Vacuum ultraviolet spectroscopy of high-pressure helium microbubbles in metals

Surface Science 126 (1983) 66-79 North-Holland Publishing Company

VACUUM ULTRAVIOLET SPECTROSCOPY HELIUM MICROBUBBLES IN METALS A.A. LUCAS,

S.E. DONNELLY

OF HIGH-PRESSURE

and J.P. VIGNERON

Institute for Research in Interface Sciences, FNDP,

B - 5000 Namur,

Belgium

and J.C. RIFE Naval Research Laboratory, Received

15 September

Washington,

DC 20375, USA

1982

This paper reviews recent investigations and presents new results on the spectroscopic properties, in the vacuum ultraviolet, of composite materials made of metal containing inert gas bubbles of microscopic size. The basic interest of such systems, from the point of view of Surface Science, lies in the often important role played by the gas metal interface on account of the small size of the bubbles. Three techniques have been used, namely Absorption, Electron Energy Loss and Fluoresence Spectroscopies to study thin film samples. Most of the data presented here concern the helium/aluminium composite containing a few at% of helium. The spectral range explored, between 5 and 30 eV, covers regions where spectral features are assignable either to the metal matrix or to the helium gas. Between 5 and 20 eV, EELS of thin He/AI films reveals, in addition to the usual Al bulk plasmons and AI/AI,O, (boundary) plasmons of the metal film, two new loss continua, in the range 8.5 to 12.5 eV. The first band between 12.5 and 10.5 eV is assigned to spherical bubble plasmons. The assignment of a second, similar broad loss peak between 8.5 and 10.5 eV as being due to oxidized bubble plasmons is still tentative. Between 20 and 25 eV, Absorption Spectroscopy allows detection of the helium resonance line strongly broadened and shifted towards higher energies. The detailed line shape information, interpreted with the help of a theoretical model which will be summarized here, gives access to the density and pressure state of the gas in the bubbles. Such information is relevant to the understanding of the mechanical and other properties of gas containing materials of nuclear technological interest. The paper also reports new data, obtained for the first time, by Fluorescence Spectroscopy in the range 13-25 eV. The fluorescence of the He/AI composite is excited by an electron beam of a few keV energy. The spectrum consists of two broad continua, reminiscent of the emission spectra of high pressure helium gas and of low-temperature liquid helium: an intense band between 600 and 1000 A (21 to 13 eV) and a weaker band from 500 to 600 A (25-21 eV). The strong band and the long-wavelength part of the weaker band are assigned to delayed molecular fluorescence from He; excimers while the short-wavelength part of the weak band originates from prompt, non-self-absorbed atomic emission from the blue shifted resonance level series. The quantum efficiency of the electron-excited bubble fluorescence of He/Sri and He/AI specimen has been found adequate to be exploited in the construction of a new, solid state, VUV light source. Finally the paper presents new spectroscopic results obtained by VUV absorption from annealing and cooling experiments on

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A.A. Lucas et al. / High -pressure

He microbubbles

in metals

61

thin He/Al composites. In the annealing experiments, the resonance hne spectrum exhibits spectacular evolution traceable to drastic alteration of the size distribution of the bubbles as a result of their thermal growth. In the cooling experiment, we have observed, for the first time, spectral changes which appear to be correlated with a gas-solid phase transition in the bubbles. If confirmed by experiments currently underway, this observation opens the perspective of studying high pressure phenomena in inert gases without elaborate high-pressure equipment.

1. EELS spectrum below 15 eV Fig. 1 reproduces a portion of the EELS spectrum from thin Al films [l] either free of He (curve b) or containing 1.45 at% He (curve a) in a uniform distribution of bubbles 50 A in diameter. The features, common to both curves, at 1.5, 6.75 and 15 eV are due to an Al band transition, the Al-Al,O, interface plasmon and the Al bulk plasmon, respectively. The broad shoulder, between 12.5 and 10.5 eV appears to be due to excitation of the multipole series of bubble plasmons whose frequencies are given by

E(O) = -

&es

(I=

(1)

1,2,...),

where e(w) and es are the Al metal and He gas dielectric functions, respectively. In the frequency range under consideration and at the high gas density in the bubbles, one has (see below) es = 1.1 [2]. The solutions of (1) are then close to the usual void plasmon spectrum: they extend from w, = 12 eV for the I = 1 dipole plasmon mode down to w, = 10.4 eV for the I * 1 flat surface modes (the I= 0 mode coincides with the Al bulk plasmon). The EELS

0

2

4

6

6

10

12

Energy

Fig. 1. Electron-energy implanted film with

loss spectra

14 (eV)

below

15 eV of (curve b) nonimplanted

Al film and (curve a),

1.45at% He. The Al bulk plasmon peak heights have been matched at 15 eV.

::,

Relative

energy

loss

probability

Optical

density ~,

Relative

energy probability

loss Optical

density

70

A.A. Lucas et al. / High-pressure

He microbubbles

in metals

shows several lines of the resonance series (1s -+ nP) riding on a broad continuum similar to the absorption spectrum of the same sample. This has been discussed in ref. [I]. The interpretation of the blue shift was guided by the observation of a similar effect in liquid He and the explanation proposed by Surko et al. [lo]. The shift is attributed to a cage effect created around the 2p electron of an excited atom by the pseudopotential repulsion of the 1s’ closed shell of neighboring ground state atoms. The spatially more extended 2P state is raised in energy more than the tight 1s ground state, resulting in a net blue shift. The width of the line is attributed to its inhomogeneous shift in the disordered fluid. The dependence of the line shape on He density is what the experimentalists are trying to exploit in order to give access to the pressure state of the bubbles. Here we want to summarize the theoretical analysis recently advanced by the authors [ 1 l] to account for the observed lineshapes. The line intensity is given by static line broadening theory as the Fourier transform [ 121 (3) where Q(r)

=n/dR

(1 - exp[ -if”,(R)])

g(R),

and where w0 is the unperturbed atomic line position, n the He density and g(R) the radial pair distribution function (RPDF) of the fluid. A,(R) is the interaction energy between two atoms at a distance R. Pair additivity of the interaction is assumed to hold. This interaction is divided into a long-range and a short-range component:

(5)

A,(R)=A’-P(R)i-ASP(R).

The long-range term is the dipole-dipole coupling between the two atoms in the electric field of the incident light wave. To evaluate this term, we write the dynamic polarizability CY(W)of the He atoms, in the vicinity of the resonance frequency, as lx(W)

a0

= 1 -

w”/wf

+a,. -

iwy/w,

(6)

1ye represents the IS --, 2P contribution to the static polarizability of the polarizability due to the reground state whereas (Ye is a nearly constant mainder of the He excitation spectrum. For free atoms the values of these parameters would be a, = e2f/m& = 0.0675 As3 where f = 0.276 is the IS --, 2P oscillator strength [ 131 and cyn = 0.1375 A’ as required by the known value

A.A. Lucas et al. / High-pressure

71

He microbubbles in metals

of the total ground state polarizability (~a + LX~= 0.205 A3 [14]. In fluid, (~a and (Ye may be somewhat different from these unperturbed (6) y is a small width characterizing the relaxation processes of the level in the fluid. With (6) it is easy to show that the dipole-dipole coupling of gives rise to a frequency shift

the dense values. In resonance two atoms

A”,“(R) = ~hw,,tx,T( R),‘[ 1 + cu,T( R)] ,

(7)

where

T(R)=

1 - 3 cos*e R3

cos(k*R),

and where fr - B is the angle between The short range term Asp(R)

R and the light wavevector

k.

= cos*t? ATG( R)

(8)

is the “final state” interaction of the pair of atoms, i.e. the interaction energy of the He; excimer in which the 2p orbital of the excited atom makes an angle 8 with the vector distance R to the ground state atom. A?“(R) is the electronic energy of the D’Z, state as calculated by Guberman and Goddard [15]. The co& factor in (8) embodies our neglect of the interaction energy in the II state configuration (0 = r/2). The A?G(R) energy curve is plotted in fig. 4. Its major feature, in the present context, is the large repulsion hump for R 2 2 A originating from the Pauli principle induced repulsion of the 1s* closed shell of the ground state atom. The overall blue shift at high fluid density will be attributed to this Pauli repulsion effect. Let us firstly discuss the line position as predicted by eqs. (3) and (4) (see ref. [ 1 l] for details). If we expand the exponential in (4) in powers of A,, the first non-vanishing term, introduced back into (3). gives the line position at t~=q,+n/dRA~~(R)g(R)tn~dRA;~(R)g(R).

(9)

To this order, the shifts are also additive. The long-range term in which g(R) can be replaced can be written AoLR = &+,na,j’dR

T( R),‘[ 1 + na,l’dR

by a unit step function

T(R)],

where /’ excludes the origin. The R integral is the z-z Fourier transform of the dipolar tensor [16,17]:

(10) component

of the

(11)

12

A.A. Lucas et al. / High -pressure He microbubbles

in metals

I 4

2

6 Distance

8

(A)

Fig. 4. The electronic energy of the He; excimer in the D’B: (3 SO, 2p) state as reproduced from ref. [ 151.Note the strong repulsion hump for R > 2 A. At large R, the energy coincides with the isolated atom 2P level, taken here as zero energy level.

where E is the 3 x 3 unit tensor and the zero superscripts designate unit vectors. Substituting in (lo), we obtain the result, valid up to first order in n, AWLa=_2

jnna,w,

9

The same red shift the dielectric function examining the role of dielectric function of E&W) = 1 +

(12) expression was obtained in ref. [ 1 l] from an anlysis of of the He gas. This approach is also more convenient for the metal substrate which is not included in eq. (9). The the gas is given by the Lorenz-Lorentz expression [ 161

47VKi( w) 1 -+x(U)

.

(13)

From this, we can discuss the two extreme cases where the bubbles are either much larger or much smaller than the wavelength (600 A). Intermediate cases are not amenable to a simple analysis. If the bubbles are big (they can be prepared with submicron size), the gas in them responds as an infinite medium and the metal matrix plays no role. The absorption coefficient is then proportional to Im ,/w) which has a Lorentzian peak where eg has a pole, i.e. at

A.A. Lucas et ai. / High -pressure He microbubbles in metals

73

the transverse exciton frequency 4nna,/3 1 - 47rnff,/3

i/2

==~a(1 -$mffO), (14) i i.e. the same result as in (12). Thus, in large bubbles or in macroscopic samples, the dipolar effect causes a red shift of relative order 2na, due to the inner Lorentz field. The relevance of this effect for the spectrum of liquid helium [lo] is further discussed in ref. [ 11). For intermediate size or very small bubbles, one cannot neglect the effect of the metal substrate. If, as in most of our samples, the bubble diameters are much smaller than the wavelength and if the bubble volume fraction f relative to total volume is small (say, less than lo%), it is legitimate to analyse the optical properties of the He/Al composite in terms of an effective medium dielectric function [ 18,191

W-W 0 lt

Z(w) =f + 3fi(e, --f)/(fg

+ 2r),

(15)

where C(W) is the metal dielectric function as before. Whereas eq. (13) embodies the inner Lorentz field of the dense He fluid, eq. (15) correctly includes the depolarizing effect of the spherical metal/gas surface in the dipolar appro~mation. The absorption coefficient of the composite around the resonance line is now proportional to

(16) where l = 0.5 is the Al dielectric constant around 20 eV [6]. It has a Lorentzian peak at C,(W) + 2~ = 0, i.e. at the resonance line solution of eq. (1) for I = 1. This is (17) up to first order in n. Hence the overall effect of the long-range term is to give a net blue shift contribution to the line position linear in density and of relative order nag. On that basis alone, and with a reasonable value of (~a= 0.1 A3, say, our typical blue shifts of order 10% (2 eV) would imply densities of order n = O.l/ar, = 1 A-‘, an impossibly high value (16 times Al density!). The conclusion we reach is that the total long-range effect, although relevant for discussing low densities [ 111, is inadequate to account for our bubble data. Turning now to the short range term in (8), its evaluation requires knowledge of a reliable RPDF g(R), since only the near neighborhood of the origin contributes due to the short range nature of ASP(R). For liquid helium, we

14

A.A. Lucas et al. / High -pressure He microbubbles in metals

have used [ 1 l] the experimental g determined by neutron scattering [20]. This allowed us [ 1 l] to reinterpret the experimental VUV reflectivity data on the liquid He surface [lo]. The result was an absorption line having a dipolar red shift of 0.12 eV (from eq. (12)) and a Pauli repulsion blue shift of 0.36 eV, thus adding up to a net blue shift of 0.24 eV, in quite close agreement with the observed line position in reflectivity [ 111. Lacking experimental data on the RPDF g for high pressures and temperatures [21], we have used a theoretical model, namely the Percus-Yevick distribution function of hard spheres. The model was constructed so as to take proper account of the density and temperature dependences [ 111. The end result is a series of curves giving the blue energy shift A&,

T) = nj-dRA;R(R)

g,,(R,

n, T),

(18)

as a function of density n for various parameter values of T. The room temperature curve is shown in fig. 5. For n > 0.03 A it is nearly linear and can be parametrized as A,, (eV) = 31n (wp3)

-0.15.

(19)

Density n (x 1 0z2 cm-3) Fig. 5. The theoretical blue shift, a function of the density, calculated over the excimer repulsion curve of fig. 4.

from a statistical average

A.A. Lucas et al. / High -pressure He microbubbles in metals

15

Thus our observation of a 1.4 eV blue shift in the samples of fig. 2 is indicative of a density of n - 0.05 Ae3, i.e. nearly one He atom per Al vacancy in the bubbles. From the He gas equation of state [22], this corresponds to a pressure of 7 kbar, close to the 8 kbar surface tension pressure 2y/r of equilibrium bubbles of 25 A radius. The work in ref. [ 1 l] further discusses line widths on the basis of eqs. (3) and (4), but we will not repeat the arguments here except to mention that the theoretical widths, calculated from the Pauli repulsion effect, are in fair agreement with observed ones.

3. Fluorescence

spectra

The emission spectrum from a discharge in He gas is well known to consist of sharp atomic lines at low pressures and broad molecular bands at higher pressures, above a few tens of Torr [23]. In the VUV region, the emission spectrum of dense helium is dominated by a broad continuum extending between 600 and 1000 A. It is attributed to transitions, back to the dissociative He, ground state, from quasistable He; excimer vibrational states associated with minima in the potential energy curves similar to the one shown in fig. 4

[151. Recently [24,25], electron-bombarded liquid helium has also been found to emit a luminescence spectrum similar to that of the high-pressure gas. It occurred to us that a similar emission could perhaps be observed from our helium containing composites if these were bombarded with, say, energetic electrons. The idea is akin to that of using energetic inert gas ion projectiles to generate continuous spectra in the VUV from solid targets [26,27]. The important fact here is that large quantities of helium can be trapped into solid materials (up to and beyond 30 at%) in the form of bubbles of controlable size. It should be noted that an Al matrix with 30 at% helium has an average helium density of 2 X 1O22 cm- 3. From the He equation of state [22], maintaining this density in a macroscopic gas container at room temperature would require a pressure of 1 kbar, for which no window with sufficient strength and VUV transparency exist. Thus our bubble-containing metals provide a natural container to hold the gas for a fluorescence or luminescence experiment, provided the optical depth separating the bubbles from the external metal surface is not too large and that an efficient excitation mechanism can be found. Al metal and excitation by electron bombardment were found to be the most favorable arrangement. Indeed Al is notable for its good VUV transparency [6] (absorption coefficient of 0.2 X lo5 cm-’ at 600 A) while electrons of a few keV energy will readily penetrate the metal within the absorption depth. The details of the experiment will be described elsewhere [28]. One typical

76

A.A. Lucas et al. / High -pressure He microbubbles in metals

result for the emission spectrum is shown in fig. 6. In its gross features the spectrum is remarkably similar to the other fluid spectra. The intense peak around 780 A is again assigned to A, B, C ‘2” --) X’Z, transitions. The multi-atom processes [23] of excimer formation necessary for this fluorescence seem to be sufficiently favored by the high density environment to compensate for the decreased lifetimes of atomic excitations. The fact that the radial pair distribution function calculated [ 1 l] for room-temperature, high density gas has its first peak around 2 A, i.e. close to the maximum in the hump of excimer curves [15], may help to understand the ease of excimer formation. The lower band extending between 500 and 650 A is attributed to excimer emission for its upper part and to prompt atomic fluorescence for its lower part, below 600 A. Indeed, the relative transparency of Al in this range and the small optical thickness of the He bubbles allow radiation from the blue shifted atomic resonance line and higher excitation lines to escape from the sample. An absolute quantum efficiency at least of order 1 VUV photon per 10

400

600

800

Wavelength

1

(A)

3

416CI

660 Wavelength

(A)

Fig. 6. The fluorescence spectrum of an electron-bombarded He/AI composite showing intense He; excimer luminescence above 600 A and weaker He atomic fluorescence below 600 A. Fig. 7. Absorption spectra before (curve a) and after (curve b) annealing to 500°C of a He/AI sample with 1.5 at% of He. Note the development of the unperturbed He atomic line at 584 A in the annealed specimen. The transmission electron micrographs of each sample are sketched in the figure.

A.A. Lucas et al. / High -pressure

He microbubbles

in metals

17

incident electrons was determined with a He/Sri sample [28] bombarded with 5 keV electrons. Similar brightnesses were obtained from Al samples, both in thin film transmission geometry and with thick targets in the reflection mode. The light output and a number of obvious advantages over discharge sources were found significant enough to construct and patent a new solid state VUV light source based on the above principles [28,29].

4. Annealing

and cooling experiments

In this section we wish to demonstrate the possibilities offered by VUV spectroscopies for investigating the thermal behavior of the bubbles and their inner gas content by annealing or cooling runs. Fig. 7 illustrates a typical annealing experiment [9] carried out after helium implantation of an Al film. The absorption spectrum before annealing (fig. 7a) is typical of a sample containing 1.5 at% He in a fairly uniform distribution of bubble sizes as confirmed by the Transmission Electron Micrograph sketched in the figure. It consists of a single broad, nearly structureless peak shifted by 1.5 eV and of width 1.3 eV. After annealing to 500 keV the absorption spectrum (fig. 7b) shows a drastic and irreversible change. There is now a sharp peak at 584 A which can unambiguously be identified as the unperturbed atomic resonance line. This line rides on a broad continuum representing the remnant of the previous band. The TEM picture, sketched in fig. 7b, reveals a highly irregular distribution of bubble sizes. In particular the sample contains large, faceted bubbles several hundred A in size which have been able to grow during the anneal by acquiring thermally generated, mobile vacancies. These large bubbles must contain lower pressure helium (a few hundred bars) exhibiting atomic like absorption. The smaller bubbles still present are responsible for the remaining broad continuum. A detailed monitoring of the line shape as a function of annealing temperature is possible and, in conjunction with TEM, should yield new information on the kinetic of bubble growth. Finally, fig. 8 shows a comparison between the braod absorption continua of the same He/Al film sample at room temperature (curve a) and liquid nitrogen temperature (curve b). The lines are strongly blue shifted by as much as 80 A (3.5 eV) indicating the presence of very small high-pressure bubbles, as confirmed by TEM. The transition between curve a and curve b during the cooling run occurs smoothly over the temperature range between 200 and 150 K. As seen from fig. 5, a 3.5 eV shift is characteristic of densities of order n = 11 X 10” cmm3. The theoretical melting curve n(T) recently calculated by Young et al. [22] predicts a fluid-solid transition at 175 K for that density. Thus fig. 8 might be the first ultraviolet spectroscopy observation of a phase transition at high pressure in helium. If corroborated by current experiments, this would constitute a striking confirmation of the capability of VUV spec-

78

A.A. Lucas et al. / High -pressure He microbubbles in metals

IO

Fig. 8. Absorption spectra of a He/Al composite taken at room temperature (curve b). Note the large blue shift (80 A) of the lines indicating high-density in line shape is probably associated with He solidification in the bubbles.

(curve a) and at 77 K bubbles. The change

troscopy to make a quantitative assessment of the He pressure state in gas containing metals. As much as one can judge from the asymmetric line shapes in fig. 8, the cold spectrum appears to be significantly narrower than the warm one. Such narrowing would indeed be expected in the crystalline phase due to a tendency towards reduction of the inhomogeneous broadening characteristic of the disordered phase.

Acknowledgements This work is carried out as a part of the IRIS project supported by the Belgian Ministry of Science Policy. Two of us (S.E.D. and J.C.R.) acknowledge the partial support of NATO in the form of a Research Grant (No. 1970) and one of us (S.E.D.) acknowledges the provision of a European Science Exchange Fellowship from the Royal Society.

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References [I] J.C. Rife, SE. Donnelly, A.A. Lucas, J.M. Gilles and J.J. Ritsko, Phys. Rev. Letters 46 (1981) 1220. [2] M. Lallemand and D. Vidal, J. Chem. Phys. 66 (1977) 4776. [3] J.C. Ashley and T.L. Ferrel, Phys. Rev. B14 (1976) 3277. [4] M. Natta, J. Physique Cl (1970) 53. [5] M. Schmeits, J. Phys. Cl4 (1981) 1203. (61 H.J. Hagemann. W. Gudat and C. Kunz, DESY Report No, SR-74/7, 1974 (unpublished); J. Opt. Sot. Am. 65 (1975) 742. [7] E.A. Stern and R.A. Ferrell, Phys. Rev. 120 (1960) 130. [8] SE. Donnelly, J.C. Rife, J.M. Gilles and A.A. Lucas, J. Nucl. Mater. 93/94 (1980) 767. [9] SE. Donnelly, J.C. Rife, J.M. Gilles and A.A. Lucas, IEEE Trans. Nucl. Sci. NS-28 (1981) 1820. [ 10) C.M. Surko, G.J. Dick, F. Reif and W.C. Walker, Phys. Rev. Letters 23 (1969) 842. [ll] A.A. Lucas, J.P. Vigneron, S. Donnelly and J.C. Rife, Phys. Rev., submitted. [ 12) P.W. Anderson, Phys. Rev. 86 (1952) 809. [ 131 B. Schiff and C.L. Pekeris, Phys. Rev. 134 (1964) A638. (141 R.P. McEachran, A.G. Rijman and A.D. Stauffer, J. Phys. BlO (1977) L681. [15] S.L. Guberman and W.A. Goddard III, Phys. Rev. Al2 (1975) 1203. [16] C. Kittel, Introduction to Solid State Physics (Wiley, New York, 1956). [17] A.A. Lucas, PhD Thesis, unpublished; A.A. Lucas. Physica 35 (1967) 353. [18] G.G. Grandqvist and 0. Hunderi, Phys. Rev. 16 (1977) 35 13. [19] K. Ohtaka and A.A. Lucas, Phys. Rev. B18 (1978) 4643. [20] E.C. Svensson, V.F. Sears, A.D.B. Woods and P. Martel, Phys. Rev. B21 (1980) 3638. [21] The most recent measurements concern liquid helium up to 25 atm: H.N. Rotkoff and R.B. Hallock, Phys. Rev. B, to be published. [22] D.A. Young, A.K. McMahan and M. Ross, Phys. Rev. B24 (1981) 5119. [23] J.R. Samson, Techniques of Vacuum Ultraviolet Spectroscopy (Wiley, New York, 1967). [24] M. Stockton, J.W. Keto and W.A. Fitzsimmons, Phys. Rev. Letters 24 (1970) 654. [25] CM. Surko, R.E. Packard, G.J. Dick and F. Reif, Phys. Rev. Letters 24 (1970) 657. [26] R.S. Bhattacharya, K.G. Lang, A. Scharmann and K.H. Schartner, J. Phys. Dl 1 (1978) 1935. (27) K.W. Hill, J. Comas, D.J. Nagel and A.R. Knudson, Phys. Scripta 20 (1979) 652. [28] S.E. Donnelly, J.C. Rife and A.A. Lucas, submitted. [29] A.A. Lucas, S.E. Donnelly and J.C. Rife, Luxemburg Patent No. 84136 (1982).