Dynamic Local Structure in Caesium Lead Iodide: Spatial Correlation and Transient Domains.

Metal halide perovskites are multifunctional semiconductors with tunable structures and properties. They are highly dynamic crystals with complex octahedral tilting patterns and strongly anharmonic atomic behavior. In the higher temperature, higher symmetry phases of these materials, several complex structural features are observed. The local structure can differ greatly from the average structure and there is evidence that dynamic 2D structures of correlated octahedral motion form. An understanding of the underlying complex atomistic dynamics is, however, still lacking. In this work, the local structure of the inorganic perovskite CsPbI3 is investigated using a new machine learning force field based on the atomic cluster expansion framework. Through analysis of the temporal and spatial correlation observed during large-scale simulations, it is revealed that the low frequency motion of octahedral tilts implies a double-well effective potential landscape, even well into the cubic phase. Moreover, dynamic local regions of lower symmetry are present within both higher symmetry phases. These regions are planar and the length and timescales of the motion are reported. Finally, the spatial arrangement of these features and their interactions are investigated and visualized, providing a comprehensive picture of local structure in the higher symmetry phases.

Imperfections are not 0 K: free energy of point defects in crystals.

Defects determine many important properties and applications of materials, ranging from doping in semiconductors, to conductivity in mixed ionic-electronic conductors used in batteries, to active sites in catalysts. The theoretical description of defect formation in crystals has evolved substantially over the past century. Advances in supercomputing hardware, and the integration of new computational techniques such as machine learning, provide an opportunity to model longer length and time-scales than previously possible. In this Tutorial Review, we cover the description of free energies for defect formation at finite temperatures, including configurational (structural, electronic, spin) and vibrational terms. We discuss challenges in accounting for metastable defect configurations, progress such as machine learning force fields and thermodynamic integration to directly access entropic contributions, and bottlenecks in going beyond the dilute limit of defect formation. Such developments are necessary to support a new era of accurate defect predictions in computational materials chemistry.

Anharmonicity and Ultralow Thermal Conductivity in Lead-Free Halide Double Perovskites.

The lead-free halide double perovskite class of materials offers a promising venue for resolving issues related to toxicity of Pb and long-term stability of the lead-containing halide perovskites. We present a first-principles study of the lattice vibrations in Cs_{2}AgBiBr_{6}, the prototypical compound in this class and show that the lattice dynamics of Cs_{2}AgBiBr_{6} is highly anharmonic, largely in regards to tilting of AgBr_{6} and BiBr_{6} octahedra. Using an energy- and temperature-dependent phonon spectral function, we then show how the experimentally observed cubic-to-tetragonal phase transformation is caused by the collapse of a soft phonon branch. We finally reveal that the softness and anharmonicity of Cs_{2}AgBiBr_{6} yield an ultralow thermal conductivity, unexpected of high-symmetry cubic structures.

Lead-Free Halide Double Perovskite Cs2 AgBiBr6 with Decreased Band Gap.

Environmentally friendly halide double perovskites with improved stability are regarded as a promising alternative to lead halide perovskites. The benchmark double perovskite, Cs2 AgBiBr6 , shows attractive optical and electronic features, making it promising for high-efficiency optoelectronic devices. However, the large band gap limits its further applications, especially for photovoltaics. Herein, we develop a novel crystal-engineering strategy to significantly decrease the band gap by approximately 0.26 eV, reaching the smallest reported band gap of 1.72 eV for Cs2 AgBiBr6 under ambient conditions. The band-gap narrowing is confirmed by both absorption and photoluminescence measurements. Our first-principles calculations indicate that enhanced Ag-Bi disorder has a large impact on the band structure and decreases the band gap, providing a possible explanation of the observed band-gap narrowing effect. This work provides new insights for achieving lead-free double perovskites with suitable band gaps for optoelectronic applications.

Phase Stability of Dynamically Disordered Solids from First Principles.

Theoretical studies of phase stability in solid materials with dynamic disorder are challenging due to the failure of the standard picture of atoms vibrating around fixed equilibrium positions. Dynamically disordered solid materials show immense potential in applications. In particular, superionic conductors, where the disorder results in exceptionally high ionic conductivity, are very promising as solid state electrolytes in batteries and fuel cells. The biggest obstacle in living up to this potential is the limited stability of the dynamically disordered phases. Here, we outline a method to obtain the free energy of a dynamically disordered solid. It is based on a stress-strain thermodynamic integration on a deformation path between a mechanically stable ordered variant of the disordered phase, and the dynamically disordered phase itself. We show that the large entropy contribution associated with the dynamic disorder is captured in the behavior of the stress along the deformation path. We apply the method to Bi_{2}O_{3}, whose superionic δ phase is the fastest known solid oxide ion conductor. We accurately reproduce the experimental transition enthalpy and the critical temperature of the phase transition from the low temperature ground state α phase to the superionic δ phase. The method can be used for a first-principles description of the phase stability of superionic conductors and other materials with dynamic disorder, when the disordered phase can be connected to a stable phase through a continuous deformation path.

Unraveling Hidden Mg-Mn-H Phase Relations at High Pressures and Temperatures by in Situ Synchrotron Diffraction.

The Mg-Mn-H system was investigated by in situ high pressure studies of reaction mixtures MgH2-Mn-H2. The formation conditions of two complex hydrides with composition Mg3MnH7 were established. Previously known hexagonal Mg3MnH7 (h-Mg3MnH7) formed at pressures 1.5-2 GPa and temperatures between 480 and 500 °C, whereas an orthorhombic form (o-Mg3MnH7) was obtained at pressures above 5 GPa and temperatures above 600 °C. The crystal structures of the polymorphs feature octahedral [Mn(I)H6]5- complexes and interstitial H-. Interstitial H- is located in trigonal bipyramidal and square pyramidal interstices formed by Mg2+ ions in h- and o-Mg3MnH7, respectively. The hexagonal form can be retained at ambient pressure, whereas the orthorhombic form upon decompression undergoes a distortion to monoclinic Mg3MnH7 (m-Mg3MnH7). The structure elucidation of o- and m-Mg3MnH7 was aided by first-principles density functional theory (DFT) calculations. Calculated enthalpy versus pressure relations predict m- and o-Mg3MnH7 to be more stable than h-Mg3MnH7 above 4.3 GPa. Phonon calculations revealed o-Mg3MnH7 to be dynamically unstable at pressures below 5 GPa, which explains its phase transition to m-Mg3MnH7 on decompression. The electronic structure of the quenchable polymorphs h- and m-Mg3MnH7 is very similar. The stable 18-electron complex [MnH6]5- is mirrored in the occupied states, and calculated band gaps are around 1.5 eV. The study underlines the significance of in situ investigations for mapping reaction conditions and understanding phase relations for hydrogen-rich complex transition metal hydrides.

Understanding Antiferromagnetic Coupling in Lead-Free Halide Double Perovskite Semiconductors.

Solution-processable semiconductors with antiferromagnetic (AFM) order are attractive for future spintronics and information storage technology. Halide perovskites containing magnetic ions have emerged as multifunctional materials, demonstrating a cross-link between structural, optical, electrical, and magnetic properties. However, stable optoelectronic halide perovskites that are antiferromagnetic remain sparse, and the critical design rules to optimize magnetic coupling still must be developed. Here, we combine the complementary magnetometry and electron-spin-resonance experiments, together with first-principles calculations to study the antiferromagnetic coupling in stable Cs2(Ag:Na)FeCl6 bulk semiconductor alloys grown by the hydrothermal method. We show the importance of nonmagnetic monovalence ions at the BI site (Na/Ag) in facilitating the superexchange interaction via orbital hybridization, offering the tunability of the Curie-Weiss parameters between -27 and -210 K, with a potential to promote magnetic frustration via alloying the nonmagnetic BI site (Ag:Na ratio). Combining our experimental evidence with first-principles calculations, we draw a cohesive picture of the material design for B-site-ordered antiferromagnetic halide double perovskites.

Structural Dynamics Descriptors for Metal Halide Perovskites.

Metal halide perovskites have shown extraordinary performance in solar energy conversion technologies. They have been classified as "soft semiconductors" due to their flexible corner-sharing octahedral networks and polymorphous nature. Understanding the local and average structures continues to be challenging for both modeling and experiments. Here, we report the quantitative analysis of structural dynamics in time and space from molecular dynamics simulations of perovskite crystals. The compact descriptors provided cover a wide variety of structural properties, including octahedral tilting and distortion, local lattice parameters, molecular orientations, as well as their spatial correlation. To validate our methods, we have trained a machine learning force field (MLFF) for methylammonium lead bromide (CH3NH3PbBr3) using an on-the-fly training approach with Gaussian process regression. The known stable phases are reproduced, and we find an additional symmetry-breaking effect in the cubic and tetragonal phases close to the phase-transition temperature. To test the implementation for large trajectories, we also apply it to 69,120 atom simulations for CsPbI3 based on an MLFF developed using the atomic cluster expansion formalism. The structural dynamics descriptors and Python toolkit are general to perovskites and readily transferable to more complex compositions.

Lattice Dynamics and Electron-Phonon Coupling in Double Perovskite Cs2NaFeCl6.

Phonon-phonon and electron/exciton-phonon coupling play a vitally important role in thermal, electronic, as well as optical properties of metal halide perovskites. In this work, we evaluate phonon anharmonicity and coupling between electronic and vibrational excitations in novel double perovskite Cs2NaFeCl6 single crystals. By employing comprehensive Raman measurements combined with first-principles theoretical calculations, we identify four Raman-active vibrational modes. Polarization properties of these modes imply Fm3̅m symmetry of the lattice, indicative for on average an ordered distribution of Fe and Na atoms in the lattice. We further show that temperature dependence of the Raman modes, such as changes in the phonon line width and their energies, suggests high phonon anharmonicity, typical for double perovskite materials. Resonant multiphonon Raman scattering reveals the presence of high-lying band states that mediate strong electron-phonon coupling and give rise to intense nA 1g overtones up to the fifth order. Strong electron-phonon coupling in Cs2NaFeCl6 is also concluded based on the Urbach tail analysis of the absorption coefficient and the calculated Fröhlich coupling constant. Our results, therefore, suggest significant impacts of phonon-phonon and electron-phonon interactions on electronic properties of Cs2NaFeCl6, important for potential applications of this novel material.

Diverging Expressions of Anharmonicity in Halide Perovskites.

Lead-based halide perovskite crystals are shown to have strongly anharmonic structural dynamics. This behavior is important because it may be the origin of their exceptional photovoltaic properties. The double perovskite, Cs2 AgBiBr6 , has been recently studied as a lead-free alternative for optoelectronic applications. However, it does not exhibit the excellent photovoltaic activity of the lead-based halide perovskites. Therefore, to explore the correlation between the anharmonic structural dynamics and optoelectronic properties in lead-based halide perovskites, the structural dynamics of Cs2 AgBiBr6 are investigated and are compared to its lead-based analog, CsPbBr3 . Using temperature-dependent Raman measurements, it is found that both materials are indeed strongly anharmonic. Nonetheless, the expression of their anharmonic behavior is markedly different. Cs2 AgBiBr6 has well-defined normal modes throughout the measured temperature range, while CsPbBr3 exhibits a complete breakdown of the normal-mode picture above 200 K. It is suggested that the breakdown of the normal-mode picture implies that the average crystal structure may not be a proper starting point to understand the electronic properties of the crystal. In addition to our main findings, an unreported phase of Cs2 AgBiBr6 is also discovered below ≈37 K.

Na-Ni-H Phase Formation at High Pressures and High Temperatures: Hydrido Complexes [NiH5]3- Versus the Perovskite NaNiH3.

The Na-Ni-H system was investigated by in situ synchrotron diffraction studies of reaction mixtures NaH-Ni-H2 at around 5, 10, and 12 GPa. The existence of ternary hydrogen-rich hydrides with compositions Na3NiH5 and NaNiH3, where Ni attains the oxidation state II, is demonstrated. Upon heating at ∼5 GPa, face-centered cubic (fcc) Na3NiH5 forms above 430 °C. Upon cooling, it undergoes a rapid and reversible phase transition at 330 °C to an orthorhombic (Cmcm) form. Upon pressure release, Na3NiH5 further transforms into its recoverable Pnma form whose structure was elucidated from synchrotron powder diffraction data, aided by first-principles density functional theory (DFT) calculations. Na3NiH5 features previously unknown square pyramidal 18-electron complexes NiH5 3-. In the high temperature fcc form, metal atoms are arranged as in the Heusler structure, and ab initio molecular dynamics simulations suggest that the complexes are dynamically disordered. The Heusler-type metal partial structure is essentially maintained in the low temperature Cmcm form, in which NiH5 3- complexes are ordered. It is considerably rearranged in the low pressure Pnma form. Experiments at 10 GPa showed an initial formation of fcc Na3NiH5 followed by the addition of the perovskite hydride NaNiH3, in which Ni(II) attains an octahedral environment by H atoms. NaNiH3 is recoverable at ambient pressures and represents the sole product of 12 GPa experiments. DFT calculations show that the decomposition of Na3NiH5 = NaNiH3 + 2 NaH is enthalpically favored at all pressures, suggesting that Na3NiH5 is metastable and its formation is kinetically favored. Ni-H bonding in metallic NaNiH3 is considered covalent, as in electron precise Na3NiH5, but delocalized in the polyanion [NiH3]-.