J. Phys. Chem.
1248-1252
I. Eisele, R. Lapple, and L. Kevan, J . A.m. Chem. Soc., 91, 6504 (1969). 1. Elsele and L. Kevan, J . Chem. Phys., 55, 5407 (1971). T. Huang, I. Elsele, and L. Kevan, J. Phys. Chem., 78, 1509 (1972). L. Kevan, “Physics and Chemistry of Ice”, F. Whalley, S. J. Jones, and L. W. Gold, Ed., The Royal Society of Canada, 1973, p 156. J. B. Verberne, H. Loman, J. M. Warman, M. P. de Haas, A. Hummel, and L. Prinsen, Nature (London), 272, 343 (1978). P. P. Infelta, M. P. de Haas, and J. M. Warman, Radiat. Phys. Chem., 10, 353 (1977). C. H. Seager and D. Emin, Phys. Rev., 2, 3421 (1970). P. Hobbs, “Ice Physics”, Clarendon, Oxford, 1974. N. F. Mott and H. S.W. Massey, “The Theory of Atomic Collisions”, Clarendon, Oxford, 1965, p 90. J. M. Warmnn and M. 6. Sauer, Jr., Int. J . Radiat. Phys. Chem., 3 , 273 (1971). (37) 0. E. Mogensen and M. Eldrup, Phys. Lett. A, 80, 325 (1977). (38) M. Eldrup, J . Chem. Phys., 84, 5283 (1976).
0. E. Mogensen and M. Eldrup, J . Glaciol., 21, 85 (1978). 0. E. Mogensen and M. Eldrup, Risb National Laboratory Report No. 366, 1977. M. Eldrup, 0. E. Mogensen, and J. H. Bilgram, J. Glaclol., 21, 101 (1978). M. Kopp, Thesis, Zurich, 1972. J. H. Bilgram, J. Roos, and H. Granicher, Z . Phys. B , 23, 1 (1976). F. Whalley, S. J. Jones, and L. W. GOM, Ed., “Physics and Chemistry of Ice”, The Royal Soclety of Canada, 1973. J. E. Bertie, H. J. Labbe, and E. Whalley, J . Chem. Phys., 50, 4501 (1969). B. Bullemer, I.Eisele, H. Engelhardt, N. Riehl, and P. Seige, SolM State Commun., 8, 663 (1968). H. G. Gillis, N. Klassen, and G. Teather, prlvate communication. G. Nilsson and P. Pagsberg, private communlcatlon. J. J. Weiss, Nature (London), 215, 150 (1967). K. H. Schmidt and S. M. Ander, J . Phys. Chem., 73, 2846 (1969).
Mechanism of Formation of Visible-Absorbing Excess Electrons in Crystalline Ice near 273 K Hugh A. Glllls,” George G. leather, and Carl K. Ross Division of Physics, National Research Council of Canada, Ottawa, Canada K I A ORB (Received July 17, 1979) Publicatlon costs assisted by the National Research Council of Canada
In pulse radiolysis experiments a strong dependence of yield of evi; in crystalline D20at temperatures near 273 K on dose per pulse has been found; thus at 244 K the initial yield increased by a factor of 9 in going from 5.3 to 0.17 krd per 40-11s pulse. This dependence is interpreted in terms of competition kinetics; the precursor of evi; can either react with another irradiation product or can drop into a vacancy present at equilibrium concentration to form evi;. The decay kinetics of ei; were investigated between 95 and 166 K to see if this species could be the precursor of evi;, but no definite conclusion could be reached; within this temperature range eb- appears to react with another radiation product present at a higher concentrationbut at temperatures above 166 K the decay is too fast for us to follow.
Introduction Irradiation of crystalline DzO ice leads to the production of two types of localized excess electron.’ One type (evi;) has an absorption band in the visible, the other (ei;) in the infrared, and the two types show rather different effects, on their yields and decay kinetics, of temperature, accumulated dose, dose per pulse, and doping with certain additives.l In pulse experiments the yield of evi; goes through a minimum around 230 K as the temperature is lowered from the melting point, and the steepness of the drop between the melting point and about 250 K for both crystalline D20 and H 2 0 has been commented on by a number of authors. Thus Mozumder* calculated the thermalization length of electrons in ice from the Onsager formula by taking the yield of e,g reported by Taub and Eiben3 to be the yields of electrons escaping geminate recombination. He calculated shorter thermalization lengths at lower temperatures which is an unexpected trend and opposite to that observed in liquids. Nilsson e t ala4considered that the observed electrons are only a fraction of the total escaped electronic charge, and this fraction steadily decreases as the temperature becomes lower. They decided that the missing electrons are trapped as diolectrons or in some other way. Shubin et ale5interpreted the temperature dependence of the yield of evi; as being due to a competition between recombination of electrons with positive ions and localization of electrons, with localization having an energy threshold. The inter0022-3654/80/2084-1248$0 1.0010
pretation of Razem and HamW is similar except that they considered that the rate constant for localization is given by the sum of activated and activationless terms. On the other hand, Taub and Eiben proposed that evi[ results from an electron interacting with a preexisting binding site,3and thus that the electron is a trap “seeker” rather than a “digger”. Similarly, in an earlier publication from this laboratory,’ it was concluded that at temperatures close to the melting point the trap which gives rise to ehis probably a vacancy present at equilibrium concentration before the pulse, although at much lower temperatures the vacancy trap is produced by the radiation. In addition in a very recent publication, Verberne et al. consider that ehresults from trapping at a preexisting site at temperatures above 193 K.7 In this paper we report a strong dependence of yield of evis-in crystalline D20at temperatures near 273 K on dose per pulse, which we interpret on the basis of a competition between recombination of dry electrons and their dropping into vacancies, the concentration of which is temperature dependent, to form evi;. However, the yields of e& extrapolated to zero dose still show a strong temperature dependence which we cannot explain a t present. Experimental Section The method used for growing DzO crystals and the irradiation procedures were very similar to those already described;l one difference is that in this work temperature
0 1980 American
Chemical Society
The Journal of Physical Chemistry, Vol. 84, No. 10, 1980
Excess Electrons; in Crystalline Ice
"
k',I
'1249
- I 80
-1.85
,-1.90 0 W
5-1.95
-2.00
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-;!lot
0
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000
,
,
,
1
2
3
, 4 TIME,
,
,
5
6
**a
I
2 - 3 0 5 7 8
ps
Flgure 2. Decay of absorption at 650 nm in pure crystalline D 2 0 ice. Pulse length = 40 ns: (A)dose = 2.47 krd, T = 244 K; (e)dose = 2.47 krd, T = 269 K.
sometimes used and in measuring yields it was necessary to correct for some decay during the pulse. We do not understand the decay kinetics of e ~but - in agreement with others3v4we find that the initial half-life depends strongly on dose and therefore the decay is not predominantly geminate. Empirically, for 40- (and lo-) ns pulses, when was measured more precisely and conveniently with a log OD at 650 nm is plotted against time, there is a rapid Hewlett-Packard 2802A digital thermometer rather than initial decay followed by a linear portion extending for at with a thermocouple. Absorption in the visible and in the least a few microseconds (see Figure 2). The rapid initial infrared was followed with an EG&G SHS-100 silicon decay does not seem to be related to a spectral shift bephotodiode aind a Barnes A-100 room temperature InAs cause, in an experiment at 252 K, similar initial decay rates photodiode, respectively; the characteristics of these dewere found at 550,650, and 800 nm for the same dose per tectors have 'been described.8 Signals from the optical pulse. We define OD, as the OD at mid-pulse estimated detectors were fed into a Tektronics R7912 transient diby a short linear extrapolation of the initial rapidly degitizer, the output of which in turn went to a Digital Equipment Co. 9 computer for storage and proce~sing.~ caying part of the curve and OD, as the OD extrapolated to the mid-pulse time from the linear slower portion of the The dose/pulse was varied at constant pulse length by plot of log OD vs. time. The ratio OD,,/OD,, is indeplacing various thicknesses of aluminum plate between the pendent of dose/pulse, the same for 10- and 40-ns pulses, end of the electron beam tube and the sample. Considerable care was taken in this work to ensure that and it does depend on temperature (OD,,/OD, is 31.16, the previously reported effect of accumulated dose on e& 1.11, 1.07, and 1.05 at 244, 252, 259, and 269 K, respectively). So for the 300- and 1600-ns, pulses, OD,, was yields1 was always very small, and therefore the yields for estimated by measuring OD, from a plot of log 01)vs. evis- reported here pertain to previously unirradiated time and by taking OD,,/O6,, from these results with crystals. Crystals were annealed by heating to about 263 K after they had received a maximum of 30 krd, and frethe shorter pulses. quent checks were made to verify that crystals that had If there happens to be a lot of decay before our first received 30 krd after being annealed gave essentially the observation time of about 15 ns after the start of a 10-ns same yields of e ~as- previously unirradiated crystals. For are too low, pulse, so that our estimates of OD,,/OD,, measurements of yields and decay curves of ek-, the same our conclusion that the initial yield of e, depends strongly checks were made but the maximum dose received by a on dose/pulse (see below) would still be qualitatively crystal before annealing was 10 krd. correct because of the independence of OD,,/OD,, on the dose per pulse. Also this independence means that the Results initial fast decay seen in Figure 2 cannot be due to the tail 1. Yields of e& at 73 K. In the previous publication1 of the geminate decay of evl[ seen at 73 K.' The initial on crystalline D20 ice from this laboratory it was reported fast decay could be due to a minor reaction of evi; with that at 76 K G E is constant within experimental error one species, such as a rapidly diffusing hydrogen atom, (&lo%)for a variation of dose/pulse of a factor of 4.5. We while the main slower decay reaction is due to reaction !with have repeated these measurements and extended the range another species, such as relaxed D30+. of dose/pulse slightly to a factor of 8.1 (0.36-2.90 krd) for Figure 3 shows yields of evl[ for crystals at 244 K as a 10-ns pulses. The results are plotted in Figure 1;we see function of dose per pulse for pulse lengths of 40,300, and that within experimental error over this range of dose/ 1600 ns. It is seen that the yield of en[ depends both on pulse there is neither a variation in yield (at mid-pulse Gc dose per pulse and the pulse length. = 7200 f 350 at 650 nm) nor in initial half-life. The Figure 4 shows the reciprocal of the yield of em- plotted temperature of the liquid nitrogen bath, through which against dose per pulse at four different temperatures, lwith helium was bubbled to prevent boiling, was more accuthe pulse length constant at 40 ns. rately measured in this work as 73 f 1 K. 3. Order of Decay of e,;. With the aim of determiining 2. Yields of cui; at Temperatures near 273 K. Most if e,- could be a precursor of evl; at higher temperatures of the work reported here was done with 40-11s (at half(see below), decay curves for e,- were measured at two or maximum) pulses, but 300- and 1600-ns pulses were more values of dose per pulse at each of several temperFlgure 1. Decay of absorption at 650 nm in pure crystalline D 2 0 ice at 73 K. Pulse length = 10 ns. Times are measured from the beglnnlng of the pulse: (0) dose = 2.90 krd, C = 1; (a)dose = 0.67 krd, C = 4.3; (A)dose = 0.36 krd, C = 8.1.
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The Journal of Physical Chemistry, Voi. 84, No. IO, 1980 500 -
0
DOSE ( K r o d s l / P U L S E
Initial (mid-pulse)yields of e, measured at 650 nm, at 244 different pulse widths: (A)300-ns wide; (0) 1600-nswide; (0) 40-ns wide.
Ftgure 3.
K for various doses with
1
1
I
I
I
I
1
,
.
rn
200
400 600 TIME ( n s )
800
J
Flgure 5. Secondorder plots for decay of ek-,measured at 2300 nm. Concentrations of e, and its reaction partner are assumed to be equal and different in A and B, respectively. Times are measured from the beginning of the 4 0 4 s pulse. T = 149 K. In both A and B, for B, dose = 1.4 krd; for 0, dose = 6.9 krd. In B, for B, A is taken as 4 X and k is calculated to be 4.2 X 10" M-' s-'; for 0, A is taken as 9 X loT3and k is calculated to be 3.8 X 10'' M-' s-'.
TABLE I: Yields of eh- in D,O Ice Extrapolated to Zero Dose /Pulse
--
T,K
10-4Gea 0.87 1.19 1.54 1.82
244 252 259 269 a
Measured at 650 nm.
G
2.32 2.22 2.08 1.65
0.38 0.54 0.74 1.10
Taken from ref 4.
between dropping into a trap such as a vacancy (0) to form evis-or reaction with a radiation product which we designate as X:
e-- + X
k2 --.+
no evi;
(2)
It follows that 0' 0
1
I
2
I
3
I
4
I
5
11 6
DOSE (Krods)/PULSE
Figure 4. Reciprocals of yields of e",;, measured at 650 nm, as a function of dose per pulse at different temperatures. The pulse length was 40 ns.
atures. Figure 5 shows the results obtained at 149 K. Measurements could not be made reliably above 166 K because the initial half-life for decay decreases to the point where the response time of the InAs detector interferes with the measurement.
Discussion 1. Yields o f e v i l as a Function of DoselPulse. The yields and decay kinetics of evi; from the irradiation of crystalline D20 at 73 K are independent of dose per pulse (Figure I), as required by the two-step spur mechanism suggested for its f0rmation.l At temperatures of 244 K and higher evi; no longer decays predominantly by geminate recombination, since it has been observed previou~l?~and we find in this work that the initial half-life for decay depends strongly on the dose in the pulse. The results shown in Figures 3 and 4 indicate that, for a constant pulse length, the yield of e ~ ; also depends strongly on dose per pulse at temperatures of 244 K and higher. This suggests that the precursor of e ~ -which , we indicate here as e-, undergoes a competition
1 = - l + MXI G(e&) G(e--) G(e-)k,[a]
(3)
For [XI = ai,where i is the current during the micropulse (see below) and a is a proportionality constant - -1 - - l + kzai (4) G(e~;-) G(e-) G(e-)kl[o] Equations 3 and 4 are strictly correct oniy if the relative concentrations of 0 and X remain constant during the reaction, which would happen for example if both [o]and [XI are much larger than the initial [e-]. Equation 4 indicates that a plot of l/G(evi;) or 1/G( e ~ - )against t i or dose per pulse for constant pulse length should be a straight line, and Figure 4 shows that in fact, for 40-11s pulses, reasonably linear plots are obtained for temperatures between 244 and 269 K. G(e-) at a particular temperature can be obtained by dividing the reciprocal of the appropriate intercept of Figure 4 by the value of t a t that temperature. Values of E were taken from ref 4 to obtain the values of G(e-) given in Table I. These E'S should be considered somewhat uncertain since they are based on the following assumptions: (a) For crystalline H20tmagis the same as for hydroxide -HzO glasses at 77 K, i.e., 2.0 X lo4 M-l cm-l*l0 , (b) The oscillator strength is temperature independent for the crystals; (c) In the crystalline phase replacement of H20 by D20 increases emax
Excess Electrons in Crystalline Ice
The Journal of Physical Chemlstry, Vol. 84, No. 10, 1980
ln-=-C
I\
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0.7
C
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I
\
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1 I
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4 0.31 u
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i
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Flgwe 6. Plot of log (intercept/slope) against 4.
7-l
41
for the data of Figure
by 28%, just as it does in the liquid phase. The G(e-)'s of Table I should represent the yields of free electrons, i.e., those that escape geminate recombination. Even the G at 269 K is somewhat less than the G of escaped solvated electrons in water, which is about 2.7. These G's should be more appropriate to use in calculating thermalization lengths than the less accurate data of Taub and Eiben3 that were used by MozumderB2However, our decrease in G(e-) is still too great to be explained by the Onsager relationship, i.e., calculated thermalization lengths decrease with decrease in temperature. Equation 4 indicates that'the slopes and intercepts of Figure 4 are related by the relationship intercept - _-k1[oI --
-
dope k2a A plot of log (iintercept/slope) against 1/T should give a straight line, from the slope of which one should be able to calculate the Arrhenius parameter E, where E = El AHfororm,~ - E2 if a is independent of temperature, where El and E2are the activation energies of reactions 1 and 2. Figure 6 shows a plot of log (intercept/slope) against 1/T, from the slope of which E = 10.5 kcal mol-' or 0.46 eV per molecule. E2is expected to be very close to zero (X may be D30+,D, or OD) and El is expected to be small (perhaps 0.1-0.2 eV), so that this result indicates that pHfornoN 0.3-0.4 eV. AHfomO has been estimated at 0.5 eV on the assumption that it should be very close to the heat of sublimination of water.ll However, more recent estimates are 0.3-0.4 eV from the rate of self-diffusion in ice12and 0.28 f 0.07 eV from an investigation of the annealing behavior of y-irradiated ice by positron annihilation techniquc!s.13 SO the slope of Figure 6 seems to be about right foir the mechanism proposed. An upper limit to the heat of formation of a vacancy can be estimated from the observation that for a 36-krd 1600-11s pulse, G Efor evi; was 2.3 X lo3 (see Figure 3), which corresponds to a concentration of 3.9 X lo* M. Our assumption that all e*- at this temperature results from e- reacting withi preexisting vacancies means that this must be the lower limit to C, the equilibrium concentration of vacancies, which is also given by the Boltzmann expression:
+
ASform.0
mform.0
R
RT
1251
where Co is the cencentration of D20 molecules. No reare available. If it is taken as liable estimates of Asforno zero, then the lower limit of C corresponds to an upper limit of AHfo& of 0.35 eV. However, aSfornOis expected to be positive since the formation of a vacancy allows more freedom of motion for the molecules surrounding it, so the upper limit indicated by the yield of evi[ for the 36- krd pulse must be somewhat higher than 0.35 eV. Equation 4 indicates that l / G t should be linear in dose per pulse for a given pulse length, and for a constant dose/pulse it should be inversely proportional to the pulse length. The latter proportionality is approximately true for the results obtained with 40- and 3004s pulses shown in Figure 3. Thus based on the slopes and intercepts from Figure 4 for the 40-11s pulse, GE(e~i,-) for 300-ns pulses of 4 and 14 krd should be 5.1 X lo3 and 2.5 X lo3, respectively, and in fact are 4.0 X lo3 and 2.5 X lo3, respectively. However, the yields for the 1600-ns pulse are not even qualitatively in agreement with this relationship in that they are less than for 300-11s pulses of the same dose, instead of being greater (Figure 3). A fact to be borne in mind is that a pulse from the S-band linac used in these experiments consists of a train of micropulses about 10-ps wide and separated from each other by about 350 ps. Species X probably disappears by second-order reactions and, if i is sufficiently large, then essentially all X from one micropulse disappears before the next micropulse begins. However, for 1600-ns pulses the current i in a micropulse is BO small that the concentration of X probably changes very little between micropulses, and therefore the concentration of X builds up during the pulse. Because of this buildup, the yield of e& would be lower than indicated by eq 4. However, it is still not clear why the yields for the 1600-ns pulse should be lower than for a 300-11s pulse of the same dose. 2. Decay Kinetics for e;. One possibility for the species identified simply as e- in reactions 1and 2 is eh-. Thermal decay of ei; in D20 ice at 4 K is accompanied by growth of e*-,14 which suggests strongly that ei, can be converted, at least partially, to evi; under these conditions. In addition there is fairly good evidence that ei; is a precursor of e*- in two aqueous glasses, namely, ethylene glycol-D20 and BeF2-D20, at 76 K.16J6 The dependence of yield of e ~ on- dose indicated in Figures 3 and 4 seems to require that the precursor of e& undergo a reaction which is second order in initial concentration and which does not produce evis-,and we would like to know if ei; fulfills this requirement at temperatures of 244 K and higher. In ref 1 it was shown that at 73 K the initial decay of eh- follows second-order kinetics and, what is much more significant, for a fourfold variation in initial concentration, the initial slopes of plots of 1/OD vs. time are the same within experimental behavior. Figure 5A shows that at somewhat higher temperatures the half-life for decay of eir- still depends strongly on the dose per pulse, but it is no longer obvious that the initial slopes of the plots of 1/OD vs. time are independent of initial concentration. Deviations from straight-line behavior at longer times suggest that the concentration of ei; is always lower than that of its reaction partner. A possible reason is that a fraction of e- reacts with another reaction product, such as OD radicals, rather than being trapped as ei; or recombining with D20+. In ref 1 it was suggested that the reaction partner of ehmight be D20+;an unrelaxed D30+, which would also be expected to have a high mobility, is another possibility and
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The Journal of Physical Chemistty, Vol. 84, No. I
l
l
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7
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Gillis, Teather, and Ross
10, 1980
13
IO3/ T (K)
Flgurr 7. Arrhenius plot of secondsrder rate constants for decay of ek- in D20 ice, measured at 2300 nm.
we assume this is the case in the following discussion. We assume that for a given dose and temperature the difference ([D30+]- [ei[]) remains constant during the decay of ek-. The integrated expression for second-orderkinetics with reactants at unequal concentrations is well known and In terms of optical density (OD) and extinction coefficient ( e ) for ei; and the optical pathlength (1) is
where A = ([D30+]- [ei;])cl. We fitted A so that plots of In (1+ A/OD) vs. time gave straight lines; the data of Figure 5A are replotted in this way in Figure 5B. The fit is not very sensitive simply to the choice of A, but the further requirement that k must be the same within experimental uncertainty for the different doses used at a particular temperature leads to a narrow range for the choice of A and therefore a small uncertainty in the calculated k. The extinction coefficient at the wavelength used (2300 nm) was taken as 3.5 X IO4 M-l cm-l from ref 1. The k's determined in this way were plotted according to the Arrhenius expression in Figure 7. In ref 4 evidence was presented which indicates that at 73 K ei[ has a low mobility, and therefore the large rate constant for its decay is due to the high mobility of its reaction partner. From the results of Figure 7, since the error bars are uncertain, it appears there may be some real variation of k with T between 73 and 155 K; the mobility of protons in H20 ice single crystals has a maximum at 118 K,17 and so presumably the mobility of unrelaxed D30+ (or whatever is the reaction partner of ek-) could also show some temperature dependence in this region. At temperatures higher than 166 K the rate constants for ei; decay could not be measured reliably because of the response time of our InAs detector but, qualitatively, they increase rapidly with increase in temperature. These higher rate constants could be due to a sharp increase in the mobility of ei; or to another decay reaction for ei; becoming important above 166 K. Thus our study of the decay of ei; does not enable us to make any definite conclusion about the possibility of ek- being a precursor of evl; at temperatures of 244 K and higher. 3. Comparison with Conductivity Results. Some comparisons between our results and those of a study of excess electrons in irradiated ice by a conductivity method by Verberne et al.' can be made, even though H20 ice and much lower doses were used in the conductivity work. The
radiation source used in the conductivity experiments was a Van de Graaff accelerator which of course does not give fine-structure pulses, so that the difference in dose rate between these experiments and ours is greater than the number of rads per pulse would indicate. Verberne et al. find that the major charge carrier at -120 "C is the electron, and it has a mobility in the range 20 f 10 cm2 V-' s-la7 As they point out, this very high mobility must mean that the electron is dry. The second-order rate constant we find for ei; between 76 and 133 K corresponds to a mobility of only 1.1X lom2em2 V-'s-l . Verberne et al. report that, at temperatures of -80 "C and below, the first half-life of the dry electron depends almost inversely on the end-of-pulse electron concentration, with doses per pulse between 6 and 60 rd.7 Thus ion recombination would seem to be the major dry electron reaction below -80 "C. In our previous optical study the yield of evi; was found to be very small at temperatures of -80 "C and below and seemed to be geminate,l which would not be seen in the conductivity experiments. However, a large yield of ei; was found at -120 "C, at -80 "C the yield was still appreciable,l and with a faster germanium detector we have seen absorption due to ei, at temperatures as high as -53 "C. If even a small fraction of dry electrons gives ei;, G(ei;) should depend on the dose per pulse. The result shown in Figure 5, and our measurements at higher and lower temperatures indicate that G(ei;) at a given temperature is independent of dose per pulse to &lo%. Thus it seems that the dry electron is not a precursor of ei;. Verberne et al. find that pseudo-first-order trapping of the dry electron becomes significant above -80 "C and dominant above -40 "C at their low dose rates.7 They find the rate constant for trapping increases between -80 and -40 "C and this increase corresponds to an activation energy of -0.6 eV, which compares favorably with the activation energy we find from the slope of the straight line in Figure 6 of 0.46 eV. Acknowledgment. We are grateful to Professor W. H. Hamill for very helpful discussions of this work.
References and Notes G. V. Buxton, H. A. Glllis, and N. V. Klassen, Can. J . Chem., 55, 2385 (1977). A. Mozumder, J . Chem. Phys., 50, 3153 (1969). I. A. Taub and K. Elben. J . Chem. Phvs.. 49. 2499 (1968). G. Nllsson, H. Christensen, P. Pagsberg,-and S. 0. Nlelsen, J : Phys. Chem., 76, 1000 (1972). N. V. Shubln, Y. I. Sharanin, T. E. Pernikova, and G. A. Vinogradov, J . Phys. Chem., 76, 3776 (1972). D. Razem and W. H. Hamill, J. Phys. Chem., 62, 488 (1978). J. B. Verbeme, H. Lotman. J. M. Warman, M. P. de Haas, A. Hummell, and L. Prinsen, Nature (London),272, 343 (1978). G. G. Teather, N. V. Klassen, and H. A. Gillis, Int. J , Radlat. Phys. Chem., 8, 477 (1976). C. K. Ross, K. H. Lokan, and G. G. Teather, Computers Chem., 3, 89 (1979). H. Hase and L. Kevan, J . Chem. Phys., 54, 908 (1971). N. H. Fletcher, "The Chemical Physics of Ice", Cambridge University Press, London, 1970, p 162. 0. E. Mogensen and M. Eldrup, Phys. Len. A , 60, 325 (1977). M. Eldrup, J , Chem. Phys., 64, 5283 (1976); 0.E. Mogensen and M. Eldrup, Risb National Laboratory Report No. 366, available from Jul. Giellerup, StYvgade 87, DK-1307 Copenhagen K, Denmark. H. Hase and K. Kawabata, J. Chem. Phys., 65, 64 (1976). G. V. Buxton, H. A. Glllis, and N. V. Klassen, Can. J . Chem., 54, 367 (1976). T. Q. Nguyen, D. C. Walker, and H. A. Gillis, J. Chem. Phys., 69, 1038 (1978). U. Eckener, D. Helmreich,and H. Engelhardt In "Physicsand Chemistry of Ice", E. Whalley, S. J. Jones, and L. W. Gold, Ed., Royal Society of Canada, Ottawa, 1973, p 242.
