J . Phys. Chem. 1990, 94, 1937-1944
1937
Reduction of UO,+, by Atomic Hydrogen J. Abrefah,* D. F. Dooley, and D. R. Olander* Materials and Chemical Sciences Division, Lawrence Berkeley Laboratory and Department of Nuclear Engineering, University of California, Berkeley, California 94720 (Received: April 7 , 1989; In Final Form: August 28, 1989)
The modulated molecular beam technique with in situ mass spectrometric phase sensitive detection was used to study the kinetics of atomic hydrogen reduction of hyperstoichiometric uranium dioxide. The atomic hydrogen portion of an incident mixed-collisionless H/Hz beam chemisorbed onto urania surface with a sticking probability of 0.7 f 0.1. A major fraction of the chemisorbed H atom recombined to produce H, gas, and only a small fraction entered the parallel channel leading to water production. Both the recombination and the water production processes were linear with respect to the incident H-atom beam intensity. The recombination step was rapid, but a slow desorption-like step controlled the kinetics of water production. A phenomenological model was fitted to the data.
1. Introduction I n this and the preceding work,' the kinetics of the reduction of hyperstoichiometric urania by atomic hydrogen
are studied by the technique of molecular beam mass spectrometry. I n this method, a beam of reactant gas (hydrogen atoms in this case) impinges on a small spot on the heated surface of the solid reactant. The desorbing reaction product ( H 2 0 ) , along with hydrogen atoms which simply scatter from the surface without reaction, are detected in a free flight by a mass spectrometer which has a line-of-sight view of the reacting surface. Although many ceramic oxides, including U02+x,can be reduced by molecular hydrogen, this reaction is immeasurably small in the molecular beam method, which detects only reaction events that occur in a single reactant molecule collision. The low reactivity is due to the difficulty of dissociating thermal-energy H, on an oxide surface, in contrast to reactive metals such as tungsten, on which dissociative adsorption occurs in more than 1 in 10 H2 impacts. Thus, for reasons of detectability, the surface reaction on oxides has to be assisted by prior dissociation of the H2 into atoms, which are orders of magnitude more reactive than molecules. The primary information obtained in the experiments is the reaction probability, which is the ratio of the flux of water leaving the surface to the flux of impinging hydrogen atoms. When a reaction removes from the surface one component of a twecomponent solid (oxygen in this case), the resulting depletion of this constituent requires replenishment by diffusion from the bulk solid. The overall reaction given by eq 1 may be limited by the kinetics of the surface reaction proper, by bulk diffusion of oxygen to the surface, or by a combination of both these steps. In ref 1, the latter process was investigated. Surface reaction kinetics is the subject of the present paper. The present investigation utilizes the same equipment as the previous work.' An important feature of the experimental method is modulation or chopping of the incident molecular beam before it strikes the surface. This has two objectives. First, the signals received by the mass spectrometer are modulated at the same frequency as the incident beam, and ac or lock-in detection greatly improves the signal-to-noise ratio. Second, modulation in effect time tags the incident reactant beam, and a surface residence time inherent in slow surface kinetics prior to reemission in the form of a product molecule appears in the output as a phase difference between the modulated reactant and product signal^.^^^ The phase lag contains information on the kinetics of the processes occurring on or beneath the surface and can be used quantitatively to test the data against models of the surface reaction. ( 1 ) Olander, D. R.; Dooley, D. F. J . Nucl. Mater. 1986, 139, 237. ( 2 ) Jones, J.; Siekhaus, W.; Olander, D. R. J . Vac. Sci. Technol. 1972.34,
567. (3) D'Evelyn, M. P.; Madix, R. J . Surf. Sci. Rep. 1984, 3, 413.
0022-3654/90/2094-1937$02.50/0
In the previous study,' the incident H atom beam was modulated at a constant low frequency (20 Hz). The phase lag was small, indicating that the experiment was effectively a steady-state one. The only advantage of the modulated mode of operation was improvement of the signal quality. This type of operation is suitable for observation of long-term changes in surface reactivity, from which the coefficients of surface and volume diffusion of oxygen on and in U 0 2 can be determined. Because of low equivalent pressure of the H-atom beam ( lo4 Torr) the surface reaction also contributed to controlling the overall reduction rate. Although the effects of surface reaction kinetics had to be considered in the previous study,' little detail on this aspect of the overall reduction reaction could be obtained because the beam modulation feature of the technique was not fully exploited. In the present study, the modulation frequency is included as a primary experimental variable (along with solid temperature and incident reactant beam intensity) and the phase lag is measured in addition to the reaction probability. This additional information aids in decomposing the overall reaction into its constituent steps and in determining the rate constants for each. Prior knowledge of the contributions of the oxygen transport properties obtained in the long-term transient reactivity study' helps the surface reaction analysis by reducing the number of unknown parameters that must be fitted to the data. It should be noted that two very different time scales are involved in the reaction. The characteristic times of the bulk and surface diffusion steps (i.e., 12/D, where I is a characteristic specimen dimension and D is the appropriate diffusion coefficient) are of the order of seconds to hours.' The surface chemical steps, on the other hand, have characteristic times of the order of milliseconds or less and require beam modulation frequencies in the range 20-1000 Hz to be detected. An example of mechanistic analysis of a very similar surface reaction is provided by Grabke's study of the reaction of H2 with Fe0.4 Here, the mechanism was found to involve the reaction of adsorbed hydrogen atoms (produced by dissociation of H2 striking the surface) with surface oxygen to produce hydroxyl radicals. These were rapidly scavenged by other adsorbed H atoms to produce H 2 0 , which immediately desorbed. In a study of the reduction of the mixed oxide (U,Pu)02 by H2, WoodleySfound the rate to be proportional to the square root of the H2 pressure. This strongly suggests the role of surfaceadsorbed atomic hydrogen produced by the equilibrium adsorption step H,(g) = 2H(ads) for which the law of mass action gives n
a
(PH2)1/2, where n is
(4) Grabke, H. J.; Gala, A. Symposium on High Temperature Gas-Metal Reaction in Mixed Environments; Jannson, S. A,, Foroulis, 2. A. Eds.; The Metallurgical Society of AIME, 1972; page 348. (5) Woodley, R. E. Hydrogen Reduction of Mixed-Oxide Fuel: Reaction Kinetics and Their Application to Fuel Processing, HEDL-TME 75-136, 1976.
0 1990 American Chemical Society
1938 The Journal of Physical Chemistry, Vol. 94, No. 5, 1990
n
Mixed Beam Source
n
0 Quadrupole
f Mass Filter Chopper !l
m
Reference Signal
I
Preamplifier
Phase Shifter, 6
I
Signal Amplitude, S.
Integrator
Figure 1. Schematic of molecular beam experimental apparatus. T h e beam is a mixture of H and H2, and the target is U02+x.
the concentration of adsorbed hydrogen atoms on the oxide surface and P H 2is the hydrogen gas pressure. Use of a predissociated hydrogen beam replaces the above source of surface hydrogen by a direct supply from the beam
-
H(g) H(ads) for which the probability per impact is 7, the sticking probability. The subsequent surface reaction in which H(ads) takes part should be independent of whether the supply is from a molecular or atomic flux. On the other hand, at atmospheric pressures of molecular hydrogen, surface kinetics of U02+xreduction are so fast that the process is completely controlled by oxygen diffusion in the solid.6
2. Experimental Procedure The reduction of the hyperstoichiometric uranium dioxide is investigated in the molecular beam apparatus shown in Figure 1. A complete description of the experimental technique is given el~ewhere,~ including details of the equipment’ and the furnace for generation of the atomic hydrogen beam.* The apparatus consists of three differentially pumped chambers separated by orifices through which the reactant and product gases flow. The mixed molecular and atomic hydrogen beam is generated in the source chamber, which contains a resistively heated tungsten tube ( ~ 2 5 0 0K) containing hydrogen at a few Torr pressure. Under these conditions, the gas is about 30% dissociated. The mixed H and H2 flux from the source tube is mechanically modulated by a rotating slotted disk before passing through a 1-mm collimating orifice into the reaction chamber where the U02+x specimen is located. The collisionless reactant beam of atomic and molecular hydrogen has a diameter of =3 mm at the target surface with an equivalent atomic hydrogen beam intensity of approximately Torr. The H-atom beam intensity a t the surface is determined quantitatively from the measurement of the total gas flow rate through the source tube and a gas-kinetic-theory calculation of the fraction of this efflux which reaches the target.’ A portion of the scattered hydrogen (atomic and molecular) and the H 2 0 product issuing from the uranium dioxide surface are collimated into the detection chamber housing a quadrupole mass spectrometer. This detection axis is specular to the incident beam direction. Both are fixed at 45’. The signal from the mass spectrometer is analyzed by a lock-in amplifier, which derives its reference signal from the chopper motor. The output of the lock-in detector is converted to suitable reaction measures. The H and H2 signals provide a direct measure of the sticking probability of H atoms on U02. The H and H 2 0 signals are treated to yield the apparent reaction probability, t, and the phase lag, 6,of the (6) Lay, K. W. J . Am. Cerum. SOC.1970,53, 369. (7) Abrefah, J. The Reation of Silicon with Atomic Hydrogen by Modulated Molecular Beam Mass Spectrometry, Ph.D. Thesis, LBL-24382, 1982. (8) Balooch, M.; Olander, D. R. J. Chem. Phys. 1975,63, 4772.
Abrefah et al. water reaction product. These reactivity measures are functions of the three experimental parameters; beam modulation frequency, f, the H-atom beam intensity, I , , and the target temperature, T . The urania target is heated by electron bombardment and the temperature is measured by an infrared pyrometer viewing the beam spot on the surface. The experiment is conducted in the temperature range of 383-1293 K, a t chopping frequencies between 20 and 1000 Hz, and with H-atom beam intensities of l .5 X 10I6to 6.6 X 10I6 atoms cm-2 s-l at the target surface. High-purity research-grade deuterium gas, which is further purified by a passage through a palladium filter, is used instead of the common isotope, protium. This is done because the water product (D20) appears at a mass number (20) in the mass spectrometer that is different from the H 2 0 background peak, thus improving the signal-to-noise ratio. However, the generic name hydrogen is used here to refer to either isotope. Three oxygen-excess urania samples, UO2.004, U02.0i5,and U02.03pwere used as well as a nominally stoichiometricspecimen. In addition, a hypostoichiometric sample was prepared by reducing U 0 2 in 1 atm of hydrogen at 2123 K in a separate furnace. At the temperatures of the molecular beam experiments, hypostoichiometric urania exists as a two-phase mixture of metallic uranium and oxide of nearly exact stoichiometry. This specimen did not react with the H atoms. An untreated single-crystal U 0 2 sample of nominal exact stoichiometry reacted with atomic hydrogen. A polycrystalline sample of U 0 2 which was prepared by heating a U 0 2 pellet in H 2 / H 2 0 environment at 1750 K for several hours also reacted with the atomic hydrogen. These nominally stoichiometric U 0 2 specimens (the single crystal and the heat-treated polycrystal) were probably slightly hyperstoichiometry and an O / U ratio of 2.001 was arbitrarily assigned to them. The-reacted U 0 2 specimens were later examined for possible surface contaminants by EDAX (energy dispersive analysis of X-rays) and the results were negative. The bulk O/U values were measured by the ignition method9after equilibration in a CO2/CO atmosphere.
3. Results and Data Analysis 3.1. Characteristic of the Incident Beam. The extent of hydrogen dissociation and the intensity of the H-atom beam issuing from the source oven were determined from the pressure of the room-temperature H2 in the upstream feed line that supplied gas to the system, which was varied from 1.5 to 6.0 Torr. The gas pressure in the tungsten oven is lower than the upstream value and was determined by the pressure drop in the feed line and the temperature and extent of dissociation in the oven. Analysis of this flow system’ permitted calculation of the total gas pressure in the oven, PH2+ PH, where the latter are the pressures of molecular and atomic hydrogen, respectively. These pressures are related by the equilibrium constant for hydrogen dissociation Kd
= pH2/pH2
(2)
The flux of each species from the oven for a free molecular flow through the orifice is given by the effusion formula (3) where A,,, is the area of the hole in the tungsten tube and Toven is the oven temperature. P, and m, are the pressure of species n in the oven and its mass, respectively. H and H2 are denoted by n = 1 and n = 2, respectively. The intensity of the beam of species m striking the target is In= v n / r d 2
(4)
where d is the distance between the source tube and the target (4 cm). In order to verify the accuracy of this calculation, the direct beam was analyzed by a second mass spectrometer located in the ~
_
(9) Hagemark, K.; Broli, M. J Inorg. Nucl. Chem. 1966, 28, 2837.
_
The Journal of Physical Chemistry, Vol. 94, No. 5, 1990 1939
Reduction of U02+*by Atomic Hydrogen
hydrogen sticks to the surface. Since only a small fraction of the latter returns to the gas phase as the water reaction product, the primary process on the surface is recombination of the chemisorbed atoms. Thus the measured sticking probability, 7, is essentially equal to the recombination coefficient of atomic hydrogen on uranium dioxide. The H2+signal detected by the mass spectrometer, Sz,consists of two components, the first arising from the scattered H2 in the incident beam and the second due to molecular hydrogen formed from surface-adsorbed H atoms. The H+ signal, SI,consisted of three parts: the fraction 1 - q of the incident H atoms that scatter from the surface, and the components arising from the fragmentation of the two H2 components by electron impact. The H2+signal exhibited no phase lag with respect to the H+ signal, nor did either signal vary with the frequency of modulation of the incident beam. This behavior indicates that surface recombination occurs in a time short compared to the modulation period. The ratio SI/S2is linearly dependent on the intensity of the H-atom beam. This observation does not prove that recombination is a first-order process with respect to the surface H-atom concentration; it simply reflects the fact that there is no other channel or comparable efficiency for removing hydrogen from the surface. Since the surface recombination step is fast compared to the beam modulation period, a quasi-steady-state analysis of the hydrogen signals suffices. The signals SI and S2 are related to the incident fluxes II and I, and to the desorbed flux of recombined hydrogen, 1/2vIl, by
'"X 0
,-,iri,,,l,
..
I
I
/ I
Figure 2. Calculated H-atom beam intensity at the U 0 2 surface and the measured and calculated H2-to-H flux ratios versus the upstream H2 source pressure.
target chamber on the beam axis with the target removed. The measured output signals for H+ and H2+are related to the fluxes of each species by Sld
= a,'I,
+ a1212
S t = a2212
(5) (6)
where a; is the instrumental factor relating the signal of ion i to the flux of neutral species n in the ionizer of the mass spectrometer a: = K a : o n r i y i ( M n / T n ) 1 ~ 2
(7)
In this equation, K is a species-independent constant, a: is the fraction of neutral species n that produces ion i upon electron impact (Le., the cracking pattern of n ) , an is the total ionization cross section of neutral n, and r i and yi are the transmission efficiency and secondary electron coefficient of the electron multiplier, respectively, for ion i. For quadrupole mass spectrometers, ri is approximately unity for masses up to 20 amu.I0 Values of yi are given by Asano.II The ratio of the species mass number to its temperature in the last term of eq 7 accounts for the density-sensitive nature of the mass spectrometer detector. The ratio of the mass spectrometer signals for the two hydrogen species is obtained from eq 5 and 6
from which the ratio of the H-atom and molecular hydrogen fluxes can be determined from the measured signal ratio of H to H2. The a-factor ratios needed for this purpose are estimated as follows:
-a l = l az2
where the superscript 1 s refers to the scattered atomic hydrogen flux and 2 s and 2R designate the scattered and recombined H2, respectively. Assuming that the scattered H 2 and H fluxes have the same angular distribution as the desorbed H2 flux, which is probable because the surface is rough on an atomic scale, the a factors in eq 9 and 10 are the same form as given by eq 7. However, the effective temperatures of the species leaving the surface are in general not equal to the oven or the surface temperatures. The temperature of the scattered H and H2, T,s and T2s, respectively, depend upon the thermal accommodation coefficient of these two species, while that of the recombined H 2 is probably close to the surface temperature, T . Solving eq 9 and 10 for the sticking probability gives 1-A q = i T z where
2)"'
= (1.0)(0.7)(0.67)(0.7) = 0.33
az2G2Y2
The ionization cross section ratio was taken from ref 10. a l l is by definition equal to unity and a22= 0.98.Io The a-factor ratio accounting for cracking of H2 to H+ is
The a-factor ratios are a 1 2 s / a 2= 2 sa 1 2 R / a 2=2 R 0.015
(14)
a11s/a22 =s0.34 ( T 2 s / T l s ) 1 / 2
(15)
and Figure 2 shows the calculated H-atom flux at the target and the measured and calculated H2-to-H flux ratios as functions of the upstream source pressure P,. Agreement between the observed and theoretical beam intensity ratios is good. 3.2. Hydrogen Atom Recombination on the U 0 2 Surface. Although the molecular hydrogen component of the incident beam simply scatters from the solid, a large fraction of the atomic (IO) UTI Quadrupole Mass Spectrometry M a m a [ ; 1OOC-02; 1977. ( 1 I ) Asano, M.; Kimura, H.; Kubo, K. Muss Spccfrosc. 1979, 27, 157.
The sticking probability was computed for each experiment from the measured signal ratios and the incident beam intensity ratios taken from Figure 2. The temperature ratio in eq 15 was assumed to be unity and TZ in eq 15 was taken to be 2500 K (zero thermal accommodation coefficient of H2), Figure 3 shows the experimental sticking probabilities of atomic hydrogen on U02,001for a 4-fold variation in the incident flux of atomic hydrogen and a 50-fold variation in modulation frequency. The vertical groups
1940 The Journal of Physical Chemistry, Vol. 94, No. 5, 1990 I
I
- 1
0
o/t =
2 001
S,ngie Crystal. Uot H e d t T r P a t e d 2 Polycrystalline Annealed i n H,/H,O
0 O/L' = 2 015 h o t Heal T r e a l e d
1 zoo
fioo
100
800
lion
1200
loop
I
1 1 1
Temperature ( h )
Figure 3. Temperature variation of the experimental sticking probability of atomic hydrogen on UO,,,, (unheated single crystal and H2/H20 annealed polycrystalline samples) for H-atom beam intensities of (1.6-6.7) X I O t 6 cm-, s-' and frequencies of 20-1000 Hz.
0
" .
0
0
8
00.
0
i
where i = ( - 1 ) 1 / 2 and pwis a complex number representing the fundamental mode of the periodic water flux from the surface. The corresponding amplitude of the incident H-atom signal, I , , is real because by definition it has no phase angle. The fundamental mode of the water signal is =
ffwwFw
The alpha-factor ratio in the denominator is given by eq 16, and
Heat Treated
100
(17)
where aWw is the alpha factor defined by eq 7 for production of H 2 0 + from H 2 0 molecules emitted from the surface. Combining eq 9 and I O to give I , and using eq 18 for F,, eq 17 yields
Po l y c r y s t a I I In e I!ra n i a
'! 0 0
= Fw/Il
0
O / l = 2.036
\nl
heavier oxygen and uranium atoms, to which energy transfer is less efficient than on adsorbed hydrogen. However, this explanation must also be rejected because of the absence of beam-intensity dependence o f t at constant temperature. Thus, the trends exhibited in Figures 3 and 4 appear to be a real effect of surface temperature on H-atom sticking on UOz. Figure 5 shows that the sticking probability at T = 858 K is independent of the O/U ratio of the solid, provided that the data for the preannealed U02,0alspecimen are ignored. This is consistent with the data for UOzOlsat 990 K, which are plotted on Figure 3. 3.3. Water Production. The reaction of hydrogen atoms with urania to produce water vapor is characterized by a reaction product vector because the water signal Swexhibits both amplitude attenuation, e , and a phase lag, 4, with respect to the scattered H-atom signal. The lock-in amplifier rejects the dc component of the signal from the mass spectrometer and responds only to the first Fourier component. The reaction product vector for water is defined by
3,
0 0
.
Abrefah et al.
600
Pori
:n.ro
Temperature ( k l
Figure 4. Temperature variation of the experimental sticking probability of atomic hydrogen on untreated U02.036for the same frequency and intensity conditions as in Figure 3 .
of points represent variations in these two parameters. There is no consistent change of sticking probability with beam intensity or modulation frequency within these ranges. The scatter in the data indicate an accuracy of 0.1 in the sticking probability. The data demonstrate distinctly different sticking probabilities sf atomic hydrogen on U02,ml.The polycrystalline specimen, which received a prior high-temperature heat treatment in mixed H20-H2, gave anomalously high 7 values. The untreated single crystal of UO,,,, showed sticking probabilities consistent with that of U02,015. A similar plot for U0,,036is shown in Figure 4. Figures 3 and 4 show a consistent trend of 9 with temperature. This may represent a real decrease in atomic hydrogen sticking on U 0 2 with increasing temperature, but other explanations are possible. For example, the trend may be due to desorption of impurity gases supplied by the vacuum system at high temperature. However, this does not appear to be likely; water, for instance, is easily removed from U 0 2 by vacuum outgassing at 373 K to a level of 10 ppm. Another possible explanation of the trends seen in Figures 3 and 4 is the reduction of the surface coverage of atomic hydrogen at high temperature. At low temperatures, the surface may be completely covered with H atoms, providing an efficient bed for removal of kinetic energy from the incident H atoms and maximizing the sticking probability. As the coverage is reduced at high temperatures, the incident H atoms encounter
(1.4)(0,35)(0.74)(0.32)(
= 0.12
(
(20)
The water cracking fraction, uwwis 0.73,1° the ionization cross section ratio is 0.35,1° and the ratio of the secondary electron coefficients is taken from Asano.I1 The phase lag in eq 19 is the phase difference between the water signal S, and the scattered H signal, SI. The water product signal, S,, changes slowly with time after an initial rapid decrease.' For calculation of the reaction probability t from eq 19, S, values measured in the nearly steady-state period following the initial transient were used. The sticking probabilities needed in eq 19 are taken from eq 1 1 for each experiment, so the variations in this quantity seen in Figures 3 and 4 do not affect the water reaction probability. Most of the experimental data were taken at a fixed temperature of 858 K to investigate the effect of oxygen transport processes on the kinetics of the chemical reaction.' At this temperature, the reactivity decreases very rapidly with decrease in the O/U ratio. For the nominally stoichiometric U 0 2 (which is assigned an initial O/U of 2.001) a small but measurable reactivity is detected. Thus the reactivity quickly approaches zero as O/U goes to 2. On the other hand, the phase lag is not strongly dependent on the surface O/U ratio. The points in Figures 6-9 represent the experimental apparent reaction probabilities and phase lags as each of the principal experimental variables are changed. The curves are fits to the reaction model, which is discussed below. Figures 6 and 7 show an increase in reactivity with temperature increase but the phase lag shows the opposite behavior. The
The Journal of Physical Chemistry, Vol. 94, No. 5, 1990
Reduction of U02+xby Atomic Hydrogen responses of the phase lag and apparent reaction probability to temperature changes are similar to that observed for most simple surface reactions. The H 2 0 product reaction probability and phase lag are not affected by changes in the atomic hydrogen beam intensity. These data are plotted as the vertical groups of points on Figures 8 and 9. There is no systematic variation of the data points with intensity. The frequency response of the apparent reaction probability and phase lag is shown in Figures 8 and 9. There is a small change of apparent reaction probability with increase in frequency. The phase lag, however, changes from 5’ to 60° within the frequency range of 20-1000 Hz, indicating that surface chemical steps have time constants in the millisecond range. 4. Reaction Model 4.1. Phenomenological Description. The model that best fits the data is similar in many respects to the mechanism proposed for the reaction of atomic hydrogen and s i l i c ~ n . ~ .In ’ ~this system it is known that the dangling bonds on the silicon surface exposed to gaseous hydrogen are capped by strongly bound hydrogen atoms. Recombination to form H2 and volatilization of silane take place by reaction of a weakly bound overlayer of hydrogen with this underlayer, which at all times completely covers the surface. In the hydrogen reaction with U02+x,two types of strongly bound hydrogen must be distinguished. That attached to the oxygen in the normal lattice positions, designated as 0,-H, and that bound to the interstitial oxygen which is responsible for the deviation from exact stoichiometry (Le., the x in UO2+,). The latter, denoted by 0,-H, reacts with hydrogen in the weakly bound overlayer to form water; interstitial oxygen lost by this process must be resupplied by diffusion from the bulk. The surface of the solid during reaction consists principally of 0,-H, since the concentration of 0,-H is never more than a few percent of the total oxygen concentration. By analogy to the silicon-hydrogen system, the concentration of the former is taken to be constant at all times. Sticking of atomic hydrogen on the surface is represented by
H(g) -1, H(ads)
(21)
where the sticking probability, 7,is constant and independent of the coverage and H(ads) represents the weakly bound adsorbed hydrogen. Surface recombination proceeds by the reaction of adsorbed H atom and a hydrogen atom in the strongly bound layer attached to the lattice oxygen ion H(ads)
+ 0,-H -% H,(g) + O(surface)
(22)
peak intensity of H-atom beam. The first term on the right of eq 24 is the atomic hydrogen source term due to chemisorption from the beam. The second and last terms account for losses due to recombination and water production, respectively. The rate of the latter is assumed to be proportional to the excess oxygen concentration at the surface, x(0,t) = (O/U)s,,f, - 2. Due to the dominant recombination process, the water-production term is negligible. In addition, eq 24 is simplified by assuming quasi steady state (since no phase lag was measured for the recombination process). Thus, the concentration of adsorbed hydrogen is given by
O(surface)
+ H(ads)
fast
0,-H
(23)
In eq 22, k, is the rate constant for the recombination step, which is linear in the adsorbed H-atom concentration. This feature is necessary to reproduce the linearity observed in the water production reaction. A bimolecular recombination reaction between H(ads) species would have introduced a nonlinearity into the water channel. Since the surface is always saturated with the 0,-H species, its concentration is incorporated into the rate constant k,. The above reaction scheme is consistent with the observed independence of the sticking probability of the stoichiometry of the oxide. The surface mass balance describing the time variation of the surface concentration n ( t ) of weakly bound H atoms is dn/dt = ?I,g(t) - 2k,n
- 2k,nx(O,t)
(24)
where g ( t ) is the square-modulated gating function and I , is the (12) Abrefah, J.; Olander,
D. R. Surf.
Sci. 1989, 209, 291.
(25)
n = I/z~Ilg(t)/kr
The linear dependence of the water product signal on the atomic hydrogen beam intensity suggests a first-order channel leading to H 2 0 in the mechanism. This step is attributed to the addition of adsorbed hydrogen to the surface oxygen interstitials H(ads)
+ 0,-H
H-0,-H
(26)
followed by a slow step leading to the observed product
H-0,-H
kd ---*
H2O(g)
(27)
where k, and kd are rate constants for the above reactions. The surface balance for the H-0,-H intermediate concentration, m(t), is
dm/dt = k,nx(O,t) - kdm
(28)
Bulk diffusion of interstitial oxygen, which supplies the surface with reactant, is represented by the elementary step
D
O,(bulk)
O,(surface)
(29)
where D is the chemical diffusivity of oxygen in the UOZ+*lattice. At the surface, oxygen interstitials were rapidly attacked by hydrogen O,(surface)
+ H(ads)
fast
0,-H
(30)
Oxygen diffusion is governed by
where z is depth from the surface and x = O/U - 2 is the local deviation from stoichiometry. The surface boundary condition for the above equation is
DCu(
g)
2=O
The surface is quickly resaturated by H atoms from the adsorbed layer
1941
kw = k,x(O,t)n = 1/2711g(t)-~(0,t) (32) kr
where n is given by eq 25, and C, is the concentration of uranium atoms in UOz. The boundary condition far from the surface is
x(..,t) = xi
(33)
where xi is the O/U ratio of the bulk specimen (0.001, 0.004, 0.015, or 0.036). Diffusion of oxygen along the specimen surface, which is important in analyzing long-term reactivity changes,’ is not needed in the present analysis. 4.2. Fourier Analysis. The variables g ( t ) , x , and m are expanded as a first Fourier series
+ gleiwr)
(34)
x = xo(z,t) + ,?(z)eiwr
(35)
g = (1/2)(1
m = mo
+ fieiwr
(36)
where i = (-l)Il2, w = 2rf is the modulation frequency in radians/s, and g , = r/4 is the first Fourier component of a square-modulated beam. The subscript 0 denotes the long-term transient concentrations and quantities with the tilde over the symbol are the Fourier components excited by beam modulation.
1942
Abrefah et ai.
The Journal of Physical Chemistry, Vol. 94, No. 5, 1990
80
eo
Y W
a 40
m
m
8
R
20
o S i n g l ? C r y s t a l . > i r l H?nL T r P a t r d e Polycrpstallinr. \ o t Hent Trpntpd
:I P n l y r r y s t a l l i n P . i n n r a 1 i . d
in H,/H,O 0
o s
1
2 s
2
1 5
3
10'/T (K ')
c
02
2 11
11
I n i t i a l 0, I
Figure 5 Sticking probability of atomic hydrogen on hyperstoichiometric urania a t 858 K Ignoring the heat treated sample data (squares), 7
Figure 6. Arrhenius plot of reaction probability and phase lag for UOzml at a frequency of 20 Hz and 4.0 X IOi6 cm2s-l atomic hydrogen beam intensity
shows no significant variation with changes in O/U ratio TABLE I: Sticking Probability and Rate Constants in the Proposed Mechanism Obtained from the Curve Fitting Procedureo
reaction sticking of H branching ratio water release a
constant 7 = 0.73
f 0.12
k,, = (2.8 f 0.4) X lo3 exp(-8 f I / R T ) kd = (3.9 f 0.6) X I O 4 exp(-4 i I / R T ) s-l
The activation energies are in kilocalories per mole
Equations 28, 31, and 32 are algebraically solved to obtain the fundamental mode of the flux of water leaving the surface
The quantity k,, in eq 37 is k w / k r ,which is the branching ratio characterizing the relative rates of the two reaction channels given in eq 22 and 26. The term /3 is
P = 4C"(Do)1i2/qI,kw,
I
i z
1 4
1 8
1 8
2
z z
a 4
a 6
2 8
1 0 P / T ( K ')
Figure 7. Arrhenius plot of reaction probability and phase lag for U02036 at a frequency of 20 Hz and 4.0 X 10l6cm-2 s-I atomic hydrogen beam
intensity
The estimated value of /3 from approximate values of the parameters contained in the above equation is 5 X lo4, which is far greater than 1. Thus, the expression within the parentheses in eq 37 is unity. The water apparent reaction probability and phase lag are contained in the reaction product vector equation
A
(10
o/u =
2.001 40 W
a
2
m 0
m
20
2
Substituting eq 37 into 38 yields the model predictions of c and
4
0
(39) @ =
tan-l ( w / k d )
(40)
4.3. Fitting the Model to the Data. The time-variation of the reaction probability shown in Figures 2-5 of ref 1 depicts a pronounced change in the reactivity only at the initial stages of the experiment, after which the variation becomes small. This decrease in reactivity with time is mainly due to the time variation of the surface interstitial oxygen concentration at the beam spot. Since the decrease in reaction probability during the later part of the experiments is small, the excess surface oxygen concentration x,(O,t) during this period can be represented by a time-averaged values X, without appreciable loss in accuracy. R is obtained by dividing the bulk stoichiometry parameter xi (Le., 0.001, 0.004, 0.015, or 0.036) by a numerical factor, which from Figure 7 of ref 1 is estimated to be = 4. The factor varies from = 8 at the
0 0 001 10
a - ,
,
1
100
--
1000 1
0
Frequency (Hr)
Figure 8. Frequency dependence of apparent reaction probability and phase lag for U02.00iat a temperature of 1293 K and H-atom intensities (1.6-6.7) X 1OI6 cm2 s-l.
center of the beam spot to = 1.5 at the edge of the beam. A range of values of x i / x between 2 and I O were tested to check the sensitivity of the results to this factor. The results show less than 5% deviation of the fitting parameters from the corresponding values obtained when the factor of 4 is used. The results of fitting the model to the experimental data are shown as curves in Figures 6-9 and the rate constants obtained
Reduction of U02+xby Atomic Hydrogen
The Journal of Physical Chemistry, Vol. 94, No. 5, 1990
1943
had been reduced in H2 at high temperature prior to testing, suggests that only the Willis-type interstitial a n i ~ n s lparticipate ~,~~ in the reduction reaction. It appears that the strong bonds between uranium ions and oxygen ions in regular lattice positions cannot be readily broken by atomic hydrogen. Interstitial oxygen from the lattice flows to the beam spot on the surface by diffusion and is converted to Oi-H species by the weakly bound atomic hydrogen present on the surface. This species further reacts with H(ads) to produce the H 2 0 product as suggested by eq 26. However, the first-order recombination mechanism (eq 22) is explained by the H(ads) reaction with a different strongly bound H atom to the lattice oxygen, O,-H. This implication is supported by the high recombination coefficient of hydrogen atoms on the preannealed stoichiometric specimen (upper points in Figure 3) and the hypostoichiometric specimen. The obvious elementary step H(ads)
Frequency (Hz)
Figure 9. Frequency dependence of apparent reaction probability and phase lag for U02,036at a temperature of 858 K and H-atom intensities (1.6-6.7) X 10I6 cm2 s-'.
from the fitting process are listed in Table I. The error limits of the parameters are shown as dashed lines in Figures 6-9.
5. Discussion The sticking probability given in Table I was determined from the water reaction probability data; it is in good agreement with the values shown in Figures 2-5, which were obtained solely from the hydrogen signals. Comparison between the experimental data points and the theoretical model shows good agreement for the frequency dependence of the apparent reaction probability and the phase lag (Figures 8 and 9). The agreement of the experimental and theoretical apparent reaction probability with changes in temperature is quite good (Figures 6 and 7). The theory falls short in predicting accurately the temperature dependence of the phase lag but the curve follows the same trend as the experimental points. The deviation of the experimental phase lag from the theoretical curve is partly due to experimental error in accurately measuring small signals at low temperatures where the water product channel is very weak. This uncertainty is shown as error bars on the experimental data points in Figures 6 and 7. The assumption of an average excess surface oxygen concentration (xo(O,t))about one-fourth of the bulk value (xi) is justified. However, the choice of this ratio affects the prediction for the U02,001specimens more than it does for the specimens with higher degrees of hyperstoichiometry; the small excess oxygen concentration in the nominally stoichiometry material could easily be reduced to near zero at the beam spot. The predicted phase lag, however, is not affected by the choice of this factor. The model analysis predicts a phase lag that is independent of the surface excess oxygen concentration (eq 40). This is consistent with the experimental observation which shows no change in phase lag with changes of the specimen O/U ratio. Comparison of the detailed surface reaction analysis presented here with the long-term reactivity transient analysis in ref 1 is in order. In the latter, the reaction probability at 858 K and 20-Hz modulation frequency was represented by (41) where A was found to be = 24. Using the rate constants given in Table I in eq 39 for these conditions gives A = 9. The reason for this discrepancy is that the determination of the reaction probability in ref 1 did not account for the 1 - 7 factor in eq 19, which omission gave t values a factor of 3 larger than those computed from the raw data in the present study. The assumption in the reaction model that chemisorbed hydrogen reacts with excess oxygen (Le., oxygen above and beyond perfectly stoichiometric U 0 2 ) is borne out by the good agreement between the model and the ensemble of water reaction data. This fact, and the observed inability of atomic hydrogen to reduce the exactly stoichiometric oxide, which is present in the specimen that t
= Axo(0,t)
-
+ H(ads)
-
H2(g)
would introduce a nonlinearity in the water production channel, which is not observed experimentally. H-atom recombination therefore occurs in a linear process (not second order in H(ads)) which does not involve the excess oxygen that supplies the H 2 0 reaction channel. The branching ratio k,, is the ratio of the rate constants of the elementary steps given by eq 22 and 26. The positive activation energy of this quantity given in Table I indicates that breakage of the 01-H bond by the weakly bound adsorbed hydrogen atom and formation of the H 2 molecule requires less energy than removing the Oi-H species from the crystal lattice in forming the waterlike unit designated as H-Oi-H. Neither the nature of this unit nor the type of process that eq 27 represents is suggested by the rate constant kd listed in Table I. The very low preexponential factor rules out simple desorption of bound water from the surface. Such a process should be very fast at the temperatures of the experiments and moreover, should s-I. have a preexponential factor Equation 27 could represent short-range diffusion of the H-0-H unit to a site on the surface from which release is favored. Were this so, the reciprocal of kd would represent the mean time for the surface species to diffuse to the desorption site from its point of creation. At 858 K, the mean lifetime ( T = kd-l from Table I) is 0.3 ms. The surface diffusion coefficient of the H-Oi-H unit is likely to be similar to that of oxygen, which was determined in ref 1 to be D,= 1 cm2 s-I. For these conditions, the mean travel distance is = ( D s ~ ) 1=/ 2200 pm, which is unreasonably large; the grain size of the specimens is less than 20 pm. The remaining possibility is that eq 27 represents a slow process by which the H-Oi-H unit extricates itself from the U 0 2 lattice at the surface, following which escapes to the gas phase occur rapidly. 6. Conclusions The interaction of atomic hydrogen with U02+xresults primarily in recombination of the adsorbed H atoms to release H2. This process occurs on a time scale shorter than a few hundred microseconds and is thus not detectable by the modulated beam method. However, the recombination coefficient, which is essentially equal to the sticking probability of H on UOz, is close to unity (0.7 f 0.1). It is independent of H-atom incident beam intensity and specimen oxygen-to-uranium ratio; however, it decreases with increasing temperature. Recombination is first order with respect to the H-atom beam intensity, a conclusion based upon the linearity of the water-production channel. A minor reaction channel paralleling recombination produces water by attachment of adsorbed hydrogen to the excess (interstitial) oxygen at the surface. The distinct phase lag of the water product with respect to the incident H-atom beam and the manner that the phase lag varies with modulation frequency (13) Willis, B. T. M. J . Phys. 1964, 25, 431. (14) Willis, B. T. M. Nature 1963, 197, 755.
1944
J . Phys. Chem. 1990, 94, 1944-1948
indicate a single, slow, first-order removal process, the nature of which could not be ascertained.
Materials Sciences Division of the U S . Department of Energy under Contract No. DE-AC03-76SF00098.
Acknowledgment. This work was supported by the Director, Office of Energy Research, Office of Basic Energy Sciences,
83-7.
Registry No. H, 12385-13-6; U02,m,,1344-57-6; U02,036r 109676-
Forward and Reverse Energy Transfer in Langmuir-Blodgett Multilayers K . Sienick? DPpartement de Physique-COPL, UniuersitP Laual, QuPbec, P.Q., Canada G I K 7P4 (Received: April 10, 1989; In Final Form: September 27, 1989)
The transport of electronicexcitationsamong chromophoresrandomly distributed in Langmuir-Blodgett multilayers is described. In this theoretical analysis, it has been assumed that excitation energy can be transferred forward and reverse between two-dimensional layers. Fluorescence decays have been calculated for each layer. A numerical analysis of fluorescencedecays is given in order to show the influence of reverse energy transfer on photophysical properties of Langmuir-Blodgett multilayers. The discussion of results in connection with recent and future experimental studies is presented.
(1) Introduction One of the most important functions of the antenna pigments is the collection of light energy from the sun. There are several different types of antenna pigments; chlorophyll a and b in green plants, chlorophyll c in some algae, and bacteriochlorophyll a, b, or c in bacteria. Another important class of pigments is represented by such accessory pigments as carotenoids and phycobiliproteins. It is well-known that, after light absorption by a pigment molecule, the electronic excitation energy is transferred until it is trapped by a reaction center. There has been a large effort devoted to the understanding of mechanisms of energy transfer and trapping by the antenna pigments.l Recently, this effort was enhanced by the search for photochemical molecular devices and an artificial analogue of the biological antenna capable of harvesting solar light. The main objective of supramolecular photochemistry* was to construct an appropriate assembly of molecular components capable of performing light-induced functions. There are several functions that can be realized by photochemical molecular devices, between them (i) generation and migration (or transfer) of electronic excitation energy, (ii) photoinduced electron transport, and (iii) photoinduced conformational changes. Yamazaki et al.3” have studied excitation energy transfer in Langmuir-Blodgett multilayers. In a recent paper3 of those authors, the studies of sequential excitation energy transfer in Langmuir-Blodgett films consisting of sequences of a donor layer (D) and three acceptor layers (Al, A,, A,) have been presented. In the analysis of fluorescence decays mentioned, the authors assumed that two-dimensional energy transfer for four layers is PC APC Cha.’ This moving in one direction, Le., PE assumption is only partially fulfilled for this system because the Forster critical is 63 %, between PE and PC and 61 A between PC and APC. However, the critical radius for reverse energy transfer is 13 A between PC and PE and 44 A between APC and PC. The question arises-is the reverse energy-transfer process really negligible? One of the preconditions for transfer of excitation energy from an excited donor molecule to acceptor molecule is a partial overlap between the donor fluorescence band and the acceptor absorption, which is usually expressed by the spectral overlap integral9
- - -
SCHEME I
where I is the wavenumber, is the molar decadic excitation coefficient of the acceptor, andfD(ij) is the spectral distribution of the donor fluorescence normalized to unity. The spectral overlap integral is related to the critical distance RODA, corresponding to the donor-acceptor separation at which the probability of emission is equal to the probability of energy transfer, and is given by
where ( x 2 ) is a factor depending on the mutual orientation of the transition moments of the interacting molecules, a,, is the quantum yield of donor fluorescence, and N’is the number of molecules per millimole. One can easily see that for some molecules a similar precondition described as above could be also fulfilled for reverse energy transfer from acceptor to donor molecule. As an example, the respective critical radii for PE and PC molecules have been given above. Recently, we have theoretically studied the problem of forward and reverse energy transfer in the presence of energy migration.I0J1 ( 1 ) Biological Events Probed by Ultrafast Laser Spectroscopy; Alfano, R. R., Ed.; Academic: New York, 1982. (2) Supramolecular Photochemistry; Balzani, V., Ed.; Reidel: Dordrecht, The Netherlands, 1987. ( 3 ) Yamazaki, I.; Tamai, N.; Murakami, A,; Mimuro, M.; Fujta, Y. J . Phys. Chem. 1988, 92, 5035. (4) Tamai, N.; Yamazaki, T.; Yamazaki, I. J . Phys. Chem. 1987, 91, 841. ( 5 ) Tamai, N.; Yamazaki, T.; Yamazaki, I. Chem. Phys. Lett. 1988, 147, *c
42.
IDA =
Jmf~(V)
t ~ ( D ) 3 -dt, ~
(1.1)
’
Present address: DEpartement de Chimie, Universite du Montreal, Montreal, Quebec. Canada H3C 337.
0022-3654/90/2094- 1944$02.50/0
( 6 ) Yamazaki, I.; Tamai, N.; Yamazaki, T. J . Phys. Chem. 1987,91,3572. (7) Abbreviations: PE, phycoerythrin; PC, phycocyanin; APC, allophycocyanin; and Chla, chlorophyll a. For more description, see ref 8. (8) Grabowski, J.; Grantt, E. Photochem. Photobiol. 1978, 28, 39. (9) Forster, Th. 2. Naturforsch. A . 1949, 4 , 321.
0 1990 American Chemical Society
