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\DOI{10.5802/crgeos.234}
\datereceived{2023-04-20}
\datererevised{2023-07-26}
\dateaccepted{2023-09-06}
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%\makeatletter
%\def\TITREspecial{\relax}
%\def\cdr@specialtitle@english{Geodynamics of continents and oceans - A tribute to Jean Aubouin}
%%\def\cdr@specialtitle@french{G\'eodynamique des continents et des Oc\'eans - Hommage \`a Jean Aubouin}
%\makeatother

\CDRsetmeta{articletype}{review}

\title{Recent advances in petrochronology: from dates to ages and rates
of deep orogenic processes}

\alttitle{Progr\`{e}s r\'{e}cents en p\'{e}trochronologie : des dates
aux \^{a}ges et aux vitesses des processus orog\'{e}niques profonds}

\author{\firstname{Loic} \lastname{Labrousse}\CDRorcid{0000-0001-7576-7570}\IsCorresp}
\address{Sorbonne Universit\'{e}, CNRS-INSU, Institut des Sciences de
la Terre Paris, ISTeP UMR 7193, F-75005 Paris, France}
\email[L. Labrousse]{loic.labrousse@sorbonne-universite.fr}

\author{\firstname{Guillaume} \lastname{Bonnet}\CDRorcid{0000-0002-4128-9037}}
\addressSameAs{1}{Sorbonne Universit\'{e}, CNRS-INSU, Institut des
Sciences de la Terre Paris, ISTeP UMR 7193, F-75005 Paris, France}
\email[G. Bonnet]{gbonnet01@gmail.com}

\author{\firstname{Camille} \lastname{Fran\c{c}ois}\CDRorcid{0000-0002-6808-9369}}
\addressSameAs{1}{Sorbonne Universit\'{e}, CNRS-INSU, Institut des
Sciences de la Terre Paris, ISTeP UMR 7193, F-75005 Paris, France}
\address{Commission de la Carte G\'{e}ologique du Monde, 77 rue Claude
Bernard, 75005 Paris, France}
\email[C. Fran\c{c}ois]{francois.camille555@gmail.com}

\author{\firstname{Antoine} \lastname{Godet}\CDRorcid{0000-0001-7298-5142}}
\address{E4M, D\'{e}partement de g\'{e}ologie et de g\'{e}nie
g\'{e}ologique, Universit\'{e} Laval, Qu\'{e}bec, Canada}
\address{Natural Resources Canada, Geological Survey of Canada, 
490 rue de la Couronne, Qu\'ebec (Qu\'ebec), G1K 9A9, Canada}
\email[A. Godet]{antoine.godet.1@ulaval.ca}

\author{\firstname{Thomas} \lastname{Gyomlai}\CDRorcid{0000-0002-0544-7229}}
\addressSameAs{1}{Sorbonne Universit\'{e}, CNRS-INSU, Institut des
Sciences de la Terre Paris, ISTeP UMR 7193, F-75005 Paris, France}
\email[T. Gyomlai]{thomas.gyomlai@sorbonne-universite.fr}

\shortrunauthors

\begin{abstract}
In order to decipher the prevalent processes active at depth in
orogenic systems, their time sequence and their rates have to be
assessed. This is essentially done via absolute dating of accessory and
rock-forming metamorphic minerals. The interpretation of dates, now
produced in high quantities and low uncertainties, with geochemical and
textural information thanks to \textit{in situ} dating techniques, into
ages with a geological meaning, is based on sophisticated
multi-disciplinary approaches. The wealth of data produced during the
last decades in internal zones of mountain chains today questions some
of the seminal concepts in geodynamics as well as in petrochronology.
The concept of closure temperature \cite{Jager1967} but also the
notions of metamorphic unit or metamorphic event are now to be
considered in the light of campaign-style dating projects, that enable
a comprehensive and statistical interpretation of age patterns from the
mineral scale to the geodynamic process scale.
\end{abstract}

\begin{altabstract}
Afin de distinguer les processus pr\'{e}dominants en profondeur dans
les syst\`{e}mes orog\'{e}niques, leur s\'{e}quence temporelle et leurs
vitesses doivent \^{e}tre \'{e}valu\'{e}es. Cette d\'{e}marche est
aujourd'hui possible gr\^{a}ce essentiellement \`{a} la datation
absolue des min\'{e}raux accessoires et des min\'{e}raux des
paragen\`{e}ses m\'{e}tamorphiques. L'interpr\'{e}tation des
\guillemotleft{}~dates~\guillemotright{} mesur\'{e}es, aujourd'hui
produites \textit{in situ} en grande quantit\'{e} et avec de faibles
incertitudes, en \guillemotleft{}~\^{a}ges~\guillemotright{} \`{a}
signification g\'{e}ologique, repose sur des approches
multidisciplinaires incluant des informations g\'{e}ochimiques et
texturales elles aussi recueillies \textit{in situ}. L'abondance de
donn\'{e}es produites au cours des derni\`{e}res d\'{e}cennies dans les
zones internes des cha\^{i}nes de montagnes, remet aujourd'hui en
question certains concepts fondateurs, aussi bien en g\'{e}odynamique
qu'en p\'{e}trochronologie. La notion de temp\'{e}rature de fermeture
\cite{Jager1967} mais aussi les notions d'unit\'{e} m\'{e}tamorphique
ou d'\'{e}v\'{e}nement m\'{e}tamorphique sont d\'{e}sormais \`{a}
consid\'{e}rer \`{a} la lumi\`{e}re de projets de
\guillemotleft{}~campagnes de datations~\guillemotright{}, qui
permettent une interpr\'{e}tation statistique des distributions
d'\^{a}ge de l'\'{e}chelle du min\'{e}ral \`{a} l'\'{e}chelle du
processus g\'{e}odynamique.
\end{altabstract}

\keywords{\kwd{Petrochronology}\kwd{Tectonics}\kwd{Metamorphism}}

\altkeywords{\kwd{P\'etrochronologie}\kwd{Tectonique}\kwd{M\'etamorphisme}}


\maketitle

\twocolumngrid

\end{noXML}

\section{Introduction}

The developments of geochronology and tectonics have numerous
intrications. The advent of modern geochronology is associated with the
improvements in mass spectrometry in the 1930s and 1940s, but the
earliest published dates are older, including measurements of elemental
lead in uranium-rich minerals by \citet{Holmes1911}, in what is
considered as the first geochronology paper 
\cite[in][]{Davisetal2003}. Interestingly, the first U--Pb age review was
published by \citet{Barrell1917} so that the two first geologists
basing their understanding on geochronology data were Holmes, who
linked continental drift to mantle convection \cite{Holmes1928}, and
Barrell, who elaborated the notion of lithosphere in the seminal
``Strength of the Earth'' paper series \cite{Barrell1914}. So deep
tectonics and high temperature geochronology actually share the same
genealogy.

In the early 1960's the first understanding of the link between
metamorphic series and orogeny, i.e. the enunciation of metamorphic
gradients \cite{Miyashiro1961}, is partly based on K--Ar ages. The
application of radiochronology to the internal zones of mountain belts
was also immediate with the seminal K--Ar and Rb--Sr ages by Emilie
J\"{a}ger and coworkers  \cite{Jageretal1961,Jager1962} on the
Simplo-Ticinese high temperature metamorphic dome, which could be
considered as the cradle of metamorphic dating. K--Ar or Rb--Sr ages
produced had 2 to 3 Myr uncertainties for 18 to 20 Ma absolute values,
i.e. 5 to 15\% relative precision. This allowed the systematic
discrepancy of K--Ar or Rb--Sr ages yielded by biotite and muscovite to
be brought out in the very same decade \cite{Armstrongetal1966}, at
the same time tools were developed to assess the statistical
significance of the produced ages [with the MSWD parameter for
instance, \citealp{York1966}]. 

Based on the notion of closure temperature of \citet{Jager1967,
Dodson1973} formulates the effect of temperature and diffusion on
isotope concentrations and sets the first framework used for
interpreting radiometric data: crystallization or cooling ages. We may
try to elaborate on the present-day difficult emancipation from this
framework.

A decisive stage to mention along these 60 years is the advent of
\textit{in situ} dating, with the elaboration of secondary ion mass
spectrometry (SIMS) and sensitive high-resolution ion microprobe
(SHRIMP), the laser ablation--inductively coupled plasma--mass
spectrometry (LA-ICP-MS) techniques and recent development of
collision--reaction cell mass spectrometers allowing to resolve the
isobaric interferences. While the time-consuming isotopic 
dilution--thermal ionization mass spectroscopy (ID-TIMS), tuned by
\citet{Tiltonetal1955}, still has the highest age resolution with less than
0.1\% 2$\sigma $ precision and accuracy \cite{Schalteggeretal2015},
SIMS and SHRIMP, developed in the 70's and 80's respectively, yield
\textit{in situ} dating of 10 to 30~$\upmu$m diameter domains with a
shallow pit depth and a precision now below 3\% \cite{Schoene2014}.
LA-ICP-MS, the easiest method to set up, most of the time requires
larger analytical volumes (up to 100~$\upmu$m spots, with depth about
the same order) and yields ages with a 3\% resolution in the shortest
analytical time \cite{Schalteggeretal2015}.

The present contribution does not have the pretention to add to the
list of extensive petrochronology reviews 
\cite{Kohnetal2017, Kohn2016,Kylander-Clarketal2013, Schoene2014} but rather
proposes to elaborate on how the use of radiometric ages in metamorphic
petrology is currently changing from pinning PT paths in time to
assessing duration of processes (i.e. metamorphism and deformation) and
hence their characteristic time-scale and rates, and eventually
associating \textit{in situ} dating and strain analysis at the mineral
scale rather than adding ages along of a PT-strain path. This approach
actually fits into the larger definition of petrochronology
``\unskip\textit{the branch of Earth science that is based on the study of
rock samples and that links time (i.e., ages or duration) with specific
rock-forming processes and their physical conditions}''
\cite{Engietal2017}. The scope of the present review is restricted to
regional metamorphism, from HP to UHP conditions and UHT conditions,
down to greenschist facies. The latest stages of exhumation through
lower temperatures, mainly documented through thermochronology studies
will not be elaborated on here. 

The classical approach remains two-fold depending on whether the
datable mineral is a major rock-forming mineral or an accessory phase,
whose paragenetic significance is not explicit. \textit{In situ} dating
of radioactive accessory minerals is now extremely precise but requires
the obtained ``dates'', i.e. the numerical values deduced from isotopic
and elemental ratios measures \cite{Schoene2014} to be mutually
correlated and linked to index minerals for their interpretation as a
meaningful metamorphic ``age''. The second approach based on the direct
dating of rock-forming minerals involves K--Ar, Rb--Sr, Sm--Nd or Lu--Hf
radiogenic systems, on ubiquitous silicates such as mica or garnet. The
principal issue is then the significance of the dates obtained, in
terms of crystallization, strain or cooling age for instance. 

A new landscape is now emerging with on one side the use of more
sophisticated chemical systems including U-rich minerals such as
rutile, allanite or even epidote in equilibrium assemblages, blurring
the limit between major and accessory phases, and on the other side the
lowering of analytical sensitivity allowing to date practically any
mineral [U--Pb on garnet, \citealp{Millonigetal2020}, Rb--Sr on illite
and\break adularia in ancient faults, \citealp{Tillbergetal2020}, or U--Pb on
calcite from faults, see \citealp{LacombeBeaudoin}, this volume], so that
the alternative expressed above is fading.

On the other side, the better understanding of diffusion processes and
the confrontation of experimentally determined diffusion coefficient to
natural data or modelling of effective diffusion of ions through
crystal lattices also challenges the orthodoxy of the Dodson
alternative: crystallize or cool. The role of fluids and strain in the
opening of minerals to isotopic and elemental fluxes is now well
documented.\looseness=-1

The richness of the present-day toolbox is best expressed in the
``multi-tool'' and ``campaign-styles'' approaches that now question the
significance of tectonic units in time and space. The advent of
microstructural geochronology \cite{Moseretal2017} with the use of TEM
and atomic probe tomography (APT) that combines imaging with elemental
and isotopic composition measurement at the nanometer scale, is perhaps
the next break-through in high temperature geochronology as it directly
images how crystalline defects control isotope concentrations, and
hence how strain can be dated.
 
\section{Two strategies to pin ages along PT paths}

\subsection{Ages from accessory minerals}

\subsubsection{Based on textures}\label{sec2.1.1}

The strongest textural evidence used in the relative dating of
accessory and rock-forming phases remains the host-inclusion
relationship, the datable mineral being itself included or bearing
inclusions. The most reliable dating of Ultra-High Pressure (UHP)
metamorphic peaks, for instance, is based on this principle: an
inclusion of coesite in dated zircon grains, evidences that these grew
in the coesite stability field. Even though diamond-hosting zircons
were dated in the Kokchetav massif as early as 2001
\cite{Hermannetal2001}, the case of zircon from the Caledonian UHP
province of Northeast Greenland [NEGEP, North East Greenland Eclogite
Province, \citealp{Gilotti1993}] is perhaps the one that had the most
critical impact on the understanding of UHP metamorphism tectonic
significance. Dating of zircon grains hosting inclusions symptomatic of
UHP eclogite facies (e.g. garnet, omphacite, and coesite, Figure~\ref{fig1}A 
has demonstrated that the NEGEP UHP episode\break occurred in the
Carboniferous \cite[356--350 Ma,][]{McClellandetal2006}, i.e. late
in the Caledonian collision sequence. The thermo-mechanical
implications of such a late UHP stage for collision dynamics is not
fully understood yet \cite{GilottiMcClelland2007}. The inclusion of
datable minerals in rock-forming minerals also offers the potential to
date their growth. Among decisive studies in this prospect, the
extensive dating of monazite grains in inclusion in garnet from an
upper amphibolite facies pelitic schist from the Grouse Creek Mountains
(Northwest Utah, USA) is often cited \cite{Hoischetal2008}. The age of
monazite grains constitutes an upper bound for the age of the garnet
growth itself [\citealp{Kohn2016}, Figure~\ref{fig1}B].

\begin{figure*}
\includegraphics{fig01}
\caption{\label{fig1}Inclusion relationships between datable and index
minerals. (A) UHP Eclogite facies paragenesis as inclusions in a zircon
core from the North Eastern Greenland Eclogite Province. SHRIMP dating
spot in coesite-bearing zone 2 yields 357 ${\pm}$ 6 Ma for the UHP
stage \citep[modified after][]{McClellandetal2006}. (B) U--Pb ages of
monazite inclusions depending on their structural position in garnet
volume (as their radial position cubed). Data from
\citet{Hoischetal2008}. In red: linear interpolation, as in
\citet{Hoischetal2008}; in green maximum age curve for garnet growth,
as in Kohn, 2016; in blue: polynomial interpolation.}
\vspace*{-2pt}
\end{figure*}


\subsubsection{Based on trace elements fingerprinting}

\textit{In situ} Rare Earth Elements (REE) signature of zircon domains
can be produced by LA-ICP-MS and/or SHRIMP analysis
\cite{Schalteggeretal1999,Rubatto2002}. Such data is now
routinely obtained together with ages on zircon, but also monazite or
titanite with Split Stream (LASS)-ICP-MS 
[\citealp{Kylander-Clarketal2013},
{Figure~\ref{fig2}A}]. The slope of the REE signature in
the HREE (Heavy Rare Earth Elements) domain and the absence/presence of
a Europium anomaly (Eu/Eu*) are among the most widely used criteria. A
depletion in the HREE domain is generally consistent with a growth
episode in the garnet stability field while the depletion in Eu
suggests growth in equilibrium with a Ca-bearing phase such as
plagioclase. Although the effect of bulk rock composition, growth and
breakdown of major and other accessory phases, the presence of melt
[{Figure~\ref{fig2}B,C}, \citealp{Walczaketal2022, Pitraetal2022}] or the oxygen
fugacity \cite{Kohn2016} 
may alter these trends, they remain an
effective tool for the interpretation of calculated dates in zircon
\cite{Rubatto2017} as well as in monazite 
\cite[][for instance]{Fosteretal2002,Holderetal2015, Larsonetal2022}. Nevertheless, growth of
zircon, or monazite, considered at the equilibrium with existing
garnet, or plagioclase, does not imply coeval growth of both major and
accessory minerals \cite{Kohn2016, Pitraetal2022}. 
\looseness=-1


\begin{figure}
\includegraphics{fig02}
\vspace*{-3pt}
\caption{\label{fig2}\fontsize{9.7}{12}\selectfont
Rare Earth Elements spectra of eclogite-facies and
retrogression-related zircons showing different behaviors. (A) Western
Gneiss Region, Norway \cite[data from][]{Kylander-Clarketal2013}
Pressure peak zircons with ages above 415 Ma show negative slope
spectra in the HREE domain while younger zircons associated to
retrogression show positive slope. (B) Montagne Noire, France 
\cite[data from][]{Pitraetal2022}: Both old (${>}$320 Ma, associated to
regional HP stage) and young (${<}$320 Ma, associated to regional
partial melting) zircons appear depleted in the HREE domain, (C) Seve
Nappe, Swedish Caledonides \cite[data from][]{Walczaketal2022} Two
successive HP stages zircon populations show REE spectra similar to
inherited zircon cores.}
\end{figure}

\subsubsection{Based on 4+ cations thermometry}

Titanium substitutes for Si in zircon, while Zr substitutes for Ti in
rutile and titanite \cite{Zacketal2004, Kohn2020}. These
substitutions have been calibrated in temperature over the whole
metamorphic range (400~\textdegree C--1000~\textdegree C) at fixed and
varied pressures and yield $T$ estimates with uncertainties lower than
${\pm}$25~\textdegree C \cite{Watsonetal2006,
Tomkinsetal2007,Haydenetal2008}. Zr-in-rutile and
Ti-in-zircon methods are actually based on cation exchanges assuming
that quartz, rutile and zircon are costable (i.e. with activities $=$ 1).
Corrections should be applied when the SiO$_{2}$ activity is
lower than 1 or for instance when the peak temperature is known to lie
in the coesite field \cite{Kohn2020}. Based on the similarly low
diffusivities of Pb and Ti in zircon, the Ti-in-zircon thermometry is
expected to yield the crystallization condition of the dated zircon
domain. Zirconium-in-rutile thermometry is also expected to yield
equilibration at peak temperature, although some cases of relict cores
with preserved prograde temperatures or incomplete equilibration cases
due to shielding or slow diffusion at the aggregate scale have been
described for rutile \cite{Kohn2020}. 

\subsection{Ages from rock-forming minerals}

\subsubsection{Pinning dates along the crystal growth history}

Among metamorphic rock-forming minerals, mica and garnet are perhaps
the most popular for dating. In the past 20 years, the
$^{39}$Ar--$^{40}$Ar radiometric method has
been predominantly used to date mica, by opposition to Rb--Sr, until
recently not accessible \textit{in situ} and still hampered by the
availability of homogeneous standard materials \cite{Jegaletal2022}.
However, in recent years, the addition of a reaction cell between the
quadrupoles in the MS device has enabled the use of reacting gases of
various reaction affinities with isobaric elements to resolve isobaric
interferences at $m = 87$. In the case of mica, this allows to separate
$^{87}$Sr and $^{87}$Rb and enables
\textit{in situ} Rb--Sr dating [with O$_{2}$,
NO$_{2}$ or NH$_{3}$ as reacting gases,
\citealp{Zacketal2016, Hogmalmetal2017}]. The obtained
biotite-only isochrons are based on a large amount of data points that
compensates for their large uncertainties, adds a textural control, and
requires simpler processing compared to the ID-TIMS approach
(Figure~\ref{fig3}).



\begin{figure*}
\vspace*{-1pt}
\includegraphics{fig03}
\caption{\label{fig3}Example of hygrochronometry with the dating of
fluid-driven crystallization of phengite, related to a metasomatic
K-enrichment in metavolcanite previously devoid of mica, from the
Kampos-Lia subunit in Syros, Greece. Phengite is associated with
chlorite and gradually replacing garnet and provides ages around 36 Ma.
Synthetic pressure--time path showing the metasomatic event, which
corresponds to a punctual event occurring during exhumation of the
previously subducted Kampos-Lia subunit. Modified from
\citet{Gyomlaietal2023}.}
\vspace*{-1pt}
\end{figure*}

In garnet, the comparison of Lu--Hf and Sm--Nd ages yielded by
ID-MC-ICP-MS or TIMS analysis on whole-rock and garnet fractions from
the same rocks shows recurrent older Lu--Hf ages and younger Sm--Nd ages
\cite{Ibanez-Mejiaetal2018, Baxteretal2017,
Johnsonetal2018}. This has been assigned to different closure
temperatures, different diffusion rates and different partition
coefficients. Thus, at constant grain size and cooling rates, the Sm--Nd
isotopic system has a lower closure temperature (${<}$700~\textdegree C)\break
compared to Lu--Hf [${>}$750~\textdegree C e.g.
\citealp{Schereretal2001, Smitetal2013}]. Diffusive exchange
with the matrix also plays a role, as a net loss or gain of parent
isotopes may influence the chronometer systematics 
\cite[e.g.][]{BlochGanguly2015}. A significant Rayleigh fractionation for
lutetium also yields Lu--Hf ages to be weighted towards the timing of
garnet core crystallization, while the Sm--Nd method yields ages
representative of the average grain growth \cite[][for instance]{Smitetal2013,
Lotoutetal2018} or homogenization at HT peak conditions.
By trying to link garnet age to prograde metamorphic reactions, fine
analyses \cite[e.g.][]{Konrad-Schmolkeetal2008,Godetetal2020b}
have shown that the early uptake in Lu during
prograde growth of garnet could actually relate to the breakdown of
Lu-rich low-grade minerals such as chlorite. Lu--Hf dating of garnet for
a mafic protolith could therefore approximate the crossing time of the
chlorite-out garnet-in reaction, while Sm--Nd age could relate to the
successive epidote or amphibole-out reactions occurring along a burial
sequence \cite{Baxteretal2017}.

While new alternatives to mechanical micro-sampling have emerged, based
for instance on laser ablation coupled with ID-TIMS analysis
\cite{Logueetal2022} or MC-ICP-MS \cite{Tualetal2022} on smaller and
smaller texturally selected domains in rocks, \textit{in situ} dating
of garnet using triple quadrupole LA-ICP-MS technique appears to be a
promising alternative. The setup of the triple quadrupole LA-ICP-MS
allows to resolve the mass interference at 176 amu between Lu, Hf and
Yb [with NH$_{3}$ as a reacting gas,
\citealp{Simpsonetal2021}] and enables \textit{in situ} Lu--Hf dating. 

\subsubsection{Challenging the closure temperature paradigm}

The closure temperature concept \cite{Jager1967} actually stems from
the interpretation of Rb--Sr and K--Ar ages on micas from the
Simplo-Ticinese high temperature metamorphic dome. The dated thermal
event was considered as associated to limited strain and
temperature-driven diffusion as the first order process governing the
diffusion of radioactive decay products. Even though temperature was
indeed a first order parameter controlling the regional age pattern,
some old ages were preserved in the alpine-age domain 
\cite{ArnoldJager1965}, evidencing from the start that some processes
different from thermally activated diffusion (i.e. recrystallization,
fluid influx) were required at the local scale to fully reset the
considered chronometers \cite{Villa1998}. The refinement of the
closure temperature concept by also introducing an ``opening
temperature'' and a ``resetting temperature'' along the prograde path 
\cite{GardesMontel2009} actually makes it much more complex for age
interpretation. Indeed, as these two prograde thresholds frame the
closure temperature value, a complex set of combinations appears
depending on the temperature interval in which the considered mineral
crystallized. 

Eventually the closure temperature estimates given by the Dodson
equation are based on diffusion coefficients, themselves mostly deduced
from experiments. The differences between experimental conditions and
nature [fluid regime, crystal defects density in minerals, see 
\citealp{Ntemeetal2022} for discussion for Ar] seem to systematically
yield minimum values for effective closure temperature in nature.

Even for minerals considered as refractory to isotope disturbance in
most of the metamorphic\break conditions, a purely diffusive model does not
explain all natural data. Monazite, for instance, is prone to
decoupling between ages (i.e. U--Pb system behavior) and textures (cores
{vs} rims) in the supra-solidus domain
[$T > 800\ndash850$~\textdegree C;
\citealp{Weinbergetal2020}]. However, at odds with the phase equilibria
models predicting complete dissolution above ${\sim}$850~\textdegree C
\cite{Kelseyetal2008, YakymchukBrown2014}, subsolidus prograde
monazite might still preserve their age in granulitic domains
experiencing partial melting \cite[e.g.][]{Didieretal2015,
Nicolletetal2018, Godetetal2020a}. 

U--Pb apatite dating, often used as a thermochronometer, can also be
considered as a valuable tracker of fluid rock-interactions over the
greenschist to amphibolite facies temperature interval
\cite{Kirklandetal2018}. In the Central Alps, apatite grains from
alpine upper greenschist to amphibolite facies orthogneiss preserve
their hercynian ages \cite{Henrichsetal2019}, although they reached
temperatures close to or even beyond the acknowledged closure
temperature for Pb in apatite [375--550~\textdegree C,
\citealp{Cochraneetal2014}]. This contrasted behavior is attributed to
different fluid regimes, orthogneiss remaining relatively dry compared
to their cover counterparts. 

Therefore, it seems that discussing ages on the a priori basis of the
closure temperature paradigm alone runs counter to the precision (both
analytical and scientific) reached today, that allows a case-by-case
analysis of the conditions under which an isotopic system may close.
Considerations on the size of the Ar ion for instance
\cite{Villa1998, BosseVilla2019} and modelling of its
interactions with the crystalline framework \cite{Ntemeetal2022} point
to the conclusion that its thermal diffusion is actually less efficient
in pristine crystals than estimated via experiments. Considering the
closure of a mineral as the end of its interaction with the external
media, through fluids, whose properties and amount relate to
temperature, but also strain, rather than a direct effect of
temperature is perhaps a more comprehensive paradigm. The term
``hygrochronometry'' \cite{Villa2016} is sometimes used for this
purpose. Identifying such fluid-driven recrystallization allows to date
punctuated fluid ingression, in particular in strain-free samples, with
duration below dating precision [\citealp{Gyomlaietal2023},
{Figure~\ref{fig3}}].

A convincing example of how fluids, together with strain, can actually
control the behavior of paragenetic chronometers at the aggregate scale
is given by \citet{Airaghietal2018} on micaschists from the
Longmen Shan belt, China, that have experienced peak metamorphic
conditions of 530~\textdegree C to 580~\textdegree C. In situ
$^{40}$Ar--$^{39}$Ar dating of biotite
porphyroblasts cores yielded prograde ages, significantly older than
their rims, returning ages close to peak stage defined by allanite
crystallization ({Figure~\ref{fig4}}). White mica yielded scattered
ages with 3 distinct generations, the two younger being texturally
related to retrogression ({Figure~\ref{fig4}}). The age difference of
more than 40 Myr between biotite rims ages and white mica ages is
plainly at odds with any of the estimates for closure temperature of
muscovite and biotite for argon [estimated at 280 and 450~\textdegree C
respectively in \citealp{Airaghietal2018}]. However, a plausible
explanation is given by the contrasting crystal habits of the two
phases, the biotite porphyroblasts having been shielded from a series
of resetting mechanisms, i.e. fluid-driven recrystallization and
intra-grain porosity development, active in the white mica generations.
White mica hence recorded several stages of fluid-influx/strain, while
biotite retained its high $T$ crystallization age.

\begin{figure}
\includegraphics{fig04}
\caption{\label{fig4}Temperature--time path and successive
$^{39}$Ar--$^{40}$Ar ages obtained on biotite cores and rims, apatite
and white mica from the Longmen Shan micaschists 
\cite[data from][]{Airaghietal2018}. Frequency curves are summed normal
distribution curves for each age normalized to their maximum. White
mica and biotite closure temperature values as estimated by
\citet{Airaghietal2018}.}
\end{figure}

\section{Out of the classical alternative}

\subsection{Blurring the lines between accessory and rock-forming minerals}

Among accessory minerals, some show phase equilibria relationships that
allow their growth/{\ubreak}breakdown to be linked to metamorphic paragenesis
and hence what is referred to as ``reaction dating''.

Zircon is perhaps the least-constrained datable accessory mineral in
terms of reactions. Relationships with melt and supercritical fluids at
high $P$ and $T$ have been documented \cite{Hermannetal2013} but also at
low $T$, as numerous prograde ages have been assessed on basis of
meticulous case-by-case analysis \cite{McClellandLapen2013,
GervaisCrowley2017, Godetetal2020b}. The
titaniferous phases have stability fields that depend on rock
chemistry, $P$, $T$, and xH$_{2}$O \cite{Engietal2017,
Kohn2020}. In regular and UHP eclogite-facies assemblages,
rutile is usually the stable titaniferous mineral.
\citet{Bonnetetal2022} used this specificity in high and
ultrahigh-pressure metamorphic units in the Dora-Maira Massif, Western
Alps. In addition to the textural equilibrium of rutile with peak
minerals, coupled rutile Zr thermometry and geochronology offers an
opportunity to evaluate equilibration conditions across samples
{(Figure~\ref{fig5})}. The stability field of titanite to
pressure conditions ${<}$ 1.5 GPa makes it a good marker of
exhumation \cite{Spenceretal2013}. For higher temperature metamorphic
rocks (peak $\geq 800$~\textdegree C) the interpretation of
rutile ages is more complex. For example, the oldest titanite ages in
the WGR (Norway) imply that decompression under 1.5 GPa be older than
405 Ma \cite{Spenceretal2013}, whereas rutile ages are systematically
younger on a regional scale [375--400 Ma, 
\citealp{ScharerLabrousse2003, Kylander-Clarketal2008,
Cuttsetal2019}]. Rutile ages have therefore been interpreted
as early cooling ages after their crystallization as part of the
eclogite facies paragenesis. \looseness=-1

\begin{figure*}
{\vspace*{-3pt}}
\includegraphics{fig05}
{\vspace*{-2pt}}
\caption{\label{fig5}(A) Map of the Dora-Maira massif showing the
existence of several subunits of subducted continental crust. (B)
Cross-section showing the nappe-stack structure of the massif. (C)
Combination of rutile U--Pb geochronology and Zr-in-rutile thermometry
in high and ultrahigh-pressure rocks from the Dora-Maira massif,
Western Alps \cite[data from][]{Bonnetetal2022}. Pb closure
temperatures are evaluated at cooling rates between 10 and
100~\textdegree C/Myr, using diffusion parameters of \citet{Cherniak2000}.
Colors correspond to different units. Error bars are
${\pm}$2$\sigma$.}
{\vspace*{-3pt}}
\end{figure*}

Monazite, xenotime, allanite and their possible mutual relationships
have also been described in detail \cite{Janotsetal2008,
Manzottietal2018}. Allanite, preserved above 450~\textdegree C in Ca-rich
rocks, breaks down into monazite and xenotime above 560--610~\textdegree C
in Ca-poor rocks. The incorporation of monazite and xenotime into the
NCKFMASHMnPFCeY chemical system \cite{SpearPyle2010} is consistent
with this observation. The monazite field actually coincides with the
amphibolite facies, shifted towards greenschists, resp. granulites, if
the Ca content of the rock is particularly low, resp. high
\cite{Schulz2021}. In addition to these phase relationships, monazite
shows a range of reaction textures that allow a finer interpretation of
the ages obtained. Zoned metamorphic monazites are now currently
documented \cite[e.g.,][]{Soretetal2022}.
Retrograde allanite ${\pm}$
apatite coronas around monazite can develop in metagranites and
metapsammopelites. These can be dated \textit{in situ}
\cite{Hentscheletal2020} and provide a fine-scale constraint for
retrograde paths. So-called ``satellite'' textures
\cite{Fingeretal2016}, which are more difficult to date because finer,
are also symptomatic of thermal events or retrograde fluid entry
pulses.

The relationship between monazite and garnet is itself a topic of
recurrent debate. Thermochemical considerations predict that monazite
and garnet are not expected to grow together \cite{SpearPyle2010,
Kohn2016}. In several cases, ages on monazites indeed frame ages on
garnet \cite[for instance,][]{Godetetal2020b}. A study on cogenetic
rock pairs showing or not garnet also highlights that monazites grow
earlier in garnet-free rocks, and later in garnet-rich rocks
\cite{SchulzKrause2018}. However, monazite grains as inclusions in
garnet peritectic rims have been interpreted as the result of prograde
breakdown of apatite under suprasolidus conditions
\cite{Manzottietal2018, Godetetal2021}. 

The extreme sensitivity of monazite to variations in the fluid regime
of rocks makes them a hygro-petrochronological tool of choice
\cite{BosseVilla2019}. 

\subsection{Multi-method approach and the comparison of independent ages}

Multi-method petrochronological approach linking determination of PT
path based on the rock chemistry, texturally-controlled dating of
accessory and major phases, yields the best input for the thorough
building of PTt-strain-fluids paths in mountain belts internal zones,
but also feeds the debate about relative behaviors of the different
chronometers with natural evidence. 

In the Southeastern Churchill Province (SECP), Canada, quantitative
$P$--$T$--$t$-strain-fluid paths were built by combining U--Pb 
zircon--monazite
and Lu--Hf garnet dating with phase equilibrium modeling, empirical
thermobarometry, and trace element mapping. Timing of initial
collision, duration of anatexis, and pace of crustal assembly at
mid-crustal levels were then estimated [\citealp{Godetetal2021},
Figure~\ref{fig6}A]. A metatexite from the Tasiuyak Complex,
yields a singular PTt evolution with garnet Lu--Hf date
indistinguishable from U--Pb monazite age(Figure~\ref{fig6}B), and
older than U--Pb zircon age (Figure~\ref{fig6}C). A core-to-rim
decrease of Lu concentrations (Figure~\ref{fig6}D) is
consistent with preserved growth zoning and the authors interpreted the
date as being weighted toward the timing of core crystallization in
subsolidus conditions. Petrographic investigations show apatite
inclusions within subsolidus garnet cores, and monazite in suprasolidus
garnet rims and matrix (Figure~\ref{fig6}E). Altogether, the
Lu--Hf garnet chronometer constrains the timing of crustal thickening
and sets a minimum age for the onset of continental collision; and the
monazite and zircon U--Pb records bracket the duration of anatexis
estimated at ${\sim}$10 to 50 Myr [Figure~\ref{fig6}F;
\citealp{Charetteetal2021,Godetetal2021}]. 

\begin{figure*}
\includegraphics{fig06}
\caption{\label{fig6}Composite figure modified after
\citet{Godetetal2021}. (A) Simplified geological architecture of the
Southeastern Churchill Province, Canada. The red star shows the
location of the dated sample in northern Torngat Orogen. THO $=$
Trans-Hudson Orogen. (B) Lu--Hf garnet isochron. WR $=$ Whole rock; Grt $=$
garnet fraction. (C) U--Pb monazite and zircon chronology. (D) Lutetium
distribution in garnet (LA-ICP-MS map). (E) Grey-scaled microXRF image
showing the textural location of accessory phases. We note that apatite
(in pink) is exclusively observed in garnet-cores and monazite (in
green) in garnet-rims and matrix. (F) Composite $P$--$T$--$t$ path 
\cite[modified
after][]{Godetetal2021}. The inferred $P$--$T$ path is after
\citet{TettelaarIndares2007}. The wet and restitic solidii are from
\citet{Whiteetal2007} and \citet{Charetteetal2021}, respectively.}
\end{figure*}

When compiling PTt paths based on multi-method approach in the case of
UHP metamorphism, that encompasses the largest $P$ and $T$ variations
\cite{McClellandLapen2013} some general considerations arise: (i)
the chronometer sequence depends at first order on the maximum
temperature reached. Along HP--LT gradients, rocks with PT paths
remaining below 600~\textdegree C will tend to show prograde zircons,
while rocks experiencing higher temperatures
(above 700~\textdegree C)
will tend to develop zircons along their retrograde path, controlled by
interaction with melt \cite{Hermannetal2013}, (ii) garnet grows along
the prograde to peak temperature conditions in most cases. The distinct
dating of cores and rims \cite{Tualetal2022}, or the combined use of
Lu--Hf and Sm--Nd \cite{Johnsonetal2018, Charetteetal2021}
might even yield multiple ages along this interval and hence an
estimate of tectonic processes rates (cf. Section~\ref{sec2.4}) and (iii)
monazite appears to be a trustful record of low-grade stages under
subsolidus conditions, in most cases framing garnet growth 
\cite[e.g.][]{Godetetal2020b}, even though equilibrium between the two
phases has to be carefully assessed based on rock chemistry
\cite{Hoischetal2008, Kohn2016}.
Rutile has a more
complex behavior and can be, in the same rock, shielded in garnet and
then yields prograde ages or gives later ages when located in the
matrix \cite{Bonnetetal2022, Jacobetal2022}.

These rules of thumb however require to be discussed in the light of
error propagation for ages stemming from different methods and labs.
Indeed, ages obtained on different minerals, via different methods and
in different labs need to be compared using the largest acceptation of
uncertainty. Uncertainties stemming from the isotopic and elemental
ratios uncertainty of the primary reference material must be added with
uncertainty due to long-term excess variance of the secondary standard
and the uncertainty on the used decay constant
\cite{Horstwoodetal2016}. For instance, for the multi-method PT-path
produced for the Tasiuyak terrane, in the Churchill Province by
\citet{Godetetal2021}, the propagation of external errors on zircon
ages does not significantly change the uncertainty on
$^{207}$Pb/$^{206}$Pb ages, which lays close
to 10 Myr for 1900 Ma ages. Even though the used constant decay for
lutetium is constrained by comparison with U--Pb ages 
\cite{Soderlundetal2004}, the full uncertainty on Lu--Hf ages is close
to twice the internal uncertainty, changing from 12 Myr to 20 Myr for
1900 Ma absolute values. In this regard, distinguishing
tectono-metamorphic stages or evaluating rates over periods shorter
than 30 Myr at 2000 Ma is actually impossible on the sole comparison of
U--Pb zircon and Lu--Hf garnet ages.

\subsection{Campaign-style dating: spatial resolution in the field and statistical approach}

The methods based on laser ablation (LA-ICP-MS) and its sophistications
now allow the massive production of \textit{in situ} age data with
textural and possibly geochemical control. This opens possibilities for
mapping approaches at large geodynamic scale (e.g. orogen) as well as a
statistical approach of the age distribution according to the methods
used. Campaign-style \textit{in situ} Lu--Hf analysis of garnets from 25
felsic gneisses, metapelites and migmatites from the Western Gneiss
Region, Norway \cite{Tamblynetal2022} resulted in the systematic
distinction of unexpected inherited Neoproterozoic cores from
Caledonian high-pressure overgrowth. Campaign-style \textit{in situ}
dating on titanites \cite{Mottrametal2019} over 2000 km of lateral
continuity within the GHS reveals a continuous east--west gradient in
titanite ages, correlated with an eastward decrease in GHS\break thickness. A
lateral variation of the wedge dynamics (with later accreted and
thicker units to the east) appears thanks to this study. So gaining
spatial resolution at the thin-section scale comes together with
gaining spatial resolution in the field.

Massive acquisition campaigns also produce such a quantity of
homogeneous data in method and analytical error, that a statistical
approach is possible, following the example of detrital zircon studies.
Age frequency curves on different minerals (often zircon and monazite)
can thus be used to decipher the different phases of a single
metamorphic event in different units or to estimate the duration of
this event [\citealp{Tayloretal2016, Dingetal2021},
{Figure~\ref{fig7}A,B}]. Rather than assessing the peak timing, the
frequently bimodal monazite and zircon age distribution curves allow to
frame the regional temperature peak and estimate its duration. Such
results actually constitute a breakthrough in the petrochronological
data value as it assigns an age to the studied metamorphic events but
also yields access to their duration and hence their characteristic
time-scale.

\begin{figure*}
\includegraphics{fig07}
\caption{\label{fig7}Comparison of zircon and monazite ages during
process. Monazite and zircon U/Pb age distribution patterns for the
South Granulite terrain, India (A) \cite{Tayloretal2016} and the
Eastern Greater Himalayan Sequence in China (B) \cite{Dingetal2021}
for partial melting duration. Histograms are built summing even normal
distribution for each age. Duration of the partially molten stage is
deduced from the time delay between retrograde zircon and prograde
monazite age peaks. (C) Shear event in the Coast Shear Zone British
Columbia, Canada \cite{Moseretal2022} from U--Pb age populations
defined on the basis of intra-gran strain patterns deduced from EBSD
analysis. Deformed grain domains are defined by an average
misorientation of the analysis laser spot higher than 2\textdegree. Rims
and cores are defined on the basis of Ce mapping. Dashed lines
represent best Gaussian fits for main peak. Average ages given are
centers and deviations for these.}
\end{figure*}


\subsection{Assessing the duration of processes}\label{sec2.4}

Thanks to the development of \textit{in situ} analysis, modern
geochronology techniques allow to date various texturally and
chemically constrained mineral generations and estimate the duration of
the processes associated with successive crystallization events. For
example, dating the overall activation interval of shear zones is
possible thanks to recrystallization caused by strain and the partial
preservation of prior generations. This is the case in Syros, where the
activity of the Lia shear zone was dated from 53 to 37~Ma using the
$^{40}$Ar--$^{39}$Ar \textit{in situ} method
\cite{Laurentetal2021}. 

Ages obtained in various minerals and/or generations can also be pinned
along the PT path allowing to estimate the duration of burial and
exhumation of metamorphic rocks. This is particularly the case with the
multi-method approach, involving multiple geochronometers with various
crystallization timing and/or diffusion resetting. 

As an example, the residence duration of rocks in the supra-solidus
domain in collision context is determined more and more precisely. As
early as 2011, for example, titanite ages from the GHS calcschists
showed that the latter had resided in the\break supra-solidus domain for more
than 10 Myr prior to the initiation of the Main Central Thrust
\cite{KohnCorrie2011}. Bimodal frequency curves of ages on
monazite and zircon suggest that the duration of the supra-solidus
phase could reach 22 to 24 Myr locally [\citealp{Dingetal2021},
{Figure~\ref{fig7}B}]. In the Central Alps, zircon ages from migmatitic
gneiss sampled along the Insubric Line \cite{Rubattoetal2009} also
show a residence time of 10 Myr under anatexis conditions. The detailed
age distribution implies that this 10 Myr period actually represents a
succession of shorter time scale fluid ingression pulses responsible
for partial\break melting \cite{Rubattoetal2009}. In older orogens\break [Eastern
Ghats, India, \citealp{Korhonenetal2013}; Churchill Province, Canada,
\citealp{Charetteetal2021,  Godetetal2021}] the molten state
period can even reach 30 to 70 Myr respectively, according to the
multi-method paths produced. The density and precision of the ages
obtained today thus allow to highlight long partially molten stages
within ancient or recent collisional systems. The evidence of these
long-lasting stages implies that partial melting can last for a long
time without inducing strain localization \cite{KohnCorrie2011}
and that partially molten systems probably constitute
temperature-buffered reservoirs, capable of persisting under the joint\break
effects of latent heat of partial melting \cite{Labrousseetal2015},
fluid circulations \cite{Rubattoetal2009}, or shear heating
\cite{Dingetal2021}.

\subsection{Microstructural geochronology: using strain to interpret dates}

The usual approach to date a deformation event in high-grade rocks is
to first establish a pressure--temperature--deformation path by
identifying the paragenesis and their relationship to strain, then add
absolute ages from accessory minerals by relative chronology to major
phases (cf. Section~\ref{sec2.1.1}), and thus obtain a
pressure--temperature--time--deformation path. However, datable minerals
can also be direct carriers of deformation markers. The joint use of
\textit{in situ} dating methods and grain-scale deformation analysis
(e.g. EBSD, TEM or APT) allows to directly establish a link between
isotopic signal and deformation.

In medium-temperature mylonites (amphibolite facies) from the Seve
nappe, Norwegian Caledonides, EBSD analysis of titanite aggregates
elongated in the mylonitic foliation \cite{Giuntolietal2020} shows
weak texturing, which is symptomatic of low internal plastic
deformation and thus of efficient recrystallization during the
formation of these aggregates. The U--Pb analysis on these aggregates,
although discordant, gives well-constrained lower intercepts
interpreted as the age of mylonitic foliation development. EBSD
analysis of datable phases can on the other hand show strong textures
symptomatic of active plastic deformation mechanisms in inherited
minerals. In one zircon from a Siberian xenolith \cite{Timmsetal2011},
subgrain boundaries, defined by weak misorientations in EBSD maps,
consistently show Ti depletion and REE enrichment relative to subgrain
cores. These crystal-scale strain localization zones are also
systematically poorer in Pb and thus appear younger than the host
zircon, based on SHRIMP analyses. This precursor study shows that
deformation-assisted REE and Pb redistribution processes are faster (by
5 orders of magnitude according to the authors) than
temperature-activated\break diffusion. 

In mylonitic gneiss calcsilicates from the Coast Shear Zone, British
Columbia, the identification of bent zones characterized by strong
disorientations and fluid-associated recrystallization rings has been
coupled with \textit{in situ} LASS analyses, which simultaneously
provide ages, Zr contents, and REE spectra of ablated domains
\cite{Moseretal2022}. A direct correlation appears between ages and
misorientation, and the bent domains are statistically younger than the
titanite rims and cores ({Figure~\ref{fig7}C}). The question of interpreting this
age difference as the duration of shear zone activation or as the
effect of a single deformation event 10 Myr later than the initial
crystallization of the titanites remains open
\cite{Klepeisetal1998, Moseretal2022}, but access to the
duration of the deformation stage is within reach\break here.

The ultimate refinement in terms of correlation between isotopic signal
and intra-crystalline structure comes from the application of atom
probe tomography (APT) to silicates which opens the way to
``nano-geochronology'' \cite{Moseretal2017}. Mapping the exact
position of each lead atom in the prepared sample allows the
identification of heterogeneities in their distribution at the
nanoscale. Tests have been carried out on ancient and therefore
lead-rich accessory minerals for half a dozen years and open new
perspectives. Coupled TEM and APT study of a monazite from Rogaland,
Norway, shows that radiogenic Pb is concentrated in clusters that
behave as closed nano-systems while the whole grain can be considered
as an open system \cite{Seydoux-Guillaumeetal2019}. The development
of such nano-scale Pb clusters has been linked to the mineral strain in
some cases. On 1.7 Ga monazites [Sandmata Complex, India,
\citealp{Fougerouseetal2021}] from rocks deformed at 980 Ma, a coupled
EBSD, TEM and APT approach shows that mechanically twinned domains are
depleted in Pb. The nano-scale age calculated on the twinned domain
corresponds to the age acknowledged for the deformation from coupled
HR-EBSD and SHRIMP analysis \cite{Ericksonetal2015}. It seems that
lead is released during the shearing associated with the twinning by
breaking and rearranging of the bonds with the oxygen ion framework
which preferentially affects the Pb retention sites. The high
dislocation density of the progressing twin tip could expel large Pb
ions from the mineral at much higher rates than other recrystallization
mechanisms. 

It is therefore the deformation itself that is datable, in the cases
where it acts as a much more efficient mechanism for resetting the
isotopic signal than competing processes.

\section{Discussion: impact of petrochronology data on deep tectonics concepts}

The description of strain patterns in the inner zones of mountain belts
is based on the definition of distinct tectonic units as finite volumes
of rock, derived from the lower or upper colliding plate, with a
defined paleogeographic origin and bounded by zones of localized
strain. Understanding this finite deformation as the result of a
continuous process or as a sequence of deformation phases ($D_i$) is a
duality inherent to tectonic analysis \cite{Fossenetal2019}.
Nevertheless, the distinction of successive metamorphic parageneses
($M_i$) and the collection of point ages associated directly or indirectly
with these parageneses tend to provide a discrete or sequential
picture of the time dimension of the evolution of the internal zones:
each unit is characterized by a succession of deformation phases $D_i$ and
metamorphic imprints $M_i$, which distinguishes it from its surrounding
counterparts. The increase in the spatial density of age data within
and across these units, plus the increased precision of these ages,
including for old processes (older than 1 Ga), and their association
with one or several precise stages along PT paths, leads to (i) question
the very notion of unit, (ii) question the meaning of the successions of
different ages within the same unit, (iii) search for the spatial scale
and thus the process that controls the age pattern and (iv)~apprehend
the possible secular variation of orogenic processes time scale.

\subsection{Questioning the notion of unit}

Campaign-style studies and regional compilations make it possible to
map age patterns within domains of variable size [unit size: Cycladic
Blueschists, \citealp{GlodnyRing2022}, or the GHS,
\citealp{Mottrametal2019}, massif scale: Lepontine Alps,
\citealp{Bostonetal2017}, internal zone: Western Gneiss Region,
\citealp{Wiestetal2021}, or whole orogen: Capricorn orogen,
\citealp{Olierooketal2019}]. In some cases, age distributions, in
addition to the structural dataset, allow subunits to be distinguished.

In the Dora Maira nappe stack, HP to UHP subunits are distinguished
thanks to metamorphic $P$--$T$ gaps (up to 2 GPa and 250~\textdegree C) and
diverse lithological compositions \cite[e.g.][]{Chopinetal1991,
Groppoetal2019, Manzottietal2022}. U--Pb ages obtained in
rutile in the southern part of the massif, show a downward-decrease
trend across the nappe-stack [\citealp{Bonnetetal2022},
{Figure~\ref{fig5}}]. This is again consistent with the progressive
burial of upper to lower units from {ca.}\ 40 to {ca.}\ 33~Ma. 
However, given the large maximum pressure (hence depth ?)
differences between the units, the preservation of the paleogeographic
order of units within the nappe stack implies that exhumation of each
unit was so fast that the next unit only reaches peak after exhumation
of the previous unit at least to similar depths. Fast exhumation rates
for these units are in line with those calculated for the UHP unit of
the massif by \citet{RubattoHermann2001}. The younger limit for
exhumation of all units is a common retrogression event throughout the
massif dated by U--Pb geochronology on titanite at {ca.}\ 33--32 Ma
\cite{RubattoHermann2001, Bonnetetal2022}. Units
significance is both paleogeographic and tectonic, and hence age and
structural patterns coincide.

The paradigmatic section of the Upper Cycladic Blueschists Unit (UCBU,
{Figure~\ref{fig8}}) divided into 2 \cite{Schumacheretal2008,
GlodnyRing2022} or 3 subunits \cite{Laurentetal2017,
Laurentetal2021, Kotowskietal2022} on the island of Syros, shows the
relationships between PT evolution, age pattern and deformation at
different scales. A consensus emerges that the UCBU evolved in a
thermo-kinetically stationary subduction channel system
\cite{Uunketal2022}, even though significant differences in exhumation
PT path between some units are documented \cite{Trotetetal2001,
Laurentetal2018}. The younging downward of HP stage ages evidences the
progressive burial of upper to lower subunits from 51 to 43 Ma, as
distal to proximal parts of a former passive margin
\cite{Wijbransetal1990, GlodnyRing2022, Kotowskietal2022,
Uunketal2022}. The evolution of Rb--Sr and
$^{40}$Ar--$^{39}$Ar ages on micas across
these subunits is consistent with an increasing footprint of
greenschist retrogression towards the bottom of the stack
\cite{Laurentetal2021, GlodnyRing2022}. The age difference between
HP stage and greenschist deformation yields a characteristic 10 Myr
time interval for exhumation of these units \cite{GlodnyRing2022}.
The debated delineation of subunits within the UCBU is based on
lithological correlations, structural analysis, metamorphic grades,
isotopic signal but also protolith and metamorphic ages
({Figure~\ref{fig8}}). Increasing the density of protolithic and
metamorphic ages allows to refine these subunits.\break The distinction of
the middle and lower allochthons based on strain analysis
[\citealp{Laurentetal2021}, {Figure~\ref{fig8}A}] produces monomodal
ages patterns, while \citet{Kotowskietal2022} delineation yields a
bimodal age pattern for the lower CBU. The uppermost/middle UCBU
boundary is both a large-scale shear zone and an age shift in HP and
retrogression stages \cite{GlodnyRing2022}. A systematic decrease
in $^{40}$Ar--$^{39}$Ar ages on phengites
towards the core of the shear zones delineating these subunits is also
observed at the decameter to hectometer scale \cite{Laurentetal2021}.
The debated distinction between a lowermost and a middle unit, is
actually supported by a local 15 Myr age gap across the Delfini shear
zone \cite{Laurentetal2021}, 
so that definition of tectonic units based on their age pattern
cannot be elaborated on without a consideration of
the sampling scale behind age populations.

\begin{figure*}
\vspace*{5pt}
\includegraphics{fig08}
\vspace*{3.5pt}
\caption{\label{fig8}Comparison of the proposed subunits delineation in
Syros from (A) \citet{Laurentetal2016}, (B)~\citet{Kotowskietal2022} and
(C) \citet{GlodnyRing2022} associated with the literature near-peak ages
depending on this delineation. For age compilation see
\citet{GlodnyRing2022} and \citet{Gyomlaietal2023}.}
\vspace*{4pt}
\end{figure*}

In other cases, unit boundaries defined on protolith affinities and
deformation localization do not match the contrasts inferred from age
patterns. This is the case within the WGR, where the Bl\aa{}h\o{}
nappe, defined as an equivalent of the Seve nappe allochthon
\cite{Robinson1995} reached UHP conditions during the Scandian
collision. The mismatch in age patterns between the northern and
southern portions implies that this allochthonous unit was disrupted
into several subunits prior to its involvement in continental
subduction, or that the different domains constitute two distinct units
mixed up until now \cite{Marchetal2022}. The age distribution,
especially prograde, within the WGR parautochthon also shows jumps that
do not correspond to deformation localization zones. The eastward
continuation of the major Nordfjord Shear Zone
\cite{Labrousseetal2004} into the Lom Shear Zone \cite{Wiestetal2021}
or even the Geiranger Shear Zone \cite{Young2018} are supported more
by jumps in age patterns than by structural evidence
\cite[][and Supplementary material]{Wiestetal2021}. Thus, it appears that in the
deep dynamics of the convergence zones, age patterns and deformation
patterns do not match as well as in more superficial systems. Extending
the duplex accretionary prism model to converging systems involving
metamorphism up to 500~\textdegree C and 1 GPa \cite{Angiboustetal2022}
or more broadly the accretionary tectonics of small cold orogens [as
opposed to large hot orogens, \citealp{Chardonetal2009,
JamiesonBeaumont2013}] indeed tends to show that considering
tectono-metamorphic units as finite and coherent volumes over their
entire PTt history is conclusive. The generalization of this approach
to larger-scale structures, involving in particular high-temperature
basement units possibly affected by anatexis, comes up against the
complexity of age patterns. It would therefore be more relevant to
consider that materials beyond a certain localized--distributed strain
transition [deeper than the acknowledged brittle--ductile transition;
\citealp{Cooperetal2017}] behave as continuous fluids in which the
strain localization itself shows a timescale \cite{Giraultetal2022} of
the same order of magnitude as that of the movement of the materials
(i.e. 10 Myr). 

\subsection{The tectonic meaning of age sequences}

Multi-method studies in particular led to move petrochronology out of
the $M_i/D_i$ approach \cite{Orioloetal2022} and to extend the progressive
approach to the interpretation of age patterns. The documentation of
several age populations in the same rock or unit, favored by the large
number of dates produced and their interpretation as ages on the basis
of textures or geochemical signatures, yields different conclusions
depending on the time scale on which these populations are distributed.
In the early Earth times, for example for the Warrawoona greenstone
belt and the associated Mount Edgar granitoids in the Pilbara craton in
Australia, two distinct metamorphic ages have been documented and
assigned to distinct burial and exhumation cycles during sagduction
processes, which are partial (and crustal) convective overturns between
supracrustal greenstones/sediments cover and their granitoid basement
at 3312 ${\pm}$ 5 Ma (U--Pb on zircon) and 3343 ${\pm}$ 5 Ma [U--Pb on
monazite inclusions trapped in garnet; \citealp{Francoisetal2014}].
Interestingly, the recorded PTt conditions support fast, gravity-driven
tectonics, where surface sedimentary rocks were buried until lower
crust conditions and exhumed back to the surface in less than 10 Myr.
Over a shorter interval, in the Seve nappe complex (SNC) of the
Norwegian Caledonides, \citet{Walczaketal2022} distinguished two
successive burial stages at $483 \pm 4$~Ma and $439 \pm 4$~Ma by
laser ablation depth-profiling on zircons. The distinction of two types
of age profiles and geochemical signatures allowed the old age to be
associated with eclogite facies and the young one with granulite
\mbox{facies,} consistent with two successive decompression episodes after a
first peak of HP and a second of HT.
These are therefore not just
points that are dated along the PT path but trends. The new HP stage in
the SNC, 20 Myr older than regionally documented [460 Ma, 
\citealp{BruecknerVanRoermund2007}] is interpreted as the signature of
successive burials of the same unit in the same convergence zone. A
similar petrochronological approach on zircon, titanite and allanite
from gneiss of the Sesia zone, Italian Alps \cite{Rubattoetal2011}, is
also consistent with two successive burial stages in the eclogite
facies, less than 20 Myr apart.

Such PTt paths support the ``Yo-yo subduction'' model, first proposed on
the basis of thermochronology and sedimentology data in the Nigde
Massif, Turkey \cite{Umhoeferetal2007} on a time scale of about 60
Myr. In the case of the Nigde Massif, the recurrence of HP stages is
attributed to changes in boundary conditions along a strike-slip shear
zone [the Central Anatolian Fault Zone, \citealp{Umhoeferetal2007}].
Other interpretations of Yo-yo subduction do not rely on changes in
boundary conditions to\break explain successive tectonic--metamorphic events
but on material displacement in a stationary subduction system. The
estimated time intervals (20 ${\pm}$ 10 Myr) would then be a
characteristic time for the circulation of matter in the subduction
interface \cite{Agardetal2009} unless it is the finest grain at which
we can distinguish different events. Stages have actually been
distinguished over shorter intervals, like for instance the four
successive phases of growth recorded over 20 Myr by zircon from the
high-deformation metasedimentary m\'{e}lange of the Nirgua Complex, in
the Venezuelan Cordillera \cite{Vieteetal2015}. The method used
reproduces with comparable resolution the results of previous
thermochronology studies, and modifies their previous interpretation as
a thermal signal. The different episodes are supposed to last less than
1 Myr with a recurrence time of 5 Myr and represent either thermal
pulses or pulses of fluid arrival during a single metamorphic event. In
Western Papua New Guinea, U--Pb ages obtained on zircon from HP
metasedimentary rocks and eclogites highlight a very fast burial and
exhumation in less than 10 Myr  \cite{Francoisetal2016}. Similarly,
Eastern Papua records an UHP metamorphic event (with coesite
occurrence) at ca. 4 Ma \cite{Baldwinetal2004}. These two examples are
the youngest documented eclogites exposed in the Earth surface. The
significance of these very short time scales can be understood either
as short-term variations in boundary conditions (heat advection, fluid
flow) for a volume of rock that is moving on a longer time scale or as
the rapid movement of the volume of rock in boundary conditions that
are evolving on a longer time scale (in the case of a long-lived as in
Papua-New Guinea). In both cases it is the competition between
advective processes (of fluids or solids) and diffusion processes (of
heat or fluids) that controls the actual time scale documented. Fully
coupled thermo-mechanical numerical models of subduction systems
produce complex PTt paths during the progressive individualization of
oceanic units in subduction settings with notably transient
decompression on the order of 0.5~GPa on time scales of 2 to 3 Myr
\cite{Blanco-Quinteroetal2011, Ruhetal2015}. The
state-of-the-art resolution of petrochronology thus provides a tectonic
meaning to the complex path shapes predicted by thermo-mechanical
models  \cite[][and references therein]{Gerya2022}.

\subsection{Secular evolution of geodynamic processes}

The accumulation of ages obtained on HP--LT metamorphic rocks [with
pressures higher than 2.5 GPa and or thermal gradients lower than 300
K/GPa, \citealp{BrownJohnson2018}] yielded the identification of their
massive emergence to the Neoproterozoic (at the end of the Tonian i.e.
700 Ma) which has been interpreted as the signature of the appearance
of modern plate tectonics on Earth \cite{Stern2005}. This data is
undoubtedly altered by preservation bias, due on the one hand to
retrogression and polymetamorphism, as complex as the rocks are old 
\cite{Palinetal2020}, but also due to the erosion of the superficial
parts of ancient orogenic wedges in which HP--LT relics are most often
imbricated \cite{Willigersetal2002}. The continual addition of older
ages to the list of HP--LT metamorphic occurrences
\cite{Palinetal2020, Brownetal2022} is likely evidence
of such a preservation\break bias.

This being said, the occurrence of HP--LT minerals or parageneses is not
unequivocal evidence for the establishment of modern tectonics. First,
local production of HP rock does not imply the establishment of global
plate tectonics \cite{Deweyetal2021}. Indeed, crustal-scale sagduction
tectonics is prone to produce metamorphic rocks with PTt paths
undistinguishable from modern tectonics [0.9--1.1 GPa and
450--550~\textdegree C i.e. 500 K/GPa;  \citealp{Francoisetal2014}]. The
only difference is actually the space scale of the metamorphic pattern:
lithospheric for modern-day subduction {vs} crustal for
sagduction and the maximum of pressure reached. 

(Ultra) High Pressure--Low Temperature ((U)HP--LT) metamorphic rocks
such as eclogites provide crucial clues for the geodynamic processes,
as these rocks have only been described in modern orogens. Indeed,
the PTt conditions recorded by the eclogites and some index minerals
they contain (e.g. omphacite, coesite, glaucophane, lawsonite,
carpholite) are indisputable indicators of the presence of a deep
subduction involving the burial of a relatively cold crust in the
mantle at great depth (${>}$70~km). These types of rocks are not produced
in the Archean \cite{Agardetal2005, BrownJohnson2018} where
the maximum recorded pressures do not exceed 1.5 GPa
({Figure~\ref{fig9}}). A transition period during the Paleoproterozoic
records the first occurrences of eclogites worldwide during the
amalgamation of the Columbia/Nuna Supercontinent 
\cite{Francoisetal2018, Francoisetal2022},
even if no UHP markers (such as
coesite) are observable ({Figure~\ref{fig9}}). HP metamorphic rocks
could also betray strong stress deviators, and thus significant mean
pressures without significant burial in convergence zones
\cite{YamatoBrun2017}. It is beyond the scope of this paper to discuss
the significance of the pressures recorded by metamorphic rocks
\cite{HobbsOrd2017}, but in any case, the occurrence of (U)HP--LT
(${>}$1.5 GPa) metamorphic rocks over large spatial scales
does reflect the development of a strong lithosphere prone to
subducting or supporting high stress deviators.



\begin{figure*}
\includegraphics{fig09}
\caption{\label{fig9}Evolution of metamorphism markers through
Precambrian times [data from Stern and Gerya, personal communication and
\citealp{BrownJohnson2018}]. Yellow circles: $P< 1.5$ GPa, blue
circles: $P$ 1.5 to 2.5 GPa, red circles: $P > 2.5$ GPa. Cooling rates
deduced from metamorphic rocks PTt paths over the 4 Ga geological
record \cite[data][]{Brownetal2022}. Conservative estimates of
uncertainties of ${\pm}$50~\textdegree C on temperatures and ${\pm}$5\% 
on ages have been extended to cooling rates values.}
\end{figure*}

Multi-method approach further allows to estimate time intervals for one
same rock or unit and thus to access rates, so far underutilized in the
debate on the secular evolution of Earth dynamics
\cite{Chowdhuryetal2021}. Provided that age differences are compared
accounting their complete source of uncertainties, differences between
the age of metasedimentary detrital rock protoliths, inferred from
detrital zircons for ancient times, and the age of metamorphism allow
to assess, along with an estimate of the maximum depth reached, an
apparent burial rate (in km/Myr) characteristic of the incorporation of
foreland basins into their related wedge. The compilation of available
estimates \cite{Nicolietal2016} shows a secular decrease in the
calculated maximum rates attributed to the gradual decrease in juvenile
crust production as well as a decrease in the diversity of active
orogenic processes \cite{Nicolietal2016, Palinetal2020}. The age
difference between metamorphic peak and retrogression assemblages
allows, together with the estimate of associated $T$ conditions, to
calculate cooling rates [in \textdegree C/Myr,
\citealp{Chowdhuryetal2021, Brownetal2022},
{Figure~\ref{fig9}}]. Solid diffusion profile modeling, or
geospeedometry, yields comparable trends but the systematic one
order-of-magnitude discrepancy between the two methods likely suggests
that different things are being measured \cite{VieteLister2017,
Brownetal2022}. The secular trend in both cases is an exponential
increase in cooling rate with time, with perhaps a jump in the early
Phanerozoic, revealed by fine statistical analysis of the limited data
set \cite{Brownetal2022} over the complete Earth history, although the
restriction of the same data set to Precambrian times only does not
show any trend (Figure~\ref{fig9}). The cooling rates are also
anti-correlated with the T/P gradients 
\cite[][Supplementary material]{Brownetal2022}. 
These trends support the model of a 
gradual shift in orogenic
dynamics from large hot peel-back orogens \cite{Chowdhuryetal2017}
where large heat flows limit the capacity of lithospheric rocks to
localize strain \cite{Chardonetal2009, Gapaisetal2009}
to smaller and colder orogens where early and perennial localization of
deformation allows for large relative vertical motions of the tectonic
units, and thus larger cooling rates. Although the effect of external
dynamics on the secular evolution of tectonics is not negligible,
including the lubrication and stabilization of subduction zones by
sedimentary inputs to the trench \cite{SobolevBrown2019}, it
appears that the characteristic depth of the distributed--localized
strain transition \cite{Cooperetal2017} that separates shallow and
deep orogen dynamics \cite{Labrousseetal2004} or suprastructure and
infrastructure \cite{Culshawetal2006} appears to be the first-order
parameter that controls the characteristic operating time of orogenic
systems. 

\section{Conclusion}

While the understanding of inner mountain belts evolved from the
mapping of their structural and metamorphic boundaries in the field, to
the understanding of thermo--chemo--mechanical processes behind the
strain, fluid flow and reactions localization in space and time,
petrochronology emerged, based on the interpretation of \textit{in
situ} ages in the light of geochemical and microstructural data
acquired at the scale of tenth of microns analysis spots. The wealth of
data produced now allows to estimate the duration of crucial processes
along PTt path, such as the residence time in the supra-solidus domain,
or the characteristic time of strain localization within the crust.
Even if propagation of errors still blurs the image we have of the
early Earth geodynamics, the precision, accuracy and amount of data
produced by dating techniques allows campaign-style exploration of
large portions of inner mountain belts, and lead to a more dynamic
definition of tectonometamorphic units. Age patterns within or across
these units emphasize that they only behave as finite and coherent
bodies in the shallowest structural levels of orogenic wedges, and
behave more as continuous visco-plastic fluids at greater depth and
temperature, in which strain localization itself has a characteristic
time, and inheritance-related mechanical contrasts only play a minor
role. 

The next step forward shall come from the coupling of \textit{in situ}
dating techniques with strain analysis at the same (EBSD) or higher
(APT) resolution. These approaches should shortcut the long path that
we still have to walk to pin strain and ages along a same
pressure--temperature path, as it directly evidences the links between
isotopes retention or diffusion and crystal lattice defaults.

\section*{Declaration of interests} 
The authors do not work for, advise, own shares in, or receive funds
from any organization that could benefit from this article, and have
declared no affiliations other than their research organizations. 

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