NEW DATA ON He³

The present note is a supplement to the review[^1] printed in the April issue of this journal.

In [^1] the works of a number of investigators were considered, devoted to the question of the distribution of the isotope He³ between liquid helium and vapor at temperatures below the λ-point. According to these works, the ratio of the concen-

tration of He³ in the vapor to the concentration in liquid helium, \(\dfrac{C_V}{C_L}\), depends on the total concentration \(\dfrac{\mathrm{He}^3}{\mathrm{He}^4}\) at \(\dfrac{\mathrm{He}^3}{\mathrm{He}^4}\sim 10^{-5}—10^{-6}\), i.e., Henry’s distribution law is violated already for very dilute solutions of He³ in He⁴. It was also pointed out there that such a violation of Henry’s law is very unlikely; the observed dependence of \(\dfrac{C_V}{C_L}\) on \(\dfrac{\mathrm{He}^3}{\mathrm{He}^4}\) can be explained by the fact that in these experiments the distribution of He³ was nonequilibrium because of the influence of the mobile surface of the film and the presence of heat flows in the liquid helium.

Recently a new paper appeared by Lane, Fairbank, Aldrich, and Nier³. The authors recognized their previous results as erroneous, owing to the action of the two masking effects mentioned, and carried out measurements with a new apparatus, to a considerable extent free of the shortcomings of the previous one. The new apparatus (Fig. 1) is a U-shaped tube with an enlargement \(B\) in one knee. In the upper part of the enlargement there is a blind glass partition with a thin glass appendage \(S\), separating the enlargement \(B\) from the tube \(T\) leading upward. The instrument is immersed in a bath with liquid helium and protected by screens \(R\). The tube \(T\) is carefully evacuated; helium is admitted into the narrow knee \(C\), and, condensing, it fills the lower part of the enlargement. In the enlargement above the helium level an atmosphere of saturated helium vapors is formed; the entire inner surface of the vessel, covered with a helium film, is at one and the same temperature, and therefore the film is at rest. The heat flows in the liquid helium in the volume \(B\) are considerably reduced by the fact that the heat reaching the liquid helium, mainly owing to the film effect in the narrow knee \(C\), passes through the walls into the helium bath. To take a sample of helium vapor, the appendage \(S\) is broken by the weight \(W\), and the helium vapors rush through the tube \(T\) into the previously evacuated ampoule \(E\).

Fig. 1. Apparatus for determining \(\dfrac{C_V}{C_L}\).

The authors obtained the following results: at \(1.8^\circ\) K, in the case of total concentration \(\dfrac{\mathrm{He}^3}{\mathrm{He}^4}=36.5\cdot 10^{-6}\), \(\dfrac{C_V}{C_L}\) was found to be 97, and in the case \(\dfrac{\mathrm{He}^3}{\mathrm{He}^4}=1.2\cdot 10^{-6}\), \(\dfrac{C_V}{C_L}=58\), and in another experiment 44 (in the previous paper, at \(\dfrac{\mathrm{He}^3}{\mathrm{He}^4}=1.2\cdot 10^{-6}\), \(\dfrac{C_V}{C_L}\) was less than 0.04, and according to the data of Daunt et al., at \(\dfrac{\mathrm{He}^3}{\mathrm{He}^4}=(30—40)\cdot 10^{-6}\), \(\dfrac{C_V}{C_L}\approx 3\)). These results testify to the absence, below the \(\lambda\)-point, of a sharp drop in \(\dfrac{C_V}{C_L}\), and also to a weakening of the “dependence” of \(\dfrac{C_V}{C_L}\) on the total concentration of He³. The authors of the paper indicate

to the sources of experimental errors not eliminated by them, which are undoubtedly reflected in the results, namely: heat flows in volume \(B\) due to heat conduction through tube \(C\) and the action of both masking effects during the time of sampling. It is precisely these errors that explain why, in two experiments at one and the same total concentration, different values of \(\dfrac{C_V}{C_L}\) were obtained (44 and 58). Therefore the values of \(\dfrac{C_V}{C_L}\) should be treated with caution, and no special meaning should be attached to the difference between the values of \(\dfrac{C_V}{C_L}\) (58 or 44 and 97) for different total concentrations. All the more strange is the authors’ statement that, in their opinion, there should exist a dependence of \(\dfrac{C_V}{C_L}\) on \(\dfrac{\mathrm{He}^3}{\mathrm{He}^4}\), and that the results of their latest work confirm the presence of such a dependence.

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Concerning the properties of pure \(\mathrm{He}^3\), physicists expressed various assumptions; special interest was shown in the properties of liquid \(\mathrm{He}^3\). F. London and Rice, as well as Tisza, proceeding from their theoretical views, expressed doubt that \(\mathrm{He}^3\) could be liquefied at all.

From data on the change in the elasticity of vapors over helium enriched with \(\mathrm{He}^3\), Fröhen, Reynolds, and Lane determined by extrapolation the boiling temperature of \(\mathrm{He}^3\), equal to \(2.9^\circ\mathrm{K}\). De Boer and Lunbeck\(^3\) made an estimate of the critical pressures and temperatures of \(\mathrm{He}^3\) by comparing the critical parameters of a series of inert gases, hydrogen, and nitrogen. According to their estimates, \(T_k = 3.1\text{–}3.5^\circ\mathrm{K}\), \(p_k = 0.93\text{–}1.35\) atm. In the same way these authors obtained an approximate temperature dependence of the elasticity of \(\mathrm{He}^3\) vapor. The validity of one or another assumption could be proved only by experiments with pure \(\mathrm{He}^3\).

Fig. 2. Dependence of the vapor pressure of \(\mathrm{He}^3\) and \(\mathrm{He}^4\) on temperature.

Robinson and Potter (see\(^4\)) obtained pure \(\mathrm{He}^3\) in an amount of \(20\ \mathrm{cm}^3\) under normal conditions. \(\mathrm{He}^3\) was obtained as a result of the \(\beta\)-decay of tritium \(\mathrm{H}^3\) (half-life\(^5\) of the order of 10 years). The tritium was separated from \(\mathrm{He}^4\) by means of a palladium absorber; the resulting \(\mathrm{He}^3\) was purified of hydrogen isotopes by means of chemical absorbers of hydrogen. Simon, Grilly, and Hammel\(^4\) condensed this \(\mathrm{He}^3\) and measured its vapor pressure in the temperature interval \(1.2\text{–}3.3^\circ\mathrm{K}\). The \(\mathrm{He}^3\) was in a steel capillary immersed in a helium bath to a fixed depth. The upper end of the capillary was connected to a manometer and to an aspirator. At a certain temperature value the gaseous \(\mathrm{He}^3\) began to condense, raising the mercury level in the aspirator. From the moment condensation of \(\mathrm{He}^3\) began in the capillary

pressure ceased to increase and became independent of the volume, being equal to the saturated-vapor pressure of He³ at the given temperature. The critical temperature of He³ proved to be equal to \(3.3^\circ\mathrm{K}\), the boiling point at atmospheric pressure \(3.2^\circ\mathrm{K}\). In Fig. 2 the dependence of the elasticity of the vapors of He³ and He⁴ on temperature is presented.

In their subsequent work⁶ Grilly, Hammel, and Sydoriak used a glass capillary instead of a metal one. This made it possible for them to verify visually that the condensed phase of He³ is a liquid. In addition, the authors determined the temperature dependence of the densities of liquid and vaporous He³ in the temperature interval \(1.27—2.79^\circ\mathrm{K}\). The method of their measurements was as follows: when the mercury level in the aspirator was lowered, a certain volume of liquid in the capillary, measured with a cathetometer, evaporated. The mass of the evaporated liquid is equal to the sum of the mass of the saturated vapor in the same volume and the mass of the gas at room temperature in the volume that was freed by the mercury in the aspirator. These measurements give values only of the difference between the densities of the liquid and the vapor. To obtain the densities themselves, the authors used the law of “rectilinear diameter” (the Mathias law), which consists in the fact that near the critical point the arithmetic mean of the densities of the liquid and the vapor, taken at one and the same temperature, is a linear function of temperature and is represented on the graph of density versus temperature by a straight line. To draw such a “diameter” one must have two values of the mean density. One value the authors obtained by assuming that at the lowest temperatures the density of the He³ vapors coincides with the density of an ideal gas. Then the authors determined the critical density by averaging the values obtained from the equations of state of van der Waals and Dieterici, using the known values of the critical pressure and critical temperature. The authors convinced themselves that all the assumptions they made are justified in the case of He⁴. In Fig. 3 the dependence of the densities of liquid and vaporous He³ and He⁴ on temperature is shown. The “diameters” are shown by dashed straight lines. Using data on the densities of the liquid and vapor, and also the dependence of the vapor pressure on temperature, the authors find the temperature dependence of the heat of evaporation; the heat of evaporation is represented by a smooth curve and has a maximum at a temperature between \(1.7—2.2^\circ\mathrm{K}\), equal to \(4.5\) cal/g.

Fig. 3. Dependence of the density of liquid and vaporous He³ and He⁴ on temperature.

After it was possible to liquefy He³, it remained to find out whether liquid He³ undergoes a superfluid transition. The question of the existence of a \(\lambda\)-transition in He³ was discussed by Miller⁶. The elasticity of saturated vapors possessing the properties of an ideal gas is determined with great accuracy by the formula \(\log p = \dfrac{C_p}{R}\log T + \dfrac{a}{T} - i\) (for helium vapors

\[ \frac{C_p}{R}=\frac{5}{2}, \quad a_i \text{ and } i \text{ are constants}). \]

The functional dependence

\[ \log p-\frac{5}{2}\log T \]

on

\[ \frac{1}{T} \]

for such vapors is represented by a straight line. Miller, making use of Sidoriak’s data, constructed the dependence

\[ \log p-\frac{5}{2}\log T \]

on

\[ \frac{1}{T} \]

for He\(^3\) (Fig. 4). It turned out that it is represented by a broken line consisting of two straight segments meeting at \(T=1.9^\circ\mathrm{K}\). This allowed Miller to suggest that at a temperature of \(1.9^\circ\mathrm{K}\) He\(^3\) undergoes a phase transition.

[In the graph: vertical axis \(\log p-\frac{5}{2}\log T\); horizontal axis \(1/T\).]

Fig. 4. Dependence of \(\log p-\dfrac{5}{2}\log T\) on \(\dfrac{1}{T}\).

It is difficult to say what causes the break found by Miller—whether it is the nonideality of the vapors, or the inaccuracy of Sidoriak’s measurements, etc. One thing is unquestionable: at the point of a second-order phase transition there can be no break in the curve of the dependence of the vapor elasticity on temperature. At this point the radius of curvature changes discontinuously in the curve. In the approximation, however, in which the formula given above is written, the \(\lambda\)-point cannot exist at all.

[In the graph: vertical axis “mass flow rate \((10^{-8}\,\mathrm{g/sec})\)”; horizontal axis “temperature \((^\circ\mathrm{K})\)”.]

Fig. 5. Dependence of the rate of flow of He\(^3\) and He\(^4\) on temperature.

be detected, and the formula on both sides of the \(\lambda\)-point should be the same.

The experimental solution of the question of whether He\(^3\) becomes superfluid was carried out by Osborn, Weinstock, and Abraham\(^8\). These authors set up an experiment in which the flow of liquid He\(^3\) through a slit \(7\cdot 10^{-5}\) cm wide was observed. Such a slit was formed by cooling a platinum wire soldered into Pyrex between a platinum and a Pyrex washer, owing to the different coefficients of expansion of these materials. The liquid helium that seeped through the slit entered a tube connected with a large volume; the pressure in this volume was very low, and therefore the helium that had flowed through evaporated completely. The rate of flow of the liquid helium could be judged from the change in the vapor pressure in this volume, measured with a manometer. The results of the experiment are shown in the figure. It is seen from the figure that below \(2.19^\circ\) K the rate of flow of He\(^4\) increases sharply, which corresponds to the transition of He\(^4\) into the superfluid state. For He\(^3\) no such change in the rate is observed in the temperature interval from 3.02 to \(1.05^\circ\) K; in other words, down to \(1.05^\circ\) K He\(^3\) does not pass into the superfluid state.

It should be noted that pure He\(^3\) was obtained by the authors in the same way as in\(^4\).

K. Tumanov.

CITED LITERATURE

1. K. A. Tumanov, UFN 37, 405 (1949).
2. C. T. Lane, H. A. Fairbank, L. T. Aldrich a. A. O. Nier, Phys. Rev. 75, 46 (1949).
3. J. De Boer a. R. J. Lunbeck, Physica 14, 510 (1948).
4. S. G. Sydoriak, E. R. Grilly a. E. F. Hammel, Phys. Rev. 75, 303 (1949).
5. B. V. Aivazov and M. B. Neiman, UFN 36, 145 (1948).
6. E. R. Grilly, E. F. Hammel a. S. G. Sydoriak, Phys. Rev. 75, 1103 (1949).
7. A. R. Miller, Nature 163, 283 (1949).
8. D. W. Osborne, B. Weinstock a. B. M. Abraham, Phys. Rev. 75, 988 (1949).