R. A. PAEITERNAK AND N. ENDOW
4044
The curves in Figures 1 and 2 also permit the prediction of the bond lengths, Re, of the six hydrides listed in Table I for which no experimental values were found. These are: ASH, 1.53 A; SeH, 1.47 A; SbH, 1.74 A; TeH, 1.67 A; PoH, 1.79 A; and AtH, 1.76 A. It is to be expected that the first two will be the most accurate, since the curve for the third row fits the data better than do those for the fourth and fifth rows.14 It must be stressed that the model which has been proposed in this paper is a rough one, intended only to describe some general features of the A-H interactions. Nothing has been said of the small-scale distortions of the electron clouds from which come the binding forces. Clearly it is not being suggested that hydrogen fluoride, for example, is made up of two spherical charge dis-
tributions side by side. However, this model does provide, it is believed, some physical insight into the structures of these molecules.
Acknowledgment. The author wishes to thank Professor Harrison Shull for his kind support and encouragement and Dr. Norman T. Huff for his comments about this paper. (14) A good idea of the accuracy of these predictions can be obtained by comparing them to the observed A-H bond lengths in the corresponding polyatomic hydrides. These are: AsHs, RO = 1.519 f 0.005 A; SeHp, RO = 1.46 f 0.01; SbHs, RO = 1.707 f 0.005 A; and TeHz, Ro = 1.7 A. (“Interatomic Distances-Supplement,” ref 7.) The results of this comparison are most encouraging, especially when one takes into account the fact that bond lengths in diatomic hydrides are generally slightly larger than in the corresponding polyatomic hydrides.
Sorption of Deuterium at Very Low Pressures by Molybdenum Filmsla
by R. A. Pasternaklband N. Endow Stanford Research Institute, Menlo Park, California (Received July 2 1 , 2966)
The thermodynamics and the kinetics of deuterium adsorption by porous molybdenum films have been studied at very low pressure over a temperature range of 77-373°K. The isobars and isotherms, and isosteric heats derived from them, indicate the existence of at least two adsorption states, one of which is stable only at temperatures below 200°K. The rat,e curves show a corresponding change in character. At all temperatures the sticking probability on the exposed surfaces is high, about 0.5; however, at low temperatures the internal surfaces are reached by flow through the pores and at high temperatures by fast surface diffusion. Consideration of the interrelation between binding energy and activation energy of diffusion strongly suggests that deuterium is adsorbed atomically even in the low-temperature state.
Introduction The sorption kinetics of gases on porous metal films is undoubtedly more complex than on filaments because, in addition to the surface process itself, transport of the adsorbate from the exposed to internal surfaces may be therate-determining step. For this reason the study of films provides significant information on surface mobility and the state of binding of the adsorbed species. The Journal of Physical Chemistry
This paper describes the kinetics and thermodynamics of deuterium sorption by porous molybdenum films; a similar study of nitrogen sorption has recently been published.2 (1) (a) This research was supported by the Research Division of the U. S. Atomic Energy Commission; (b) Sardar Patel University, Vallabh Vidyanagar, Gujarat State, India. (2) R. A. Pasternak, N. Endow, and B. Bergsnov-Hansen, J . Phys. Chem., 7 0 , 1304 (1966).
DEUTERIUM SORPTION BY MOLYBDENUM FILMS
Experimental Section The apparatus and the experimental procedure have been described in detail previously.2 Base pressures in the lO-lO-torr range were obtained routinely, and pressures of about 1 X 10-9 torr could be maintained during the deposition of the films by electron-beam evaporation. I n order to minimize the production of carbon monoxide by the ion gauges in the presence of hydrogen or deuterium (which has been generally observed in ultrahigh-vacuum studies), thorium oxide coated iridium filaments were employed at emission currents at 0.2 ma. Tests in a similar system containing a mass spectrometer had indicated that under such operating conditions both carbon monoxide production and hydrogen pumping were negligible. Deuterium from a lecture bottle (99.5% Dz) was admitted to the gas reservoir through a silver-palladium leak. The adsorption characteristics of deuterium and hydrogen on molybdenum had been found to be identical within the precision of the present technique. 3a Deuterium was used in preference to hydrogen because ion gauge sensitivity and pumping could be determined by passing the gas stream from the unit through a helium leak detector. 3b For the experimental conditions employed, ion gauge pumping was negligible. Four films were studied; they were deposited at liquid nitrogen temperature and annealed at 100" for about 5 min. The temperature dependence of saturation coverage and of the adsorption kinetics was studied primarily by the constant-pressure technjque.*p4 Flash desorption was employed only for qualitative checks, because of the difficulty of establishing a definite final temperature (which critically determines the coverage). For films 1 and 2, the adsorption kinetics and saturation amounts were observed first a t film temperatures of 300 and 373"K, respectively; the temperature was then lowered in steps to 77"K, and at each step the adsorption rates and the increment in coverage were determined. After desorbing part of the deuterium (by raising the temperature of the film), the adsorption experiments were repeated. Both the detailed kinetics and the increments in coverage were well reproducible (see Table I) ; contamination effects became noticeable only about 1 day after film deposition. The same experimental procedure was employed for films 3 and 4, except that they were held at 77°K during the first exposure to deuterium and then warmed to 330°K. The pressure dependence of coverage was investigated by a dynamic approach. The film was saturated with deuterium at a specific, steady-state pressure, defined by constant flow through a small conductance (0.6 1. sec-' of Dz) out of the cell. The gas supply was then cut off suddenly, and the pressure in the cell was re-
4045
Table I: Sorption of Deuterium on Molybdenum Films a t a Nominal Pressure of 2.5 X lo-* Torr" 3
2
4
5
Initial
Adsorption
Initial sticking probability
Amount sorbed, 1014 molecules/cm2
1 2 3 4
Clean film 3 00 273 195
300 273 195 77
0.49 0.20 0.27 0.41
81.0 7.0 18.7 16.0
5 6 7 8 9 11 12
298 255 233 213 195 171 133 87
255 233 213 195 171 133 87 77
0.22 0.18 0.15 0.15 0.13 0.14 0.32 0.27
7.4 5.4 4.0 2.4 3.8 3.4 8.7 2.7
13
301
195
0.39
25.2
14
298
77
0.49
19.1
1
-Temp, Expt no.
10
OK-
The amounts refer to unit geometric areas. 50 pg/cma; true surface area, 36 cm2.
Film 1: weight,
corded continuously. The amount desorbed was evaluated as a function of pressure by integrating the pumpout curves and correcting them for deuterium originally in the cell volume. Except for room-temperature experiments, the gas and film temperatures were not identical, because only the film substrate was thermostated. The data reported here are not corrected for the temperature difference. The error introduced in the thermodynamic function is small; moreover, it has generally been found that the gas temperature has little effect on the kinetics of adsorption on metals. At the end of the runs the true film areas were determined by xenon physisorption as described previously6 and the film weights by chemical analysis (Table 11).
Results Adsorption Kinetics. In Table I the initial sticking probabilities and the amounts of deuterium sorbed are listed for the sorption experiments with film 1, at a pressure of about 2.5 X lo-* torr. Column 1 is the se(3) (a) B. Bergsnov-Hansen and R. A. Pasternak, J . Chem. Phys., (b) B. Bergsnov-Hansen, N. Endow, and R. A. Pasternak, J . Vacuum Sci. Tech., 1, 7 (1964).
45, 1199 (1966);
(4) R. Gibson, B. Bergsnov-Hansen, N. Endow, and R. Pasternak, Transactions, 10th National Symposium, American Vacuum Society, Boston, Mass., 1963, p 88. (5) N. Endow and R. A. Pasternak, J . Vacuum Sci. Tech., 3 , 196 (1966).
Volume 70.Number 1% December 1966
4046
R. A. PASTERNAK AND N. ENDOW
Table 11: Summary of Deuterium Sorption D a t a on Molybdenum Films" 1
2
Film
W b
no.
PC;
1 2 3 4
5:! 26 82
3
A,C cm2
36 32' 20 58
4 A/W, cm2 Irg-1
0.69 0.77 0.71
7 AM/A,
5
6
AM,d
M,C
1014
1014
1014
molecules
molecules
molecules cm-2
M/AM
42 41 22
123 109 41 160
1.1 1.1' 1.1 1.5
2.9 2.7 1.9 1.8
88
8
a The data refer to 1 cm2 of the geometric area. W = film weight. A = true area as determined by xenon adsorption. AM = increment in coverage between 300 and 77°K. e M = deuferium coverage a t 77°K. Derived by comparison with film 1. No experimental data were obtained.
'
COVERAGE
quence number of the experiment; column 2 the temperature a t which the film was equilibrated prior to the run; column 3 the adsorption temperature; column 4 the initial sticking probability; and column 5 the amount sorbed per unit geometric area of the film. The reproducibility in repeat series is within the precision of the experimental technique. I n Figure 1, four adsorption curves are shown; the logarithm of the sticking probability is plotted us. the amount adsorbed per unit geometric area. Two kinetic patterns were observed; curves a and b represent one type, c and d the other. Curve a was obtained when fresh film 1 was exposed to deuterium at 300"K, and curve b when the same film, after equilibration with deuterium at 273"K, was cooled to 195°K. These two curves have the same character and differ only in the amounts adsorbed during the run; the sticking probability is high, and declines very little with coverage to near-saturation. Curve c represents an adsorption run with the fresh film 3 at 77"K, and curve d, a run with film 1 at 77"K, after equilibration a t 195°K. These two curves also have similar characteristics except that the amounts sorbed differ. The sticking probability is initially high and remains so until an amount is adsorbed comparable to a monolayer on the exposed surface ; it then decreases pronouncedly, passes through a flat range, and finally drops rapidly to zero. Sticking probability curves of type a were observed at temperatures of 195°K and higher, and those of type c a t 77 and 87"K, irrespective of the initial coverage of the surface. The initial sticking probability is high a t all temperatures but is somewhat lower for small incremerit in 'Overage '); it 's Of the magnitude found for hydrogen adsorption on a molybdenum ribbon.6 The Journal of Physical Chemistry
-1014molecules
Figure 1. Sticking probability curves of deuterium on molybdenum films, nominal pressure 2.5 X 10-8 torr. The abscissa represents the amount per unit geometric area absorbed during the particular experiment : (a) film 1, adsorption a t 300°K on clean film; (b) film 1, adsorption a t 195°K after equilibration at 273°K; (c) film 3, adsorption a t 77°K on clean film; (d) film 1, adsorption at 77°K after equilibration a t 195°K.
Isobar. The steady-state coverages for film 1 are listed in Table I ; they are in principle smaller than the true saturation amounts, since in the technique employed a sticking probability of 0.002 cannot be distinguished from zero. The deviation may be significant for thick films and particularly at the lowest temperatures where the sticking probability curves flatten out (Figure 1). With this limitation, adsorption is reversible in respect to temperature, and the data represent an isobar. I n Figure 2a, curve a, the averaged isobar for film 1,is plotted in terms of coverage per square centimeter of the true surface; the data for film 2 are shown also, normalized so that the two isobars coincide a t 300°K (Table 11). Close agreement is found over the entire temperature range. The coverage increases with decreasing temperature and approaches a constant value, but increases again at about 150°K. Apparently a second adsorption state for deuterium becomes significant at the lowest temperatures. In the temperature range of 300-77"K, films 3 and 4, which were initially exposed to deuterium at 77"K, show the same characteristics as films 1 and 2. Quanti(6) R. A. Pasternak and H. U. D. Wiesendanger, J. Chem. Phys., 34, 2062 (1961).
DEUTERIUM SORPTION BY MOLYBDENUM FILMS
t
-1
-
i
6.0 -
-
50
4047
10-5 1
(b)
0)
0 3
-
40
L
0 +
I
10'6
3
-
v)
W v)
P
[L
B
Q
I 0-7
w1 3 0 -
a
2
'87°K
I
2 2 0 0
0 1.0
-
1
c 0
L 50
103
150 200 250 300 F I L M TEMPERATURE--OK
L 350 400
Figure 2. ( a ) Isobars of deuterium on molybdenum films, nominal pressure 2.5 X 10-8 torr: ( 0 )film 1, (0) film 2. (b) Isobar of hydrogen on tungsten filaments ( A ) (Hickmotta), p = 2.5 X torr; hydrogen on tungsten films ( 0 )(Brennan and Hayesg), p = torr.
tative data for the four films are summarized in Table 11. The film weights (column 2) vary by a factor of about 3, but the true surface areas ( A ) per unit weight (column 4) are the same within the precision of the measurements, about 70 m2 g-l. (For film 2 no such data could be obtained because of system failure, but the true area is derived by comparison with film 1.) Between 300 and 77"K, the increment of deuterium coverage ( A M ) per square centimeter of the true surface area is identical for films 1 and 3 (column 7). It is somewhat higher for film 4; we suspect that this difference is due to experimental uncertainties. For films 1 and 2 the coverage, M , at 77°K (column 6) is the sum of the increments adsorbed in the temperature series. For films 3 and 4 it is the total amount adsorbed during the initial adsorption at 77°K. The ratio M / A M (column 8) is significantly lower for films 3 and 4. Either equilibrium is approximated extremely slowly when the entire amount of deuterium is adsorbed in one step at 77"K, or else the film structure opens up on interaction with the gas at higher temperatures. A qualitative observation supports either interpretation. When thick film 4 was warmed rapidly to about 200°K after initial adsorption at 77"K, no significant amount of deuterium was released. However, on repeating the desorption experiment after readsorbing deuterium at 77"K, an amount was evolved comparable to that taken up. Knor and Ponec17in a study of hydrogen sorption by annealed, porous nickel films, made similar
01
02
\338"K
\236"K
1
1
I
!
03
04
05
06
AMOUNT DESORBED-
I O l 4 molecules cm-'
Figure 3. Isothermal desorption of deuterium from molybdenum, film 2. The amounts desorbed refer to the true surface area.
observations: at low temperature, the quantity of hydrogen sorbed by a fresh film increased with increasing temperature. However, on subsequent temperature cycling, the same film exhibited a (reversible) isobar which decreased with increasing temperature, as observed in this study. The temperature dependence of deuterium coverage is very similar to that found previously for hydrogen-ontungsten filaments; the coverages reported by Hickmatt* (extrapolated to our experimental pressures) are shown in Figure 2 (curve b). The two isobars can be brought to approximate coincidence by introducing a scale factor of about 2 for the coverage. This factor may be due to different crystallographic orientations and to uncertainties in ion gauge calibration and in the estimated true surface areas of the films. Coverages for hydrogen on tungsten films at 273 and 90°K and a pressure of 10-0 torr, reported by Brennan and Hayes,9 are also marked in Figure 2; they are of the same magnitude as the present data. Isotherms and Isosteric Heats. A series of experimental degassing curves for film 2 at constant temperature are plotted in Figure 3 as log p us. Au, the amount leaving the film during the runs. The data fit straight lines except a t the very beginning, and at pressures in the low lO-?-torr range. The former deviation is due to the finite time required to stop the gas flow; the latter is due to degassing of the walls of the cell, as was shown in blank runs. At any given temperature, parallel curves (7) Z. Knor and V. Ponec, Collection Czech. Chem. Commun., 26, 37
(1961). (8) T.W.Hickmott, J . Chem. Phys., 32, 810 (1960). (9) D. Brennan and F. H. Hayes, Trans. Faraday Soc., 60, 589 (1964).
Volume 70, Number 18 December 1966
R. A. PASTERNAK AND N. ENDOW
4048
TEMPERATURE
I ' I
-
200
400300
I
I
OK
90
00
7
y'
0
0
I
I
I
I
I
1
2
3
4
5
u 12 13
II RECIPROCAL TEMPERATURE
-
0.5
1.0
I
!
I
I
I
1.5
2.0
2.5
3.0
3.5
COVERAGE
4.0
- 10'4molecules cm-*
Figure 4. Isotherms for deuterium on molybdenum, film 2. The coverage refers to the true surface area.
were obtained irrespective of the initial steady-state pressures which were varied by a factor of up to 100. In the degassing experiments, the geometric area of the film was about 300times the areaof the conductance; thus the rate of removal of gas was slow. Furthermore, the adsorption kinetics indicates fast surface diffusion at temperatures of 195°K and higher; thus, virtually uniform surface coverage was probably maintained. We therefore assume that the system passed through quasi-equilibrium states (this is also supported by the independence of the slopes on the initial pressure) ; consequently the degassing curves represent segments of isotherms. By adding to them the appropriate surface coverages obtained from the isobar (Figure 2), the Temkin isotherms'') shown in Figure 4 are obtained. Their slopes are plotted vs. the reciprocal temperature in Figure 5. For temperatures to 195°K they fit a straight line which does not go through the origin. It is doubtful whether this empirical relationship is of fundamental significance; however, the slopes at 77 and 87°K do not fit the pattern; a change in adsorption mechanism between 195 ana 87°K is again indicated. In his flash filament study of hydrogen on tungsten filaments, HickmottBhas obtained data which also fit Temkin isotherms. He assumes, in accordance with a theoretical treatment by Brunauer, et al.,ll that the slopes are inversely proportional to temperature. In the present study the isotherms were determined experimentally over a pressure range of about two powers of ten; a linear extrapolation over the same interval was assumed to be justified. A series of isoThe Journal of Physical Chemietry
1 10-3
OK-'
Figure 5. Slope of the isotherms plotted us. reciprocal temperature.
steres was derived from the isotherms within these pressure limits; they are plotted in Figure 6 as log p us. 1 / T . (The isosteres derived from the isotherms at 77 and 87°K are not shown.) The isosteres are, with two exceptions, determined by at least three points and cover a temperature range of up to 100°K. They can be approximated by straight lines, the slopes of which are proportional to the isosteric heats. The linearity of the isosteres shows that the binding energy is a function of surface coverage only and does not depend on temperature. The isosberic heats are plotted in Figure 7 (curve a) as function of relative coverage, which is expressed as fraction B of the coverage at 195°K and a pressure of 2.5 torr. At B = 1, the isosteric heat is about 15 X kcal; it increases gradually with decrease in coverage. At B = 1.2, representative for the temperatures of 77 and 87"K, the isosteric heat is only 3 kcal mole-'. The pronounced change in slope of the heat curve between 87 and 195°K again indicates a change in the state of binding. Heats of adsorption of hydrogen on tungsten films as a function of coverage have been measured by calorimetry.9*12They are approximately differential heats, which in turn differ only by RT cal mole-' from isosteric heats. The heats measured by Brennan and Hayesg at a temperature of 195°K are also plotted in Figure 7 (curve b); the saturation coverage is taken as unity. The agreement between the two heat curves is (10)M.I. Temkin, Russ. J . Phy8. Chem., 15, 296 (1941). (11) S.Brunauer, K. S. Love, and R. G. Keenan, J . Am. Chem. Soc., 64,751 (1942). (12)0.Beeck, Advan. C&Ul2&3, 2 , 151 (1959).
DEUTERIUM SORPTION BY MOLYBDENUM FILMS
TEMPERATURE-”K
4049
40
250
I
200
1
I
I
1
I
/
I
-
‘I-
2 3
0 4 h
t ‘0.5
-
m
‘
6
7
8 9
IO 2.0
2.5 3.0 3.5 4.0 4.5 RECIPROCAL TEMPER AT UR E OK-’
-
~.OXIO-~
Figure 6. Isosteric of deuterium derived from isotherms.
rather satisfactory in view of the widely different approaches employed in the two studies. It again indicates that the heat of adsorption is a function of surface coverage only and does not depend on temperature or pressure.
Discussion Both the thermodynamic and the kinetic data presented here indicate the existence of a t least two binding states for deuterium, one of which is populated only at low temperatures. This is in agreement with flash filament studies of hydrogen on tungsten moreover, the high-energy state for hydrogen on molybdenum6and on tungsten13-16 has been resolved into a t least two additional states; since these states differ very little in energy, they undoubtedly cannot be observed on films because of their crystallographic heterogeneity. The change in adsorption kinetics with temperature also suggests two modes of binding. Irrespective of the temperature, deuterium is adsorbed on the exposed surfaces at a rate which declines little with coverage (as has been observed for both molybdenum and tungsten filaments). At the higher temperatures, a significant fraction of the adsorbate has a high mobility and is removed continuously to the internal surfaces by surface diffusion; thus, the sticking probability remains high almost to saturation of the entire surface. In contrast, at 77 and 87°K the adsorbate is immobile. Therefore,
the internal surface can be reached only by those gas molecules that hit a pore entrance, the area of which represents only a small fraction of the total geometric area. The observed drop in sticking probability is due to this geometric factor; the gas flow through the pores themselves is rapid.17 A transition from high to insignificant surface mobility at about 180°K has been found in a field emission microscopy study of hydrogen on tungsten. l8 This observation supports our interpretation of the adsorption kinetics. A comparison of estimated activation energies of diffusion with the observed heats of adsorption indicates that deuterium is adsorbed atomically at all the temperatures studied. The average number of surface jumps, n, made by an adsorbed particle between impacts of gas molecules on the same adsorption site is approximately n = 10‘jp-l exp[-(AH/RT)] where AH is the activation energy of diffusion and p the pressure.2 If we postulate somewhat arbitrarily that the adsorption step is rate determining for n larger than 100, the torr is approximately limiting value of AH at p = 55T kea1 mole-’. Moreover, the ratio of the activation energy of diffusion to the binding energy is of the magnitudeof 1:5t01:3.19 At temperatures of 77, 195, and 300”K, the highest activation energies still allowing fast surface diffusion ~~~
~~
~
(13) E. W. Muller, Ergeb. Exakt. Naturw., 27, 290 (1953). (14) P. A. Redhead, Proc. Symp. Electron Vacuum Phys., Balatonfoldwar, Hung., 1962, 89 (1963). (15) L. J. Rigby, Can. J . Phys., 42, 1256 (1964). (16) F. Ricca, R. T. Medana, and G. Saini, Trans. Faraday SOC.,61, 1492 (1965). (17) J. H. de Boer, “The Dynamic Character of Adsorption,” The Clarendon Press, New York, N. Y., 1953. (18) R. Gomer, R. Wortman, and R. Lundi, J . Chem. Phys., 26, 1147 (1957). (19) G. Ehrlich in “Structure and Properties of Thin Films,” John Wiley and Sons, Inc., New York, N. Y., 1959, pp 425-475.
Volume YO. Wumber 12 December 1966
R. A. PASTERNAK AND N. ENDOW
4050
are 4, 11, and 16.5 kcal mole-', and the upper limit for the associated binding energies assuming a ratio of 1 :5 are 20, 55, and 82 kcal mole-l, respectively. Thus, the low surface mobility of deuterium a t 77°K implies that its binding energy is significantly larger than 20 kcal mole-'; deuterium is therefore bound in atomic form, since molecular adsorption cannot be associated with such a high energy. There is little doubt that also a t higher temperatures deuterium is adsorbed in atomic form. The binding AHat)kcal (g-atom),-', can be calenergies, 1/2(103 culated from the isosteric heats AHst shown in Figure 7. They are 53, 60, and 70 kcal (g-atom)-' at 77, 195, and 300"K, respectively, much larger, close to, or smaller than the values estimated as upper limits for fast surface diffusion at these temperatures. Thus, the proposed model for the adsorption kinetics is at all temperatures consistent with atomic adsorption. In an unsaturated layer deuterium exhibits less, if any, surface mobility since the isosteric heat, and therefore the binding energy, is higher. Thus, during the adsorption process deuterium cannot spread uniformly over the entire surface but penetrates the film progressively, since it can move fast only over those surface areas which are already close to saturation. This
+
The J o u d of Physical ChemiStv
picture for the adsorption process implies that the calorimetric heats of adsorption measured on films are not truly differential heats but represent some weighted average. This averaging process should be particularly pronounced at low coverages and/or low temperature and result in experimental heats with a smaller coverage dependence than the true differential heats. Such an effect is noticeable in the data of Brennan and Hayes;s the heat curve at 273°K is steeper than that at 195°K. At 9O"K, when surface diffusion is negligible, the heat is constant over the entire coverage range.
Concluding Remarks After conclusion of this study the preprint of a paper by Hayward, et aL120became available; these authors investigated the sorption of hydrogen by evaporated molybdenum films at low temperatures and pressures. Although the techniques employed and the logic of their approach differ appreciably from the present study, close agreement is obtained in overlapping areas. In particular, the kinetic curves at 77°K and the interpretation of the data in terms of surface diffusion are very similar. (20) D. 0 . Hayward, N. Taylor, and F. C. Tomkins, private communication.
