Formation of high-aspect-ratio nanocavity in LiF crystal using a femtosecond X-ray free-electron laser pulse

Domain: physics
Published: 2025-12-17
Editorial outcome: major_revision

Abstract
Recentresearchanddevelopmentintotheformationofnanoscalechannelsas
acentralcomponentofnanofluidicbiochipsystemsrevolutionizedthebio-
logicalandchemicalfields.Explorationofnewpathwaystoformnanochannels
isincreasinglynecessarytoprovideanewgenerationofanalyticaltoolswith
accuratecontrolofliquidfluidflow,highselectivityandincreasedmassflow
rate.Here,wedemonstratethatasingle9-keVpulsefromX-rayfree-electron-
lasercanformananoscalemm-longcavityinLiF.Thelaser-generatedshock
pressureresultsinchannelformationwith>1,000length-to-diameteraspect
ratio.Thedevelopmentofvoidisanalyzedviacontinuumandatomistic
simulationsrevealingasequenceofprocessesleadingtothefinallongcavity
structure.Thisworkpresentsthestudyofmm-longnanochannelformationby
asinglehigh-brillianceX-rayfree-electronlaserpulse.WithMHzrepetitionrate
X-rayfreeelectronlaseropensanewavenueforthedevelopmentoflab-on-
chipapplicationsinanymaterial,includingthosenon-transparenttooptical
lasers.

Introduction
Thefast-expandingareaofresearchintothesearchfornewwaysto technologiesarethemajordrivingforcesforthesearchfornewcost-
form nanochannels with high, more than 1000 length-to-diameter effectivefabricationtechniquesforachievingsmallerchannelcross-
aspectratios,isdrivenbytherequesttoprovideanewgenerationof sections,higherprecision,anddevice-to-devicereproducibility2,5–7.
nanofluidic analytical tools for biological applications1–3. Analytical From a fundamental perspective, chemical reactions, synthetic
nanosystemscomposedofarraysofcloselypackednanochannelshold chemistry,andproteindynamicsinnanochannelsaredifferentfrom
promisestoprovideaccurateandhighlyselectivemoleculartransport, their largerchannelanalogs.It hasbeenwidelyreported thatsome
ultra-sensitiveanalysisatasingle-cellandsingle-molecularlevel4–6.The transport properties of confined liquids demonstrate significant
small, nanoscale-level sample volumes for diagnostics, applications deviationsfromthebulkvalues,includingdiffusioncoefficient,shear
suchasDNAmappingandseparation,theincreaseddemandforhigh viscosity,andthermalconductivity8,9.Theuniquefeaturesofunusual
throughput screening technologies, and advanced lab-on-chip liquid flow in nanochannels include nonlinear transport due to a
surfacechargeattheinterfaceofthesolutionandthenanochannel material35.LiFisoftenusedasafluorescentX-raydetector,whichis
wall,Coulombblockade,andultrafastwatertransport10,11.Newelec- ensured by the possibility of creating color centers (CCs) when
trochemicalphenomenaareemergingforinvestigatingfundamental exposedtoelectromagneticradiationwithaphotonenergyofmore
physicsandchemistryprinciplesinthenanoscale,newfluidphysics, than14eV36–38.ThelowatomicmassofLiFallowsdeeppenetrationof
andnewprinciplesthatgoverntransportinnanochannels10,12,13.
X-rayphotons into the sample (d =475μm for 9keV) and precise
Amongthevariousnanochannelfabricationtechnologies,ultra- imprintoftheX-raybeamwithsubmicronspatialresolutionobserved
fastlaserprocessingisapromisingtoolforthefabricationofnano- byfluorescenceopticalmicroscope.
fluidicsduetoitsflexibility,versatility,highfabricationresolution,and Theresultsofourexperimentalstudies,supportedbythesimula-
three-dimensional fabrication capability14–16. Ultrafast lasers are a tions,showthatnanochannelswithalargelength-to-diameterratiocan
categoryofpulsed laserswith ultrashort pulseduration from a few beformedbyasingleshotfromahigh-intensityX-rayFELwithsuffi-
picoseconds (1ps=10−12s) down to several tens of femtoseconds cientlyhighphotonenergy.Similarresultscanalsobeformedinmetals,
(1fs=10−15s).Duetoveryshortpulseduration,theyhavehighpeak semiconductors,ceramics,polymers,virtually—inanyopticallyopaque
intensities that can modify transparent materials by multiphoton ortransparentmaterialswhichisbeyondthereachofopticallasers.

Results
Experimentalmethod
The experiment was conducted at the high-energy-density (HED)
instrumentoftheEuropeanX-rayFreeElectronLaser(EuXFEL)39.An
X-raybeamwithaphotonenergyof9keV(λ=0.138nm)andadura-
tion of ~20fs (full width at half maximum (FWHM)) was focused
throughberylliumcompoundrefractivelenses(CRLs)intoaspotwith
asizeofd FWHM=0.41μm,seeFig.1a.Amoredetaileddescriptionofthe
focalspotsizemeasurementsforthisexperimentisgiveninref.29.
The target was a circle LiF crystal with a diameter of 20mm and a
thicknessof2mm,andwasputatthepointofbestfocusingofthe
beam. Two regimes of single-pulse irradiation of a LiF crystal were
investigated:E 1=26.7μJperpulseandE 2=81μJperpulse(theenergy
ofthepulsewasmodifiedwithan attenuation filter), with the esti-
matederrorsof10%.TheresultingintensityoftheX-raypulsesonthe
sample surface was correspondingly 1.0×1018W·cm−2 and
3.1×1018W·cm−2.Undertheseconditions,theabsorbedenergydensity
has the maximal values of ξ 1=297kJ·cm−3 and ξ 2=895kJ·cm−3,
respectively(see“Methods”sectionforconversiondetails).Thelast
energy density corresponds to 0.62 absorbed photons per cubic
nanometer,whichisabout100timessmallerthanthenumberofF
atomsintheLiFcrystalatnormalconditions.Itisalsoworthnoting
thatbothoftheenergydensitiesaretwoordersofmagnitudehigher
than the damage thresholdof LiF crystal(∼ 4kJ·cm−3 per pulse),as
determinedinourpreviouswork35.Aftereachsingle-pulseirradiation,
thecrystalwasmovedinadirectionperpendiculartothebeamsothat
thenextirradiationwouldfallonthefreshsurfaceofthesample.Shots
with strong attenuation (up to 10−6) were previously performed to
obtain the intensity distribution inside the beam. Such an intensity
obviously did not damage the crystal. We concluded that the XFEL
beam had a Gaussian-like intensity profile in the investigated
focalplane.
AnanalysisoftheinteractionareaoftheXFELbeamwiththeLiF
samplewasperformedwiththreedifferentreadoutsystems(Fig.1b,
see “Methods” section for details). A scanning electron microscope
(SEM)wasusedtostudythedamageonthesurface,Fig.1b(StepI).A
confocallaserscanningmicroscope(LSM)influorescencemodewas
usedtovizualizetheXFELbeamtracethroughoutthedepthoftheLiF,
Fig.1b(StepII).ThisispossiblebecausetheLiFcrystalisafluorescent
medium,andwhenirradiatedwithX-rays,CСsarecreatedinit,the
distribution of which corresponds to the irradiation area36,40,41. For
additional analysis of deep damage near the LiF surface, the well-
knownfocusedionbeam(FIB)–SEMtechnology42,43wasused,etching
layerbylayerdeepintotheLiFsample(thefirstfewtensofmicro-
meters from the surface along the XFEL propagation axis) with
simultaneousvisualizationofthefracturemorphologybySEM(45/90°
to the XFELbeam),Fig.1b(StepIII).

Morphologyofthegeneratedcavity
First,thesurfaceoftheexposedLiFsamplearoundinteractionwiththe
XFEL beam was analyzed with an SEM. Figure 2a–e shows the scan
results after a single-pulse X-ray exposure with ξ 1=297kJ·cm−3 (a,b)
andξ 2=895kJ·cm−3(d,e).Ascanbeseenfromtheimagesobtainedby
scanningwithanelectronbeamatanangleα=45°totheLiFsurface
(Fig.2a,d),inbothcasestherearetwoqualitativelysimilarstructures:a
craterwithclearlyvisiblebulgesoffrozenmaterialalongitsedges(in
purple),aswellas,theareaofdelaminationandspallingawayfromthe
influenceoftheX-raybeam.Viewingthedamagedsurfaceatanangle
α=90° (along the axis of incidence of the XFEL beam), Fig. 2b, e,
reveals an additional feature in the damage pattern—a hole in the
central area of the beam (burgundy area). The observed damage
structurefortwoLiFirradiationregimesthushasthefollowingfea-
tures,Fig.2b,e:Clearlyvisibleholeintheareaofmaximumimpact
intensity r =0.3×1μm2 (r =0.4×1.1μm2)—burgundy area.
hole-1 hole-2
Theindices1and2refertoξ 1andξ 2;cylindricalmeltingregionaround
acraterwitharadiusr =0.7μm(r =1.65μm)—purpleregion.
melt-1 melt-2
We refer to the annular area between the burgundy and dashed-purple
contours as a crater. We emphasize that both the melting region and
the region of the hole entrance have a round shape. They are therefore
caused by plastic processes and melting, and not by a brittle fracture of
the crystal. In this respect, these areas differ clearly from the area of the
cracks; area of spalling of material with diverging cracks up to dis-
tancesr =3μm(r =10μm)fromthecenterofthebeam.
cracks-1 cracks-2
If we compare the characteristic sizes of the damage for two
irradiationenergydensities,itbecomesclearthatthesizeoftheentry
into the cavity is approximately the same. Along with the melting
radius r /r is ~2.2 times larger, the size of the crackarea in
melt-2 melt-1
r /r is~3.3timeslarger,withtheratioofirradiationcases
cracks-2 cracks-1
ξ /ξ =3.
2 1
Thedistributionoftheabsorbedenergydensityξoftheincident
beamonthesurfaceoftheLiFcrystalisshowninFig.2c,ffortwo
irradiationregimes(see“Methods”forcalculationdetails).Notethat
the distributions are plotted ona logarithmic scale up to the value
ξ=10−2J·cm−3thatcorrespondstothethresholdforreadoutofthePL
signalofF andF +CCswithLSM36,44.AscanbeseeninFig.2c,f,the
2 3
decreaseofξ(x)isquitesharp(strong)—thelevelofintensitydecreases
etimesrelativetpoffiffitffihemaximumoftheGaussianfunctionataradius
r 1=e=FWHM=2= 2=0.296μm. It is worth paying attention to the
valueoftheabsorbedenergydensityξattheboundariesofthechar-
acteristicstructures(2–3).Tocausespallingofthematerial(case3),
thevalueofξmustbehigherthantheelasticlimitforLiFof~4kJ·cm−335
[dashed-blue horizontal lines in Fig. 2c, f]. However, as shown in
Fig.2b–e,ξismuchsmallerthan0.01kJcm−3intheregionofcracks.
Consequently,thepressuresdirectlyassociatedwithaheatingprocess
(isochoricasitwillbeconsideredbelow)intheseradiiaremuchlower
than100atm,andtheseamplitudesarecompletelyinsufficientforthe
brittlefractureofaLiFcrystal.Asimilarremarkappliestothemelting
region (case 2) in Fig. 2b–e. It should be underlined that Young’s
modulusofLiFof64.8kJ·cm−3,whichindicatespressureat64.8GPa,
wheretheshockwaveconvertsintoanacousticwave.Meltingrequires
an increase in internal energy of about 6kJ·cm−3 compared to the
restingstateatroomtemperature.However,attheedgeofthemelting
area(dashed-purplecontour),thelocalenergyvalueisthreeordersof
magnitudelower(~0.03kJ·cm−3).Consideringtheabove,theformation
ofregions(2–3)(meltingregion–crackregion)isduetotheattenua-
tionoftheshockwaves(SW)generatedbytheinfluenceoftheXFEL
beamoncharacteristicamplitudes.Theinitialamplitudeoftheshock
waveisdeterminedbytheenergyofthelaserpulse,buttheattenua-
tion of the shock wave during propagation in LiF is much slower
comparedtothedecreaseinabsorbedenergydensity.
Atthenextstage,thestructureoftheinternaldamage(deepinthe
sample)wasinvestigated,namelytheholeobservedatthebottomof
thecrater(burgundyareainFig.2b,e).NotethattheuseofAFMfor
this purpose is not sufficient because, under our experimental con-
ditions,theareaaffectedbythebeamwithd FWHM=0.41μmistoosmall
andtoodeeptobefullyinspectedbyastandardAFMtip.Therefore,to
investigatetheinternalstructureofthedamage,weusedaconfocal
laserscanningmicroscopewithalayer-by-layerreadingofthePLsignal
deepintheLiFsample(uptoz=1200μm)withastepΔz=1μmnear
thecrystalsurfaceandwithastepΔz=10μmforz>20μm(seemore
details in Methods). The measurements were performed using the
microscopeZeissLSM700influorescencemode.Figure3ashowsthe
sequenceofPLimages(ontheright)forthecaseofξ 1=297kJ·cm−3and
asketchofobservedinternalstructuresatcorrespondingdepths(on
theleft).Imagesshowthepresenceofacraterwithacentralholein
depthuptoz~2μm.Intriguingly,aftertheholeclosure(PLsignalis
clearly seen at z~2–8μm, indicating the presence of matter in this
region),indeeperlayersthePLsignaldisappearedagain,anditwas
absentdowntoz~1000μm.Thus,along,narrowchannelisformed
alongthebeampropagationthroughtheLiFsample.Inthesketchthat
interprets the obtained images, three main zones are respectively
highlighted:(zone1)isacraterandawaistintheformofaplug,(zone
2)isacavityintheformofanarrow,deepchannel,and(zone3)isthe
closureofthecavity.Notethatsincetheprimaryanalysisofthesample
surfacewasdonewiththeSEM,weseeabrightPLsignaloutsidethe
X-raybeamregioninthefirstlayersoftheimages(Fig.3a–z=2–8μm),
which is explained by the excitation of CCs created by the electron
beamonthesurface.
InFig.3b,themeasurementsofthetransversalsizeofthechannel
vsthedeptharepresentedforbothirradiationcasesξ 1(inblack)andξ 2
(inred).Wecanseethatafterasinglepulseirradiationbythebeam
withd FWHM=0.41μmиξ 1=297kJ·cm−3,thedamageofLiFhasacom-
plex structure with the following characteristic dimensions: crater
(∼2μm),layerofmatter(“plug”∼7μm),anultra-deepchannel(length
L c ∼1000–1100μm) with a diameter d c ∼0.6μm throughout the
entiredepth.
ThechannelformedinLiFhasaveryhighaspectratio(d c/L c~1/
1600–1/1800). A similar restructuring of material structure was
observedfortheirradiationregimewithξ 2=895kJ·cm−3,Fig.3(b-red
dots),butwithaslightlylargerchannelwidthandlength.Becausethe
workingdistancewaslimitedto1.1mmwiththe×100objectiveused,
wewerenotabletoobservethedepthofthechannel’send,sothe
aspectratioisinfactevenhigherintheseexperiments.
Figure 3c shows the dependence of the decay of the energy
density ξ within the LiF crystal for two irradiation modes
(ξ 1=297kJ·cm−3─blackcurve,ξ 2=895kJ·cm−3—redcurve)(calculation
details in “Methods” section). One can see that the value of
ξ 1[z=1000–1100μm]=12–18kJ·cm−3, where the channel ends, is
~16–25timeslowerthanatthesurfaceξ 1[z=0μm]=297kJ·cm−3.The
experimentally determined channel formation threshold is ξ th~3–4
timeshigherthanthethresholdfortheonsetofLiFdielectricdamage
foundinourpreviouswork35.
To verify thatthe observed absence of the PL signalin the LiF
imagesinthecentralregionoftheXFELbeam(Fig.3a)isduetothe
absenceofmatter(formationofacavity),weappliedFIB-SEMtech-
nologytoopentheexpectedchannellayerbylayer.Beginningatthe
craterarea,theionbeamablatedtheLiFsamplelayerbylayertoa
depthofseveraltensofmicrometersfromthesurface.Simultaneously,
theSEMvisualizedthefracturemorphologyatanangleof45°tothe
samplesurface(seeFig.1b,StepIIIand“Methods”sectionfordetails).
TheLiFsurfacewaspreliminarilycoatedwiththeprotectivelayerof
platinum.Figure4showstheresultsofthecorrespondingSEMmea-
surementsaftercrystaletchingforanexposurecaseξ 2=895kJ·cm−3.
Bothinawidefieldofview(Fig.4a)andwithagreatermagnification
image(Fig.4b),theexistenceofacylindricalcavityunderthecrater
bottom is clearly seen as a black region. Also, Fig. 4b emphasizes
detailsnearthejointofthecraterwiththecrater-initialchannelarea.
Thecraterhastheshapeofaconewithabasesizeof~3.3µm,whichis
consistentwiththemeltingarear =3.3µminFig.2e,f.Theimages
melt-2
in Fig. 4a, b) show a similar fracture structure as the PL images in
Fig.3a:(1)crater(cone-shaped),(2)thinsubstancelayer(plug),and(3)
expandedcavity.AccordingtotheSEMimagesforthecaseofexpo-
sureξ 2=895kJ·cm−3,Fig.4b,thecavitywidthdecreasesfrom2.8to
2µmatdepths up toz=21µm,whichalsocorrespondstothemea-
surementsofthisvaluefromthePLimagesinFig.3(b—reddots).At
greaterdepths,thechannelnarrowstoaradiusof0.4μmanditssize
remainspracticallyunchanged,seeFig.3(b—reddots).
Theexperimentalresultsontheformationofadeepcavitywithan
ultra-high aspect ratio inside the LiF material require a theoretical
explanation,assuchaphenomenonhasnotbeenpreviouslyobserved.

Multi-methodsimulations
Theaimofthenumericalsimulationistorelatetheenergyreleaseof
theXFELbeamtothefeaturesformed(crater,plug,cylindricalcavity
radius,andchannelfloor).Sincetheformedstructurehasacomplex
morphologyandahighaspectratio(seeFig.3a—zones1–3),aquan-
titativedescriptionwithasinglemodelandonecomputationalcode
cannotdescribethewholephysicsoftheformationofsuchanelon-
gatedstructure.Takingintoaccountoursimulationresultsobtained
forvariousenergydensitiesdepositedatthedifferentdepths,theLiF
samplewasdividedintothefollowing(seeFig.3a):(zone1)wherethe
craterandthesubstanceplugareproducedbysuperpositionofthe
cylindrical rarefaction wave with the unloading waves propagated
from the free surface (3D SPH and 2D Hydrodynamic (HD) simula-
tions);(zone2)includesthemostpartoflongcavityproducedbythe
cylindrical rarefaction wave (2D SPH and molecular dynamic (MD)
simulations);(zone3)whereenergydepositionisnearathresholdof
cavity formation. Here, the cavity is produced by cavitation in the
stretchedmelt,andthecavityfloorisformedbycrystallizationofthe
melt(MD).
Weshouldunderlinethatthephasetransitionintoaplasmastate
happenswithinafemtosecondattheveryearlystageofthepulse.
The
20-fs pulse intensity is at the level of 3.1×1018W·cm−2, which is far
below the criterion for the nonlinear saturable absorption of 9-keV
photonstoemergeinsolids(asanexample,itwasdemonstratedin
refs.45,46forFe).Duetothelongattenuationlength,themaximal
absorbedenergydensitynearthesamplesurfaceisξ 2=895kJ·cm−3for
suchalaserpulse,whichcorrespondstotheconcentrationofabsor-
bed photons 0.62nm−3 is about 100 times smaller than the con-
centrationofFatomsintheLiFcrystal(61atomsnm−3).Forthisreason,
we assume a linear absorption process for our experimental condi-
tions. The formation of the cavity does not depend on a detailed
descriptionofthealmostisochoricformationoftheplasmainavery
shorttime(~fs),butonlyontheprofileoftheinputenergy.Thestageof
formationofthehotzonewithplasma(i.e.,theprocessesofionization,
decelerationoffastelectronsandradiativetransfer)isnotimportant
forthedescriptionoftheformationofthecavity,sincetheradiusof
thehotzoneisknownfromtheexperimentandweusethedensityof
depositedenergy(notincident)todeterminetheinitialpressureand
temperaturefromtheequationofstateformodelingthemotionof
matterleadingtotheformationofthecavity.Inthefollowingsimu-
lations,weusedthedistributionoftheenergydensityinsidetheLiF
crystal,asshowninFig.3c.
Tosimulatethedynamicsofcavityopening,aswellasdamageto
lithiumfluorideasaresultofirradiation,theLiFmodelimplemented
withintheframeworkofthesmoothedparticlemethod47,48(seedetails
in Methods)is used as inour previous work35. Figure4c shows the
simulatedcurvesofthecavityradiusRandtheradialvelocityofits
boundaryυ rasafunctionoftime.Thediagramshowsthatthecavity
expandsandreachesitsmaximumsizeinthefirstfewnsafterthestart
of irradiation. At time t∼3ns, the growth of the cavity practically
stops,ascanbeseenfromthevelocitycurveυ r(t).Afterthat,itssize
remainsalmostunchanged,asitisobservedintheexperiment.
The contraction of the cavity begins after the arrival of a rar-
efactionwavefromthefreeboundaryofthetarget,whichreducesthe
pressureinside the cavity to zero. To account for the effectof this
rarefactionwaveinour2Dsimulations,thepressureinsidethecavity
startstodropafteracertaintime,correspondingtothedepthofthe
simulatedlayer.Inoursimulations,thepressuredropoccurswithin
∼10ns.Afterthepressurehasdroppedtozero,elasticforcesaround
thecavityleadtoareductioninthechannelradius.Thediagramin
Fig.4cshowsthatinthetimeintervalt=10–20ns,theradialvelocity
υ r(t)becomesnegative,andatthesametime,theradiusofthecavity
r(t)beginstodecreasesharply.Afterthepressureinsidethecavityhas
completelydissipated,att>20ns,thecavitycontinuestonarrowdue
to inertia, but at a much slower speed. The diagram of the radial
velocityυ r(t)showsthatitapproacheszeroatt>30ns,i.e.,thechange
in cavity size practically comes to a standstill. From this moment
onwards,theradiusofthecavitytendstowardsitsasymptoticvalue.
Figure4dshowsacomparisonofthecavityradiusasafunctionof
depth,whichwasdeterminedintheexperimentandinthesimulation
in irradiation mode ξ 2=895kJ·cm−3. In the graph, the gray markers
correspondtothesimulatedmaximumcavityradiusreachedinthe
expansion stage of the cavity, the black markers correspond to the
finalcavityradiusinthesimulations,andtheredmarkerscorrespond
to the experimental results. Firstly, there is a good quantitative
agreementbetweenthesimulationsandtheexperimentaldata.Sec-
ondly,onecanseefromtheabovediagramthatinthesimulations,the
finalsizeofthecavityisapproximatelythesameatdifferentdepths(it
decreasesslightlywithdepth),althoughthemaximumachievablesize
variesgreatly.Theexperimentalsoshowsasimilarpicture:thetrans-
versesizeofthecavityremainspracticallyunchangedovertheentire
depthofthechannel.Anoticeablewideningisonlyobservednearthe
freesurface.
The insets (e2, e3) to Fig. 4 show the images of LiF damage
obtainedinthesimulationsfortheirradiationmodeξ 2=895kJ·cm−3at
differentdistancesfromtheirradiatedsurfaceofthesample—depth
390μm(e2)and660μm(e3),respectively.Thegraycolorinthefig-
uresrepresentstheintactmaterial,andtheblackcolorcorrespondsto
thedamagedarea.Thecentralpart,showninwhite,isacavity.From
thepicturesabove,onecanseethatthedamagedareadecreaseswith
depth. This is quite natural, as the specific energy absorbed and,
therefore,theamplitudeoftheshockwavedecreasewithdepth.Here,
the material is damaged along clearly defined damage bands, the
concentrationofwhichgraduallydecreaseswiththedistancefromthe
areaofinitialheating.Theappearanceofcracksis clearlyobserved
aroundthenanochannel.Thecrackspropagateupto5µmawayfrom
thechannel,andtheirappearancegraduallydecreaseswiththedepth
ofthechannel.
Toanalyzethedynamicsofthecavityopeningnearthesurface
sample, an additional SPH simulation was performed in a
3-dimensionalenvironment.Incontrasttotheexpansionofthecavity
intothedepth,here,thetypeofdeformationismainlydeterminedby
thesuperpositionofthecylindricalrarefactionwavewiththeunload-
ingstresswavepropagatedfromthefreesurfaceofthesample.Inthe
insets(e1,f1)toFig.4,theradialυ randaxialυ zvelocitiesdeterminedin
the3DSPHsimulationareshowninalongitudinalsection.Fromthe
abovefigures,onecanrecognizethebeginningoftheformationofa
crater similar to the one observed in our experiments
(seeFig.4b).Fromthevelocitydistributionυ rshowninFig.4e1,itis
clearlyvisible thatthe crater continues to expand near the surface,
whileatdepththecavityhasalreadystartedtocontract(thebluecolor
inthelowerpartofthefigure(e1)correspondstothenegativeradial
velocity). The underestimation of the final radius determined in
2-dimensionalsimulations forthecaseofcavityexpansionnearthe
surface(Fig.4c),therefore,seemsreasonable,astheinfluenceofthe
freesurfacewasnotconsidered.Ina3-dimensionalsimulation,where
suchan influence should be considered naturally, the radius of the
craterismanytimeslargerthantheradiusofthecavityatdepth.
Itisalsonoteworthythatthedamageandpressuredistributions
determinedinthesimulationshaveacross-shapedpatternsimilarto
theexperimentalimagesofaconfocalmicroscope,seeFig.3aand
Fig.4e1,e2,f2,f3.Thereasonwhythedamagedareaformsastruc-
tured cruciform shape in the simulations is that the SPH particles
initially occupy the nodes of a close-packed 2-dimensional lattice.
Thus,therearespecialdirectionsalongwhichthedamageprefersto
propagate in theLiFcrystal. It wasconfirmed by a test run witha
homogeneous liquid-like packing of SPH particles, which provides
angle-independent damage and pressure distributions. A similar
picture emerges in the experiment since the LiF sample contains
preferential directions related to the lattice orientation of the
investigatedcrystals.
Finally,todeterminethethresholdforcraterformationandcavity
opening, two-dimensional high-spatial resolution simulations were
carriedoutusinga2DHDcodeforabsorbedenergydensitiesξfrom
10.5kJ·cm−3to28kJ·cm−3withastepof3.5kJ·cm−3(seeSupplementary
InformationI).Itwasfoundthatthefirstsignsoftheformationofa
surfacestructureleadingtotheformationofacraterwereobservedat
valueξ =14kJ·cm−3,whichisgenerallyconsistentwiththeresultsof
crat
our early experimental work35. The calculated threshold value for
cavityopeningwasξ cavity=28kJ·cm−3,whichisslightlyhigherthanthat
observedinFig.3c(12–18kJ·cm−3).
To explain the mechanism of formation of the cross-shaped
structurevisibleinthePLimages(seeFig.3a)aroundthecavityatthe
sample depth z>8μm, the large-scale MD simulation of the radial
materialmovementinadeepsliceofLiFcrystalperpendiculartoa
rapidlyheatedcylindricalchannelwasperformed(see“Methods”for
moredetails).Sinceeveninalarge-scaleMDsetup,thesamplesizeis
limitedbyamicrometer,ourMDsimulationsareintendedtoobtaina
qualitativedescriptionofbasicprocessesleadingtotheformationofa
cavityinthedepthoftheLiFcrystalheatedtopeaktemperaturesand
pressuresmuchlowerthanthosestudiedabove,withtheusageofthe
SPHmethod.
Simulation resultspresentedinFig.5awereobtainedlongafter
fast heating of a cylindrical sample with a radius of 300nm (in XY
plane)andthicknessof8.1nmalongtheZ-axiswithperiodicalcondi-
tions.TheheatingwasperformedbytheLangevinthermostatwitha
characteristictimeof20fsusingatargetGaussian-liketemperature
profileinacentralspotwitharadiusof30nm.Materialmeltedupto
23nm.Thepeaktemperatureof19,000Kandpressureof67GPaare
generated at the central axis, as seen in Fig. 5a1, where profiles of
densityandpressureareshownforafewearlytimesafterheating.See
thefull-scalesimulationinthecorrespondingSupplementalVideo1.
Thehighpressureinthecentralhotspot(channelcross-section)
generatesadivergingcylindricalshockandaconvergingrarefaction
wave,whichbothcausearadialflowofmaterial,leadingtoadecrease
in plasma pressure and temperature within the channel. Soon, the
divergingshockwavesplitsintoafastelasticshock(precursor)anda
slow plastic shock wave, see Fig. 5a1. As in the SPH simulation, the
surroundingcoldcrystalisdamagedbythisplasticshockwaveuntilit
weakensenough.Duetotheface-centeredcubic(fcc)crystalstructure
ofLiF,fourcornerdamagesectorsareformedaroundtheradialcracks,
whichcanbeseeninFig.5a,similartothoseobservedinNaCl49.After
traveling a sufficient distance from the central axis, the diverging
shockwaveattenuatesandbecomespurelyelastic.Thentheirrever-
sibledamageceases,andthecoldsolidbeginstoelasticallyresistthe
radialoutflowofmaterialfromthechannel.Soon,theflowvelocity
reducestozero,andtheremainingpressureofabout1–2GPainthe
hotfluidwithinthechannelcomestothemechanicalequilibriumwith
thetighteningelasticstressinthesurroundingcoldsolid.Thus,atthe
givenrelativelylowenergydeposition,thecylindricalcavityisstillnot
formedinthechannelfilledbyhotfluidwith2–3timeslessdensity
thaninthesolidstate,seeFig.5a1.Atthispoint,therapid(acoustic)
stage of material transformation ends,andalongcoolingstageofthe
channel fluid, leading to liquid-vapor phase separation and crystal-
lizationofthemelt,begins(seethecorrespondingdiscussioninFig.5b
below).ItisworthnotingthatourMDsimulationsperformedathigher
energy depositionshowcavityformationattheendoftherapidstage
ifthepeakpressureexceeds~100GP,atwhichtherarefactionwave
generateshighenoughradialvelocitytoproduceacavityfilledbyahot
gasforashorttime.
Figure 5a shows the 2D distributions of the damage and the
equivalentvonMisesstressafterthedamagehasceased,aswellasthe
experimental PL image at a depth of z=10μm. It is important to
underlinethatthebright,cross-shapedPLsignalcannotbecausedby
theXFELbeambeingangularlyuniformaboutitsaxis.Suchanangular
dependenceoftheconcentrationofCCsinLiFcouldariseunderthe
influenceofasufficientlystrongshockwavethatcreatesfoursectors
withcracks,wheretheequivalent(shear)stress is reduced.Outside
thesesectors,thematerialbehaveselastically,asshownbythecruci-
formareaofhighresidualshearstressinthemiddleofFig.5a,where
theCCspreviouslycreatedbytheXFELbeamcanbeerased.Thus,the
concentrationofCCsshouldremainhighinfourspotsaccordingto
the experimental distribution in the right Fig. 5a. The observed
increasedbrightnessofthethinrimaroundthecavityisprobablydue
eithertorapidcrystallizationofthemeltonthecoldchannelwallsor
toaveryhighconcentrationofdamageleadingtoamorphizationof
thecrystal.
WehavealsoperformedadditionalMDsimulationsofslowpro-
cessesleadingtotheformationofthecavityatrelativelylowenergy
depositionnearthecavityfloor(Fig.3).Suchprocessesaredrivenby
theslowlossofheatfromthehotmeltfillingthecylindricalchannel
intothesurroundingcoldcrystal.Atthislatestage,thepressureinthe
channeldecreasesduetothecoolingofthemelt,buttheradiusofthe
channelremainsalmostunchangedastheelasticstressesdevelopedin
thesurroundingsolidmaterialpreventthechannelfromnarrowing.
Thismeansthatthepressureinthemeltcanbecomenegativeeven
beforeitfreezes,whichcreatestheconditionsforcavitation,leadingto
theformationofcavitiesinsidethechannel.
Simulation results presented in Fig. 5b were obtained during
long-term cooling of molten LiF in a cylinder with a length of
1000nmsurroundedbyrigidwallsataradiusof10.3nm.Theinitial
samplewasobtainedbymeltingsolidLiFwithalineartemperature
gradientfrom1300Katthebottomofthecylinderto1500Katthe
top. The pressure of 1.8GPa was established along the cylinder,
whichisclosetothatremainedafterthestopofmaterialmovement
intheMDsimulationoftheearlystageofevolutionshowninFig.5a.
Then the Langevin thermostat was applied to x- and y-velocity of
atomstocooltheinitialtemperaturedistributionby900Ktoatarget
slopeof300–500KalongZ-axiswiththecharacteristiccoolingtime
of200ps.Figure5bshowsonlypartofthesamplenearthecavity
floor—see the full-scale simulation in the corresponding
SupplementalVideo2.
Figure5b(left)showstheprocessesofcrystallizationandcavita-
tioninthecylindricalchannelwiththefixedsolidwalls,throughwhich
theheatflowssimultaneouslyovertheentirelengthofthechannel.In
thedeeppart,themelthasalowertemperaturethanintheupperpart,
so crystallization starts at the bottom and spreads upwards in the
channel.Thespeedofmovementofthecrystallizationfrontiscon-
trolledbythedegreeofundercoolingofthemeltandcan,inprinciple,
exceedthespeedofsoundiftheheatislosttothechannelwallsfast
enough.However,thecoolingrateisslow,sothecrystallizationpro-
cessproceedsbelowthespeedofsound.Cavitationbeginswhenthe
negativepressureinthemeltfallsbelowthetensilestrengthofthe
liquid. This strength decreases with increasing temperature so that
cavitationpropagatesfromtoptobottomalongthechanneltowards
the crystallization front—as shown in the schematic z–t diagram in
Fig. 5b(right). Our interpretation is that the sharp cavity boundary
deepintheLiFcrystalseen inFig.3biscausedbythecessationof
cavitationuponmeetingwiththecrystallizationfront.Itisofinterest
toobserveinSupplementalVideo2thatbelowthecavityfloor,thefast
homogeneous crystallization results in the formation of nanovoids
betweensolidgrainsbyreasonofthemuchlowerdensityofmoltenLiF
comparedtosolidLiF(by25%).
Itshouldbenotedthatthesimulatedcavitationstartswithinde-
pendentnucleationofafewsmallvoidsinatinyarea,butsoonthey
coalesce into a single bubble with a diameter of the channel of
20.6nm.Inexperimentalconditions,thesizeofthechannelisabout
600nm, and cavitation may result in the formation of a foam-like
material, which willdecay, producing liquid filaments and droplets.
Finally,suchdropletswillreachthecoldcavitywallsandbefrozen,like
observedinref.17.Butthisscenarioisrealizedonlyifthewallsare
alreadyinasolidstate,i.e.,atalargeenoughcoolingrateofmolten
materialinthechannel.Otherwise,thewallsshouldbesmooth.

Methods
Targetdetailsandconditionsofexposure
AcircleLiFcrystalof2mmthicknessand20mmdiameter(two-sided
polishedwithR z=0.05μm)wasusedasthetargetsample.Toensure
consistencyandreproducibility,eachexposurewasperformedona
freshsamplelocation.
We investigated two single-pulse irradiation regimes of a LiF
crystalwithpulseenergiesE =26.7μJperpulseandE =81μJperpulse
1 2
(10%error).Inbothregimes,thesamplesurfacewasatthepointof
best focus. The reduction in pulse energy was achieved by using a
beamattenuator.Toestimatetheextentoftheimpactonthesample,
weusedtheabsorbedenergydensityperpulseξontheLiFsurface,
calculatedas:

E E (cid:3)4(cid:3)lnð2Þ
ξ½z=0(cid:2)=
S(cid:3)
pu
d
lse =
π
p
(cid:3)
u
d
lse
(cid:3)d 2
ð1Þ
att att FWHM

whereE pulse-pulseenergy,d att-attenuationlengthinmatter,d
FWHM
–
beamsizeathalfmaximum.
Considering the beam size and the attenuation length
d att=475μmof9keVphotonsinLiF55,theabsorbedenergydensity
was ξ =297kJ·cm−3 and ξ =895kJ·cm−3 on the sample surface. The
1 2
attenuationofthebeamasitpropagatesinLiFisduetotwofactors.
The first is the absorption in the substance, and the second is the
attenuationduetothegeometricdivergenceofthebeam.Asympto-
tically,outsidethewaistzone,thebeamisnotacylinderduetothe
broadening,butaconewithaverysmallbutfiniteopeningangleatthe
tipofthecone.Thedensityoftheabsorbedenergyξonthebeamaxis
zisthesame:

(cid:3) (cid:4) S
ξ½z(cid:2)=ξ 0 ½z=0(cid:2)exp (cid:4)z=d att Sð 0 zÞ ð2Þ

hereξ
0
—densityofabsorbedenergyonthetargetsurface,i.e.,atz=0,
S andSðzÞ—cross-sectionalareaofthebeamatthesurfaceanddepth
0
zofthecrystal,respectively.
Theradiusr (z)ofthebeamcross-sectionatdepthzisequalto:
" (cid:5) (cid:6) # 2 ! 3
e w S l i e e l s c l t - t r k r u o n c n o t w u d r n i e ff s , r t a b 12 c o t t p i h o h n a w s a e e n r o d e f i c g d o e e m r n m t p i a l fi e n e m i d u e m i n n , t a a t r n h y d e a a b l n as e i e n x r i p - t m i e o r o i r m d a i n e fi n d e t o d a m l v ly o s n l t u e r m u w c e t b u t b r 8 y e - r2 beam ðzÞ=r2 0 1+ z z R 2 =r2 0 4 1+ lnð 2 2 π Þz r λ 2 0 M2 2 5 ð3Þ

wherer
0
isthespotradiusofthebeamatthefocalplane,z Risthe
Rayleighrange,λisthewavelengthofthephoton,andM2isthebeam
qualityfactor.
UsingEqs.(2and3)andtheparameterM2=3,whichwefound
earlierinwork35foragivenfocusingoftheXFELbeam,weplottedthe
dependenceofthedecayξ½z(cid:2)intheLiFcrystal,presentedinFig.3c:

ξ ½z =0(cid:2) (cid:3) (cid:4)
ξ½z(cid:2)=
1+
(cid:7)0 lnð2ÞzλM2 (cid:8) 2 exp (cid:4)z=d att ð4Þ
2πr2 0

Investigationofcavitymorphology
Afterirradiation,theLiFcrystalwasexaminedusingvariousreadout
systems,seeFig.1b:StepI—aSEMwasusedtoexaminesurfacedamage
-HELIOSNANOLAB600I,FEI.StepII—toobtaininformationaboutthe
intensitydistribution of the incident beaminside the crystal,a Carl
Zeiss LSM 700 confocal laser scanning microscope in fluorescence
modewasused.SincetheLiFcrystalisafluorescentmedium,X-ray
irradiationcreatesCCsinit,thedistributionofwhichcorrespondsto
theirradiationarea35,56.Themeasurementswereperformedusingan
excitation laser with a wavelength of λ =488nm and an objective
las
withamagnificationof×100.Thesignalwasrecordedlayerbylayer
withalayerthicknessofΔz=1μmataspatialresolutionof0.25μm
(fieldofview200×200μm2).StepIII—Forseveraltestpoints,theFIB-
SEM,FEIHeliosNanoLab600I)technologywasused,whichmadeit
possibletoexaminethestructureofthedestructionareainitscross-
section,i.e.,itsdepth.Incontrasttoanelectronmicroscope,theFIB
inherently destroys the sample. When the high-energy ions hit the
sample,theyblastatomsoffthesurface.TheFIBtoolwasusedtoetch
theLiFsamplelayerbylayerintheareanexttothedamage,whilean
SEMwasusedtovisualizethemorphologyofthedamage(perpendi-
cular to the XFELbeampropagation plane). The preparationofthe
samplebeforemillingconsistedofathingoldcoating(afewnm)on
the whole surface, followed by a thin protective layer of platinum
locallydepositedonthetopofthehole.Theplatinumlayercanbeseen
inthecross-sectionSEMimagesattheholeentrance.Then,FIBmilling
wasperformed,varyingthecurrentfromnA(foropeningaviewing
section)topA(forpreciseslicingofthehole).

Simulations
We used a simulation approach of simulations to characterize our
channel formation. Three types of simulations were used: smooth
particlehydrodynamic(SPH),MD,andHD.Theresultsofthelastare
showninSupplementaryInformation.
Firstly,our2DSPHcodeequippedwiththeLiFdamagemodel35
(seeSupplementaryInformation II)wasusedtosolvetheproblemof
cavityexpansioninthezones1and2regions(seeFig.3a).Sincethe
heatingzoneoftheincidentXFELbeaminthematerialactsonthecold
solid material like a gas piston at pressure changing with time, the
problemcanbesimplifiedbyreplacingthehotmaterialzonewitha
boundaryconditionforthepressureP(t)setattheboundarybetween
hotandcoldmaterial.InSPHsimulations,toaccountfortheinitial
laserheatingwithinacylinderwitharadiusr =205nm,auniform
beam
heating is given by the specific energy e(z)=ξ(z)/ρ, calculated
accordingtoEq.(4)atacertaindepthzfromthesamplesurface.
Theinstantaneousheatingduetotheabsorptionofalaserpulseis
accompaniedbyapressurejumpofΔP(z)=(γ−1)ρ e(z),whereγ≃1.75
0
istheadiabaticexponent,ρ =2.65g·cm−3isthenominaldensityofLiF.
0
Suchlocalizedheatingleadstotheformationofastrongshockwave,
which propagates through the “cold” material (outside the heating
area) and leads to its damage. However, it is worth noting thatthe
amplitudeoftheshockwavedecreasesquiterapidlywithmovingaway
from the heating area, which limits the damage area to about ten
micronsorless,seeinsets(f2,f3)toFig.4.
Toanalyzethedynamicsofthecavityopeningnearthesurface
(zone 1 inFig. 3a), the modeling wasperformed in a 3-dimensional
environment,forwhichtheaxialsymmetryoftheflowwasnotused.
Thus,althoughthenear-surfaceflowhastwospatialcoordinates(r,z),
thesimulationusesSPHparticlesthatareinitiallyarrangedinagridin
theCartesian(x,y,z)coordinatesystem—accordingly,thisisreferred
toasa3Dsimulation.Heatingofmaterialwasappliedinstantaneously
byincreasingtheinternalenergyofSPHparticlesaccordingtoagiven
radialGaussiandistributionofenergydepositionwithinacylinder,i.e.,
thegaspistonmodelwasnotusedinthose3Dsimulations.
MDsimulationsofLiFwereperformedwithanewlydeveloped
pairwisepotentialforinteractionbetweenLi+andF-ionsinthefol-
lowingform:

(cid:9) (cid:3) (cid:4) (cid:10)
exp (cid:4)r=d a a a
V ij ðrÞ= q i q j r + r4 4 + r6 6 + r8 8 fðr,r c Þ ð5Þ

whereq iandq jaretheknownelectricalchargesofi-andj-ions,while
d,a ,a ,a are fitting parameters presented with more detailed
4 6 8
description in Supplementary Information III. The shielding with
lengthd isusedtoescapetime-consumingcalculationsofthelong-
rangeCoulombforces.
Thesmoothingfunctionfðr,r
c
Þcausestheabovepotentialtogo
tozerowithaninteratomicdistancer approachingthecutoffradius
r c=0:875nm.Thepotentialparameterswerefittedtotheknowncold
pressurecurve57,58inawiderangeofcompressionandstretchingby
usingthestress-matchingmethod59.Theobtainedpotentialprovides
themeltingtemperatureof990Kandreproducestheexperimental
differenceof25%betweenthedensitiesofmoltenandsolidLiFatthe
meltingpoint.AllMDsimulationswereperformedwithourin-house
parallelcode60.

Dataavailability
AlldataareavailableinthemaintextorSupplementaryInformation.
Source data are provided with this paper. The data that support the
findingsofthisstudyareavailablefromthecorrespondingauthorsupon
request. Data recorded for the experimentat the European XFEL are
availableathttps://doi.org/10.22003/XFEL.EU-DATA-002575-00.Source
dataareprovidedwiththispaper.

Codeavailability
SPHsimulationswereperformedwithourin-houseprivatecodeCSPH-
VD3basedonthecontactSPHalgorithmwiththeRiemannsolver47and
utilizing the Voronoi dynamical domain decomposition (VD3) for
parallelization48. MD simulations were performed with our in-house
code MD-VD3 based on the classical MD method with the velocity
VerletintegratorandutilizingtheVD360.Thecodeisavailableupon
requestto6asi1z@gmail.com.TheHDcodeisbasedonthe2DBaer-
Nunziato model of multifluid hydrodynamics61 using an HLLC-type
Riemann solver. The code is available upon request to
petchu@mail.ru.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "Reviewer report on the manuscript entitled \"Formation of high-aspect-ratio nanocavity\nin LiF crystal using a femtosecond of x-ray FEL pulse\" by Sergey S. Makarov et al.\n:: General comments\nThe authors present a very detailed and comprehensive study of single-shot x-ray FEL induced nanocavities in a LiF crystal.\nThe post-mortem analysis of the sample, carried out using laboratory techniques (SEM, FIB-SEM, LSM, etc.),\nis corroborated by numerical simulations. Overall, the presented work is commendable.\nAs a general impression, I question the use of an outstanding FEL source like EuXFEL, which can operate at MHz (!) repetition rate,\nfor single-shot damage on materials. Alternative low repetition rate x-ray FELs are probably more appropriate for this class of\nexperiments.\nThe authors do not seem interested in exploiting the real potential of their FEL source and do not mention the possibility of\nexploring\nthe picosecond and nanosecond formation dynamics of the FEL-induced nanocavity. Some kind of pump-probe approach,\nusing a fs-laser in combination with the intense FEL pulse or even a double x-ray pulse, would make their study more\nintriguing.\nThe authors emphasize the importance of demonstrating the formation of a deep cylindrical submicron cavity.\nIn particular, they claim that the \"radial extrusion\" process is the main mechanism behind the cavity formation.\nThis conclusion may attract the attention of some specialized readers but probably does not represent significant information\nfor the broader FEL community. More interestingly, the authors suggest the possibility of investigating polymorphic\nFEL-driven phase transitions in solids. However, they do not explain if there exist specific\nexperimental approaches that enable monitoring the formation of sample allotropes around the\nnanocavity\non the picosecond and nanosecond timescales after FEL exposure.\n:: Detailed Comments\nLine 70: \"required MJ/cm3 level of energy concentration\" should be \"required MJ/cm3 level of energy density.\"\nLine 77: \"XUV/x-ray FELs represent promising tools for direct nano-patterning of solids.\" X-ray FELs can certainly be used\nfor nano-patterning;\nhowever, the authors should clarify that the operational costs and limited beamtime of FELs do not permit considering them\nideal facilities\nfor regular operation of these kinds of applications.\nLine 173: There is a strike-through in the number \"2\".\nLine 227: There are irregular fonts here\n:: Conclusions\nThe employed methods are valid, and the quality of the presentation is very good; however, the significance of the\nconclusions\nis rather limited, especially considering the actual potential of the EuXFEL source. Optimization and constant improvements\nof x-ray FELs achieved in the last decade foster the use of these sources for more ambitious experiments,\nsuch as those involving ultrafast or nonlinear phenomena.\nInstead, the key result of the presented study is limited to the characterization of FEL nanocavities in LiF using conventional\nlaboratory instrumentation and theoretical simulations. This kind of investigation was innovative 15 years ago when x-ray\nFELs became available,\nbut today its impact has decreased and does not justify publication in Nature Communications, in my opinion.\nI would recommend publishing the manuscript in an alternative specialized journal.", "reviewer_2": "In this study, holes with an aspect ratio of more than 1:1000 are drilled using single-pulsed hard X-rays. The diameter and\nthe depth of the obtained holes are measured by a combination of fluorescence LSM and FIB+SEM. The authors try to\nexplain the formation of the holes including the observed three substructures by the three different simulation methods: SPH,\nMD, and HD.\nThe determined huge aspect ratio of the holes is exciting and processing holes with a diameter from 1 – 2 µm and a depth of\nmore than 1 mm using single-pulsed radiation is unique to the best of my knowledge. The obtained experimental results may\ncontribute to different promising applications as discussed by the authors.\nDespite the unique experimental results, I have to mention a few critical points which should be addressed before\npublication.\nIntroduction:\nThe authors discuss conventional drilling using laser radiation. The description is too general, as different drilling strategies\nand techniques exist enabling also a high aspect ratio of the holes.\nThe section should be checked in terms of the references being often missing to some statements, such as “However, large\nlength-to-diameter ratios cannot be achieved in this way (as a rule, this ratio does not exceed values in the order of one or\nfew tens).”\n“This situation differs fundamentally from the usual picture of laser ablation with the formation of a shallow crater whose\ndepth is small compared to the beam diameter, see e.g.1,19.“ The authors should discuss why the ablation mechanism\ndiffers fundamentally and also what are the differences to the creation of voids\ninside of transparent materials using highly intensive laser radiation.\nMorphology of the generated cavity in combination with the simulations:\nThe sections should be revised as some explanations and descriptions of simulated processes for forming the cavity are\noften only given in the text and are not supported by the figures of simulations. Either the authors have to extend the\nmanuscript, or I recommend adding it to the supplementary material.\nMorphology of generated cavity:\n“To verify that the observed absence of the PL signal in the LiF images in the central region of the XFEL beam in Fig. 3A is\ndue to the absence of matter (cavity), we cut the LiF sample layer by layer near the expected cavity to a depth of a few tens\nof micrometers from the surface (see Methods for details)” According to this sentence, the LSM measurements are just\nverified up to a few tens on micrometers, but in Fig 4 D the maximum measured depth is more than 700 µm. Which one is\ncorrect? Additionally, the final depth of the drilling hole is not verified. The authors also should add some SEM micrographs\nat positions several 100 µm deep in the material. Those micrographs might be added to the supplementary material.\nIf the final depth of the holes is more than 1 mm, shouldn’t they are visible in an optical microscope in transmission through\nthe side?\nMulti-method simulations:\nThe authors should also discuss the absorption process as due to the excitation of the material a decrease in the optical\npenetration depth might be expected, as for usual ultrafast laser radiation in the VIS range.\nThe authors present three different simulation methods to explain different processes in the formation of the final hole. The\nauthors should discuss the limits of each simulation method to clarify why each method can explain only the selected use\ncase. From my point of view, MD represents the most powerful method, and as a simulation of the complete hole is not a\nlimitation, so why not only MD simulations are used?\nDiscussion:\nMost paragraphs do not discuss the results but provide instead an outlook for further investigation or a comparison with other\nresearchers. Therefore, the section should revised to represent a discussion of the results.", "reviewer_3": "NCOMMS-24-27119 “Formation of high-aspect-ratio nanocavity in LiF crystal using a femtosecond of x-ray FEL pulse” by\nMakarov et al.\nMakarov et coworkers propose a method of volumetric ablation and nanostructuring of materials using ultrashort (20 fs) hard\nx-ray pulses at 9 keV provided by the FLASH source in Hamburg. The focused x-ray pulse can generate high aspect ratio\nnanostructures in the volume of a dielectric LiF sample. A range of theoretical continuum and atomistic models are used to\nsimulate the formation of the cavity and the surrounding pressure effects. Claim is made that the technique can be used to\nnanostructure bulk metallic materials where no alternatives for volume ablation exists. The modification process based\nmainly from dimensional analysis and electron microscopy, and supported by theoretical models is associated with shock\ninduced amorphization and cavitation.\nAltogether this is a very solid scientific works, where the interaction of short x-ray pulses for nanoprocessing is becoming\nhighly relevant. Demonstrating their importance for a range of structures in materials is appealing and interesting. The\ndiscussion is pertinent and insightful, with sometimes a dispersion in the analysis coming from the different models that\nobscures a clear conclusion on the nanocavitation process and the surrounding amorphization.\nNevertheless, some of the claims leave the impression of being rather speculative or at least far-fetched. I will indicate below\nsome\n1. The manuscript is scarce in details concerning matter excitation or ionization. It is expectable that saturation of x-ray\nabsorption in the FEL micro-spot occurs, given the high dose. No further details are given about the ionization mechanisms,\ncollisional processes, inner-shell decay or scattering, and how these affect the energy deposition profile. No information is\ngiven on how fast energy couples to the material at the electronic and molecular level, and how fast phase transitions may\noccur. I feel that such a discussion may be important to state the level of energy density as the main ansatz for the\nsimulation.\n2. The attenuation depth (at 1/e) of 475 um and the existence of a cavity at more than 1000 um in depth may suggest that at\nsurface the energy density is about one order of magnitude above the cavitation threshold. Below the cavity end one notices\n(Fig 3) modification that is not pressure related but merely a phase transformation. Is the possible saturation expected to give\na different energy density profile with less peak energy density and larger widths as reported here based solely on\ngeometrical consideration? A study of the threshold of the cavity process with different energies down to the threshold (and\nnot in a single pulse) could illuminate the energy evaluation (according to the estimation a cavity should be formed for input\nenergies in the 1uJ range, four times above the modification threshold given in Ref. 25). I note also the remarkable stability\nof the cavity along propagation (1000um) despite the variation of the energy density for more than an order of magnitude\n(Fig. 3A).\nA discussion based on the energy density required to kick-start a process is given at page 9. The main argument is\ndimensional, saying that melting or cracking occur in regions where estimated local energy density based on pulse profile is\ntoo small so the process is not driven by local energy but by shock pressure coming from the central area, triggered by fast\niscochoric heating (the argument is that the melting area has a radius of 0.6 um with respect to the 0.3um at 1/e2 expected\nfrom the x-ray pulse, low energy case). A full proof of such discussion would require the measured metrology of the X-ray\npulse at the measured plane as scattering and absorption saturation may locally modify the profile with respect to Fig. 2C.\nSecondly, it is important to highlight the process dynamics; for example, a relaxation of a lower density amorphous phase\nupon cooling may create (due to the density mismatch) type of stress components that will generate spallation or cracking of\nthe adjacent areas. This will provide a hint to the state of the material when it suffers the modification, as its evolution may\ndepend on it. Third, thermal transport may be active as long as the sample is hot and heat may propagate in the\nsurroundings. More arguments may be needed to support the statement in addition to the crude geometrical evaluation.\n3. The suggestions several times in the text of TPa pressure levels as well as polymorphic transformations are not really\nsupported here, though these appear as key elements of the discussion.\n4. The authors suggest, quite understandably, a strong interest for metals however their use case is a dielectric where\noptical Bessel Gauss pulses can produce similar high aspect cylindrical geometries for nanocavities that do not require\nMJ/cm3. This puts forward some inconsistencies in the interpretation of nanocavity formation with optical and x-ray pulses,\nthough dimensionally cavities and surrounding amorphous or stressed regions are similar. The dynamic behaviour\nsuggested here seem equally different from the one reported with optical pulses and this issue should be addressed. Phase\ntransitions, mismatch in amorphous and crystalline densities, and heat transport were also suggested to explain\nmodifications observed post mortem, without invoking high levels of mechanical shock.\n5. A comprehensive and relevant simulation package is used to analyse the hydrodynamics and MD aspects of the process\nstarting with the evaluated input energy density profile (hence the need to accurately confirm it). Timescales in the range of\nns are found (Fig. 4C) while sub-ns times are given in Juodkazis et al. PRL 2006 and several tens of ns are given in\n(Nguyen et al. Ultrafast Sci. 2024). Such discrepancies may perhaps be explained by the nature of the material and\nirradiation conditions but I feel correlations should be made as similar processes are discussed. What would be the\ntheoretical energy threshold for cavity formation when all heating, structural transformation, and relaxation processes are\naccounted for and how the phase transformation of the material influences the process? Some elements of the discussion\nare given at Fig. 6 but the times of several ps shows apparently some inconsistencies with Fig. 3.\nThe MD simulation brings into the discussion the cooling of the hot melt and its influence on the cavitation, while so far the\ndiscussion was dominated by shock launch. Perhaps a conclusive and convergent discussion coming from the different\ncodes used here may put forward the main common elements, with a focus on the nanocavity formation; the key element of\ninterest.\n6. To the stress distribution, there may be several elements leading to such a distribution. As a general note, radial transport\nwill create perpendicular stress components and similar polarization patterns.\nIn conclusion, this is a very interesting and original report. It reads nicely even though sometimes the discussion gains in\ncomplexity when surface and volume processes are discussed and mixed. Nevertheless, I feel that at this point, despite the\nhigh level of scientific discussion, the comprehensive analyses and theoretical simulations, and the originality of the\nirradiation conditions, the manuscript does not illuminate new physical aspects related to the interaction of short energetic\npulses and matter in the cavitation range. Cavities and nanobubbles where reported in dielectric materials in several\noccasions and their conditions analysed, with perhaps conclusions that may also be relevant to this work and also\nalternative formation scenarios. The cylindrical relaxation geometry was found optimal for generating high aspect ratio\nnanochannels up to 1:10000. What appears notable here is the high energy density values, that may potentially create\nspecific relaxation conditions for the X-ray pulse. Their validation is therefore critical to the scenarios proposed here and to\nthe conclusive section of the manuscript. The claimed extreme conditions need therefore further experimental insight to be\nconfirmed (with arguments in addition to the dimensional analysis using a pulse profile propagation in “vacuum”), as similar\npost-mortem damage and cavity appearances can be achieved optically at lower energies (energy density at least one order\nof magnitude lower), with similar sections for cavities and surrounding amorphous regions. The authors should demonstrate\nwhy secondary processes such scattering and absorption saturation as well as fast diffusion cannot increase the interaction\nsection. The similarities and differences with respect to the cavitation induced by optical (Bessel) beams either in terms of\nenergy density or process dynamics should be outlined. At the same time elements of beam metrology in interaction at high\ndoses should be given in support of the dimensional analysis. This will help to clearly indicate the shock scenario as most\nprobable, opposite to a transformation related to local energy density and not driven by propagating mechanical waves.\nReferences to extreme polymorphic transformations should be demonstrated otherwise their appear speculative in the\ncontext.\nTherefore, despite the interest of the report, I cannot give a positive recommendation for publication in Nature\nCommunications. However, I may reconsider if direct and convincing experimental proof of high shock levels is given\ntogether with the associated polymorphic transformations, transient or permanent, including the validation of the energy\ndensity levels.\nMiscellaneous.\nThe addition of drawings in Fig;2 makes it difficult to evaluate what the authors correlate with melting. The SEM appearance\nis not by itself the strongest argument for melting."}, "author_response": "We would like to thank the referees for the work they performed and their impression of the\nmanuscript.\nTo make proofreading easier, we have highlighted in red all differences with the previous\nversions. The following document contains our answers (written in blue) to the referee’s comments\n(written in black).\nAfter taking into account the reviewers' criticism regarding the importance and possible\napplications of the results of our work, we completely rewrote the sections abstract, introduction\nand discussion to cover these aspects in more detail.\nOn behalf of all co-authors,\nS. Makarov\n=====================================================================\nREVIEWER COMMENTS\n=====================================================================\nReviewer #1 (Remarks to the Author):\nReviewer report on the manuscript entitled \"Formation of high-aspect-ratio nanocavity\nin LiF crystal using a femtosecond of x-ray FEL pulse\" by Sergey S. Makarov et al.\nGeneral comments\n1. The authors present a very detailed and comprehensive study of single-shot x-ray\nFEL induced nanocavities in a LiF crystal. The post-mortem analysis of the sample,\ncarried out using laboratory techniques (SEM, FIB-SEM, LSM, etc.), is\ncorroborated by numerical simulations. Overall, the presented work is\ncommendable.\nAs a general impression, I question the use of an outstanding FEL source like\nEuXFEL, which can operate at MHz (!) repetition rate, for single-shot damage on\nmaterials. Alternative low repetition rate x-ray FELs are probably more appropriate\nfor this class of experiments.\nReply: Today only XFELs such as EuXFEL, LCLS and SACLA XFEL allow to perform\nexperiments for investigation long nano-cavities in solids. This is possible thanks to a wide\nrange of photon energy (several keV are required), high intensity and pulse energy (~ 1 mJ)\nof such X-ray sources. EuXFEL as well as LCLS and SACLA XFEL are often used in\nsingle-pulse mode for a variety of physics applications, especially for high energy density\nphysics experiments (MHz mode is rather intended for biological/chemical research).\nThis manuscript presents the very first demonstration of the ability to form a\nnanochannel in solid material with a single X-ray pulse generated by an XFEL. With the\ncurrent abilities of the available X-ray lasers at EuXFEL and LCLS-II generating ultrashort\nhigh-energy X-ray pulses with up to MHz repetition rate this work laid a solid background\nfor producing up to a million of nanochannels per second (!). This is the quintessence of\nthe presented experimental evidence, supported by thorough computational analysis, that a\nnanochannel in fact can be formed by a single pulse generated by a MHz repetition rate\nlaser.\n2. The authors do not seem interested in exploiting the real potential of their FEL\nsource and do not mention the possibility of exploring the picosecond and\nnanosecond formation dynamics of the FEL-induced nanocavity. Some kind of\npump-probe approach, using a fs-laser in combination with the intense FEL pulse or\neven a double x-ray pulse, would make their study more intriguing.\nReply: The formation of nanochannel with more that ×1000 times aspect length-to-\ndiameter ratio with a single XFEL pulse is a first step on the long way toward the\nunderstanding the mechanism of high energy density deposition above the strength of\nmaterial inside the bulk, the following generation of radially-symmetric shockwave, and\nanalysis of the ‘frozen’ compressed material states surrounding the void formed in the\nisochoric conditions of conservation of mass.\nThe essence of using ultrashort laser pulses with sub-picosecond pulse duration is\nto create the high energy density required for transition of the materials to the state of warm\ndense matter, which in turn leads to a strong shock wave and the following rarefaction wave\nresponsible for the void formation. The picosecond-range and nanosecond pulses are longer\nthan the electron-ion energy transfer time and thus are not suitable, as suggested by the\nReviewer, for nanochannel formation. According to our estimates the electron-ion energy\nexchange time in LiF is ~4.8 ps [Phys. Rev. B 73, 214101 (2006)]. The energy deposition\ntime should be a few times shorter, <1 ps, to create the high-energy density state of matter\nbefore the deposited laser energy could dissipate into the bulk through the electron-ion\ncollisions.\nWe thank the Reviewer for the advice of using pump-probe experiments to observe\nthe process of material restructuring under the shock wave propagation. The pump-probe\napproach to observe the shock-wave dynamic and analysis of the surrounded compressed\nshell is exactly the following step we want to apply for XFEL beam time. These plans are\npresented our publications (see, for example, Ref.[ Phys. Rev. Lett. 126, 015703, 2021] in\nthe manuscript and recently published in work [Phys Rev Research 6, 023101, 2024]). So\nfar, our applications for beamtimes were unsuccessful due to “… very high complexity of\nthe proposed experiments to be successful within the frames of available beam time”.\n3. The authors emphasize the importance of demonstrating the formation of a deep\ncylindrical submicron cavity. In particular, they claim that the \"radial extrusion\"\nprocess is the main mechanism behind the cavity formation. This conclusion may\nattract the attention of some specialized readers but probably does not represent\nsignificant information for the broader FEL community. More interestingly, the\nauthors suggest the possibility of investigating polymorphic FEL-driven phase\ntransitions in solids. However, they do not explain if there exist specific experimental\napproaches that enable monitoring the formation of sample allotropes around the\nnanocavity on the picosecond and nanosecond timescales after FEL exposure.\nReply: We agree that ‘radial extrusion’ should be better presented in physical terms such\nas “radially expanding shock wave and the following rarefaction wave responsible for the\ncompression of surrounding material and formation of void – so called (“radial\nextrusion”).”. However, we respectfully disagree with the Reviewer’s statement that “This\nconclusion may attract the attention of some specialized readers but probably does\nnot represent significant information for the broader FEL community.” Laser-induced\nmicroexplosion in confined geometry has already demonstrated the ability to form new\nhigh-density thermodynamically non-equilibrium material states which cannot be formed\nby any other means due to the record-high rate of energy deposition and quenching. The\nexamples include but not limited to the formation of bcc-Aluminium (Nat. Comm. 2, 455\n(2011)); at least two new Silicon phases, (Nat Comm. 6, 7555 (2015)) and other material\nnon-equilibrium phase transformations into polymorphs with novel and exotic properties\n[Phys. Rev. Lett. 96, 166101 (2006); Sci. Rep. 6, 34286 (2016); Opt. Mater. Express. 1,\n1150 (2011)] which undoubtedly attract attention from a very broad range of scientific and\nengineering communities.\nWe stress here that the presented results demonstrate the first significant step\ntowards expansion laser-induced confined microexplosion into the domain of optically\nnon-transparent materials. We should also underline that it is technically difficult to observe\nthe formation of polymorphs over time. But it is possible to observe formed polymorphs\nthat remain in an equilibrium or metastable state. This is done in the same way as was\npresented in the work [Sci. Rep. 6, 34286 (2016)].\n:: Detailed Comments\n4. Line 70: \"required MJ/cm3 level of energy concentration\" should be \"required\nMJ/cm3 level of energy density.\"\nReply: Thank you, corrected\n5. Line 77: \"XUV/x-ray FELs represent promising tools for direct nano-patterning of\nsolids.\" X-ray FELs can certainly be used for nano-patterning; however, the authors\nshould clarify that the operational costs and limited beamtime of FELs do not\npermit considering them ideal facilities for regular operation of these kinds of\napplications.\nReply: We agree with reviewer, definitely, today, this is a project of a scientific interest.\nWe have significantly changed the \"discussion\" section and, in particular, added the\nfollowing remark:“…We should underline that this manuscript presents the very first\ndemonstration of the ability to form a nanochannel in solid material with a single X-ray\npulse generated by an XFEL. With the current abilities of the available X-ray lasers at\nEuXFEL and LCLS-II generating ultrashort high-energy X-ray pulses with up to MHz\nrepetition rate this work laid a solid background for generating up to a million of\nnanochannels per second. This is the quintessence of the presented experimental evidence,\nsupported by thorough computational analysis, that a nanochannel can be produced by a\nsingle pulse generated by a MHz repetition rate laser. It opens a new avenue for the\ndevelopment of nanochannel sieves for lab-on-chip applications in any material, including\nthose that are not transparent to optical lasers…”\n6. Line 173: There is a strike-through in the number \"2\".\nReply: Thank you, corrected\n7. Line 227: There are irregular fonts here\nReply: Thank you, corrected\n:: Conclusions\nThe employed methods are valid, and the quality of the presentation is very good; however,\nthe significance of the conclusions is rather limited, especially considering the actual\npotential of the EuXFEL source. Optimization and constant improvements of x-ray FELs\nachieved in the last decade foster the use of these sources for more ambitious experiments,\nsuch as those involving ultrafast or nonlinear phenomena. Instead, the key result of the\npresented study is limited to the characterization of FEL nanocavities in LiF using\nconventional laboratory instrumentation and theoretical simulations. This kind of\ninvestigation was innovative 15 years ago when x-ray FELs became available, but today its\nimpact has decreased and does not justify publication in Nature Communications, in my\nopinion. I would recommend publishing the manuscript in an alternative specialized\njournal.\nReply: The significance of the presented results, in our opinion, is underestimated by the\nReviewer – see our replies 1-3 to previous comments above. The major limitation in using\ntightly focused optical Gaussian beam in confined microexplosion is imposed by laser pulse\ndiffraction, which limits the radius of the focal spot and thus the absorption depth where\nthe energy is absorbed. To increase the number of atoms rearranging into the\nunconventionally structured crystal lattices, the development of a method altering a much\nlarger volume of modified structure is required, specifically a method that deposits energy\ninto the electrons faster than it can be transferred to the ions. Ultrashort XFEL pulses in\nhard, several keV, X-ray energy open up entirely new and unique possibilities for highly\ntargeted laser restructuring of materials. The presented results constitute a robust\nbenchmark for the formation of broad range of exotic high-pressure material with\nextraordinary properties and to studies of highly non-equilibrium electron and ion\ndynamics in warm dense matter.\nThank you for your considerations.\n=====================================================================\nReviewer #2 (Remarks to the Author):\nIn this study, holes with an aspect ratio of more than 1:1000 are drilled using single-pulsed hard\nX-rays. The diameter and the depth of the obtained holes are measured by a combination of\nfluorescence LSM and FIB+SEM. The authors try to explain the formation of the holes including\nthe observed three substructures by the three different simulation methods: SPH, MD, and HD.\nThe determined huge aspect ratio of the holes is exciting and processing holes with a diameter\nfrom 1 – 2 µm and a depth of more than 1 mm using single-pulsed radiation is unique to the best\nof my knowledge. The obtained experimental results may contribute to different promising\napplications as discussed by the authors.\nDespite the unique experimental results, I have to mention a few critical points which should be\naddressed before publication.\nIntroduction:\n1. The authors discuss conventional drilling using laser radiation. The description is\ntoo general, as different drilling strategies and techniques exist enabling also a high\naspect ratio of the holes.\nThe section should be checked in terms of the references being often missing to some\nstatements, such as “However, large length-to-diameter ratios cannot be achieved in\nthis way (as a rule, this ratio does not exceed values in the order of one or few tens).”\n“This situation differs fundamentally from the usual picture of laser ablation with\nthe formation of a shallow crater whose depth is small compared to the beam\ndiameter, see e.g.1,19.“ The authors should discuss why the ablation mechanism\ndiffers fundamentally and also what are the differences to the creation of voids\ninside of transparent materials using highly intensive laser radiation.\nReply: Thank you, the first mentioned sentence was removed. We have substantially\nrewritten the abstract and introduction sections in order to give the reader a better\nunderstanding of the significance of this work.\n2. Morphology of the generated cavity in combination with the simulations:\nThe sections should be revised as some explanations and descriptions of simulated\nprocesses for forming the cavity are often only given in the text and are not\nsupported by the figures of simulations. Either the authors have to extend the\nmanuscript, or I recommend adding it to the supplementary material.\nReply: Thank you, we have substantially rewritten the simulation section and added more\ndetails.\nMorphology of generated cavity:\n3. “To verify that the observed absence of the PL signal in the LiF images in the central\nregion of the XFEL beam in Fig. 3A is due to the absence of matter (cavity), we cut\nthe LiF sample layer by layer near the expected cavity to a depth of a few tens of\nmicrometers from the surface (see Methods for details)” According to this sentence,\nthe LSM measurements are just verified up to a few tens on micrometers, but in Fig\nAdditionally, the final depth of the drilling hole is not verified. The authors also\nshould add some SEM micrographs at positions several 100 µm deep in the material.\nThose micrographs might be added to the supplementary material.\nReply: Thank you, corrected. We would like to note here that the sample has been milled\nup to the depth of only a few 10s of microns to verify the formation of voids. Milling\nsamples more than to 1-mm depth would take weeks or months of using focused ion beam\nis practically impossible. However, the confocal microscope images presented in Fig.3\ndemonstrate the dark spot in the beam axis which is experimental evidence of the void\nformation up to the depth of more than 1,100 µm.\nThus, we combine two methods: (1) FIB and (2) Confocal microscope - to confirm\nthe presence of a long cavity inside the crystal. FIB allows you to examine samples to a\ndepth of several tens of micrometers, while a confocal microscope can look at the entire\ndepth of the sample. However, each of these methods has its drawbacks: FIB has a limited\ndepth of observation, and a confocal microscope, although it can see blackness, cannot\nalways determine whether it is a void. Nevertheless, thanks to the combination of the two\nmethods, we can be sure that the voids really exist and reach a depth of more than 1000\nmicrometers, which is confirmed by our measurements and complex of simulations.\n4. If the final depth of the holes is more than 1 mm, shouldn’t they are visible in an\noptical microscope in transmission through the side?\nReply: It is difficult (one might even say it is impossible for our experimental conditions).\nThe LiF sample has transverse dimensions of the order of cm and a cavity diameter of 1\nµm. To see the cavity in an optical microscope, the sample must be cut around the cavity\nin the form of a rod with a diameter ~ mm (which is practically impossible without\ndestroying the cavity by cracking the sample). However, due to the fact that the LiF crystal\nis a fluorescent medium, we have a distribution of color centers (F , F +) within the entire\n2 3\nsample (essentially a 3D distribution of the X-ray beam). Thus, monitoring the internal\nstructure of the cavity with a non-destructive method ─ using a confocal laser scanning\nmicroscope by recording the intensity of a fluorescent signal within the beam image.\nMulti-method simulations:\n5. The authors should also discuss the absorption process as due to the excitation of the\nmaterial a decrease in the optical penetration depth might be expected, as for usual\nultrafast laser radiation in the VIS range.\nReply: There is a fundamental difference between laser radiation in the visible range and\nhard X-rays. Visible radiation has a frequency lower than the plasma frequency in the metal.\nIn the case of dielectrics - the material is transparent, there is a phenomenon of optical\nbreakdown. The dielectric begins to absorb visible radiation after breakdown. Whereas in\nX-rays the situation is fundamentally different - the material absorbs immediately =\nregardless of intensity = no optical breakdown.\nThe laser intensity of ~3*1018 W/cm2 is well below the intensity required to generate\nnonlinear absorption effects in LiF. Before the numerical modelling of the experiment,\nwhich (simulations) took years to complete, estimates were made. These are estimates for\nthe physical model you are writing about.\nUsing the provided in manuscript the maximal absorbed energy density of 895 kJ/cm3\n(the highest one in our experiment) it is easy to estimate the number of 9 keV photons\nabsorbed in a unit volume. This concentration of absorbed photons is about 0.62 per a cubic\nnanometer, which is about 100 time smaller than the concentration of Fluorine atoms in\nLiF crystal at normal conditions (61 atoms/nm3).\nF (Fluorine) with rather deep K-shall (900 eV) dominates in absorption. One 9 keV\nphoton is absorbed at one F-atom. This means that the maximal probability that the photon\nwill encounter an already ionized fluorine atom is about 1%, which can be neglected.\nWe conclude that (1) the consideration of hollow ions, (2) absorption saturation, and\n(3) the increase of the d length due to this saturation all need not be considered under our\natt\nconditions. The approximation with linear absorption and tabulated value of d (Henke\natt\nTables) is completely adequate to our formulation of the problem.\nAccording to the above estimates, fluxes with intensities greater than I ~ 1020\nthrNonLin\nW/cm2 are required for the attenuation length of d to increase by creating a high order ~1\natt\nconcentration of hollow ions. It should be noted that the rate of Auger processes is high.\nThe hole closure on the K-shell due to Auger processes occurs in femtosecond times. While\nour duration is 20 fs. Therefore, the estimate of I is the lower limit of the required\nthrNonLin\nintensities. In fact, the required intensity is even higher.\nMore details in the Multi-method simulations section have been added. In particular:\n“…Phase transition into a plasma state happens within a femtosecond at the very earlier\nstage of the pulse. The 20-fs pulse intensity is at the level of 1018 W/cm2, which is far\nbelow the criterion the nonlinear saturable absorption of 9-keV photons to emerge in solids\n(as example it was demonstrated in works (PRL 127, 163903 (2021); Nature 5080 (2014))\nfor Fe). Due to long attenuation length the maximal absorbed energy density near the\nsample surface is ξ = 895 kJ/cm3 for such laser pulse, which corresponds to the\n2\nconcentration of absorbed photons 0.62 nm-3 is about 100 times smaller than the\nconcentration of F atoms in LiF crystal (61 atoms/nm3). For this reason, we consider linear\nabsorption process in our experimental conditions….”.\n6. The authors present three different simulation methods to explain different\nprocesses in the formation of the final hole. The authors should discuss the limits of\neach simulation method to clarify why each method can explain only the selected use\ncase. From my point of view, MD represents the most powerful method, and as a\nsimulation of the complete hole is not a limitation, so why not only MD simulations\nare used?\nReply: Since even in large-scale MD setup the sample size is limited by a micrometer, our\nMD simulations are intended to obtain qualitative description of basic processes leading to\nformation of cavity in depth of LiF crystal heated to peak temperatures and pressures much\nlower than studied above with the usage of SPH method. More details in the simulation\nsection have been added. In particular:\n “The aim of the numerical simulation is to relate the energy release of the XFEL\nbeam to the features formed (crater, plug, cylindrical cavity radius, channel floor).\nSince the formed structure has a complex morphology and a high aspect ratio (see\nFig. 3A - Zone 1-3), a quantitative description with a single model and one\ncomputational code cannot describe the whole physics of the formation of such an\nelongated structure. Taking to account our simulation results obtained for various\nenergy densities deposited at the different depths, the LiF sample was divided into\nthe following (see Fig. 3A): (zone 1) where the crater and the substance plug are\nproduced by superposition of the cylindrical rarefaction wave with the unloading\nwaves propagated from the free surface (3D SPH, 2D HD); (zone 2) includes the\nmost part of long cavity produced by the cylindrical rarefaction wave (2D SPH,\nMD); (zone 3) where energy deposition is near a threshold of cavity formation. Here\nthe cavity is produced by cavitation in the stretched melt and the cavity floor is\nformed by crystallization of the melt (MD).\nWe should underline that the phase transition into a plasma state happens\nwithin a femtosecond at the very earlier stage of the pulse. The 20-fs pulse intensity\nis at the level of 1018 W/cm2, which is far below the criterion the nonlinear saturable\nabsorption of 9-keV photons to emerge in solids (as example it was demonstrated\nin works52,53 for Fe). For this reason, we assume a linear absorption process for our\nexperimental conditions. The formation of the cavity does not depend on a detailed\ndescription of the almost isochoric formation of the plasma in a very short time (~\nfs), but only on the profile of the input energy. The stage of formation of the hot\nzone with plasma (i.e. the processes of ionization, deceleration of fast electrons and\nradiative transfer) are not important for the description of the formation of the\ncavity, since the radius of the hot zone is known from the experiment and we use\nthe density of deposited energy (not incident) to determine the initial pressure and\ntemperature from the equation of state for modeling the motion of matter leading to\nthe formation of the cavity. In the following simulations, we used the distribution\nof the value of ξ inside the LiF crystal, as shown in Fig. 3C.”\n MD simulation sections: …“Since even in large-scale MD setup the sample size is\nlimited by a micrometer, our MD simulations are intended to obtain qualitative\ndescription of basic processes leading to formation of cavity in depth of LiF crystal\nheated to peak temperatures and pressures much lower than studied above with the\nusage of SPH method. At such low energy deposition the rarefaction wave may not\nbe high enough to produce a cavity during wave action.”\nDiscussion:\n7. Most paragraphs do not discuss the results but provide instead an outlook for\nfurther investigation or a comparison with other researchers. Therefore, the section\nshould revised to represent a discussion of the results.\nReply: We decided to discuss the results obtained immediately after providing the\nexperimental/modelling data and to compare them with the data from the literature. We\nbelieve that this makes it easier for the reader to understand the material. We consider the\n\"Discussion\" section as a conclusion where we describe the prospects for using the obtained\ndata. Nevertheless, we have added more details to the \"Discussion\" section and expanded\nthe discussion of the results in the \"Results\" section.\n=====================================================================\nReviewer #3 (Remarks to the Author):\nNCOMMS-24-27119 “Formation of high-aspect-ratio nanocavity in LiF crystal using a\nfemtosecond of x-ray FEL pulse” by Makarov et al.\nMakarov et coworkers propose a method of volumetric ablation and nanostructuring of materials\nusing ultrashort (20 fs) hard x-ray pulses at 9 keV provided by the FLASH source in Hamburg.\nThe focused x-ray pulse can generate high aspect ratio nanostructures in the volume of a\ndielectric LiF sample. A range of theoretical continuum and atomistic models are used to\nsimulate the formation of the cavity and the surrounding pressure effects. Claim is made that the\ntechnique can be used to nanostructure bulk metallic materials where no alternatives for volume\nablation exists. The modification process based mainly from dimensional analysis and electron\nmicroscopy, and supported by theoretical models is associated with shock induced amorphization\nand cavitation.\nAltogether this is a very solid scientific works, where the interaction of short x-ray pulses for\nnanoprocessing is becoming highly relevant. Demonstrating their importance for a range of\nstructures in materials is appealing and interesting. The discussion is pertinent and insightful,\nwith sometimes a dispersion in the analysis coming from the different models that obscures a\nclear conclusion on the nanocavitation process and the surrounding amorphization.\nReply: Thank you for encouraging comments!\nNevertheless, some of the claims leave the impression of being rather speculative or at least far-\nfetched. I will indicate below some\n1. The manuscript is scarce in details concerning matter excitation or ionization. It is\nexpectable that saturation of x-ray absorption in the FEL micro-spot occurs, given\nthe high dose. No further details are given about the ionization mechanisms,\ncollisional processes, inner-shell decay or scattering, and how these affect the energy\ndeposition profile. No information is given on how fast energy couples to the\nmaterial at the electronic and molecular level, and how fast phase transitions may\noccur. I feel that such a discussion may be important to state the level of energy\ndensity as the main ansatz for the simulation.\nReply: Dear reviewer, the authors thank you for this comment. Using the provided in\nmanuscript the maximal absorbed energy density of 895 kJ/cm3 (the highest one in our\nexperiment) it is easy to estimate the number of 9 keV photons absorbed in a unit volume.\nThis concentration of absorbed photons is about 0.62 per a cubic nanometer, which is about\n100 time smaller than the concentration of Fluorine atoms in LiF crystal at normal\nconditions (61 atoms/nm3).\nF (Fluorine) with rather deep K-shall (900 eV) dominates in absorption. One 9 keV\nphoton is absorbed at one F-atom. This means that the maximal probability that the photon\nwill encounter an already ionized fluorine atom is about 1%, which can be neglected.\nWe conclude that (1) the consideration of hollow ions, (2) absorption saturation, and\n(3) the increase of the d length due to this saturation all need not be considered under our\natt\nconditions. The approximation with linear absorption and tabulated value of d (Henke\natt\nTables) is completely adequate to our formulation of the problem.\nAccording to the above estimates, fluxes with intensities greater than I ~ 1020\nthrNonLin\nW/cm2 are required for the attenuation length of d to increase by creating a high order ~1\natt\nconcentration of hollow ions. It should be noted that the rate of Auger processes is high.\nThe hole closure on the K-shell due to Auger processes occurs in femtosecond times. While\nour duration is 20 fs. Therefore, the estimate of I is the lower limit of the required\nthrNonLin\nintensities. In fact, the required intensity is even higher.\nMore details in the Multi-method simulations section have been added. In particular:\n“…Phase transition into a plasma state happens within a femtosecond at the very earlier\nstage of the pulse. The 20-fs pulse intensity is at the level of 1018 W/cm2, which is far\nbelow the criterion the nonlinear saturable absorption of 9-keV photons to emerge in solids\n(as example it was demonstrated in works (PRL 127, 163903 (2021); Nature 5080 (2014))\nfor Fe). Due to long attenuation length the maximal absorbed energy density near the\nsample surface is ξ = 895 kJ/cm3 for such laser pulse, which corresponds to the\n2\nconcentration of absorbed photons 0.62 nm-3 is about 100 times smaller than the\nconcentration of F atoms in LiF crystal (61 atoms/nm3). For this reason, we consider linear\nabsorption process in our experimental conditions….”.\n2. The attenuation depth (at 1/e) of 475 um and the existence of a cavity at more than\n1000 um in depth may suggest that at surface the energy density is about one order\nof magnitude above the cavitation threshold. Below the cavity end one notices (Fig 3)\nmodification that is not pressure related but merely a phase transformation. Is the\npossible saturation expected to give a different energy density profile with less\npeak energy density and larger widths as reported here based solely on\ngeometrical consideration? A study of the threshold of the cavity process with different\nenergies down to the threshold (and not in a single pulse) could illuminate the energy\nevaluation (according to the estimation a cavity should be formed for input energies\nin the 1uJ range, four times above the modification threshold given in Ref. 25). I\nnote also the remarkable stability of the cavity along propagation (1000um) despite\nthe variation of the energy density for more than an order of magnitude (Fig. 3A).\nReply: Dear Ref, Thank you for your subtle comments on the text. Let’s answer step by\nstep.\n2.1. The attenuation depth (at 1/e) of 475 um and the existence of a cavity at more than 1000\num in depth may suggest that at surface the energy density is about one order of magnitude\nabove the cavitation threshold.\nReply: That's right, the energy density at the surface of 895 kJ/cm3 is much greater than\nthe energy density of about 10 kJ/cm3 at the depth at which the cylindrical cavity ends.\nThere are three fundamentally different zones along the beam axis. The shortest\nfirst zone is located near the sample surface. Its length is of the order of a dozen beam\ndiameter. The longest second zone with length of the order of units of absorption lengths\nd . And the transitional zone, where the empty cavity ends. Its length is on the order of a\natt\nfraction of the absorption length d .\natt\nIt should be emphasized that the cavitation phenomenon takes place deep in the\nthickness of the target, i.e. at the end of the cavity in the third zone. There is no cavitation\nin the first two zones. In the second zone, the cavity formation is caused by radial rejection\nof the substance (the concept of zones will be further specified below).\nIn this case, the substance is pushed radially in the direction away from the beam\naxis. And crystallizes after its radial shift. The empty cavity arises mainly due to integral\nirreversible swelling of the target itself. The displacements of the macro-target boundaries\nare small because the size and volume (~1 cm3, see Fig. 1) of the target are much larger\nthan the cavity volume (of the order of 10-9 cm3). Possible densification due to solid-solid\nphase transition also maybe takes place.\nLet’s discuss definition of «cavitation»: Classical cavitation is a phenomenon with\nthe formation of bubbles filled by vapor in regions where the pressure falls below the\npressure of saturated vapor in equilibrium with liquid at a given temperature.\nUnder our conditions, cavitation happens via formation of voids (empty bubbles\nwithout vapor) in the stretched liquid under negative pressure. And the amplitude of such\npressure must exceed the rupture/fragmentation threshold of resistance of the liquid to the\ntensile stress, for which the evaporation into the void is not required. In this case\nvoids/bubbles are formed randomly in a volume, due to thermo-fluctuations in density of\nthe stretched liquid.\nIn our case, the cavity in zone two is not formed by such cavitation of bubbles. It is\nformed in an axisymmetric flow directed radially from the beam axis.\nCavitation, in the spirit of the definitions given to this phenomenon above, takes\nplace in the third zone, where radial flow is relatively slow and the temperature of melting\nis not so high as in the second zone. It is a slow process governed by colling rate of melt.\nIt is caused by the formation of a channel with liquid inside the rigid solid matrix around\nthe channel — the solid walls surrounding confined liquid are rigid.\nIn this case, the unusual cavitation occurs due to an extremely large density jump\nduring melting/crystallization in ionic salts - up to 25% of the volume. Accordingly, during\ncooling and crystallization of the liquid phase, a sharp volume reduction (shrinkage) occurs\nand cavitation-type ruptures in the freezing liquid inside quasi fixed (quasi rigid) solid walls\nare possible, see MD simulations.\nAbout the three-zone classification: There are three qualitatively different zones\nalong the beam axis.\nIn the upper zone, the material motion is determined by the interaction between two\ndifferent rarefaction waves -- the first is a hemispherical rarefaction wave propagating from\nthe free surface of sample, the second is a rarefaction wave travelling in radial direction\nbehind the diverging cylindrical shock. The depth of this zone into the target thickness is\nof the order of a dozen beam diameters at the surface; the diameter is 410 nm. Here the\nflow depends on time and two spatial coordinates – the 2D flow.\nAt the top of the second zone, the local absorbed energy per unit length along the\naxis is approximately the same as in the first zone. The matter is that the length equal to\n~10 beam (~5-10 um) diameters is much less than the absorption length of 475 µm.\nBut in the 2nd zone the rarefaction wave coming from the 400 nm diameter spot at the free\nsurface of a target is not significant. It is not significant both in amplitude (three-\ndimensional attenuation when propagating from the spot to distances greater than the spot\ndiameter) and in time delay relative to the processes initiated by a cylindrical divergent\nshock wave at a depth greater than a dozen beam diameters.\nIndeed, the speed of light is \"infinite\". In the second zone, the significant changes\noccur in times for which the rarefaction wave travels distances of the order of the beam\ndiameter. Whereas the wave from the surface must travel many diameters to get here (this\nis said to explain the lag of the rarefaction wave running from the surface into the volume).\nThird zone is associated with lower energy deposition (but above the threshold of\ncavity formation) in the depth of cavity (near the cavity floor), where the radial rarefaction\nwave itself is too weak to cause formation of voids in the melt. Please see detailed\ndiscussion in Sec. MD simulations of cavity formation.\nTaking into account the above, we have updated the text about the division into\nzones in line 335: «…Taking to account our simulation results obtained for various energy\ndensities deposited at the different depths, the LiF sample was divided into the following\n(see Fig. 3A): (zone 1) where the crater and the substance plug are produced by\nsuperposition of the cylindrical rarefaction wave with the unloading waves propagated\nfrom the free surface (3D SPH, 2D HD); (zone 2) includes the most part of long cavity\nproduced by the cylindrical rarefaction wave (2D SPH, MD); (zone 3) where energy\ndeposition is near a threshold of cavity formation. Here the cavity is produced by cavitation\nin the stretched melt and the cavity floor is formed by crystallization of the melt (MD)…».\n2.2. “Below the cavity end one notices (Fig 3) modification that is not pressure related but\nmerely a phase transformation.”\nReply: The density of the absorbed energy decreases toward deeper into the target volume.\nRapidly absorbed energy increases the pressure if the rate of growth of absorbed energy 20\nfs far exceeds the hydrodynamic time scale d /c – diameter of a beam divided to speed\nbeam s\nof sound. Pressure increase generates material motion. On the other hand, an increase in\nenergy causes melting if the energy density is above the melting threshold.\n2.3. “Is the possible saturation expected to give a different energy density profile with less\npeak energy density and larger widths as reported here based solely on\ngeometrical consideration?”\nReply: It is said above that we can neglect the formation of hollow ions with high accuracy.\nTherefore, we can use the linear absorption/attenuation length d = 475 um.\natt\nThe question remains whether the cascade of secondary electrons will not expand\nthe radius of the energy release region. That is, the radius r at which the thermalization of\neff\nsecondary electrons occurs. The path length of electrons decreases rapidly as the kinetic\nenergy of a free electron decreases. Therefore, the most dangerous are electrons with\nenergies on the order of keV.\nSo, how large is the increase in the radius of the energy deposit r compared to the\neff\nradius r of a 9 keV photon beam?\nbeam\nIt is very important to emphasize the following.\nThe excess of radius r over radius r does not depend on the beam intensity.\neff beam\nIn the experiment, the LF is used exactly as a radius detector by the glow of the\ncolor centers. Small intensities are used to avoid strong deformations and damage to the\ndetector. This is how the beam radius was determined in our previous articles: J\nSynchrotron Radiat. 2023 Jan 1;30(Pt 1):208-216. doi: 10.1107/S1600577522006245 and\nOpt. Express 31, 26383–26397 (2023).\nThat is, the beam radius r is unknown to us. For the beam radius we take the\nbeam\neffective radius r . This is the radius that includes the broadening due to the cascade of\neff\nsecondary electrons.\nAlso, simulation by Monte-Carlo package not included into the paper gives for the\nradial spreading of the cascade generated by 9 keV photons the values ~ 100-150 nm.\nOn the other hand, there is a law of conservation of energy. The broadening of the\nphoton beam energy release radius could affect our results following from the physical\nmodel and numerical simulations only if the broadening radius turned out to be larger than\nthe cavity radius. The cavity radius in zone 2 has been measured experimentally and is\napproximately 350 nm, see Fig. 3.\nSupplementary argument. The calculation in the adopted physical approximation\nagrees with the data on the radial size of the cavity and its extent in depth.\n2.4. A study of the threshold of the cavity process with different energies down to the\nthreshold (and not in a single pulse) could illuminate the energy evaluation (according to\nthe estimation a cavity should be formed for input energies in the 1uJ range, four times\nabove the modification threshold given in Ref. 25).\nReply: Ref. 25 is Opt. Express 31, 26383–26397 (2023). This work focuses on much\nsmaller intensities ~ 1-10 kJ/cm3 than those ~1000 kJ/cm3 analyzed in this paper.\nDear reviewer, the article Opt. Express 31, 26383 (2023) is devoted to the study\nnamely of threshold effects. But these are effects on the free surface of our target. On the\nsurface, as mentioned above in our reply to 2.1, the interaction of two different rarefaction\nwaves determines the picture. One of them comes from the free surface, the other is radial\nfrom the beam axis.\nThe paper Opt. Express 31, 26383 (2023) can only be applied to a qualitative\nassessment of the situation in zone three of the long channel at huge energy densities of ~\n103 kJ/cm3 at the entrance to the single crystal. These energy densities are 100-1000 times\nabove the threshold considered in paper Opt. Express 31, 26383 (2023).\nTo understand the physical situation in zone three, an original MD simulation was\nperformed. It turned out that in order of magnitude the thresholds at the surface and in the\ndepth are comparable. This is physically clear. But the picture in zone three, i.e. in the end\nzone of the hollow cylinder turned out to be complex and physically meaningful.\nNamely:\n1) A large jump of volume reduction in ionic salts (LiF refers to them) during solidification.\n2) Solidification of a liquid in a channel with solid low-deformable walls.\nThe last part of comment 2\n2.5 I note also the remarkable stability of the cavity along propagation (1000um) despite the\nvariation of the energy density for more than an order of magnitude (Fig. 3A).\nReply: It is impossible to bend the channel. Unabsorbed photons propagate along the\nnormal to the surface, and the channel diameter changes slightly along its length (on the\nscale of the Fig.3B it is not so noticeable). The channel diameter changes along its length\ndue to the angular divergence of the beam. At a length z of 920 μm, the diameter doubles -\nsee formula (3) in Methods ( = 0.138 nm; M2=3, r = 205 nm):\no\n𝑧 2 ln(2)𝑧𝜆𝑀2 2\n𝑟2 (𝑧) = 𝑟2[1+( ) ] = 𝑟2[1+( ) ]\n𝑏𝑒𝑎𝑚 0 𝑧 0 2π𝑟2\n𝑅 0\nThe length of doubling the diameter is:\nz2 = 2Pi(205 nm)2/ ( Log[2]  M2 ) = 920 um.\n3. A discussion based on the energy density required to kick-start a process is given at\npage 9. The main argument is dimensional, saying that melting or cracking occur in\nregions where estimated local energy density based on pulse profile is too small so\nthe process is not driven by local energy but by shock pressure coming from the\ncentral area, triggered by fast iscochoric heating (the argument is that the melting\narea has a radius of 0.6 um with respect to the 0.3um at 1/e2 expected from the x-ray\npulse, low energy case). A full proof of such discussion would require the measured\nmetrology of the X-ray pulse at the measured plane as scattering and absorption\nsaturation may locally modify the profile with respect to Fig. 2C. Secondly, it is\nimportant to highlight the process dynamics; for example, a relaxation of a lower\ndensity amorphous phase upon cooling may create (due to the density mismatch)\ntype of stress components that will generate spallation or cracking of the adjacent\nareas. This will provide a hint to the state of the material when it suffers the\nmodification, as its evolution may depend on it. Third, thermal transport may be\nactive as long as the sample is hot and heat may propagate in the surroundings.\nMore arguments may be needed to support the statement in addition to the crude\ngeometrical evaluation.\nReply: Dear reviewer, this is the second part of your comment #2. Thank you for these\nopinions.\nTwo aspects are addressed in this commentary. (1) The melting radius and the\ncracking radius are discussed. (2) The intensity profile of the photon beam in the plane\nperpendicular to the beam axis.\nIt is also said that it is necessary to describe the dynamics of the process which is\ninitiated by the absorption of the beam energy.\nResponse.\nWe consider very high intensities with energy ~1000 kJ/cm3, which are more than\ntwo decimal orders of magnitude above the modification, cracking and melting thresholds.\nUnder these conditions, the radiatively initiated flow goes through several different\nphases/stages in time as the shock expands and its amplitude weakens down to the\nmelting/cracking stages. We are now talking about zones one and two along the axis of the\ncylinder. The main achievement of the paper is the proof of the formation of a long empty\ncylinder - cavity.\nIn zone 2, such an empty\\hollow cylinder is formed before the considered flow\nweakens to the cracking stage.\nAdditional subsidiary achievements are:\n(a) the reasoning about melting and cracking in zone 1.\n(b) on the cruciform character of the damage outside the hole of the hollow cylinder.\nCircles (a) and (b) are external to the cavity hole. Observation (b) is an interesting\nobservation. It turns out to be typical for a single crystal with a packing of cubic character.\nHere is a reference to the paper [Laser Pulse Induced Dislocation Structure in Ionic\nCrystals, From the book Volume 66, Number 2 August 16, A.V. Gobbunov , E. M.\nNadgornyi and S. N. Valkovskii, https://doi.org/10.1515/9783112501269-006], see Fig\nbelow:\nWe are sure that the reasoning about the phenomena of melting and cracking due to\nthe action of a divergent shock wave weakening as it propagates is correct. Indeed, the\nshock wave in cylindrical geometry attenuates in a power-law manner as a function of\nradius and time.\nDetailed studies of the photon beam intensity wings are devoted to our previous\nworks. They are based on experimental measurements. It is shown that the attenuation of\nthe beam intensity in the plane perpendicular to the beam axis follows Gauss's law. It is a\nvery fast strong attenuation proportional to the exponent: exp(-r2/r 2). Of course, this law\nbeam\nof attenuation is much faster than the power-law rate of attenuation.\nThe power-law attenuation of a cylindrical shock has been considered here\n[Attenuation and inflection of initially planar shock wave generated by femtosecond\nlaser pulse, Optics & Laser Technology, Volume 152, August 2022, 108100]:\np ∝ 1/r (3/4),\nSW\nl ∝ r (1/4),\nSW\nl/r → 1/r (3/4).\nSW SW\nHere “p” is amplitude of a shock, “r ” is instant radial position of a shock front,\nSW\n“l” is thickness of a shock compressed layer behind the shock front.\nThat is, the amplitude of the shock wave is attenuated in a power-law manner with\nan exponent of 3/4. This attenuation rate is much weaker than the attenuation with radius\naccording to the Gaussian law.\nIn addition, as it propagates, the compressed shell behind the wave front becomes\nthinner and thinner.\n4. The suggestions several times in the text of TPa pressure levels as well as\npolymorphic transformations are not really supported here, though these appear as\nkey elements of the discussion.\nReply: TPa pressure level is the Young modulus of diamond, representing the limit of\npressure for material transformation and the following studies of their unusual physical and\nchemical properties with diamond anvil cell. This pressure limit corresponds to the energy\ndensity achieved by concentrating 1 µJ of laser energy in 1 µm3 volume of material which\nis easily reached by optical and now – x-ray ultrashort laser pulses. We mention this TPa\npressure to demonstrate that laser-induced microexplosion leads to new non-equilibrium\nphase transformation pathways and opens up a range of new material end phases with novel\nmaterial properties.\n5. The authors suggest, quite understandably, a strong interest for metals however\ntheir use case is a dielectric where optical Bessel Gauss pulses can produce similar\nhigh aspect cylindrical geometries for nanocavities that do not require\nMJ/cm3. This puts forward some inconsistencies in the interpretation of nanocavity formation\nwith optical and x-ray pulses, though dimensionally cavities and surrounding\namorphous or stressed regions are similar. The dynamic behaviour\nsuggested here seem equally different from the one reported with optical pulses and this issue\nshould be addressed. Phase transitions, mismatch in amorphous and crystalline\ndensities, and heat transport were also suggested to explain\nmodifications observed post mortem, without invoking high levels of mechanical shock.\nReply: We have recently experimentally demonstrated using Bessel-Gaussian beams that\ncylindrical 2-D expansion of shock wave is more efficient way to achieve shock wave\npressure above 1 TPa and the resulted density is ~1.2 time higher than that previously\nreached with 3-D microexplosion with conventional Gaussian beams (Opt. Express 30,\n6016 (2022)). This demonstration is directly relevant to the presented here microexplosion\nexperiments with focused XFEL pulses.\n6. A comprehensive and relevant simulation package is used to analyse the\nhydrodynamics and MD aspects of the process starting with the evaluated input\nenergy density profile (hence the need to accurately confirm it). Timescales in the\nrange of ns are found (Fig. 4C) while sub-ns times are given in Juodkazis et al. PRL\n2006 and several tens of ns are given in (Nguyen et al. Ultrafast Sci. 2024). Such\ndiscrepancies may perhaps be explained by the nature of the material and\nirradiation conditions but I feel correlations should be made as similar processes are\ndiscussed. What would be the theoretical energy threshold for cavity formation\nwhen all heating, structural transformation, and relaxation processes are\naccounted for and how the phase transformation of the material influences the process?\nSome elements of the discussion are given at Fig. 6 but the times of several ps shows\napparently some inconsistencies with Fig. 3.\nThe MD simulation brings into the discussion the cooling of the hot melt and its\ninfluence on the cavitation, while so far the\ndiscussion was dominated by shock launch. Perhaps a conclusive and convergent discussion coming from the different\ncodes used here may put forward the main common elements, with a focus on the\nnanocavity formation; the key element of interest.\nReply: The reviewer indicated the articles for quartz irradiated with an 800 ns laser. In our\nexperiment we had hard X-rays. The difference from optics we added in the introduction\nsection. In general, difference in the time scales of observed processes (in our article and\nJuodkazis et al. PRL 2006 and Nguyen et al. Ultrafast Sci. 2024) is related to the size of the\nirradiated spot. Hydrodynamic evolution (characteristic) time is determined by hot spot size\n(heating area) divided the speed velocity c . The speed of sound does not depend much on\ns\nsolid materials, so the main spread in time scales is determined by the size of the hot spot\n(for large spots, it is necessary to consider large hydrodynamic times, as for the case of\noptics in the articles mentioned).\nAlso, in the article by Nguyen et al Ultrafast Sci. 2024 the energy input was small, the\nrarefaction wave was weak to create a cavity. However, heating led to a phase transition to\nthe amorphous quartz with HIGHER density than normal one. Thus, negative pressure\narose, and many nanobubbles are independently formed, but a unique long cavity is not\nformed in opposite to our case. The proposed mechanism of nanopore formation in article\nis not realized in our conditions (since amorphous LiF most likely does not exist as a stable\nphase). However, the nanovoids can be also formed in LiF below the cavity floor. We have\nadded a new statement in our manuscript (see MD simulation Section): “It is of interest to\nobserve in Supplemental Video 2 that below the cavity floor the fast homogeneous\ncrystallization results in formation of nanovoids between solid grains by reason of much\nlower density of molten LiF compared to solid LiF (by 25%).”\nTo make clear on different mechanisms of cavity formation (depending on deposited\nenergy density) we have added in the revised manuscript the following classification:\n“Taking to account our simulation results obtained for various energy densities deposited\nat the different depths, the LiF sample was divided into the following (see Fig. 3A): (zone\n1) where the crater and the substance plug are produced by superposition of the cylindrical\nrarefaction wave with the unloading waves propagated from the free surface (3D SPH, 2D\nHD); (zone 2) includes the most part of long cavity produced by the cylindrical rarefaction\nwave (2D SPH, MD); (zone 3) where energy deposition is near a threshold of cavity\nformation. Here the cavity is produced by cavitation in the stretched melt and the cavity\nfloor is formed by crystallization of the melt (MD).”\n7. To the stress distribution, there may be several elements leading to such a\ndistribution. As a general note, radial transport will create perpendicular stress\ncomponents and similar polarization patterns.\nReply: Such specific cross-shaped stress distribution is not formed in our SPH hydrocode\nsimulations if material is considered as an ideal elastic-plastic matter. The application of a\ndamage model (with stress relaxation produced by a damage parameter) for material\nrepresented by SPH particles with lattice packing (rather than homogeneous liquid-like\npacking) is essential to reproduce the cross-shaped pattern. Thus, the symmetrical radial\nflow of material itself cannot create such pattern. Also see the revised manuscript with a\nnew statement on 425 line: “It was confirmed by a test run with a homogeneous liquid-like\npacking of SPH particles, which provides an angle-independent damage and pressure\ndistributions.”\nThe LiF crystal as a lattice with angle-dependent strength responds to shock\ncompression by an angle-dependent damage distribution, which results in the\ncorresponding stress relaxation. Our atomistic MD simulation demonstrates such response.\nPerhaps the radial transport of heat was meant. But such transport may create only\nangle-independent stress field if the initial temperature distribution was axial-symmetric.\nWe think that this is the case since the spatial profile of X-ray pulse was axial-symmetric\nwith high precision.\nIn conclusion, this is a very interesting and original report. It reads nicely even though sometimes\nthe discussion gains in complexity when surface and volume processes are discussed and mixed.\nNevertheless, I feel that at this point, despite the high level of scientific discussion, the\ncomprehensive analyses and theoretical simulations, and the originality of the irradiation\nconditions, the manuscript does not illuminate new physical aspects related to the interaction of\nshort energetic pulses and matter in the cavitation range. Cavities and nanobubbles where\nreported in dielectric materials in several occasions and their conditions analysed, with perhaps\nconclusions that may also be relevant to this work and also alternative formation scenarios. The\ncylindrical relaxation geometry was found optimal for generating high aspect ratio nanochannels\nup to 1:10000. What appears notable here is the high energy density values, that may potentially\ncreate specific relaxation conditions for the X-ray pulse. Their validation is therefore critical to\nthe scenarios proposed here and to the conclusive section of the manuscript. The claimed extreme\nconditions need therefore further experimental insight to be confirmed (with arguments in\naddition to the dimensional analysis using a pulse profile propagation in “vacuum”), as similar\npost-mortem damage and cavity appearances can be achieved optically at lower energies (energy\ndensity at least one order of magnitude lower), with similar sections for cavities and surrounding\namorphous regions. The authors should demonstrate why secondary processes such scattering\nand absorption saturation as well as fast diffusion cannot increase the interaction section. The\nsimilarities and differences with respect to the cavitation induced by optical (Bessel) beams\neither in terms of energy density or process dynamics should be outlined. At the same time\nelements of beam metrology in interaction at high doses should be given in support of the\ndimensional analysis. This will help to clearly indicate the shock scenario as most\nprobable, opposite to a transformation related to local energy density and not driven by propagating\nmechanical waves. References to extreme polymorphic transformations should be demonstrated\notherwise their appear speculative in the context.\nTherefore, despite the interest of the report, I cannot give a positive recommendation for\npublication in Nature Communications. However, I may reconsider if direct and convincing\nexperimental proof of high shock levels is given together with the associated polymorphic\ntransformations, transient or permanent, including the validation of the energy density levels.\nReply: Thank you for your high appreciation of our work and detailed review. This work\npresents the first, to our knowledge, study of mm-long nanochannel formation by a single\nhigh brilliance X-ray free electron laser pulse. Intense X-ray pulses generated by free-\nelectron-lasers offer new avenues for formation of nanochannels for nanofluidic systems in\nany solid material. We tried to give convincing answers to all questions, as well as expand\non the theses in the text of the article. Thanks to your comments, we have significantly\nrevised the manuscript. In particular, the discussion section put forward an idea about\npolymorphs as a direction for future research and experiments. Since we did not study this\nissue in detail in our experiment, we removed the text from the introduction. However, we\nhave shown that shock wave with TPa-level pressure is formed in this experimental\nconditions that leads to «radial extrusion» of matter. Such pressure can lead to the formation\nof void surrounded by a compressed shell with novel metastable polymorphic structures.\nThe major difficulty in studying such polymorphs produced around a tiny optical focal spot\nis the very low, of the order of femtograms, quantity of material, which makes it extremely\ndifficult to detect and characterise their unusual structural and electronic properties. Here,\nwe demonstrate that the volumes of shockwave affected material can be increased by >1000\ntimes by hard X-ray pulses from free-electron lasers.\nMiscellaneous.\nThe addition of drawings in Fig;2 makes it difficult to evaluate what the authors correlate with\nmelting. The SEM appearance is not by itself the strongest argument for melting.\nReply: The SEM measurements shown in Figure 2 (at two observation angles – 45 and 90\ndegrees) demonstrate us clear signs of melting in the purple area: (1) a smooth inner surface\nof the circle area (Fig.2a,d) (the surface was levelled by capillary tension), which also led\nto influxes of matter (see e.g. Fig. 2d – molten substance); a cylindrically symmetrical\nregion within the purple fill, Fig.2b,e (in the case of spallation and destruction, broken chips\nare always observed, as can be seen outside the purple region). It is also consistent with\nsimulation data.\nWe would like to thank the referees for the work they performed and their impression of the\nmanuscript.\nTo make proofreading easier, we have highlighted in red all differences with the previous\nversions. The following document contains our answers (written in blue) to the referee’s comments\n(written in black).\nOn behalf of all co-authors,\nS. Makarov\n=====================================================================\nREVIEWER COMMENTS\n=====================================================================\n“I note at the same time a technologically-geared introduction which seems far-fetched for\nXFEL as similar performances can be reached easier with optical beams.”\nResponse:\nThe introduction specifically highlights the limitations of optical beams in nanochannel\nformation. The main limitation is the possibility of creating such structures only in optically\ntransparent materials. An additional complication is introduced by the nonlinear light-matter\ninteraction with a strong dependence of energy deposition on fluctuating local carrier density.\nThis aspect limits the possibility of controlled creation of nanochannels. The fundamental\nnovelty of our study lies in the first-ever demonstration of millimetre-long nanochannel\nformation with an aspect ratio exceeding 1,000, using a single X-ray free-electron laser pulse\nwith photon energy in the 10 keV range, which absorption is linear and well-controlled in\ncontrast to optical photons. Importantly, virtually all materials are transparent at these photon\nenergy levels, enabling the formation of smooth nanochannel even in materials that are opaque\nto optical wavelengths—this represents a fundamentally new opportunity in the field.\n“Moreover, resemblances of X ray damage with optical damage on surface (exfoliation\npresent on ionic crystals in fs laser ablation experiments) and in the bulk (cavities are\nexpected for tight-focused excitation in cylindrical and spherical geometries) raises\nquestions about the expected extreme behaviors. Are extraordinary processes to be expected\nat 0.3-0.9MJ/cm3 levels given that sub-micron cavities can be obtained with a tenth of\ndeposited energy?”\nResponse:\nWe agree that the shallow sub-micron craters with an aspect ratio up to ~10 could be\nobtained at the surface with much smaller deposited energy density due to the ejection of the\nmaterial close to the sample surface. However, the formation of long nanochannels with much\nhigher aspect ratio does not involve the removal of material away from the channel due to the\nvery fast quenching of material in ultrashort laser-matter interaction in the bulk of the material.\nInstead, the extraordinary processes observed at deposited energy densities of 0.3–0.9 MJ/cm³\nresult from a fast transition into a hot highly pressurized state of matter. This state is\ncharacterized by solid-state density and ionized plasma temperatures of several tens eV,\ncommonly referred to as warm dense matter (WDM).\nThe resulting radially expanding shock wave pressure exceeds the material’s Young’s\nmodulus and leads to the formation of a void in the material with compressed nanochannel\nwalls – see the first description of these extraordinary processes in Refs.[32,33] in the\nmanuscript. Moreover, it was experimentally demonstrated (Appl.Phys.Lett. 110, 161907) that\nthe high-aspect ratio nanochannel formation is due to the shock wave compression of the\nmaterial, which is fundamentally different to the shallow sub-micron cavities formed at the\ntenth of deposited energy due to formation of an ablated shallow crater on the surface. In those\nexperiments the array of nanochannels formed in WDM conditions using an optical Bessel\nbeam resulted in the reduced volume of the sample by ~22-29%, while the sample mass was\nreduced only by 0.3-0.8%. Thus, our results provide compelling evidence that WDM\nconditions can be achieved and that high aspect ratio nanochannels can be formed using hard\nultrashort XFEL pulses.\n“Without clear indications (for example, the absence of experimental confirmation of sub-\nns shock and cavity dynamics), the physics here becomes less singular. Theories and models\nabout materials under constraints were discussed in various occasions. The demonstration\nI suggested is the structural proof of matter following extreme evolution with a potential\ndynamic view of the process. Despite the compelling comments and numerical methods,\nsuch a proof was not given and statements remain partly speculative. The novelty remains\nutilization of XFEL source (notwithstanding the proof-of-concept material also transparent\nat optical wavelengths). I have the feeling that strength lies more in the perspectives that\nwere proposed. I therefore maintain the initial recommendation.”\nResponse:\nWe fully acknowledge that experimental confirmation of shock wave propagation and\ncavity formation dynamics would provide direct validation of the physical processes involved\nin nanochannel formation. In response to this, we are actively developing such experiments\nusing a pump-probe technique, where both pump and probe pulses are in the X-ray spectral\ndomain. These experiments are at the forefront of current technological capabilities, requiring\nultra-precise alignment, high temporal resolution, and significantly enhanced X-ray detection\nsensitivity. Despite these challenges, ongoing advancements in XFEL capabilities – including\nhigher photon energy and increased pulse intensity, make experimental studies of nanochannel\nformation dynamics increasingly feasible in the very near future.\nAt this stage, the simulation presented in our manuscript remains the only viable approach\nto uncovering these dynamics. The choice of a transparent material in our experiments is\nspecifically justified by the ability to visualize the nanochannel beyond its initial few tens of\nmicrons using a confocal optical microscope – currently the only method available for\nassessing the full length of the nanochannel.\nFollowing your recommendations, we have carefully revised our manuscript to remove any\npotentially speculative statements. All modifications are highlighted in the manuscript file.\nDear Reviewer,\nThank you very much for your constructive comments and for your kind words describing the\ndiscussion in our manuscript as “very good and particularly rich.” Below we provide our responses\nto the specific points you raised.\nQ1: The main question, in my opinion, is whether the manuscript demonstrates physical\ntransformations not achievable by other means or illuminates unique mechanisms of\ntransformation. These points remain unanswered to me.\nReply: The key experimental result of our work is the first demonstration of the delivery and\nlocalization of X-ray laser energy down to sub-micron dimensions over a millimetre-long focal\nregion within a solid material, achieving an energy density of up to 0.9 MJ/cm³. This is\naccomplished through an unprecedented concentration of X-ray energy over a long focusing\ndistance.\nThe resulting energy density significantly exceeds the Young’s modulus of the material and\nleads to the formation of high-aspect-ratio hollow nanochannels, a transformation that is both\nexperimentally characterised and theoretically substantiated in the manuscript.\nTo our knowledge, this is the first observation of nanochannel formation in the bulk of a solid\nmaterial induced by a single ultrashort X-ray pulse. The distinctiveness, reproducibility and\nlocalisation of this transformation clearly demonstrate a novel physical mechanism of\nnanochannel formation uniquely accessible through X-ray free-electron laser (XFEL)\nirradiation.\nThese findings open a new path for high-aspect-ratio nanochannel formation in a wide range\nof solids, including inaccessible to optical lasers. This capability creates new opportunities for\nexploring transport phenomena, nanoscale fluid dynamics, and fundamental physics and\nchemistry principles that govern ultrafast nonlinear flow of liquid in nanochannels.\nQ.2: Choice of material: If this is a key point, why not demonstrating the technique on\nmaterials that have no other alternatives?\nReply: We respectfully disagree with the Reviewer’s interpretation of the manuscript’s key\npoint. Our principal contribution is not the specific choice of material but the experimental\ndemonstration and theoretical validation of the ability to concentrate energy from a single\nXFEL pulse to levels approaching ~MJ/cm³ within a solid, – much above the yield strength of\nany material. We should also underline that the demonstrating the universality of the channel\nformation method in all materials using an XFEL, as you requests, cannot be achieved in a\nsingle beam time experimental slot. Having conducted experiments and extensive simulations\nfor LiF crystal, we can assert that this method works in this material. Furthermore, based on\nother experimental works and an understanding of the basic physical mechanisms common to\nall materials, we suppose that the method is universal for dielectrics, semiconductors and\nmetals.\nWe believe that the article contains significant results that encourage the continuation of this\nkind of research by other laboratories. That's how science works. A step forward is being taken\nby one group. This spark initiates the global scientific community to take the next steps.\nQ3. Why not demonstrate the technique on materials that have no other alternatives?\nReply: We addressed this point in our prior response (Round 2) *, but we elaborate further here.\nWe selected LiF as the demonstration material primarily because it is optically transparent and\npermits a straightforward correlation between nanochannel length and the 9-keV X-ray linear\nabsorption depth. This greatly simplifies optical diagnostics (e.g., Fig. 3) and supports accurate\nmodeling and interpretation of the results.\nWhile LiF is the focus of this initial study, our aim is to establish a clear and well-understood\nsystem for establishing and validating the proposed mechanism. This lays the groundwork for\nfuture work exploring a broader range of materials, particularly optically opaque and\ntechnologically relevant solids. As example, it was already demonstrated in work [52 from the\nmain article] that a similar structure in the form of an extended cavity with a diameter of 4 μm\n(aspect ratio 1:10) was produced in the Si semiconductor after irradiation with focused XFEL\npulse (d = 1 μm, τ = 20 fs) with a photon energy of 10 keV and an absorbed energy density\nFWHM\nξ = 430 kJ cm-3 per pulse. We should point out that the described mechanisms apply to any type\nof material where a high energy density region is rapidly created. In this region, distinctions\nbetween materials are erased, and a very high-pressure plasma forms. The surrounding cold\nmaterial then moves like a fluid under this pressure. This also indicates the universality of the\nhollow channel formation mechanism along almost its entire length, with the exception of the\nchannel's very end (zone 3). At this point, the material's strength and thermophysical properties\nmight lead to differences in how various materials behave. Therefore, we believe that similar\nhollow structures will be observed when irradiating metals with XFELs, for which\nexperimental results are currently lacking.\nQ.4: Mechanism and the discussion of extreme mechanics involved in the void formation.\nAlternative scenarios (e.g., Yao et al.) exist for nanostructuring without shock compression.\nOn the mechanism and discussion of extreme mechanics: … Experimental evidence is required to\nsupport the shock-based mechanism.\nReply:\nWe respectfully disagree with the interpretation that the formation of high-aspect-ratio\nnanovoids can generally proceed without shock compression. In our scenario, the formation of\nthe hollow nanochannel is a direct result of the following sequence of events:\n1. The localized and absorbed X-ray energy density (~MJ/cm³) is several times higher than\nthe Young’s modulus of LiF (~65 GPa).\n2. This energy input ionizes the material in the focal volume, forming a confined plasma.\n3. The plasma rapidly expands, launching a strong shock wave that compresses the\nsurrounding solid material.\n4. The rarefaction wave, which follows the shock front (as required by mass conservation),\ncreates the void, resulting in the observed hollow channel.\nTo move atoms away from their equilibrium positions inside a solid and form a void, the energy\ndensity must exceed the mechanical strength of the material, which is characterized by the\nYoung’s modulus. This is consistent with our calculations and modeling.\n* Our reply from Round 2 discussion: “The choice of a transparent material in our experiments is\nspecifically justified by the ability to visualize the nanochannel beyond its initial few tens of microns using\na confocal optical microscope – currently the only method available for assessing the full length of the\nnanochannel.”\nIn the study by Z. Yao et al. with optical Bessel beam indicated by the Reviewer\n(https://doi.org/10.1364/OE.26.021960) the estimated energy density in PMMA is ~13 GPa†,\nwhich is significantly higher than the bulk modulus of PMMA of ~2-3 GPa, and its yield\nstrength 0.05-0.1 GPa (see [https://doi.org/10.1016/j.rinp.2016.05.004],\n[https://www.google.com/url?sa=t&source=web&rct=j&opi=89978449&url=https://www.sc\niencedirect.com/topics/agricultural-and-biological-\nsciences/polymethylmethacrylate%23:~:text%3DPolymethylmethacrylate%2520(PMMA)%2\n520is%2520a%2520strong,and%252050%2520MPa%2520%255B44%255D.&ved=2ahUK\nEwiUjLmQw7SOAxWgHRAIHYq7BJkQzsoNegQIJhAa&usg=AOvVaw0BFxnd8eFUNltenQY-\nDyIO]). Therefore, even in that case, the formation of voids involves a shock-driven\nmechanism.\nOur theoretical model and numerical simulations confirm the central role of shock wave\ndynamics in the formation of high-aspect-ratio voids observed in our experiments. We are\nconfident that for the extreme energy densities generated by XFEL pulses, shock wave\ndynamics appear to be the dominant process.\nConclusion:\nThis article is the fruit of the work of many co-authors and many laboratories over a long period\nof time. The experimental results were completed by 2021. It took three years to build a physical\nmodel and numerical simulation. Finally, our efforts to publish the article have been ongoing for\nmore than a year (since April 2024).\nWe believe that our responses address the Reviewer’s concerns and clarify both the novelty and\nsignificance of our results. The manuscript presents the first demonstration of bulk nanochannel\nformation via localized X-ray absorption at ultrahigh energy densities, supported by experimental\nevidence and physical modeling. These findings establish ultrafast X-ray irradiation as a\nfundamentally new tool for nanostructuring.\nWe respectfully ask the Reviewer to reconsider their evaluation and recommend the manuscript\nfor publication in Nature Communications without further delay.\nKind regards,\nSergey Makarov (on behalf of the authors)\n† In the paper by Z. Yao et al, the laser pulse energy at the input to the optical system is E = 60 µJ. By\nconsidering very conservatively the efficiency of SLM and losses in the optical system forming the Bessel\nbeam as ~20-50%, the average length of the channel formed as L = 500 μm and the radius of the channel\nas r = 1 μm, the energy density in the plasma column is 𝑃=0.35×𝐸/(𝐿×𝜋𝑟2) = 0.35×6×10-\n5𝐽/(500𝜇𝑚×𝜋×(1𝜇𝑚)2) ≈ 1.3×104 𝐽/𝑐𝑚3=13 𝐺𝑃𝑎."}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors have thoroughly revised the manuscript,\naddressing most of the comments and criticisms raised by the reviewers.\nThey have done a commendable job, resulting in a significantly improved version.\nThe novelty of the experiments, as well as their potential impact on applications,\nis now clearer.\nThe message conveyed by the manuscript is more effective.\nIn its current form, the work can be considered for publication in Nature Communications.", "reviewer_2": "The authors answered my remarks and updated the manuscript accordingly. The manuscript is now much clearer and easier\nto understand. It can be accepted in terms of content.", "reviewer_3": "The authors gave new insights in their detailed response. I emphasize very interesting physical discussions, tackling a wide\nrange of assumed conditions. I note at the same time a technologically-geared introduction which seems far-fetched for\nXFEL as similar performances can be reached easier with optical beams. Moreover, resemblances of X ray damage with\noptical damage on surface (exfoliation present on ionic crystals in fs laser ablation experiments) and in the bulk (cavities are\nexpected for tight-focused excitation in cylindrical and spherical geometries) raises questions about the expected extreme\nbehaviors. Are extraordinary processes to be expected at 0.3-0.9MJ/cm3 levels given that sub-micron cavities can be\nobtained with a tenth of deposited energy? Without clear indications (for example the absence of experimental confirmation\nof sub-ns shock and cavity dynamics), the physics here becomes less singular. Theories and models about materials under\nconstraints were discussed in various occasions. The demonstration I suggested is the structural proof of matter following\nextreme evolution with a potential dynamic view of the process. Despite the compelling comments and numerical methods,\nsuch a proof was not given and statements remain partly speculative. The novelty remains utilization of XFEL source\n(notwithstanding the proof-of-concept material also transparent at optical wavelengths). I have the feeling that strength lies\nmore in the perspectives that were proposed. I therefore maintain the initial recommendation."}, "author_response": ""}, {"round": 3, "reviewer_comments": {"reviewer_3": "The main question in my opinion is if the manuscript, notwithstanding its quality of the discussion -which is very good and\nparticularly rich-, demonstrates physical transformations not achievable by other means or illuminate unique mechanisms of\ntransformation. These points remain unanswered to me.\n-Choice of material: I agree with the authors with the limitation of optical beams for non-transparent materials. If they work\nremarkably for generating nanostructures with high aspect ratio in dielectrics (and also with minimal nonlinear distortions,\nthe case of non-diffractive beams) they cannot work on other materials. Therefore, my interrogation, if this is a key point,\nwhy not demonstrating the technique on materials that have no other alternatives? Many characterization techniques exist\nnowadays to probe the development of the nanochannel in the bulk of non-transparent materials. The argument of the first\nuse of a XFEL pulse to this end should be accompanied by a demonstration that actually illuminates this advantage.\n-To the mechanism and the discussion of extreme mechanics involved in the void appearance. The formation of volume\nnanovoids with optical beams (including high aspect voids formed by Bessel beams -and I’m referring to volume structures\nwith aspect ratios exceeding 100 or 1000 and not to shallow surface craters) does not necessarily involve shock\ncompression, according to recent studies. The authors presented (quite selectively in my opinion) references to this extent\nas also occurring in the case of optical beams, but they would agree with me that the image of residual traveling elastic\nwaves is not a proof for shock compression (Yu et al https://doi.org/10.1364/OE.26.021960). Alternative scenarios exist for\nhigh aspect nanostructuring occurring at far lower energy density (up to hundred times lower). The proposed scenario for X-\nray is plausible, possibly probable at high energy density, but not every formation of a nanocavity should be seen through\nthe prism of extreme physics. If high energy physics transformation is implied, experimental evidence is due. Structural\ncharacterization in the material neighboring the cavity illustrating massive distortions, density changes or new high-pressure\nstructural arrangements, could have provided strong evidence to the proposed scenario.\nTo conclude, this is a solid and enlightening piece of physical discussion but it insufficiently illuminates the process of\nnanovoid formation and its unique manifestation under X-ray exposure, with experimental evidence being in my view\nnecessary to validate the hypotheses. One could perhaps go with the argument of first demonstration of linear absorption\nvolume structuring, but the mechanism validation is important for the community after years of employment of microexplosion\nconcepts. The points indicated in the perspectives will nonetheless establish ultrafast X-ray irradiation as unique\nnanostructuring means."}, "author_response": ""}, {"round": 4, "reviewer_comments": {"reviewer_1": "I really appreciate the considerable effort made by the authors to clarify all the points raised by the reviewers.\nThe presented work is highly commendable, resulting from an impressive combination of experimental and theoretical research.\nWhile the findings may call for further progress and refinement of the adopted methodologies, this is quite natural in frontier research\nwith x-ray FELs. At the current stage, the results reported by the authors already have considerable impact and are likely to\nstimulate the scientific community to further explore the field. Possible next steps and improvements could be briefly outlined\nin a few short perspective sentences at the end of the Discussion. Overall, I confirm my opinion that the manuscript fully\ndeserves publication in Nature Communications.", "reviewer_2": "As already stated in my last decision, the manuscript can be accepted in terms of content. The newly added explanations\nfurther enhance understanding. Further experimental investigations are not necessary for this study, in my opinion."}, "author_response": ""}]

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