AN EXPERIMENTAL TEST OF ISING-MODEL PREDICTIONS OF THE BEHAVIOR OF CARBON DIOXIDE NEAR THE CRITICAL POINT
Ising-model calculations by Howard Tarko and Michael Fisher predict that contours of constant susceptibility and constant correlation length are incongruous in the vicinity of the critical point, i.e., (chi) r('-(gamma)) while (xi) r('-(nu))(1 + 0.17(theta)('2)), where r and (theta) are restricted cubic-model parameters. An experiment using an optical probe (a focused, vertically polarized helium-neon laser beam) to measure the susceptibility and correlation length of carbon dioxide near the critical point was devised to test this prediction. The experiments were conducted over the temperature range -2.2 mK < (DELTA)T < 14.5 mK. The susceptibility as a function of temperature and height in the fluid was determined by measuring the vertical deflection of the optical probe. The correlation length was determined by constructing Ornstein-Zernike plots based on measurements of horizontal-scattering intensities. The horizontal-scattering data were corrected for attenuation and for double scattering. An independent measurement of the fluid's turbidity provided a cross-check of the susceptibility and correlation-length measurements. The experimental data resulting from this research were analyzed in two ways. First, the cubic-model parameters r and (theta) were estimated from the height of the optical probe in the fluid and the estimated temperture difference T - T(,c). Next, the same parameters were estimated, with slightly different results, using the height of the optical probe and the measured susceptibility. The measured values of the correlation length were interpreted using the Tarko-Fisher critical-scattering function. The result, using the first method of estimating r and (theta), is that the correlation length can be represented by (xi) = 0.141 r('-0.63) (1 + 0.12(theta)('2)), with a RMS deviation of 3.0%. The result using the second method of calculating r and (theta) is that (xi) = 0.139 r('-0.63) (1 + 0.16(theta)('2)), with a RMS deviation of 1.7%. These experimental results lead to the conclusion that the Tarko-Fisher predictions accurately portray the incongruity of the susceptibility and correlation-length contours as well as the scattering function near the critical point.