-~ ~
~
Table XI. Calculated Values for
A’
and Equilibrium Constants
Compound
Structure
Proton
A0
KCL~
Valeronitrile
CH3CH2CH2CH2‘CN
1
4
1
4-Methylvaleronitrile
CH3CH-CH2CH2’CN
1
4
11
1
5
4
1
2 1 1
17
2 1 2
17
20
3
4 1 4
1
2
26
I
CH3
Hexanenitrile
CH3CH2CH2CH2CH2’CN
Acrylonitrile
2
3
Methacrylonitrile
1 2
3
Allyl cyanide
3,3-(Tetramethylene dioxy) dipropionitrile a Significant to
1 2
NCCH2’CH2OCH2CH2CH2CH2OCH2CH2’CN
one figure.
where [L]” = concentration of ligand in mol/l., A = differential shift of equilibrium mixture, and x = mole ratio of initial concentrations of chelate/ligand. Utilizing the above expression, values of K C L were obtained and are given in Table XI. These appear to be in agreement in magnitude with the value of 12 reported for the acetone/ FOD system (2) and for amine and alcohols (20). The values of KCL are only significant to one digit since the calculation of KCLinvolves small differences between sets of experimental data, i.e., differential shifts and mole ratios. Constant values for the equilibrium constants were (10) I. Armitage, G. Dunsmore, L. D. Hall, and A. G. Marshall, Chem. Cornmun., 1971, 1281.
not obtained in several cases, suggesting that those systems were not simply 1:l complexes in the concentration range studied or that experimental accuracy was insufficient. Equilibrium constants for mono and difunctional groups in general are still under investigation. Work is under way to extend the study of these organonitrile-shift reagent complexes to l3C NMR observations in order to further elucidate bonding in the structures and other factors involved in their formation. Received for review October 31, 1972. Accepted February 1, 1973. Presented a t the Pittsburgh Conference on Analytical Chemistry and Applied Spectroscopy, March 6-10, 1972.
External Standards in X-Ray Photoelectron Spectroscopy A Comparison of Gold, Carbon, and Molybdenum Trioxide William P. Dianis and Joseph E. Lester’ Department
of C h e m i s t r y , N o r t h w e s t e r n U n i v e r s i t y , Evanston, 111. 60207
The binding energies of the 4fs/2 and 4f7/2 peaks of gold and lead in Pb3O4 were measured and found to differ from the previous literature values. We suggest the following values: for gold, 4f5/2 = 87.7 eV, 4f7/2 = 84.0 eV; for Pb304, Pb 4f512 = 142.7 eV, Pb 4f712 = 137.8 eV. When making binding energy measurements in nonconductors, a surface charge may build up, causing an error in the observed binding energies. The abilities of M o o 3 , 1416
ANALYTICAL C H E M I S T R Y , VOL. 45, NO. 8, J U L Y 1973
vapor-deposited gold, and carbon impurity to compensate for surface charge errors were evaluated. I t was concluded that the use of gold and carbon, but not Mo03, as an external standard would allow one to correct for surface charge errors. However, uncertainty about the carbon 1 s binding energy makes it an unsatisfactory standard. Criteria for appropriate binding energy references are discussed.
X-Ray photoelectron spectroscopy is a method for accurately measuring the binding energy of inner shell electrons in solids, liquids ( I ) , and gases ( 2 ) . In the case of solid samples, the accuracy of a binding energy measurement depends upon a knowledge of the spectrometer work function, and if the sample is nonconducting upon the amount of surface charge ( I ) . The surface charge correction is given in the following equation.
EBEis the binding energy, E,,, is the observed kinetic energy, GsP is the spectrometer work function, and GCH is the surface charge. Since the presence of a positive surface charge creates an additional potential barrier for the photoelectrons, the observed kinetic energy is decreased, and the correction is negative. As the field of X-ray photoelectron spectroscopy has developed, the need for a universally recognized binding energy reference has become increasingly clear. Elements with one well-established binding energy value already allow one to measure directly the spectrometer work function. For example, Baer et al. ( 3 ) in studies of the valence bands of transition metals, have used the midpoint of the low energy edge of the valence band of palladium which corresponds to its Fermi level as the reference energy. Assigning a value of zero to the binding energy a t the Fermi level allows one to directly measure the spectrometer work function. The subsequent work on graphite ( 4 ) using this calibration procedure yielded a second reliable binding energy that can be used as a check in calibration procedures. However, these elements by themselves do not constitute a general binding energy reference. Such a reference would be used with a compound in such a way that one could simultaneously measure the spectrometer work function and correct for surface charge errors. Siegbahn ( 1 ) first suggested that the carbon 1s line from pump oil vapors be used as a reference, and he assigned it a binding energy of 285.0 i 0.4 eV. Many workers have followed his lead, but recently the use of the carbon Is line has been questioned. Nordling e t al. ( 5 ) have suggested that polarization of the thin layer may shift the carbon 1s binding energy from its nominal value. They concluded that mixing two samples together to measure relative chemical shifts or mixing a sample with a reference such as graphite ( 5 ) or Pb304 (6) gave better results. In addition, K N 0 3 has been used as a reference in a study of nitrogen compounds (7), and Na4Pz07 has been used for phosphorous compounds (8). An alternative to using carbon in “pump oil” is provided by depositing a thin layer of noble metal on the surface of the sample and using the 4f peaks of the metal as a binding energy reference (9-11). Hnatowich et al. have shown that Au 4f peaks shift by the 1 Person
to whom correspondence should be addressed.
K . Siegbahn, C. Nordling, A . Fahlman, R. Nordberg, K. Harnrin, J . Hedman, G . Johansson, T. Bergmark, S.-E. Karlsson, I . Lindgien, and 6. Lindberg, Nova Acta Regiae SOC.Sci. Upsai.. 20 (1967) K . Siegbahn, C. Nordling, G . Johansson, J . Hedman, P. F. Heden, K. Harnrin. U . Gelius. T. Bergrnark, L. 0.Werme, R. Manne, and Y . Baer, “ESCA Applied to Free Molecules,” North-Holland Publishing Co., Amsterdam, 1969. Y . Baer. P. F. Heden, J . Hedman, M . Klasson, C. Nordling, and K. Siegbahn, Physica Scripta. 1, 55 (1970) K. Harnrin, G . U. Gelius, C. Nordling, and K . Siegbahn, Physica Scripta, 1, 277 (1970). R. Nordling. H . Brecht, R. G . Albridge, A . Fahlman, and J . R. Van Wazer, lnorg. Chem., 9 , 2469 (1970). W . J . SteC, W . E. Mlrgan. R. G . Albridge, and J . R . Van Wazer. Inorg. Chem.. 11, 219 (1972). J . J . Jack and D. M . Hercules, Anal. Chem., 43, 729 (1971). W . E. Swartz and D. M . Hercules, Anal. Chem.. 43, 1066, (1971). J. M . Thomas, E. L. Evans, M . Barber, and P. Swift, Trans. faraday SOC.,67, 1875 (1971).
Figure 1. Drawing of the gold deposition apparatus as it is positioned in the source region of the spectrometer
( a ) Copper block holding sample; ( b ) stainless steel rod, attached to the spectrometer through a battery; (c) hollow cylindrical shutter; ( d ) COW mator for gold beam; (e) gold-tungsten filament assembly-9 cm from target. X-Rays originating from X-ray gun in source region (gun not shown) travel horizontally to the sample, Photoelectrons leave vertically.
amount of the induced surface potential on BaS04. They did not indicate if the C 1s peak also followed the surface potential ( I O ) . The work of Hnatowich et al. did, however, lead to a direct comparison of an internally mixed standard, M003, with vapor-deposited gold. Swartz, et al. (12) concluded that MOOS was superior to vapor-deposited gold. Thus, we have several different external standards, but it is not clear if their use results in binding energies which agree with one another. Furthermore, there are a t least three different values in the literature for the binding energy of the Au 4f7,~ level ( I , 13, 14). This study was undertaken to remeasure the Au 4f binding energies and to determine what errors are likely to occur when using one of the different standards.
EXPERIMENTAL Apparatus. Spectra were recorded on a n AEI ESlOO B spectrometer using A1 K a radiation (1486.6 eV). Calibration of the instrument (see Procedure below) was done using Mg K a radiation (1253.6 EV). A vacuum of 3 X IO-’ Torr or better was maintained throughout the experiment. Some spectra were recorded with a dc potential applied to the sample rod ( b in Figure 1). In this case the sample rod was connected to a dc power supply stable to f.0.02 V. The voltage applied to the rod was continuously monitored with a digital voltmeter. Gold was vapor deposited onto various samples with the apparatus shown in Figure 1. Its use is described below. Complex gold spectra were deconvoluted with the aid of a Model 310 Du Pont curve resolver. Reagents. Gold foil, gold wire, platinum foil, graphite wafers of high purity, and reagent grade Moo3 and Pb304 were all used without further purification. Procedure. Gold foil, platinum foil, and graphite wafer samples were mounted directly on a copper block ( a in Figure 1) attached to a stainless steel rod ( b in Figure 1). Pb304 was pressed onto an aluminum plate, and the plate was then mounted on the copper block. h1003 was pressed onto platinum foil and the foil (10) D. J . Hnatowich, J . Hudis, M . L. Perlman, and R. C. Ragaini, J. Appl. Phys., 42,4883 (1971). (11) J . M . Thomas, I . Adarns, and M . Barber, Solid S a f e Cornrnun., 9, 1571 (1971). (12) W. E . Swartz, P. H . Watts, J . P. Watts, J . W . Brasch, and E. R. Lippincott, Anal. Chem., 44, 2001 (1972). (13) J . Bearden and A . Burr, Rev. Mod. Phys., 39, 125 (1967). (14) C. S . Fadley and D. A. Shirley, J . Res. Nat. Bur. Stand. Sect. A , 74, 543 (1969).
ANALYTICAL CHEMISTRY, VOL. 45, NO. 8, JULY 1973
1417
T
3400[
n
Mo
I
f
t
1
'
2500.> k
*p,. '. '
z"
2100-
W
t ! 9
BINDING ENERGY
l
i
238
-z
i
L.
1000+l i '
-
k
l
l
l
1
*.
1700,
234 230 226 BINDING ENERGY Figure 2. Carbon Is, gold 4f,and molybdenum 3d spectra from Moo3 with an applied bias of - 5 V
287
283
279
BINDING ENERGY
A u , gold 4f region: Mo, molybdenum 3d region; C, carbon 1 s region
Table I. Binding Energies of Gold and Platinum
I. Au on Pt: Assuming carbon C 1 s impurity = 285.0eV Pt 74.8 71'5 13.2 12.8 Au 88.0 84.3 II. Au on Pt: Assuming platinum 4 f 7 / 2 = 71.2eVa Pt 74.5 71'2 13.2 12.8 Au 87.7 84.0 I I I. Au on C: Assuming graphite 1s = 284.3b Au 87.6 83.9 VI. X-Ray atomic energy levelsC Pt 74.3 71.1 12.1 11.7 Au 86.4 82.6 a Pt 4 f 7 / 2 value from C. Cook, Y. Wan, U. Gelius, K. Hamrin, G . JohansSon, E. Olsson, C . Mordling, and K. Siegbahn, J. Amer. Chem. SOC., 93, 1904 (1971). The carbon C 1s impurity peak was at 284.7 eV. bReference 4 . From ref 13.
was then mounted on the copper block. When no dc potential was applied to the sample rod, the rod was grounded to the spectrometer. Before beginning the experiments described in this paper, the calibration of the instrument was checked in the following way. First, a Mg X-ray target was installed and a gold foil sample was inserted in the spectrometer. The X-ray gun is isolated from the sample area by a thin aluminum foil window. Primary X-rays penetrate the window, but bremsstrahlung radiation and stray electrons from the X-ray gun are filtered out. Electrons used to generate Mg X-rays also generate weak aluminum X-rays from this window. Therefore, the spectrum contains two 4f7/2 peaks of gold. One peak arises from photoelectrons generated by the Mg radiation and the other arises from photoelectrons generated by A1 radiation. The separation of these two peaks to the difference in energy of the two photon sources is 233.0 eV. Appropriate electronic adjustments were made so that the gold 4f7n peaks did indeed differ in observed kinetic energy by 233.0 eV. Scanning was controlled by a P D P 8/S computer. Kinetic energy was scanned in increments of 0.1 eV, and counting times were chosen to yield S / N > 30 for the major peaks in the spectrum; if necessary, repetitive scans were summed. The final digitized spectrum was used as input to a Fortran smoothing program. Smoothing was performed in the following way. A 13-point seament of the spectrum was fitted to a parabola using a linear least-squares computer routine. The average value of the intensity at the middle of the segment was calculated from the parameters for the parabola and the position of the point. A new segment was then chosen by dropping the first point of the segment and adding the next point in the original spectrum. This procedure was repeated until average values had been calculated a t all interior points of the spectrum. A smooth line was then drawn through the averaged intensities. An analysis of position and fullwidth-at-half-maximum (FWHM) was carried out on the simpler spectra with a second Fortran program. In this program, Gauss1418
ANALYTICAL CHEMISTRY, VOL. 45, NO. 8, JULY 1973
ian peak shapes were fit to the spectrum by a modified GaussNewton nonlinear least-squares routine (15). The gold deposition apparatus is shown in Figure 1. On the spectrometer, access to the source region is obtained through two insertion locks. The copper block holding the sample is attached to a stainless steel rod and placed in front of the X-ray beam. In order to protect other parts of the source region, a hollow cylindrical shutter was attached to a second stainless steel rod and placed in the source region through the other insertion lock. Part of the cylinder was cut away so that in one orientation of the shutter, the copper block is shielded from the gold vapors, but when the shutter is rotated B O " , the block is exposed (the copper block is also rotated so that the sample is perpendicular to the beam). The gold source consisted of 0.020-in. diameter gold wire wrapped around a 0.010-in. diameter tungsten filament. The ac heated filament was operated a t a temperature such that a thin layer of gold could be deposited on the sample after 10-20 sec of exposure. The binding energy of the gold 4f peaks were measured by first vapor-depositing a thin layer of gold onto a platinum foil or graphite wafer substrate and then determining the gold-platinum or gold-graphite peak separations. In these experiments, the gold layer was sufficiently thin to allow examination of the substrate peaks after the gold deposition. In general, the substrate peaks were attenuated by less than 50% by the gold film. The binding energy of the lead 4f peaks in Pb304 was measured in the same way. In the first instance, the gold 4f binding energies were determined using the substrate for reference (see Results and Discussion). The gold 4f values we obtained were then used to assign the P b 4f binding energies. Since oxides have been used as binding energy references, we chose to examine the influence of an applied potential upon the observed kinetic energy of the 3d peaks in Moos. Gold was deposited onto M O O 3 and the carbon Is, gold 4f, and molybdenum 3d peaks were examined. A dc potential was then applied to the copper block to simulate sample charging due to photoelectron emission from an insulating sample. The three spectra were recorded again at potentials of - 2 . 5 , zt5.0, and zk7.5 V.
RESULTS AND DISCUSSION Table I shows the binding energies of platinum, gold on platinum, carbon contamination on platinum, and gold on graphite. While these spectra have been recorded many times by different workers, it has not been pointed out that a discrepancy exists between the binding energies for gold and platinum given by Bearden and Burr (13) and the values obtained by X-ray photoelectron spectroscopy. Based on the data of Bearden and Burr, the spacing between the gold and platinum 4f5,z peaks should be 12.1 eV; we find it is 13.2 f 0.1 eV. Furthermore, this spacing is a directly measured experimental quantity, independent of any binding energies assigned to gold or platinum peaks, and independent of spectrometer work function. No surface charge correction is necessary for metals. In (15) D W. Marquardt,J S l A M 2,431 (1963).
~
Table II. Shifts in Binding Energy as a Function of Applied Bias for Mo 3d, C Is, and Au 4f5/2 on Moo3 Applied bias
MO 3d3/2, eV
0
0
+5.Ov
-0.8 -1.4 -2.3 +2.4
+ 7 5v
4-4.0
-2.5 -5.0
-7.5
c 1%
ALI
eV
-0.8 -1.4 -2.40 4-25 +4.0
4f512,
I540
eV 0
0
-2.1 -4.9 -7.3 4-4.8 +7.5
-0.8
-1.3 -1.9 +2.4
4-4.0
1
-2.5 -5.0
BO--
-7.5 +4.9 4-7.5
m-.
view of the consistency in the values we obtained for the 4f peaks of gold using two different substrates for reference, we conclude that the table of Bearden and Burr is in error and that the gold 4f7,2 peak should be assigned a binding energy of 84.0 f 0.3 eV. The 4f5/2-4f7/2 separation was observed to be 3.71 ( 2 ) eV. We note that our value of 84.0 eV for the 4f7 2 peak agrees exactly with the value obtained by Fadley and Shirley (14) but disagrees with the value given in the book of Siegbahn et al. ( I ) . Using our values for the gold 4f peaks, we deduced that the 4f5/2 and 4f7 2 peaks of lead in Pb304 had binding energies of 142.7 and 137.8 eV, respectively. Van Wazer's (6) value for the 4f7 2 peak of Pb304 was 138.5 eV. The binding energy of the carbon impurity in our sample of Pb304 was found to be 284.5 eV. As described in the experimental section, the molybdenum 3d, gold 4f, and carbon Is peaks of Moo3 were examined with a dc potential applied to the sample. Figure 2 shows a typical set of spectra recorded with an applied voltage of -5.0 V. An ordinary molybdenum spectra was observed along with two carbon peaks and three prominent peaks in the gold region. Figure 3 shows the gold spectra at the other voltages. The general shape of the molybdenum peaks was the same a t all applied voltages. The carbon spectrum also showed evidence that two peaks were present at each applied voltage. From Figure 3, one can see that the complexity of the gold spectra varied. When no voltage was applied, the binding energies of the molybdenum 3d3 2 and 3d5/2 peaks (relative to gold 4f7,2 = 84.0 eV) were found to be 235.5 and 232.3 eV, respectively. Swartz and Hercules (16) obtained values of 235.6 and 232.5 eV. However. when a potential bias was applied to the sample, the binding energy of the molybdenum peaks did not change by the amount of the applied voltage. Table I1 shows the change in the molybdenum 3d3/2 peak binding energy as a function of applied voltage. Using a Du Pont Curve Resolver, the positions of the two peaks in each carbon spectrum were determined. In each case, the binding energy of one carbon peak was shifted from its value at zero bias by the amount of the applied bias, while the other peak was shifted by the same amount as the molybdenum peak. An analysis of the gold spectra showed that in every case they could be deconvoluted into two sets of doublets. One doublet was shifted from its zero-bias binding energy by the amount of the applied bias and the other was shifted by the same amount as the molybdenum peak. We believe that these spectra can be easily explained. The MOO3 did not cover the entire area irradiated by the X-rays. Thus, gold on the surface of MOO3 would give one doublet and gold directly in contact with the platinum substrate would give another doublet. The two doublets would not coincide if the two regions of gold were a t different potentials. The carbon spectrum would consist of carbon on Moo3 and carbon in electrical equilibrium with the substrate. The complex gold spectra cannot be the re(16) W. E. Swartzand D. M. Hercules,Ana/, Chern., 43, 1774 (1971).
a
1660.-
b
1460.-
1260.-
.
..I
1060.-
>.
k
2 W
IOIO--
2 910-
C
810-
t., ...; 102
98
94
90
86 "DING
82
78
74
ENERGY
Figure 3. Gold on MOOS taken at different applied voltages (a) -7.5 V; ( b ) -2.5 V: ( c ) +5.0 V; ( d ) + 7 . 5 V. The doublet marked Pt in d is due to the Pt 4f7,2 levels of the substrate
sult of an overlap of gold and platinum peaks. Spectrum d in Figure 3 shows two strong peaks a t the far right of the spectrum. These are the platinum 4f peaks and they are shifted by the amount of the applied voltage. Three conclusions can be reached from this analysis. First, a t least in this case, the binding energy of the carbon impurity was a function of the surface charge on the Moo3. Second, since MOO3 did not shift its peak position by the amount of applied voltage, if one mixed MOO3 with another sample and tried to use the molybdenum 3d312 peak for a binding energy reference, one could not assume that the molybdenum peak would shift position as a function of surface charge on the other sample. In short, MOO3 would be a poor binding energy reference. The problem probably does not lie with MOO3 per se but in the fact ANALYTICAL CHEMISTRY, VOL. 45, NO. 8, JULY 1973
1419
~~~~
~
~
Table I l l . FWHM of Carbon, Molybdenum, Gold, and Platinum Peaks in eV I. Carbon peaksa
1s 2.05 (5)a 1.96 (4) 1.86 (4) 1.77 (4)
C o n MoO3-before Au dep C on Moo3-after Au dep C on Pt-before Au dep C on Pt-after Au dep 1 1 . Molybdenum peaksa Moo3-before Au dep MOOS-after Au dep I1I. Pt and Au 4f peaksa Pt-before Au dep Pt-afte'r 19 hr in vacuum (before Au dep) Pt-after Au dep Au-on Pt Au-on Moo3
3d3/2 1.75 (4) 1.62 (4)
3dwz 1.70 (3) 1.61 (2)
4f5/2 1.89 (6)
4f7/2 1.60 (4)
1.70 (8) 1.75 (7) 1.41 (5) 1.42 (6)
1.52 (6) 1.58 (6) 1.26 (4) 1.28 (6)
a The number in parenthesis is the standard deviation obtained from the variance-covariance matrix generated by the computer program (see text for a discussion of this Doint).
that it is not a good conductor. We would, therefore, question the use of any external standard with poor conducting properties, such as ionic salts or metal oxides. Third, in the three different substances studied here, the binding energy of the carbon Is impurity was not 285.0 eV. We would agree with the criticism of Hnatowich et al. (IO) that one cannot be certain of the origin of the carbon contamination. While pump oil is certainly one source of contamination, it may not be the predominant one in every sample. Some contamination undoubtedly results from normal laboratory handling. Furthermore, many surfaces are catalytically active. Even if the only source of contamination were the pump oil, the interaction of the vapor with the actiie surface might shift the binding energy of the carbon. Therefore, one cannot be certain that one is looking a t the same type of carbon every time. A more critical examination of the carbon, molybdenum, and platinum peaks before and after gold deposition showed that changes occur in the FWHM. The FWHM obtained from our least-squares computer program are given in Table 111. For both the platinum and the Moo3 substrates, there is a slight decrease in the FWHM of the carbon peak after the gold deposition. The line width of the molybdenum peaks also decreases after the gold deposition. Perhaps the line widths of the carbon and molybdenum peaks are somewhat dependent upon the surface conditions. I t is likely that slight variations in the surface charge would cause a broadening of these peaks. The highly conductive gold coating may help the flow of electrons on the surface, thereby equalizing the surface charge.
1420
ANALYTICAL CHEMISTRY, VOL. 45, NO. 8, JULY 1973
Objections to the above analysis might be raised because of the larger uncertainties in the estimates of the FWHM. Our computer program estimates standard deviation from formulas derived from linear least-squares theory. It is well known that these formulas are not precisely correct in nonlinear situations (17, 18). An analysis of the sensitivity of the sum-of-the-square-of-the-residuals to changes in the position and FWHM parameters has led us to suspect that linear least-squares theory significantly over-estimates the standard error in this nonlinear situation.
CONCLUSIONS As a result of these experiments, we believe that several factors should be considered when choosing an external standard. First, the standard should have a well-defined binding energy that is insensitive to its environment. This point is particularly important if the sample is to be subjected to some cleaning treatment in the spectrometer. For example, Moo3 would not be a desirable standard if the sample was to be cleaned by ion bombardment. Naguit and Kelly (19) have reported that under heavy ion bombardment Moos decomposes to form MoOz, with a change in conductivity of 11orders of magnitude. Second, since in many compounds surface charge errors are significant, the standard should be a good conductor. One would like the magnitude and variation of surface charging across the sample to be as small as possible. Therefore, thin samples are preferred to thick ones. If ejected photoelectrons are replaced by a flow of electrons from the bulk of the sample to the surface, then powder samples of small particle size are preferable to samples of large particle size. Furthermore, the standard should have a fairly high concentration near the surface. This requirement might be difficult to meet when mixing two samples together, as the particle size will always b s large with respect to the depth in the sample from which electrons are ejected. Thus, it is conceivable that the standard might be partially insulated from the surface charge. We do not mean to imply that mixing a reference with a powdered sample of interest is an unsatisfactory procedure; indeed mixing gold dust with a sample might be an acceptable alternative to vapor deposition of gold. However, we do suggest that an investigation of the effect of particle size on the reliability of binding energy determinations for insulating powders would be valuable. Received for review August 28, 1972. Accepted January 22, 1973. This work was partially supported by ARPA through the Northwestern University Materials Research Center. The spectrometer was purchased with NSF support (Grant GP-28134). (17) N. R. Draper and H. Smith, "Applied Regression Analysis," Wiley, New York, N.Y., 1966. (18) J. Guttman and D. Meeter, Technometrics. 7, 623 (1965). (19) H. M. Naguit and R. Kelly, J. Phys. Chem. Soiids, 33, 1751 (1972).
