critical density fluctuations at the origin
of nucleation in various systems such as colloidal particles or protein
solutions~\cite{42,43}. The subtle exploration of MRO
contradicts a fundamental hypothesis of the Classical Nucleation Theory
that assumes an initial homogeneous state. This represents a key step
to resolve the theory/experiment mismatch observed in the rate of
nucleation kinetics.


The nanoscale organization of glasses can be a major route, yet poorly
explored, to finally design the glass structural organization.
Manipulating the extent of heterogeneities could be exploited as an
effective strategy to master the nanostructure and crystal formation in
glass-ceramics~\cite{31,44}.


\section{Fe clusters in silicate glasses}\label{sec4}


Cation clustering in concentrated glasses may be put in evidence by
comparing the experimental MRO with the one expected from glass
stoichiometry. Combining neutron diffraction with Fe isotope
substitution and Empirical Potential Structure Refinement (EPSR)
simulations~\cite{45}, the existence of three Fe-populations in a
NaFeSi$_{2}$O$_{6}$ glass was evidenced, by contrast to the structure
of the corresponding crystalline phase, which contains only octahedral
Fe$^{3+}$. Majority network-forming $^{[4]}$Fe$^{3+}$ (about 59\% of
total Fe) shares corners with SiO$_{4}$ tetrahedra, and is randomly
distributed in agreement with a network-forming role, similar to that
of $^{[4]}$Al$^{3+}$ in NaAlSi$_{2}$O$_{6}$ glass (Figure~\ref{fig5}). By contrast,
minority $^{[5]}$Fe$^{2+}$ and $^{[5]}$Fe$^{3+}$ cations (about 36\%
of total Fe) tend to segregate. This provides an original picture of
the structure of this glass, differing from the tridimensional
structure expected from its stoichiometry and observed in
NaAlSi$_{2}$O$_{6}$ glass~\cite{46}. By contrast to most Fe-bearing
sodium silicate glasses, NaFeSi$_{2}$O$_{6}$ glass crystallizes into an
isochemical crystalline polymorph~\cite{47}. The presence of
segregated high-coordinated Fe-sites may explain the ability for this
glass to crystallize in a pyroxene structure.




\begin{figure}
\includegraphics{fig05}
\caption{Medium range organization of NaFeSi$_{2}$O$_{6}$, as derived
from EPSR simulations. It shows a clustering of Fe$^{3+}$, due to the
high fraction of 5-coordinated Fe$^{3+}$ sites. This structure is
different from that of the NaAlSi$_{2}$O$_{6}$ glass, based on a random
distribution of tetrahedral Al$^{+3}$ sites~\cite{45}.\label{fig5}}
\end{figure}






Clustering efficiency may be quantified by the relative proportion of
Fe in the second coordination shell around Fe. This parameter is only
dependent on glass stoichiometry if cations are randomly distributed.
For NaFeSi$_{2}$O$_{6}$ glass, EPSR simulations indicate a value of
0.42, larger than the value of 0.33 predicted in a random distribution
model. This anomalous behavior of Fe cations arises from an efficient
clustering of $^{[5]}$Fe sites. A similar contrast between randomly
distributed $^{[4]}$Fe and clustered $^{[5]}$Fe sites has been
evidenced by molecular dynamics simulations in Li(Al,Fe)Si$_{2}$O$_{6}$
glasses~\cite{48}.


Edge-sharing linkages between Fe$^{2+}$ and Fe$^{3+}$ sites in Fe
clusters give rise to unusual optical and magnetic properties. A
noticeable consequence of the presence of Fe$^{2+}$ and Fe$^{3+}$ in
silicate glasses is their color. At low Fe concentration, oxide glasses
melted in air exhibit light greenish coloration due to the presence of
minority Fe$^{2+}$, as Fe$^{3+}$ $d$--$d$ crystal field transitions are
spin forbidden and do not contribute to glass color. At high
Fe-concentration, glasses exhibit a dark brown color caused by a
Fe$^{2+}$--Fe$^{3+}$ intervalence charge transfer (IVCT), which causes
electron-hopping processes between edge-sharing $^{[5]}$Fe$^{2+}$ and
$^{[5]}$Fe$^{3+}$ sites \cite{49,50}. As electron hopping is
easier if the two sites have similar symmetries~\cite{50}, an
efficient coloration is consistent with Fe-clusters based on
edge-sharing $^{[5]}$Fe$^{3+}$ and $^{[5]}$Fe$^{2+}$.


Electron Paramagnetic Resonance (EPR) provides unique information on
the structure of~glasses containing paramagnetic ions and associated
superparamagnetic clusters~\cite{51}. The presence of Fe-clusters in
glasses has been observed at Fe-concentration as low as 0.1~mol\%
Fe$_{2}$O$_{3}$ using EPR~\cite{52,53}. The nature of these
clusters has been investigated recently by Fe K-edge HERFD-XANES (High
Energy Resolution Fluorescence Detected-XANES) for soda-lime silicate
glasses synthesized under different oxidation conditions
(Figure~\ref{fig6}). The reduced glass presents an additional
absorption at an intermediate energy between the pre-edge and the main
edge, around 7116~eV. This feature is not visible in the case of
glasses synthesized under air or under oxidizing conditions for which
there is almost no absorption between the pre-edge and the main edge.
Similar features have been previously observed in hematite,
ferrihydrite \cite{54} or in maghemite and
Fe$_{3}$PO$_{7}$~\cite{55}. They are ascribed to delocalized states
due to interactions caused by the presence of Fe ions as a second
neighbor, via an oxygen-mediated $4p$-$3d$ intersite hybridization
(Fe(4$p$)--O(2$p$)--Fe$^\prime$(3$d$))~\cite{56}. These covalency effects
indicate edge-linkages between Fe-polyhedra and involve
$^{[6]}$Fe$^{3+}$ or $^{[5]}$Fe$^{3+}$ cations preferably to
$^{[4]}$Fe$^{3+}$, as observed in minerals~\cite{57}. By analogy,
iron clusters in glasses would be favored by Fe$^{3+}$ located in
[5]-fold or [6]-fold coordinated sites: this could suggest that reduced
glasses contain a higher proportion of Fe$^{3+}$ occurring in 5- and/or
6-fold coordination than the corresponding oxidized glasses that rather
favor non-connected tetrahedral Fe$^{3+}$ sites. This is a consequence
of the Lowenstein exclusion rule~\cite{58}, which predicts that the
linkage between tetrahedral sites of trivalent cations is energetically
unfavored as it leads to the formation of oxygen triclusters.

\begin{figure}
\includegraphics{fig06}
\vspace*{-10pt}
\caption{Effect of oxidation conditions on HERFD-XAS spectra at the Fe
K-edge in soda lime silicate glasses containing 0.5~wt\% of
Fe$_{2}$O$_{3}$ and synthesized under reducing (blue) or oxidizing
conditions (yellow) and in air (green).\label{fig6}}
\end{figure}

There is a clear trend for a heterogeneous Fe distribution in glasses.
Among the various Fe species, $^{[4]}$Fe is randomly distributed in
the network and shares corners with other cationic (framework)
tetrahedra. The FeO$_{5}$ polyhedra tend to share edges among themselves. 
This trend towards $^{[5]}$Fe
clustering confirms the presence of domains enriched in network
modifier cations, as predicted by the modified random network model. 


\section{Fe clusters in natural obsidians}


{Obsidians are volcanic glasses that are widespread and possess most
glass properties: glass transition, density, brittleness,
hardness{\ldots} They usually contain about 1~wt\% Fe, but most common
colors of obsidians, ranging from brownish to smoke-grey to black, with
infrequent mahogany or green hues~\cite{59}, differ from the
greenish synthetic silicate glasses. As resulting from melt degassing
during ascent and cooling during emplacement, their peculiar formation
conditions have attracted interest since decades to understand the
origin of their original properties.


Iron speciation in obsidians reveals the presence of Fe-clusters as
shown by various spectroscopic methods, such as EPR or M\"{o}ssbauer}
\cite{51,60,61} or Raman micro-spectroscopy~\cite{62}. Rock
magnetism confirms the presence of diluted Fe$^{3+}$ in the glassy
matrix and of magnetite nanolites~\cite{63}. Nanolites were recently
suggested to play a significant role in volcanic processes, during the
transition from effusive to explosive regime~\cite{64}.
Spectroscopic data have shed light on the correlation between
Fe-speciation and the optical properties of obsidians demonstrating
that the majority of Fe-sites does not occur within the glass structure
but belong to mixed-valence, magnetite-like clusters~\cite{65}.
These clusters are responsible for the dark coloration of obsidians
through electron hopping between neighboring Fe$^{2+}$ and Fe$^{3+}$
sites. At a molecular scale, these clusters are unique witnesses of the
extensive degassing of a rising silicic magma.

The optical absorption spectrum of an obsidian glass is quite different
from that of a synthetic Fe-bearing glass (Figure~\ref{fig7}). Located
near 10,000~cm$^{-1}$, the Fe$^{2+}$ crystal-field absorption band is
Gaussian-shaped and significantly narrower than in the spectrum of a
synthetic silicate glass. It indicates an octahedral coordination with
a limited site distribution between regular and slightly distorted
sites. The optical properties of magnetite-like clusters give rise to
such a band~\cite{66}. The high intensity of this band is explained
by an exchange-coupled pairing process enhanced by a coupling between
neighboring Fe$^{2+}$-sites contained in the Fe-clusters \cite{67}.
This is a marked difference with synthetic glasses where the Fe$^{2+}$
band shows an asymmetrical shape in relation with a broad site
distribution between $^{[5]}$Fe$^{2+}$ and $^{[4]}$Fe$^{2+}$ sites.
Crystal-field bands for Fe$^{3+}$ are located at the same positions in
obsidian and synthetic glasses, but with a lower intensity in the
former than in the latter, due to different Fe-redox values.

\begin{figure}
\includegraphics{fig07}
\caption{Comparison of the optical absorption spectra of a Lipari
obsidian (black) and a soda-lime glass (red). The spectra are
normalized to the intensity of the Fe$^{2+}$ absorption band near 
10,000~cm$^{-1}$. Vertical dashed lines indicate that the weak
Fe$^{3+}$ transitions in the UV and near-UV occur at the same position.
By contrast, the position and width of the Fe$^{2+}$ absorption band near
10,000~cm$^{-1}$ are different in obsidian and synthetic soda-lime
glass, showing a different Fe-speciation.\label{fig7}}
\vspace*{7pt}
\end{figure}

The transmission window, in the visible region, is obscured by a broad
absorption band that contributes to the black color of most obsidians
(Figure~\ref{fig7}). At low temperature, the intensity of this band
increases dramatically (Figure~\ref{fig8}), a signature specific of a
Fe$^{2+}$~$\Leftrightarrow$~Fe$^{3+}$ IVCT. Indeed, IVCT intensity
increases with decreasing temperature, as observed in a large number of
minerals \cite{68}. This property has been explained by an
exchange-coupling model~\cite{69}. By contrast, the
Fe$^{2+}$crystal-field band in synthetic nanomagnetites, at the same
position as the one found in obsidians, retains a temperature
independence of the wavenumber and intensity values~\cite{66}. The
presence of an IVCT is a direct consequence of Fe-clustering in
obsidians. The shape of the IVCT band shows a possible additional
contribution from a Fe$^{2+}$~$\Leftrightarrow$~Ti$^{4+ }$ charge
transfer. The presence of Ti-magnetite-like clusters in obsidians may
be at the origin of Ti-rich magnetite nuclei. 

\begin{figure}
\includegraphics{fig08}
\caption{Optical absorption spectra of Mono Crater (Panum Dome \#2)
obsidian, at ambient T and 10~K. The broad band near 18,000~cm$^{-1}$
is sharply intensified at 10~K, an indication of an intervalence charge
transfer Fe$^{2+}$~$\Leftrightarrow$~Fe$^{3+}$, caused by the presence of Fe-rich
clusters in obsidian. The UV cutoff (that corresponds to an oxygen to
metal charge transfer) shifts to higher wavenumbers. By contrast, the
Fe$^{2+}$ absorption band located near 10,000~cm$^{-1}$ remains
unchanged.\label{fig8}}
\end{figure}

At room temperature, the EPR spectra of obsidians are characterized by
a broad and intense signal linked to superparamagnetic clusters
encompassing the whole field range, above which are superimposed weak
narrow signals (1500~G and 3500~G) of paramagnetic (isolated) Fe$^{3+}$
\mbox{(Figure~\ref{fig9}).} The EPR data obtained at low temperature (down to
77~K) are different. The intensity of the superparamagnetic
contribution decreases sharply, indicating the presence of
superparamagnetic clusters (Figure~\ref{fig9}). These spectacular
variations arise from magnetic coupling involving Fe$^{3+}$ ions within
the clusters. By contrast, the intensity of the paramagnetic isolated
Fe$^{3+}$ signals increases with decreasing temperature, following a
Curie's law in 1/T that characterizes their paramagnetic behavior
\cite{65}. These data confirm the pioneering studies of Regnard
\etal~\cite{61}, based on low temperature M\"{o}ssbauer spectra
recorded in presence of an external magnetic field, which gave the
first evidence of ultra-fine magnetite-like clusters in obsidians.

\begin{figure}
\includegraphics{fig09}
\caption{X-band Electron Parmagnetic Resonance signal of Fe$^{3+}$ at
293~K (red) and at 77~K (black). The sharp signal near 1500 G and the
weak features near 700~G and 3200~G are typical signatures of
(paramagnetic) diluted Fe$^{3+}$. The broad contribution in the obsidian
spectrum at room temperature is attenuated at 77~K, indicating the
presence of Fe$^{3+}$ in superparamagnetic Fe-rich clusters.\label{fig9}}
\end{figure}


\section{Discussion and conclusion}\label{sec6}

Information about the molecular-scale structure of multicomponent
glasses comes from a combination of spectroscopic and
diffraction/scattering measurements complemented by numerical modeling,
providing information on local geometry, site symmetry, and the nature
of the chemical bonds. These data have resulted in an improved
knowledge of the structural properties of glass components in oxide
glasses, demonstrating a contrasted behavior between the polymeric
network and the cations. By contrast to the largely covalent,
directional bonds between network formers and oxygen that are
associated to low values of diffusion coefficients, the ionic character
of the cation-oxygen bonds facilitates their diffusion within the glass
structure. In simulated silicate melts, the diffusion coefficients of
Ca and Na may be larger than that of Si by 3 and 5 orders of magnitude,
respectively, at 2000~K~\cite{70}. This distinct nature of the
chemical bonds between network formers and cations favors a
heterogeneous cation distribution and may lead to the formation of
clusters and crystallization nuclei.


{The structure of silicate glasses is based on a short-range order,
which obeys the basic rules of crystal-chemistry}~\cite{71,72}.
A random network model, proposed by Warren as an extension of the
Zachariasen's model~\cite{73}, gives only a partial view on the
behavior of cations in glasses. It assumes that most cations are
randomly distributed, filling the interstices of the polymerized
network. This oversimplified representation of glass structure, in
which cations are not expected to occur in well-defined sites, has been
experimentally dismissed, resulting in the more recent modified random
network (MRN) model~\cite{3,6}. MRN recognizes an intrinsic
heterogeneous nature of glass structure. It incorporates the covalent
bonding of silicate tetrahedra with the ionic nature of the
cation-oxygen bonds in a heterogeneous picture of the silicate glass
structure. It recognizes cation--cation interactions, providing a
rationale for a large range of glass properties, such as cation
diffusion, glass dissolution, optical properties, etc. {\ldots}

\break
The chemical or structural fluctuations in glasses here presented
demonstrate some similarities between two different cations, Zr$^{4+}$
and Fe$^{2+/3+}$, shedding light on the mechanisms of amorphous to
crystal transformation. Provided a local charge compensation exists,
tetrahedral Fe$^{3+}$ and octahedral Zr$^{4+}$ correspond to a
network-forming position with cation polyhedra being corner shared with
the glassy network, as indicated by the Fe--Si and Zr--Si contributions
evidenced in the EXAFS spectra. In that case, the MRO is not compatible
with the formation of cation clusters.  
By contrast, Fe- and Zr-rich clusters are
based on edge sharing cation polyhedra, in a topological configuration
not predicted by a random model. Edge sharing linkages provides more
topological constraints than corner sharing, following the basic rules
of structural chemistry~\cite{74}. As a consequence, an edge
sharing geometry shows a more limited structural disorder as compared
with a corner sharing geometry, which may also induce a local ordering
favoring crystal nucleation. Such edge-sharing topology favors also
cation--cation interactions and results in original glass properties,
e.g. color or magnetic properties.

\section*{Conflicts of interest}
Authors have no conflict of interest to declare.

\section*{Acknowledgements}
Our work on glass structure has largely benefitted, over decades, from
the experience of Phil Gaskell on the medium range organization of
silicate glasses. We want also to dedicate this structural review to
Neville Greaves, with which we shared, also during decades, animated
fruitful discussions on glass structure and the importance of large
user facilities for a better understanding of glass structure.

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