Probing physical properties of confined fluids within individual nanobubbles
D. Taverna, M. Kociak, O. Stéphan, A. Fabre, E. Finot, B. Décamps, C. Colliex
aa r X i v : . [ c ond - m a t . m t r l - s c i ] A p r Probing physical properties of confined fluids within individual nanobubbles
D. Taverna, M. Kociak, O. St´ephan, C. Colliex, A. Fabre, E. Finot, B. D´ecamps, and C. Colliex Laboratoire de Physique Solides, CNRS, UMR8502, Universit´e Paris-Sud, Orsay, France C.E.A. Centre d’ Etudes de Valduc, Is-sur-Tille, France Laboratoire de Physique, UMR CNRS 5027,Universit´e de Bourgogne,Dijon , France Laboratoire de Chimie M´etallurgique des Terres Rares, UPR 209 du CNRS, Thiais, France (Dated: November 16, 2018)Spatially resolved electron energy-loss spectroscopy (EELS) in a scanning transmission electronmicroscope (STEM) has been used to investigate as fluidic phase in nanoubbles embedded in ametallic
P d P t matrix. Using the 1 s → p excitation of the He atoms, maps of the He distri-bution, in particular of its density an pressure in bubbles of different diameter have been realized,thus providing an indication of the involved bubble formation mechanism. However, the short-rangePauli repulsion mechanism between electrons on neighboring atoms seems insufficient to interpretminute variations of the local local measurements performed at the interface between the metaland the He bubble. Simulations relying on the continuum dielectric model have show that thesedeviations could be interpreted as an interfzce polarization effect on the He atomic transition, whichshould be accounted for when measuring the densities within the smaller bubbles. Confined fluids in nanosized volumes constitute chal-lenging objects for both basic and technological aspects.The investigation of the structural features and dynam-ics of nanojets has given rise to spectacular experimentalstudies and theoretical simulations [1]. Another ideal sys-tem is represented by gas confined in nanocavities. It isthe case of inert gas atoms coalescing as a fluid or a solidto fill nanocavities in metals, with spherical or facetedmorphologies depending of the local pressure. In thecase of Xe in Al, an interfacial ordering has been demon-strated by high resolution electron microscopy [2]. Thesesmall gas-filled cavities therefore behave as high-pressurecells, providing the boundary conditions for the evalua-tion of the physical properties of encapsulated gases. Amost challenging problem is the evaluation of gas densityand pressure in such cavities.Among the possible systems, He nanobubbles in met-als have attracted the attention of many researchers, be-cause of their high technological interest in the aging ofthe mechanical properties of materials involved in nu-clear reactors [3]. Measurements averaging the informa-tion over large populations of bubbles, the size distribu-tion of which being controlled by TEM, have first beenperformed by NMR [4] and by a combination of opticalabsorption and electron energy-loss spectroscopy (EELS)[5]. The first of these studies has revealed a solid-fluidtransition at 250K for bubble pressures ranging from 6to 11 GPa (i.e. He atomic densities from about 100 to200 nm − ) . The second study comparing UV absorptionspectroscopy on a synchrotron and high energy resolu-tion EELS without spatial resolution on He + implantedAl thin foils, have identified the blue shift of the He1 s → p transition (with respect to its value of 21.218eV for the free atom) as a hint for evaluating the localpressure . Theoretically, Lucas et al. [6] have confirmedthat this blue shift of the He K-line should be attributedto the short-range Pauli repulsion between the electrons of neighboring He atoms. Consequently, this effect shouldincrease linearly with the density of the He atoms in thehigh-pressure fluid phase likely to exist in these nanosizedbubbles. J¨ager et al. [7] have confirmed this linear rela-tion between the measured energy shifts (∆ E ) and theaverage bubble radii ( r ) , the larger shift correspondingto the higher He density and consequently to the smallerradii.With the development of scanning transmission elec-tron microscopy (STEM) techniques, capable of measur-ing spatially resolved EELS spectra for different positionsof a sub-nm probe on the specimen, new possibilitieswere offered to perform analysis on individual nanobub-bles [8]. The most comprehensive study up-to-date hasbeen conducted by Walsh et al. [9], who proposed a pro-cedure for estimating directly the helium density in asingle nanobubble. However, this work did not take intoaccount the influence of interface excitations on the es-timation of the internal density. A more fundamentalissue which has not been addressed in the case of he-lium bubbles is the potential occurrence of density inho-mogeneities close do the surface, due to the interactionbetween the confined fluid and the matrix. The investi-gation of such effects requires a refined characterizationat a sub-nanometer scale.In this letter, we present a study of the physical param-eters (density, pressure, energy of the He K-line) definingthe state of He inside nanobubbles, by using spatially re-solved EELS to map their variations at the nanometerscale. The variations between bubbles of different sizeare in agreement with the standard interpretation in theliterature, while a refined description is required for theevolution of the He signal within an individual bubble.By using the continuum dielectric model, we show thatthe discrepancies can be explained invoking an effect ofsurface polarization at the interface between the He andthe metallic surface. This leads to the necessity of a cor- FIG. 1: A: EELS spectra acquired at the centre of bubblesof different size (thick lines) and corresponding fit of the Pdplasmon (thin lines). B: Subtracted He signal. The shift ofthe He K-line for bubbles of different size is obvious. rection of the EELS estimation of the He density insidesmall bubbles.The results are issued from an 8-month aged tritiatedPd Pt alloy which exhibits a largely dispersed popu-lation of voids (from 2 to 20 nanometers in diameter).The EELS measurements have been performed in a VGSTEM HB 501 with a field emission gun operated at 100kV and a homemade detection system formed by a Gatan666 PEELS spectrometer optically coupled with a CCDcamera. Spectrum-images made typically of 64 ×
64 spec-tra could then be acquired with the following conditions: acquisition time of 200 ms per spectrum, probe of 0.7nm with step increments of ranging from 1.5 to 0.5 nm.Fig. 1A shows three EELS spectra corresponding to aselection of pixels at the centre of three bubbles of dif-ferent sizes (B1, B5 and B7) visible on fig. 2A. Thesespectra correspond to positions where the electron beamhas crossed both the metallic matrix and the bubbles.They all exhibit four major peaks (around 7, 17, 26 and33 eV respectively), which are attributed to the low en-ergy loss spectrum of the Pd alloy matrix. The sharperline between 22 and 23 eV is the signature of the He Kedge.In order to be more quantitative, the He signal of eachspectrum has been isolated by fitting the palladium con-tribution with 4 Gaussian curves (fig. 1B) . We can thenidentify any change in position, width, total intensity andpossible occurrence of fine structures or satellites on theHe K-line, related the different bubbles. For each probeposition, the He K-line intensity can be evaluated by in-
FIG. 2: Maps extracted from a spectrum-image of a selectedarea of the sample. A: Bright field image of the analyzedarea. Bubbles showing He signal are evidenced. B: Heliumchemical map. C: Map of the He density inside the He filledbubbles. D: Map of the energy shift of the He K-line. Thereference energy is chosen as that of the atomic He (21.218eV) tegrating the signal over a window of typically 4 eV andthe results ( I He ) are displayed as a 2D map (fig. 2B)of the localization of He atoms. It must be noticed thatnot all the voids contain He atoms. The next step is totransform the He K-line intensity map into a cartogra-phy of the absolute estimated He density n (expressedin atoms/nm ) . This can be calculated from the relation[9]: n = I He / ( σ He I z d ) , where σ He is the cross section ofthe helium 1 s → p transition for the used experimen-tal conditions (see[9] for calculation), I z is the integratedintensity of the elastic peak, d is the local thickness atthe pixel position of the analyzed He nano-volume. Thisparameter is the source of highest uncertainties. We havetested several approaches, but finally we estimated it ex-perimentally as the complement to local thickness mea-surements of the matrix. The resulting density map isshown on fig. 2C.The mean helium density inside a bubble is estimatedby averaging the calculated values over a selection ofpixels corresponding to central positions. The resultsrange from 15 to 35 He atoms per nm , the highest valuebeen obtained for one of the smaller bubble B1. Theenergy shift, defined as the difference between the mea-sured peak position inside the bubbles and the nominalK-line of atomic He [6], is mapped on fig. 2D and variesfrom about 1 up to 2 eV. In order to verify the predictedlinear dependence of ∆ E ( n ), we have plotted in fig. 3Aour results issued from several spectrum-images (emptysquares). A satisfactory fit to a law ∆ E = C n n + D canbe obtained with C n = (44 ± · − eV · nm and D FIG. 3: A: Experimental relation between energy shift andmeasured density. Empty squares represent uncorrected den-sity value; linear fit law: ∆ E = (0 . ± . n +(0 . ± . . Filled square represent density value corrected by surface ef-fects; linear fit law:∆ E = (0 . ± . n + (0 . ± . . Error bars correspond the standard deviation calculated onthe selection of pixels of the density map, and therefore arelarge for small bubbles having a bad statistics. B: Experimen-tal relation between pressure and the inverse of the bubbleradius. Empty circles are deduced from uncorrected densityvalues; linear fit law P = (0 . ± . × /R + (0 . ± . . Filled circles account for surface effects; linear fit law P =(1 . ± . × /R + (0 . ± . . The theoretical linear re-lation for elastic deformation of the Pd Pt matrix is alsodisplayed. Error bars are estimated by calculating the varia-tion of the equation of state in the density range defined bythe corresponding density error bars. Error bars for correctedvalues (not shown) are identical to those for uncorrected val-ues = 0 . ± . eV. The value of C n lies significantly higherthan those measured by J¨ager et al. [7] and Walsh et al. [9] but is close to that determined by McGibbon [8].Another relevant parameter is the internal pressure.In fact, if the bubble deforms the matrix elastically, theradius dependence of the bubble pressure is supposed toobey an inverse proportionality law P = 2 γ/r (where γ is the surface energy). Following the procedure indicatedin [9], we calculate the pressure from the measured n byusing a semi-empirical equation of states (see supplemen-tary materials and [9, 10]). The results are shown in fig.3B (empty circles). The pressure inside the bubbles isshown to increase roughly from 0.1 to 0.3 GPa (i.e. in arange well below the solid to liquid transition pressure), FIG. 4: Experimental profiles of the estimated density ( filledcircles) and of the blue-shift of the He K-line (filled squares)as a function of the mean local thickness d. Data are extractedfrom a spectrum image of 40 ×
40 pixels (spatial sampling of0.5 nm), acquired on a bubble of 19.5 nm diameter For com-parison, the corresponding simulated profiles of the He-K linedensity (empty circles) and energy position (empty square)arealso displayed. when the diameter of the bubble decreases from 17 to5 nm. A reasonable value for the surface energy of thePd Pt alloy is γ = 1 . Jm − , to be compared to ourexperimental slope 0 . Jm − . Then, the bubbles seem tobe under-pressured at the moment of our TEM observa-tion.The spectrum-image technique offers the extra possi-bility of exploring any potential intra-inclusion spatialdependence. A varying contrast seems visible withinlarger bubbles in fig. 2C and 2D, where the densitydrops while the energy shift increases close to the sur-face of the bubbles. In order to further investigate thisbehavior, fig. 4 shows experimental profiles of densityand shift as elaborated from a spectrum-image of a 19.5nm bubble, probed with a better lateral sampling of 0.5nm. Each point of the two profiles has been calculatedselecting annular regions of pixels corresponding to thesame analyzed thickness, and fitting the He 1 s → p transition with a Gauss function to calculate the energyposition and the intensity. From the centre to the bub-ble surface a 37 percent drop is observed for n while theenergy shift increases by 0.17 eV, which is one order ofmagnitude smaller than the shift between different bub-bles. This anticorrelation is in contradiction with thegeneral tendency previously observed between individualbubbles. Indeed, when only Pauli repulsion between Heatoms is taken into account, such a density drop shouldlead to a 0.35 eV shift toward lower energies. In orderto evaluate the potential occurrence of surface effects, wehave performed EELS spectra simulations, by adaptingto the case of embedded spheres the continuum dielectricmodel which has proved its efficiency for modeling localsurface phenomena in nanosized systems, such as single-walled nanotubes [11, 12]. As an input for the simulation,we used a lorentzian dielectric constant corresponding toa He fluid of constant density [6]. After simulation ofspectra for different local thicknesses d , the procedureused to extract n and ∆ E on experimental data is ap-plied. The resulting simulated profiles are compared tothe experimental ones in fig. 4B. Both ∆ E and n varia-tions are reproduced but underestimated. Consequently,the major part of the effect can not be attributed toa real change in the density, since the model assumesa constant one, but to the influence of surface excita-tions on the measurement. We stress that the evidencedsurface effect is not due to an usual plasmon mode, be-cause it does not correspond to a pole (resonance) butto a maximum of the dielectric response of the sphere Im (( ǫ He − ǫ m ) / ( ǫ He +2 ǫ m )) (where ǫ He and ǫ m are the di-electric constants of He and of the metallic matrix respec-tively). An interface plasmon excitation is expected at alower energy value (of the order of 7 eV), and is ratherunsensitive to the helium density. However, the dielectricformalism commonly used to model plasmon excitationsfurnishes reliable (similar) interpretations for the effectsof interface polarization on the atomic transition. It iswell known that such a formalism is very sensitive to theinput dielectric constants of both materials, and discrep-ancies between simulated and experimental data can bepartially explained by a lack accuracy of the lorentzianmodel adopted for He as well as of the experimental dataused for Pd. Nevertheless, the energy shift of He K-line isexplained by the contribution of a surface “mode” whichenergy, for this particular system, is slightly higher thanthat of the bulk He line (see supplementary materials).The decrease of the estimated density can be related toa companion effect known, for plasmons, as a boundaryeffect or “Begrenzung” effect [13]. This effect is com-monly interpreted as a modification in the probability toexcite bulk modes due to the occurence of surface excita-tion, and reveals itself as a negative contribution to theintensity of the bulk He line, the importance of which in-creases as the He thickness decreases. We point out thatthis is the first time that this surface effect, which hasbeen thoroughly investigated for valence electron excita-tions, is evidenced on an atomic-type excitation, usingEELS.Therefore, beside its intrinsic fundamental interest,this surface-induced decrease in the density estimatedfrom atomic transition signal should be taken into ac-count in the study of the bubble formation mechanism.We calculated a correction coefficient G to apply to ex-perimental intensities in order to account for surface ef-fects in the estimation of n . Such a coefficient is givenby the ratio G = I wos /I tot , where I wos is the He-K in-tensity simulated excluding surface contributions (ideal case), and I tot is the total simulated intensity(real case).The resulting ∆ E ( n ) corrected relation is displayed infig. 3A (filled squares). The linear fit gives an estima-tion of the slope C n decreased of 19 percent and closerto the values in the literature. Even larger is the cor-rection to relation between the pressure and the inverseradius (filled circles in fig. 3B), with a slope increasedby a factor close to 2. Nevertheless the comparison ofthe corrected data-set to the linear relation characteris-tic of the elastic deformation regime (also displayed in3B) confirms that the bubbles are under pressured.In conclusion, the present analysis of the confined Hefluidic phase, at their interface with the embedding ma-terial, has evidenced an interface-induced effect on theatomic-like spectral transition in He. Consequently, a re-liable estimation of the helium internal density and pres-sure requires a correction from this surface effect, espe-cially in the case of small bubbles. This effect can beof much broader interest, and it should also be identi-fied in quite different situations, such as those encoun-tered on semi-core loss edges (Hf- O , ) in dielectric thinfilms [14].From another point of view, the interpretationof residual discrepancies between experiments and simu-lations, when exploring the influence of the distance fromthe interface, require further modeling, accounting forchanges in Pauli repulsion and in Van der Waals forcesclose to the interfaces.We thanks L. Henrard, A. A. Lucas, Ph. Lambin andP. Loubeyre for fruitful discussions [1] M. Moseler and U. Landman, Science , 1165 (2000).[2] S. Donnelly, R. Birtcher, C. Allen, I. Morrison, K. Fu-ruya, M. Song, K. Mitsuishi, and U. Dahmen, Science , 507 (2002).[3] A. A. Lucas, Physica B , 225 (1984).[4] G. Abell and A. Attalia, Phys. Rev. Lett. , 995?997(1987).[5] J. Rife, S. Donnelly, A. Lucas, J. Gilles, and J. Ritsko,Phys. Rev. Lett. , 1220 (1981).[6] A. Lucas, J. Vigneron, S. Donnelly, and J. 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