A Technique for Measuring Equilibrium Thermodynamic States of Liquid Metals at High Temperatures and Pressures

Abstract

This paper presents a method for overcoming temperature and pressure limitations inherent in conventional techniques for measuring equilibrium thermodynamic data. The method can be applied to conducting materials that can be resistively heated and that do not dissociate in the liquid phase; and it is thus particularly suitable for investigating pure liquid-metal thermodynamic data. The technique has been applied extensively to lead at temperatures exceeding 5000 K and at pressures up to 2 kilobars. A cylindrical material specimen 1 mm in diameter and 25 mm long is interposed between two current leads and mounted axially concentric with a high-pressure cell. After the cell is pressurized with helium, a current pulse from the overdamped discharge of a high-voltage capacitor bank heats the wire at such a rate that its expansion is nearly isobaric. The energy deposited in a central segment of the sample is computed by integrating the product of the current flowing in the segment with the resistive voltage developed across it. With these data, sample resistance can also be calculated during a major portion of the time that current flows. Because mounting constraints limit sample expansion to the radial dimension, the equilibrium volume is calculated from the expanded diameter, which is measured by means of pulsed x-radiography.

Equation of state and transport measurements on expanded liquid metals up to 8000/sup 0/K and 0. 4 GPa

“…Application of Bqs. (3)(4)(5)(6)(7)(8) and (4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19) to individual channels designated i and j, and a small amount of algebraic manipulation, produces an expression for the TCT temperatures that is analogous to Bj. (3-13).…”

“…Harrison (76) and discussed in detail by Bgelstaff. (77) 2 ^ ~z ,,e r/R w(r) = ~T + C e c (5)(6)(7)(8)(9)(10)(11)(12)(13)(14) Evaluation of the matrix element with this potential function produces the Harrison bare sphere form factor: . Given any temperature, Tm.…”

“…To demonstrate the effect of screening the Ashcrof t hollow core form factor is used both with simple Linhard dielectric screening and the more complex screening of Bq. (5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17). In both cases the parameter R is the 0.57 A chosen by Ashcroft to produce a form factor that correctly predicts the known band gap of lead. '…”

“…As revealed in Bqs. (5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21) and (5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22) the electron mass enters directly into the resistivity both through the t-matrix and in the coefficients of the q-space integral.…”

“…While the technique involved some iteration to ensure a smooth joining of the new data to the old, the uncertainty was always greater for this procedure than for the cases in which a high temperature melting transition provided a "self" calibration point (see Bq. [3][4][5][6][7][8][9][10]. What is needed then is a method of superimposing the intensity of a known standard radiator on the data trace.…”