1118
G. R. A. JOHNSONAND M. SIMIC
Primary Processes in the Formation of Hydrogen Atoms in the Radiolysis of Water Vapor
by G. R. A. Johnson and M. Simic hbOTatOTy of Radidiolt Chemistry, School of Chemistry, The University, Newcastle upon Tyne, Enoland (Received November 89, 1966) Accepted and Transmated by The Faraday Sockty
(June 37, 1966)
+
In the radiolysis of D20 C~HS mixtures, the energy absorbed by each component contributes to the formation of D atoms. The yield due to the energy absorbed by C3Hs (G(D),o = 4.6 f 0.3) is explained in terms of proton transfer from propane positive ions to D20 and subsequent formation of D atoms by neutralization of the hydronium ion produced. In the presence of N2O or of SF6, which act as electron scavengers, G(D),O = 0 showing that D atoms are not formed when hydronium ions are neutralized by the negative ions from N20 and SF6. The yield due to the energy absorbed by D2O was G(D)wo = 7.6 f 0.4 in the absence and G(D),.,O = 4.9 f 0.4 in the presence of electron scavengers. It is concluded that neutralization of hydronium ions by electrons gives D atoms with a yield corresponding to G = 2.7 0.8, and that D atoms are also formed (G = 4.9 f 0.4) by reactions which do not involve hydronium ion neutralization.
*
Introduction Several studies have been made of the radiationinduced decomposition of water vapor. l-6 It is generally assumed that hydrogen atoms are formed by two main processes : neutralization of hydronium ions and dissociation of excited Hydronium ions are formed by the reactions
+ eH30+ + OH
yields of hydrogen atoms formed by hydronium ion neutralization and by other processes in irradiated water vapor.
Experimental Section H20 and D 2 0 (Norsk Hydro-Elektrisk 99.83%) were distilled from alkaline KMn04 and then redistilled.
(1)
(1) R. F. Firestone, J . Am. Chem. Soc., 79, 5593 (1957). (2) J. H. Baxendale and G. P. Gilbert, Discussions Faraday SOC.,36,
(2)
(31
186 (1963). (3) J. H. Baxendale and G. P. Gilbert, J . Am. Chem. Soc., 8 6 , 576 (1964). (4) A. R. Anderson, B. Knight, and J. A. Winter, Nature, 201, 1026 (1964). (5) A. R. Anderson, B. Knight, and J. A. Winter, Trans. Faraday SOC.,6 2 , 359 (1966). (6) A. R. Anderson, B. Knight, and J. A. Winter, Nature, 209, 199 (1966). (7) E. J. Hart and R. L. Platzman, Mech. Radiobiol., 1, 176 (1961). (8) F. Fiquet-Fayard, J . Chim. Phys., 57, 453 (1960). (9) P. F. Knewstubb and A. W. Tickner, J . Chem. Phys., 38, 464
is well established in the photolysis of water but the extent to which this process occurs in the radiolysis has not previously been established. The main aim of the present work was to determine the relative
(10) P. Kebarle and A. M. Hogg, ibid., 42, 798 (1965). (11) G. Black and G. Porter, Proc. Roy. SOC.(London), A266, 185 (1962). (12) J. R. McNesby, I. Tanaka, and H. Okabe, J . Chem. Phys., 36, 605 (1962).
HrO --+H20+
HzO+
+ HzO
and, a t the pressures used in radiolysis, will be present mainly as clustered ions, H30+(Hz0),, where n 2 7.9810 I n the absence of any component capable of capturing electrons, neutralization of the clustered hydronium ions will occur mainly by reaction with electrons. Dissociation, following electronic excitation, t o give hydrogen atoms HzO --+
The Journal of Physical Chemistry
H
+ OH
(1963).
FORMATION OF HYDROGEN ATOMSIN
THE
RADIOLYSIS OF WATERVAPOR
Propane and propene (Phillips research grade), SF6 (I.C.I., 99.95%), and N2O (British Oxygen Gases, medical grade) were condensed a t 77°K and distilled still several time before use. Irradiations were carried out in Pyrex vessels (-400 ml) fitted with break-seals. Before filling, the vessels were baked in air at 500" for a t least 6 hr and pumped to torr. The weighed water sample, after deaerating by freezing and pumping at 77"K, was distilled into the irradiation vessel while this was at 77°K. Required amounts of additives were introduced by condensing from a gas sample vessel (known PTIT). The wssels were sealed before warming to room temperature. Two different 6oCoy-ray sources, of about 400 and 1000 curies, were used. During irradiation, the vessels were heated in an oven with the temperature contro'led to k 2 " . The dose rate was measured by the N20 dosimeter assuming G(N2:i = 12.0.13 The energy absorbed in the water vapor (E,) was calculated from that in N 2 0 (E,) assuming the energy absorbed in each gas to be directly proportional to its electron density. The energy absorbed in the propane (E,) was calculated from E,, using the ratio of stopping powers per molecule obtained by Meisels.'* The total energy absorbed in a mixture (Et)is the sum of the energies absorbed in the components. The dose rates used were 6 X 10l6 to 2 X 10'' ev mole-' sec-' in D20. Gases present, after irradiation, which were noncondensable at 77"K, were transferred to a gas buret by means of a one-stage diffusion pump and a Toepler pump. After I'VT measurement, the gas composition was determined mass spectrometrically.
Results G(X)t, G(X),,, and G(X), are the number of molecules of product X formed per 100 ev absorbed by the gas mixture, by the water fraction, and by the propane fraction, respectively. The energy fractions are fw = E,/Et and fp -= E,/Et. The yields obtained by extrapolation to j , = 0 and fw = 0 are written G(X)wO and G(X),O, respectively. D20 C3Hs Mixtures. The hydrogen yields from D20 C3H8 mixtures were independent of the temperature of radiolysis between 100 and 185" and were linear with dose to the highest dose used (-3 X 1019 ev mole-'). Erroneously low yields were obtained if the radiolysis temperature was near the boiling point of water a t the water vapor pressure used. The quantity of water in each experiment therefore was selected so that the boiling point, a t the pressure used, was at
+
+
1119
6
6 4
2
0 0.2
0
0.4
0.6
0.8
1.0
0.4
0.2
0
fp.
1.0
0.6
0.8
fv.
+
mixtures ( 140°,density Figure 1. Radiolysis of DzO CSH~ 0.8-2.7 g 1.-1). Dependence of G(HD)t and G(H2)t on the fraction of dose absorbed by CsHs ( f p = E p / E t )and by CJHS; D20 (fw = E,/Et). HD yields: 0,from D20 0, with N2O (-3 mole yo); Q, with SFc (-0.3 mole %). Hz yields: 0, from DtO CaH8; ,. with N20 (-3 mole %); 0 , with SFB(-0.3 mole 70).
+
+
least 20" below the irradiation temperature. The D 2 0 vapor concentrations used were from 1.3 X to 6.2 X mole l.-I. In Figure 1, G(HD), and G(H2)t from D2O C3Hs are plotted against fp and fw. The yields obtained by extrapolation to f, = 0 and f N = 0 are G(HD)wo = 7.6 f 0.4 and G(HD),O = 4.6 f 0.3, respectively. Also, over the concentration range studied, G(H.Jt = f,,G(H2)p0,where G(H2),0 = 6.3 f 0.3. DzO C3H8 N2O (or SF6) Mixtures. In the presence of N20 (3 mole %) or of SFs (0.3 mole %), G(HD)t = f,G(HD),O where G(HD),O = 4.9 f 0.4 (Figure 1). To obtain this value from the measured HD yield, it was necessary to determine the extent to which the energy absorbed by the Y20 or SF6 in these mixtures contributed to the formation of HD. For this purpose, a study was made of the radiolysis of D2O 4-NzO and DzO SF6 mixtures, with small amounts of C3H8 (1.5 mole %) present. In Figure 2, G(HD)t, from these mixtures, is plotted against the fraction of energy absorbed by NzO or by SF6. In the case of D20 N20, over the whole concenwhere tration range studied, G(HD)t = f,G(HD),O, G(HD),O = 4.7 * 0.4. This shows that the energy absorbed by N 2 0 does not contribute to the yield of
+
+
+
+
+
(13) G. R. A. Johnson, J . Inorg. Nuel: Chem., 24, 461 (1962). (14) G. G. Meisels, J. Chem. Phys., 41, 51 (1964).
Volume 71,Number 4
March 1967
G. R. A. JOHNSON AND M. SIMIC
1120
0.9
0.8
d 0.7
0
0.6
0.4
0.2
0.8
1.0
0.2
0
0.6
fN20 Or fSF6.
1.0
0.4
0.6
0.8
fR0.
+
+
Figure 2. Radiolysis of DzO NzO and DzO SFBmixtures (1400, density 0.8-2.7 g l.-l) with C3Hs (-1.5 mole %). Dependence of G(HD)t and G(N2)t on the fraction of dose absorbed by DzO( f w = E,/&). HD yields: 0, DzO NzO; 0, DzO NzO with SF6 (-0.3 mole %); 0, DzO SFs. Nz yields: 0, DzO + NzO; H, DzO NzO with SF6 (-0.3 mole %).
+
+
+
+
+
HD. In the case of DzO SF6, there appears to be a small contribution, at high SFC concentrations, from the energy absorbed by SFe. However, it may be concluded that the contribution of the energy absorbed by SF6 to the HD yield is negligible in the experiments where SF6 was present a t a concentration of 0.3 mole %. The Nz yields from DzO NzO with c3H8 (1.5 mole yo),in the presence and absence of SFe (0.3 mole %), are also given in Figure 2. The extrapolated value G(N2),O = 4.2 f. 0.4 in the absence and zero in the presence of SFe. Molecular Hydrogen. The yield of Dz from the various systems is plotted against fw in Figure 3. G(D2), decreased with decreasing f w for D 2 0 C3H8 mixtures and increased with decreasing fw for DzO NzOor DrO SFemixtures.
+
+
+
Discussion Formation of H D and Hz from DzQ The system D 2 0 since the reaction D
+
c3H8
+
Mixtures.
+ C3H8 was selected for investigation
+ C3He +HD + C3H7
(4)
2 X lo6 M-' sec-1 16,16) results in efficient scavenging of D atoms, and the product of this reaction can be distinguished both from the Hz produced by the reaction of H atoms formed from C3H8,and from the Dz formed as a molecular product from DzO. Furthermore, both charge transfer and proton transfer
(k4
N
The Journal of Physical Chaistrtry
0.5
0.8
1.0
0.6
0.4
0
0.2
fw.
Figure 3. Formation of Dg from DzO vapor (140') in the presence of various additives. Dependence of G(D& on the fraction of dose absorbed by water (f-.= E,/Et): 0,DzO CSHS;0, DzO CaHe with NzO (2.5 mole %). 0, DzO CaH8 with SFS(0.3 mole %); 0, DzO N& with CaHs (1.5 mole %); D, DIO NzO with CsH8 (1.5 mole %), and SFB(0.3 mole %); 0, DzO SFBwith CaHs (1.5 mole %).
+
+
+
+
+
+
from hydronium ions to C3Hs can be excluded on energetic grounds
D30'
D30'
+ CsHs +D + DzO + CsH8' + C3H8
---f
D2O
(AH = 4.8 ev)
(5)
(AH = 2.9 ev)
(6)
+ C3HeD'
(AH was calculated assuming proton affinities P(C3H8) = 4.3 ev, P(D20) = 7.2 ev17 and ionization potentials I(C3H8) = 11.2 ev, I(D) = 13.6 ev. It is also assumed that the proton affinity of DzO is the same as that of HzO and that the hydration energies of the ions can be neglected.) From the results (Figure l), it may be concluded that the energy absorbed by both DzO and C3H8 contributes to the D atom yield. Thus the linear dependence of G(HD), on the fraction of energy absorbed by each component is most reasonably explained by fpG the assumption that G(HD), = fWG(HD),O (HD),O, where G(HD),O = 7.6 f 0.4 and G(HD),O = 4.6 f. 0.3 are the values of G(HD)t at f,, = 0 and fw =
+
(15) H. A. Kazmi, R. J. Diefendorf, and D. J. Le Roy, Can. J. C h a . , 41, 690 (1963). (16) H.I. Schiff and E. W. R. Steacie, ibid., 29, 1 (1951). (17)F. W.Lampe and 1.H. Field, Tetvahedron, 7 , 189 (1958).
FORMATION OF HYDROGEN ATOMSIN
THE
RADIOLYSIS OF WATERVAPOR
0, respectively. The value of G(HD),O = 7.6 f 0.4 is in agreement with previously reported values for hydrogen atom yield from water vapor measured using organic scavengers. Radiolysis of C3H8 can give a number of different positive ions. It may be assumed that C3H8+ and C3H7+ will be the main positive ionsl8 reacting with DzO. The proton-transfer reaction
C3H8+
+ D2O
C3H7
+ HDzO+
(7)
(k, = 1.2 X 1012 Ai'-1 sec-') has been observed in a mass ~pectrometer.1~Evidence for proton transfer from C3H7+to H20, i.e., the reaction analogous to
C3H7+
+ D2O +C3H6 + HDzO+
has been obtained from mass spectrometric studies of ions in CH4 H2O mixtures.20 Proton-transfer reactions of this type, Le., from a carbonium ion to a molecule of sufficiently high proton affinity, have also been postulated in the radiolysis of liquid hydrocarbons.21 HD20+ ions formed by reactions 7 and 8 will enter into the equilibrium
+
HD20+
+ D20
D30+
+ HDO
(9)
By comparison with similar proton-transfer reactions in the gas phase,21it may be assumed that equilibrium will be rapidly established. Since D2O is always in considerable excess over any HDO formed by reaction 9, D30+ will be the only positive ion involved in the neutralization reaction. The observed G(HD), = 4.6 is close to the yield of positive ions in propane, G(RH+) = 4.3, calculated from the value of W(C3H8) = 23.4.14 This suggests that all of the positive ions from propane aye capable of undergoing proton transfer (reactions 7 and 8) and that neutralization of the resulting D 3 0 + ion gives one D atom per neutralization. N20 and SFs can capture electrons to form negative ions.22 In the presence of these scavengers, therefore, neutralization of the hydronium ions by negative ions will occur rather than neutralization by electrons. Since, when N20 or SF6 are present, G(HD),O = 0, it appears that neutralization of D30+, by the negative ions from these scavengers does not result in D atom formatlion. The yield of H2, G(HZ), = 6.3 f 0.3, supports the assumption that d l the positive ions from propane react with D20 by reactions Or *' This conclusion may be drawn from a comparison of the present results with those obtained in a study of hydrogen formation in the radiolysis of In the radiolysis of pure C3H8, hydrogen is formed by two processes: via H atoms proelectron recombination and duced by positive ion by decomposition of excited propane mOleCUleS. The
+
1121
formation of H atoms from positive ions can be prevented by the addition of electron scavengers (NzO, SF6, CC14) and the yield with these present is G(Hz) = 5 a t 20". Recent workz3has shown that the yield of Hz from C3H8 NzO is slightly dependent upon the temperature of radiolysis and that, a t 140", the temC3H8 experiments, G(Hz) = perature of the DzO 6.2 f 0.2. This value is close to G(HZ)~O from DzO C3H8 mixtures, in agreement with the view that in both cases the formation of H atoms from propane positive ions is eliminated. Furthermore, G(Hz),O is not depressed by the addition of electron scavengers (Figure 1) confirming that, in the presence of DzO, the Hz yield from propane results from processes other than positive ion neutralization. The above conclusion, that the D30+ ions formed via reactions 7, 8, and 9 give one D atom per ion when neutralized by electrons and no D atoms when neutralized by the negative ions from NzO or SF6, holds over the whole concentration range studied, since G(HD),O is independent of fp (Figure 1). It is, therefore, reasonable to assume the same behavior on neutralization for the D30+ ions formed as a result of energy absorption by D20. On this basis, it is possible to explain the depression of the H D yield from G(HD),O = 7.6 f 0.4 to G(HD),O = 4.9 f 0.4 by N2O and SFe (Figure 1). The residual yield in the presence of these scavengers must be due to a process or processes not involving D30+neutralization. (In the following discussion these processes are referred to as the "residual process.") It follows that the yield of D atoms due to D30+ neutralization corresponds to the depression of the HD yield, AG (HD),O = 2.7 f 0.8. This is slightly less than value for the yield of hydronium ions, G(D30+)w= 3.1-3.6, calculated from reported values of W(H20).8 Any possibility that the observed effect of NZO and SFC in D20 radiolysis is due to D atom scavenging, e.g., by the reactions
+
+
+
+ NzO +OD + SzO D + SFt3 -+- D F + SFs
D
(10)
(11)
may be excluded since G(HD), is independent of the concentration of n - 2 0 and of SF6 up to molar ratios NzO/C3Hs = 80 and SFij/C3& = 30 (Figure 2). Since (18) P. Ausloos and R. Gorden, J. Chem. Phys., 41, 1278 (1964). (19) F. W. Lampe, F. H. Field, and J. L. Franklin, J . Am. Chem. sot.. 7 9 , 6132 (1957). (20) M. S . B. Munson and F. H. Field, ibid., 8 7 , 4242 (1965). (21) W. R. Busler, D. I-I. Martin, and F. Williams, Discusswns Faraday Soe., 3 6 , 102 (1963). (22) G. R. A. Johnson and J. hl. Warman, Trans. Faraday SOC.,61, 1709 (1965). . , (23) G. R. A. Johnson, M. Simic, and L. Redpath, unpublished results
Volume 71, Number 4
March 1967
1122
G. R. A. JOHNSON AND M. SIMIC
a change of 10% in the measured G(HD), would have been detected, it follows that the rate constant ratios are k&O >_ 800 and k 4 / k n 2 300. The former ratio may be compared with the value ~ H + c , H J ~ H + N , o 400 calculated from reported values for these cons t a n t ~ . ’ ~The * ~ ~inability of NzO and SFa to depress the HD yield below G(HD), = 4.9 may be contrasted with the effect of propene, which is an efficient hydrogen atom scavenger. With propene present (C3H6/ CaH8mixtures is C3H8 = l.O), the yield from D2O depressed to G(HD), < 0.1. This is in accord with 40 calcuthe rate constant ratio kH+c8HJkH+C,H8 lated from reported rate constant^.^^ Reactions in the Presence of N20 and of 8F6. Assuming that the mixture law holds for DzO NZO mixtures, the total Nz yield should correspond to G(N2)t = f,G(Nz),O fNloG(Nz)N,oo. The results (Figure 2) indicate that there is some deviation from the mixture law. This deviation and the values of G(N2)N,ooin the absence and presence of SF6 will be discussed elsewhere. G(Nz),O = 4.2 f 0.4 lies 3 between G(e-), and 2G(e-), (where (G(e-), is the electron yield). A value corresponding to 2G(e-), would be expected if NZis formed by
-
+
-
+
+
-
+ N20 +NO+ 00- + N20 +Ns + 02e-
It is possible that the reaction 0-
+ D20 +OD + OD-
(14)
can compete with reaction 13. If it is assumed that reaction 14 does occur, it must compete to the exclusion of reaction 13 a t all N20 concentrations used, since G(Nz),O does not increase with increasing f N I 0 (Figure 2). In this case, Nz must be formed by some process other than reactions 12 and 13, with G(N2) = 1 f 0.5. Baxendale and Gilbertz6 have suggested that methanol, the part of the N2 in the system H20 yields in excess of G(e-) may be due to the reaction of free radicals with NzO. Similarly, free radicals from C3H8 may react to give Nz, e.g.
+
C3H7
+ NzO
+C3Hi’O
+ N2
(15)
However, this seems improbable since SFBdecreased G(NZ),O to zero (Figure 2) and, to explain the effect of SF6 in terms of a competition between SFs and NzO for the free radicals, it would be necessary to make the unreasonable assumption that the specific rate for reaction with SF6 is a t least loo0 times that for reaction with NzO. If it is assumed that all of the 0- ions react according The Journal of Physical Chemistry
D30+
+ OD-
DzO
+ DzO
(16) This is in keeping with the finding that D atoms are not formed by hydronium ion neutralization under these conditions. With SFs present, the predominant negative ion will be SFs-. Since neutralization of D30+ by this ion does not give D atoms, it follows that neutralization does not simply involve electron transfer but that rearrangement occurs, e.g.
D30’
+ SFs-
DzO
+ HF + SFs
(17) Hydrogen Atom Formation by Processes Other Than Hydronium Ion Neutralization. Under mass spectrometric conditions, approximately 18% of the positive ions are formed by the processs --f
HzO --ic OH+
+ H + e-
-
(18) In the radiolysis, this could result in G(H) 0.7, but the actual extent of this process cannot be determined from evidence available a t present. Reaction 18 would probably not alter the yield of hydronium ions since the chargetransfer reaction
(12) (13)
-
t o reaction 14, when NZO is present neutralization of hydronium ions will involve reaction 16.
OH+
+ H2O
--+
OH
+ HzOf
(19)
may be expected to occu1.8 and would be followed by reaction 2. The majority of hydrogen atoms which contribute to the “residual” yield presumably result from electronic excitation (reaction 3). From the value of the “residual” yield, assuming a contribution of G = 0.7 from reaction 18, it appears that the yield due to reaction 3 corresponds to G 4.2. This is quite close to the value G 3.3 calculated for this process by Fiquet-Fayard.s It is of interest to compare the yield of hydrogen atoms from excitation in the vapor phase with that in liquid water. It has been suggested that the formation of hydrogen atoms (G 0.6) in neutral aqueous solutions is due to e x c i t a t i ~ n . ~This ~ has not been definitely established and other possible modes of hydrogen atom formation have been discussed.28 However, the yield of atoms from excitation in liquid water is clearly less than in the vapor phase. In the liquid it is possible that the observed yield is decreased by either (a) deactivation of excited states before dissociation and/or
-
-
-
(24) (25) (26) (27) (28)
M. Schiavello and G. G. Volpi, J . Chem. Phys 37, 1510 (1962). B. A. Thrush, Progr. Reaction Kinetics, 3 , 65 (1965). J. H. Baxendale and G. R. Gilbert, Science, 147, 1571 (1965). J. T. Allan and G. Scholes, Nature, 187, 218 (1960). C. Lifshitz and G. Stein, Israel J. Chem., 2 , 337 (1964).
1123
DIFFUSIONCOEFFICIENTS FOR GASESIN LIQUIDS
(b) rapid recombination, within the solvent cage, of the free radicals produced by dissociation. However, since the quantum yield in the photolysis of liquid water (1470 A) is close to unity,29processes (a) and (b) do not appear t,o be important, at least for water excited photolytically. This suggests either that the excited states produced by photolysis of liquid water differ markedly from those produced radiolytically or that the radiolytic excitation process responsible for decomposition in the vapor phase does not occur in the liquid phase. Molecular Yield of Hydrogen. The value of G(D2)w = 0.64 f 0.06 obtained in D20-rich mixtures (Figure 3) agrees with values for the molecular yield of hydrogen reportbedp r e v i o u ~ l y . ~G(D& ~ ~ from DzO
+
C3Hs decreased with increasing CaHs concentration , suggesting that CSHS may react with some precursor of Dz. In the systems D2O N20 and DzO SFs, on the other hand, G(D2)wincreased as the concentration of N20 or SFe increased. This indicates that the energy absorbed by NZO and by SFs can, to some extent, contribute to the formation of Dz. Further investigation of these effects would be of interest.
+
+
Acknowledgments. We thank Professor J. J. Weiss for his interest and Dr. G. Scholes for helpful discussions. The work was supported financially by the Atomic Energy Research Establishment, Harwell, England. (29) U. Sokolov and G . Stein, J . Chem. Phys., 44, 2189 (1966).
Diffusion Coefficientsfor Gases in Liquids from the Rates of Solution of Small Gas Bubbles
by Irvin M. Krieger, George W. Mulholland, and Charles S. Dickey Department of Chemistry, Case Institute of Technology, Cleveland, Ohw
(Received August 31, 1966)
A new technique is described for suspending a small gas bubble in a liquid and measuring its size as a function of time while it dissolves. From these data and the gas solubility, diffusion coefficients for the gas in the liquid can be calculated. The experimental technique involves catching a bubble on a fine horizontal fiber and photographing its projected image. To analyze the data, Fick’s law is integrated for unsteady, spherically symmetrical conditions; the resultant equation is fitted to the data by an iterative least-squares technique. Results are presented for 0 2 , N2, and He in HzO and in organic liquids.
Introduction The study of the liquid state encompasses both equilibrium and nonequilibrium phenomena. Diffusion, which is the transport of matter under the influence of a concentration gradient, is an important nonequilibrium process for which an adequate general theory is not yet available. Diffusion in dilute gases has been treated successfully by the kinetic theory, as has the diffusion of colloidal particles in a continuous
medium. The diffusion of ordinary molecules in a dense gas or a liquid has shown itself to be much less tractable, however. To stimulate and guide the development of theory, it would be desirable to have on hand a large body of accurate diffusion coefficient measurements on many diversified systems. Unfortunately, the data available are meager and, judging from the discrepancies among different techniques and observers, they are Volume 71, Number 4 March 1967
