Solid Hydrogen Neon - Atmospheric Pressure Van der Waals Compounds

Dr. Stephen C. Bates

Thoughtventions Unlimited LLC

40 Nutmeg Lane

Glastonbury, CT 06033


The objectives of this proposed program are the study, experimental preparation, and analysis of a crystalline van der Waals compound of H2 and Ne, where the compound is formed at pressures on the order of 1 atm. The H2/Ne compound would be a van der Waals crystalline solid made of uniformly and atomically dispersed H2 and Ne. A number of van der Waals compounds have been demonstrated to exist at high pressures; this work develops techniques for creating related compounds at low pressure and offers explanations why such crystals have not been previously demonstrated. The characteristics and properties of a H2/Ne crystal will be predicted, together with its stability. A dynamic route to its formation is developed based on gas phase deposition crystal growth techniques. The cryogenic apparatus for the experiments will be assembled and experiments will be performed to grow this crystalline material. Established diagnostic techniques will be applied to verify the existence of the H2/Ne crystals. Theoretical and experimental results will be generalized to develop techniques for forming analogous van der Waals crystals composed of reactive materials.


Overall Technical Objectives: The overall technical objectives of the program are to model and define the characteristics of a H2/Ne crystal at cryogenic temperatures, to develop techniques to grow this crystal, and to demonstrate its formation experimentally using appropriate diagnostics techniques.

Significance. This program is designed to provide fundamental advances in the science of van der Waals (vdW) solid state interactions. The work is intended to be primarily experimental, but significant theoretical work will be performed, and the experiments will be closely related to modeling. The stability of vdW solids has been investigated in terms of minimum free energy calculations and molecular potentials, but experimental research indicates that an isotropic, long range, and many-body effects often dominate the formation and stability of solid phases on practical time scales. These effects need to be explored much more thoroughly to establish the correct details of the physics and mechanics of vdW cryogenic solids, their formation, and their application to scientific and engineering problems. Improved understanding and working techniques should lead to the creation of a variety of widely useful materials.

Quantum solids form a special class of materials. Within this small set of materials H2 exhibits many unusual properties as a result of the intricacies of the interactions between molecules with J=0 and J=1; ortho and para H2. H2 is almost unique because it can be treated theoretically based on fully ab initio principles. As a result, an increased understanding and improved description of H2 compounds may have broad theoretical implications both for the treatment of related solids, and for extending the application of theory to other solid compounds and solid properties.

The concepts and experimental techniques developed in this program may also lead to the creation of a broad class of metastable cryogenic crystals that would allow the investigation of a variety of issues in chemical reactivity and solid state physics. A long-term goal is the development of engineering materials that are cryogenically stabilized with high reactivity or large energy content.

Project Benefits. The long-term goal of this program is to find experimental techniques and theoretical guidelines for fabricating energetic cryogenic materials. Such materials would bring revolutionary changes to propulsion and energy storage. Additional applications of cryogenically stabilized materials include novel electronic materials, new synthesis routes for solid-state chemistry, and stable supply of highly reactive materials. The experimental and modeling techniques developed in this effort should be applicable to the formation of a broad new class of solid materials, their study, and establishment of their properties.

In The Short Term. This project is expected to provide significant contributions to fundamental science in the area of cryogenic van der Waals solids. Advances are expected in the areas of modeling, growth, properties, and prediction of the stability of vdW solid compounds.

The Context. Cryogenics is an expensive technology that has only recently been commercialized (LN2), although its scientific history is long and its military history is over 60 years old. The study of solids that only form at low temperatures was enabled by the ability to make significant quantities of cryogenic liquids; liquid helium was not generally available until 1923 [1]. The lowest temperature (at moderate pressures) cryogenic solid, H2, has been an experimental reality for over 70 years; the hcp structure of para-H2 was reported in 1930 [2]. The temperature dependence of chemical reactivity was established well over 100 years ago, but cryochemistry [3] is a recent and stumbling development.

Commercial applications for cryogenic solids are far fewer than those for cryogenic liquids. Solid CO2 is a commonly used refrigerant and is used for cleaning. Solid cryogens are used as radiation targets (e.g. [4]) and for long term storage of cryogens in space (e.g. [5]). Measurement of the chemical and mechanical properties of solid cryogens has been limited by the difficulty of testing in a thermally isolated environment. However, since optical access is compatible with thermal isolation there is extensive optical property data available for pure and impurity laden cryogenic solids (matrix isolation spectroscopy [6]).

More recently the development of diamond anvil cell apparatus and appropriate microscopic optical diagnostic techniques (e.g. [7]) has enabled experimental research into the study of condensed gases at high pressure, with a variety of astrophysical applications and implications. This research has led to the discovery of ordered cryogenic vdW solid compounds (e.g. [8]) for a number of species at very high pressures. It provides an unequivocal demonstration that vdW compounds exist but suggests that these compounds cannot be formed at lower pressures.

The Logic of the Approach. This proposal seeks funding for work that will allow scientific and engineering research leading to the fabrication of van der Waals (vdW) solid compounds at moderate pressures (not far from atmospheric pressure). The long term goal is to make a solid compound combining H2 with a highly reactive specie, and to define the rules and techniques for making such solids. The short-term goal is the first demonstration that a vdW compound crystal can be formed at moderate pressure. The path proposed here to the formation of the vdW compound is the result of extensive research into the pertinent issues but is not optimized. It is plausible and motivated by the following reasoning.

Why vdW Compounds? Although the immediate goal of this program is fundamental research into vdW compound crystals, the long-term goal of this research is to create a High Energy Density Material (HEDM). For host matrix/reactive species HEDMs, a relatively high reactive species concentration is required to greatly increase the energetic content of the overall material [9]; on the order of 10 mole %. Such high reactive species concentrations lead to at least two generic difficulties involved in the creation of these materials: 1) at high concentrations the average nearest neighbor distance is such that reaction occurs due to random concentration fluctuations, and 2) during the process of high concentration deposition the addition of the reactive species to the solid leads to reaction as a result of the energetic interaction between molecules being added and those in the solid.

The creation of vdW compounds allows the formation of a stable crystal with high relative concentrations of separated species, and it allows the formation of this crystal at low temperature with low kinetic/thermal energy species. The existence of vdW compounds has been conclusively demonstrated at high pressures, and various stability arguments and experimental data imply that these or related compounds can be created at pressures on the order of 1 atm or less, at least in a long-term metastable form.

The vdW compound allows the species to coexist at least in a metastable state in a cryogenic matrix, where it would be stabilized to some extent by the H2 (and probably stabilize the H2). The stability of the added species in the compound depends on the activation energy of same-species recombination in the context of the solid and the deposition process. Beyond chemical stability, engineering stability must also be concerned with response to external perturbations; species surrounded by H2 molecules would be chemically isolated to a certain degree (except near crystal faults) and therefore probably more stable.

Why H2? Solid H2 [10] has been chosen as a host matrix because: 1) it is the most well known of the cryogenic solids, 2) it has been and can be theoretically described to a much greater degree than other cryogenic solids, 3) knowledge gained of its properties is likely to have fundamental importance, 4) a common, simple, somewhat reactive host is desired for engineering purposes - either O2 or H 2. O2 has unusual magnetic properties and a number of solid phases, whereas (para)H2 is a simple, spherically symmetric molecule, with a single, simple phase. The unique properties of O2 may make it a more suitable candidate in the longer term, but a priori this molecule presents a number of complications experimentally and theoretically that make it more difficult to deal with and generalize from. The primary complication associated with H2 is that it is a quantum solid that exhibits a number of unusual properties.

Why H2/Ne? Given the choice of H2 as the host matrix, the choice of a compounding species is critical, and should be one that leads to a combination of the highest chance of experimental success with the most general application. Ideally the chosen species would be highly reactive, capable of stabilization and implantation (two separate issues), and easily diagnosable. To date no highly reactive species been found that can be combined with H2 in high concentrations (in spite of major efforts e.g. [11]).

The experimental complications of using a reactive species are formidable. Reactive species have very complex vdW interactions, both short range and long range. These interactions make it entirely probable that one particular sample species will not form a vdW compound with H2, while another species may readily form a compound. Not even vdW compounds of inert species combined with H2 have been found at pressures near one atm, so it seems most practical as a first effort to try to create a low pressure vdW compound based on species related to those formed at high pressure. Once the interaction and formation rules of these compounds are established, one could move on to the more difficult reactive species with some guidelines in hand. It is possible that there are general characteristics of reactive species that may make forming vdW compounds with H2 impossible, but the generic science will still be valid, and it may be possible to use this science to form vdW compounds with O2 or even with nature's largest stable vdW species - C60 that has symmetry comparable to H2 and the rare gases.

Given the goal of creating a H2X vdW compound, where X is an inert species, one must assess which species is most likely to lead to successful compound formation. The noble gases such as Ne, Ar, and Xe, as well as the common cryogenic gases N2, CO2, CO, and CH4 are the obvious candidates. The high-pressure vdW compound experiments cited throughout this proposal strongly imply, both theoretically (loosely) and experimentally that crystallization from a liquid mixture will not lead to equilibrium compound formation at low pressures.

The alternate concept that will be investigated in this work is to form the crystal using vapor phase deposition. In this case (meta)stable crystals could be formed either through epitaxial growth on a substrate, or as a result of configurational relaxation from a more amorphous, but compositionally identical solid mixture. To perform epitaxial growth of a crystal with weak bonds or a locally uniform amorphous mixture using vapor phase deposition, the vapor molecules should be deposited at as low a temperature with as narrow a thermal dispersion as possible. This also minimizes the temperature rise of the solidifying substrate, since the heat release is smaller during condensation. Minimizing heat release is very important for the deposition cryogenic solids, as a result of their poor solid thermal conductivity. The gas (aside from He and H2) with the lowest condensation temperature and lowest heat of solidification (by far) is Ne.

Neon has a number of other advantages for this program. Its molecular volume is small enough relative to H2 that it falls in the proper range of relative species sizes to form a Laves phase crystal [12] of the form H2(Ne)2 similar to the vdW compounds formed at high pressure. Ne can also be considered an isotopic impurity in H2 with very similar Leonard Jones potential parameters; the species size difference occurs mostly as a result of the large zero point energy of H2. H2 is a quantum solid, whereas quantum effects in Ne are much smaller. Ne has the added advantage (for this approach) that it is not soluble with H2 to a significant degree either as a liquid [13]or as a solid [14]. For this reason partial solid mixtures that might obscure the detection of the vdW compound are very unlikely to occur, as opposed to the alternate possibilities. Furthermore, H2/Ne mixtures have been extensively studied and characterized (e.g. [1415]).

The combination of Ne with H2 is thus very strongly suggested for use in this project to create a vdW compound with H2.

Issues in vdW Solids. Cryocrystals: [16] In a macroscopic system of cryocrystal molecules the interaction between molecules is responsible for the transition of the system with decreasing temperature from the gaseous into the liquid and ultimately into the solid state. The properties of the solid are determined by this interaction and by its effect on the internal properties of the molecules. The intermolecular interaction plays a central role in the study of the solid cryogens and can be defined through a variety of descriptions. The instantaneous interaction for fully specified configurations of all the nuclei and electrons in the system, the expectation value over the ground electronic state for a given nuclear configuration, the expectation value of this quantity over the vibrational or rotational states of the molecules and, in the solid, the average value of the interaction over the lattice vibrations all contribute to the interaction. In addition to these forms of the pairwise additive interaction, nonadditive interactions arise in systems of three or more molecules that play an important role in connection with certain properties of the solid. The calculation of the various effective interactions involves not only the structure but also the arrangement and the various states of motion of the molecules.

Quantum Solids. Quantum solids are those with significant zero-point energy where anharmonic effects in the lattice dynamics have increased beyond the treatment of perturbation theory. The degree of quantum effects is quantified by the de Boer quantum parameter [17] λ * = [h/2π σ (Mε )1/2], where h is Planck's constant, M is mass, and σ and ε are length and energy parameters such that the potential V(σ) = 0 and V(Rm) = -ε ; Rm is the location of the minimum in the potential. Aside from a host of effects on solid behavior, molecular volume scales with λ * such that although H2 and Ne have similar σ and ε parameters, an H2 molecule is significantly larger than a Ne atom. Modeling of the quantum H and He crystals (+ isotopes) is fundamentally different from other materials, although the simplicity of the systems allow theoretical treatments that would otherwise be impractical.

Solid H2. Basic Facts: H2 is one of the most extensively studied forms of matter (e.g. [17], [18]) because many of its important properties can be predicted theoretically from first principles, and because these results can be compared in detail with experimental data. The theory of H2 has often functioned as a testbed of general theories of atomic and molecular behavior. Despite this work, the common mechanical properties of solid H2 are beyond calculation, in part due to the non-ideality of the macroscopic crystal.

H2 Properties Briefly: 1) para-H2: nucleon spins antialigned, J=0; ortho-H2: J=1; stable para/ortho ratio of H2 = f(T); @ 300 K H2 is 75% o-H2; at 20.4K H2 is 0.21% o-H2; conversion rate constant = 0.0114 hr-1 with a large heat of conversion. Most of the physical properties of H2 are mildly dependent on the relative spin state mixture; specific heat and thermal conductivity change significantly in some temperature ranges [19]. H2 has a triple point temperature of 14 K and a triple point pressure of 0.070 atm (54 torr). Solid H2 generally has a hcp lattice, except fcc at very low T's [18]. H2 is highly compressible - by 50% at 10 kbar. Density = 0.088, 0.20 and 0.31 g/cm3 for H2, D2 and T2, respectively. The engineering properties of solid cryogenic H2 has been compiled by Dr. Bates [10] in contrast to standard thermodynamic properties [20].

Solid H2 Surfaces. Experiments involved with deposition on solid H2 surfaces consider that at temperatures above 3 K, there is a liquid H2 layer on surface of the solid. This means that true gas-to-solid deposition on H2 can only take place at temperatures below 3 K. The experimental evidence for this is:

Accretion on Solid H2. The adsorption of weakly bound films is an established topic with many applications, where details of the underlying processes are recent discoveries. He and H2 are important as particularly clean and relatively simple quantum systems. Among the most striking surface phenomena of these materials is that 4He does not wet Cs substrates at very low temperatures, although a prewetting transition does occur in this same system. For molecular H2 triple-point wetting has been observed; the surface is completely wetted above the triple point temperature T3; incomplete wetting occurs at lower temperatures [21], [22]. Experimental [23] and theoretical [24] work has shown that H2 exhibits prewetting transitions on alkali metals. Particular interest in H2 films occurs because the topmost layers appear to remain liquid down to temperatures far below T3 [22] and perhaps down to zero Kelvin due to zero-point motion. Investigations of physisorbed films of molecular H2 on different substrates [21] concentrate on H2 but include the heavier H2 isotypes, both in equilibrium and nonequilibrium, metastable states.

Albrecht et. al. [25] reported detailed results of wetting phenomena on solid H2. Most of this data on H2 films was obtained using the surface plasmon (SP) resonance technique (ATR; attenuated total reflection method), that provides very accurate information about both the thickness and the roughness of the physisorbed material. Using condensation from a gas it was found that the deposited film is smooth up to a thickness around 12 A. Beyond that value, the SP resonance width starts to broaden considerably. This dependence was interpreted as the build-up of a smooth, homogeneous film up to a limiting thickness d1 of 3 to 4 monolayers, beyond which the condensing molecules aggregate to form bulk crystallites. Such a behavior is known during film deposition as Stranski-Krastanov growth.

These experiments show that at a low temperature homogeneous H2 films in equilibrium can be grown on substrates such as Ag or Au only to a thickness of a few monolayers. If a thicker film, prepared at higher T, is slowly cooled, its thickness will decrease, and excess material either desorbs or coagulates on the film to form bulk crystallites, depending on the experimental conditions. This is a general film phenomenon because the coagulation process can take place at extremely low temperatures. Apparently above a transition temperature around 3 K the diffusion processes are fast enough for a surface film to relax towards its quasi-equilibrium dewetted state within a few minutes. Their analysis yielded an Arrhenius-like behavior, τ ∝ exp(-Δ E/kBT). The energy Δ E can be associated with the activation energy for surface diffusion. The activation energy for bulk diffusion is so high that this mechanism is negligible in the temperature range considered here. They obtained Δ E ≅ 23 K [25] for the case of H2, in close agreement with the value determined by Weiss using surface acoustic waves.[26]

This study of the wetting and surface transport properties of H2 films shows that the surface-molten layer that is induced by zero-point-motion does not exist at very low temperatures in these films. Higher temperature accretion studies of H2 crystal growth and H2 mixtures will thus normally produce pure crystallites of the depositing species at temperatures over about 3 K. Since the wetting behavior is determined by a delicate competition between adsorbate-adsorbate and adsorbate-substrate forces, it is probable that some substrates will exhibit complete wetting even below the triple point temperature, including perhaps more complex, multilayer systems.

Impurities in Solid H2. Impurities in solid H2 have larger effects on the properties of this solid than in most materials. Almost any impurity will be much larger that the H2 molecules, and will have a much larger mass, greatly changing the dynamics of the light H2 lattice. There have been indications that impurities stabilize the quantum solids. Gordon [27] has shown stabilization of solid He and there are indications that H2 is stabilized as well [28]. Solid H2 also exhibits important effects of spin impurities. The J=1 ortho-H2 state has very different diffusion behavior in solid para-H2 because the electric quadrupole interactions are not present in the symmetric para-H2 molecule.

Naturally occurring isotopic impurities can also be important in H2 and other cryocrystals. The isotopic compound HD occurs in a ratio of 3200:1 of H2 molecules in nature, but can be much greater, depending on the source of the H2 (electrolysis). Ne is approximately 91% Ne20, 8.8% Ne22, and 0.26% Ne21; other species have coexisting isotopes that vary in concentration from small to significant fractions.

Solid Diffusion. The diffusion rate of species within a cryogenic matrix or compound is not well known in general. Assuming the basic classical diffusion law D = D0exp(-ED/kBT), for self-diffusion, D0 values are estimated to be 3 x 10-3 for H2 and 4 x 10-4 for D, with activation energies ED/kB of about 200 K [16] at zero pressure. This would imply D(4 K) = 6 x 10-25 cm2/s. At low temperatures quantum diffusion (tunneling) leads to much high actual diffusion rates; D(H2) = 2 x 10-6e-112/T, so that D(H2,4 K) = 1.4 x 10-18 cm2/s. The absolute numbers are very small; quantum diffusion is difficult to measure experimentally. As an example of this diffusion rate, for planar diffusion from 100% concentration into a semi-infinite body at 4 K, the concentration would reach 50% 1 nm away in 2 hours.

The case of more interest is that of a larger species than H2 moving toward another of its kind as a result of attractive forces between these two atoms. In this case the heavier and larger molecules must essentially plow through a mass of H2 molecules, and the diffusion rate would be expected to be much slower than the movement of light and small H2 molecules. Diffusion in practical materials is strongly dependent on lattice imperfections - vacancies and a variety of structural imperfections.

Vacancies in solid H2 are equilibrium lattice defects and their concentration is unambiguously determined by temperature and pressure. According to various estimates, at the triple point (T = 13.81 K) of H2 the concentration of vacancies is from 0.1 - 0.01 %, decreasing rapidly with decreasing temperature. Dislocations and packing defects are the main defects in single crystals and polycrystalline samples (with respectively large grains) of pure H2. The maximum density of dislocations in para-H2 is on the order of 1010 cm-2, whereas in normal H2 it can be an order of magnitude higher. In well-annealed single crystals the density of dislocations can be decreased to values perhaps as low as 102 - 103 cm-2 [29]. One would thus expect diffusion in solid H2 to be strongly dependent on the history and preparation of the sample.

Quantitative research on the recrystallization rate of H2 is lacking. Experiments at the Institute for Low Temperature (ILT, Kharkov, Ukraine) have shown that the recrystallization rate of H2 must be relatively large, because fine-grained H2 samples could not be created [29]. A sample of solid H2 grown with 1 cm dimensions over one hour gave grain dimensions within the crystal of about 1 mm. Under slower growth rates (hours) 1 cm3 samples became single crystals.

Relaxational Diffusion. Diffusion proper is quite different from short-range relaxation, which is also called reclusterization or configurational relaxation. Configurational relaxation takes place in a macroscopically homogeneous mixture without external fields, and involves the evolution of the two-particle correlation function, whereas diffusion deals with the single-particle correlation function. If in the case of classical migration, where the energy needed for motional displacement is comparable with or exceeds the Debye energy, the configurational-relaxation constant is proportional to the diffusivity; in the quantum case where tunneling motion is important the situation is quite different. The probability of tunneling to a neighboring site is the smallest among the characteristic energies involved; the processes of the migration of isolated impurities and reclusterization differ essentially and obey different laws.

Interaction Potentials. There has been a great deal of work done to define and confirm binary potentials. The H2 potential (e.g. [18]) has been detailed extensively. Compilations exist for a variety of element pairs in their ground state (e.g. [30] for alkali-inert pairs). Predictions of the spectroscopic effects of these potentials have been confirmed in detail in many cases. The difficult problem in solid state vdW compounds is to define and model the many-body and long range effects. Somewhat different potentials are used to explain different effects in the solid modeling. Impurities in solid H2 are thought to have important effects on the nearest neighbor sphere of surrounding H2's. The displacement of nearest neighbor shells would be expected to have major effects on solids with high impurity concentrations, but these effects would be very different in a regular crystal compound.

van der Waals Crystal Compounds. A significant number of binary vdW compounds have been found to exist experimentally at high pressure. The list includes Ne(He)2 [8], A(H2)2 [7], [31], CH4(H2)x [32], N2-CH4 system, and He(N2)11 [33]. That these are true compounds has been confirmed in a number of ways. Diffraction patterns show a regular structure characteristic of neither pure specie, the solid compound melts congruently to give a liquid of fixed stoichiometry independent of a starting liquid composition, and a variety of optical diagnostics support structural assignments of the spectral lines predictably modified from those of the pure substances. If a mixture were formed, since the constituent species differ in size, the average unit cell volume increases linearly with component concentration. Single crystals of the compounds often are seen to grow with distinctive geometric shapes. The crystal structure can also be plausibly predicted based on free energy calculations and by hard shell packing models [12].

Binary phase diagrams that have not (yet) been shown to form vdW compounds have been investigated for a long time. H2He [34], A-N2 [35], A-O2 [36], A-CO [37]are examples. These mixtures do exhibit a variety of unusual phases and phase transitions, partially as a result of the close free energy difference between the hcp and fcc phases.

Hard Shell Species Crystal Compounds. The intermolecular interactions of vdW compounds are by definition small compared with those of common materials. The relative magnitudes that are involved are illustrated by comparing the approximate binding energy of an H2-H2 cryogenic dimer - 2.9 cm-1 [38] with the binding energy of H2 itself - 104 kcal/mole, or 36,400 cm-1. Because during solidification interactions vdW molecules remain unchanged except for small perturbations, these interactions can be treated for some purposes as interactions between hard spheres whose size is determined by some consistent measure of the size of the molecule/atom. In assigning a size, quantum species have a size larger than that implied by their potential energy as a result of the effect of the zero-energy vibrations of the molecules.

The fact that high-pressure vdW compounds are often of the AB2 stoichiometry with a Laves phase crystal structure is often explained as a natural consequence of the packing stability of a binary mixture with a certain relative species size (close to 1.2), using as a reference metal lattice formation [12]. Although there is no doubt of the existence of this structure and its stability, this approach is clearly inadequate in many situations, especially when the long range forces are important. Counterexamples of the simple packing rules include He(N2)11 [33]. The general implications of hard sphere packing are still relevant, however, with important implications for vdW crystal structure and stability.

General hard shell packing [39],[12],[40] has been shown to generate both simple and highly complex structures, some (AB13) formed purely as a result of entropy-driven formation [39], rather than by free energy minimization. The most commonly found AB2 structure is made up of alternating hexagonal layers of the small and large particles. The large particles (A) form close packed layers aligning directly above each other along the c axis while the small particles (B) occupy trigonal prismatic sites between these layers and form planar hexagonal rings. This structure would be appropriate for epitaxial growth. It should be noted that this structure is not the structure of high pressure vdW compounds found experimentally. X-ray results [7] show these to be a closely related Laves phase structure. General packing investigations [39],[40] imply that the diameter ratios (dA/dB) need to be in the range 0.5 - 0.8, with possible islands of stability at higher dA/dB. Larger dA/dB leads to a random alloy with fcc structure.

Spectroscopy. Spectra of cryogenic solids have been used to elucidate many properties of the solid. Para-H2 is unusual in that the spectral lines and impurity lines in the solid are much sharper than they are in the gas phase. Detailed intermolecular interactions and exciton exchanges can be read studied with clarity (e.g. [41]). Aside from deducing details about intermolecular potentials [42], trapping sites [43], and electromagnetic environment, the spectra can be used to study long range crystalline interactions. The amount work and literature on this subject is tremendous; detailed spectra for work on pure and impurity-laden solid H2 are readily available for this project.


This work seeks to explore and define the properties of a H2/Ne crystal, its formation, and the conditions under which it is stable. From this point on the term solid H2 is assumed to refer to pure para-H2. Experimentally, standard catalysts convert para-H2 from normal H2.

The issues investigated in this task will be: 1) The crystal structure of H2Ne, 2) The stability of the H2/Ne crystal, 3) The material properties of the H2/Ne crystal, 4) H2/Ne modeling, and 5) The possibility and rules of forming a crystal of H2X where X is a reactive species with appropriate characteristics.

Crystal Structure and Stability. A H2/Ne compound was hypothesized by Dr. Bates before he was aware of the extent and the implications of recently discovered high pressure vdW compounds, which can be used to imply the stability of a related H2(Ne)2 compound. Such Laves phase compounds form when the size ratios of the component species are near 1.20 [31],[12]. The hcp lattice spacing of H2 is ao = 3.76 A, which is also the effective molecular diameter in a hcp lattice, whereas the spacing of Ne at 16 K is ao = 4.88 A [44]. Like related rare gas solids, Ne is a solid with the fcc structure, so that its effective atomic diameter is 4.88/√ 2 = 3.17, and the H2/Ne effective diameter ratio is about 1.19. The σ parameters for H2 and Ne potentials are 2.96 and 2.79 [16] respectively to give a ratio of 1.06; the reduced molar volume [17] of H2 relative to Ne resulting from quantum effects implies a further size factor of 1.09 to give a ratio of 1.16, which is consistent with the relative lattice parameters. Since the proposed H2Ne2 structure arises from alternating layers of larger (H2) and smaller (Ne) species, there should be a number of ways to create this (meta)stable lattice using gas phase deposition. The compound cannot be formed from the liquids because they are not miscible at low pressure, or by deposition onto the H2 solid above 3 K as a result of the liquid layer on its surface. At this point H2/Ne will be designated by its probable stoichiometry: H2Ne2

It is important to ask the questions: Why have H2Ne2 crystals not been detected previously? Why have no related low pressure vdW compounds have been found in experimental research? The research behind this proposal implies that the general reason that H2Ne has not been created previously is that there is no simple or natural dynamic route to its formation.

Why there has been no previous work toward H2Ne2: 1) Ne is not soluble in H2 to any significant extent; the energy created by distortion of the H2 lattice as a result of the addition of Ne is too great to permit the external addition of Ne, which must add as a substitutional impurity. This has made the solid solution route to forming H2Ne impossible. 2) Recent experimental studies discussed above show that the surface of a H2 crystal at temperatures above about 3 K is liquid; newly deposited mixed species will not wet the surface, instead forming pure crystallites on the surface during the deposition process. Previous experimental work has been done in general at temperatures higher than 3 K as a result of the difficulty of achieving very low temperatures; these temperatures would prevent the formation of H2Ne2 via condensation from the gas. 3) Almost no work has been done in the field of epitaxial growth of cryogenic crystal mixtures; little work has been done in the entire field of vdW epitaxy until recently. 4) There is a narrow concentration range for stable formation of the H2Ne2 crystal. 5) The small concentrations of a H2Ne2 crystal that may have been created are very difficult to detect. No route has been developed to cause preferential deposition at appropriate sites to allow ordering of the H2 and Ne.

Indications that Low Pressure vdW Compounds have been Found. There has been work that implies the formation of Ne(H2)n complexes in solid solutions at low pressure [14]. The inference is based on molar volume arguments as a result of the specific excess volume resulting from the addition of Ne.

A number of possibly relevant features were noted in early work by Barrett on A-X phase diagrams. A δ phase was found for high concentrations of A in O2 at low temperature that was distinct from the low temperature O2 α phase, the cubic pure A phase, and the intermediate-concentration A/O2 hcp phase. Furthermore, at higher concentrations whether the δ phase formed depended on whether it was formed from the α or the β higher temperature phase. In spite of broad similarities between N2 and CO (size, boiling temperature, melting temperature, isoelectronic, etc.) the phase diagrams of A-N2 [35] and A-CO [37] are completely different. The authors conclude that the stability of the various crystal structures formed by these comparatively simple species depend on an extremely subtle balance of forces that extend over quite a long range compared with the nearest-neighbor distance so that structure formation must be considered as a complex many body problem.

H2/Ne Mixtures. The solubility of H2/Ne mixtures has been extensively investigated at the ILT [45], [46]. H2 crystals are stable enough that Ne is not soluble in H2 to any significant extent. Forming a crystal from a gas or liquid mixture results in physical mixtures of pure H2 and pure Ne crystallites [45]. H2 is soluble in Ne, however; H2 can be dissolved in Ne with H2 concentrations up to 40% [45] at liquid He temperatures, so a more complex picture of H2Ne crystal formation must be at work. Research at the ILT has shown the following characteristics of H2/Ne mixtures: a) The molar volume of solid H2 increases after injection of a comparatively low quantity of Ne; b) Impurity effects on the molar volume of H2 decrease and even disappear with added Ne at temperatures above 13 K; c) The upper limit of the heat capacity of H2 degrades with added Ne at temperatures of about 6 K; at higher temperatures this impurity effect on heat capacity disappears. These phenomena appear in quantum crystals only.

Solubility. A comment on liquid H2/Ne liquid solutions is relevant. H2 and Ne are completely miscible at temperatures above about 29 K. At lower temperatures there is a liquid-liquid immiscibility region, but there is still some region of miscibility. At higher pressures measured excess mixing volumes have been attributed to quantum effects associated with H2. Prof. Johnson has shown that the excess volume of mixing H2 and Ne at higher pressures is explained by accurate potential interactions rather than quantum effects; results are very sensitive to the cross-interaction potential. It is recognized that subtle differences in the potential used and its interactions may be important for modeling work.

Material Properties. The basic description of the postulated H2Ne2 crystal is that of a fcc or hcp crystal with alternating layers of light and heavy species. The complexity of the crystal description in terms of its detailed properties arises from the quantum mechanical behavior of the H2 molecules. Ne is a closed shell atom, with negligible dipole or higher order moments. H2 molecules, even with their inherent nuclear asymmetry, have a nearly spherical potential surface. H2 also has significant electronegativity. The material is expected to be highly sensitive to impurities; the effect of Ne isotopes is unclear. Macroscopic properties of the crystal such as specific heat and thermal conductivity can be measured, and microscopic properties such as optical properties can be measured using only a thin layer of the crystal or micro crystals spread throughout a solid. As a result of the delocalized nature of the electron structure of H2, a H2Ne2 crystal will have some very unusual properties electronic and optical properties.

Solid Modeling. Computational modeling can be used both to predict some of the properties of the solid and the process of configurational relaxation.

Interaction Potentials. The semi-empirical Silvera-Goldman potential [47] has been shown to be accurate for describing the properties of solid and fluid H2 [48], [49] the adsorption of H2 on graphite [50] and for describing the properties of fluid H2Ne mixtures [15]. The Silvera-Goldman potential is an isotropic pairwise additive potential that includes an effective three-body term. We have developed an accurate two-body H2-H2 potential from high-level ab initio calculations [51] and an explicit three-body potential is now under development [52]. For the purposes of this research the semi-empirical Silvera-Goldman potential should be sufficient. However, if we find that higher accuracy is needed for this work we can switch to the first-principles explicit three-body potential. We have tested several neon-neon interaction potentials [15], [49] and found that the Lennard-Jones (LJ) potential with parameters from Morales and Nuevo [53] performed the best for pure fluid Ne properties, including vapor-liquid equilibrium. The LJ potential was more accurate than the semi-empirical Aziz Hartree-Fock dispersion potential [54]. There is no guarantee that the LJ potential will be more accurate than the Aziz or some other potential for computing solid-fluid equilibrium. For this reason we will re-evaluate all the potentials in the literature for accuracy in computing solid properties and solid-liquid freezing points.

The H2-Ne cross interaction potential is expected to be very important in determining the behavior of the solid mixture. Previous work in Johnson's group has shown that the widely-used Lorentz-Berthelot combining rules are completely inadequate for describing the excess thermodynamic properties of the H2/Ne fluid mixture [15]. This was rather surprising, given that neon and hydrogen have very similar potential parameters. The H2-Ne potential developed by Faubel and coworkers [55] was found to give excess volumes in good agreement with experimental values [15]. The Faubel et al. Potential [55] for cross interactions will be evaluated for accuracy in describing the interactions in the solid phase. Calculations of solid mixture properties from model potentials can be compared with first-principles calculations as a check on the accuracy of the model potentials. Unfortunately, the first-principles methods available for computing properties of crystalline solids are typically not accurate enough for van der Waals solids. Density functional theory is known to fail for many van der Waals complexes. The work of Diep and Johnson showed that a very high level of electron correlation (CCSD(T)) and very large basis sets were required to accurately compute the H2-dimer potential [51].

Computational Solid Properties. Computational modeling can be used both to predict some of the properties of the solid and the process of configurational relaxation. Challa and Johnson [15] have demonstrated the importance of the accuracy of the interaction potentials in computing the properties of fluid H2+Ne mixtures. We expect the properties of the solid to also be sensitive to the potentials employed. Our first task will be to verify the accuracy of the H2 and Ne potentials for the respective pure solids. Recent work on computing the freezing transitions will be used as a guide in this work. Solid-fluid equilibrium has been computed from simulations for complex structured molecules such as alkanes [56], [57], [58], [59] as well as for simple molecules [60], [61]. An order parameter method has been developed to calculate freezing transitions in porous media [62], [63].

Owing to the lack of precise data for solid H2/Ne mixtures we plan to evaluate the accuracy of the H2-Ne interaction potential by performing high-level quantum chemical calculations. All-electron calculations will be carried out with a series of basis sets (aug-cc-pVnZ, n=3,4) using coupled clusters with singles, doubles, and perturbational triple excitations, CCSD(T). The MP2, MP3, MP4 energies will also be extracted and the convergence of the potential with respect to the level of theory and basis set will be evaluated. This follows our approach with the hydrogen dimer [51]. Three-body interactions will be explicitly accounted for by performing calculations with 2H2+Ne and H2+2Ne clusters.

Once the potentials have been verified or corrected we will proceed to compute the freezing temperature of the H2/Ne crystal using techniques like those used previously for complex and simple fluids. We will compute the structure and the equilibrium properties (bulk modulus, etc.) from simulations. These calculations will employ Feynman's path integral formalism [64]. Free energy calculations will be used to distinguish the equilibrium structure of the material.

Generic H2X Crystals. The proposed work seeks to use the formation of H2Ne2 as a guide to forming a (H2)n(X)m crystal, where X is a reactive species. Unlike Ne, X would be larger, not smaller than H2, and it would have long-range interaction effects from its outer electron shells that would dominate effects seen in H2Ne2. The basic argument for the relevance of the H2Ne work is that 1) the modeling and the basic experimental size-stability-packing effects are general for vdW compounds; they can be modified by the appropriate long range forces to apply to H2X, 2) the experimental crystal formation and diagnostic techniques developed in this program will be relevant to any vdW deposition.

X must behave as a vdW species, which means that it must have self-reaction and H2 reaction activation energies that are greater than the thermal and quantum mechanical activation energies it encounters. Some atomic species are thus excluded. For example C reacts with H without a barrier, whereas B forms a vdW complex with H2 because significant energy is required to form H-B-H, the stable product of B and H2 [65]. Finding which species have Eact > 0 is difficult because the relevant reaction energy surfaces are often 3-D, reaction intermediates are not well known, and reactions in general have not been studied at low temperatures. Energy barriers can also be created artificially by applying external fields that restrict orientational interactions. It seems likely that a suitable X can be found (perhaps with an O2 matrix), but significant research through other programs will be necessary.

A generic experimental problem that must be overcome is the deposition of species at low temperature. In the past implanted species had high energy (furnace vapors, laser ablation, nozzle expansion). Work has been done using He/H2 cluster deposition (e.g. [66]), but it is difficult to achieve high concentrations with this technique as well. Dr. Bates is developing experimental techniques to avoid this problem, either by deposition followed by solid phase concentration, or by cold deposition in gaseous He.


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