Photoelectric work function measurements on nickel crystals and films

SURFACE

SCIENCE 24 (1971) 572-586 0 North-Holland

PHOTOELECTRIC

WORK

NICKEL B. G. BAKER,

FUNCTION

CRYSTALS B. B. JOHNSON

Publishing Co.

MEASUREMENTS

ON

AND FILMS and G. L. C. MAIRE*

School of Physical Sciences, Ninders Adelaide. South Australia

Received 28 July 1970; revised manuscript

University,

received 23 September 1970

Photoelectric emission has been measured from nickel surfaces prepared by cutting bulk single crystals and by evaporating films in ultrahigh vacuum. For single crystal planes identified by LEED, the electron work functions were determined as (1 lo), 5.04 eV; (100) 5.22 eV and (11 l), 5.35 eV. It is shown that under favourable conditions these crystal planes can be identified, and their extent estimated, from photoelectric emission measurements on heterogeneous nickel surfaces. Results obtained from nickel films epitaxed on mica and rock salt show that these surfaces are usually not sufficiently homogeneous to permit the work function of the preferred orientation to be determined accurately.

1. Introduction Although the work function of polycrystalline nickel has been measured many times there are few measurements for clean, well characterized nickel crystalsi-3). The principal experimental difficulty has been to prepare well defined surfaces, sufficiently homogeneous to allow the electron emission to be unequivocally assigned to a particular crystal plane. The photoelectric method for determining the electron work function is particularly susceptible to errors arising from even small heterogeneous regions. Atomically rough surfaces, and crystal planes with surface atoms of low co-ordination, generally have low work functions. The presence of such regions on an otherwise well-defined crystal of higher work function results in a lowering of the photoelectric threshold and an estimation of the work function biased in favour of the low work function region. This influence of patch fields on photoelectric emission has long been recogniseda-8) and in principle it is possible to differentiate between patches on a surface provided they are large enough and have sufficiently different work functions. * Present address: Laboratoire

de Chimie, Faculte des Sciences, 14-Caen, France. 572

PHOTOELECTRIC

WORK

FUNCTION

MEASUREMENTS

ON NICKEL

573

It is the purpose of this paper to present experimental results for photoelectric emission from nickel surfaces prepared by cutting bulk single crystals and by evaporating films in ultrahigh vacuum. The experiments are interpreted to obtain values for the work functions of the (1 lo), (100) and (111) planes of nickel and a method is developed for identifying and estimating the extent of these planes on heterogeneous nickel surfaces. 2. Experimental procedure 2.1. APPARATUS The experiments on bulk single crystals were made in a Varian LEED chamber with a silica window fitted to a side port. The crystal was turned through 90” from the normal incidence diffraction position when photoelectric measurements were made. An anode was provided at another side port to the chamber. Evaporated films were prepared and examined in a glass ultrahigh vacuum system fitted with metal valves and a triode ion pump. Both systems maintained a vacuum of -5 x 10-l’ torr after the usual bakeout cycle. For the photoemission measurements a grating monochromator with high pressure xenon lamp and achromatic condenser lens (Bausch and Lomb) provided a focussed ultraviolet beam of satisfactory spectral purity. A calibration of light intensity with wavelength was determined using a quartz vacuum thermocouple. The photocurrents were measured with a vibrating reed electronmeter (Vibron, Model 62A). 2.2. SPECIMENPREPARATION Three nickel crystals were prepared by spark erosion cutting from a cylindrical single crystal of nickel. The orientations of the cut faces, determined by X-ray diffraction, approximated (11 l), (100) and (110). These crystals were electropolished before mounting in the LEED chamber. Each crystal was then treated by successive argon ion bombardment and vacuum annealing. On some occasions it was found necessary to heat the crystal in oxygen and then in hydrogen followed by ion bombardment and annealing. In each case the quality of the LEED pattern was taken as evidence of the progress of the cleaning procedure. The annealing temperatures were determined by a thermocouple welded on to the side of the crystal. Nickel films were evaporated in the glass photocell (fig. 1) from spectroscopically standardized nickel wire (0.5 mm diam.). This wire had been outgassed by previous use for evaporation of a film in another high vacuum system. After bakeout and prolonged outgassing of the nickel filament and specimen mounting block, pressures of < 1O-9 torr were achieved. During

574

B. G. BAKER,

B. B. JOHNSON

AND G. L. C. MAIRE

the evaporation of the film the pressure was maintained at < lo-* torr and was generally -2 x lo-’ torr near the conclusion of the evaporation. The detail of the procedure for evaporated films depended on the nature of the substrate. The experiments on vacuum cleaved mica involved the greatest complexity, but since they include the essential features of the other experiments, their description serves to illustrate the method. A mica specimen (fig. 2) had an air cleaved region at one end with an evaporated coppernickel film thermocouple and two evaporated nickel contact strips. The thermocouple permitted accurate measurement of the film temperature during deposition and the contact strips ensured that there was good electrical

Fig. 1. Glass photocell: A, monel block; B, mica substrate; C, quartz window; D, nickel evaporation source; E, cleaving arm; F, glass-metal seal; G, pumping line; H, photocurrent collector lead.

Fig. 2.

Mica substrate: A, copper-nickel film thermocouple; B, mounting holes; C, nickel film contact strips; D, cleaving bar,

PHOTOELECTRIC

WORK

FUNCTION

MEASUREMENTS

ON NICKEL

575

contact with the film. These contact strips were also used to monitor film resistance during deposition to ensure that films of adequate thickness (> 1000 A) were deposited. The cleaving bar was inserted at this same cleavage plane after the mica specimen was screwed to the mounting block. The cleaving of the specimen was achieved by the magnetic movement shown (fig. 1) only after the completion of outgassing and the achievement of ultimate vacuum conditions. 2.3. PHOTOELECTRIC MEASUREMENTS The monochromator was operated at constant slit width (0.3 mm = 1.O nm band pass) and the photocurrent determined at wavelength intervals of 1 nm ranging from beyond the threshold down to 220 nm. The photocurrents were then corrected to constant light intensity by means of the calibration determined previously. The anode potential was + 180 V. The photocurrent (10-15-10- l2 A) was measured by connecting the specimen to the input resistor (1012 ohm) at the electrometer. Careful electrical shielding was required and the outside of the glass photocell was coated with “Aquadag” and earthed. 3. Results from nickel crystals The prepared nickel crystals were separately mounted in the LEED chamber and, after the cleaning procedures described above, gave high contrast spot patterns with electron energies of 80-90 V. These patterns identified the crystal faces as (1 lo), (100) and (111) respectively. The photoelectric emission from each crystal was determined at 293°K. After this measurement the crystal was returned to the diffraction position and the pattern checked. The photoelectric measurement was then repeated. Background pressures throughout were < 1O-9 torr. The photoelectric results for the three crystals are plotted in fig. 3. 4. Interpretation of results 4.1. PHOTOELECTRIC EMISSION FROM A HETEROGENEOUS SURFACE The work function

is usually

determined from the spectral distribution of method. A plot of log (I/T2) versus function,

photoelectrons by the Fowler isotherm hv/kT is compared with the theoretical log(l/T2) where x= (hv- hv,)/kT, described by Fowlerg).

hv,

= B + logf$(x),

is the work

function

(1) and

4 is the function

576

B. G. BAKER,

B. B. JOHNSON

AND G. L. C. MAIRE

If I is the photocurrent measured in an experiment then the constant B incorporates, among other things, the total area of surface emitting and the intensity of the incident light. For an experiment in which the illuminated area of the specimen is constant and the photocurrents are expressed at constant light intensity, the work function is calculated readily from the displacement needed to fit the experimental curve to the theoretical curve. The theoretical Fowler curve is shown by the broken line in fig. 3a, where it is compared with the photoemission from the (110) nickel crystal. It is obvious that no displacement can fit the result to the theoretical curve. However, the observation can be accounted for by considering that the surface does not have a unique work function but consists of regions with at least two different thresholds.

I

I ", -15 ‘=

b

j -16/.,*, -17 -

/*

/= ,[

1

L

c

,* /--'

-16 -

.*-

-17 -

-18160

Ic

Y

.y

/**

f I 170

180

I 190

, 200

I 210

I 220

lhg/kTi

Fig. 3. Photoelectric emission from nickel single crystals: (a) (110) plane, (b) (100) plane, (c) (111) plane; experimental points (O), full lines computed (see text), broken line calculated for a homogeneous surface [eq. (l)].

PHOTOELECTRIC

Fowler’s

theory

WORK

is readily

FUNCTION

extended

MEASUREMENTS

ON NlCKkL

to heterogeneous

surfaces

577

provided

it is assumed that the different patches act independently and that, apart from the area factor, the constant B is the same for all patches. It then follows that Iog(Z/T’)

=

B + log 1 nj 4(Xj) 9 .i

(2)

where 4(xj) is the Fowler function for theJth patch constituting a proportion nj of the total surface emitting. The total photocurrent is thus the summation of the currents arising from the different regions of the surface. Although the proportions (nj) determined by eq. (2) are subject to some uncertainty if the constant B is not the same for all patches, the work functions are not subject to error from this source. 4.2. WORK

FUNCTIONS OFNICKEL CRYSTALS

The line fitting the points in fig. 3a is generated from eq. (2) by a model which assumes that 3% of the surface has a work function of 4.44 eV and that 97% has a work function of 5.04 eV. Since this surface gave a well defined LEED pattern characteristic of (110) nickel it can be concluded that the work function of this crystal plane is 5.04 eV. The small fraction of the surface with the lower work function might arise from rough nickel surface, particularly near the edge of the crystal, or could possibly be due to emission from the tantalum support which surrounded the crystal. It is important to note that, ‘while the low work function region constitutes only a small proportion of the emitting surface, it contributes a gross feature to the experimental photoemission curve. In fact the high work function region of the surface can only be resolved because it predominates. The experimental result for the (110) crystal was most favourable in that the existence of two thresholds was suggested by the shape of the curve. The results on the other two crystals are less obvious. However, it was found that by assuming three thresholds the data could be fitted. The parameters generating the lines fitting the experimental points in fig. 3 are shown in table 1. In each case the highest work function is associated with the largest proportion of the emitting surface and is to be identified with the work function of the defined nickel surface. The fitting of the model to the experimental points was achieved by an iterative procedure on a digital computer. The number of thresholds to be assumed was decided by inspection of the data and by consideration of plots of JZ versus v. These plots approximate a straight line for a surface with a single threshold, but resolve into a number of lines characteristic of each threshold when the surface is heterogeneous. Starting values for the iteration procedure were also obtained from these plots. The com-

578

B. G.BAKER,

B. B. JOHNSON

TABLE

AND G. L. C.MAIRE

1

Work functions of nickel crystals Work function (eV)

Fraction of emitting surface

(110)

5.04 (4.44

0.97 0.03)

(100)

5.22 (4.37 (4.17

0.95 0.04) 0.01)

(111)

5.35 (4.53 (4.06

0.89 0.09) 0.02)

Surface crystal plane

puter adjusted the work function and proportion parameters in eq. (2) to achieve a fit within experimental error on all of the data points. The experimental errors to be associated with each point were provided with the data. The results are least accurate at the extremes of the wavelength range scanned. At high wavelengths the photocurrent was small and could not be measured with high accuracy. At low wavelengths the photocurrent was measured accurately, but the correction for the fall in intensity of the radiation from the monochromator became large. It is this last factor which particularly limits the accuracy of the determination on the (111) crystal. In this case the work function is estimated as 5.35 + 0.05 eV. For the other crystals the accuracy is estimated to be: (loo), 5.22kO.04 eV, and (1 lo), 5.04+ 0.02 eV. These errors were found from the maximum variation of the work functions which permitted a fit within experimental error without constraint on the patch proportions. 5. Evaporated nickel films 5.1. FILMS ON PYREX Photoelectric measurements for three nickel films deposited on Pyrex are shown in fig. 4. These results exhibit the same deviation from the Fowler curve for a homogeneous surface as was observed for the nickel crystals. The procedure of section 4.1 has therefore been applied here and the curves in fig. 4 have been computed to fit the experimental points from the parameters listed for films,1 2 and 3 in table 2. In each case it is found that the major fraction of the surface has a work function corresponding closely with that found for either the (100) or (111) crystal plane of nickel. It must be recognised that the fraction of a surface emitting with a partic-

PHOTOELECTRIC

WORK

FUNCTION

TABLE

MEASUREMENTS

ON NICKEL

579

2

Work functions of evaporated

nickel tims Error

Film

Deposition temnerature

Substrate

Work function

Fraction of

W

with work function * (eV)

surface

1

Pyrex

300

5.20 5.04 4.87

0.02 0.04 0.04

0.95 0.02 0.03

2

Pyrex

250

5.34 5.22 5.01

0.02 0.02 0.04

0.94 0.05 0.01

3

Pyrex

250

5.30 5.20 5.04

0.04 0.02 0.04

0.50 0.48 0.02

4

Pyrex

0

5.16 5.00 4.82

0.03 0.02 0.04

0.52 0.45 0.03

5

Pyrex

-196

4.54

0.02

1.0

Sintered at 250

5.32 5.17 5.06

0.05 0.02 0.04

0.28 0.67 0.05

6

Cleaved and polished NaCl

300

4.47 4.39

0.06 0.02

0.75 0.25

7

Vacuum cleaved mica

320

5.12 4.93 4.82

0.02 0.02 0.04

0.85 0.13 0.02

8

Air cleaved mica

320

5.12 4.95

0.02 0.03

0.92 0.08

I -15

I

’

-

-18 -

200

210

220

hV/ kT

Fig. 4.

Photoelectric

emission from evaporated nickel films on Pyrex film 1 (a), film 2 (O), film 3 (A).

substrates:

580

B. G. BAKER,

B. B. JOHNSON

AND

G. L.C.

MAIRE

ular work function is relative to the other parts of that surface which are detected. In the case of film 1 the result should not be interpreted as indicating the absence of the (111) crystal plane, but rather that its extent is too small to be detected. In fact the emission from the (111) surface could only be detected with certainty for this film if it exceeded about 25 per cent of the total surface. /

-16 -

170

180

190

200

210

220

230

hQ/kT

Fig. 5.

Photoelectric emission from evaporated nickel films, on cleaved and polished sodium chloride (0, film 6) and vacuum cleaved mica (0, film 7).

The situation is quite different for film 2 where (111) predominated over (100). In this case the small amount of (100) surface is reliably measured as it has the lower work function. Film 3 showed approximately equal amounts of (100) and (111). For each of these films the detection of the close packed planes has been facilitated by the virtual absence of rough surface of low work function. The deposition temperature of 2.9%300°C has apparently resulted in a fairly well annealed surface. The films were examined by electronmicroscopy after the photoemission measurements. In transmission, the electronmicrographs were typical of polycrystalline nickel films with no preferred crystal orientation evident in the diffraction patterns. Film 2 appeared to have larger crystals than films 1 and 3. Shadowed replicas of films 1 and 2 are shown in fig. 6. Film 2, which had been found to emit with the work function of the (111) plane predominant, is seen to be strongly faceted. It is concluded that these facets have the (111) surface orientation. The replica for film 1 is less well defined but generally the crystals are flatter. There was no intentional variation in the conditions of deposition of films 1, 2 and 3 and, although such films were occasionally produced, the conditions for reliably depositing preferred (111) films are not known. Films deposited at lower temperatures might be expected to be rougher. The low work functions found for films 4 and 5 are typical of films deposited at these temperatures. The emission from film 5, deposited at liquid nitrogen

PHOTOELECTRIC

Fig. 6.

IElectronmicrograph

WORK

FUNCTION

MEASUREMENTS

ON NICKEL

581

replicas of nickel films on Pyrex: (a) film 1, (b) fill n 2.

582

B. G. BAKER,

B. B. JOHNSON

AND

G. L. C. MAIRE

temperature, was not resolved. The work function of 4.54 eV was too low to permit any higher work function regions to be detected. It is concluded that this low temperature film has extensive rough regions of low work function. Sintering of this film at 250°C and pressures c2 x low9 torr resulted in an increase in the work function and the result could again be resolved into contributions identifiable as (100) and (111). Similar results for films deposited at - 196 “C have been reported previously by Suhrmann and Wedlerls) who found 4.58 eV for the unsintered film, 5.09 eV after sintering at 100°C and 5.25 eV after sintering at 200°C. 5.2. EPITAXED FILMS The epitaxial growth of films on crystalline substrates has been generally accepted as the most promising technique for producing extensive, well oriented, clean metal surfaces. The photoelectric technique was therefore applied to nickel films deposited on rock salt and mica. A rock salt crystal, cleaved and polished before mounting in the photocell, was the substrate for film 6. The bulk orientation of this film, determined by transmission electron diffraction (fig. 7a) was essentially (lOO), but the work function (table 2) was x4.5 eV. It must be concluded that the surface of this film was rough, a fact also revealed by electronmicrographs. Mica substrates cleaved in air or in vacuum, resulted in films of (111) orientation as shown by the electron diffraction pattern (fig. 7b). Replica and transmission electronmicrographs showed films 7 and 8 to be fairly flat with some grooving at twin boundaries. However, these single crystal films did not have the work function characteristic of the (111) nickel surface. The analyses of the photoemission curves for these films (fig. 5 and table 2) show that the proportion of rough surface is 8-15 per cent. Under these circumstances the predominant work function (5.12 eV) is not easily interpreted and may represent (111) surface with emission modified by the presence of other surface features. There appears to be no significant difference between films on air cleaved and vacuum cleaved mica. While it may be possible to produce epitaxed films of greater surface perfection, the results on the above films show that the bulk structure deduced from the transmission electron diffraction pattern is not a reliable indication of the surface orientation. The photoelectric technique described here is a more sensitive indicator of the surface structure. 6. Discussion The work function for the (100) nickel surface, determined here as 5.22-L-0.04 eV, is in agreement with the result of Farnsworth and Maddenl)

PHOTOELECTRIC

Fig. 7.

WORK

FUNCTION

MEASUREMENTS

ON NICKEL

583

Electron diffraction patterns from nickel films on (a) sodium chloride and (b) mica.

584

B.G.BAKER,

B. B. JOHNSON

AND G. L. C. MAIRE

for a nickel crystal characterized by LEED. The results for (111) and (110) nickel, 5.35kO.05 and 5.04+0.02 eV respectively, are in agreement with those found by Parkll). Various other values have been reported. Asadullin and Shuppes) found 4.9 eV for (100) nickel by the contact potential difference method. However, this value was relative to a polycrystalline nickel surface assumed, without obvious reason, to have a work function of 4.61 eV. Kashetov and Gobatyia) found thermionic work functions of 5.22, 4.89 and 4.64 eV respectively for the (11 I), (100) and (110) planes of nickel. Their crystals were annealed in vacuum and in hydrogen. However, Weiserrs) has recently reported a work function of 4.9 eV for a (100) nickel surface known to be contaminated by carbon. This suggests that the surfaces investigated by Kashetov and Gobatyi were contaminated and in fact no evidence was offered to substantiate the effectiveness of their cleaning procedures. The present calculation of work functions from the photoelectric emission from heterogeneous surfaces is based on an extension of Fowler’s theory. While many experimental results have been interpreted successfully in terms of the Fowler theory for a homogeneous surface, there are a number of reports of deviations similar to those shown in figs. 3 and 4. Jamison and Cashmanb) noted that after heating an evaporated calcium film to lOO”C, a plot of log(Z/T2) against hv/kT could not be fitted by Fowler’s function. If it was assumed that the surface was no longer homogeneous, the plot could be accurately fitted by assuming two patches with different work functions emitting independently. The patch with the higher work function had an effective area 69 times that of the lower work function surface. This term “effective area” was used to include such factors as optical adsorption, electron reflection and emission efliciency as well as the actual area emitting. Other papers which show similar deviations for the work functions of gas-free surfaces include Mann and DuBridges), where sodium films on Pyrex could not be fitted with a single Fowler function; Farnsworth and Winchc), who found (111) silver single crystals to be non-homogeneous; and Ames and Christensens), whose results deviated from the theoretical near the threshold. In each case, the experimental results could be fitted to the theory if it was assumed that the surface was heterogeneous and that the separate surfaces emitted independently. Anderson and Klemperer13) found that when they adsorbed oxygen onto nickel films, the results obtained could most readily be explained by assuming surface heterogeneity. This result is different from the preceding ones, as the nickel film initially appeared to be homogeneous. If experimental curves displaying multiple thresholds are resolved by

PHOTOELECTRIC

WORK

FUNCTION

MEASUREMENTS

ON NICKEL

585

fitting Fowler curves to the separate sections, the work function obtained for the surface with the higher threshold frequency can be very inaccurate. This was pointed out by Anderson et al.14), who demonstrated that the results of Suhrmann et al.15), when plotted in the form of J1 against v, give two intersecting straight lines. From the intercepts of these lines with the v axis, a reasonable estimate of the work functions of the two patches could be obtained. The higher threshold frequency found14) was quite different from that previously givenIs), even though both methods yield similar values for the lower work function. The basic assumption of the method employed in the present work is that the patches emit independently. Herring and Nichols7) investigated the conditions under which the patches of a heterogeneous surface could be distinguished in both thermionic and photoemission. Their calculation, based on the normal energy approximation, predicts that, for the low collecting fields usually employed in photoemission studies, a patch with a work function less than the area weighted average cannot emit independently. Small portions of surface with low work function should not therefore show up in the experimental plot. The results of Jamison and Cashman4) conflict with this prediction as do our results, where patches, whose effective areas are only a few per cent of the surface, have a noticeable effect on the plot of log(Z/T’) against hv/kT. Heills) studied the related problem of the reflection coefficient of electrons impinging on a heterogeneous surface. Using the classical equations of particle motion for a surface consisting of a number of patches with different electrostatic surface barriers, he found that, at the threshold of energy, 92-95x of the electrons were channelled into the more positive patches (those of lower work function). For electron emission from the metal, this means that photons with energies below the average work function will produce electron emission through the low work function patches, contrary to the conclusion of Herring and Nichols7). One further factor which must be considered however is the influence of electron-electron and electronphonon collisions which reduce the mean free path of the electron in the metal. When these effects are taken into consideration, the conclusion reached is that electrons within about 10 A of the low work function regions have a high emission probability and thus, small patches of low work function can emit independently. Eq. (2) is therefore suggested as an adequate description of photoemission from a heterogeneous metal surface, provided that the electronic properties of the metal are reasonably approximated by Fowler’s assumptions. This is the case for nickel. It might be expected that the true work functions of the (111) and (100) planes would not be measured if regions of low work function were widely

586

B. G. BAKER,

B. B. JOHNSON

AND

G. L. C. MAIRE

dispersed throughout the surface, since the electron emission would be modified by the interaction of the patch fields. Low values were noticed (table 2) for films deposited on mica and on Pyrex at 0°C. The films on mica were single crystals with (111) orientation, but showed grooving at twin boundaries and other surface roughness. The 0°C films had small crystals (-400 A) and were undoubtedly rough on an atomic scale. The technique described here is obviously of greatest value for well annealed surfaces having high work function crystal planes predominant. Under favourable conditions it has been shown that the relative amounts of (111) and (100) surface can be determined for nickel films deposited on Pyrex at 200-300°C. Acknowledgements We wish to thank Dr. C. Herring for drawing our attention to the relevance of Heil’s paper. We also thank Dr. J. V. Sanders who took the electronmicrographs and Dr. P. J. Jennings for helpful discussion. This work was supported by the Australian Research Grants Committee. One of us (G.L.C.M.) gratefully acknowledges the support of Centre National de la Recherche Scientifique, France. References H. E. Farnsworth and H. H. Madden Jr., J. Appl. Phys. 32 (1961) 1933. A Kashetov and N. A. Gorbatyi, Soviet Phys.-Solid State 10 (1969) 1673. R. Asadullin and G. N. Shuppe, Zh. Tekh. Fiz. 24 (1954) 205. N. C. Jamison and R. J. Cashman, Phys. Rev. 50 (1936) 624. M. M. Mann Jr. and L. A. DuBridge, Phys. Rev. 51 (1937) 120. H. E. Farnsworth and R. P. Winch, Phys. Rev. 58 (1940) 812. C. Herring and M. H. Nichols, Rev. Mod. Phys. 27 (1949) 185. I. Ames and R. L. Christensen, IBM J. Res. Develop. 7 (1963) 34. R. H. Fowler, Phys. Rev. 38 (1931) 45. R. Suhrmann and G. Wedler, Z. Angew. Phys. 14 (1962) 70. R. L. Park, private communication. C. Weiser, Surface Sci. 20 (1970) 143. J. S. Anderson and D. F. Klemperer, Proc. Roy. Sot. (London) A 258 (1960) 350. J. S. Anderson, E. A. Faulkner and D. F. Klemperer, Australian J. Phys. 12 (1969) 469. 15) R. Suhrmann, G. Wedler and E.-A. Dierk, Z. Phys. 153 (1958) 96. 16) H. Heil, Phys. Rev. 164 (1967) 887.

1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14)