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\DOI{10.5802/crphys.149}
\datereceived{2022-09-29}
\daterevised{2023-01-25}
\dateaccepted{2023-02-22}
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\dateposted{2023-04-20}
\datepublished{2024-04-26}
\begin{document}

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

\title{New pathways to control the evolution of the atomic motion in
metallic glasses}

\alttitle{Nouvelles voies pour contr\^oler l'\'evolution du mouvement
atomique dans les verres m\'etalliques}

\author{\firstname{Antoine} \lastname{Cornet}}
\address{Universit\'{e} de Lyon, 
Universit\'{e} Claude Bernard Lyon 1, CNRS, 
Institut Lumi\`{e}re Mati\`{e}re, F-69622, 
Villeurbanne, 
France}
\address{European Synchrotron Radiation Facility, 
71 avenue des Martyrs, CS 40220, 
Grenoble 38043, 
France} 
\email[A. Cornet]{antoine.cornet@univ-lyon1.fr}

\author{\firstname{Beatrice} \lastname{Ruta}\CDRorcid{0000-0002-1240-0533}\IsCorresp}
\addressSameAs{1}{Universit\'{e} de Lyon, 
Universit\'{e} Claude Bernard Lyon 1, CNRS, 
Institut Lumi\`{e}re Mati\`{e}re, F-69622, 
Villeurbanne, 
France}
\addressSameAs{2}{European Synchrotron Radiation Facility, 
71 avenue des Martyrs, CS 40220, 
Grenoble 38043, 
France} 
\email[B. Ruta]{beatrice.ruta@univ-lyon1.fr}

\keywords{\kwd{Metallic glasses}
\kwd{Physical aging}
\kwd{X-ray photon correlation spectroscopy}
\kwd{Atomic dynamics}
\kwd{Synchrotron radiation}
\kwd{Structural relaxation}}

\altkeywords{\kwd{Verres m\'etalliques}
\kwd{Vieillissement}
\kwd{Corr\'elation de photons des rayons X}
\kwd{Dynamique atomique}
\kwd{Rayonnement synchrotron}
\kwd{Relaxation structurelle}}

\begin{abstract}
Metallic glass formers are a relatively new entry in glass physics,
which has attracted large interest in both physics and materials
science communities due to the unique mechanical and structural
properties of these materials. Physical aging is however one of the
main obstacle to their widespread use as it affects their properties at
all length scales. The knowledge of the microscopic mechanisms inducing
aging and relaxation is therefore extremely important for both
fundamental and applied sciences. In this article we present a review
of the recent advances made with the X-ray photon correlation
spectroscopy technique on the study of the collective particle motion
and physical aging in metallic glasses at the atomic level. {We show
that a careful tuning of the sample preparation or the application of
specific thermal protocols have the potential to drive the glass into
more aged or rejuvenated microscopic configurations with different
stabilities.}
\end{abstract}

\begin{altabstract}
Les verres m\'etalliques sont des mat\'eriaux qui suscitent une grande
attention en raison de leurs propri\'et\'es exceptionnelles, notamment
leur r\'esistance \`a la corrosion ainsi que leur haute r\'esistance
\`a la fracture combin\'ee \`a une large d\'eformation \'elastique. De
plus, certaines compositions permettent une vitrification avec des
vitesses de refroidissement relativement lente, permettant la
synth\`ese de mat\'eriaux massifs, avec des rayons critiques de
synth\`ese sup\'erieurs au centim\`etre, ouvrant la voie \`a une
utilisation industrielle des verres m\'etalliques.

N\'eanmoins, tous les verres sont sujet \`a une relaxation spontan\'ee
vers l'\'etat liquide, plus ou moins lente, appel\'ee vieillissement,
et qui affecte la structure, la dynamique et les propri\'et\'es
macroscopiques du verre. Dans le cas des verres m\'etallique, les
effets du vieillissement sont particuli\`erement importants, incluant
une fragilit\'e accrue du verre, et bloquent leur potentiel applicatif.

De fait, la connaissance et la compr\'ehension des m\'ecanismes
microscopiques associ\'es au vieillissement font l'objet d'une
recherche intense, tant du point de vue applicatif que fondamental.
Dans cet article, nous pr\'esentons les r\'ecents d\'eveloppements de
la spectroscopie de corr\'elation des photons des rayons X (X-ray
Photon Correlation Spectroscopy, ou XPCS), qui permet de quantifier la
mobilit\'e atomique au sein des mat\'eriaux d\'esordonn\'es, et son
application pour caract\'eriser le vieillissement des verres \`a
l'\'echelle microscopique. Nous montrons que des protocoles thermiques
ou m\'ecaniques appropri\'es au niveau de la synth\`ese et la
pr\'eparation des verres m\'etalliques permettent de modifier la
stabilit\'e du mat\'eriau vitreux, et d'aboutir \`a un verre rajeuni ou
vieilli.
\end{altabstract}

\maketitle

%\vspace*{-2pt plus 1pt minus 1pt}

\end{noXML}

\let\rmmu\upmu

\section{Introduction}\label{sec1}
Glasses are essential materials in our daily life and they have
accompanied progresses in civilization for millennia. Although they are
used in a wide range of applications, spanning from engineering to
medicine or environmental science, a full comprehension of the
mechanisms responsible for their unique properties is still 
missing~\cite{1}. Within the broad family of glassy materials, metallic
glasses (MGs) are considered a relatively young entry. Discovered in
the nineteen sixties, in few decades they have obtained a dominant role
in material science and are currently considered among the most
actively studied metallic  materials~\cite{2}. MGs present an
outstanding combination of properties such as high strength, large
elastic elongation and high corrosion resistance. In addition, in the
temperature region between the glass transition temperature and the
crystallization temperature, MGs can be easily deformed in very precise
complex shapes, which makes them promising candidates for many
small-scale devices for advanced technological applications, like fuel
cell electrodes, storage devices and micro electro-mechanical 
systems~\cite{3}. Metallic glasses are extremely interesting materials
also for fundamental science. Thanks to the nature of the metallic
bonds, their microscopic dynamics is subject only to translational
motion, which make them model candidates for the study of the glass
transition nature. MGs share also many similarities with colloidal 
materials~\cite{4}, and can be used to find common properties between
hard and soft glass formers materials.

As all glasses, MGs are unstable with time and exhibit physical aging.
This means that all their properties evolve spontaneously with time and
are strongly influenced by the material production and processing.
Physical aging can be particularly severe in MGs, more than in other
glasses like network or molecular systems, and can lead to ductile to
brittle transitions, fractures and crystallization. Aging can therefore
produce annoying technological drawbacks, since it makes the amorphous
arrested state difficult to control during technological 
applications~\cite{5,6}. In this respect, the knowledge of the
microscopic mechanisms responsible for relaxation and aging in MGs is
critical as it allows to predict and control the behaviour of glasses
over time and during applications. 

In the last decade, coherent X-rays and in particular the X-ray photon
correlation spectroscopy (XPCS) technique have emerged as a powerful
tool to probe the collective atomic motion of MG during 
aging~\cite{7,8}. This technique monitors the fluctuations in the
scattered intensity generated by the impinging of coherent X-rays on
disordered systems, and provides information on the intermediate
scattering function (ISF), $f(q,t)$, and thus on the electron density
fluctuations at a length scale $2\uppi/q$ defined by the probed
wave-vector  $q$~\cite{9}. 

Aging studies on MGs have revealed a complex behavior~\cite{7}. At the
microscopic level, aging is intermittent and dominated by the interplay
between density-driven rearrangements associated to the release of
residual stresses, and ordering processes at length scales
corresponding to the medium range order, which do not affect the local 
density~\cite{10,11,12}. Numerical simulations and elastic measurements
suggest avalanche-like mechanisms triggering the relaxation in 
glasses~\cite{13}. Aging is found hierarchical even at the macroscopic
scale, and multiple relaxations have been reported during long time
enthalpy recovery and stress relaxation measurements in polymers and
metallic  systems~\cite{14,15,16}. 

After briefly recalling these results, we present here some recent
attempts which have been made to control the evolution of the
collective particle motion and therefore the aging in MGs by applying
external parameters such as stresses, thermal cycling or specific
sample
preparations. 

\section{Atomic motion across the glass transition} 
Metallic glasses are usually produced by rapidly cooling the
corresponding melt with rates of the order of $10^{4}$--$10^{6}$~K/s.
Such a fast quenching is fundamental to avoid crystallization and
freeze the system in an amorphous solid state. On approaching the glass
transition temperature,  $T_{g}$, from the liquid phase, the collective
particle motion evolves from diffusive at high temperatures to a regime
of activated dynamics in the supercooled liquid  phase~\cite{17,18}. In
this region the intermediate scattering function splits in two main
processes:  (i)~a fast microscopic decay associated to the rattling of
the particles in the cage formed by the neighbouring particles, and 
(ii)~the main structural relaxation process corresponding to the escape
of the particles from their  cages~\cite{19}. The latter process
corresponds to the long-time decay of the ISF and can be modelled by
the empirical Kohlrausch--Williams--Watts (KWW) function
$f(q,t)=f_q\exp(-t/\tau)^\beta$. In this expression, $\tau$ is the
structural relaxation time and describes the time necessary for the
system to reorganize the structure in a more stable configuration at
the probed length scale. In the liquid phase,  $\tau(q)$ is equal to
the equilibration time and is proportional to the viscous flow. The
parameter  $\beta(q)$ provides instead information on the degree of
heterogeneity of the dynamics and on the nature of particle motion, and
$f_{q}(q)$ is the non-ergodicity parameter representing the long-time
plateau preceding the structural relaxation. 

Upon further decreasing the temperature, the structural relaxation time
increases by several orders of magnitude until the material solidifies
in a metastable glassy state. Studies on MGs have shown that the glass
transition is accompanied by a dynamical crossover at the atomic level
where the decay of the ISF evolves from the well-known stretched
exponential shape (i.e. described by  $\beta<1$) of supercooled
liquids, to an unusual compressed form in the glass which can be
modelled with an exponent  $\beta>1$~\cite{4}. The same transition is
reported also by heating from the glassy state. An example of the
dynamical crossover occurring in MGs at the glass transition
temperature is reported in  Figure~\ref{fig1}a. This figure shows the
temperature evolution of the intensity--intensity correlation functions,
$g_2(q,t)$ measured with XPCS at the atomic scale upon heating a glass
of Vit4 from ambient temperature up to the liquid phase with a heating
rate of  1~K/min~\cite{20}. In this case, the as-cast glass was relaxed
at 600~K prior to the measurements to remove the presence of stresses
related to the fast-quenching used during the sample preparation. XPCS
measurements were performed at the maximum of the static structure
factor during isotherms every 5~K from 520~K up to 675~K. We recall
that the $g_2(q,t)$ functions are proportional to the intermediate
scattering functions being $g_2(q,t)=1+f(q,t)^{2}$~\cite{9}. The
corresponding KWW parameters $\tau$ and  $\beta$ are shown in 
Figures~\ref{fig1}b and~c. Three different dynamical regions
have been reported for MGs and are visible in the  figure. At low
temperatures (blue data), the correlation functions vary little with
temperature, with an almost constant structural relaxation time and a
constant shape parameter  $\beta>1$, which has been attributed to the
occurrence of a stress-induced dynamics~\cite{20}. In the  glass
transition region (pink data),  $\tau$ increases in an Arrhenius way
with a small activation energy, and is accompanied by a continuous
decrease of $\beta$ toward a stretched value $\beta<1$ which is then
reached for temperatures, $T$, larger than the glass transition
temperature $T_g=600$~K. At these temperatures, the system is in the
liquid phase and the relaxation time decreases with the typical super
Arrhenius behaviour of supercooled metallic liquids (red values) and is
accompanied by a constant stretched parameter describing the decay of
the correlation functions, close to the value reported with mechanical 
measurements~\cite{20}. Several attempts have been made to explain the
compressed decorrelation in the glassy state, from both theoretical and
numerical  sides~\cite{21,22}. A comparison with macroscopic
mechanical measurements associates the dynamical crossover to the
separation between the anelastic and viscoelastic response to
mechanical stresses at  $T_g$, the former being active also well below
$T_g$~\cite{23}. Numerical simulations in metallic liquids
glass-formers report on the existence of compressed intermediate
scattering functions in the high temperature liquid phase which appear
related to an increasing number of icosahedral clusters on approaching
the vitrification and generate additional frustration in the 
material~\cite{24}. Whether a similar argument could be applied to the
glassy state is not verified yet. Experiments in soft glasses report
instead on a very similar dynamical crossover in a variety of systems
including colloids, foams, biopolymers and microgels measured with both
X-ray and light scattering photon correlation 
spectroscopy~\cite{25,26}. In these cases, the crossover is often
accompanied by a transition from diffusive dynamics, i.e. described by
a sub-quadratic dependence of the relaxation time, $\tau(q)=1/q^{2}$,
to an anomalous super-diffusive, ballistic-like particle motion with
$\tau(q)\approx1/q$. Stress relaxation in the disordered structure can
qualitatively describe this phenomenology, although a detailed
understanding is still  missing~\cite{21,22,27}. At present, the idea
is that the dynamics of soft glasses are triggered by random collapses
of the structure due to highly stressed regions in the material. In MGs
these regions could be associated to the presence of elastic
inhomogeneities at the nanometric  scale~\cite{28}, which could be
related to the presence of flow  units~\cite{2}. Information on the
wave-vector dependence of the dynamics in MGs could help clarifying the
nature of the dynamical crossover. Due to the out-of-equilibrium nature
of glasses, such information is very difficult to obtain below  $T_g$
both experimentally and with numerical simulations and only few
information about the dynamics in the supercooled liquid phase have
been reported so  far~\cite{18}.

\begin{figure}
\vspace*{2pt}
\includegraphics{fig01}
\vspace*{4pt}
\caption{\label{fig1}(a)~Temperature dependence of the correlation
functions measured with XPCS in a Vit4 MG during isothermal steps of 
5~K between 520~K and 675~K, obtained by heating the glass with a rate
of 1~K/min. The as-cast sample was annealed at 600~K prior to the
measurements to remove eventual stresses related to the sample
preparation. The data are collected at  $q=2.6~\AA^{-1}$
corresponding to the first maximum of the atomic structure factor. 
(b,c)~Corresponding shape parameter (b) and structural relaxation
time (c) obtained by modelling the data in (a) with a KWW function.
Taken  from~\cite{20}.}
\vspace*{4pt}
\end{figure}

\begin{figure}
\includegraphics{fig02}
\caption{\label{fig2}Temporal evolution of the structural relaxation
time measured with XPCS in binary and ternary rapidly quenched MG
obtained upon heating the as-cast glasses up to specific temperatures
in the glassy state with slow heating rates (3~K/min for
Pd$_{77}$Si$_{16.5}$Cu$_{6.5}$ and  Zr$_{67}$Ni$_{33}$, 1~K/min for 
Mg$_{65}$Cu$_{25}$Y$_{10}$). The data are rescaled for the initial
value of the relaxation time at each temperature,  $\tau_{0}(T)$  and
reported as a function of the time elapsed since the beginning of the
isotherm (waiting time,  $t_{w}$) rescaled by a parameter $\tau^*$ that
describes the short time exponential growth rate during aging though
the expression $\tau(T,t_{w})= \tau _{0}(T)\exp (t_{w}/\tau^{*})$.
Pd$_{77}$Si$_{16.5}$Cu$_{6.5}$ data are taken from  Ref.~\cite{11},
Mg$_{65}$Cu$_{25}$Y$_{10}$ data from  Ref.~\cite{4} and the
Zr$_{67}$Ni$_{33}$ data from  Ref.~\cite{29}.}
\end{figure}

\break
The main difficulty arises from the impossibility to compare data
acquired at different times due to the strong evolution of the
microscopic dynamics due to physical aging. The first studies on the
dependence of the collective atomic motion on aging have been performed
on rapidly quenched MGs, i.e. on ribbons of amorphous metals which were
produced with a fast cooling rates of $10^{6}$~K/s from the melt and
then subsequently heated up in the glassy state. Studies on binary and
ternary fast quenched MGs, showed the occurrence of two dynamical
regimes which are summarized in  Figure~\ref{fig2}: a first exponential
increase of the relaxation time during isotherms in the glass, followed
by an anomalous stationary regime at longer annealing times (see
Figure~\ref{fig2}). X-ray diffraction studies suggest that the first
fast dynamical regime arises from density release mechanisms likely
involving the annihilation of defects or excess free volume stored in
the system, while the stationary regime would be more related to
ordering processes occurring at a length scale corresponding to the
medium range  order~\cite{11}. During this stationary regime, the
system is trapped in a metastable state from which aging seems then to
pursuit through irregular, intermittent evolutions of the collective
particle motion which would bring the system in another metastable
state. An example of this intermittent dynamics is shown in 
Figure~\ref{fig3} for a multicomponent ribbon of
Au$_{49}$Cu$_{26.9}$Si$_{16.3}$Ag$_{5.5}$Pd$_{2.3}$ measured during an
isothermal annealing of 5~h at 377~K, well below the glass transition
temperature  $T_g=396$~K of this composition.  The figure reports the
temporal evolution of the two-times correlation functions (TTCF),
another important quantity which can be extracted from an XPCS
experiment. The TTCF is a time resolved version of the standard
intensity--intensity correlation functions and provides information on
the temporal evolution of the correlation between configurations
measured at different times $t_1$ and $t_2$. Each pixel on the TTCF
expresses the correlation between the intensity of two frames acquired
at times $t_1$ and  $t_2$ in a colour coded fashion. The main diagonal
from bottom left corner to the top high corner indicates increasing
elapsed times from the beginning of the measurement and corresponds to
the condition  $t_1=t_2$, hence showing maximum correlation in red.
Horizontal or vertical lines (in the lower and upper quadrants
respectively) from a single point along the main diagonal corresponds
to correlation measured at increasingly longer delay time  $\Delta
t=t_2-t_1$ from this fixed reference frame. The loss of correlation
(blue values) occurs when the system has relaxed in a new
configuration. The width of the yellow profile along the main diagonal
is therefore proportional to the structural relaxation time, the larger
this width is, the slower is the dynamics.

\begin{figure}
\includegraphics{fig03}
\vspace*{3pt}
\caption{\label{fig3}(a)~TTCF measured with XPCS in an Au-based alloy
during isothermal annealing at 377~K for 5~h below  $T_g$. Data show a
crossover between two stationary regimes, termed $a$ and $b$, connected
by a short period of aging occurring after about 7000~s from
temperature equilibration. (b)~Continuation of the TTCF at longer
annealing times showing that the dynamics keep stationary in the regime
$b$ for longer times. (c)~Intensity correlation functions calculated by
temporal averaging the data collected in the two stationary regimes
reported in panel (a). Taken   from~\cite{15}.}
\vspace*{1pt}
\end{figure}

In the specific case of  Figure~\ref{fig3}a, the TTCF shows two
stationary regimes, termed $a$ and $b$, with constant intensity
profiles along the main diagonal but different relaxation times, being
the dynamics in the regime ``$b$'' slower than in  ``$a$''. A short
temporal period of aging leads to a ``smooth'' transition between these
two distinct metastable configurations after about 7000~s from the
beginning of the isotherm. Standard intensity--intensity correlation
functions can be obtained by temporal averaging the frames
corresponding to each stationary regime ($a$ and $b$) and can be used
to quantify the increase in the relaxation time induced by the aging,
as shown in  Figure~\ref{fig3}c.

Similar intermittent aging dynamic has been reported in few other
compositions and often dominates the dynamics when the glass is
subjected to mechanical  deformations~\cite{30}. Although there is a
common idea of an avalanche like particle motions triggering the aging,
a clear explanation for the observed behaviour is still missing.
Multiple aging regimes have been observed in few macroscopic studies in
metallic, polymeric and chalcogenide glass  formers~\cite{14,15,16}. In
these works, the authors report on the existence of multiple decays
during enthalpy relaxation interconnected by stationary regimes
suggesting a strong connection with the atomic scale dynamics. 

\section{Controlling the aging through external parameters}
Last decades have witnessed an impressive amount of excellent
scientific works aimed toward the control of the relaxation behavior
and physical aging in MGs by using physical vapor deposition 
techniques~\cite{31}, or by altering the relaxation state by applying
external parameters, such as  stress~\cite{32} or extreme thermal
cycling~\cite{33}.

Since the excellent works of Ediger and his group on organic glassy 
compounds~\cite{31}, the possibility to dramatically improve the
stability of a glass by creating the amorphous solid state by means of
physical vapour deposition techniques has fascinated the glass
community. The basic idea is that during the deposition the particle
mobility at the free surface is orders of magnitude larger than in the
bulk and allows for a more efficient particle packing, lowering the
energy of the system and bringing therefore the glass in a deeper
minimum of the potential energy landscape. Ultrastable glasses formed
by physical vapour deposition are considered as an analogue of glassy
materials aged for geological times. Among their different physical
chemical properties, their improved thermal stability, signalled by a
higher calorimetric glass transition temperature on heating, makes them
excellent promising candidates for many technological applications. The
first vapour deposited MG was produced by the group of  K. Samwer and
exhibited an increased stability of about 10~K with respect to the
standard fast-cooled  glass~\cite{34}. This work paved the way to a
large number of studies, although the possibility to obtain metallic
ultrastable glasses has been largely  debated~\cite{35,36,37}.
Structural studies of vapour deposited MG have shown that by lowering
the deposition rate is possible to improve the stability up to 60~K
with respect to standard cooled glasses  (Figure~\ref{fig4}a).
Curiously, this improved stability comes with a less ordered structure 
(Figure~\ref{fig4}b) with respect to an ordinary rapidly cooled 
MG~\cite{38}. 

\begin{figure}
\includegraphics{fig04}
\caption{\label{fig4}(a)~Differential scanning calorimetric profiles of
an ordinary (i.e. fast quenched) MG and MGs produced by physical vapour
deposition highlighting the increasingly stability and thus larger
$T_g$ on lowering the deposition rate. An increase of  $T_g$ up to 60~K
can be obtained with the slowest deposition rate.  (b)~Reciprocal space
(inset) and real space static profile of an ordinary and a vapour
deposited MG showing larger stability in the calorimetric profile. The
improved stability comes with a less ordered structure than in a
standard MG. Taken from  Ref.~\cite{38}.}
\end{figure}

The influence of the ultrastability on the collective particle motion
and aging has been investigated in an MG of  Cu$_{50}$Zr$_{50}$
produced by physical vapour deposition following the procedure reported
in  Ref.~\cite{34,35}. Signatures of an improved stability have been
reported at the atomic scale in vapour-deposited MG.
This is shown in 
Figure~\ref{fig5}a which reports correlation functions \mbox{measured} with
XPCS in different vapour-deposited MGs: as-prepared, and pre-annealed
at different annealing temperatures $T_a$, above and below the
calorimetric $T_g$ and then cooled back to ambient temperature prior to
the measurements. Data collected during an isotherm in the glassy 
state show that the relaxation dynamics is slower in the as-cast vapour
deposited MG with respect to that measured on the same material,
pre-annealed at higher temperatures  (Figure~\ref{fig5}). This means
that the highest stability, and thus the slower relaxation time, is
obtained with the vapour deposition protocol, while it decreases with
further thermal annealing. This process, called in the work
\textit{anti-aging}, is opposite to the standard slowing down of the
relaxation dynamics due to physical aging induced by thermal
treatments. Indeed, in conventional MG, the dynamics slows down
significantly by pre-annealing the desired glass just below its
$T_g$~\cite{7}.  This process does not apply to vapour deposited MG as
their structure already corresponds to the most stable state and thus
to a deeper minimum configuration in the potential energy landscape. 

\begin{figure}
\vspace*{2pt}
\includegraphics{fig05}
\vspace*{4pt}
\caption{\label{fig5}(a)~Intensity scattering functions measured with
XPCS in a Cu$_{50}$Zr$_{50}$ ultrastable glass as-cast and pre-annealed
at different temperatures $T_a$ (1~min annealing, heating rate:
7~K/min). Data have been acquired after heating the samples in the
glassy state at 476~K. The increased stability of the vapour deposited
glass is signalled by the longer decay times (violet data) with respect
to the same glass annealed at higher temperatures prior to the
measurements. (b)~Relaxation times corresponding to the data in the
left panel (violet diamonds) together with relaxation times measured in
a standard fast-quenched MG which was pre-annealing at different
temperatures  $T_a$ prior to the experiment (1~min annealing, heating
rate: 7~K/min) and then measured with XPCS at 476~K. While the
pre-annealing at high temperature slows down the dynamics of the
standard MG due to aging, the ultrastable glass loses its improved
stability with thermal heating. Taken  from~\cite{35}.}
\vspace*{4pt}
\end{figure}

Similar anti-aging has been observed in metallic glasses recovered from
anelastic and plastic deformation. The applied shear promotes the glass
to a higher energy state evidenced through exothermic events upon
further  annealing~\cite{39}, with reported values including a
sevenfold increase of the relaxation enthalpy in a
Zr$_{50}$Cu$_{40}$Al$_{10}$ MG between the annealed and deformed 
states~\cite{40}. Deformation also moves the glass structure toward an
apparent lower density and higher disorder  state~\cite{41,42}, in an
opposite way with respect to the aging described above. 

Shear stress can also alter the microscopic dynamics as it triggers
plasticity localized in narrow shear bands, which accommodate the
stress and eventually lead to catastrophic failure. Structurally, these
bands are characterized by high disorder, density 
changes~\cite{43,44}, nano-cavities~\cite{45}, and potential 
nano-crystals~\cite{46,47}. Typical dimensions of X-ray beams are much
larger than the thickness of the shear bands,  5--10~$\rmmu$m against
10--200~nm  respectively~\cite{45,48}, which prevents the monitoring of
the dynamics within the shear bands with XPCS. However, results from
site-specific XPCS in the vicinity of a single shear band in a
Zr$_{65}$C$_{25}u$Al$_{10}$ MG revealed an acceleration of the atomic
scale dynamics  10~$\rmmu$m away from the shear band 
(Figure~\ref{fig6}a), a length scale greater than the shear band
classical thickness by three orders of  magnitude~\cite{49}.

\begin{figure}
\vspace*{2pt}
\includegraphics{fig06}
\vspace*{4pt}
\caption{\label{fig6}Temperature dependence of characteristic time
$\tau$ obtained from site-specific isothermal XPCS measurements at
10~$\rmmu$m from an individual shear band and in the bulk in a
Zr$_{65}$Cu$_{25}$Al$_{10}$ MG (as-cast from suction casting, stepwise
heating from the ambient temperature). The significant decrease of
$\tau$ in the shear band vicinity demonstrate an effect in an area much
larger than the shear band itself. Figure taken  from~\cite{49}.}
\vspace*{4pt}
\end{figure}

Interestingly, the acceleration of the dynamics remains constant during
heating from room temperature to $0.95\times T_g$ 
(Figure~\ref{fig6}). This indicates that the structural and dynamical
changes due to the shear band do not relax back to the as-cast (or
annealed) state during the experimental time even close to $T_g$, and
that the faster dynamics could persist over a very long time at ambient
temperature, enabling true control of the glassy dynamics.

The fast dynamics near a single shear band described above occur also
in the case of a severely deformed bulk MG. Results from XPCS performed
on Pd$_{40}$Ni$_{40}$P$_{20}$ glasses annealed and later deformed
through high pressure torsion  show a trend nearly identical to the
single shear band case before structural relaxation close to
$T_{g}$~\cite{50}.

Different deformation protocols not triggering the formation of shear
bands can also induce rejuvenation or affect the dynamics. Hydrostatic
compression was shown to allow large volumetric changes without the
development of shear bands, and leads to a significant rejuvenation
visible from calorimetry  measurement~\cite{51}. How this translates to
the atomic scale dynamics compared to sheared samples remains an open
question. On the other hand, while the deformation of a metallic glass
below the yield stress of the material do not produce permanent
modifications by definition, XPCS performed in-situ during the elastic
bending of Zr$_{44}$Ti$_{11}$Cu$_{10}$Ni$_{10}$Be$_{25}$ glassy ribbons
shows a deformation influence on the dynamics that depends on the
thermal history of the  sample~\cite{30}. On the as-cast samples
quenched from the melt by rapid cooling, the deformation increases the
intermittent nature of the aging. On the other hand, when the sample
has been brought to a lower energy state by pre-annealing just below
$T_{g}$, the deformation leads to faster but steady dynamics.

\break
All these works show how the relaxation dynamics of MGs can be tuned by
different experimental protocols, which can involve either the glass
formation or their treatment. While physical vapor deposition can
effectively bring the glass in lower energy microscopic configuration
associated to larger barriers and longer times for structural
rearrangements, applied stresses and\unskip\break 
deformations rejuvenate the
system, bringing the glass in a microscopic state characterized by fast
structural relaxation times but at the same time more homogeneous
dynamics with respect to physical aging. Further studies will be
necessary to better clarify the controlling physical mechanisms
controlling the collective particle motion.

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

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