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Konstantin Iakoubovskii, Kazutaka Mitsuishi, Kazuo Furuya

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[Structure and pressure inside Xe nanoparticles embedded in Al](https://mdr.nims.go.jp/datasets/0e7dcc69-b57a-41e3-8c29-470317925117)

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Structure and pressure inside Xe nanoparticles embedded in AlKonstantin Iakoubovskii* and Kazutaka MitsuishiQuantum Dot Research Center, National Institute for Materials Science, 3-13 Sakura, Tsukuba 305-0005, JapanKazuo FuruyaHigh Voltage Microscopy Station, National Institute for Materials Science, 3-13 Sakura, Tsukuba 305-0005, Japan�Received 27 April 2008; published 7 August 2008�Crystalline and amorphous xenon nanoparticles were produced in aluminum by Xe+ ion implantation andwere characterized with high-resolution electron microscopy combined with electron energy loss �EEL� spec-troscopy. Unusual distributions of the aspect ratio and of the diameter of the crystalline particles were observedand explained, respectively, by minimization of the surface energy and of the strain energy due to the specificlattice mismatch between Al and Xe. Matrix oxidation was revealed as an important phenomenon accompa-nying the amorphization of Xe particles. Significant variation of relative EEL peak intensities with Xe particlesize was observed and associated with unequal pressure inside different particles. The thus revealed variationwas utilized to map the pressure distribution inside individual particles with a nanometer spatial resolution.DOI: 10.1103/PhysRevB.78.064105 PACS number�s�: 68.35.Dv, 61.46.Hk, 61.72.U�, 68.37.LpI. INTRODUCTIONNoble gases, introduced by ion implantation or nuclearprocesses, are insoluble in metals and therefore precipitateinto particles.1–7 Characterizing the associated phenomena isimportant both for science and technology. In particular, theyhave an impact on the development of fusion and fissionreactors and help us in understanding the structure of nano-particles embedded in a crystalline matrix.Among numerous combinations of the matrix and noblegas element, much attention has been paid to the Al/Xe sys-tem for the following reason: Because of the small size of thenoble gas precipitates �typically between 1 and 40 nm�, theyare almost exclusively studied with transmission electron mi-croscopy �TEM�. Large difference in the atomic number Zbetween Xe �Z=54� and Al �Z=13� results in much strongerelectron scattering from Xe that greatly facilitates TEM ob-servations, especially using the high angle annular dark field�HAADF� imaging.2 Therefore the Al/Xe system will be themain topic of this paper.In addition to enhanced TEM observability, Xe particlesin Al are remarkable in their structure. Three types of par-ticles usually coexist: crystalline, semicrystalline, and amor-phous �see Fig. 1�. This variety is understood as follows:1,4the particles are pressurized by the matrix with the pressureincreasing as the inverse particle diameter1 /d. Large par-ticles �d�10 nm� are amorphous �or liquid�. At the criticalsize �10 nm, the pressure reaches 0.41 GPa, which isenough to crystallize Xe at room temperature.4 As a result,d�10 nm particles are cubo-octahedral nanocrystals havingthe same fcc structure as the Al matrix but �50% largerlattice spacing a �aXe�0.61 nm and aAl=0.405 nm�. Par-ticles with d�10 nm could also be “semicrystalline,” i.e.,their center is amorphous, but the top three surface layers areordered by the interaction with the matrix.1The above arguments explained the structure of embeddedXe particles using a single parameter, namely, the particlesize and the associated pressure difference. In this paper, weinvestigate other factors: the matrix oxidation, the differencein the lattice parameter between Xe and Al, and the surfaceenergy of the particles.The compression of Xe particles by the Al matrix madethem a unique object where pressure effects on solid Xe canbe investigated at ambient conditions without complex high-pressure equipment, such as a diamond-anvil cell. In thispaper, we exploit this advantage in studying the pressureeffects on electronic transitions in solid Xe. The latter wereFIG. 1. HAADF STEM image of Xe precipitates in polycrystal-line Al �scale bar 10 nm, �110� axis normal to the picture�. Note thecoexistence of crystalline �c1,2�, semicrystalline �s1,2�, and amor-phous �a1,2� particles of similar sizes. Crystalline particles exhibitcubo-octahedral or octahedral �o1,2� shapes, and the �110� projec-tion of the particle o1 contains only nine atoms. The particles in thebottom �c2 and s2� and top areas �c1, o1,2, and s1� belong to differentAl grains; they share a �110� vertical axis but have different in-plane orientations. The arrow marks one of the numerous smallwhite shapeless features, which do not contain Xe. Drawing overparticle c1 outlines the definition of its normalized aspect ratio A=N100 /2N111 in terms of the number of �111� and �100� Xe planes.PHYSICAL REVIEW B 78, 064105 �2008�1098-0121/2008/78�6�/064105�6� ©2008 The American Physical Society064105-1http://dx.doi.org/10.1103/PhysRevB.78.064105monitored with electron-energy-loss spectroscopy �EELS� ina scanning transmission electron microscope �STEM�. Thisallowed us not only to characterize individual nanoparticlesbut also to map, with nanometer spatial resolution, pressurerelated changes of the electronic structure inside the par-ticles.II. EXPERIMENTAL DETAILSAluminum foils were prepared by electrochemical polish-ing of well annealed high-purity Al disks. The foils had poly-crystalline structure with thickness varying between 20 and60 nm and with a grain size of a few hundred nanometers.They were implanted with 30-keV Xe+ ions to a dose of�1019 m−2 and then annealed at 300 °C for 1/2 h in vacuumin order to remove the residual radiation damage. Micro-scopic observations and spatially resolved EEL measure-ments were performed with a 200-keV high-vacuumaberration-corrected Jeol-2500SES scanning STEM �spotsize of �0.1 nm� equipped with a Gatan Enfina EEL spec-trometer.III. EXPERIMENTAL RESULTSA. Crystalline structure of Xe particles and its dependenceon the matrix oxidationOur STEM observations �Fig. 1� revealed a diameterrange of �7–10 nm where crystalline, semicrystalline, andamorphous Xe particles coexist; in this range, the particlestructure does not often follow the diameter-pressure argu-ments, i.e., larger particles can be crystalline and smallerones amorphous.In order to check whether chemical composition can ac-count for this observation, we analyzed the EEL spectra inand around the particles. Apart from the Al and Xe EELpeaks �discussed further in Sec. III D�, oxygen K-edge sig-nals at �530 eV were detected and chosen for analysis.Their weakness required relatively long acquisition time inorder to achieve appropriate signal-to-noise ratio. Therefore,instead of spatial mapping, multiple line scans were per-formed for a large number of particles, and the representativeresults are summarized in Fig. 2. They revealed homoge-neous oxygen distribution around crystalline and semicrys-talline particles and oxygen accumulation around the amor-phous ones. This oxygen distribution can be understood asfollows: Aluminum surface is covered by �4 nm of naturaloxide.8 Ion implantation not only introduces Xe but also re-coils surface oxygen into the sample. TRIM calculations pre-dict that in a “good quality” crystalline Al matrix covered by4-nm oxide, the 30-keV Xe ions will be implanted at21�5 nm and the oxygen will be recoiled into Al to a depth�1 nm. Therefore, oxygen will not reach Xe particles, andthus their structure will be crystalline �provided their size is�10 nm and the matrix pressure is sufficient for Xe crystal-lization�. Therefore, the oxygen in the EEL profiles of crys-talline �and semicrystalline� particles probably originatesfrom the surfaces of the Al foil. If a large void in Al iscreated, e.g., as a result of sample preparation or local Alremoval due to spatial fluctuations of the ion-beam intensity,then the depth of the oxygen recoil could substantially in-crease, thus resulting in the oxidation of the void surface.Presence of extended void would reduce the pressure; thelatter could become too small for Xe crystallization resultingin amorphous particles. In summary, the oxidation of Al/Xeinterface revealed in this paper might not be the primarycause of Xe amorphization, but it is certainly an accompany-ing process revealing the weakened regions in Al.B. ‟Magic numbers” of planes in the crystalline Xe particlesIn order to assure the coexistence of different Xe particlesin a certain diameter range, dozens of high-resolutionHAADF STEM images were processed, and the results arepresented in Figs. 3 and 4. The histogram of Fig. 3�a� notonly confirms the coexistence range of �7–10 nm but alsoreveals an unusual oscillatory diameter distribution of thecrystalline particles. In Fig. 3�b�, we have reanalyzed thedata of Fig. 3�a� in terms of the number of Xe �111� and�100� planes rather than the corresponding distances. Suchanalysis reduces errors originating from the imperfect micro-scope calibrations, sample misalignment, and inaccuratechoice of directions along the particle. An oscillatory behav-ior was confirmed such that the even number of planes wasobserved more frequently than the odd ones.Note that an oscillatory diameter distribution has beenobserved for Pb particles in Al.9,10 It was successfully ex-plained by minimization of the strain energy originating fromthe lattice mismatch between Pb and Al, and we haveadopted below that model to the Al/Xe system.Dashed line in Fig. 3�b� presents a corresponding simula-tion of the �111� histogram using a product of a Gaussian andBoltzmann distributions asexp�− �N111 − 11�2/70 − �V�2/kT� . �1�Here N111 is the number of �111� planes, V is the particlevolume, �=18 K � / �3 K+4 �� 18 K /49 GPa forXe,11 � is the shear modulus of Al, and K is the bulk modu-0 2 4 6 8 10 12 14 16 180.00.20.40.60.81.0crystalline (c1)semi-crystalline (s1)amorphous (a1)OxygenEELsignal(arb.units)distance (nm)FIG. 2. �Color online� Representative line scans of the inte-grated oxygen K-edge EEL signal acquired across a crystalline �c1�,semicrystalline �s1�, and amorphous �a1� particles of Fig. 1. Oxygenaccumulation at the Xe/Al interface is revealed for the amorphousparticles.IAKOUBOVSKII, MITSUISHI, AND FURUYA PHYSICAL REVIEW B 78, 064105 �2008�064105-2lus of Xe. The first �Gaussian� term accounts for the scarcityof large and small crystalline Xe particles. Its apparent over-estimate of the number of small particles is partly due to theelevated difficulty of their experimental detection. The sec-ond �Boltzmann� term contains the strain energy ES=�V�2.The Moiré-fringe function �=minp�p ·aAl /aXe−N111�, wherep is an integer, accounts for the lattice mismatch between thehost and guest crystals. In case of Pb in Al the mismatch isonly 20%, and thus the period of ��N111� oscillations is rela-tively large ��8 lattice planes�. However, for Xe in Al themismatch is �50% and the ��N111� period is about twolattice planes only. Continuous models, such as strain model,might not work in such a clearly discrete case, and thus theobservation of a two-plane period for Xe in Al is not trivial.C. Aspect ratio of the crystalline Xe particlesWe have also analyzed the distributions of Fig. 3 in termsof the normalized aspect ratio A. In order to improve theaccuracy of measurements, it was defined as �see Fig. 1� A=N100 /2N111, i.e., in terms of the number of �111� and �100�planes rather than corresponding distances.10 For analysispurposes, this normalized aspect ratio is plotted as a functionof the particle volume rather than the number of planes. TheA�V� plot of Fig. 4 exhibits an unusual asymmetry such thatlarger aspects are preferred to the smaller ones, and thespread is decreasing with the particle volume. FollowingGibbs,12 this interesting behavior can be explained by mini-mizing the energy of the Al/Xe interface at fixed particlevolume as follows: The interface energy Eif of a cubo-octahedron can be expressed4 as a function of the aspect ratioand volume,Eif = � 3�111V2/31 − 3�1 − �100/ � 3�111��1 − A�2�1 − 3�1 − A�3�2/3 . �2�Here �100 and �111 are the interface tensions for the corre-sponding planes, �100 /�111=1.05.4 Figure 4�b� demonstratesthat Eif is an asymmetric function of A that naturally explainsthe asymmetry of the A�V� distribution of Fig. 4�a�. Themaximum deviation of A can be found by a simple graphicalprocedure of defining maximum energy fluctuations �hori-zontal dashed line in Fig. 4�b�� and deducing the correspond-ing extremal Ae values for each particle volume. The thusdeduced Ae�V� dependences �dashed lines in Fig. 4�a�� agreewell with the experiment.Note that the total energy of a Xe particle in Al includesseveral terms, such as the edge, vertex, interface, and strainenergies. The former two can be neglected but the latter twoare essential.10 However, in our analysis we have selectedonly the strain energy for Fig. 3�b� and the interface energyfor Fig. 4�a� because of the following reasons: As confirmedby the analysis of Fig. 4�a�, the interface energy �Eq. �2��accounts for the shape �aspect ratio� of Xe particles. It wasnot included in the fitting of Fig. 3�b� �Eq. �1�� because thefigure—for reasons of increasing the experimentalaccuracy—is presented vs the number of planes, and theshape information there is hidden in the difference betweenthe �111� and �100� distributions. On the other hand, minimi-zation of the strain energy �Eq. �1�� explains why certainnumbers of Xe planes are preferred �see Fig. 3�b��. However,strain energy is only a minor high-frequency component ascompared to the interface energy.10,13 It will not affect sig-nificantly the maximum range of the aspect ratio, which isbeing fitted in Fig. 4�a�. Note also that the interface energyalone has been treated semicontinuously �see Fig. 4�b��;1 10051015202530 CrystallineSemi-crystallineAmorphousNumberofparticlesParticle size (nm)4 8 12 16 2005101520253035 (b)(a)(100)(111)fitNumberofparticlesNumber of Xe crystalline planesFIG. 3. �Color online� Histograms of Xe nanoparticles in Al as afunction �a� of the particle size and �b� of the number of Xe �111� or�100� crystalline planes. Note a coexistence of crystalline, semic-rystalline, and amorphous particles in the diameter range 7–10 nm�a�. Details of fitting the �111� distribution �dashed line in �b�� areoutlined in the text.0.1 1 100.40.50.60.70.80.91.0 (a)AspectratioVolume of Xe particle (nm3)0.4 0.5 0.6 0.7 0.8 0.9 1.002468101 nm34 nm38 nm3Surfaceenergy(arb.units)(b)Aspect ratioFIG. 4. �Color online� Top panel: the aspect ratio A, defined inFig. 1, as a function of the volume of the crystalline Xe particles inAl. Bottom panel: surface energy calculated for three particles;minimum energy is set at zero. The energy fluctuations �horizontaldashed line� define the maximal range of A values �A 1�, which ispresented by lines in the top panel.STRUCTURE AND PRESSURE INSIDE Xe… PHYSICAL REVIEW B 78, 064105 �2008�064105-3however, if the �discrete� strain energy is included, then theparticle volume cannot be fixed and a more complex mini-mization approach should be used.10D. Effect of pressure on the electronic transitions in XeparticlesSimilar to optical absorption, EEL spectroscopy probeselectronic structure via electronic transitions induced by theincident electron beam.14 In connection with Xe, it is instruc-tive to consider first a reference gas spectrum14 shown by theblue line in Fig. 5. Three bands are observed, originatingfrom transitions between discrete atomic levels and conven-tionally labeled O23, N45, and M45. In this study, we shallfocus on the two O23 features labeled as A and B.Strong matrix contributions hampered the previous EELstudies of noble gas nanoparticles.5–7 In this paper, matrixsignals were minimized by selecting thin regions where large�up to 40 nm� Xe particles were surrounded by a few nano-meter thin Al layer. A representative spectrum is shown bythe red curve in Fig. 5; it is similar to the Xe gas spectrum;however, an extra broad peak is observed at �20 eV. Thelatter is associated with plasmon excitations and is a uniquefeature distinguishing solid Xe from gas.15 Relative intensi-ties of the A and B peaks varied from particle to particle, butthe comparison of the absolute intensities was hampered bydifferent amounts of Xe. In order to compensate for thiseffect, we have selected isolated round particles and normal-ized their spectra to the particle diameter. Normalization re-vealed �see Figs. 6 and 7� that the intensity of peak A wasconstant but the strength of peak B increased with decreasingparticle size. This observation naturally explains the anoma-lous B /A ratio reported previously.6,7Regarding the origin of this intensity variation, we wouldfirst note that it was independent of the particle crystallinity.Thus the crystal symmetry contribution is insignificant here.Interface effects are important because the ratio of “surface”to “bulk” atoms is larger for smaller bubbles. Therefore, wehave remeasured the spectra of Fig. 6, focusing the �0.1 nmprobe into the center or the edge of the particle, relying onthat many more interface atoms will be sampled in the lattercase. No significant difference was observed, thus suggestingminor role of Al/Xe interfaces in this case. In particular, wedid not observe coupling to the “bubble surface plasmon”possibly because of the larger sizes of our Xe particles��3 nm compared to �1 nm of Refs. 6 and 7�.Continuous variation of the B /A peak ratio with the par-ticle size prompted pressure effects. Therefore we have con-verted the particle size into pressure17 and added a pressurescale in Fig. 7. This procedure revealed quadratic increase inthe B /A ratio with the pressure.In order to assert pressure effects on our EEL spectra it isagain instructive to analyze the Xe gas spectra. The gas spec-trum of Fig. 5 was recorded at low resolution for compara-tive purposes; better resolved spectra are reproduced in thetop part of Fig. 6. They were recorded in another study16 at0° and 90° scattering angles that enhanced dipole-allowedFIG. 5. �Color online� Electron energy-loss spectrum from anamorphous 40-nm Xe particle in Al and a Xe gas reference spec-trum �Ref. 14�, both measured with �0.8 eV resolution. The spec-tra are plotted in a double-logarithmic scale for presentation pur-poses. Symbols O23, N45, and M45 conventionally identify theassociated atomic transitions, while A and B label the peaks used inthe pressure measurements discussed below.7 8 9 10 11 12 13B2B3B1A B6 nm40 nm3 nmXe particlesin Al, 0°0°90°Xe gasEELsignal(arb.units)Electron loss energy (eV)FIG. 6. �Color online� Bottom part: lines and symbols showbackground subtracted EEL spectra from Xe particles in Al with thesizes 3, 6, and 40 nm. Second-order polynomials were used as thebaselines and the spectra are normalized to the particle diameter.Top part: lines show a reproduction of the high-resolution EELspectra from Xe gas �Ref. 16� measured in 0° and 90° scatteringgeometries. The 90° spectrum reveals an extra strong forbiddenpeak B2, which explains the variation of the B-peak intensity withXe particle size.FIG. 7. �Color online� Solid squares present the ratio of B to AEEL peak intensity �see Figs. 5 and 6� as a function of particle size.The latter has been converted into pressure inside the particles usingthe previously reported data �Ref. 17�. Dashed line is a second-order polynomial fit.IAKOUBOVSKII, MITSUISHI, AND FURUYA PHYSICAL REVIEW B 78, 064105 �2008�064105-4and dipole-forbidden transitions, respectively. The selectivityis however not perfect, and the allowed lines appear in the90° spectrum. Those spectra reveal the multiplet structure ofthe peak B dominated by a forbidden line B2 and allowedlines B1 and B3.Because of obvious technical difficulties, pressure depen-dence of EEL spectra has not been studied previously. How-ever, effect of pressure on electronic transitions, regardlessof how they are induced, is well known. In particular, pres-sure mixes the electronic transitions of similar energies; ifone of them was dipole forbidden, then it could become�partly� allowed and its intensity will increase nonlinearlywith the pressure. A representative example is the 0.396 �al-lowed� and 0.401 eV �forbidden� electronic transitions inZnO.18 Moderate pressures ��0.5 GPa� increase the inten-sity of the latter from zero to half of that of the former, andthe increase is quadratic with the pressure. Insignificant lineshift is observed, meaning that for two states to becomemixed their energies do not have to become equal or evenchange much.The above arguments can explain the results of Figs. 6and 7 as follows: Increasing internal pressure mixed B1, B2,and B3 transitions, thus making allowed the forbidden peakB2 and strengthening the integral B peak. This interpretationis supported by the quadratic pressure dependence of theinduced peak intensity �see Fig. 7� and by the shape of the Bpeak �see bottom part of Fig. 6�: At small pressures �particlesize 40 nm�, its flat top suggests an unresolved B1 /B3 dou-blet, while at larger pressures �sizes 3 or 6 nm�, the pointedshape appears as an unresolved B1–3 triplet. Note that the lineshapes are unresolved here possibly not because of the insuf-ficient spectral resolution but because of solid-state andstrain related broadening. Indeed, the B1–3 peaks could not beseparated in solid Xe films even when measured with high-resolution spectrometers.19,20E. Mapping pressure inside individual Xe nanoparticlesThe observations of Figs. 6 and 7 bring us to a remarkableconclusion that electronic properties and pressure in Xenanoparticles can be mapped with a subnanometer spatialresolution of TEM. As a test, we have monitored the pressuredistribution inside Xe particles in Al as outlined in Fig. 8. Itstop part is a HAADF STEM image showing several roundand elongated amorphous bubbles. The latter originated fromincomplete aggregation of individual particles, as revealed inprevious in situ experiments.3 The A and B EEL peaks weremeasured at every image point; their ratio was converted intothe pressure using Fig. 7 and was plotted in the bottom panel.This panel reveals that the pressure is homogeneous in theindividual round bubbles but not in the elongated aggregates.This pressure inhomogeneity could originate from severaleffects, such as residual stresses, incomplete bubble aggrega-tion, or presence of Al or Al oxide membranes separating theparticles.21 The analysis of associated phenomena is beyondthe scope of this paper, and the underlying physics could berelatively trivial. However, the demonstration that electronicproperties of �noble gas� nanoparticles and the associatedpressure effects can be monitored at room temperature withsubnanometer spatial resolution is important.IV. SUMMARY AND CONCLUSIONSCrystalline Xe nanoparticles in Al exhibit unusual distri-butions of their diameter and aspect ratio, which can be ex-plained by minimization of the strain and surface energies,respectively. The particle crystallinity can be associated withthe matrix oxidation, which was neglected previously.Background-free EEL spectra from individual Xe nano-particles demonstrate that the electronic structure of the par-ticles, in the first approximation, does not differ from that ofsolid Xe. However, the relative intensities of the low-energyEEL peaks exhibit systematic changes with the particle sizewell into the nanometer range. This phenomenon is ex-plained by the variation in the internal pressure, which mixesallowed and forbidden EEL transitions thereby altering theirintensities. The relative peak intensities were applied to mapthe pressure inside individual Xe nanoparticles, and nano-meter scale resolution has been achieved. The thus devel-oped approach is not limited to Xe in aluminum and can beapplied to a wide range of nanostructures.ACKNOWLEDGMENTSThe authors are grateful to S. E. Donnelly for a usefuldiscussion. This research was partially supported by Ministryof Education, Science, Sports, and Culture �MEXT� throughthe grant in aid for Young Scientists �B� 2005 17710120-6816, World Premier International Research Center Initiativeon Materials Nanoarchitronics, and the Nuclear ResearchProject.FIG. 8. Top panel: high angle annular dark field image of Xenanoparticles �white features� in Al. Bottom panel: map of pressureinside the particles �in GPa� deduced from the B /A EEL peak in-tensity ratio �see Figs. 6 and 7�. Note that the top left particleexploded during the scan and that the pressure inside the smallestparticles could not be deduced because of the large thickness in thissample area.STRUCTURE AND PRESSURE INSIDE Xe… PHYSICAL REVIEW B 78, 064105 �2008�064105-5*iakoubovskii.konstantin@nims.go.jp1 S. E. Donnelly, R. C. Birtcher, C. W. Allen, I. Morrison, K.Furuya, M. Song, K. Mitsuishi, and U. Dahmen, Science 296,507 �2002�.2 K. Mitsuishi, M. Kawasaki, M. Takeguchi, and K. Furuya, Phys.Rev. Lett. 82, 3082 �1999�.3 R. C. Birtcher, S. E. Donnelly, M. Song, K. Furuya, K. Mitsu-ishi, and C. W. Allen, Phys. Rev. Lett. 83, 1617 �1999�.4 C. W. Allen, R. C. Birtcher, S. E. Donnelly, M. Song, K. Mitsu-ishi, K. Furuya, and U. Dahmen, Philos. Mag. Lett. 83, 57�2003�.5 K. Furuya, K. Mitsuishi, M. Song, and T. Saito, J. Electron Mi-crosc. 48, 511 �1999�.6 A. vom Felde and J. Fink, Phys. Rev. B 31, 6917 �1985�.7 A. vom Felde, J. Fink, T. Muller-Heinzerling, J. Pfluger, B.Scheerer, G. Linker, and D. Kaletta, Phys. Rev. Lett. 53, 922�1984�.8 T. Campbell, R. K. Kalia, A. Nakano, P. Vashishta, S. Ogata, andS. Rodgers, Phys. Rev. Lett. 82, 4866 �1999�.9 U. Dahmen, S. Q. Xiao, S. Paciornik, E. Johnson, and A. Jo-hansen, Phys. Rev. Lett. 78, 471 �1997�.10 J. C. Hamilton, F. Leonard, E. Johnson, and U. Dahmen, Phys.Rev. Lett. 98, 236102 �2007�.11 J. R. Packard and C. A. Swenson, J. Phys. Chem. Solids 24,1405 �1963�.12 J. W. Gibbs, Trans. Conn. Acad. Arts Sci. 3, 343 �1878�.13 Note that for Xe in Al �111�1.05 J /m2, �9 GPa �Refs. 4 and11� but for Pb in Al �111�0.445 J /m2, ��96 GPa �Refs. 9and 10�. Therefore the ratio of strain energy to interface energyis �25 times smaller for the Al/Xe than for the Al/Pb system.14 Transmission Electron Energy Loss Spectrometry in MaterialScience and the EELS Atlas, edited by C. C. Ahn �Wiley, Wein-heim, Germany, 2004�.15 J. D. Nuttall, T. E. Gallon, M. G. Devey, and J. A. D. Matthew,J. Phys. C 8, 445 �1975�.16 A. Delage and J. D. Carette, Phys. Rev. A 14, 1345 �1976�.17 M. Song, K. Mitsuishi, K. Furuya, C. W. Allen, R. C. Birtcher,and S. E. Donnelly, J. Microsc. 215, 224 �2004�.18 E. V. Lavrov and J. Weber, Phys. Status Solidi B 243, 2657�2006�.19 J. E. Demuth, P. Avouris, and D. Schmeisser, Phys. Rev. Lett.50, 600 �1983�.20 K. Wandelt, W. Jacob, N. Memmel, and V. Dose, Phys. Rev.Lett. 57, 1643 �1986�.21 R. J. Cox, P. J. Goodhew, and J. H. Evans, J. Nucl. Mater. 126,117 �1984�.IAKOUBOVSKII, MITSUISHI, AND FURUYA PHYSICAL REVIEW B 78, 064105 �2008�064105-6