40 ELECTRICAL METHODS OF NONIDEAL PLASMA GENERATION

2.1.3Density measurements.

For the purpose of measuring the density of nonideal plasma of metals, a technique was developed based on measuring the intensity of γ–radiation of metal under investigation. The apparatus for this is described by Alekseev (1968) and Korshunov et al. (1970). A thick–walled tungsten tube is defined by a thin tungsten bottom at one end and by an elastic bellows at the other. This element is filled with cesium under vacuum and sealed o . Located beneath the cell is a point measuring volume. In order to avoid convection, the vacant space is filled with a tungsten insert. The metal under investigation was pre–activated in the reactor by slow neutrons. The density was measured using the method of recording the γ–radiation from the measuring volume, led out via a special port in a high–pressure chamber and collimated with the aid of a lead collimator. For γ-quantum recording, use was made of a CsI scintillator and a photomultiplier. The number of pulses from the detector (proportional to density) and the temperature were recorded in digital form for subsequent computer processing. This method was used to measure the cesium density at temperatures of up to 2500 ◦C and pressures of up to 60 MPa. The method su ers from poor accuracy (ca. 10%) in measuring low vapor densities. This is because the absolute error in measuring the cesium density amounted to ±0.005 g cm−3.

More accurate data were obtained using a constant-volume piezometer where the cesium vapor pressure was measured by the compensation method. Stone et al. (1966) and Novikov and Roshchupkin (1967) used an elastic membrane introduced in the piezometer as a pressure cell. This reduced the range of temperatures under investigation because of the adverse e ect of high temperatures on the elastic properties of the membrane. Volyak and Chelebayev (1976) removed the membrane from the heated volume. This permitted p − ρ − T measurements of cesium vapors at 5.2 MPa and 1940 K.

A schematic of the apparatus is shown in Fig. 2.18. Essentially, it comprises a piezometer consisting of a cylindrical chamber (1) with a volume of 50–100 cm−3 placed in a heater (2). On heating the piezometer, the pressure of cesium vapors in the chamber is transmitted through a column of liquid cesium in capillary (3) to membrane (4) of an induction null pressure cell (5). Consequently, the membrane deflects. By applying an argon pressure to its other side, the membrane is brought into “zero” position.

The specific volume of cesium vapor was determined as the ratio of the piezometer chamber volume (with due regard for its thermal expansion) to the mass of cesium vapor in the chamber. The accuracy of experiment (±0.65%) was estimated from the error of the compressibility coe cient.

The results of density, temperature, and pressure measurements enable one to construct the p − ρ − T equation of state (Alekseev et al. 1970a; Kikoin et al. 1973; Chelebaev 1978). The thermodynamic equation of state for mercury and cesium are shown in Figs. 2.19 and 2.20, respectively.

The most exact measurements of curves of phase equilibrium for cesium and rubidium were performed by Jungst et al. (1985) (Fig. 2.21). The revealed asym-

PLASMA HEATING IN FURNACES

41

Fig. 2.18. Element for measuring the cesium vapor density (Volyak and Chelebaev 1976): 1, piezometer; 2, graphite heater; 3, capillary with liquid cesium; 4, membrane; 5, “zero” manometer pressure cell; 6, heat shields; 7, heat insulation; 8, apparatus body; 9, pressure gauges; 10, argon–cleaning system.

metry of branches of these curves is indicative of the invalidity of the law of the rectilinear diameter in a relatively wide temperature range.

Important information on the structure of the material is provided by neutron di raction studies of the structure factor. The static structure factor S(q) is directly related to the binary correlation function g(r):

S(q) = 1 + n dr exp(−i q·r)[g(r) − 1], (2.4)

where n is the particle density of the medium. The static structure factor of rubidium was measured by Noll et al. (1988) and Winter et al. (1988) (Fig. 2.22).

The basic error is due to the inaccuracy of discrimination of the background intensity whose quantitative evaluation is very di cult to accomplish. How-

ever, it can be evaluated from the requirements of satisfying the rules of the

∞

sum q2dq[S(q) − 1] = 2π2n, the asymptotics S(∞) = 1, and the value at zero

0

S(0) = nkT χT, where χT is the isothermal compressibility. Proceeding from this and the reproducibility of S(q), which is measured using di erent measuring cells and furnaces, it was concluded on the error of S(q) amounts to ±5% for q >13 nm−1 at low temperatures. On heating, the error increases to ±l5%.

42 ELECTRICAL METHODS OF NONIDEAL PLASMA GENERATION

g cm

MPa

.	.	.	.	.	.	.	.	˚C
Fig. 2.19. Thermodynamic equation of state for mercury (Kikoin et al. 1973).
It follows from Fig. 2.22 that, at ρ < 0.66 g cm−3							(which is twice as high

as than the critical density ρc), the behavior of S(q) with high values of q is fully smoothed while the behavior at low values of q points to sharply increasing scatter, which is analogous to the behavior of S(q) of argon. From here, it follows that the critical fluctuations are not a factor defining the beginning of the “metal– nonmetal” transition.

2.1.4Sound velocity measurements

In the acoustic method of “fixed distance” (Vasil’ev and Trelin 1969; Winter et al. 1988) the sound velocity is determined by the time, taken by a sound pulse to pass the known speed base in the medium under investigation, and the attenuation of sound is determined by the decrease in its amplitude. The test assembly is shown diagrammatically in Fig. 2.23. Longitudinal sound oscillation is excited in the medium being investigated by means of piezoelectric transducers (1). Two sound ducts (3) are separated by a niobium ring (5). The ring is filled with the test substance, and the ring width is the speed base. A niobium ampoule (2) is heated to the desired temperature. As the pressure varied, mercury introduced into the chamber (6) was forced out into an expander (which is not shown in Fig. 2.23).

The measuring scheme enables one to register, separately, the pulse which passed through both sound ducts (3), and the pulse which was singly reflected from the internal interface between the medium and receiving duct line before