Aggregate States of Liquid Helium1

W. H. Keesom, Leiden.

Owing to the extraordinarily small magnitude of its internal forces, helium, discovered in the solar chromosphere in 1868 and obtained from terrestrial sources by Ramsay in 1895, is a substance that approaches the ideal gases far more closely than any other substance known to us. It is a thermometric gas par excellence, for its extremely low critical temperature and boiling point make it possible to extend the temperature scale almost down to absolute zero.

Fig. 1.

The first investigators who attempted to obtain liquid helium were Dewar and Olszewski. The method they used—cooling the gas with liquid hydrogen and subsequently expanding it—proved insufficient, and complete success in this direction was achieved only in 1908 by Kamerlingh Onnes, who resorted to a procedure that had been used ten years earlier by Dewar in the liquefaction of hydrogen. Fig. 1 shows a diagram of such an apparatus. Helium from cylinders is forced into a cooler, where it was cooled first by means of hydrogen vapor and then by liquid hydrogen boiling under reduced pressure at \(-258^\circ\mathrm{C}\). After this, the cooled helium was passed

in a coil, is subjected to the expansion associated with this and, by virtue of the Joule–Kelvin phenomenon, partially passes into the liquid state. As a consequence, the lower part of the vessel for cooling helium was somewhat modified, so that it could be carried over into a cryostat and physical measurements could be made. In later experiments, aimed at obtaining the very lowest temperatures, Kamerlingh-Onnes used an entire battery of Lenger condensation pumps connected with a whole series of powerful mechanical pumps. In order to decide the question of the transition of helium at such extremely low temperatures into the solid state, he placed in a Dewar vessel with liquid helium a small metal cylinder which, by means of a long rod, could be moved in the vertical direction.

All these experiments showed that, whereas hydrogen boils at \(20^\circ K\) and, under reduced pressure, becomes solid already at \(10^\circ\), helium, which has a boiling temperature of \(4.2^\circ\), does not solidify even at a temperature lying slightly above \(0.8^\circ K\). At this temperature helium remains in the liquid state even under the very small pressure of its own saturated vapor.

Fig. 2.

My experiments, which made it possible to obtain helium in the solid form, showed quite clearly that for the transformation of helium into the solid state there is required not only such a temperature at which the intra-atomic forces overcome the thermal motion sufficiently for the atoms to be able to group themselves into a crystalline lattice, but, in addition, the action of an external pressure is also required, which must be sufficiently high to bring the intra-atomic forces into action. Without the application of such a pressure helium remains liquid even at the lowest of the temperatures attained, although at some temperature it may indeed pass into a new liquid state of aggregation.

The apparatus used in these experiments is shown schematically in Fig. 2. The lower ends of two metal tubes \(B_1\) and \(B_3\), connected by a narrower tube, were immersed in liquid helium; in these tubes the compression of helium was produced by means of a small hydraulic press filled with glycerin. When the piston \(P\) was pulled out, the mercury, filling the two remaining cylinders \(C\) up to half their height, rises in the right-hand cylinder and carries with it

helium from the storage vessel through valve \(K_1\) into the left cylinder. Then valve \(K_1\) is closed, and, by means of piston \(P\), the helium is forced through valve \(K_3\) into the system of tubes. In order that the fact of the transition of helium into the solid state could be established, these tubes were connected with the branches of a differential manometer consisting of a steel tube \(D\), the lower end of which is located in the same steel chamber \(E\) with a certain quantity of mercury. If, in the lower part of tube \(B_8\), the formation of a plug of solid helium takes place, and if, with valve \(K_1\) closed, valve \(K_2\) is opened for a moment, then a certain quantity of gaseous helium escapes; the pressure in the right-hand part of tube \(B_8\) becomes lower than in the left-hand part, and the mercury in the steel tube of the differential manometer rises. This tube contains a thin platinum wire included in one of the branches of a Wheatstone bridge, so that the rise of the mercury entails a deflection of the galvanometer pointer. Another method, which was studied later and which was proposed by Keesom, consists in the fact that, in the glass tube \(F\), connected with the rest of the apparatus by a metal tube, there is a rod of soft iron \(H\), which can be raised and lowered with the aid of a magnet; the glass tube \(F\) was in fact located in a helium cryostat, which, for simplicity, is not indicated in the drawing.

By varying the temperature of the helium bath by changing the pressure over the liquid helium and by determining the pressure necessary for blockage of the tube by helium to occur, it was possible to obtain a melting curve for helium for pressures from 25 to 140 atmospheres and for temperatures from \(1.2^\circ\) to \(4.2^\circ\) K. It turns out that this melting curve, in its lower part, becomes almost parallel to the temperature axis and shows no tendency whatever to intersect the vapor-pressure curve at the triple point, so that the simultaneous existence of the solid and gaseous phases appears impossible (below the critical temperature of helium).

Experiments carried out with the glass tube revealed no changes either in volume, or in state, or at the interface either between gas and liquid or between liquid and solid phases. Nevertheless, the presence of solid helium could be considered proven in this case as well, since a plug of such helium could be felt with the aid of the iron rod. It is quite evident that, at the pressures corresponding to this case (about 90 atmospheres), the densities and refractive indices for all three phases are almost identical.

In a whole series of experiments on the measurement of the dielectric constant of liquid helium, which were carried out jointly with Prof. Wolfke of Warsaw, it was possible to note that this constant undergoes a rather abrupt change in magnitude at a temperature of \(2.3^\circ\) K, coinciding with the temperature at which Kamerlingh-Onnes and Boks observed the maximum value for the density of the liquid.

From this one may conclude that there exist two modifications of liquid helium, namely—liquid helium I, stable at temperatures above 2.3°, and liquid helium II, stable at lower temperatures; the density of the former is approximately 0.1% higher than the density of the latter.

Dana and Kamerlingh Onnes made measurements of the specific heat of liquid helium, which, however, were not published, since its excessively high values at temperatures around 2.3° seemed inconsistent with other data. This discrepancy evidently depends on the heat of transformation of helium I into helium II, which by calculation turns out to be \(-0.13 \frac{\mathrm{cal}}{2}\). The sudden change also occurs in the heat of vaporization; moreover, for helium II its value is greater than for helium I; conversely, the surface tension of helium I exceeds the corresponding value for helium II by 3%.

It should be noted that this transformation occurs at a temperature which, in the sense of Van der Waals’s law of corresponding states, is analogous to the melting temperatures of other substances.

Thus helium has a triple point: liquid helium I—liquid helium II—vapor. Up to the present time such a triple point has been observed only in certain substances of complex composition exhibiting a mesomorphic state (i.e., in liquid crystals); whether this is also the case for helium can be shown only by further investigations. Fig. 3 is a diagram of the various states of helium; it shows the saturated-vapor pressure curve, the triple point, and the curve of melting points. Between liquid helium I and liquid helium II there should lie a transition curve, but it still remains unknown whether it intersects the melting-point curve, as shown in the diagram, or bends toward the pressure axis.

1. From a lecture delivered before the Fifth International Congress of Refrigeration in Rome on April 13, 1928, Nature, 122, 847, 1928. ↩