Phase transition temperatures of 405-725 K in superfluid ultra-dense hydrogen clusters on metal surfaces

Ultra-dense hydrogen has been studied in two forms, ultra-dense protium p(0)^1,2 and ultra-dense deuterium D(0).^3,4 These quantum fluids H(l=0)³ consist of chain clusters H_2N(0). Both forms are superfluid at room temperature⁵ as evidenced for example by a fountain effect. They also show a Meissner effect at room temperature, which means that the long chain-like clusters lift in a static magnetic field.^6,7 This effect is less pronounced for p(0),⁷ presumably due to its slightly more complex cluster structure compared to D(0).^2,7 The experimental methods used to study these materials are laser-induced time-of-flight (TOF) or time-of-flight mass spectrometry (TOF-MS).^4,8–10 The density of the ultra-dense material is around 10²⁹ cm⁻³, corresponding to a theoretical D-D distance of 2.23 pm³ and the normal experimental distance of 2.3 ± 0.1 pm.^4,8–10 The materials form thin films on metal surfaces but not on polymer surfaces.¹¹ This shows that the interaction of the superfluid phase with the metal carrier surface is strong. Due to the large difference in scale between the ultra-dense material and the carrier surface (typically 2 pm instead of 200 pm for the carrier), many novel effects may be possible. It means for example that an entire chain cluster H_2N may fit in between two metal atoms on the surface, and that diffusion of small clusters into the surface may be fast. As for ordinary superfluids,¹² a transition temperature should exist at elevated temperature (here above room temperature) for the superfluid layer to a non-superfluid state. This is the first study to investigate such properties of the ultra-dense materials, and it mainly explores the differences between p(0) and D(0) and between different metal carrier surfaces. More accurate measurements of the transition points probably require different methods, since the heat due to the analyzing laser pulse decreases the precision of the transition temperature determination.

Rydberg matter has been studied extensively in our group here in Göteborg and two different types of such matter have been observed.. These two forms are clearly different both concerning angular momentum properties and energy. In Fig. 1, the relation between the various forms of hydrogen are shown in an energy-distance diagram.

Ordinary Rydberg matter consists mainly of planar clusters with the conduction electrons in Rydberg-like orbits.^13–16 It was predicted around 1980 by Manykin et al.^15,16 Such Rydberg matter is a generalized metal with l > 0 instead of l= 0 for an ordinary metal.¹⁴ It is described by the value of the electron orbital angular momentum which is the same for all conduction electrons in each cluster. This is indicated for example for hydrogen as H(l) thus as H(1), H(2) etc. H may indicate all isotopes of hydrogen, or the material is indicated more precisely by using p, D or T.

More recently, another form of Rydberg matter has been detected and studied, where the electron orbital angular momentum l is zero. The Rydberg matter structure is in this case instead given by the spin angular momentum s > 0. This quantum number was identified experimentally to have values s = 1, 2 or 3, giving an interatomic distance of only 0.57 pm in level s = 1.³ This type of matter is usually called ultra-dense hydrogen with notation as H(0) for simplicity, with most studies concerned with the level s = 2 with experimental H-H bond distance of 2.3 ± 0.1 pm.^4,8–10 The notation H(-1) was used in previous papers to indicate the presumed “inverted” state of the ultra-dense material.⁴ This notation is now replaced with H(0) or H(l=0), or with H(0, s=1,2,3) pointing more clearly to the important spin angular momentum quantum number. Most experiments with ultra-dense hydrogen have in fact studied ultra-dense deuterium D(0) due to its slightly simpler structure, with less interaction between the nuclei due to their Boson properties.

The quantum mechanical basis for D(0) was first discussed by Winterberg,^17,18 pointing out the similartity to other superfluids.¹² Berezhiani et al.¹⁹ predicted a dense deuterium phase with both superfluid and superconducting properties.

Experimental studies of clusters of ultra-dense hydrogen H(0) show that they are chain clusters of the form H_2N with N an integer. This form is shown at the top in Fig. 2. Each H₂ “bead” is formed by a pair H-H which rotates around the cluster axis. The electrons may form a vortex in each long cluster. Each such cluster shows a Meissner effect, thus it floats in a static magnetic field.^6,7 This is characteristic for a superconducting material. Hirsch²⁰ describes the superconducting state of a material as having large Rydberg-like orbits. This is similar to an ordinary RM cluster state with l > 0, but here with the plane of the orbit given by the magnetic field direction, not by the geometry of the cluster as in the case of an ordinary (orbital angular momentum-based) RM cluster. Only a few of the electrons in each cluster are simultaneously in such high Rydberg-like states.

In the Meissner experiments on D(0),⁶ it was clearly observed that small clusters D₃(0) and D₄(0) do not float in the magnetic field, thus they do not show a Meissner effect. Long chain clusters D_2N float in the static magnetic field. The small clusters do not have a main axis due to their symmetry as shown at the bottom in Fig. 2. It was concluded in Ref. 5 that such small clusters probably do not form a superfluid layer on the metal carrier surface used in the experiments. These results indicate that a material formed from such small symmetric ultra-dense clusters will not have superfluid or superconductive properties.

The apparatus has been described in several publications, for example in Ref. 4. It has a base pressure of <1 × 10⁻⁶ mbar and is shown in Fig. 3. The central source part is described in Ref. 9. The emitter is a cylindrical (extruded) sample of an industrial iron oxide catalyst doped with K,^21,22 a so called styrene catalyst type Shell S-105 (obsolete). This type of catalyst is an efficient hydrogen abstraction and transfer catalyst. The emitter is mounted in the tight-fitting opening of a metal tube. This source metal tube can be heated by an AC current through its wall up to 400 K. Hydrogen gas (99.9995% pure hydrogen, naturally containing 0.016% D) or deuterium gas (99.8%) is admitted through the tube at a pressure up to 1 × 10⁻⁵ mbar in the chamber. In some test experiments, the gas is instead admitted through a leak valve to the same pressure, without heating the source. The mounting of the metal carrier is constructed for direct heating with a 50 Hz AC current. The carrier metal foil with dimension 12 × 15 mm has a thickness of 0.2 mm which is enough to avoid fast boring through with the laser beam. It is spot welded to two thinner foils of Ta with thickness 0.1 mm. In some cases (Pt and Ir) the metal is instead in the form of rods with 2 mm diameter spot-welded onto a Ni foil. The carrier foil is at 45^o to the vertical direction and mounted approximately 1 cm below the source tip. The heating current through the carrier and its supporting foils is taken from an external ring transformer with a few turns of secondary winding. The lower supporting foil is longer and it is thus the main heater for the carrier by conduction. It is always hotter than the carrier foil. The carrier foil thus has a small voltage drop over it and a relatively weak magnetic field from the heating current. The temperature of the carrier is measured by a type K thermocouple (TC), spot welded at the upper half of the carrier foil. The cold end of the TC is at the screw support on the arms holding the carrier foil, at a distance of 20 cm from the carrier. Due to factors like heating by the laser impact, the temperature of the carrier is not determined better than ±25 K during each experiment. The cold end of the TC increases with time of heating of the carrier foil, of the order of 10-20 K during a typical experiment. This gives a lower temperature reading. The carrier can be moved back and forth in the chamber along the laser beam though a fine screw in a linear motion feed-through, so positioning the carrier and the laser beam point of impact in front of the detector slit.

A Nd:YAG laser with an energy of <125 mJ in 5 ns long pulses at 10 Hz is used at 532 nm. The laser beam is focused on the carrier at the center of the chamber with an f = 400 mm spherical lens. The lens is mounted in a vertical motion translation stage. The intensity in the beam waist of (nominally) 70 μm diameter is relatively low, ≤10¹² W cm⁻² as calculated for a Gaussian beam. A dynode-scintillator-photomultiplier detector which measures the time-of-flight (TOF) spectra of the neutral and ionized flux from the laser initiated processes is shown in Fig. 3. The detector can be rotated around the center of the chamber and is here used at 45^o and 70^o relative to the incoming laser beam. The fast particles impact on a steel catcher foil in the detector, and fast ions ejected from there are drawn towards a Cu-Be dynode held at -7.0 kV inside the detector. The total effective flight distance for the particles from the laser focus to the catcher foil is 101 mm by direct measurement and internal calibration.^4,23 The photomultiplier (PMT) is Electron Tubes 9128B with single electron rise time of 2.5 ns and transit time of 30 ns. This PMT is covered by Al foil and black plastic tape giving only a small active cathode area of 2-3 mm² to avoid saturation. Blue glass filters in front of the PMTs remove the signal from the laser light. A fast preamplifier (Ortec VT120A, gain 200, bandwidth 10-350 MHz) is used. The signal from the PMT is sometimes collected on a fast digital oscilloscope (Tektronix TDS 3032, 300 MHz). A multi-channel scaler (MCS) with 5 ns dwell time per channel is normally used (EG&G Ortec Turbo-MCS). Each MCS spectrum consists of the sum of 500 laser shots.

The laser-induced mass spectrometry used here is described in several publications.^3,4,8–10 Due to the very short bond distances in ultra-dense hydrogen and also in low levels of ordinary hydrogen Rydberg matter H(1) and H(2), the kinetic energy release (KER) given to the cluster fragments by the Coulomb explosions (CE) induced by the laser pulse is quite high. It is also well-defined, due to the easy removal of the orbiting electrons by the laser pulse, without any large changes of the structure before the fs long repulsion period between the fragments.²⁴ The total kinetic energy of the fragments gives directly their initial distance as

where ε₀ is the vacuum permittivity, e the unit charge on the fragment ions and E_kin the sum kinetic energy for the fragments (KER) from the CE. The fraction of the KER that is observed on each fragment depends on the mass ratio of the fragments. The kinetic energy is determined by measuring the time-of-flight (TOF) of the fragments and then converting this quantity to kinetic energy. Often a light monomer fragment is ejected from a large cluster, thus taking away most of the kinetic energy which is easily measured. In the case of long H(0) chain clusters, a central fragmentation is often observed, thus giving two identical cluster fragments, each carrying half the total KER. The most common state of H(0) has s = 2.³ It has 2.3 pm H-H distance and gives a total KER of 640 eV.

The metal surfaces used as carriers for H(0) are both high temperature melting metals like Ta and softer metals like Ni. Typical spectra are shown in Fig. 4 for ultra-dense protium p(0) on Ta carrier and in Fig. 5 for ultra-dense deuterium D(0) also on Ta. The shortest TOF limits for the various excitation levels of the hydrogen materials^3,14 are indicated in the figures. They are also given in Table I. It is observed directly from the figures that the peaks associated with long chain clusters H_N(0) disappear at a quite well defined temperature. This means that above this transition temperature, only the small, H₃(0) and H₄(0) clusters in the peak at around 400 ns TOF remain. The H₄ cluster probably has a tetrahedron shape. These small clusters (both H₄ and H₃) were shown not to float in the magnetic field in Meissner experiments.⁶ It is believed not to have any special quantum properties giving interactions in the adsorbed layer on the metal surface. Thus a phase only containing such clusters is believed to not be superfluid. The transition temperatures for different carrier metals and for both p(0) and D(0) are collected in Table II. All these material combinations show the same behavior as exemplified in Figs. 4 and 5, with a relatively well-defined transition temperature and a higher transition temperature for the p(0) layer than for the D(0) layer. This indicates a stronger interaction with the carrier surface for D(0), possibly due to the boson properties of the deuterons.

In Figs. 4 and 5, a tentative assignment is made of the cluster peaks in the H(0) signal at low temperature. Since the peaks have no sharp structure, just the maximum TOF is given in terms of symmetrical fragmentation of the clusters H_2N as H_N↔H_N. This means that each fragment has an energy of 320 eV, giving a total kinetic energy release of 640 eV as expected for the bond distance of 2.3 pm.³ 

A few experiments have been done to observe the possible difference in the behavior with a diffuse gas inlet into the chamber relative to that using the ultra-dense hydrogen source in Figs. 4 and 5. A few such spectra are shown in Fig. 6. In general, the signal from all H(0) clusters is lower when using diffuse gas, which is expected since the source is not in contact with the admitted hydrogen gas. The source with its catalyst is still located above the carrier in these experiments, so some H(0) is probably formed in the source also with a diffuse gas inlet. Otherwise, the behavior with diffuse gas is similar to that with the special H(0) source.

Results have also been obtained for the behavior of H(0) at high temperatures. For example, on Ni the signal due to D₄(0) clusters decreases at higher temperatures, as shown in Fig. 7. This behavior is more pronounced for D(0) than for p(0). This effect is not observed on Ta surfaces, and is concluded to be due to diffusion of the hydrogen atoms into the metal surface. That D(0) is more sensitive to diffusion loss is in agreement with the transition temperature being lower for D(0), both effects indicating a stronger interaction of D(0) with the metal surface and less interaction within the superfluid layer.

The detector has been used both at angle 45^o and 70^o relative to the incoming laser beam in all the experiments. Thus, data like Figs. 4 and 5 exist for both these angles. The results for these two angles are similar in intensity and temperature variation, which shows that the ejected flux from the sample has a broad angular distribution and that the signal observed is not influenced by any directive effects from the sample. The same conclusion can also be drawn from the fact that the Pt and Ir samples are in the form of 2 mm rods, while the other data are from foils. This means that the local surface is quite random and has a negligible effect on the signal observed. The transition temperatures in Table I are averages of the results from the 45^o and 70^o detector positions.

The results obtained are in the form of TOF distributions as a function of starting temperature. The temperature of the target increases at worst 50 K due to the laser pulse-energy (< 1 W) during the measurement of each spectrum which takes 50 s. The starting temperatures given for each spectrum are approximately 25 K lower than the average temperature during the measurement of the spectrum. Thus the transition temperatures given are not more accurate than ±25 K. Since it is observed from the spectra that the significant changes in peak structure (which indicate strong changes in the cluster composition) take place over temperature ranges of a similar size, a better precision is not needed. Of course, the total amount of H(0) on the surface also changes due to other parameters like the previous history for the adsorbed layer. However, the procedure used for each series of spectra is the same and the differences between the results for different material combinations are thus the most significant results. It is possible to find the transition point both by step-wise increase or decrease of the sample temperature. Another method is to cut off the heating current at high temperature and then let the sample cool by itself with the laser running down to the point where the large H(0) clusters are observed again. This process is thus easily repeatable and reproducible, and does not have any observable time constant or delay.

One important point to discuss is the possibility that the apparent transition point is caused by a general loss of hydrogen from the surface or bulk of the metal, in the form of desorption from the sample tested. In Figs. 4 and 5 it is shown that higher excitation levels of hydrogen Rydberg matter exist unchanged at high temperature, thus with large concentrations of hydrogen bound on the surface. These forms of hydrogen have much smaller bond energy than the ultra-dense hydrogen, as can be concluded from the different bond distances. It is known that H(1) has a bond distance of 153 pm, while H(0) in its most common spin state s = 2 has 2.3 pm. Thus, the bond energy is approximately 60 times smaller in H(1) than in H(0). It is highly unlikely that H(1) can exist on the metal surface while the long chain-clusters in H(0) are desorbed, with their typical bond energies of several hundred eV. It is concluded that the vanishing of the H_2N(0) clusters is due to a real phase change in the superfluid H(0) surface layer on the metal.

In the Meissner studies of p(0)⁷ it was indeed concluded that no symmetric p₄(0) clusters existed, since they were not observed to stay on the magnet surface. This may mean that such clusters are not in the form of tetrahedrons as in Fig. 2, which the corresponding D₄(0) clusters⁶ apparently are. Instead, they may just be formed from two p₂(0) pairs, which are more loosely connected, maybe even giving a typical cluster axis. In the present series of experiments, no large difference in the intensity of the typical peak at 300-400 ns in the TOF spectra has been observed for p(0) relative to D(0), so this gives no information on the preferred shape. Several different fragmentation patterns may give intensity in this rather broad peak at 300-400 ns. In the case of p(0), the formation of p₂ boson pairs mimicking D in the cluster structure was discussed previously.^2,7 This may of course prevent clear conclusions on the exact form of the p₄(0) and p₃(0) clusters.

The most important results are that the transition temperature is higher for p(0) than for D(0), and that the transition temperature changes considerably for different surfaces. Both these results indicate a strong interaction between the metal carrier surface and the ultra-dense hydrogen layer.

Laser-induced time-of-flight is used to probe a layer of ultra-dense hydrogen, both p(0) and D(0), to find if there exists a transition temperature for this room-temperature superfluid layer. A transition point is found, varying in the range 405-725 K for different metal carriers. High-melting metals give a higher transition temperature, and that point for p(0) is always higher than that for D(0). Above the transition temperature, the superfluid and superconductive long chain-clusters H_2N(0) have disappeared, and only the normal small clusters like H₄(0) remain. The higher Rydberg matter level H(1) remains on the surface at high temperature, thus extensive desorption does not take place.