Harnessing interpretable and unsupervised machine learning to address big data from modern X-ray diffraction.

The information content of crystalline materials becomes astronomical when collective electronic behavior and their fluctuations are taken into account. In the past decade, improvements in source brightness and detector technology at modern X-ray facilities have allowed a dramatically increased fraction of this information to be captured. Now, the primary challenge is to understand and discover scientific principles from big datasets when a comprehensive analysis is beyond human reach. We report the development of an unsupervised machine learning approach, X-ray diffraction (XRD) temperature clustering (X-TEC), that can automatically extract charge density wave order parameters and detect intraunit cell ordering and its fluctuations from a series of high-volume X-ray diffraction measurements taken at multiple temperatures. We benchmark X-TEC with diffraction data on a quasi-skutterudite family of materials, (CaxSr[Formula: see text])3Rh4Sn13, where a quantum critical point is observed as a function of Ca concentration. We apply X-TEC to XRD data on the pyrochlore metal, Cd2Re2O7, to investigate its two much-debated structural phase transitions and uncover the Goldstone mode accompanying them. We demonstrate how unprecedented atomic-scale knowledge can be gained when human researchers connect the X-TEC results to physical principles. Specifically, we extract from the X-TEC-revealed selection rules that the Cd and Re displacements are approximately equal in amplitude but out of phase. This discovery reveals a previously unknown involvement of [Formula: see text] Re, supporting the idea of an electronic origin to the structural order. Our approach can radically transform XRD experiments by allowing in operando data analysis and enabling researchers to refine experiments by discovering interesting regions of phase space on the fly.

Order-Disorder Transitions in (Ca_{x}Sr_{1-x})_{3}Rh_{4}Sn_{13}.

The classification of structural phase transitions as displacive or order-disorder in character is usually based on spectroscopic data above the transition. We use single crystal x-ray diffraction to investigate structural correlations in the quasiskutterudites, (Ca_{x}Sr_{1-x})_{3}Rh_{4}Sn_{13}, which have a quantum phase transition at x∼0.9. Three-dimensional pair distribution functions show that the amplitudes of local atomic displacements are temperature independent below the transition and persist to well above the transition, a signature of order-disorder behavior. The implications for the associated electronic transitions are discussed.

Fragile 3D Order in V_{1-x}Mo_{x}O_{2}.

The metal-to-insulator transition in rutile VO_{2} has proven uniquely difficult to characterize because of the complex interplay between electron correlations and atomic structure. Here, we report the discovery of the sudden collapse of three-dimensional order in the low-temperature phase of V_{1-x}Mo_{x}O_{2} at x=0.17 and the emergence of a novel frustrated two-dimensional order at x=0.19, with only a slight change in electronic properties. Single crystal diffuse x-ray scattering reveals that this transition from the 3D M1 phase to a 2D variant of the M2 phase results in long-range structural correlations along symmetry-equivalent (11L) planes of the tetragonal rutile structure, yet extremely short-range correlations transverse to these planes. These findings suggest that this two dimensionality results from a novel form of geometric frustration that is essentially structural in origin.

A two-dimensional type I superionic conductor.

Superionic conductors possess liquid-like ionic diffusivity in the solid state, finding wide applicability from electrolytes in energy storage to materials for thermoelectric energy conversion. Type I superionic conductors (for example, AgI, Ag2Se and so on) are defined by a first-order transition to the superionic state and have so far been found exclusively in three-dimensional crystal structures. Here, we reveal a two-dimensional type I superionic conductor, α-KAg3Se2, by scattering techniques and complementary simulations. Quasi-elastic neutron scattering and ab initio molecular dynamics simulations confirm that the superionic Ag+ ions are confined to subnanometre sheets, with the simulated local structure validated by experimental X-ray powder pair-distribution-function analysis. Finally, we demonstrate that the phase transition temperature can be controlled by chemical substitution of the alkali metal ions that compose the immobile charge-balancing layers. Our work thus extends the known classes of superionic conductors and will facilitate the design of new materials with tailored ionic conductivities and phase transitions.

The Subchalcogenides Ir2In8Q (Q = S, Se, Te): Dirac Semimetal Candidates with Re-entrant Structural Modulation.

Subchalcogenides are uncommon compounds where the metal atoms are in unusually low formal oxidation states. They bridge the gap between intermetallics and semiconductors and can have unexpected structures and properties because of the exotic nature of their chemical bonding as they contain both metal-metal and metal-main group (e.g., halide, chalcogenide) interactions. Finding new members of this class of materials presents synthetic challenges as attempts to make them often result in phase separation into binary compounds. We overcome this difficulty by utilizing indium as a metal flux to synthesize large (millimeter scale) single crystals of novel subchalcogenide materials. Herein, we report two new compounds Ir2In8Q (Q = Se, Te) and compare their structural and electrical properties to the previously reported Ir2In8S analogue. Ir2In8Se and Ir2In8Te crystallize in the P42/mnm space group and are isostructural to Ir2In8S, but also have commensurately modulated (with q vectors q = 1/6a* + 1/6b* and q = 1/10a* + 1/10b* for Ir2In8Se and Ir2In8Te, respectively) low-temperature phase transitions, where the chalcogenide anions in the channels experience a distortion in the form of In-Q bond alternation along the ab plane. Both compounds display re-entrant structural behavior, where the supercells appear on cooling but revert to the original subcell below 100 K, suggesting competing structural and electronic interactions dictate the overall structure. Notably, these materials are topological semimetal candidates with symmetry-protected Dirac crossings near the Fermi level and exhibit high electron mobilities (∼1500 cm2 V-1 s-1 at 1.8 K) and moderate carrier concentrations (∼1020 cm-3) from charge transport measurements. This work highlights metal flux as a synthetic route to high quality single crystals of novel intermetallic subchalcogenides with Dirac semimetal behavior.

CsV_{3}Sb_{5}: A Z_{2} Topological Kagome Metal with a Superconducting Ground State.

Recently discovered alongside its sister compounds KV_{3}Sb_{5} and RbV_{3}Sb_{5}, CsV_{3}Sb_{5} crystallizes with an ideal kagome network of vanadium and antimonene layers separated by alkali metal ions. This work presents the electronic properties of CsV_{3}Sb_{5}, demonstrating bulk superconductivity in single crystals with a T_{c}=2.5 K. The normal state electronic structure is studied via angle-resolved photoemission spectroscopy and density-functional theory, which categorize CsV_{3}Sb_{5} as a Z_{2} topological metal. Multiple protected Dirac crossings are predicted in close proximity to the Fermi level (E_{F}), and signatures of normal state correlation effects are also suggested by a high-temperature charge density wavelike instability. The implications for the formation of unconventional superconductivity in this material are discussed.

Reciprocal space imaging of ionic correlations in intercalation compounds.

The intercalation of alkali ions into layered materials has played an essential role in battery technology since the development of the first lithium-ion electrodes. Coulomb repulsion between the intercalants leads to ordering of the intercalant sublattice, which hinders ionic diffusion and impacts battery performance. While conventional diffraction can identify the long-range order that can occur at discrete intercalant concentrations during the charging cycle, it cannot determine short-range order at other concentrations that also disrupt ionic mobility. In this Article, we show that the use of real-space transforms of single-crystal diffuse scattering, measured with high-energy synchrotron X-rays, allows a model-independent measurement of the temperature dependence of the length scale of ionic correlations along each of the crystallographic axes in sodium-intercalated V2O5. The techniques described here provide a new way of probing the evolution of structural ordering in crystalline materials.

Author Correction: Reciprocal space imaging of ionic correlations in intercalation compounds.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Coherent band excitations in CePd3: A comparison of neutron scattering and ab initio theory.

In common with many strongly correlated electron systems, intermediate valence compounds are believed to display a crossover from a high-temperature regime of incoherently fluctuating local moments to a low-temperature regime of coherent hybridized bands. We show that inelastic neutron scattering measurements of the dynamic magnetic susceptibility of CePd3 provides a benchmark for ab initio calculations based on dynamical mean field theory. The magnetic response is strongly momentum dependent thanks to the formation of coherent f-electron bands at low temperature, with an amplitude that is strongly enhanced by local particle-hole interactions. The agreement between experiment and theory shows that we have a robust first-principles understanding of the temperature dependence of f-electron coherence.

Local Orthorhombicity in the Magnetic C_{4} Phase of the Hole-Doped Iron-Arsenide Superconductor Sr_{1-x}Na_{x}Fe_{2}As_{2}.

We report on temperature-dependent pair distribution function measurements of Sr_{1-x}Na_{x}Fe_{2}As_{2}, an iron-based superconductor system that contains a magnetic phase with reentrant tetragonal symmetry, known as the magnetic C_{4} phase. Quantitative refinements indicate that the instantaneous local structure in the C_{4} phase comprises fluctuating orthorhombic regions with a length scale of ∼2 nm, despite the tetragonal symmetry of the average static structure. Additionally, local orthorhombic fluctuations exist on a similar length scale at temperatures well into the paramagnetic tetragonal phase. These results highlight the exceptionally large nematic susceptibility of iron-based superconductors and have significant implications for the magnetic C_{4} phase and the neighboring C_{2} and superconducting phases.

Charge Density Wave in the New Polymorphs of RE2Ru3Ge5 (RE = Pr, Sm, Dy).

A new polymorph of the RE2Ru3Ge5 (RE = Pr, Sm, Dy) compounds has been grown as single crystals via an indium flux. These compounds crystallize in tetragonal space group P4/mnc with the Sc2Fe3Si5-type structure, having lattice parameters a = 11.020(2) Šand c = 5.853(1) Šfor RE = Pr, a = 10.982(2) Šand c = 5.777(1) Šfor RE = Sm, and a = 10.927(2) Šand c = 5.697(1) Šfor RE = Dy. These materials exhibit a structural transition at low temperature, which is attributed to an apparent charge density wave (CDW). Both the high-temperature average crystal structure and the low-temperature incommensurately modulated crystal structure (for Sm2Ru3Ge5 as a representative) have been solved. The charge density wave order is manifested by periodic distortions of the one-dimensional zigzag Ge chains. From X-ray diffraction, charge transport (electrical resistivity, Hall effect, magnetoresistance), magnetic measurements, and heat capacity, the ordering temperatures (TCDW) observed in the Pr and Sm analogues are ∼200 and ∼175 K, respectively. The charge transport measurement results indicate an electronic state transition happening simultaneously with the CDW transition. X-ray absorption near-edge spectroscopy (XANES) and electronic band structure results are also reported.

The NeXus data format.

NeXus is an effort by an international group of scientists to define a common data exchange and archival format for neutron, X-ray and muon experiments. NeXus is built on top of the scientific data format HDF5 and adds domain-specific rules for organizing data within HDF5 files, in addition to a dictionary of well defined domain-specific field names. The NeXus data format has two purposes. First, it defines a format that can serve as a container for all relevant data associated with a beamline. This is a very important use case. Second, it defines standards in the form of application definitions for the exchange of data between applications. NeXus provides structures for raw experimental data as well as for processed data.