146	WEAKLY IONIZED PLASMAS

Table 4.8 Parameters of negative alkali ions (Gogoleva et al. 1984)

Parameter	Li	Na	K	Rb	Cs
E, eV	0.620	0.548	0.501	0.486	0.470
E2, eV	0.55	0.49	0.45	0.43	0.42
De(A2−), eV	0.96	0.66	0.47	0.43	0.40
Re(A2−), a0	6.1	7.2	8.9	9.8	10.5
ν(A2−), cm−1	213	92	63	38	28
De(A3−), eV	0.90	0.59	0.49	0.40	0.38
Re(A3−), a0	11.2	13.2	16.3	18.2	19.3

While the situation appears very simple for alkalis and a number of other metals, it is very di erent in the case of mercury. As demonstrated by the measurements of Rademann et al. (1987) (Fig. 4.8), clusters of mercury are metallized only at m 70. In this case, as in a number of other situations, this is due to the fact that mercury is an uncommon metal (see Section 4.5).

The ionization potential Im and electron a nity Em of Alm clusters were measured by Seidl et al. (1991); see, also, the review by De Heer (1993).

Considerably less experimental information is available on negative alkali complexes A−m although in a number of experiments in gas discharge plasmas quite heavy complexes were reliably identified, for instance, complexes K−m up to m = 7 (Korchevoi and Makarchuk 1979). It is known that the binding energies of an electron with an atom and diatomic molecule are substantially smaller than the binding energy of positive ion with the same particles. Table 4.8 lists the parameters of ions A−, A−2 , A−3 . Here E1 and E2 are the energies of electron a nity for an atom and molecule, D(A−2 ) is the dissociation energy of A−2 A− + A, and D(A−3 ) is the dissociation energy of A−3 A−2 + A. Also, Re and ν are internuclear distances and vibrational frequencies.

For the energy of the electron a nity to a heavy complex, one can write an expression similar to Eq. (4.29),

E(R) = E(∞) − e2/2R.

(4.30)

Obviously, E(∞) = I(∞) = Ae, where Ae is the electron work function for the metal. This dependence is plotted in Fig. 4.7.

4.3.3Ionization equilibrium in alkali metal plasma

In order to determine the composition of a plasma formed by electrons (e), atoms (A), diatomic molecules (A2), diand triatomic positively charged ions (A+2 and A+3 ), and diatomic negatively charged atoms (A−2 ), let us consider the following processes:

LOWERING OF IONIZATION POTENTIAL AND CLUSTER IONS

147

I, eV

10

1

8

2

6

4

0 0.1 0.2 0.3 0.4 R −1, 108 cm−1

Fig. 4.8. Ionization energy of mercury clusters I versus cluster radius R (Rademann et al.

1987): 1 — plotted by experimental points, 2 — calculated with Eq. (4.29).

e + A+ A,	nen+/na = k1;
e + A A−,	nena/n− = k2;
A + A A2,	na2 /n2 = k3;

A + A+ A+2 , nan+/n+2 = k4;

(4.31)

A2 + A+ A+3 , n2n+/n+3 = k5;

A2 + e A−2 , n2ne/n−2 = k6

where ki are chemical equilibrium constants. Equations (4.31), along with the conservation of charge and total number of particles, enable one to determine the concentration of any component. After simple transformations we get

	= k n		1 + na/k4	+ n2	/(k3k5)		(4.32)
n2				a		.
		a 1 + na/k2		+ na2
e	1				/(k3k6)

It is readily seen that the primary fraction in Eq. (4.32) represents the e ect of molecular ions on ne. Individual components in the numerator (denominator) correspond to the contribution of a positive (negative) ion. Obviously, the inclusion of cluster ion A+4 would lead to the emergence of a subsequent series term in the numerator, whereas the inclusion of A−3 ion would lead to that in the denominator, and so on.

Figure 4.9 shows the composition of charged components in a plasma of cesium vapors, as calculated on the p = 2 MPa isobar. The chemical equilibrium constants (4.31) were used for this (their parameters are listed in Table 4.9). The temperature dependencies of the equilibrium constants ki are

ki = ciT ηi exp(−Ei/kT ).

The peculiarities mentioned above show up in Fig. 4.9. As the temperature decreases, heavy ions play an increasingly important role: an A+ ion, prevailing