Extraordinarily complex crystal structure with mesoscopic patterning in barium at high pressure

Nested order-disorder framework containing a crystalline matrix with self-filled amorphous-like innards

Solids can be generally categorized by their structures into crystalline and amorphous states with different interactions among atoms dictating their properties. Crystalline-amorphous hybrid structures, combining the advantages of both ordered and disordered components, present a promising opportunity to design materials with emergent collective properties. Hybridization of crystalline and amorphous structures at the sublattice level with long-range periodicity has been rarely observed. Here, we report a nested order-disorder framework (NOF) constructed by a crystalline matrix with self-filled amorphous-like innards that is obtained by using pressure to regulate the bonding hierarchy of Cu₁₂Sb₄S₁₃. Combined in situ experimental and computational methods demonstrate the formation of disordered Cu sublattice which is embedded in the retained crystalline Cu framework. Such a NOF structure gives a low thermal conductivity (~0.24 W·m⁻¹·K⁻¹) and a metallic electrical conductivity (8 × 10⁻⁶ Ω·m), realizing the collaborative improvement of two competing physical properties. These findings demonstrate a category of solid-state materials to link the crystalline and amorphous forms in the sublattice-scale, which will exhibit extraordinary properties.

The synthesis and characterization of new crystalline-amorphous hybrid materials is challenging. Here, the authors report the preparation of a nested order-disorder framework by applying high pressure to a nested copper chalcogenide Cu₁₂Sb₄S₁₃.

Pressure tuned incommensurability and guest structure transition in compressed scandium from machine learning atomic simulation

Scandium (Sc) is the lightest non-main-group element and transforms to a host-guest (H-G) incommensurate structure under gigapascal (GPa) pressures. While the host structure is stable over a wide pressure range, the guest structure may exist in multiple forms, featuring different incommensurate ratios, and mixing up to generate long-range "disordered" guest structures. Here, we employed the recently developed global neural network (g-NN) potential and the stochastic surface walking (SSW) global optimization algorithm to explore the global potential energy surface of Sc under various pressures. We probe the global minima structure in a system made of hundreds of atoms and revealed that the solid-phase transition between Sc-I and H-G Sc-II phases is fully reconstructive in nature. Above 62.5 GPa, the pressure will further destabilize the face-centered tetragonal (fct, Sc-IIa) guest structure to a body-centered tetragonal phase (bct, Sc-IIb), while sustaining the host structure. The structural transition mechanism of this work will shed light on the nature of the complex H-G structural modifications in compressed metals.

Probing extreme states of matter using ultra-intense x-ray radiation

Extreme states of matter, that is, matter at extremes of density (pressure) and temperature, can be created in the laboratory either statically or dynamically. In the former, the pressure-temperature state can be maintained for relatively long periods of time, but the sample volume is necessarily extremely small. When the extreme states are generated dynamically, the sample volumes can be larger, but the pressure-temperature conditions are maintained for only short periods of time (ps toμs). In either case, structural information can be obtained from the extreme states by the use of x-ray scattering techniques, but the x-ray beam must be extremely intense in order to obtain sufficient signal from the extremely-small or short-lived sample. In this article I describe the use of x-ray diffraction at synchrotrons and XFELs to investigate how crystal structures evolve as a function of density and temperature. After a brief historical introduction, I describe the developments made at the Synchrotron Radiation Source in the 1990s which enabled the almost routine determination of crystal structure at high pressures, while also revealing that the structural behaviour of materials was much more complex than previously believed. I will then describe how these techniques are used at the current generation of synchrotron and XFEL sources, and then discuss how they might develop further in the future at the next generation of x-ray lightsources.

Liquid structure under extreme conditions: high-pressure x-ray diffraction studies

Under extreme conditions of high pressure and temperature, liquids can undergo substantial structural transformations as their atoms rearrange to minimise energy within a more confined volume. Understanding the structural response of liquids under extreme conditions is important across a variety of disciplines, from fundamental physics and exotic chemistry to materials and planetary science.In situexperiments and atomistic simulations can provide crucial insight into the nature of liquid-liquid phase transitions and the complex phase diagrams and melting relations of high-pressure materials. Structural changes in natural magmas at the high-pressures experienced in deep planetary interiors can have a profound impact on their physical properties, knowledge of which is important to inform geochemical models of magmatic processes. Generating the extreme conditions required to melt samples at high-pressure, whilst simultaneously measuring their liquid structure, is a considerable challenge. The measurement, analysis, and interpretation of structural data is further complicated by the inherent disordered nature of liquids at the atomic-scale. However, recent advances in high-pressure technology mean that liquid diffraction measurements are becoming more routinely feasible at synchrotron facilities around the world. This topical review examines methods for high pressure synchrotron x-ray diffraction of liquids and the wide variety of systems which have been studied by them, from simple liquid metals and their remarkable complex behaviour at high-pressure, to molecular-polymeric liquid-liquid transitions in pnicogen and chalcogen liquids, and density-driven structural transformations in water and silicate melts.

Synthesis of Weaire-Phelan Barium Polyhydride

By combining pressures up to 50 GPa and temperatures of 1200 K, we synthesize the novel barium hydride, Ba₈H₄₆, stable down to 27 GPa. We use Raman spectroscopy, X-ray diffraction, and first-principles calculations to determine that this compound adopts a highly symmetric Pm3¯n structure with an unusual 534:1 hydrogen-to-barium ratio. This singular stoichiometry corresponds to the well-defined type-I clathrate geometry. This clathrate consists of a Weaire-Phelan hydrogen structure with the barium atoms forming a topologically close-packed phase. In particular, the structure is formed by H₂₀ and H₂₄ clathrate cages showing substantially weakened H-H interactions. Density functional theory (DFT) demonstrates that cubic Pm3¯n Ba₈H₄₆ requires dynamical effects to stabilize the H₂₀ and H₂₄ clathrate cages.

crystIT: complexity and configurational entropy of crystal structures via information theory

The information content of a crystal structure as conceived by information theory has recently proved an intriguing approach to calculate the complexity of a crystal structure within a consistent concept. Given the relatively young nature of the field, theory development is still at the core of ongoing research efforts. This work provides an update to the current theory, enabling the complexity analysis of crystal structures with partial occupancies as frequently found in disordered systems. To encourage wider application and further theory development, the updated formulas are incorporated into crystIT (crystal structure and information theory), an open-source Python-based program that allows for calculating various complexity measures of crystal structures based on a standardized *.cif file.

A chemical perspective on high pressure crystal structures and properties

The general availability of third generation synchrotron sources has ushered in a new era of high pressure research. The crystal structure of materials under compression can now be determined by X-ray diffraction using powder samples and, more recently, from multi-nano single crystal diffraction. Concurrently, these experimental advancements are accompanied by a rapid increase in computational capacity and capability, enabling the application of sophisticated quantum calculations to explore a variety of material properties. One of the early surprises is the finding that simple metallic elements do not conform to the general expectation of adopting 3D close-pack structures at high pressure. Instead, many novel open structures have been identified with no known analogues at ambient pressure. The occurrence of these structural types appears to be random with no rules governing their formation. The adoption of an open structure at high pressure suggested the presence of directional bonds. Therefore, a localized atomic hybrid orbital description of the chemical bonding may be appropriate. Here, the theoretical foundation and experimental evidence supporting this approach to the elucidation of the high pressure crystal structures of group I and II elements and polyhydrides are reviewed. It is desirable and advantageous to extend and apply established chemical principles to the study of the chemistry and chemical bonding of materials at high pressure.

Unusually complex phase of dense nitrogen at extreme conditions

Nitrogen exhibits an exceptional polymorphism under extreme conditions, making it unique amongst the elemental diatomics and a valuable testing system for experiment-theory comparison. Despite attracting considerable attention, the structures of many high-pressure nitrogen phases still require unambiguous determination. Here, we report the structure of the elusive high-pressure high-temperature polymorph ι–N₂ at 56 GPa and ambient temperature, determined by single crystal X-ray diffraction, and investigate its properties using ab initio simulations. We find that ι–N₂ is characterised by an extraordinarily large unit cell containing 48 N₂ molecules. Geometry optimisation favours the experimentally determined structure and density functional theory calculations find ι–N₂ to have the lowest enthalpy of the molecular nitrogen polymorphs that exist between 30 and 60 GPa. The results demonstrate that very complex structures, similar to those previously only observed in metallic elements, can become energetically favourable in molecular systems at extreme pressures and temperatures.

Nitrogen has a complex phase diagram with rich polymorphism, which is challenging to characterize due to the extreme conditions and uncertain stability ranges needed to do so. Here the authors resolve one of the most elusive phases of this model system, reporting a crystalline structure with unusual complexity.

Woodpeckers and Diamonds: Some Aspects of Evolutionary Convergence in Astrobiology

Jared Diamond's argument against extraterrestrial intelligence from evolutionary contingency is subjected to critical scrutiny. As with the earlier arguments of George Gaylord Simpson, it contains critical loopholes that lead to its unraveling. From the point of view of the contemporary debates about biological evolution, perhaps the most contentious aspect of such arguments is their atemporal and gradualist usage of the space of all possible biological forms (morphospace). Such usage enables the translation of the adaptive value of a trait into the probability of its evolving. This procedure, it is argued, is dangerously misleading. Contra Diamond, there are reasons to believe that convergence not only plays an important role in the history of life, but also profoundly improves the prospects for search for extraterrestrial intelligence success. Some further considerations about the role of observation selection effects and our scaling of complexity in the great debate about contingency and convergence are given. Taken together, these considerations militate against the pessimism of Diamond's conclusion, and suggest that the search for traces and manifestations of extraterrestrial intelligences is far from forlorn. Key Words: Astrobiology-Evolution-Contingency-Convergence-Complex life-SETI-Major evolutionary transitions-Selection effects-Jared Diamond. Astrobiology 18, 491-502.

Incommensurate atomic density waves in the high-pressure IVb phase of barium

The host-guest structures of elements at high pressure discovered a decade ago still leave many open questions due to the lack of precise models based on full exploitation of the diffraction data. This concerns in particular Ba IV, which is stable in the range 12-45 GPa. With the example of phase Ba IVb, which is characterized here for the first time, a systematic analysis is presented of possible host-guest structure models based on high-quality single-crystal diffraction data obtained with synchrotron radiation at six different pressures between 16.5 and 19.6 GPa. It is shown that a new incommensurately modulated (IM) structure model better fits the experimental data. Unlike the composite models which are commonly reported for the Ba IV phases, the IM model reveals a density wave and its pressure-dependent evolution. The crucial role played by the selected model in the interpretation of structure evolution under pressure is discussed. The findings give a new experimental basis for a better understanding of the nature of host-guest structures.

Observation of a re-entrant phase transition in the molecular complex tris(μ2-3,5-diiso-propyl-1,2,4-triazolato-κ2N1:N2)trigold(I) under high pressure

We report a molecular crystal that exhibits four successive phase transitions under hydro-static pressure, driven by aurophilic interactions, with the ground-state structure re-emerging at high pressure. The effect of pressure on two polytypes of tris(μ2-3,5-diiso-propyl-1,2,4-triazolato-κ2N1:N2)trigold(I) (denoted Form-I and Form-II) has been analysed using luminescence spectroscopy, single-crystal X-ray diffraction and first-principles computation. A unique phase behaviour was observed in Form-I, with a complex sequence of phase transitions between 1 and 3.5 GPa. The ambient C2/c mother cell transforms to a P21/n phase above 1 GPa, followed by a P21/a phase above 2 GPa and a large-volume C2/c supercell at 2.70 GPa, with the previously observed P21/n phase then reappearing at higher pressure. The observation of crystallographically identical low- and high-pressure P21/n phases makes this a rare example of a re-entrant phase transformation. The phase behaviour has been characterized using detailed crystallographic theory and modelling, and rationalized in terms of molecular structural distortions. The dramatic changes in conformation are correlated with shifts of the luminescence maxima, from a band maximum at 14040 cm-1 at 2.40 GPa, decreasing steeply to 13550 cm-1 at 3 GPa. A similar study of Form-II displays more conventional crystallographic behaviour, indicating that the complex behaviour observed in Form-I is likely to be a direct consequence of the differences in crystal packing between the two polytypes.

Strain induced incommensurate structures in vicinity of reconstructive phase transitions

General conditions controlling the formation of incommensurate phases in crystals undergoing reconstructive phase transitions are analyzed in the framework of a model-free phenomenological approach. A universal trend to stabilizing such intermediate phases in the vicinity of reconstructive phase transitions stems from the fact that certain high-order improper Lifshitz invariants reduce at such transformations to ones bi-linearly coupling critical displacement gradients and strains or even to the proper Lifshitz invariant. The approach developed here introduces a universal mechanism for the formation both of premartensite incommensurate phases and complex structures with giant unit cells, as found in some elemental crystals at high pressure.

Pressure-induced normal-incommensurate and incommensurate-commensurate phase transitions in CrOCl

The high-pressure behavior of layered CrOCl is shown to be governed by non-bonded interactions between chlorine atoms in relation to a rigid framework composed of Cr and O atoms. The competition between optimizing intra- and interlayer Cl–Cl distances and the general trend towards denser packing defines a novel mechanism for high-pressure phase transitions of inorganic materials. CrOCl possesses an incommensurate phase for 16–51 GPa. Single-crystal x-ray diffraction in a diamond anvil cell provides an accurate description of the evolution of the incommensurate wave with pressure. It thus demonstrates a continuous increase of the amplitude up to 30 GPa, followed by a decrease of the wavelength until a lock-in transition occurs at 51 GPa.

Twisting phonons in complex crystals with quasi-one-dimensional substructures

A variety of crystals contain quasi-one-dimensional substructures, which yield distinctive electronic, spintronic, optical and thermoelectric properties. There is a lack of understanding of the lattice dynamics that influences the properties of such complex crystals. Here we employ inelastic neutron scatting measurements and density functional theory calculations to show that numerous low-energy optical vibrational modes exist in higher manganese silicides, an example of such crystals. These optical modes, including unusually low-frequency twisting motions of the Si ladders inside the Mn chimneys, provide a large phase space for scattering acoustic phonons. A hybrid phonon and diffuson model is proposed to explain the low and anisotropic thermal conductivity of higher manganese silicides and to evaluate nanostructuring as an approach to further suppress the thermal conductivity and enhance the thermoelectric energy conversion efficiency. This discovery offers new insights into the structure-property relationships of a broad class of materials with quasi-one-dimensional substructures for various applications.

High-pressure X-ray science on the ultimate storage ring

The advent of the ESRF, APS and SPring-8 third-generation synchrotron sources in the mid-1990s heralded a golden age of high-pressure X-ray science. The high-energy monochromatic micro-focused X-ray beams from these storage rings, combined with the new high-pressure diffraction and spectroscopy techniques developed in the late 1980s, meant that researchers were immediately able to make detailed structural studies at pressures comparable with those at the centre of the Earth, studies that were simply not possible only five years previously. And new techniques, such as X-ray inelastic scattering and X-ray nuclear scattering, became possible at high pressure for the first time, providing wholly-new insight into the behaviour of materials at high densities. The arrival of new diffraction-limited storage rings, with their much greater brightness, and ability to achieve focal-spot diameters for high-energy X-ray beams of below 1 µm, offers the possibility of a new generation of high-pressure science, both extending the scope of what is already possible, and also opening ways to wholly-new areas of investigation.

Structural simplicity and complexity of compressed calcium: electronic origin

A simple cubic structure with one atom in the unit cell found in compressed calcium is counterintuitive to the traditional view of a tendency towards densely packed structures with an increase in pressure. To understand this unusual transformation it is necessary to assume electron transfer from the outer core band to the valence band, and an increase of valence electron number for calcium from 2 to ∼ 3.5. This assumption is supported by the Fermi sphere-Brillouin zone interaction model that increases under compression. The recently found structure of Ca-VII with a tetragonal cell containing 32 atoms (tI32) is similar to that in the intermetallic compound In5Bi3 with 3.75 valence electrons per atom. Structural relations are analyzed in terms of electronic structure resemblance. Correlations of structure and physical properties of Ca are discussed.

Single photon energy dispersive x-ray diffraction

With the pressure range accessible to laser driven compression experiments on solid material rising rapidly, new challenges in the diagnosis of samples in harsh laser environments are emerging. When driving to TPa pressures (conditions highly relevant to planetary interiors), traditional x-ray diffraction techniques are plagued by increased sources of background and noise, as well as a potential reduction in signal. In this paper we present a new diffraction diagnostic designed to record x-ray diffraction in low signal-to-noise environments. By utilising single photon counting techniques we demonstrate the ability to record diffraction patterns on nanosecond timescales, and subsequently separate, photon-by-photon, signal from background. In doing this, we mitigate many of the issues surrounding the use of high intensity lasers to drive samples to extremes of pressure, allowing for structural information to be obtained in a regime which is currently largely unexplored.

Superconductivity of BaLi4 under pressure

We studied the pressure-induced superconductivity of BaLi4 up to 53 GPa by means of electrical resistivity in a diamond anvil cell. Superconductivity in BaLi4 is first observed at a pressure of 5.4 GPa with a superconducting critical temperature (Tc) of 4.5 K. Below 2 GPa, superconductivity is not observed above the minimum temperature achievable in the current study, 2 K. Between 5.4 and 12 GPa, the Tc increases steeply to its maximum value of 7 K. Above 12 GPa, the pressure dependence of Tc is complex and the sign of dTc/dP changes several times in going up to the maximum pressure studied, of 53 GPa.

Ca-VII: a chain ordered host-guest structure of calcium above 210 GPa

The recently discovered high pressure phase VII of calcium [M. Sakata et al., Phys. Rev. B 83, 220512(R) (2011)] has the highest superconducting transition temperature (T(c)) of 29 K among all the elements. Understanding the cause for such a high T(c) state is necessary to clarify its crystal structure. The structure of this phase was determined by an x-ray powder diffraction experiment and a density functional theory calculation and was not found to be the usual host-guest type but consisted of a 2×2 supercell in the tetragonal ab plane with a commensurate host-guest ratio of 4/3 along the c axis containing 128 atoms.