Basic Parameters for Electrical Discharges in Gases - Advances in

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Discharges in Gases Α. V. PHELPS Westinghouse Research Laboratories, Pittsburgh, Pa.

Combinations of the experimental parameters of electric field strength, frequency, gas density, container dimension, fractional ionization, and duration of applied voltage can be used to relate experimental data for electrical breakdown and for steady state discharges in simple gases over a wide range of these parameters. It is important that studies of the chemical effects of electrical discharges make use of these combinations of parameters and discover the addi tional parameters appropriate to the chemical aspects of the discharges.

Tnlectrical discharges have been studied over a wide range of experimental conditions, ranging from d.c. to microwave frequencies for the applied electrical fields; pressures from a fraction of a torr to many atmospheres; power levels from a few watts to several megawatts; effec tive residence times of reacting species from a few microseconds to many seconds; and gases of a wide variety of compositions. It is therefore of interest to consider briefly the applicability of basic combinations of experimental parameters developed in connection with the study of sim ple gases (6, 16, 17, 22, 35, 42, 57) and to speculate as to others which might be investigated further. The use of these combinations leads to scaling laws which may be of use in predicting the properties of various discharges. Obviously, the present comments will be very qualitative and many will have to be tested against past and future experiments in which careful measurements are made of such quantities as the electric field strength, current density, electron density and temperature, gas tempera ture, gas flow rates, etc. Although numerous references are given, there are many other references which could have been cited. 18

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We now consider some specific combinations of experimental pa rameters and some examples of their application.

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Electric Field to Gas Density Parameter Fite (21), Kaufman (29), and Lunt (37) have all pointed out that theory shows (35, 57) that provided the degree of ionization and excita tion of the gas is low the electron transport coefficients and rate coeffi cients for reactions caused by electrons in the presence of a d.c. electric field Ε and for a given gas mixture depend only on the value of E/N where Ν is the total gas density. We have used the E/N rather than the usual E/p because it is the gas density rather than the pressure ρ that is important and because we are concerned with a wide range of gas temperatures. The E/N value required to produce a given reaction rate coefficient varies considerably with the gas. As an indication of this we note that to obtain a mean electron energy of 1.5 e.v. in pure Ar one requires an E/N value of only 3 Χ 10" volts-cm. whereas to obtain the same mean electron energy in a highly polar gas such as HoO one requires an E/N of 6 Χ 10" volts-cm. . These differences are because of the fact that at these energies in pure Ar the electrons lose energy only through the recoil of the heavy argon atoms in an elastic collision whereas in H 0 the electrons lose energy very rapidly owing to the excitation of rotational and vibrational states of the molecule. Because of the large cross sections for rotational and vibrational excitation of some molecular gases, small admixtures of molecular gases in the rare gases cause large charges in the mean electron energy and in the electron transport co efficients at fixed E/N. 18

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The E/N parameter has been used by many workers (16, 17, 34, 35, 41, 50, 57) to compare measurements of the rate coefficients for the ionization of atoms and molecules by electron impact. However, only a few attempts have been made to obtain the data necessary to correlate experimental rate coefficients for chemical reactions such as molecular dissociation (29, 36, 37). Correlations of this kind are essential to the understanding of and prediction of the rates of chemical reactions in electrical discharges under various experimental conditions. Effective Electric Field Strength The concept of effective electric field strength was originally devel oped (6, 42) to take into account the observed frequency dependence of the electric field strength required for gas breakdown. However, this concept is of great general utility for reasonably homogeneous discharges since it allows one to compare the effect on the electrons of an applied

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electric field of any frequency to the effect produced by an equivalent d.c. applied field. The effective d.c. electric field E is related to the r.m.s. value of the applied field Ε by e


6

(1+ω Αβ ) 2

2

1 / 2

where v is the effective frequency of electron collisions with gas mole cules and ω is the radian frequency of the applied field. Typically the electron collision frequency under discharge conditions (19, 26, 41) is 10~ Nsec. , so that at a pressure of 1 torr at 300 °K. the quantity ω/ν = 1 at a frequency of 500 MHz. At significantly lower frequencies; i.e., below 150 MHz., E = Ε and the rate at which energy is absorbed by electrons from the electric field is independent of the frequency. The effective field relation has been found (6, 12, 42) to be good for helium and hydrogen under gas breakdown conditions; i.e., high values of E /N. The effective field concept is particularly useful for the accurate predic tion of quantities which vary slowly with E /N; i.e., electron drift velocity, average electron energy, discharge maintenance field strengths and some reaction rate coefficients. The effective field relation is least accurate at low ω/Ν in gases such as argon and methane where the cross section for momentum transfer collisions between electrons and gas molecules is a rapidly increasing function of electron energy over much of the energy range of interest. The effective field relation may also be somewhat inaccurate for ω/Ν values such that the electron energy dis tribution function relaxes significantly during one cycle of the field (25). In this case only those rate coefficients which vary as (E /N) will be accurately scaled using the r.m.s. value of the applied frequency. In cases where the effective field concept is not sufficiently accurate, the results of measurements of rate coefficients, etc., at various ω and Ν in a given gas can be shown to depend upon the parameters E/N and ω/Ν. e

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Breakdown Parameters This is the most widely investigated (6, 16, 34, 35, 42, 43, 50, 57) of the aspects of electrical discharges and will be discussed only very briefly. The results of breakdown measurements using slowly rising d.c. voltage and electrode gaps with a spacing which is small compared with the dis tance to side walls are usually given in the form of Paschen curves (35, 43, 57) of breakdown voltage as a function of the product of pressure (more correctly, gas density) gap spacing, d. By dividing the breakdown voltage by the Nd product one can express the result as the E/N value required to cause breakdown for a given value of Nd. The importance of


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the Nd product can be shown (34, 35, 43) to result from the requirement that each electron produce enough positive ions or excited molecules to cause the release of an additional electron from the cathode. Other experimental parameters, such as those describing the shapes of the electrodes and the sensitivity of the experiment for the detection of break down must be considered in precise work but are often of secondary importance for Nd values near and above that of the Paschen minimum. When the voltage is applied in the form of a short pulse of length At, the product Ν At must be included in the list of significant parameters (34, 43, 50) since the ionization must be produced in a time At with a rate coefficient set by E/N. In the limit of very short pulses the Nd parameter becomes unimportant (20, 50). At low a.c. frequencies the parameters required to correlate breakdown data for a given gas are same as for d.c. breakdown except that it is often necessary to take into account the statistical effects arising when the number of electrons avail able for initiating breakdown is low (34, 43, 50). When the number of electrons initially present is high enough to cause space charge distortion of the applied field, an additional parameter is required—e.g., the prebreakdown current (16). Gas breakdown in the presence of very high frequency electric fields of slowly increasing amplitude is often determined by the condition that the rate of electron production equals the rate of loss by diffusion to the container wall (6,42). As indicated above the rate coefficient for ioniza tion can often be expressed as a function of EJN although more cor rectly (42), it is a function of E/N and ω/Ν or Νλ, where λ is the wave length corresponding to ω. The balance between the ionization rate and the diffusion loss introduces (6, 21, 29, 42) the parameter ΝΛ where Λ is the "diffusion length" and for an infinite cylinder is the radius divided by 2.4. Note that the reflection coefficient for ions and electrons at all surfaces investigated are small—i.e., less than 1% and 50%, respectively— so that the diffusion losses may be calculated on the assumption of zero concentration at the wall. The parameters E/N, Νλ, and Ν A or combina tions of these, such as EA, Νλ, and ΝΛ, have been used to correlate experimental data for a given gas and a wide range of λ and Ν (6, 42), including very high gas densities (25). When the microwave energy is pulsed, the product Ν At becomes important ( 20, 25 ). Other special cases of possible interest to chemists are the break down in long narrow tubes where diffusion losses are important and breakdown in gases where electron attachment to the gas is the dominant electron loss process. An example of the latter case is the breakdown of SF which occurs very close to the E/N value at which the rate coeffi cients for attachment and ionization are equal (4, 43, 49). 6

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Discharge Maintenance Parameters We are concerned here with the general question of the electric field strength required to maintain a given electron density or current density in a volume reasonably far removed from electrodes such as the cathode and anode of a d.c. discharge. At moderate degrees of ionization the steady state discharge conditions are determined by a balance be tween the rate coefficient for ionization by electrons and the effective first order rate coefficient for loss of electrons by diffusion to the walls or by field controlled flow of electrons and ions to electrodes. Several authors show how the dependence of the ionization rate coefficient and the effective electron temperature on E /N can be used to predict the E /N or electron temperature required to maintain a d.c. positive column (10, 16, 17, 21, 22, 35) or a microwave plasma (29, 33, 52) for various values of ΝΛ. Note that this is the same condition as for the diffusion controlled breakdown discussed above except that the diffusion loss rate for the electrons has been lowered drastically by space charge effects (21). The lower loss rate means that the ionization rate coefficient required to main tain the discharge is lowered—i.e., that the E /N required is lowered. Because of the similarity of the breakdown and diffusion controlled plasma conditions the same parameter may be used to compare results from given gas but different experimental conditions—i.e., E/N, Ν A, and Νλ. At high gas flow rates it is necessary to add a parameter which includes the gas residence time At—e.g., Ν At. e

e

e

Since the production and loss rates for a diffusion controlled plasma are the same order in the electron concentration in this approximation, the electron concentration and the discharge current would appear to be indeterminate. In fact, they are determined (10, 17,22) by the inter action between the discharge and the electrical circuitry—i.e., the power supply with its impedance or the microwave oscillator and coupling device. In general, the larger the discharge current the lower the electric field strength available for the discharge. In the case of d.c. or low frequency a.c. discharges, a large fraction of the applied voltage is often necessary to release the required electron current from the cathode and to satisfy space charge relations at the cathode and anode ( 10, 22, 35, 56 ). The simple model of a diffusion controlled or wall stabilized plasma discussed above must be modified to take into account departure of the effective diffusion rate coefficient from the ambipolar value (2, 3, 11, 52) when the electron concentration is low enough such that the Debye length k for the plasma (21) is comparable with a diffusion length A characteristic of the discharge dimensions. Although the results of theo retical treatments of this problem are still given in terms of numerical coefficients for particular gases, an empirical expression can be given D

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which fits the available calculations (2, 11) for conditions in which the effective electron temperature is much larger than the gas temperature. Thus, the ratio of the effective diffusion coefficient in the presence of space charge, D , to the diffusion coefficient for free electrons, D , is given by (48) s

e

In D /D = [1 + ( λ ^ / Λ ) · ] " In Chemical Reactions in Electrical Discharges Downloaded from pubs.acs.org by UNIV OF CALIFORNIA SAN DIEGO on 07/23/16. For personal use only.

8

0

e

76

1

μ +

/

μ β

where μ and μ are the mobilities of the positive ions and electrons, re spectively. Further modification of the ambipolar diffusion theory is necessary when negative ions are present (5, 47, 54). The net effect of these departures from the ambipolar limit is to require that the descrip tion of a discharge include additional parameters—i.e., \ /A and the ratio of the electron and negative ion densities n/N.. +

β

D

Additional parameters may be required to describe the discharge when ionization and electron loss processes which are effectively second and higher order in the electron concentration become important at the higher degrees of ionization of the gas. Two such processes are cumu lative ionization—i.e., the ionization of excited state of molecules or atoms by electrons, and electron-ion recombination by either second or third order processes. When the rates of these processes are comparable with the rates of ionization by electron impact and loss by diffusion, they cause only small changes in the E /N (22, 58). When the rates of these "non linear" processes become large, they tend to constrict the discharge as discussed below. A second such process is the Maxwellianization of the electron energy distribution and the consequent higher ionization rate which results from energy sharing collisions between electrons (15, 38, 44). Another complicating feature of many low pressure discharges is the presence of either stationary or moving non-uniformities—i.e., stria tums (16,22,35). e

Because of the rapid variation of the ionization rate coefficient with E /N and because one is generally concerned with moderately large dis charge currents, the effect of these parameters on E /N is generally small. Thus, the simple theories of the d.c. positive column are often very useful in estimating such quantities as E /N using the appropriate values of ΝΛ for the diffusion controlled, wall stabilized plasma. As an example, we consider data for a discharge in H for which Ν A = 3 Χ 10 cm. and n / N ^10" . Theory and experiment (10,18,22,29) for a d.c. discharge near the ambipolar limit give 5 Χ 10" volts cm. as the E / N value re quired to maintain the discharge. For a microwave discharge at the same ΝΛ and n/N, theory gives the same value for E /N and experiment requires a slightly larger value of E /N (52). In the limit of low n / N — i.e., microwave breakdown—the E /N value required is only 10" voltscm. (52). Also, a 10 amp. arc (n/N ^ 10" ) in H at one atmosphere e

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pressure (10) operates at E/N = 3 Χ 10" volts-cm. for the same Ν A. While such quantities as the electron mobility or electrical conductivity per unit charge are essentially constant over this range of E /N, the mean electron energy varies approximately linearly with E /N, the rate coefficient for dissociation of the hydrogen varies by a factor of about 100, and the rate coefficient for ionization by electron impact varies by many orders of magnitude. It must be kept in mind that the gas temperature and the fractional ionization are very high in the 10 amp. arc so that ionization rate coefficients calculated for the room temperature gas are too small. Also the gas is highly dissociated at the center of the arc. 16

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Parameters Determining Constriction of the Discharge A poorly understood feature of electrical discharge is the phenome non of constriction of the current channel which is often observed at high gas pressures (J, 7, 8, 9, 23, 31, 32, 39, 40, 55, 59). Several effects are present which tend to cause a narrowing of the conducting channel. They are: (a) Magnetic forces resulting from the current flowing through the arc. These effects are expected to be most important at high currents (55).

(b) Thermal gradients which result from the flow of heat from the center of the arc to the wall (39, 40) result in a reduced gas density and higher E/N at the center of the arc. If the rate coefficient for ionization increases sufficiently rapidly with E/N then the higher ionization rate more than compensates for the faster diffusion loss of a narrower con ducting column. The ionization rate of a hot gas may be higher than that of a cold gas because of chemionization (27) or because of ionizing collisions between atoms or molecules (30). ( c ) Cumulative ionization. Cumulative ionization refers to the ioni zation of excited atoms or molecules which have been produced by electron impact. Because this process is proportional to the square of the current density, it leads to higher rates of ionization in the regions of higher current density and tends to contrast the discharge. (d) Electron-ion recombination. Some authors (31) propose that the recombination of electrons and ions at large radii leads to constriction of the discharge. (e) Electron-electron interaction. Since collisions among electrons tend to make electron energy distribution functions more Maxwellian and to increase the excitation and ionization rate coefficients, the ioniza tion rate near the center of a discharge will be higher and will tend to constrict the discharge (24). Since diffusion of the electrons and ions tends to spread the discharge radially, one expects that constriction effects will set in at higher pressures for gases which have larger ambipolar diffusion coefficients as is observed (39, 40) for helium relative to the other rare gases.

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Parameters Governing Excited State Concentrations The usefulness of a gas discharge for the production of particular chemicals is often limited by the low gas densities and low power inputs which must be used to obtain a favorable yield (37, 56). Considerable effort is being devoted to the design of the gas flow arrangement in discharge reactors so as to obtain the desired products through rapid quenching of the discharge (51, 56). Here we wish to consider the parameters relevant to this problem from the point of view of whether the excited molecular species produced by electron impact react before their excitation energy reaches equilibrium with the translational energy of the gas molecules. The excited states are produced by electronmolecule collisions and are destroyed by excited molecule-ground state molecule collisions, by electron collisions, by wall collisions, or by spontaneous radiation. At reasonably high gas densities, spontaneous radiation and loss by diffusion to the wall will be unimportant, so that, for fixed E /N the degree of excitation will increase with the degree of ionization of the gas at low degrees of ionization and will be determined by the electron temperature at high degrees of ionization. The degree of ionization over which the transition occurs will depend critically on the excited state being considered and on the electron and gas temperatures. Most of the available data is concerned with excited vibrational states of the ground electronic state (13, 45) or with radiating state of atmospheric gases (28). e

Recent studies (18, 19, 26, 41, 53) have shown that the rates of vibrational excitation of molecules by electron impact can be very large. These large cross sections may account for the large populations of vibrationally excited molecules observed (46) in flow systems. Because of these large cross, sections a large fraction of the energy absorbed by the electrons from the electric field is transferred to the gas molecules in the form of vibrational excitation (16, 18, 19). At high gas pressures and translational temperatures, this vibrational energy is rapidly degraded to translational energy (13, 45). One potentially profitable area of future investigation is the effective utilization of this form of internal energy of the molecules before relaxation occurs. Alternatively, by choosing experimental conditions so as to keep the vibrational temperature near that of the electrons one can minimize the energy lost through this process. Since the production of excited species in a stationary electrical discharge requires nonthermal electrons, one may be interested in the conditions for which the average electron energy is significantly above the average energy of the gas molecules. A simple, but not always useful answer, is that when the E /N is high enough so that the rate of electron e

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energy gain from the electric field is comparable with the rate of energy gain from the gas molecules then the electrons become nonthermal. For pure Ar at 300 °K. the mean electron energy is 10% higher than that of the gas for E /N — 5 Χ 10" volts-cm. whereas for a highly polar gas such as H 0 , the same increase in electron energy requires E /N .— 2 X 10" volts-cm. . The reason that the specification of the E /N value required to pro duce a given rise in average electron energy is not always useful, is that the increased energy the electrons gain from the electric field may cause a corresponding rise in the gas temperature. Since in a static system the excess thermal energy of the molecules is transported to the wall by a diffusion process, the temperature rise is proportional to the power input per unit volume times the square of the diffusion length or at a given E /N, to (n/N) ( Ν Λ ) . The average gas temperature rise can be kept low by flowing the gas or by pulsing the discharge as in an ozonizer (14, 36). 21

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Summary In the preceding discussion we have attempted to show that in spite of the variety of experimental arrangements used for electrical discharges, there are a relatively few combinations of experimental parameters which characterize the electrical characteristics of the more uniform portions of a discharge. These combinations, E/N, ω/Ν, ΝΑ, n/N and Ν At, have made possible quantitative comparisons of experi mental data obtained for simple gases over a wide range of ω, Ν, η, A and At. It is expected that similar comparisons can be made of the elec trical characteristics of more complex gases. The chemical behavior of these discharges depends directly upon these parameters and upon others such as the reactivity of the wall and the temperature of the gas. It is to be hoped that the search for the combinations of parameters appropriate to the chemical reactions occurring in the discharge (36, 51, 56) will be as fruitful as has been the search for the proper electrical parameters. Acknowledgement The author wishes to acknowledge helpful discussions of this paper with F. Kaufman. Literature Cited (1) Albrecht,G.,Ecker,G.,Muller, K. G., Z. Naturforsh. 17a, 854 (1962). (2) Allis, W. P., Rose, D. J., Phys. Rev. 93, 84 (1954).

(3) Belousova, L. E., Zhurnal Teknicheskoi Fiziki 35, 475 (1965); Soviet

Phys. Tech. Phys. (English transl.) 10, 369 (1965).

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(4) Bhalla, M. S., Craggs, J. D., Proc. Phys. Soc. (London) 80, 513 (1962). (5) Biondi, Μ. Α., Phys. Rev. 109, 2005 (1958). (6) Brown, S. C., "Introduction to Electrical Discharges in Gases," John Wiley and Sons, Inc., New York, 1966.


(7) Champion, K. S. W., Proc. Phys. Soc. (London) B65, 329 (1952).

(8) Ibid., B65, 345 (1952). (9) Ibid., B65, 359 (1952). (10) Cobine, J. D., "Gaseous Conductors," Chap. 9, Dover Publications, New York, 1958. (11) Cohen, I. M., Krushal, M. D., Phys. Fluids 8, 920 (1965). (12) Cottingham, W. B., Buchsbaum, S. J., Phys. Rev. 130, 1002 (1963). (13) Cottrell, T. L., Day, Μ. Α., "Molecular Relaxation Processes," Academic Press, New York, 1966. (14) Cromwell, W. E., Manley, T.C.,ADVAN. CHEM. SER. 21, 304 (1959). (15) Dreicer, H., Phys. Rev. 117, 343 (1960). (16) Druyvestyn, M. J., Penning, F. M., Rev. Mod. Phys. 12, 87 (1940). (17) Engel, A. von, Ionized Gases, 2nd ed., Oxford University Press, London, 1965. (18) Engelhardt, A.G.,Phelps, Α. V., Phys. Rev. 131, 2115 (1963). (19) Engelhardt, A. G., Phelps, Α. V., Risk, C. G., Phys. Rev. 135, A1566 (1964). (20) Felsenthal, P., Proud, J. M., Phys. Rev. 139, A1796 (1965). (21) Fite, W. L., ADVAN. CHEM. SER. 80, 1 (1969). (22) Francis,G.,"Handbuch der Physik," Vol. 22, S. Flugge, ed., SpringerVerlag, Berlin, 1956. (23) Gambling, W. Α., Edels, H., Brit. J. Appl. Phys. 7, 376 (1956). (24) Golobovskii, Yu. B., Kagan, Yu. M., Lyagushchenko, R. I., Opt. Spectr. (USSR) (English Transl.) 20, 317 (1966).

Gould, L., Roberts, L. W., J. Appl. Phys. 27, 1162 (1956). Hake, R. D., Jr., Phelps, Α. V., Phys. Rev. 158, 70 (June 5, 1967). Hand,C.,Kistiakowsky, G. Β., J. Chem. Phys. 37, 1239 (1962). Hunten, P. M., McElroy, M. B., Rev. of Geophys. 4, 303 (1966). Kaufman, F., ADVAN. CHEM. SER. 80, 29 (1969). Kelly, A. J.,J.Chem. Phys. 45, 1723 (1966). Kenty,C.,Phys. Rev. 126, 1235 (1962). King, L. Α., Appl.Sci.Res. (The Hauge) B5,189 (1955-6). Krasik, S., Alpert, D., McCoubrey, A. O., Phys. Rev. 76, 722 (1949). Llewellyn-Jones, F., "Ionization and Breakdown in Gases," Methuen and Co., Ltd., London, 1957. (35) Loeb, L. B., "Basic Processes in Gaseous Electronics," Chap. 8, Univ. of California Press, Berkeley, California, 1955. (36) Lunt, R. W., ADVAN. CHEM. SER. 21, 286 (1959). (37) Lunt, R. W., ADVAN. CHEM. SER. 80, 452 (1969). (38) Maronne, T., Phys. Rev. 141, 27 (1966). (39) Massey, J. T., Cannon, S. M. J., J. Appl. Phys. 36, 361 (1965). (40) Ibid., 36, 373 (1965). (41) McDaniel, E. W., "Collision Phenomena in Ionized Gases," Chap. 4, John Wiley and Sons, Inc., New York, 1964. (42) McDonald, A. D., "Microwave Breakdown in Gases," John Wiley and Sons, Inc., New York, 1966. (43) Meek, J. M., Craggs, J. D., "Electrical Breakdown of Gases," Oxford Uni versity Press, London, 1953. (44) Megill, L. R., Cahn, J.H.,J.Geophys. Res. 69, 5041 (1964). (45) Millikan, R.C.,White, D. R., J. Chem. Phys. 39, 3209 (1963). (46) Morgan, J. E., Phillips, L. F.,Schiff,H. I., Discussions Faraday Soc. 33, 119 (1962). (47) Oskam, H. J., Phillips Res. Repts. 13, 335 (1958).

(25) (26) (27) (28) (29) (30) (31) (32) (33) (34)


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(48) Phelps, Α. V., "Proceeding of the Conference on the Physics of Quantum Electronics," p. 546, P. Kelley, ed., McGraw-Hill Book Co., New York, 1966. (49) Prasad, A. N., Craggs, J. D., "Atomic and Molecular Processes," Chap. 6, D. R. Bates, ed., Academic Press, New York, 1962. (50) Raether, H., "Electron Avalanches and Breakdown in Gases," Butterworths, Washington, 1964. (51) Rony, P. R., Preprints Div., Fuel Chem. ACS 11 (2), 107 (1967). (52) Rose, D. J., Brown, S. C., Phys. Rev. 98, 310 (1955). (53) Schulz,G.J., Phys. Rev. 135, A988 (1964). (54) Seeliger, R., Ann. Phys. 6, 93 (1949). (55) Thonemann, P. G., Cowhig, W. T., Proc. Phys. Soc. (London) B64, 345 (1951). (56) Thornton, J. D., ADVAN. CHEM. SER. 80, 372 (1969).

(57) Townsend, J. S., "Electrons in Gases," Hutchinson's Scientific and Tech nical Publications, London, 1947. (58) Walsh, P. J., Manning,G.W., Larson, D. Α., J. Appl. Phys. 34, 2273 (1963). (59) Woolsey,G.Α., "Proceeding of the 6th International Conference on Ioni zation Phenomena in Gases," Vol. 2, p. 141, P. Hubert,ed.,S.E.R.M.A., Paris, 1965. RECEIVED June 5, 1967.

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