The physical adsorption of helium on solid argon, krypton and xenon

SURFACE

SCIENCE 44 (1974) 389400

THE PHYSICAL

ADSORPTION KRYPTON

o North-Holland

OF HELIUM

Publishing Co.

ON SOLID ARGON,

AND XENON

T. J. LEE Science Research

Council, Royal Observatory,

Edinburgh EH9 3HJ, U.K.

Received 2 January 1974; revised manuscript

received 9 April 1974

The physical adsorption of helium on solid argon, krypton and xenon has been studied experimentally in the range 4-5.2 K. Physisorption energies are derived by fitting the Arrhenius rate equation to experimental measurements of the desorption rate of He as a function of temperature. These energies are 1260 J mole-l, 1270 J mole-l and 1540 J mole-l for He on A, Kr and Xe respectively. Changes of the gas density in equilibrium with the condensed rare gas substrates during temperature cycles indicated that helium diffused into and out of the bulk of these substrates.

1. Introduction Special problems arise in consideration of monolayer and submonolayer films of atoms and molecules of low mass adsorbed on solid surfaces at low temperatures. For example, the quantum mechanical zero-point energy is of the same order of magnitude as the adsorption potential and this must be accounted for in calculations of the adsorption energy. High zero-point energy may also give rise to high surface mobility. Diffusion of adsorbed species between the surface and bulk of a substrate gas layer may occur rather easily. These factors are usually neglected in studies of physisorption of heavier molecules but previous experiments and those reported here show that they must be considered for light atoms. Theoretical studies of adsorption energy I-4), mobility293) and heat capacitys) of adsorbed layers have been made. Some experimental work also has yielded results for adsorption energies and heat capacities of helium filmslp6). The isothermal techniques used in such measurements required high area substrates, such as copper sponge, which are possibly very different from the surfaces pictured in theoretical models. To complicate the picture some workers adsorbed monolayers of argon on the high area substrates. This is a puzzling procedure since many more atoms than the nearest neighbours interact with an adsorbed helium atom. In the experiments reported in this paper the substrates were many monolayers of rare gas condensed on a single smooth copper surface. Adsorption energies were derived from 389

T, J. LEE

390

measurements of the desorption rate of adsorbed helium at temperatures between 4 and 5.2 K. At these temperatures the vapour pressure above submonolayer helium films was in the range 10-‘2-10-8 tort-; much lower desorption rates would be difficult to measure. By performing experiments at the lowest practical temperatures, diffusion effects are minimised. The adsorbate and substrates chosen for this first series of experiments were helium on rare gas solid films. A number of quantum theoretical treatments have been made for helium on rare gas solids and the experimental results reported here should prov:de a useful basis for evaluating the success of these theories. 2. Experimental

apparatus

The apparatus used for these experiments has been described previously7). The liquid helium cooled surface on which the substrates were condensed was the internal surface of a copper cylinder open at one end, the total area of this surface being 3.3 x 10F2 m2. A liquid nitrogen cooled blocking plate close to the open end of the cylinder had a central orifice through which gas was introduced. Other symmetrically placed thin orifices led to gas density measuring instruments, these being a magnetic deflection mass spectrometer (AEI-MSIO) and a bent beam ionisation gauge*). The geometry was such that only molecules from the helium cooled surface impinged on these orifices. The temperature of the condensing surface could be held at any temperature in the range 1.6 to 5.3 K by maintaining the appropriate pressure above the liquid helium reservoir. A germanium resistance thermometer, accurate to better than 0.01 K, was used to monitor the temperature of the cryostat. Known quantities of substrate gas or helium were injected onto the cooled surface by a calibrated gas handling system. An automatic system controlled the flow of gas and recorded the experimental observations on punched

paper tapelo). 3. Solid rare gas substrates

The formation and structure of condensed gas films has been reviewed recently ll). Rare gas solids condensed on the basal plane of graphite show preferred orientation but only xenon is distorted into registry with the graphite at the interface, the misfit of lattice being small for xenon. In subsequent layers the strain is faulted out and the normal bulk structure is assumed except near crystallite boundaries, where imperfections are present. Rare gas crystals also grow on amorphous substrates. On amorphous carbon substrates, rare gas solid fifms of the order of 10 nm thickness give rise to electron diffraction patterns consistent with normal

PHYS~CALADSORPTIONOF

He ONSOI_ID A,KrmmXe

391

crystal structure and lattice spacings 1s) Small crystallites are formed at low deposition temperature which recrystallise when the films are warmed. Similar results were observed when the substrate was a single crystal of silver, with the exception that for krypton the texture was influenced by the substrate at high deposition temperature. Little experimental data is available for adsorbed rare gas layers about a monolayer thick or less. On graphite, xenon forms a two-dimensional crystal structure determined by the substraterl). The characteristics of single monolayers of rare gas adsorbed on metal crystals are not predi~able~3). In the experiments described here, between 100 and 3000 monolayers of each rare gas were condensed on a plane copper surface at about 3 K. These layers should be sufficiently thick for any interfacial strain to be faulted out in the weakly bound solids, leaving small crystallites with bulk structure bounded by defects. All influence of the substrate beyond possibly causing a preferred orientation should be screened out in the first ten monolayers. This kind of substrate is completely different from a monolayer of gas condensed on a finely divided substrate where the structure of the gas layer is influenced by the substrate and the potential presented by the interacting rare gas and substrate to an approaching helium atom would be difficult to calcuiate. 4. Measurements Conventional ultra high vacuum techniques were used to evacuate the system to below lo- 9 torr, radiation shields were cooled with liquid Nz and the cryostat was filled with liquid helium. The temperature control system was set to maintain the cryostat at a constant temperature and the substrate gas to be studied was deposited until the desired thickness was achieved. Substrate thicknesses of several times XOzOmolecules rn-’ were used, as experience has shown that for condensed gas layers of thickness greater than -2 x IO”+)molecules m-’ the adsorption~desorption properties are independent of thickness?). Helium gas at room temperature was then injected in pulses 15 set long at a Aow rate of 1Ol6 moIecules m-2 set-‘. After 2 or 3 x IO’s molecules m- 2 of helium inflow, gas injection was interrupted and the temperature of the cryostat was raised to above 5 K and then lowered to about 3.5 K with data records being taken at intervals of 0.05 K or less, throughout this procedure. This cycle was sometimes repeated before further helium deposition took place. Gas injection was recommenced for a similar duration and one or two temperature cycles performed. In the first five columns of table 1 the substrate gas, its thickness and temperature of growth, the temperatures at which hefium was deposited and the surface densities of helium for which temperature cycles were performed are listed,

WOI x E'I

0~01 X P'6

rsor x P'I

osO[ x 9'1

6201 >:L.1

OEOI x 0'1

~01 X 6'Z SPO[ x E'Z

OLII

55[1

OZLI

OOSI

OZEI OOSI

ozzr

GLZI

0851

082.1 SZff OZEI

OEEI

6ZO1 x o'z

rcO[ x 1'1

OEO[ x ['E

OCOI x I'E

scO[ X 8'1

2x01 x 2'1

ZSOI x 8'1

oaor x Z'Z

IEOI x P'I

LZO[ x 6'E

8201 x Z't'

szO[ x 97

6201 x SP

0911

OSEI

OIZI

0611

OZEI 09ZI SSEI OKI OPSI 09LI

Off1

OLEI

SLEl SZEl SOPI

6101 x 9'1

6101 x

ST01 x p'z

8101 x 6'P

6101 x ['I

6101

~~01 x 5'8

LlOI x S'8

8T0[ x 0'2

JV

W

xx

JX

EI 511

SL OOPI 1'1 E'S

reO[ x I'Z

6101 x 9'1

6101 x Z'I x

S'P

SP

6101 x Z'[ 8101

x

1'1

~101 X 8'1

8101

x

9'1

OS‘S

P’f

Z'E

1201 x IE'[

a201 xzp'z

S8'Z

PB‘Z

*JV

*‘V *“V *“V

ax

ax ax

ax

ax

ax

JX JX

JV

JV

W

8101 x L'9

JO3 SJal~~~~~d qlMoJ9

JV JV

810[ x L'9

ES'E

8101 x P'I

ZZOI x SL’Z

"N

(&l.lsmolq

WWsqns

8101 x 6'2

9 pm

(T-IO" f)

SZ’E

*JV

6201 x S'Z

0151

OSZI

0811

6101 x ['I

O’S

6901 x P‘Z

ozzt

szO[ x E'9 O&O1 x 9'2

OIZI

8101 x s-t’

8pooo'O

~~01 X 6'L

OvIf

OEO[ x t"t'

9wo

LIFO PIOO.0 8'1

szO[ x 5'1

O[Z[

O&O1 x 6'8

LI‘O

8

LE’O SE OE oz OOE

8801 x 6'0

OLII

o&+01>:p'8 oeO1 x 9'1

"N

srO1 xo'z

P'I

EVO EP’O

6201 XO'Z

OPZI

SZOIX P'I

9'1 5'1 820'0

MO1 x P'E

OPZI

8201 x 6’Z ~01 X L.6 8201 x 8-Z

o'[

EE'O

6L0'0

0201 x I'L

LI'O

6.2 SS'O

0201 x 9'Z

SLZI OIEI OIEI 5991

8500'0

Z'I 11'1

~01 x 6'[

B

(r-[owr) (l-~sz--~ swoP)

0-f

O'Z SO'1

OLZI OS9 I

YlYN

al2.x uoqdJosap 01 s1y30 s$[nsa;r ayl pue sxitq umyaq [ Tlsv.J

0201 x 8'6

9

E'P

reO1 x 5'1

6201 x Z'I

810'0 8So'O ESOO'O

i &

9'1 PZ

oz.0

suo!lenba

(r-x T-3asz_w suro4e)

06

">NIN

d3Nz~O[/"N

ZL’O

2 m

PHYSICAL

ADSORPTION

OF ik

ON SOLID

A, Kr ANDxe

393

5. Sticking coefficients Sticking coefficients of helium on each substrate were measured in the manner described by Chubbra). During gas injection the gas density in the gauge rises above the equilibrium value due to reflection of molecules by the substrate. The relationship between this rise in gas density, the reflection coefficient and the known rate of helium injection was computed for the experimental structure using Monte Carlo techniques and assuming that free molecular flow conditions apply. Hence the fraction of molecules which stick could be computed. The method is most accurate for high values of sticking coeficient, for the lower values measured here it is about f 0.02 and relative values are accurate to &-0.005, For He on argon its value was 0.480 throughout the range of coverage investigated. For krypton the sticking coefficient was initially 0.380 and it increased to 0.410 at the highest coverages. In the case of xenon, the corresponding values were 0.370 and 0.470. The temperature of the incident helium gas was 290 K. 6. Variations of gas density with temperature fn all cases the variation of helium density as the cryostat temperature was cycled followed a similar pattern. This is illustrated in fig. 1 on a logarithm of hehum density against reciprocal temperature plot. As the temperature is increased at a uniform rate from the temperature at which the helium was deposited, point A, the gas density rises as shown. At B the temperature is held constant and the gas density falls to about half its highest value in about 20 sec. On decreasing the temperature the logarithm of the density falls linearly with reciprocal temperature until D where it deviates along the path D to E. Changes in temperature in the region C-D lead to reversible changes in density. In cases where a second cycle was performed the data does not retrace either of its former paths during the increase in temperature, but after initial rise in density follows a nearly linear relation until the temperature again reaches the peak value; on decreasing the tem~ratur~ the variation is close to that followed during the first decrease in temperature. Under conditions of equilibrium the gas density, n, in a gauge at uniform

NO~P.Yra table 1. The substrate, the. cryostat temperature at which it was grown and its density are shown in columns 1-3. The substrate temperature during helium deposition and the quantity of helium injected averaged over the substrate area, IV,, are in coXumns 4 and 5. Values of E and Nv from eq. (2), R=Nuexp(-EJkT), with v constant are in calumns 6 and 7, E and ~k/~ from eq. (2) with v -==kT/kare in columns 8 and 9. Values of Nv/lW of N should not be greater than either iVS or NCP for su~rmobile adsorption. Comparisons with the tatter can be seen in the last two columns.

394

T. 3. LEE

Fig. 1. Typical variation of helium gas density in a gauge with reciprocal cryostat temperature for a fixed number of helium atoms condensed on a rare gas substrate. The solid lines indicate regions where changes are reversible and values of density do not vary with time. Broken lines indicate regions where changes are not reversibfe and can show time dependence.

temperature is related to R, the rate of desorption of atoms from the surface by the equation R = &nyF, (1) where E is the mean molecular speed at the temperature of the gauge and y the sticking coefficient. ff the desorption rate, R, of helium from the rare gas substrates is governed by first order kinetics then: R = NV exp(-

E/kT),

(3

where N is the surface density of helium, E is the desorption energy,v is a factor with dimensions of frequency, k is 3oltzmann~s constant and T is the temperature of the surface. Both E and v will depend on T but only slowly compared with the exponential. To discuss the form of the curve in fig. I they will be regarded as constants. For fixed values of N, eq. (2) predicts that the logarithm of the measured gas density varies linearly with l/T. Such regions exist in the experimental data, that in fig. 1 being depicted by the full line C-U. Additional evidence that N is substantially constant is, firstly, that the line can be retraced by increasing and decreasing the temperature within limits, and secondiy, no variations in gas density with time at constant

PHYSICAL

ADSORPTlOON

OF Hie ON SOLID

A, Kr AND

xe

39.5

temperature are observed in the region C-D. On the other hand, changes in density with time do occur in ot,her regions (those shown by broken lines). Adsorption energies can be calculated from the data for which N is constant by fitting desorption rate equations. The time dependent temperature variations, like the decrease in derrsit,y at 3, are thought to be ca,used by rearrangement of the helium adsorbed on the surface with time. Possibilities are; diffusion of heEum into and out of the bulk substrate; a con~~~rational change of the adsorbed helium, e.g. formation or destruction ofclusters; the redistribution of helium over the internal surfaces of the cryopump~ and, the transport of helium from the internal to the external surfaces of the cryopump. A qualitative explanation of the experimentally observed behaviour can be constructed in terms of these ideas. In particular, the variation ofgasdensity with temperature during second {and subsequent) cycles for a given quantity of injected gas is indicative of difl’usion from surface to bulk at high temperatures and from bulk to surface at low temperatures. This implies that the solubility of helium in rare gas solids increases with temperature.

Tn the fastsectionit was pointed out that both E and v in eq, (2) have some dependence on temperature, De Boer’s) discusses three cases for which v would take different values. Firstly, the adsorbed atom is free to translate and rotate on the surface and kT% hv,, where v, is the frequency of vibrations normal to the surface (- 10” see-‘); in this case v= \ta and the assumption of constant v in eq. (2) is pertinent in this case, Secondly, free ratationand translation, but kT4 hvf, i.e. all the atoms are in the ground state. Here v=kT/h; this is likely to be the case for helium adsorbed on rare gas solids (since the zero point energy is appreciable, the condition is better expressed as kT%%t*, - E,, nib-e EQ is the zero point energy)_ Thirdly, when translation and rotation are hinderer, hv>kZ Fig. 2 shows those portions of the experimentaI data for Re on Ar from which adsorption energies are obtained. Here log(nF/4) is plotted against reciprocal temperature. The points follow straight lines within the sensitivity of the experiment showing that the temperature dependence9 of tr and E are indeed weak, If E is assumed to be constant, then eq. (2) cau be fitted to the data in fig, 2 and to similar data for Kr and Xe substrates to yield values of E and N or NIcT*//?.Wnfortunately, because of the possible redistribution of the adsorbed helium discussed in the last section, the value of N is not known. Without rcdistribution, N would be approximately equal to the total number of helium atoms i~t~~du~ into the apparatus divided by the surface area of the condensing surface. This average density N, is listed in column 5 of table 1. The adsorp-

396

T. J. LEE

I .I8

I

.I9

I

.z

1

I

.22

.23

I

..21 I/T in

.24

(K-I)

Fig. 2. Desorption rate of helium atoms from an argon substrate as a function of reciProcal surface temperature for different amounts of injected helium. (0) 144, (0) 2.88, (A) 6.66, (0) 11.2, and (0) 16.2 x 1017 atoms m-2.

tion energies and pre-exponentials derived from least squares fits to eq. (2) with v constant are in columns 6 and 7. Those derived from least squares fits to eq. (2) with v = kT/h (second case) are in columns 8 and 9. Note here that ordinates in figs. 2 are log(nE/4) and that adjustment must be made for non-unity sticking coefficients via. eq. (1). A value of 0.6 was used to arrive at the numbers in columns 7 and 9; this is the measured value for He at 77 K on argon. It is used since the interface between the gas density measuring instruments and the cold surface is at 77 K and should be approximately the same for all substrates, as the 290 K sticking coefficients show little variation. The standard errors in the fits are + 5% for the energy and f 1 order of magnitude in the pre exponential. Diffusion effects did not allow measurements at high densities to be used and consequently the error in gas density values is the major one.

PHYSICALA~S~RP~~O~OF

Adsorption

energies

the total quantity

from column

of helium injected

He

ONSOLID

A,Kr~zwXe

6 are plotted (column

in fig. 3 as a function

5). The error bars indicate

397

of the

standard error (about ? 5%) for each measurement. As the quantity of helium increases the desorption energy decreases for all substrates. The values for argon and xenon at the lowest coverage, probably about 1% of a monolayer, are high and almost certainly pertain to adsorption sites at defects which must be abundant in rare gas solids condensed at 3 to 4 K. Adsorption energies measured for quantities of helium injected between 2 and 7 x IO” molecules rnT2 are considered to be adsorption energies of helium atoms on the regular portions of the surface because there is no significant difference in energies when helium quantities are doubled within this range in the cases of argon and krypton, and the number of helium atoms injected form less than one

Number of

Fig. 3.

He

atoms injected per M2

Dependence of desorption energy on number of helium atoms injected per rnz of substrate: (0) annealed A; (A) unannealed A; (x) unannealed Kr; (+) unannealed Xe.

monolayer. OnIy one value from xenon was obtained in this range. In a later experiment it was possible to check that adsorption sites influenced the low coverage results. The apparatus had been adapted in order to maintain the substrate at temperatures between 4 and 30 K. An argon layer was condensed at about 5 K and then annealed at 30 K to remove defects before starting measurements on helium adsorption. Values of desorption energy and other parameters from these measurements are listed in the lower part of table 1 and plotted in fig. 3. Here, even for injected quantities lower than those for the annealed films, no high binding energy is measured and the values of binding energy are much the same as those measured for intermediate quantities of helium on the unannealed layer. This is evidence for

398

T. J. LEE

the existence of sites on unannealed substrates. Experiments were not performed for annealed films of krypton and xenon. At the higher surface densities the adsorption energy decreases as the density increases for all three substrates. These decreases in binding energy at higher coverages could be caused by two mechanisms, repulsive interactions between the adsorbed helium atoms which increase as the mean separation between atoms decreases, or a reduction in the attractive potential of the substrate due to the presence of helium atoms in or near the surface. The latter would occur if diffusion into the bulk takes place. That the number of atoms on the surface is not equal or related to the number of atoms injected into the cryostat is apparent from the experimental curves in fig. 2. For two similar binding energies, the desorption rate at a particular temperature can differ by about an order of magnitude for a twofold change in number of helium atoms incident on the condensing surface. If all the atoms incident on the substrate remained on the surface then the desorption rate would be proportional to the number of atoms injected (over a region of constant binding energy). 8. Pre-exponential

factors

Because of difficulties discussed above, iV, the surface density of adsorbed helium atoms, was not known in our experiments and hence it is not possible to make a full analyis of the pre-exponential terms. However N cannot be greater than that observed from the total amount of helium injected nor much greater than the substrate surface density. Highest values of the latter are 8.0, 7.2 and 6.0 x IO’* atoms me2 for argon, krypton and xenon respectively. By comparing the experimental pre-exponentials (standard error of + 1 order of magnitude) with these densities multiplied by suitable choice of v=10t2 in column 11 and v=k/h in column 12 it is found that (1) the pre-exponentials for argon and krypton are compatible with the super-mobile case, except for the high binding sites on unannealed argon, (2) for xenon results indicate restricted mobility except for helium coverages probably greater than one monolayer. This result is rather interesting since restricted mobility has been predicted for He on Xe3, “) but not for Kr or A. 9. Physical adsorption energies The adsorption energies of helium on the regular portions of our surfaces are those values which are insensitive to the coverage of helium, that is to variations of Na, N2 and N,, whose values are listed in table 1. For argon and krypton, average values of E, (table 1 column 8) are taken since from the discussions in the previous section it seems that eq. (3) is appropriate to

two cases. The values are 126UJ mnl-” for He on A and 1270 S moI-” for He on Kr, The average value for aanealed argon (A*) is a little greater than that for the unannealed case, which could be a consequence of the difference in temperature range af the two experiments. It is of the crdcr of accuracy of our experiments (&S%>. For He on Xe, the value of Ezr is40 J moi-l ) is used since eq, (3) is not an adequate representatkm.

these

Ross and stedeq deriued a value of 920 J mol-f From ex~r~m~~tal ~sot~~r~nsand a caaforimeter method for the adsorption ener~ of helium on TiU, powder coated with a ~n~~~~a~~~of argon. The isotherms of McCorr&k et al.6) indicated that the ads~~ti~~ energy of helium on ~~~o~~~oat~d copper sponge was less than that measured in the experiments reported here, This chscrepancy could be due to the difficulties mentioned in the introdwcm tion and the section on rare gas substrates, or could arise from mixing helium and argm in the monokyer substrates at higher pressures than those used in the pressssab~~~~r~rnents= ~~~e~~a~~~~sof the ~te~ct~o~ ~~~~t.~a~ between IzeJium aad rare @ks sotids hare been performed by surnrn~~~ the Van der Waafs ~ntera~t~o~s over ~~~~~t~crystaX lattices 1,a+“-)_The three dimensional ~chr~djn~r ~qu~~~#~for the helium atom in the ~ote~~t~a~field is then sofved using various spproxinations. Energies of the funda~~~~~~~‘bound state are found to be 792 3 mol-’ for We on A(lOO) by Ross and Steeler) (1961) and 806 J mol-’ by Nolfen~ bath and Salpeter2). The cislculations of Ricca et a1.3) give values of 1043 J xrrol-r and 1267 J mol- ’ for He on Kr (100) and Xe(lOO)a) and 1519 J moi”” for He on Xe(l10)4)_ Our ~~~~rnen~~ value 1540 J ~01~~ fcrr h&m on xenon is very close to the last c&se. Theoretic& adsorptioa ene-rgies oa A@ HI> and Krff 10) wouZd be e~t~rne~~ interesting if a~~~~a~~~. ShotaXd these agree with our ~x~e~~~~~ta~ values, and the trends shown in the zesults obtained so far indicate that this is probabk~ there ~~o~~dbe a. good case For performjng ex~r~rn~~~~sin which as welt as ~easurj~~ a& sorption energies the surface str~~c~u~ecan be monitored and ~rha~s controled,

Physical adsorption energies have been measured for He on solid A, Kr at~d Xe. Yihe thick substrates, low temperatures and surface densities in t&t? e~~e~~~~~~~s provide conditions which for the first time approach the t%eoreticatl mod& used for cakufation~ of” ~~sor~t~on energy. Satj~fa~~~~~ a~r~~,rn~~~has been found between ok res:suftsand some qua~~rn ~beo~~~c~~

400

T. J. LEE

calculations of adsorption energies. The desorption rate equation appropriate to supermobile adsorption is found to be applicable to He on A and Kr but not to He on Xe. Acknowledgements This work was performed while the author was a Senior Research Fellow of the Royal Observatory, Edinburgh as part of a low temperature laboratory astrophysics project financed by the Observatory. Laboratory facilities were provided by the U.K.A.E.A., Culham Laboratory. The author is grateful to L. Gowland for his assistance with the experiments and to J. N. Chubb for discussions of the experiments and their results.

References 1) M. Ross and W. A. Steele, J. Chem. Phys. 35 (1961) 862. 2) 3) 4) 5) 6) 7)

8) 9) 10)

II) 12) 13) 14) 15)

D. Hollenbach and E. E. Salpeter, J. Chem. Phys. 53 (1970) 79. F. Ricca, C. Pissani and E. Garrone, J. Chem. Phys. 51(1969) 4079. F. Ricca and E. Garrone, Trans. Faraday Sot. 166 (I 970) 959. T. L. Hill, J. Chem. Phys. 14 (1946) 441. W. D. McCormick, D. C. Goodstein and J. G. Dash, Phys. Rev. 168 (1968) 249. T. J. Lee, J. Vacuum Sci. Technol. 9 (1972) 257. T. J. Lee, in: Proc. Third Intern. Cryogenic Engineering Con& Berlin, 1970 (Communications from the Royal Observatory, Edinburgh, No. 107) p. 388. J. C. Helmer and W. H. Heyward, Rev. Sci. Instr. 37 (1966) 1652. J. N. Chubb and L. Gowland, Vacuum 17 (1967) 449. J. N. Chubb, L. Gowland, I. E. Pollard and E. K. Sinton, in: Proc. Fourth Intern. Vacuum Congress, Manchester, 1968. J. A. Venables and C. A. English, Thin Solid Films 7 (1971) 369. A. E. Curzon and A. T. Pawlowicz, Proc. Phys. Sot. (London) 85 (1965) 375. L. D. Schmidt, J. Vacuum Sci. Technol. 9 (1972) 882. J. N. Chubb, Vacuum 20 (1970) 477. J. H. de Boer, Vacuum 16 (1967) 309.