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.

Novel experimental setup for megahertz X-ray diffraction in a diamond anvil cell at the High Energy Density (HED) instrument of the European X-ray Free-Electron Laser (EuXFEL)

The high-precision X-ray diffraction setup for work with diamond anvil cells (DACs) in interaction chamber 2 (IC2) of the High Energy Density instrument of the European X-ray Free-Electron Laser is described. This includes beamline optics, sample positioning and detector systems located in the multipurpose vacuum chamber. Concepts for pump-probe X-ray diffraction experiments in the DAC are described and their implementation demonstrated during the First User Community Assisted Commissioning experiment. X-ray heating and diffraction of Bi under pressure, obtained using 20 fs X-ray pulses at 17.8 keV and 2.2 MHz repetition, is illustrated through splitting of diffraction peaks, and interpreted employing finite element modeling of the sample chamber in the DAC.

The phase diagram of Ti-6Al-4V at high-pressures and high-temperatures

We report results from a series of diamond-anvil-cell synchrotron x-ray diffraction and large-volume-press experiments, and calculations, to investigate the phase diagram of commercial polycrystalline high-strength Ti-6Al-4V alloy in pressure-temperature space. Up to ∼30 GPa and 886 K, Ti-6Al-4V is found to be stable in the hexagonal-close-packed, orαphase. The effect of temperature on the volume expansion and compressibility ofα-Ti-6Al-4V is modest. The martensiticα→ω(hexagonal) transition occurs at ∼30 GPa, with both phases coexisting until at ∼38-40 GPa the transition to theωphase is completed. Between 300 K and 844 K theα→ωtransition appears to be independent of temperature.ω-Ti-6Al-4V is stable to ∼91 GPa and 844 K, the highest combined pressure and temperature reached in these experiments. Pressure-volume-temperature equations-of-state for theαandωphases of Ti-6Al-4V are generated and found to be similar to pure Ti. A pronounced hysteresis is observed in theω-Ti-6Al-4V on decompression, with the hexagonal structure reverting back to theαphase at pressures below ∼9 GPa at room temperature, and at a higher pressure at elevated temperatures. Based on our data, we estimate the Ti-6Al-4Vα-β-ωtriple point to occur at ∼900 K and 30 GPa, in good agreement with our calculations.

The high-pressure, high-temperature phase diagram of cerium

We present an experimental study of the high-pressure, high-temperature behaviour of cerium up to ∼22 GPa and 820 K using angle-dispersive x-ray diffraction and external resistive heating. Studies above 820 K were prevented by chemical reactions between the samples and the diamond anvils of the pressure cells. We unambiguously measure the stability region of the orthorhombic oC4 phase and find it reaches its apex at 7.1 GPa and 650 K. We locate the α-cF4-oC4-tI2 triple point at 6.1 GPa and 640 K, 1 GPa below the location of the apex of the oC4 phase, and 1-2 GPa lower than previously reported. We find the α-cF4 → tI2 phase boundary to have a positive gradient of 280 K (GPa)-1, less steep than the 670 K (GPa)-1 reported previously, and find the oC4 → tI2 phase boundary to lie at higher temperatures than previously found. We also find variations as large as 2-3 GPa in the transition pressures at which the oC4 → tI2 transition takes place at a given temperature, the reasons for which remain unclear. Finally, we find no evidence that the α-cF4 → tI2 is not second order at all temperatures up to 820 K.

Identification of Phase Transitions and Metastability in Dynamically Compressed Antimony Using Ultrafast X-Ray Diffraction

Ultrafast x-ray diffraction at the LCLS x-ray free electron laser has been used to resolve the structural behavior of antimony under shock compression to 59 GPa. Antimony is seen to transform to the incommensurate, host-guest phase Sb-II at ∼11  GPa, which forms on nanosecond timescales with ordered guest-atom chains. The high-pressure bcc phase Sb-III is observed above ∼15  GPa, some 8 GPa lower than in static compression studies, and mixed Sb-III/liquid diffraction are obtained between 38 and 59 GPa. An additional phase which does not exist under static compression, Sb-I^{'}, is also observed between 8 and 12 GPa, beyond the normal stability field of Sb-I, and resembles Sb-I with a resolved Peierls distortion. The incommensurate Sb-II high-pressure phase can be recovered metastably on release to ambient pressure, where it is stable for more than 10 ns.

Femtosecond diffraction studies of solid and liquid phase changes in shock-compressed bismuth

Bismuth has long been a prototypical system for investigating phase transformations and melting at high pressure. Despite decades of experimental study, however, the lattice-level response of Bi to rapid (shock) compression and the relationship between structures occurring dynamically and those observed during slow (static) compression, are still not clearly understood. We have determined the structural response of shock-compressed Bi to 68 GPa using femtosecond X-ray diffraction, thereby revealing the phase transition sequence and equation-of-state in unprecedented detail for the first time. We show that shocked-Bi exhibits a marked departure from equilibrium behavior - the incommensurate Bi-III phase is not observed, but rather a new metastable phase, and the Bi-V phase is formed at significantly lower pressures compared to static compression studies. We also directly measure structural changes in a shocked liquid for the first time. These observations reveal new behaviour in the solid and liquid phases of a shocked material and give important insights into the validity of comparing static and dynamic datasets.

High-pressure/high-temperature phase diagram of zinc

The phase diagram of zinc (Zn) has been explored up to 140 GPa and 6000 K, by combining optical observations, x-ray diffraction, and ab initio calculations. In the pressure range covered by this study, Zn is found to retain a hexagonal close-packed (hcp) crystal symmetry up to the melting temperature. The known decrease of the axial ratio (c/a) of the hcp phase of Zn under compression is observed in x-ray diffraction experiments from 300 K up to the melting temperature. The pressure at which c/a reaches [Formula: see text] (≈10 GPa) is slightly affected by temperature. When this axial ratio is reached, we observed that single crystals of Zn, formed at high temperature, break into multiple poly-crystals. In addition, a noticeable change in the pressure dependence of c/a takes place at the same pressure. Both phenomena could be caused by an isomorphic second-order phase transition induced by pressure in Zn. The reported melt curve extends previous results from 24 to 135 GPa. The pressure dependence obtained for the melting temperature is accurately described up to 135 GPa by using a Simon-Glatzel equation: [Formula: see text], where P is the pressure in GPa. The determined melt curve agrees with previous low-pressure studies and with shock-wave experiments, with a melting temperature of 5060(30) K at 135 GPa. Finally, a thermal equation of state is reported, which at room-temperature agrees with the literature.

Ultrafast X-Ray Diffraction Studies of the Phase Transitions and Equation of State of Scandium Shock Compressed to 82 GPa

Using x-ray diffraction at the Linac Coherent Light Source x-ray free-electron laser, we have determined simultaneously and self-consistently the phase transitions and equation of state (EOS) of the lightest transition metal, scandium, under shock compression. On compression scandium undergoes a structural phase transition between 32 and 35 GPa to the same bcc structure seen at high temperatures at ambient pressures, and then a further transition at 46 GPa to the incommensurate host-guest polymorph found above 21 GPa in static compression at room temperature. Shock melting of the host-guest phase is observed between 53 and 72 GPa with the disappearance of Bragg scattering and the growth of a broad asymmetric diffraction peak from the high-density liquid.

Thallium under extreme compression

We present a combined theoretical and experimental study of the high-pressure behavior of thallium. X-ray diffraction experiments have been carried out at room temperature (RT) up to 125 GPa using diamond-anvil cells (DACs), nearly doubling the pressure range of previous experiments. We have confirmed the hcp-fcc transition at 3.5 GPa and determined that the fcc structure remains stable up to the highest pressure attained in the experiments. In addition, HP-HT experiments have been performed up to 8 GPa and 700 K by using a combination of XRD and a resistively heated DAC. Information on the phase boundaries is obtained, as well as crystallographic information on the HT bcc phase. The equation of state (EOS) for different phases is reported. Ab initio calculations have also been carried out considering several potential high-pressure structures. They are consistent with the experimental results and predict that, among the structures considered in the calculations, the fcc structure of thallium is stable up to 4.3 TPa. Calculations also predict the post-fcc phase to have a close-packed orthorhombic structure above 4.3 TPa.

Direct Observation of Melting in Shock-Compressed Bismuth With Femtosecond X-ray Diffraction

The melting of bismuth in response to shock compression has been studied using in situ femtosecond x-ray diffraction at an x-ray free electron laser. Both solid-solid and solid-liquid phase transitions are documented using changes in discrete diffraction peaks and the emergence of broad, liquid scattering upon release from shock pressures up to 14 GPa. The transformation from the solid state to the liquid is found to occur in less than 3 ns, very much faster than previously believed. These results are the first quantitative measurements of a liquid material obtained on shock release using x-ray diffraction, and provide an upper limit for the time scale of melting of bismuth under shock loading.

Diamonds on Diamond: structural studies at extreme conditions on the Diamond Light Source

Extreme conditions (EC) research investigates how the structures and physical and chemical properties of materials change when subjected to extremes of pressure and temperature. Pressures in excess of one million times atmospheric pressure can be achieved using a diamond anvil cell, and, in combination with high-energy, micro-focused radiation from a third-generation synchrotron such as Diamond, detailed structural information can be obtained using either powder or single-crystal diffraction techniques. Here, I summarize some of the research drivers behind international EC research, and then briefly describe the techniques by which high-quality diffraction data are obtained. I then highlight the breadth of EC research possible on Diamond by summarizing four examples from work conducted on the I15 and I19 beamlines, including a study which resulted in the first research paper from Diamond. Finally, I look to the future, and speculate as to the type of EC research might be conducted at Diamond over the next 10 years.

The crystal structure of methane B at 8 GPa--an α-Mn arrangement of molecules

From a combination of powder and single-crystal synchrotron x-ray diffraction data we have determined the carbon substructure of phase B of methane at a pressure of ∼8 GPa. We find this substructure to be cubic with space group I4¯3m and 58 molecules in the unit cell. The unit cell has a lattice parameter a = 11.911(1) Å at 8.3(2) GPa, which is a factor of √2 larger than had previously been proposed by Umemoto et al. [J. Phys.: Condens. Matter 14, 10675 (2002)]. The substructure as now solved is not related to any close-packed arrangement, contrary to previous proposals. Surprisingly, the arrangement of the carbon atoms is isostructural with that of α-manganese at ambient conditions.

Europium-IV: an incommensurately modulated crystal structure in the lanthanides

High-resolution x-ray powder-diffraction experiments were performed on europium metal at high pressure up to 50 GPa. At variance with previous reports, the hcp phase of Eu was observed to be stable not only to 18 GPa, but to 31.5 GPa. At 31.5(5) GPa, europium transforms to a phase (Eu-IV) with an incommensurately modulated monoclinic crystal structure with superspace group C2/c(q(1)0q(3))00. This new phase was observed to be stable to ~37.0 GPa, where another phase transition was observed. Eu-IV is the first phase in the lanthanide elements with an incommensurate crystal structure.

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

Elemental barium adopts a series of high-pressure phases with such complex crystal structures that some of them have eluded structure determination for many years. Using single-crystal synchrotron X-ray diffraction and new data analysis strategies, we have now solved the most complex of these crystal structures, that of phase Ba-IVc at 19 GPa. It is a commensurate host-guest structure with 768 atoms in the representative unit, where the relative alignment of the guest-atom chains can be represented as a two-dimensional pattern with interlocking S-shaped 12-chain motifs repeating regularly in one direction and repeating with constrained disorder in the other. The existence of such patterning on the nanometre scale points at medium-range interactions that are not fully screened by the itinerant electrons in this metal. On the basis of first-principles electronic structure calculations, pseudopotential theory and an analysis of the lattice periodicities and interatomic distances, we rationalize why the Ba phases with the common densely packed crystal structures become energetically unfavourable in comparison with the complex-structured Ba-IVc phase, and what the role of the well-known pressure-induced s-d electronic transfer is.

Lattice dynamics and superconductivity in cerium at high pressure

We have measured phonon dispersion relations of the high-pressure phase cerium-oC4 (α' phase with the α-uranium crystal structure) at 6.5 GPa by using inelastic x-ray scattering. Pronounced phonon anomalies are observed, which are remarkably similar to those of α-U. First-principles electronic structure calculations reproduce the anomalies and allow us to identify strong electron-phonon coupling as their origin. At the low-pressure end of its stability range, Ce-oC4 is on the verge of a lattice-dynamical instability and possibly a charge density wave. The superconducting transition temperatures of the fcc, oC4, and mC4 phases of Ce have been calculated, and the superconductivity observed experimentally by Wittig and Probst is attributed to the oC4 phase.

Crystal structures of dense lithium: a metal-semiconductor-metal transition

Ab initio random structure searching and single-crystal x-ray diffraction have been used to determine the full structures of three phases of lithium, recently discovered at low temperature above 60 GPa. A structure with C2mb symmetry, calculated to be a poor metal, is proposed for the oC88 phase (60-65 GPa). The oC40 phase (65-95 GPa) is found to have a lowest-enthalpy structure with C2cb symmetry, in excellent agreement with the x-ray data. It is calculated to be a semiconductor with a band gap of ∼1  eV at 90 GPa. oC24, stable above 95 GPa, has the space group Cmca, and refined atomic coordinates are in excellent agreement with previous calculations.

High pressure orthorhombic structure of CuInSe2

The structural behaviour of CuInSe(2) under high pressure has been studied up to 53 GPa using angle-dispersive x-ray powder diffraction techniques. The previously reported structural phase transition from its ambient pressure tetragonal structure to a high pressure phase with a NaCl-like cubic structure at 7.6 GPa has been confirmed. On further compression, another structural phase transition is observed at 39 GPa. A full structural study of this high pressure phase has been carried out and the high pressure structure has been identified as orthorhombic with space group Cmcm and lattice parameters a = 4.867(8) Å, b = 5.023(8) Å and c = 4.980(3) Å at 53.2(2) GPa. This phase transition behaviour is similar to those of analogous binary and trinary semiconductors, where the orthorhombic Cmcm structure can also be viewed as a distortion of the cubic NaCl-type structure.

Potassium under pressure: a pseudobinary ionic compound

Experimentally, we have found that among the "complicated" phases of potassium at intermediate pressures is one which has the same space group as the double hexagonal-close-packed structure, although its atomic coordination is completely different. Calculations on this P6(3)/mmc (hP4) structure as a function of pressure show three isostructural transitions and three distinctive types of chemical bonding: free electron, ionic, and metallic. Interestingly, relationships between localized metallic structures and ionic compounds are found.

Origin of the incommensurate modulation in Te-III and fermi-surface nesting in a simple metal

Inelastic x-ray scattering experiments have been performed on incommensurately modulated Te-III at high pressure and reveal a pronounced phonon anomaly. The anomaly is reproduced in first-principles lattice dynamics calculations of unmodulated, body-centered monoclinic (bcm) Te, which is shown to be dynamically unstable. The calculated Fermi surface of bcm Te exhibits surprisingly effective nesting for a simple, electronically three-dimensional metal. The combined experimental and theoretical results corroborate recent proposals that the modulated crystal structure of Te-III and other chalcogens is the manifestation of a pressure-induced charge-density wave state.

Two million hours of science

After over a quarter of a century, the doors of the world's first synchrotron radiation source have closed. Its contribution to materials science in the past and the future should not be underestimated.

Competition of charge-density waves and superconductivity in sulfur

A one-dimensional charge-density wave (CDW) instability is shown to be responsible for the formation of the incommensurate modulation of the atomic lattice in the high-pressure phase of sulfur. The coexistence of, and competition between, the CDW and the superconducting state leads to the previously observed increase of T{c} up to 17 K, which we attribute to the suppression of the CDW instability, the same phenomenology found in doped layered dichalcogenides.

Lattice dynamics of incommensurate composite Rb-IV and a realization of the monatomic linear chain model

Longitudinal-acoustic (LA) phonons have been studied by inelastic x-ray scattering in the high-pressure incommensurate host-guest system Rb-IV in the pressure range of 16.3 to 18.4 GPa. Two LA-like phonon branches are observed along the direction of the incommensurate wave vector, which are attributed to separate lattice vibrations in the host and guest subsystems. The derived sound velocities for the host and the guest, v(h) and v(g), respectively, are similar in magnitude [v(h)=v(g)=3840(100) m/s at 18 GPa], but our results indicate rather different pressure dependences of dv(h)/dP=140(60) m/s GPa(-1) and dv(g)/dP=280(80) m/s GPa(-1). The observations for the one-dimensional Rb guest chains are reproduced quantitatively on the basis of the monatomic linear chain model and the measured compressibility of the chains.

Observation of a wurtzite form of gallium arsenide

After a pressure decrease to ambient, the high-pressure SC16 phase of GaAs is found to transform to the hexagonal wurtzite structure. This has been suggested for GaAs in calculations but never previously observed experimentally. Wurtzite-GaAs is found to be stable at ambient pressures at temperatures up to 473 K, with a structure that is only slightly distorted from ideal. On recompression, the ratio is constant with pressure and wurtzite-GaAs transforms to the orthorhombic phase at 18.7(9) GPa.

X-ray diffraction study of liquid Cs up to 9.8 GPa

We describe an x-ray diffraction study of liquid Cs at high pressure and temperature conducted in order to characterize the structural changes associated with the complex melting curve and phase transitions observed in the solid phases. At 3.9 GPa we observe a discontinuity in the density of the liquid accompanied by a decrease in the coordination number from about 12 to 8, which marks a change to a nonsimple liquid. The specific volume of liquid Cs, combined with structural analysis of the diffraction data, strongly suggest the existence of dsp(3) electronic hybridization above 3.9 GPa, similar to that reported on compression in the crystalline phase.

Structural complexity in gallium under high pressure: relation to alkali elements

Ga-II, the stable phase of Ga between 2 and 10 GPa at room temperature, is shown to have a complex 104-atom orthorhombic structure. A new phase, Ga-V, is found between 10 and 14 GPa, with a rhombohedral hR6 structure. Ga-II has a modulated layer structure like those recently reported for Rb-III and Cs-III, with similar 8- and 10-atom a-b layers stacked along the c axis in the sequence 8-10-8-8-10-8-8-10-8-8-10-8. The cI16 structure of Li and Na can be understood as a stacking of very similar 8-atom layers. It is suggested that a Hume-Rothery mechanism contributes to the occurrence of these complex structures in such different metals.

Chain "melting" in the composite Rb-IV structure

The Bragg peaks from the structure formed by the guest chains in the incommensurate composite structure of Rb-IV are all found to broaden strongly at pressures below 16.7(1) GPa. This signals a loss of the interchain correlation. At the lowest reachable pressure before the transition to Rb-III, 16.2 GPa, the correlation length is only approximately 30 A, or 4 times the interchain distance. There is also evidence of a loss of long-range order within each chain. The chains thus exhibit the onset of the characteristics of an ordered 1D liquid.

Large structural modulations in incommensurate Te-III and Se-IV

The high-pressure phase of tellurium, Te-III, is found to have an incommensurate monoclinic structure, superspace group I(')2/m(0q0)s0, of a type previously unknown in the elements. Te-III is stable from 4.5(2) to 29.2(7) GPa; the previously reported transition to a distinct Te-IV phase at 10.6 GPa is not observed. The incommensurate wave vector of Te-III is strongly pressure dependent and varies in a strongly nonlinear way. Se-IV is found to be isostructural with Te-III.

Structure of Rb-III: novel modulated stacking structures in alkali metals

The crystal structure of Rb-III, stable between 13 and 17 GPa, has been determined from quasi-single-crystal x-ray diffraction data. It is orthorhombic, space group C222(1), with 52 atoms in the unit cell, and has an 8-10-8-8-10-8 stacking of 8- and 10-atom layers. The recently reported 84-atom structure of Cs-III can be understood as an 8-8-10-8-8-8-8-10-8-8 stacking of the same layers. These represent a new class of modulated elemental structures.

Complex crystal structure of cesium-III

The structure of Cs-III, stable between 4.2 and 4.3 GPa at room temperature, has been determined from single-crystal x-ray diffraction data. Rather than the simple fcc structure previously reported [Hall et al., Science 146, 1297 (1964)], the data yield a complex new type of elemental structure which is orthorhombic (space group C222(1)) with 84 atoms in the unit cell. No evidence could be found for the fcc form reported previously, even in a further experiment, conducted under conditions close to those used by Hall et al., which also yielded the 84-atom structure.

Pressure dependent incommensuration in Rb-IV

Rb-IV is found to have an incommensurate composite structure, comprising a tetragonal host framework and a simple body-centered tetragonal guest. This does not have the unexpectedly short Rb-Rb distances of the previously reported structure [U. Schwarz et al., Phys. Rev. Lett. 83, 4085 (1999)]. The ratio of the c-axis lattice parameters is strongly pressure dependent and approaches the commensurate value of 5/3 at the transition to phase V. A reversible broadening of the guest structure is observed below 16.5(2) GPa.

Ba-IV-type incommensurate crystal structure in group-V metals

The long-unknown crystal structure of Bi-III has been solved. It comprises a body-centered-tetragonal (bct) "host" and a bct "guest" component made up of chains that lie in channels in the host; the guest is incommensurate with the host along the tetragonal c axis. Diffraction data for Sb-II reveal that it too can be fitted with the same composite structure. The structures of these two high-pressure phases of Bi and Sb are similar to those reported recently in the alkaline-earth metals Ba and Sr.