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particles at a given u is larger in the presence than in the absence of ammonia. Nothing can be concluded from these experiments about the rate of nucleation. The experimental fact2 that fast flocculation is occurring at 35 sec means that the number of particles observed a t 2 min is determined not only by the number of primary nuclei formed
during mixing but also by the rate of fast flocculation. The fact that the observed value of n varies linearly with u, whereas according to generally accepted nucleation theory the number of primary nuclei should vary exponentially with u, indicates that the rate of fast flocculation also must vary exponentially with the supersaturation.
Electron Spin Resonance Studies of 7-Irradiated High Surface Area
Silica. I.
Identification of Defects
by G.M. Muha Ea80 Research and E T Z & W T ~Compcmy, ~~ Linda, New Jersey
(Received Auguat 9,1066)
Electron spin resonance (esr) studies have been made of the defects introduced in a high surface area silica by y-irradiation. The esr spectrum has been analyzed in terms of contributions from four distinct types of defects in the glass structure. Two of these defects are thought to be formed in the silica network by the trapping of an electron in an oxygen vacancy. There is some evidence that -10% of the oxygen vacancies have nearby hydroxyl groups. The remaining two defects are thought to consist of holes trapped in silicon-oxygen and boron-oxygen bonds. The evidence for the former assignment is not conclusive. The boron in the latter case occurs as an impurity in the silica. It is found to be trigonally coordinated in contrast to the tetrahedral coordination observed in other glasses. This result is explained in terms of the low concentration of network modifier present. The spectrum arising from the B-0 defect is described by an axially symmetric spin Hamiltonian with gll = 2.0100, g1 = 2.0023, All = 1.40 X cm-', and A* = 1.25 X 10-3 cm-1. The relationship between this €3-0defect and the A1-0 defect found in irradiated smoky quartz is briefly considered.
I. Introduction Electron spin resonance (esr) techniques have been used in a number of cases to study the nature of the paramagnetic defects introduced in glasses by ionizing radiation. For example, spectra have been reported for fused silica,1-3 alkali b ~ r a t e , ~aluminosilicatel'~* -~ and phosphateg~l0 glasses. Quite often hyperfine effects are observed. In these cases, the interpretation of the spectrum is usually based on concepts deThe Journal of Physical Chamistry
veloped in the study of defects in alkali halide crystals, viz., electrons or holes trapped at vacancies in the lattice. ~~
(1) J. 8. van Wieringen and A. Kats, Philip8 Rea. Repta., 12, 432 (1957). (2) R. A. Weeks and C. M. Nelson, J . Am. Ceram. Sac., 43, 399 (1980). (3) P. 0. Fromau, R. Petternon, and T. Vanngard, Arkiu Fyaik, 15, 559 (1959).
Y-IRRADIATED HIGHSURFACE AREASILICA
I n the work described in the present paper, a description is given of the paramagnetic defects introduced by Corn irradiation in a Vycor-type glass. This material is chemically similar to fused silica but differs physically in that it has a high surface area. This latter property enables one to study the effects of various gases on the observed defects; this work is described in the following paper“ (hereafter referred to as 11). The remarkable surface properties of this irradiated glass have previously been reported.12 The material used in the present study, usually referred to as “porous glass,” is preparedla by heating an alkali borosilicate glass above the annealing point to cause phase separation and then leaching the boric oxide rich phase with acid. The resulting material possesses a porous structure of high silica content containing some residual boron.
II. Experimental Section The erJr spectra were obtained with a Strand Model 600 X-band spectrometer equipped with a Varian V4531 variable-temperature cavity. The magnetic field was provided by a Harvey Wells L-128 magnet. Field modulation at 6 kc/sec and a 3-sec time constant were used in all cases. The modulation amplitude and microwave power level were set below the point where line broadening or saturation effects would be observed in the recorded spectrum. First derivative presentation was used in recording the spectra. The magnetic field was calibrated by a Harvey Wells F502 nmr gaussmeter, the frequency of which was monitored by a Hewlett-Packard 524C frequency counter. The g values were obtained by comparison with a DPPH sample (g = 2.0036) taped to the outside of the sample tube. All samples used in this study were prepared by Yates using methods described in detail in 11. The material was taken from a single lot of Corning 7930 porous glass containing about 3% boron plus other impurities of much lower concentration. For present purposes, it is sufficient to note that the esr spectrum was obtainable only if the irradiated sample was held under vacuum-if not, no signal was observed. Under vacuum, the samples are stable for periods in excess of 45 days as judged by the reproducibility of this esr spectrum. No esr signal was observed in samples that had not been irradiated.
In. Results and Discussion A typical spectrum of a Co%rradiated porous glass sample is given in Figure 1. The spectrum consists of a sharp asymmetric line and five somewhat broader
1391
lines superimposed on a broad background. I n addition, several weaker lines are observed within the group of five lines along with another line in the region of 3388 gauss. A search at lower fields revealed no lines due to the presence of paramagnetic imp~rities.~‘ All samples became reddish violet from the radiation treatment. The sample coloration as well as the shape and intensity of the esr lines was stable a t room temperature for periods in excess of 45 days, provided the sample was held under vacuum. The spectrum of a porous-glass sample sintered so as to have essentially zero surface area was also obtained. This spectrum resembled that shown in Figure 1 except that the group of five lines was broadened so as to appear to overlap. The weak lines within the group of five lines could not be observed. The single line at highest field remained. In contrast to the behavior of the high surface area samples, the sintered sample was stable in air. A . The Sharp Asymmetric Line. The sharp asymmetric line and the single weak line at highest field may be judged to be independent of the other linns in the spectrum by their behavior under conditions of saturation. At 77’K, it was possible to set the microwave power at a level so that these two lines were almost completely removed while the broad background and the group of five lines were reduced in intensity by less than 30%. A second piece of evidence concerning this point is offered in 11. There it is shown that the addition of CH,OH vapor to the sample “bleaches” these two lines but leaves the broad background and group of five lines essent,iallyunchanged. An expanded trace of the asymmetric line is given in Figure 2. The line is seen to be typical of that obtained from polycrystalline material with an anisotropic g tensor. On the basis of an analysis of the line shape,I6 the curve can be described as Lorentzian with (4) G. 0. Karapetyan and D. M. Yudin, Fiz. Tverd. Tela, 4, 2647 (1962); soviet Phy8.-&lid State, 4, 1943 (1963). (5) S. Laa and P. J. Bray, J. Chem. Phya., 39, 2863 (1963).
S. Lee and P. J. Bray, ibid., 40, 2982 (1964). (7) 8. Lee and P.J. Bray, Phys. Chem. GlaSse8, 3 , 37 (1962). (8) G. 0. Karapetyan, S. A. Stepanov, and D. M. Yudin, Fiz. Tverd. Tela, 6 , 1531 (1964); Soviet Phys.-Solid State, 6 , 1197 (1964). (9) G. 0. Karapetyan and D. M. Yudin, Fir. Tverd. Tela, 3 , 2827 (1961); SO&$t PhyS.-SOlid State, 3 , 2063 (1962). (IO) Y. Nakai. BUZZ. Chem. Soc. Japan, 37, 1089 (1964). (11) G. M. Muha and D. J. C. Yattas, J. Phys. Chem., 70, 1399 (6)
(1966). (12) D. J. C. Yates and P. J. Lucchesi, J . Am. Chem. SOC.,86, 4258 (1964). (13) M. E. Nordberg, J . A m . Ceram. Soc., 27, 299 (1944). (14) R. H. Sands, Phys. Reo., 99, 1222 (1955).
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I
I
I
I
I
I
I
I
1
I
I
I
I
I
1
I
B”
I
-‘
tines
Gain X 100
I 3230
I
1 3250
I
I 3270
I
I
I
3290
I 3310
’
I
I
3330
‘
h 3385
3395
Magnetio field, gauss.
Figure 1. Esr spectrum of -&radiated porous glass obtained at room temperature. Note the changes in the vertical and horizontal scales for the line at highest field.
gll = 2.0016, gL = 2.0003, and a single-crystal line width of approximately 1.3 gauss. The g values were
measured at the peaks of the derivative presentation and therefore necessarily include some error. This error has been estimatedl6 to be less than 10% of the g value variation, an amount of little importance for the present application. A line of the type described here for porous glass has been reported in a variety of other irradiated materials containing the Si02 network. Examples include irradiated borosilicates and aluminosilicate glasses,’ fused silica,lJ6 and Amersil.’a In addition, during the course of the present work, similar lines were obtained from other high surface area silicas including Quso-G3017 and Cabosil HS5.18 All of these samples exhibit an easily saturated line of approximately 1-gauss width and a g value near 2.001. From this evidence, it is concluded that the defect is associated with the Si02 network rather than with network modifiers, impurities, or peculiarities of a high surface area sample.
Weeks and Nelson2 have studied radiation-induced defects in the Si02 network in fused silica and singlecrystal quartz. For the latter material, they were able to show the presence of two paramagnetic centers which were labeled EL’and Ez‘. In addition, a direct correlation was established between the optical adsorptions at 2120 and 2300 A and the El’ and E2’ centers, respectively. Tentative m ~ d e l s * have ~ ’ ~ ~been ~ ~ proposed for the two centers which are consistent with the experimental data but offer some difficulty with respect
(15) J. W. Searl, R. C. Smith, and S. J. Wyard, PTOC. Phys. SOC. (London), 78, 1174 (1961). (16) R. A. Weeks and C. M. Nelson, J . AppZ. Phys., 31,1555 (1960). (17) Obtained from the Philadelphia Quartz Go., Philadelphia 6, Pa. This material is prepared by an unspecified precipitation technique. It has a typical surface area of 270 m*/g. (18) Obtained from the Cabot Gorp., Boston, Mass. This material is prepared by burning silicon tetrachloride. It has a typical surface area of 340 m2/g. (19) R. A. Weeks,Phys. Rev.,130, 570 (1963). (20) R.A. Weeks and E.Lell, J . Appl. Phys., 35, 1932 (1964).
”/-IRRADIATED HIGHSURFACE AREASILICA
I
3306
I
3308
I
I
I
3310
I
3312
1393
I
3314
Magnetic field, gauss.
Figure 2. Expanded view of the center portion of the spectrum shown in Figure 1. This sharp, asymmetric line is thought t o arise from a n electron trapped in a n oxygen vacancy.
to the electronic wave function involved.21 Both defects are thought to be similar in that they involve an unpaired electron trapped in an oxygen vacancy; they differ in the number of other silicon and oxygen atoms missing in the vicinity of the center.lg In the case of fused silica, the two centers cannot be resolved2 because of the averaging effect over the anisotropic interactions. The optical adsorptions can be resolved, and, on this basis, the identification with the single-crystal results is made. I n fused silica, the E,’ center predominates. 2 , 1 6 , 2 2 In the porous glass used in this work, attemptsz3 to resolve discrete bands in the optical region of the spectrum due to radiation changes were unsuccessful. A comparison of the g values for porous glass with those reported2,21for the El’ ( g l = 2.0003,g2 = 2.0006, g 3 = 2.0018) gives good agreement. Further, an integrated version of the spectrum shown in Figure 2 is in reasonable agreement with the calculated line shape for an El’ center distributed in a glass.16 On the basis of these two observations, it will be assumed that the sharp asymmetric line corresponds to one of the E’ centers previously reported, viz., an electron trapped in an oxygen vacancy. Other details concerning nearby molecules or vacancies are as yet unknown. B . High-Field Line. The weak line a t high field is 78 gauss (g = 1.96)above the asymmetric line and has an over-all width of approximately 10 gauss. Its integrated intensity is estimated to be 10% of that of
the asymmetric line. A search for a corresponding line about the same distance below the asymmetric line was inconclusive. This region fell on the rapidly rising slope of the broad background. The present work provided no direct evidence concerning the nature of the paramagnetic species responsible for this line. It may be structurally similar to the E’ center assumed to give rise to the asymmetric line since, as noted above, similar chemical and relaxation behaviors are observed. The large shift of the line from the region g = 2 suggests that a hyperfine interaction may be involved. Such interactions have been reported in other silicas. For example, in a Cow-irradiated Corning 7943 silica, a pair of lines 5 gauss wide and separated by 75 gauss have been reported.24 Deuterium substitution confirmed that the doublet was due to a proton interaction. The intensity of this doublet has been shown20 to depend upon the presence of hydroxyl groups in the silica adsorption band. as shown by the presence of a 2.7-~ Infrared studies of porous glass26also show the presence of a large number of hydroxyl groups. Little change is detected in the frequency or intensity of the OH band after Coo0 i r r a d i a t i ~ n . ~The ~ parallel between the infrared and esr results for porous glass and the Corning 7943 silica, coupled with the similar relaxation and chemical behavior noted for the assumed E’ center, suggests the following interpretation. The high-field line arises from an E’ site containing a nearby hydroxyl group. The intensity relative to the asymmetric line then implies that roughly 10% of the E’ sites contain hydroxyl groups. The simplicity of this picture is attractive, but the hypothesis clearly requires more experimental evidence. C. Group of Five Lines. A group of five lines similar to those observed in the spectrum of porous glass has previously been reported for irradiated borosilic a t e ~ . In ~ the latter case, a comparison of the spectra obtained at X- and K-band microwave frequencies with isotopically enriched BL0samples demonstrated conclusively that the five lines arise from an anisotropic boron hyperfine interaction. (21)R. H. Silsbee, J. Appl. Chem., 3 2 , 1459 (1961). (22)R. A. Weeks and E. Sonders, Proceedings of the First International Conference on Paramagnetic Resonance, Jerusalem, Israel, North-Holland Publishing Co., Amsterdam, 1963, p 869. (23) D.J. C. Yates, unpublished work. (24) (a) A. 5. Shuskus, 0. R. Gilliam, and P. W. Levy, Bull. A m . Phys. Soc., 6 , 246 (1961); (b) the Si2@ hyperfine interaction observed in single-crystal quartz is strongly anisotropic and has not been observed in glasses.2 On this basis, the possibility that the line under consideration in this section arises from a Si29 hyperfine interaction is rejected. (25) N. Sheppard and D. J. C. Yates, Proc. R o y . SOC. (London), A238, 69 (1956).
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For porous glass, an analysis of the five-line spectrum based on a similar anisotropic hyperfine interaction will be presented. The validity of this approach will be shown by the explanation of the position and intensities of other weaker lines observed in the spectrum. Of the group of five lines, the four lines on the highfield side are centered a t g = 2.0023 with an approximately equal splitting of 13.4 gauss. If these peaks are due to the HI ( M ) contribution (notation of ref 5 ) of the Bl1 hyperfine transitions, then the line widths permit a resolution such that the 18% abundant BIO ( I = 3) transitions should also be observed. The seven BO ' lines would have a splitting relative to the B" lines of m 1 / 3 (ratio of the magnetogyric ratios). Three lines with approximately the correct intensity and falling within 5% of the predicted positions are observed (Figure 1). The predicted positions of the remaining four lines are in a region overlapped by the asymmetric line and the Bll lines. The remaining line of the group of five lines lies at lowest field and is assigned to the H I [( M = 3//2) contribution. At room temperature, the other three accompanying peaks are not directly observable. At 77"K, the spectral resolution is increased sufficiently to show the presence of another line of the same phasing and intensity as the lowest field line (Figure 3a). At room temperature, this line overlaps with a Bl0 line causing the latter to appear somewhat more intense than the other two BO ' lines that are observed. This additional peak is assigned to the H II ( M = - 3//2) contribution. The possibility that this line is due to one of the M I = f l / Z components is ruled out, for, in this case, the magnitude of the splitting involved would allow all four components to be observed. If this assignment is correct, the H i ( M ) components are centered at g = 2.0100 and separated by 14.9 gauss. A sketch of the theoretical line shapes (neglecting relaxation processes) using the parameters obtained above is given in Figure 3b. The unequal intensities of the perpendicular components of the B" lines when observed at 77°K (Figure 3a) may be due to a partial overlapping with parallel components. The line width at 77°K allowed considerable precision in the measurements of the splittings of the four HI ( M ) components. As noted above, these splittings are only approximately equal. For example, by using the results from five different samples, the spacings between the four lines were found to be 13.62 f 0.08, 13.28 0.08, and 13.36 f 0.08 (and in that order from low to high field).26 These variations in the splittings do not correspond to quadrupole or second-order effects.2' They may arise from a shift in the apparent
*
The Journal of Physical Chemistry
i Figure 3. ( a ) Esr spectrum of ?-irradiated porous glass a t 77°K showing increased resolution. ( b ) Theoretical line shapes (neglecting relaxation processes) computed using magnetic parameters given in eq 1.
center of the line due to the differences in the amount of overlapping of parallel and perpendicular components for each hyperfine line. I n the case of irradiated borosilicate glass,5 the observed Bl1 line widths were considerably greater than obtained here for irradiated porous glass. In addition, the line width did not narrow at 77°K in contrast to porous glass where a narrowing by a factor of -2 is observed. The difference in behavior of the two glasses may be attributed to their difference in structure and chemical treatment prior to irradiation. In the case of porous glass, the relatively open structure may lessen line broadening due to dipolar interactions with neighboring atoms. Similarly, the strong dehydra tion treatment given porous glass before irradia(26) The value for A i / g k = 13.4 gauss quoted above is the simple average of these three spacings. The variation in the spacings makes a meaningful estimate of the experimental error in the magnetic parameters difficult. If it is arbitrarily decided to estimate the error as a tenth of the line width, the error would correspond to 0.2 gauss at 77OK. (27) B. Bleaney, Phil. Mag., 42, 441 (1951).
?-IRRADIATED HIGHSURFACE AREASILICA
tion” presumably would decrease dipolar broadening due to water molecules trapped in the glass structure. Since B” has a considerable quadrupole moment, the question of a quadrupolar interaction deserves further consideration. The effect of this interactionz7 is to cause the hyperfine spacings to become unequal and to introduce weak lines corresponding to AMI = *l, -1-2. An estimate of the magnitude of the expected effects at arbitrary orientation of the crystalline axis relative to the applied field can be made by using the upper limit of the range in B” quadrupole constants reported in nmr studies.28~2* This estimate indicates that both the shift in the position of the lines and the intensities of the extra lines are small effects. In the following, it will be a.ssumed that the integration over all orientations also gives a small effect, and, consequently, the quadrupole effects are not discrebely observable in the spectrum. ao Finally, then, the five-line spectrum can be described by the spin Hamiltonian
with I = 1/21 911 = 2.0100, g1 = 2.0023, A I ]= 1.40 X em-’, and A I = 1.25 X cm-I. D. Broad Background Line. A line similar to that making up the broad background in Figure 1 has been reported in a wide variety of silicate-based glasses.1*3~5~7~31 The apparent g value varies with the material but is always greater than that of the free electron. The line width depends upon chemical composition, typical values lying in the range from 12 to 51 gauss. Also, the line width is reported to be independent of microwave frequency3’ in some samples, but depends upon frequency in others.‘ The integrated intensity of the broad line observed in this work is too large to be explained in terms of a contribution from the polycrystalline averaging of the intensity of the boron lines discussed above. Rather, it is believed that this broad background represents an additional line, independent of the other lines described above. The evidence for this statement lies principally in the followine observations. First. the intensitv of the background line (per unit radiation dose) was always higher if the glass was not acid NO other features of the spectrum were observed to change. An effect similar to this has been observed in aluminosilicate7 glasses and fused silica.’ In these cases, the intensitv of the background line was found to depend on the alumina content and water content, respectively. Secondly, a~ discussed in part 11, the v
-
1395
initial effect of carbon monoxide on the acid-leached sample is to remove most (but not all) of the broad background but to leave the other lines unchanged. In y-irradiated synthetic fused silica, a similar broad background has been attributed to defects intrinsic to the Si0 n e t w ~ r k . ~ *The ~ ’ line width can be explained by the anisotropy in the g tensor.31 In other silicas’ and in aluminosilicate glas~es,~ the resonance is thought to arise from holes trapped on nonbridging oxygen atoms. In the case of porous glass, the present experimental results do not allow a definite assignment to be made. I n part 11, it is shown that hydrogen or deuterium added to the irradiated sample causes a “bleaching” of both the B1’ spectrum and the broad background line. Since the effect of carbon monoxide indicates the B” spectrum and the broad background are independent, while the hydrogen results suggest they are chemically similar, a reasonable hypothesis would be that the broad background arises from a Si-0 defect which is the counterpart of the B-0 defect. On the basis of electronegativity values, the Si-0 bond is intermediate between the B-0 and A1-0 bonds in covalent character. Since spectra for holes trapped on an oxygen bound to tetrahedrally coordinated boron5 and aluminum’ have been reported, a similar defect in the case of silicon might be expected. The above hypothesis is then consistent with this observation concerning the covalent nature of the bonding involved. The parallel is not complete, however, for in the silicon case, a cation is not required for charge compensation in the unirradiated material.
IV. Boron-Oxygen Defect In a previous section, it was concluded that the fiveline spectrum was the result of a B” hyperfine interaction. In the present section, an attempt will be made to interpret the parameters in the spin Hamiltonian given in eq 1. The boron hyperfine interaction observed in the glass is small compared to that observed in the free atom. Therefore, it is assumed that the “magnetic electrons” occupy extended molecular orbitals33 in(28) K. 6. Pennington and H. E. Petch, J . Chem. Phys., 36, 2151 (1962). ibid.* 3031 (1964)* (29) E. Brun and *’ (30) Other intense lines in polycrystalline spectra sometimes arise a t angles other than 0 or ~ / if 2 the g and A tensors are specially related. Since no intense “extra” lines were observed in this study, the point is not considered. For an approximate treatment of this effect, see H. R. Gersmann and J. D. Swalen, J . Chem. Phys., 36, 3221 (1962). (31) R.A. Weeks, J. A w l . Phys., 27, 1376 (1956). (32) All parameters being reported in this paper have been obtained from samples that were acid leached. For a description of the leaching process, see ref. 12.
*’,
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volving nearest neighbors, presumably oxygen. The contribution of boron to the molecular orbital may be approximated by r$ = {(u:2s> bi2p)). In this expression, { is a measure of the contribution of the boron atomic orbitals to the hyperfine interaction. The principal values of the g tensor are equal or greater than the free-electron value. I n the absence of any information concerning the excited states mixed into the ground state by the spin-orbit coupling, it will be assumed34 that the condition gll > gl = ge implies that a hole is involved. The anisotropy in the hyperfine tensor implies the hole interacts preferentially with only one of the boron nearest neighbors.,e A simple model fitting this description would be a hole trapped in a boron-oxygen bond. The system to be treated then involves seven electrons distributed in four orbitals. The hyperfine interaction for this system is represented by the operator35where the symbols
+
have their usual significance. To express the interaction as a function of the spin coordinates only, the orbital coordinates are integrated To simpilfy the integration, contributions to the matrix elements involving cross terms of boron and oxygen orbitals are neglected. Since the interaction falls off rapidly with distance, the approximation seems justified.” Comparison of the results of the integration with eq 1 gives the equalities
+ 2b2P)
All
= {‘(u’L~
A1
=
cy - bzP)
to fit the sp3 case. The latter error is equivalent to 1.4 times the line width and thus seems unjustifiably largesag Therefore, in the following it will be assumed that the B” hyperfine interaction arises from a trigonally coordinated boron. It is interesting to consider the difference in the hyperfine parameters reported here for porous glass and those reported for sodium borate glass by Lee and Bray.5 By using their experimental parameters, a calculation similar to that given above gives a per cent anisotropy [ = ( AI I - A . ) / A ’ ] of 20% compared to a theoretical value of 21% for an sp3 hybrid. This is in good agreement with their suggestion that a tetrahedrally coordinated boron was involved in the sodium borate case. I n an nmr study, Silver and Bray40 showed that the ratio of the concentration of fourto three-coordinated boron atoms in this type of glass is an increasing function of the concentration of the network modifier (NazO) present. This result suggests that the difference in coordination observed by esr in the porous glass and sodium borate glass can be understood in terms of the low sodium content (typically 50-400 ppm) of the porous glass. The explanation is in agreement with the present theory of the role of NazO as a network modifier.40 If it is assumed that the hybridization for the case of porous glass is exactly sp2, then u2 = 1/3 and { = 0.24. A similar calculation for the sodium borate glass assuming sp3 hybridization (az = l / 4 ) gives { = 0.28. The lower value of C for the sp2 hybrid presumably reflects the increased electropositive character of the sp3 hybrid relative to the sp2 hybrid, viz., a hole is more strongly “attracted” to the former since it has a higher electron density due to the formation ~
P
=
‘/6(~-’)gePegnPn
(3)
where ( 7 3 is taken over a boron 2p orbital. From an SCF calculation (including configuration interaction) for boron,38 I+(0)lz can be estimated as ~ m - ~ The . value (+) for boron has been 9.56 x estimated5 from atomic beam data as 5.41 X loz4 cm-3, Based on these values, the results cy = 6.77 X cm-’ and 0 = 1.83 X ern-l are obtained. If the isotropic hyperfine interaction is defined as A’ = ‘/3(All 2A.) = 1.30 X cm-l, then the value of {zuz must be 0.0192. A similar algebraic manipulation gives l z b 2 = 0.0273 and finally h = u2/b2 = 0.7. For sp2and sp3hybrids, h would equal 0.500 and 0.333, respectively. A 5% increase in the experimental value of A l l would give the theoretical ratio for the sp2 hybrid, whereas a larger error (14%) would be required
+
The Journal of Physical Chemistry
~~
~
~~~~~
(33) K.W.H.Stevens, Proc. Roy. SOC.(London), A219, 542 (1953); J. Owen, ibid., A227, 183 (1955). (34)C. P. Slichter, “Principles of Magnetic Resonance,” Harper and Row Publishers, Inc., New York, N. Y., 1963,Chapter 7. (35) 9. M.Blinder, J . Mol. Spectry., 5 , 17 (1960). (36) B. Bleaney and K. W. H. Stevens, Rept. Progr. Phys., 16, 108 (1953); W.V. Smith, P. P. Sorokin, I. L. Gelles, and G. J. Lasher, Phys. Rev., 115, 1546 (1959). (37) (a) M. Tinkham, Proc. Roy. SOC.(London), A236, 549 (1956); (b) A. H.Maki and B. R. McGarvey, J . Chem. Phys., 29, 31 (1958). (38) I. I. Glembotskii, V. V. Kibartas, and A. P. Yutsis, Z . Eksperim. i Teor. Fiz., 29, 617 (1955); Soviet Phys. J E T P , 2, 476 (1956). (39) (a) From eq 3 we find All / A . = (ha 2b)(ha - @ ) - I . With this expression, it is readily shown that any attempt t o fit the data to the sp3 case by varying the value of $ ( O ) 2 over a reasonable range will automatically result in a better fit for the sp* case. For example, if SCF wave functions without configuration interaction3gb are used, a 10% increase in All is required to fit the sp3 ratio, but only a 2% increase is needed to fit the spz case. In this discussion, we are assuming the major errors occur in A
