# Infrared-induced ultrafast melting of nanostructured platinum films probed
by an X-ray free-electron laser

Luca Gelisio<EMAIL_ADDRESS>Deutsche Elektronen-Synchrotron DESY,
Notkestr. 85, 22607 Hamburg, Germany  Present address: European X-ray Free-
Electron Laser, Holzkoppel 4, 22869 Schenefeld, Germany  Young Yong Kim
Deutsche Elektronen-Synchrotron DESY, Notkestr. 85, 22607 Hamburg, Germany
Present address: Pohang Accelerator Laboratory, Pohang 37673, Republic of
Korea  Seon Woo Lim  Department of Physics, Ulsan National Institute of
Science and Technology, 50 UNIST-gil, Ulju-gun, Ulsan 44919, Republic of Korea
Daewoong Nam  Pohang Accelerator Laboratory, Pohang 37673, Republic of Korea
Photon Science Center, Pohang University of Science and Technology, Pohang
37673, Republic of Korea  Intae Eom  Pohang Accelerator Laboratory, Pohang
37673, Republic of Korea  Photon Science Center, Pohang University of Science
and Technology, Pohang 37673, Republic of Korea  Minseok Kim  Pohang
Accelerator Laboratory, Pohang 37673, Republic of Korea  Sangsoo Kim  Pohang
Accelerator Laboratory, Pohang 37673, Republic of Korea  Ruslan Khubbutdinov
Deutsche Elektronen-Synchrotron DESY, Notkestr. 85, 22607 Hamburg, Germany  Li
Xiang  Department of Chemistry, Pohang University of Science and Technology,
Pohang 37673, Republic of Korea  Hoyeol Lee  Department of Chemistry, Pohang
University of Science and Technology, Pohang 37673, Republic of Korea  Moonhor
Ree  Pohang Accelerator Laboratory, Pohang 37673, Republic of Korea
Department of Chemistry, Pohang University of Science and Technology, Pohang
37673, Republic of Korea  Surface Technology Institute, Ceko Corporation, 519
Dunchon-daero, Jungwon-gu, Seongnam 13216, Republic of Korea  Chae Un Kim
Department of Physics, Ulsan National Institute of Science and Technology, 50
UNIST-gil, Ulju-gun, Ulsan 44919, Republic of Korea  Ivan A. Vartanyants
<EMAIL_ADDRESS>Deutsche Elektronen-Synchrotron DESY, Notkestr. 85,
22607 Hamburg, Germany

###### Abstract

Understanding melting in metals is a hot topic of present research. This may
be accomplished by pumping the system with infrared (IR) laser radiation, and
probing it with hard X-rays produced by an X-ray Free-Electron Laser (XFEL).
In this work we studied nanostructured polycrystalline thin films of platinum
that were illuminated by IR radiation of increasing fluences. We characterized
the structural response as well as the nucleation and propagation of the
liquid phase as a function of time delay between the IR pump and X-ray probe.
We observed partial melting of the samples for IR fluences higher than 200
mJ$\cdot$cm-2. To fit the contribution of the liquid phase to the scattering
pattern in platinum we applied a model of liquid metal. The two-temperature
model simulations were performed to understand the solid-state fraction of the
sample heating process as a function of time delay and fluence.

††preprint: Preprint

## Introduction

When infrared (IR) light from a femtosecond laser interacts with free
electrons in metals, it rapidly raises their kinetic energy, which is then
partially transferred to the atomic lattice via electron-phonon coupling [1].
This excess of energy perturbs the atomic arrangement, whose temporal
evolution can be probed, for example, by hard X-ray pulses generated by
ultrashort X-ray Free-Electron Lasers (XFELs) [2, 3, 4, 5, 6]. Due to the
exceptional properties in terms of brightness, temporal pulse duration and
transverse coherence [7, 8, 9], hard XFELs are in fact unique tools to
characterize structure and dynamics of condensed matter [10, 11, 12, 13].

One important metal for pump-probe experiments, performed, for example, at
XFELs, is platinum. Platinum is a noble metal with numerous scientific and
technological applications. It is used, for example, for medical devices [14],
in nanomedicine [15] and has a central role in cancer chemotherapy [16, 17].
It is essential for the catalysis of the hydrogen oxidation and oxygen
reduction reactions, at the core of fuel cells and electrolysers [18, 19, 20].
Due to its excellent performance and thermal stability, platinum is also
extensively employed within automotive catalytic converters [21, 22], and to
catalyse several other industrially-relevant reactions, for example, in the
oil industry [23]. The elevated chemical inertness, oxidation resistance,
melting temperature and phase stability of platinum [24] make it perfect to
produce melting equipment. For example, it is used to manufacture glass
fibres, for temperature sensors or for space industry applications [25].
Because of its properties, platinum is also used as reference for several
applications, ranging from electrodes and thermometers to pressure calibrants
[26].

Pump-probe investigations have been performed earlier on aluminum [27, 28] and
gold (for example, evidence for bond hardening [29], identification of
heterogeneous to homogeneous melting transition [30] and elucidation of the
role of grain boundaries on melting [31]). Gold is the most widely studied
element and possesses an atomic electronic configuration similar to the one of
platinum, which differs from the former by only one electron. However,
theoretical calculations predict for platinum a completely different behavior
in terms of electron-phonon coupling, and in turn of electron-lattice energy
exchange [32].

With our experiment and its interpretation, we aim at increasing the
understanding of platinum properties, and in particular of the crystalline-
liquid phase transition in nanostructured thin films. Furthermore, given
platinum phase stability and resistance to oxidation, we aspire at using this
experiment as a model for the melting process, whose detailed understanding is
of great scientific importance. Apart from increasing the comprehension of
platinum and addressing thus a fundamental problem in material science, that
is the nucleation and propagation of a liquid phase in films characterized by
nanostructured domains, the presented results are potentially of technological
relevance, given the increasing demand of ultrafast laser manufacturing [33,
34, 35, 36, 37, 38].

## Results

Platinum films of 100 nm thickness were grown on silicon nitride membranes by
electron beam evaporation. The resulting lateral dimension of the grains was
of the order of 10 nm and they were preferentially columnar with respect to
the film surface .

Figure 1:  (a) Schematic of the experimental setup. The IR laser impinges on
the sample 15 degrees apart from the X-ray beam (that is perpendicular to the
sample) on the horizontal plane. An on-line spectrometer, consisting of a
curved Si crystal in (333) scattering geometry, provides a spectrum of each
XFEL The silicon frame is moved in the xy-plane before each shot to illuminate
a different window. The X-ray scattering signal is measured on a pixelized
detector positioned 108 mm downstream from the interaction region. (b) Typical
X-ray single-pulse scattering pattern of a platinum reference sample (that is
the one without IR pump laser). The scale bar corresponds to 500 pixels in
detector units. (c) Azimuthal average of the pattern in (b) as a function of
momentum transfer where Bragg peaks from the platinum fcc {111}, {200}, {220}
and {311} family of planes can be observed. Vertical dashed lines indicate the
region that is used for further analysis of the pump-probe experimental data.

The experiment was performed at the Nano-crystallography and Coherent Imaging
instrument (NCI) of the Pohang Accelerator Laboratory X-ray Free-Electron
Laser (PAL-XFEL) [39, 4]. A schematic of the experiment setup is shown in Fig.
1a. The details of both the experiment and data analysis are provided in the
Methods section.

Figure 2:  Scattering curves at different time delays of the X-ray probe with respect to the IR pump for each IR fluence reported in Table 1. The data sets are normalized by the average maximum intensity of the reference sample, collected in absence of IR radiation.  Table 1: Flux densities ($\Phi$) and corresponding pulse energies ($\mathcal{E}$, measured using a laser power meter) used to transfer energy to the sample. The estimated energy densities absorbed by the sample $\varepsilon$ are also reported.  $\Phi$, mJ$\cdot$cm-2 |  $\mathcal{E}$, µJ |  $\varepsilon$, kJ/kg
---|---|---
100 | 28.4 | 139
200 | 57.0 | 279
300 | 85.0 | 416
400 | 113.0 | 553
500 | 141.0 | 691
1,000 | 283.0 | 1,386

The scattering curves collected during this experiment, with the subtracted
background, are shown in Fig. 2 for the different IR fluences used in this
experiment. By visual inspection, at the lowest IR fluence of 100
mJ$\cdot$cm-2 no significant differences in the scattering data are observed
at different time delays. However, starting with the IR fluence of 200
mJ$\cdot$cm-2 we observe a gradual decay of Bragg peak intensities with the
increase of time delay. While at this IR fluence both the (111) and (200)
Bragg peaks corresponding to face-centered-cubic (fcc) Pt structure are
visible for all time delays, already at 300 mJ$\cdot$cm-2 the higher order
peak (200) starts to disappear at about 100 ps. In general, the decrease of
intensities is faster the higher the IR fluence. For example, at the fluence
of 1,000 mJ$\cdot$cm-2 Bragg peaks are practically vanishing after a few
picoseconds from the IR pulse. At the same time, we would like to note here
that some intensity corresponding to the (111) Bragg peak is observed for
every fluence and time delay, indicating that some residual solid fraction is
always present in the region of the sample probed by X-rays. In fact, we
interpret the smooth continuous scattering curve which appears as the
intensity of Bragg peaks decreases, as the fingerprint of the liquid platinum
phase. By that, we conclude that platinum films are partially melted for
fluences higher than 200 mJ$\cdot$cm-2. Below, we will present a detailed
analysis of the results obtained.

Figure 3:  Parameters deduced from the fitting of the (111) Bragg peak. (a)
Integrated intensity normalized to the reference value, (b) lattice
deformation (see text for details), and (c) Full-Width at Half-Maximum (FWHM)
of the (111) Bragg peak. In all panels dashed lines are showing the values of
parameters for the reference value in absence of IR radiation. Data are
plotted as a function of the time delay between the IR pump and X-ray probe.

The parameters extracted from the fit of scattering curves are reported in
Fig. 3 as a function of pump-probe time delays. Each point shown in this
figure is the median of the corresponding dataset . Even if both the (111) and
(200) Bragg peaks are present in the investigated momentum-transfer range, we
restrict our analysis below to the former, since the behaviour of the two is
highly correlated within the resolution of our measurements .

We begin our discussion from the integrated intensity of the (111) Bragg peak
(Fig. 3a), which is proportional to the amount of crystalline fcc platinum in
the probed region of the sample. As we can see from this figure, for each
value of the incident IR fluence this quantity is reduced with respect to the
reference value (that is measured only with XFEL radiation without
illuminating the sample with IR). As discussed above, the decrease within the
investigated temporal range is negligible when the IR fluence is equal to 100
mJ$\cdot$cm-2 and modest when it is 200 mJ$\cdot$cm-2 (these will be named as
”low fluences”). On the contrary, for higher values (”high fluences”), in our
experiment, actually starting from 300 mJ$\cdot$cm-2, the integrated intensity
drops to about 1% of the reference value, and the decay is faster with higher
fluence. This occurs from about one hundred picoseconds at 300 mJ$\cdot$cm-2
to a few picoseconds for the 1,000 mJ$\cdot$cm-2 case.

The position of a Bragg peak $q_{hkl}$ is related to the lattice parameter $a$
of a cubic lattice through the known relation
$a=2\pi\sqrt{h^{2}+k^{2}+l^{2}}/q_{hkl}$. Variations of the strain value as a
function of the time delay, defined as
$\varepsilon(\tau)=\left[a(\tau)-a_{0}\right]/a_{0}$, are shown in Fig. 3b.
For low fluences, it can be observed that the lattice is expanded for each
time delay longer than approximately 10 ps. This is compatible with an
increase of the sample temperature. Assuming the expansion to be purely
thermal, a maximum temperature increase at one nanosecond, at the end of our
observation, was estimated to be about 1,300 K and 1,800 K for IR fluences of
100 mJ$\cdot$cm-2 and 200 mJ$\cdot$cm-2, respectively. The thermal expansion
coefficient was obtained from Ref.[40]. The general trend for each IR fluence
greater than 100 mJ$\cdot$cm-2 is that the lattice is progressively becoming
more compressed in the first 10 - 20 ps, up to approximately
$\varepsilon=$-0.5% at the IR fluence of 500 mJ$\cdot$cm-2. For a purely
elastic deformation, with the Young’s modulus equal to[41] 168 GPa this value
corresponds to the stress value of about 0.8 GPa. Compression is increasing
with IR fluence, except for the 1,000 mJ$\cdot$cm-2 case, likely due to the
extremely small residual solid state fraction (see Fig. 3a). After this
initial phase, for each IR fluence the lattice starts to rapidly expand up to
time delays of approximately 30 ps. This is about the time necessary for a
sound wave to transverse the thickness of the platinum sample, which is 100 nm
in our case. Indeed, if a deformation wave is traveling through the platinum
film at the (longitudinal) speed of sound [42] of 3,260 m/s, this time is 31
ps. After this point, for low fluences the strain values decrease slightly up
to time delays of about 50 ps, and then they increase again. For high
fluences, in general, the expansion diminishes, following the same trend
already observed for the residual fcc solid state fraction.

The FWHM of the 111 reflection is shown in Fig. 3c. It is inversely
proportional to the size of the coherently scattering domains and proportional
to the microstrain and thermal vibrations in the sample [43]. For each value
of the IR fluence, the peak width is initially slightly increased with respect
to the reference value. However, at about 30 ps we observe a steep increase of
the peak width followed by a fast decay. The curve has a maximum at $31.6$ ps
for fluences lower than 500 mJ$\cdot$cm-2.This is likely due to extremely
small residual fcc fraction at this time delay (see Fig. 3a), which might also
explain why the peak width for the IR fluence of 1,000 mJ$\cdot$cm-2 does not
follow a similar trend. It is interesting to note, that for low fluences, the
FWHM at $1$ ns is practically returning to its initial value. In particular,
for the 200 mJ$\cdot$cm-2 case the final FWHM value in the sub-nanosecond time
delay region is even lower than the reference one, possibly indicating an
increase of the crystallite size due to sintering of smaller grains or
relaxation of residual stresses. At the same time, for high fluences, the
values of FWHM after the peak at 31.6 ps continue to increase.

The Kirchhoff’s law predicts, for a constant pressure process, the change of
the temperature $T$ of the system as a function of enthalpy $\mathcal{H}$ to
be $\mathrm{d}T=\mathrm{d}\mathcal{H}/c_{p}(T)$. We assume also here that all
the energy absorbed by the system is increasing its temperature (see Table 1).
The above equation gives us an estimate of the sample temperature, it should
reach a maximum temperature of ${\sim}1,300$ K, and therefore remain solid,
when irradiated with an IR fluence of 100 mJ$\cdot$cm-2 (we remind that the
melting temperature for platinum at atmospheric pressure is $T_{M}$=2,041.3 K
[11]). It should be noted that this is the same temperature estimated from the
position of the (111) Bragg peak assuming ambient pressure. For the IR fluence
of 200 mJ$\cdot$cm-2 the melting should be partial, with coexistence of the
solid and liquid phases, whereas 300 mJ$\cdot$cm-2 is sufficient to transform
the solid into liquid. This picture is apparently consistent with Fig. 3a for
long time delays although an extremely small residual fcc solid state fraction
is always present according to our experimental findings. We speculate that
this might be due to chemical stabilization of platinum at its interface with
Si3N4 film, inhibiting crystal to liquid phase transition.

The scattering curve attributed to liquid, which is clearly distinguishable
from the Bragg peaks, was fitted using the model developed by Ashcroft [44,
45] (see Methods section). It should be noted that, especially for low
fluences and short pump-probe delays, this model is likely to fit the diffuse
scattering due to various defects including thermal vibrations, and might
therefore not provide correct information on the liquid phase. The area under
the broad Ashcroft’s curve, which is proportional to the amount of liquid
phase, was estimated by integrating the corresponding analytical model from
the origin of momentum-transfer space to infinity. To compensate for
fluctuations of the incoming X-ray intensities, we divided the integral by the
total intensity in the background for each diffraction pattern.

Figure 4:  Quantities extracted from the liquid phase model (see text for
details). (a) Integrated liquid phase intensity normalized to the background
intensity, (b) liquid density, and (c) temperature. In (b) the dashed and
solid lines indicate the nominal values for the liquid and solid density,
respectively and in (c) dashed and dotted lines indicate the melting and
boiling temperatures, respectively. Data are plotted as a function of the time
delay between the IR pump and X-ray probe. We excluded the lowest fluence of
100 mJ$\cdot$cm-2 at which no liquid phase was detected.

The result is shown in Fig. 4a. The general trend is that the integral of this
liquid curve increases as a function of the time delay, indicating an increase
of the liquid fraction. It also increases as a function of the IR fluence,
although there is no significant difference between 400 mJ$\cdot$cm-2 and 500
mJ$\cdot$cm-2. Moreover, at time delays of hundreds of picoseconds the values
of integrated intensities for the IR fluence of 1,000 mJ$\cdot$cm-2 are
similar to the ones for 200 mJ$\cdot$cm-2. To explain this behaviour, we
evaluated the conditions for ablation using the approach described in Ref.[46]
. According to this, the estimated crater depth is about 1 nm and 10 nm for
the IR fluences of 500 mJ$\cdot$cm-2 and 1,000 mJ$\cdot$cm-2, respectively .

In the model developed by Ashcroft [44, 45], the profile of the scattering
curve of a liquid of hard spheres is defined by their diameter $d$ and packing
density $\eta$. The two parameters are in turn related to the liquid density
of platinum $\rho_{Pt}$ by the relation $\rho_{Pt}=6\pi\eta A_{Pt}/d^{3}$,
where $A_{Pt}=195.08$ g/mol is the atomic weight of platinum. The density of
the liquid phase, shown in Fig. 4b, does not show an obvious trend for time
delays shorter than about 10 ps. As we can see from the same figure, in the
same region of time delays, the liquid density is lower the higher the IR
fluence. This observation is compatible with an increase of the liquid
temperature. However, if we exclude the data for 200 mJ$\cdot$cm-2 and 300
mJ$\cdot$cm-2, associated with a small liquid fraction (see Fig. 4a), then the
higher the fluence the less dense is the liquid. We speculate that this might
be due to the residual solid fraction (see Fig. 3a) mechanically constraining
the liquid phase. On the contrary, for all IR fluences and time delays larger
than approximately 10 ps, the liquid density is lower than the reference value
at the melting point[47] of 19.77 $g/cm^{3}$. In the same region of time
delays, it is also lower the higher is the IR fluence, compatibly with an
increase of the liquid temperature.

The temperature of the liquid phase can be estimated from Ref.[48] as
$T=(V/V_{0}-0.89125)/8.3955\times 10^{-5}$, where the volume $V$ is calculated
from the density as obtained from the Ashcroft model, and $V_{0}=4.673\times
10^{-5}$ $m^{3}\cdot kg^{-1}$. It should be noted that this equation is valid
in the interval of temperatures from 2,042 K to 5,650 K, and it assumes a
constant pressure process. Values of temperature of the liquid phase, shown in
Fig. 4c, outside this range are in general the ones corresponding to time
delays shorter than 10 ps, or to the highest IR fluence of 1,000
mJ$\cdot$cm-2. The values within the range of validity of the equation, in
Fig. 4c, confirm that the temperature of the liquid phase increases with the
IR fluence. In particular, it is approximately the melting temperature for the
IR fluence of 200 mJ$\cdot$cm-2, the temperature at which solid and liquid
coexist, and it reaches almost 4,000 K for the 500 mJ$\cdot$cm-2 case.
Interestingly, the temporal region between approximately 10 and 30 ps
corresponds to both a transition between two different states of density and
temperature, and of strain in the lattice (see, for example, Fig. 3b),
suggesting that the solid and liquid phase might experience the same
mechanical pressure.

To support the interpretation of experimental results, we performed two-
temperature model (TTM) simulations[49] . The TTM is a phenomenological
description of the spatio-temporal evolution of the temperature in a metal
following its ultrafast excitation. In this picture, the laser pulse is
absorbed by free electrons in a thin layer of about 10 nm and rapidly
increases their energy. This is then partially transferred to the lattice via
electron-phonon coupling. The TTM assumes a continuous media and does not
include any defects, like the grain boundaries, present in the investigated
samples. These grain boundaries can act as nucleation seeds for the liquid
phase, lowering the amount of energy required for the phase transition
(heterogeneous melting)[31].

Figure 5:  Solid state fraction. Dots are the median values for a given time
delay and pink crosses are the values calculated from the experimental data.
The solid black line is calculated from the TTM simulations.

In Fig. 5 we compare the fraction of fcc solid state estimated from the
experimental data and the one obtained from the TTM model. The values of
experimental data are calculated assuming that the integral of the (111) Bragg
peak is proportional to the amount of solid phase, and that there is no liquid
platinum at the time delay of 1 ps. The value of the peak integral at this
time delay is, therefore, used to normalize all the other values. For the case
of the TTM simulations, the fraction of solid is simply the thickness of the
solid phase at a given time from the IR pulse divided by the total thickness
of the simulation domain (100 nm). It is important to note here that we did
not introduce any fitting parameters in the TTM simulations. All parameters,
including the electron-phonon coupling parameter $G_{ep}$, were taken from the
known references . As can be observed from Fig. 5, the model qualitatively
captures the trends observed experimentally. For the IR fluence of 100
mJ$\cdot$cm-2 it does not predict any formation of the liquid phase, which is
compatible to our experimental findings. From the fluence of 200 mJ$\cdot$cm-2
the liquid phase is formed starting from about a few picoseconds. The time
delay for the formation of the liquid phase is becoming shorter with
increasing the IR fluence. For example, for the 1,000 mJ$\cdot$cm-2 case the
solid fraction is transformed to liquid already at time delays of about 2 ps.
For all fluences, experimental results seem to indicate a faster nucleation of
the liquid phase with respect to simulations. This could either be because our
TTM model does not include any structural defects, which are present in the
samples (homogeneous versus heterogeneous melting), or because some of the
simulation parameters are not accurate. In particular, a relevant role in
defining the temporal evolution of the atomic lattice is played by the
electron-phonon coupling. Interestingly, our simulations show, that
increasing/reducing the electron-phonon coupling parameter by twice is
reducing/increasing the start of the melt process by 10 ps. For IR fluences
from 300 mJ$\cdot$cm-2 to 500 mJ$\cdot$cm-2 we observe a second drop of the
experimental solid fraction at about 20 - 30 ps, that is not explained by the
TTM. This drop might be related to propagation of the sound wave through the
100 nm Pt sample layer. At the same time, we observe excellent agreement
between the solid fraction calculated from experimental data and the TTM for
the highest IR fluence of 1,000 mJ$\cdot$cm-2 , although, we recall, the
sample is partially ablated.

In summary, we described the evolution of platinum nanostructured films
illuminated by ultrashort IR radiation at several fluences and time delays. We
observed a deformation wave traveling perpendicular to the film at the speed
of sound, and the temperature of the films increasing as a function of time
delay. The sample remained solid when the fluence was 100 mJ$\cdot$cm-2, and
it was partially liquid for higher fluences. We observed that lattice
deformations before the sound wave travelled through the entire sample were
mostly compressive and after that they were causing expansion. Analysis of our
results with the Ashcroft’s model suggested that the density of the liquid
phase was dropping after the sound wave propagated through the sample.

To support experimental findings, we performed TTM simulations. They predicted
the sample to be solid at the IR fluence of 100 mJ$\cdot$cm-2, and partially
liquid for higher fluences, with the solid fraction decreasing the more, the
higher the fluence. We also observed an additional drop of the solid fraction
that is not described by TTM simulations at fluences from 300 mJ$\cdot$cm-2 to
500 mJ$\cdot$cm-2 and time delays longer than 30 ps. This is most probably
related to propagation of the sound wave through the 100 nm platinum sample
layer. Our TTM simulations, based on a model of a uniform layer, are not
sufficient to capture the complexity of the solid-liquid phase transition in
polycrystalline films illuminated by femtosecond IR light. In particular, the
ablation process or the presence of defects such as grain boundaries are not
taken into account in TTM model.

Finally, we believe that a deep understanding of the results presented here
will need more extensive experimental and theoretical exploration in the
future. We think that research performed at XFEL facilities will be
instrumental in answering questions outlined in this work.

## Methods

### Experiment

The X-ray beam propagating perpendicular to the sample surface was focused
using a Kirkpatrick-Baez mirror system [50] on an area of approximately 5
$\mu$m in diameter on the sample . The average X-ray photon energy during the
experiment, measured by an on-line spectrometer, was 9.7 keV . The resolution
of the on-line spectrometer was estimated to be $0.26$ eV Full-Width at Half-
Maximum (FWHM) [51]. Scattering data were collected on a Rayonix MX225-HS
detector (2,880${\times}$2,880 pixels of size 78${\times}$78 µm2 with a
2${\times}$2 binning mode). The detector was positioned downstream from the
interaction region at a distance of $108$ mm and its center was shifted from
the X-ray path by $-37$ mm and $1$ mm along the $x-$ and $y-$axes,
respectively (the reference frame is shown in Fig. 1a). The sample-detector
distance was determined by fitting platinum Bragg peaks of the reference
sample and assuming the lattice constant to be 3.9236 Å [52]. A typical
scattering pattern measured by the detector is shown in Fig. 1b. Before each
shot, the sample was moved in the plane perpendicular to the X-ray beam (the
$xy$-plane in Fig. 1a) so to illuminate a different window .

A Ti:sapphire laser (800 nm central wavelength) [53], generating 100 fs (FWHM)
pulses and focused on an area of about 110 µm (FWHM) , was used to increase
the temperature of the samples. The direction of the IR pulses was 15∘ from
the sample normal on the horizontal plane (see Fig. 1a). The values of IR
laser fluences, reported in Table 1, were varied from 100 mJ$\cdot$cm-2 to
1,000 mJ$\cdot$cm-2. The time-delay between the IR pump and X-ray probe was
varied from 1 ps to 1,000 ps with logarithmic sampling. At least 10 patterns
were collected for each combination of fluence and time-delay, moving to a
different window after each pulse. Before each X-ray pulse, the sample
position along the X-ray beam ($z$-axis) was adjusted in order to optimize the
focal plane as seen by an inline microscope. Given the uncertainty on the
focal plane position and a drift of time zero across the experiment of about
0.5 ps, the error in time delay was estimated to be of the order of 1 ps.

### Data analysis

The first step of the analysis of scattering data was the removal of the
pedestal (dark signal) and bad pixels. Each frame was further corrected by
normalizing data by solid angle, X-ray polarization, linear absorption of
X-rays by the sample, and air scattering in the sample-detector path . Some
regions of the detector were masked because the scattered intensity was
shadowed by the sample holder (see, for example, Fig. 1b ). A few detector
frames (less than 7% of the total) were considered as outliers and discarded,
for example, when the X-ray beam was too close to an edge of the silicon
frame. The average and standard deviation of the radial profile of each image
were finally computed using the wavelength deduced from the in-line
spectrometer. The momentum transfer axis ($q$) was binned with a bin size of
0.005 Å-1. A typical radial profile for the reference sample, obtained by
applying the above-mentioned pipeline to the detector images in Fig. 1b, is
shown in Fig. 1c. High-$q$ data were typically noisy and therefore the
momentum range for further analysis was restricted to the interval from 2 Å-1
to 4 Å-1 (see Fig. 1c). In this region, face-centered cubic (fcc) platinum has
two Bragg reflections, the one associated to the $\\{111\\}$ ($q-$value of
2.774 Å-1) and $\\{200\\}$ ($q-$value of 3.203 Å-1) family of planes. To
account for the contribution of scattering of X-rays by air in the optical
path and the silicon nitride substrate, a membrane (no sample) was measured
and fitted with a 4-th order Chebyshev polynomial of the first kind. The
result of the fit, $\mathcal{B}_{0}$, was then used to construct a general
background function
$\mathcal{B}(q)=\alpha\mathcal{B}_{0}\mathrm{exp}\left(\kappa q\right)$.

To fit the scattering curves we defined the following model as the sum of
three contributions: (i) the background $\mathcal{B}(q)$ (2 free parameters:
$\alpha$ and $\kappa$), (ii) a pseudo-Voigt function for each Bragg peak (4
free parameters: the central position $q_{(hkl)}$, FWHM, area of the curve,
and the Lorentzian fraction) and (iii) the melting model proposed by Ashcroft
[44, 45] for the liquid signal (3 free parameters). Ashcroft derived the
liquid structure factor of a system of hard-spheres as a function of their
diameter and packing density [44]. We additionally multiplied the structure
factor by a scaling parameter and the squared modulus of the platinum atomic
form factor (coefficients were obtained from Ref. [54]).

Competing Interests

The authors declare that they have no competing interests.

Funding

LG, YYK, RK, and IAV acknowledge the support by the Helmholtz Associations
Initiative and Networking Fund. DN was supported by the NRF of Korea (Grant
No. 2021R1F1A1051444 and 2022M3H4A1A04074153). SWL and CUK acknowledge the
support by the National Research Foundation of Korea (NRF) grant funded by the
Korea government (NRF-2022R1A2C2091815).

###### Acknowledgements.

The use of the Maxwell computational resources operated at Deutsches
Elektronen-Synchrotron (DESY) is acknowledged. The authors would like to thank
S. Lazarev for the stimulating discussions while planning the experiment. The
authors acknowledge fruitful discussions with M. Altarelli and I.K. Robinson.
The authors acknowledge careful reading of the manuscript by H.-P. Liermann
and G. Hinsley.

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