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Russian Physics Journal, Vol. 55, No. 1, June, 2012 (Russian Original No. 1, January, 2012)

PLASMA PHYSICS

INVESTIGATION OF INFLUENCE OF SODIUM ON THE WORK FUNCTION OF AN OXIDE CATHODE

V. K. Sveshnikov UDC 621.317.7:621.372

Influence of sodium on the cathode work function is considered. The electrolytic method of sodium dosage into a discharge tube is described. The block diagram of a setup and the experimental procedure for estimating changes in the work function of the barium cathode due to sodium deposition on its surface are described. The results of investigations can be used to prepare a special course in physical electronics and light sources.

Keywords: electrolytic method, oxide cathode.

Oxide cathodes made of carbonates of rare-earth metals including barium, calcium, strontium, and other

compounds are conventionally used with sodium vapors in gas-discharge devices. Cathodes operate in the corresponding sodium and inert gas vapor atmosphere. Sodium, being adsorbed on the cathode in the form of ions and atoms, decreases the cathode work function and changes its secondary-emission properties, thereby decreasing the discharge ignition voltage and the near-electrode power losses.

The block diagram of a setup and the procedure of estimating the decrease in the work function of the barium cathode due to sodium deposition by the electrolytic method are considered below.

The mechanism of changing the emission characteristics of the oxide cathode can be explained by the change of the work function of the cathode caused by the presence of a dipole sodium layer. A neutral bond is possible between the adsorbed sodium atoms and the crystal lattice of the cathode. In this case, partial pulling of the valence electron of an atom into the lattice or on the contrary, of the lattice electron into an adsorbed atom is observed. Each sodium atom polarized by adsorption forces keeping it on the surface is converted into an electric dipole.

The electric field formed by the layer of sodium dipoles on the cathode decreases the potential barrier on the cathode surface and hence increases the cathode emissivity. In the first approximation, the work function decreases by

0

1 MNΔϕ =ε

, (1)

where N is the number of sodium atoms adsorbed per unit surface area of the cathode, M is the induced dipole moment determined by a coefficient a and the polarizability

M = аЕ. (2)

The local electric field strength can be estimated from the formula [1]

M. E. Evsev’ev Mordovian State Pedagogical Institute, Saransk, Russia, e-mail: sveshnikovmgpi@mail.ru. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 58–61, January, 2012. Original article submitted July 13, 2010; revision submitted September 15, 2011.

1064-8887/12/5501-0064 ©2012 Springer Science+Business Media, Inc.

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eff2

0

( 1)16 ( 1)

qE

dε −

=πε ε +

, (3)

where qeff is the effective ion charge, d is the dipole arm, and ε is the dielectric permittivity of the semiconductor. With allowance for Eqs. (2) and (3), relation (1) assumes the form

eff2 20

( 1)16 ( 1)aq N

dε −

Δϕ =πε ε +

. (4)

From Eq. (4) it follows that the work function of the oxide cathode depends on the number of sodium atoms adsorbed on its surface. Sodium incorporation into the discharge tube in small amounts is possible due to diffusion of sodium ions through the tube coating from the melt of sodium salts under the influence of an electric field [2].

Figure 1 shows the electric circuit diagram of the setup. The discharge tube is supplied by constant voltage from the rectifier based on semiconductor diodes D1-D4. Potentiometers R1 and R4 provide smooth voltage and discharge current adjustment, respectively. Resistor R2 is used to limit the maximum discharge current. Sodium is deposited on examined cathode 3 by the electrolytic method through exhaust tube 2 immersed into sodium nitrate.

A negative potential is applied to cathode 3 relative to bath 4 filled with sodium nitrate melt when switch SA2 is in position b and toggle-switch SA1 is switched on. The electrolyte current is adjusted by potentiometer R5 and is controlled by microammeter A.

The relative change in the work function of examined cathode 3 necessary for a comparison with experimental data as a function of time t of sodium deposition can be obtained from Eq. (4) after the corresponding transformations:

eff02 2

0 0

( 1)1

16 ( 1)t aq N

dϕ ε −

= − ϕϕ πε ε +

, (5)

Fig. 1. Electric circuit diagram of the setup for estimating changes in the cathode work function caused by sodium deposition.

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where 0ϕ and tϕ are the work functions of the cathode before sodium deposition and at the moment of time t, respectively.

Let us determine the number of atoms N adsorbed per 1 m2 of the cathode surface. It can be estimated from the following reasons. The amount m of sodium that passes through glass at electrolysis current I at time t, according to the Faraday law, is

Am ItF

= , (6)

where A is the atomic weight and F = 9.65 kg⋅eq is the Faraday number. N0 sodium atoms arrive every 1 s per unit surface area of the cathode:

0L LN m I

AS FS= = . (7)

Here L is the Avogadro number and S is the active surface area of the cathode. From N0 sodium atoms, the cathode adsorbs

0(1 )dN Q N dt= α − atoms during time dt, (8)

where 1

NQN

= is the degree of coverage, N1 is the number of sodium atoms forming a monotonic layer, and α is the

coefficient of sodium condensation on the cathode.

Differentiating both parts of the relation 1

NQN

= and substituting 1dQNdt

= for dN/dt, we obtain the

differential equation

0

11NdQ dt

Q N= α

−. (9)

With allowance for Eq. (7), we obtain from Eq. (9) with initial conditions t = 0 and Q = 0:

11

1 exp LN N jtFN

⎡ ⎤⎛ ⎞= − −α⎜ ⎟⎢ ⎥

⎝ ⎠⎣ ⎦. (10)

Substituting Eq. (10) into Eq. (5), we finally obtain the relation

eff 12 2

0 10 0

( 1)1 1 exp

16 ( 1)t aq N L jt

FNd⎡ ⎤ϕ ε − ⎛ ⎞

= − − −α⎜ ⎟⎢ ⎥ϕ πε ε + ϕ ⎝ ⎠⎣ ⎦. (11)

Thus, the relative work function 0

tϕϕ

can be estimated from the electrolysis current density j and time t.

The change in the cathode work function due to sodium deposition was experimentally estimated from the normal cathode voltage drop for the discharge in the inert gas. The normal drop of the cathode voltage proportional to the cathode work function is taken to be the minimum voltage of discharge combustion determined from the volt-ampere characteristics of the glow discharge.

The influence of sodium on the work function of the oxide cathode was investigated for discharge tubes 1.8⋅10–2 mm in diameter and 8⋅10–2 mm long filled with argon at a pressure of 0.2 kPa. The cathodes coated with barium

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oxide were taken from DNaS-18 spectral lamps. For sodium deposition on examined cathode 3, exhaust tube 2 of tube 1 was immersed into cell 4 with sodium nitrate preliminary melted with heater 5 (toggle-switch SA3 was switched on). The temperature of cell heating was 570–620 K. After that, switch SA2 was put in position b, and the electrolytic current equal to 10–2 A was set by potentiometer R5.

To compare the calculated relative work function 0

tϕϕ

with experimental one, the normal cathode voltage drop

of the glow discharge before and after sodium deposition on the cathode U0 and Ut, respectively, must be determined as a function of time t.

The procedure of determining U0 and Ut was the following. At the beginning, we determined the U0 value. To this end, switch SA2 was put in position a and the tube voltage was smoothly increased by potentiometer R1 before discharge ignition. Increasing the resistance with potentiometer R4, we recorded the volt-ampere characteristic

( )U f I= of the discharge from which the cathode voltage drop across the tube was determined. The cathode voltage drop Ut after sodium deposition on the cathode was measured at room temperature after

tube cooling. The procedure of measuring Ut was similar to that of measuring U0. Figure 2 shows experimental and

theoretical dependences of 0

tϕϕ

on time t.

The relative work function 0

tϕϕ

was calculated from formula (11) for the following initial data: a =

2.59⋅10–39 F/m2 [3], qeff = 0.02e, ε = 5, N1 = 7⋅1018 m2, ε0 = 8.85⋅10–12 F⋅m–1, d = 1.89⋅10–10 m, ϕ0 = 1.4 eV, α = 0.7 [4],

L = 6.02⋅1026 kmol–1, and j = 5⋅10–3 A⋅m–2. From Fig. 2 it can be seen that 0

tϕϕ

decreases after sodium deposition on the

cathode and takes a minimum value equal to 0.82 for t > 8 min. The difference between the calculated and experimental data does not exceed 15%.

The suggested electric circuit and the procedure of investigating the influence of sodium on the work function of the oxide cathode can be used to prepare a special course in physical electronics and light sources.

REFERENCES

1. B. Ya. Moizhes, Physical Processes in an Oxide Cathode [in Russian], Nauka, Moscow (1968). 2. V. K. Sveshnikov, Electric Light Sources, in: Trudy A. N. Lodygin All-Union Scientific-Research Institute of

Light Sources, No. IX (1978), pp. 69–71.

Fig. 2. Dependence of the relative work function on time of sodium deposition on the cathode. Here curve 1 shows the experimental dependence, and curve 2 shows the calculated dependence.

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3. A. V. Vinogradov and V. P. Shevel’ko, in: Trudy P. N. Lebedev Institute of Physics of the USSR Academy of Sciences, No. 119 (1980), p. 165.

4. V. I. Subbotin, M. N. Ivanovskii, and E. A. Chulkov, in: General Problems of Heat and Mass Exchange [in Russian], Nauka Tekhnika, Minsk (1966), pp. 247–255.