Periodic Reporting for period 3 - HECATE (Hydrogen at Extreme Conditions: Applying Theory to Experiment for creation, verification and understanding)
Reporting period: 2019-10-01 to 2021-03-31
This research is directed at what is arguably the most fundamental problem in condensed matter physics: what is the equilibrium state of a system containing protons and electrons?
Specifically, my team has been investigating how materials behave at conditions of extreme pressure - comparable to those found in the interiors of giant planets. Two major techniques are used: atomistic simulations and diamond anvil cell experiments.
In atomistic simulations, we use a computer to solve the laws of Quantum Mechanics to work out the forces on atoms. Then we track the motion of the simulated atoms using a method called "Molecular Dynamics" which can be thought of as three-dimensional billiards with millions of balls. By varying the density and energy of the simulated atoms, we can model extreme pressures and temperatures, or external stimuli such as shock waves. The calculations also tell us how the material will respond to experimental probes such as scattering laser light or X-rays. This enables us to compare the simulations with experiment and verify whether the simulation is producing an accurate model of reality. Simulations can also determine difficult-to-measure properties, for example whether the material is metallic, superconducting, viscous, or transparent. Once one has confidence in the method, we can do calculations at pressures and temperatures not reached by experiment, to determine whether such experiments are likely to find anything interesting.
In diamond anvil cell experiments we create materials at high pressure by squeezing them between two diamonds. Diamond anvil cells exploit the relationship that pressure is force divided by area: a modest force applied by an Allen key to a very small (micron-sized) area can generate immense pressure. Such experiments require high precision manufacture of the gasket which holds the sample: any imperfection or misalignment can cause the diamonds to shatter, allowing the high-pressure sample to escape. Loading the sample into the cell requires great experience and patience, especially for gaseous samples such as hydrogen. Once loaded, the transparent diamonds allow us to shine highly-focussed lasers or X-rays onto the sample, to measure its properties.
Understanding how materials behave is crucial to the design of any product. High pressure metallic hydrogen is believed to be a room-temperature superconductor. Although this has yet to be demonstrated experimentally, it gave a clue that other materials with high hydrogen content would also superconduct. In 2014, the record for the highest-temperature superconductor passed from layered CuO materials to high pressure hydrogen compounds, specifically hydrogen sulphide superconducts above 200K. Since then we, and other groups, have predicted and synthesized materials with ever-high critical superconducting temperatures: hydrides with lanthanum and yttrium currently hold the record. For practical usage, the issue is that these materials exist only at extremely high pressures, around 200GPa. The ongoing challenge is to find materials with superconductivity at higher temperatures and lower pressures.
Hydrogen storage is another possible application: if we can find a lightweight compound at modest pressures rich in molecular hydrogen which decomposes to release the hydrogen on depressurisation it could replace bulky hydrogen tank systems in vehicles.
Our overall object is to ally theory and experiment in this area. In particular, there is a layer of "theory" which is used to interpret experiments based on some very strong approximations. In many cases, it is now possible to circumvent these assumptions and use the theory to directly calculated the experimental output. In the traditional approach, two independent methods, experiment and theory, are used to make models of where the electrons and atoms are, and how they move. Those two models are then compared and if they agree, both methods are validated. If the models are different, there is typically some argument about which is correct. In our newer approach theory is used in conjunction with a model to simulate the experimental results directly. Again, if the process works, the conclusions can be taken as robust. But if the experiment cannot be understood, then a single chain of reasoning can be examined to see where our understanding fails.
The first question posed in the project proposal was "Where should hydrogen be in the periodic table?" The hydrogen atom forms a single chemical bond, and so chemists routinely place it in Group VII. Molecular
hydrogen, a near-spherical object with two s-electrons, might be regarded as being Helium. The longstanding assumption among physicists has been that at high pressures atomic hydrogen would become
like the free-electron Group I elements. The most stable form of cold, metallic hydrogen is expected to adopt an unusual crystal structure previously only observed in caesium where each atom has only four neighbours. To address these issues we studied those elements too.
Our work with Group I elements brought two remarkable discoveries. For the past 70 years, the lowest-energy crystal structure of lithium was believed to be a relatively complex one called the 9R structure. We showed that this is incorrect. The actual lowest-energy structure for lithium is the commonplace face-centred cubic form. Previous workers had made their samples by cooling, which trapped the materials in a defective structure at temperatures too cold to rearrange. The crystallographic signal of this could, and was, misassigned as 9R. In collaboration with the Deemyad group in Utah, we reproduced this, then made other samples by first compressing at room temperature, then cooling, then decompressing. By this route, we made the stable face-centred cubic Lithium.
In potassium, we predict a new phase of matter, in which approximately 70% of the atoms are solid and 30% liquid at the same time, all intermingled and able to interconvert. Such a material would be rigid. But if a block were placed above a small hole, the liquid component could flow away. Some solid would convert to liquid to maintain the stable 70/30 ratio, and the flow would continue. Below the hole, the solid would reform, the overall effect meaning that the solid would pass through the hole. Such a material has only been produced in tiny quantities within diamond anvil cells, so these properties have yet to be observed. It is likely that other group-1 materials such as rubidium and sodium would have similar phases.
In addition, there are numerous more specific objectives : to predict and create materials from elements or simple molecules under pressure. This is a discovery process, and so the precise nature of the materials is not known a priori.
Specifically, my team has been investigating how materials behave at conditions of extreme pressure - comparable to those found in the interiors of giant planets. Two major techniques are used: atomistic simulations and diamond anvil cell experiments.
In atomistic simulations, we use a computer to solve the laws of Quantum Mechanics to work out the forces on atoms. Then we track the motion of the simulated atoms using a method called "Molecular Dynamics" which can be thought of as three-dimensional billiards with millions of balls. By varying the density and energy of the simulated atoms, we can model extreme pressures and temperatures, or external stimuli such as shock waves. The calculations also tell us how the material will respond to experimental probes such as scattering laser light or X-rays. This enables us to compare the simulations with experiment and verify whether the simulation is producing an accurate model of reality. Simulations can also determine difficult-to-measure properties, for example whether the material is metallic, superconducting, viscous, or transparent. Once one has confidence in the method, we can do calculations at pressures and temperatures not reached by experiment, to determine whether such experiments are likely to find anything interesting.
In diamond anvil cell experiments we create materials at high pressure by squeezing them between two diamonds. Diamond anvil cells exploit the relationship that pressure is force divided by area: a modest force applied by an Allen key to a very small (micron-sized) area can generate immense pressure. Such experiments require high precision manufacture of the gasket which holds the sample: any imperfection or misalignment can cause the diamonds to shatter, allowing the high-pressure sample to escape. Loading the sample into the cell requires great experience and patience, especially for gaseous samples such as hydrogen. Once loaded, the transparent diamonds allow us to shine highly-focussed lasers or X-rays onto the sample, to measure its properties.
Understanding how materials behave is crucial to the design of any product. High pressure metallic hydrogen is believed to be a room-temperature superconductor. Although this has yet to be demonstrated experimentally, it gave a clue that other materials with high hydrogen content would also superconduct. In 2014, the record for the highest-temperature superconductor passed from layered CuO materials to high pressure hydrogen compounds, specifically hydrogen sulphide superconducts above 200K. Since then we, and other groups, have predicted and synthesized materials with ever-high critical superconducting temperatures: hydrides with lanthanum and yttrium currently hold the record. For practical usage, the issue is that these materials exist only at extremely high pressures, around 200GPa. The ongoing challenge is to find materials with superconductivity at higher temperatures and lower pressures.
Hydrogen storage is another possible application: if we can find a lightweight compound at modest pressures rich in molecular hydrogen which decomposes to release the hydrogen on depressurisation it could replace bulky hydrogen tank systems in vehicles.
Our overall object is to ally theory and experiment in this area. In particular, there is a layer of "theory" which is used to interpret experiments based on some very strong approximations. In many cases, it is now possible to circumvent these assumptions and use the theory to directly calculated the experimental output. In the traditional approach, two independent methods, experiment and theory, are used to make models of where the electrons and atoms are, and how they move. Those two models are then compared and if they agree, both methods are validated. If the models are different, there is typically some argument about which is correct. In our newer approach theory is used in conjunction with a model to simulate the experimental results directly. Again, if the process works, the conclusions can be taken as robust. But if the experiment cannot be understood, then a single chain of reasoning can be examined to see where our understanding fails.
The first question posed in the project proposal was "Where should hydrogen be in the periodic table?" The hydrogen atom forms a single chemical bond, and so chemists routinely place it in Group VII. Molecular
hydrogen, a near-spherical object with two s-electrons, might be regarded as being Helium. The longstanding assumption among physicists has been that at high pressures atomic hydrogen would become
like the free-electron Group I elements. The most stable form of cold, metallic hydrogen is expected to adopt an unusual crystal structure previously only observed in caesium where each atom has only four neighbours. To address these issues we studied those elements too.
Our work with Group I elements brought two remarkable discoveries. For the past 70 years, the lowest-energy crystal structure of lithium was believed to be a relatively complex one called the 9R structure. We showed that this is incorrect. The actual lowest-energy structure for lithium is the commonplace face-centred cubic form. Previous workers had made their samples by cooling, which trapped the materials in a defective structure at temperatures too cold to rearrange. The crystallographic signal of this could, and was, misassigned as 9R. In collaboration with the Deemyad group in Utah, we reproduced this, then made other samples by first compressing at room temperature, then cooling, then decompressing. By this route, we made the stable face-centred cubic Lithium.
In potassium, we predict a new phase of matter, in which approximately 70% of the atoms are solid and 30% liquid at the same time, all intermingled and able to interconvert. Such a material would be rigid. But if a block were placed above a small hole, the liquid component could flow away. Some solid would convert to liquid to maintain the stable 70/30 ratio, and the flow would continue. Below the hole, the solid would reform, the overall effect meaning that the solid would pass through the hole. Such a material has only been produced in tiny quantities within diamond anvil cells, so these properties have yet to be observed. It is likely that other group-1 materials such as rubidium and sodium would have similar phases.
In addition, there are numerous more specific objectives : to predict and create materials from elements or simple molecules under pressure. This is a discovery process, and so the precise nature of the materials is not known a priori.
The early stages of the project involved mapping out the pure hydrogen phase diagram, and interpreting the experimental signatures coming from experiments on hydrogen (H), deuterium (D) and mixtures of H-D.
In a key 2017 paper "Infrared Peak Splitting from Phonon Localization in Solid Hydrogen" we reanalysed spectroscopic data from the Harvard group on H-D mixtures. This data had a very unconventional appearance which led rival groups to dispute its veracity.
Using the conventional analysis method of identifying spectroscopic peaks and assigning them to possible vibration the only plausible conclusion from the data was that H-D mixtures exhibit and entirely different set of crystal structures to hydrogen and deuterium - and at the pressures considered, H and D are identical. No theoretical explanation for this could be found. We took an alternative approach. We modelled H-D samples assuming the same crystal structure as known for hydrogen and deuterium, but calculated directly the entire spectroscopic response of the material, rather than proceding peak-by-peak. Our results showed a spectacular agreement with the experiment, both conforming our methods and the veracity of their data. What we found was that the disorder in nuclear mass causes any vibration to be localised to a few molecules in HD, whereas in pure H or pure D an excitation can travel unscattered throughout the material. The many possible local arrangements of H2, D2 and HD molecules leads to a range of possible vibrational frequencies, and in turn to a complex manifold of scattering which cannot be interpreted as a series of discrete peaks.
More technical work included "The role of van der Waals and exchange interactions in high-pressure solid hydrogen" where we showed how different levels of theory give significantly different structure, in particular a molecular-metal (previously, it had been assumed that metallization is the same process as breaking molecules).
A huge number of density-functional-theory simulation papers from other groups also appeared since 2016 reporting structures at various temperatures and pressures. Many of these, unfortunately, contained technical errors and were not carried out correctly. We too came close to making a serious error when poorly sampled statistics suggested a structure with chains of H atoms. Prior to publication, we identified the specific error causing this, and we describe our mistake in a conference paper "Charge density wave in hydrogen at high pressure", wherein we also identify a number of published papers which have the same error but got through peer review undetected.
Also in 2017, in "Simple thermodynamic model for the hydrogen phase diagram" we provided a unifying qualitative explanation for all features of the hydrogen phase diagram, in terms of three objects: free-rotating H2 molecules, fixed orientation H2 molecules and dissociated H atoms. Surprisingly, these objects can be used to build seven solid phases and a liquid more compressible that the solid. The key insight is that two H atoms occupy less volume than a molecule, and therefore dissociation is favoured at high pressure. the various phases then arise from a trade-off between bonding energy, disorder entropy and packing efficiency. Notions of packing led us to look at the famous "Kepler conjecture" as applied to the "Lennard Jones" potential beloved of introductory physics courses: In "Stacking Characteristics of Close Packed Materials" we showed an incredible dependence of the crystal structure on the range of the potential - no fewer than 50 different stability regimes were identified depending on the truncation range of the potential, a practical consideration previously regard as so unimportant that it is not even discussed in many older studies.
In hydrogen-like monovalent metals we wrote four papers on Lithium and Potassium (see above for details)
We carried out a number of experimental studies on other diatomic molecules under pressure, related calculations having been done already by other groups. The overall picture which emerges is that with increasing pressure molecular materials such as oxygen, nitrogen, chlorine, iodine etc. initially solidify in a way that optimises the energy of their quadrupole-quadrupole interactions, then they go through a series of structures wherein the molecules are increasingly efficiently packed, then undergo a polymerization process under pressure. Theory suggests they will ultimately become good metals, but at pressures beyond what we have achieved in the laboratory.
In hydrogen-rich materials we discovered a new "form" of hydrogen, a supermolecule containing 26 atoms. The supermolecule itself into 13 rotating molecules, which in turn form a near-spherical cluster with one central molecule surrounded by 12 others. This supermolecule was created as part of a compound with iodane (IH), one supermolecule per IH. With a ratio of 27:1 ithas the largest number-fraction of hydrogens of any known compound. We have predicted that the supermolecule may exist in Xe, HCl and HBr compounds, and experiments to make it are underway.
An alternative way of generating pressure is to use shockwaves, and a number of facilities around the world are appearing with this capacity. In a shock, the high pressure region behind thy shockfront only lasts for nanoseconds, so the data obtained experimentally is quite sparse. We have worked to make interatomic potentials which can be used to simulate the shock directly using molecular dynamics. It was hoped that shock would create the same thermodynamic conditions as static experiments, but data now shows that the observed crystal structures are unexpected. A first guess was that the stress behind the shock was very anisotropic but, perhaps surprisingly, our simulations showed that this was not the case: the conditions are close to isotropic pressure. Rather, the unexpected phases appear because under rapidly increasing pressure the material transforms to the most easily accessed alternative structure, which is not necessarily the thermodynamically stable one.
In related spin-off work with industrial applications, we applied our methods to semiconductors "Hydrogenation induced carrier mobility polarity reversal in single layer AlN", "Origin of the abnormal diffusion of transition metal in rutile" and aerospace alloys "Influence of transition group elements on the stability of the delta- and eta-phase in nickelbase alloys".
In a key 2017 paper "Infrared Peak Splitting from Phonon Localization in Solid Hydrogen" we reanalysed spectroscopic data from the Harvard group on H-D mixtures. This data had a very unconventional appearance which led rival groups to dispute its veracity.
Using the conventional analysis method of identifying spectroscopic peaks and assigning them to possible vibration the only plausible conclusion from the data was that H-D mixtures exhibit and entirely different set of crystal structures to hydrogen and deuterium - and at the pressures considered, H and D are identical. No theoretical explanation for this could be found. We took an alternative approach. We modelled H-D samples assuming the same crystal structure as known for hydrogen and deuterium, but calculated directly the entire spectroscopic response of the material, rather than proceding peak-by-peak. Our results showed a spectacular agreement with the experiment, both conforming our methods and the veracity of their data. What we found was that the disorder in nuclear mass causes any vibration to be localised to a few molecules in HD, whereas in pure H or pure D an excitation can travel unscattered throughout the material. The many possible local arrangements of H2, D2 and HD molecules leads to a range of possible vibrational frequencies, and in turn to a complex manifold of scattering which cannot be interpreted as a series of discrete peaks.
More technical work included "The role of van der Waals and exchange interactions in high-pressure solid hydrogen" where we showed how different levels of theory give significantly different structure, in particular a molecular-metal (previously, it had been assumed that metallization is the same process as breaking molecules).
A huge number of density-functional-theory simulation papers from other groups also appeared since 2016 reporting structures at various temperatures and pressures. Many of these, unfortunately, contained technical errors and were not carried out correctly. We too came close to making a serious error when poorly sampled statistics suggested a structure with chains of H atoms. Prior to publication, we identified the specific error causing this, and we describe our mistake in a conference paper "Charge density wave in hydrogen at high pressure", wherein we also identify a number of published papers which have the same error but got through peer review undetected.
Also in 2017, in "Simple thermodynamic model for the hydrogen phase diagram" we provided a unifying qualitative explanation for all features of the hydrogen phase diagram, in terms of three objects: free-rotating H2 molecules, fixed orientation H2 molecules and dissociated H atoms. Surprisingly, these objects can be used to build seven solid phases and a liquid more compressible that the solid. The key insight is that two H atoms occupy less volume than a molecule, and therefore dissociation is favoured at high pressure. the various phases then arise from a trade-off between bonding energy, disorder entropy and packing efficiency. Notions of packing led us to look at the famous "Kepler conjecture" as applied to the "Lennard Jones" potential beloved of introductory physics courses: In "Stacking Characteristics of Close Packed Materials" we showed an incredible dependence of the crystal structure on the range of the potential - no fewer than 50 different stability regimes were identified depending on the truncation range of the potential, a practical consideration previously regard as so unimportant that it is not even discussed in many older studies.
In hydrogen-like monovalent metals we wrote four papers on Lithium and Potassium (see above for details)
We carried out a number of experimental studies on other diatomic molecules under pressure, related calculations having been done already by other groups. The overall picture which emerges is that with increasing pressure molecular materials such as oxygen, nitrogen, chlorine, iodine etc. initially solidify in a way that optimises the energy of their quadrupole-quadrupole interactions, then they go through a series of structures wherein the molecules are increasingly efficiently packed, then undergo a polymerization process under pressure. Theory suggests they will ultimately become good metals, but at pressures beyond what we have achieved in the laboratory.
In hydrogen-rich materials we discovered a new "form" of hydrogen, a supermolecule containing 26 atoms. The supermolecule itself into 13 rotating molecules, which in turn form a near-spherical cluster with one central molecule surrounded by 12 others. This supermolecule was created as part of a compound with iodane (IH), one supermolecule per IH. With a ratio of 27:1 ithas the largest number-fraction of hydrogens of any known compound. We have predicted that the supermolecule may exist in Xe, HCl and HBr compounds, and experiments to make it are underway.
An alternative way of generating pressure is to use shockwaves, and a number of facilities around the world are appearing with this capacity. In a shock, the high pressure region behind thy shockfront only lasts for nanoseconds, so the data obtained experimentally is quite sparse. We have worked to make interatomic potentials which can be used to simulate the shock directly using molecular dynamics. It was hoped that shock would create the same thermodynamic conditions as static experiments, but data now shows that the observed crystal structures are unexpected. A first guess was that the stress behind the shock was very anisotropic but, perhaps surprisingly, our simulations showed that this was not the case: the conditions are close to isotropic pressure. Rather, the unexpected phases appear because under rapidly increasing pressure the material transforms to the most easily accessed alternative structure, which is not necessarily the thermodynamically stable one.
In related spin-off work with industrial applications, we applied our methods to semiconductors "Hydrogenation induced carrier mobility polarity reversal in single layer AlN", "Origin of the abnormal diffusion of transition metal in rutile" and aerospace alloys "Influence of transition group elements on the stability of the delta- and eta-phase in nickelbase alloys".
We released two open-source codes enabling new simulational methodologies "beyond the state of the art" when the project began: monteswitch and MIST. We had also invented method for directly calculating the spectroscopic signal from calculations of the overall polarisability, rather than identifying individual vibrations and assigning peak strengths. These proved essential in understanding the spectroscopic signal from non-harmonic materials, such a the lowest pressure solid hydrogen phase (rotating molecules) and hydrogen-deuterium mixtures (localised vibrations).