We present an $\textit{ab initio}$ study of the thermodynamic properties of cubic CaSiO$_3$ perovskite (CaPv) over the pressure and temperature range of the Earth's lower mantle. We compute the anharmonic phonon dispersions throughout the Brillouin zone by utilizing the phonon quasiparticle approach, which characterizes the intrinsic temperature dependence of phonon frequencies and, in principle, captures full anharmonicity. Such temperature-dependent phonon dispersions are used to calculate $\textit{ab initio}$ free energy in the thermodynamic limit ($N \rightarrow \infty$) within the framework of the phonon gas model. Accurate free energy calculations enable us to investigate cubic CaPv's thermodynamic properties and thermal equation of state, where anharmonic effects are demonstrated. The present methodology provides an important theoretical approach for exploring phase boundaries, thermodynamic, and thermoelastic properties of strongly anharmonic materials at high pressures and temperatures.
Thermal conductivity ($κ$) of mantle minerals is a fundamental property in geodynamic modeling. It controls the style of mantle convection and the time scale of the mantle and core cooling. Cubic CaSiO$_3$ perovskite (CaPv) is the third most abundant mineral in the lower mantle (LM) (7 vol%). However, despite its importance, no theoretical or experimental estimate of CaPv's $κ$ exists. Theoretical investigations of its properties are challenging because of its strong anharmonicity. Experimental measurements at relevant high pressures and temperatures are equally challenging. Here we present $a…
Calcium silicate perovskite (CaSiO$_3$) is one of the major mineral components of the lower mantle, but has been the subject of relatively little work compared to the more abundant Mg-based materials. One of the major problems related to CaSiO$_3$ that is still the subject of research is its crystal structure under lower mantle conditions - a cubic Pm$\bar{3}$m structure is accepted in general, but some have suggested that lower-symmetry structures may be relevant. In this paper, we use a fully first-principles vibrational self-consistent field method to perform high accuracy anharmonic vibrat…
The thermodynamics of CaSiO3 in Earth's lower mantle
École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）；National Centre for Computational Design and Discovery of Novel Materials (MARVEL)（新材料计算设计与发现国家中心）；Paul Scherrer Institut（保罗谢尔研究所）；Università di Roma Sapienza（罗马第一大学）
Correlation Matrix Method for Phonon Quasiparticles
Beijing Institute of Technology（北京理工大学）；International Center for Quantum Materials, Beijing Institute of Technology（北京理工大学国际量子材料中心）；College of Mathematics and Physics, Beijing University of Chemical Technology（北京化工大学理学院）
To address the effects of lattice anharmonicity across the perovskite to post-perovskite transition in MgSiO$_3$, we conduct calculations using the phonon quasiparticle (PHQ) approach. The PHQ is based on \textit{ab initio} molecular dynamics and, in principle, captures full anharmonicity. Free energies in the thermodynamic limit ($N \rightarrow \infty$) are computed using temperature-dependent quasiparticle dispersions within the phonon gas model. Systematic results on anharmonic thermodynamic properties and phase boundary are reported. Both the local density approximation (LDA) and the gener…
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 ph…
Halide perovskites are semiconductors that exhibit sharp optical absorption edges and small Urbach energies allowing for efficient collection of sunlight in thin-film photovoltaic devices. However, halide perovskites also exhibit large nuclear anharmonic effects and disorder, which is unusual for efficient optoelectronic materials and difficult to rationalize in view of the small Urbach energies that indicate a low amount of disorder. To address this important issue, the disorder potential induced for electronic states by the nuclear dynamics in various paradigmatic halide perovskites is studi…
Ultrafast vibrational dynamics of inorganic-organic hybrid lead halide perovskite CH3NH3PbI$ in the room-temperature tetragonal phase is investigated under moderate photoexcitation slightly below the band gap. Time-resolved optical Kerr effect signal exhibits periodic modulations due to the libration and twisting of the methylammonium molecule at 4 and 8 THz, in addition to the inorganic sublattice deformation at 1.2 THz. These oscillations are heavily damped, and their frequencies exhibit blueshifts with increasing pump density, contrary to the expectation from conventional laser heating. Our…
Understanding and predicting lattice dynamics in strongly anharmonic crystals is one of the long-standing challenges in condensed matter physics. Here we propose a first-principles method that gives accurate quasiparticle (QP) peaks of the phonon spectrum with strong anharmonic broadening. On top of the conventional first-order self-consistent phonon (SC1) dynamical matrix, the proposed method incorporates frequency renormalization effects by the bubble self-energy within the QP approximation. We apply the developed methodology to the strongly anharmonic $α$-CsPbBr$_3$ that displays phonon ins…
Amongst the X(Sn,Pb)Y$_3$ perovskites currently under scrutiny for their photovoltaic applications, the cubic B-$α$ phase of CsSnI$_3$ is arguably the best characterized experimentally. Yet, according to the standard harmonic theory of phonons, this deceptively simple phase should not exist at all due to rotational instabilities of the SnI$_6$ octahedra. Here, employing self-consistent phonon theory we show that these soft modes are stabilized at experimental conditions through anharmonic phonon-phonon interactions between the Cs ions and their iodine cages. We further calculate the renormaliz…
Doping organic metal-halide perovskites with cesium could be the best solution to stabilize highly-efficient perovskite solar cells. The understanding of the respective roles of the organic molecule, on one hand, and the inorganic lattice, on the other, is thus crucial in order to be able to optimize the physical properties of the mixed-cation structures. In particular, the study of the recombination mechanisms is thought to be one of the key challenges towards full comprehension of their working principles. Using molecular dynamics and frozen phonons, we evidence sub-picosecond anharmonic flu…
Roadmap for electronic structure, anharmonicity, and electron-phonon calculations in locally disordered inorganic and hybrid halide perovskites
Univ Rennes, INSA Rennes, CNRS, Institut FOTON - UMR 6082（雷恩大学，雷恩国立应用科学学院，法国国家科学研究中心，FOTON研究所）；Computation-based Science and Technology Research Center, The Cyprus Institute（塞浦路斯研究院计算科学与技术研究中心）；Univ Rennes, ENSCR, INSA Rennes, CNRS, ISCR - UMR 6226（雷恩大学，雷恩高等师范学院，雷恩国立应用科学学院，法国国家科学研究中心，ISCR研究所）；Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin（德克萨斯大学奥斯汀分校奥登计算工程与科学学院）；Department of Physics, The University of Texas at Austin（德克萨斯大学奥斯汀分校物理系）
An approach to compute the anharmonic peaks of the phonon dispersion curves through the ab initio calculated Hellmann-Feynman forces from a series of supercells with realistic atomic displacements of all atoms, which correspond to a given temperature, is reported. Obtained phonon dispersion bands are able to represent the positions and shapes of the anharmonic peaks. As example, the approach to cubic PbTe and perovskite MgSiO3 crystals is applied.
Structural phase transitions and soft phonon modes pose a longstanding challenge to computing electron-phonon (e-ph) interactions in strongly anharmonic crystals. Here we develop a first-principles approach to compute e-ph scattering and charge transport in materials with anharmonic lattice dynamics. Our approach employs renormalized phonons to compute the temperature-dependent e-ph coupling for all phonon modes, including the soft modes associated with ferroelectricity and phase transitions. We show that the electron mobility in cubic SrTiO$_{3}$ is controlled by scattering with longitudinal …
Band-like Carriers in a Soft, Anharmonic Lattice: Lead-Halide Perovskites
Pohang Accelerator Laboratory, POSTECH（浦项加速器实验室，浦项科技大学）；YUHS-KRIBB Medical Convergence Research Institute, College of Medicine, Yonsei University（延世大学医学院佑山-韩国生命科学研究院医学融合研究所）；Department of Physics, University of Seoul（首尔大学物理系）；Global Institute of Future Technology, Shanghai Jiao Tong University（上海交通大学未来技术学院）
Lattice thermal conductivity ($κ_{lat}$) of MgSiO$_3$ postperovskite (MgPPv) under the Earth's lower mantle high pressure-temperature conditions is studied using the phonon quasiparticle approach by combing \textit{ab initio} molecular dynamics and lattice dynamics simulations. Phonon lifetimes are extracted from the phonon quasiparticle calculations, and the phonon group velocities are computed from the anharmonic phonon dispersions, which in principle capture full anharmonicity. It is found that throughout the lowermost mantle, including the D" region, $κ_{lat}$ of MgPPv is ~25% larger than …
Importance of nonlinear long-range electron-phonon interaction for the carrier mobility of anharmonic halide perovskites
Universiteit Antwerpen（安特卫普大学）；Université catholique de Louvain（天主教鲁汶大学）；WEL Research Institute（WEL研究所）；University of Vienna（维也纳大学）；Alma Mater Studiorum - Università di Bologna（博洛尼亚大学）
Hybrid organolead perovskites (HOP) have started to establish themselves in the field of photovoltaics, mainly due to their great optoelectronic properties and steadily improving solar cell efficiency. Study of the lattice dynamics is key in understanding the electron-phonon interactions at play, responsible for such properties. Here, we investigate, via neutron and Raman spectroscopies, the optical phonon spectrum of four different HOP single crystals: MAPbBr$_3$, FAPbBr$_3$, MAPbI$_3$, and $α$-FAPbI$_3$. Low temperature spectra reveal weakly dispersive optical phonons, at energies as low as …
Despite their puzzling vibrational characteristics that include strong signatures of anharmonicity and thermal disorder already around room temperature, halide perovskites exhibit favorable optoelectronic properties for applications in photovoltaics and beyond. Whether these vibrational properties are advantageous or detrimental to their optoelectronic properties remains, however, an important open question. Here, this issue is addressed by investigation of the {finite-temperature optoelectronic properties} in the prototypical cubic CsPbBr$_3$, using first-principles molecular dynamics based o…
We investigate phonon transport in perovskite strontium titanate (SrTiO3) which is stable above its phase transition temperature (~105 K) by using first-principles molecular dynamics and anharmonic lattice dynamics. Unlike conventional ground-state-based perturbation methods that give imaginary phonon frequencies, the current calculation reproduces stable phonon dispersion relations observed in experiments. We find the contribution of optical phonons to overall lattice thermal conductivity is larger than 60%, markedly different from the usual picture with dominant contribution from acoustic ph…
In this paper we investigated the influence of the rare-earth ionic radii on the spin-phonon coupling in RE2NiMnO6 double perovskites by Raman spectroscopy. Spin-phonon in dense Nd2NiMnO6 and Gd2NiMnO6 ceramics were investigated by Raman spectroscopy at low temperatures. The magnitude of the coupling observed in comparison with other isostructural compounds shows that it is not influenced by the rare-earth ionic radius, as well as the deviation of the position of the stretching phonon in the ferromagnetic phase with relation to the anharmonic contributions follows a power law.
Organic-inorganic halide perovskites present a number of challenges for first-principles atomistic materials modelling. These `plastic crystals' feature dynamic processes across multiple length-scales and time-scales, which include: (i) transport of slow ions and fast electrons; (ii) highly anharmonic lattice dynamics with short phonon lifetimes; (iii) local symmetry breaking of the average crystallographic space group; (iv) strong relativistic (spin-orbit coupling) effects on the electronic band structure; (v) thermodynamic metastability and rapid chemical breakdown. These issues, which affec…
Naturals and synthetic perovskites are widely used functional materials thanks to their particular physical properties, such as superconductivity, ferroelectricity and photo-activity. Many of these properties are related to static or dynamic motion of octahedral units; Yet a full understanding of the relationships between perovskite crystal structure, chemical bonding and physical properties is currently missing. Several studies indicate the existence of dynamic disorder generated by anharmonic motion of octahedral units e.g. in halide perovskite structures. In this work, we derive all possibl…
The potential of lead-halide perovskites for realistic applications is currently hindered by their limited long-term stability under functional activation. While the role of lattice flexibility in the thermal response of perovskites has become increasingly evident, the description of thermally-induced distortions is still unclear. In this work, we provide a unified picture of thermal activation in CsPbBr3 across length scales, showing that lattice symmetry does not increase at high temperatures. We combine temperature-dependent XRD, Br K-edge XANES, ab initio MD simulations, and calculations o…
Second-order Raman and anharmonic lattice dynamics in lead-halide perovskites
Institute of Science and Technology Austria（科学技术奥地利研究所）；King Fahd University of Petroleum and Minerals（法赫德国王石油与矿产大学）；Interdisciplinary Research Center (IRC) for Advanced Materials, King Fahd University of Petroleum and Minerals（法赫德国王石油与矿产大学先进材料跨学科研究中心）；King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）；Center for Renewable Energy and Storage Technologies, Division of Physical Science and Engineering, King Abdullah University of Science and Technology（阿卜杜拉国王科技大学物理科学与工程学部可再生能源与储能技术中心）；Aarhus University（奥胡斯大学）
The impact of ordered vacancies on the dynamic stability of perovskites is investigated under the $\textit{ab initio}$ framework with a focus on cubic BaFeO$_{3}$ ($Pm\bar{3}m$) and vacancy-ordered monoclinic BaFeO$_{2.67}$ ($P2_{1}/m$). The harmonic approximation shows that both structures are dynamically unstable at 0 K. For the monoclinic structure, the instability is related to rotational distortions of the Fe coordination tetrahedra near the ordered vacancies. $\textit{Ab initio}$ molecular dynamics simulations in combination with the introduced structural descriptor demonstrate that both…
Halide perovskite (HP) semiconductors exhibit unique strong coupling between the electronic and structural dynamics. The high-temperature cubic phase of HPs is known to be entropically stabilized, with imaginary frequencies in the calculated phonon dispersion relation. Similar calculations, based on the static average crystal structure, predict a stable tetragonal phase with no imaginary modes. This work shows that in contrast to standard theory predictions, the room-temperature tetragonal phase of CH$_{3} $NH$_{3} $PbI$_{3}$ is strongly anharmonic. We use Raman polarization-orientation (PO) m…
The local crystal structures of many perovskite-structured materials deviate from the average space group symmetry. We demonstrate, from lattice-dynamics calculations based on quantum chemical force constants, that all the caesium-lead and caesium-tin halide perovskites exhibit vibrational instabilities associated with octahedral titling in their high-temperature cubic phase. Anharmonic double-well potentials are found for zone-boundary phonon modes in all compounds with barriers ranging from 108 to 512 meV. The well depth is correlated with the tolerance factor and the chemistry of the compos…
We predict high thermoelectric efficiency in the layered perovskite La$_2$Ti$_2$O$_7$, based on calculations (mostly ab-initio) of the electronic structure, transport coefficients, and thermal conductivity in a wide temperature range. The figure of merit $ZT$ computed with a temperature-dependent relaxation time increases monotonically from just above 1 at room temperature to over 2.5 at 1200 K, at an optimal carrier density of around 10$^{20}$ cm$^{-3}$. The Seebeck thermopower coefficient is between 200 and 300 $μ$V/K at optimal doping, but can reach nearly 1 mV/K at low doping. Much of the …
Two seemingly similar crystal structures of the low-temperature (~100 K) MAPbX$_3$ (X=I,Br,Cl) perovskites, but with different relative Methylammonium (MA) ordering, have appeared as representatives of this orthorhombic phase. Distinguishing them by X-ray diffraction experiments is difficult and conventional first-principles based molecular-dynamics approaches are often too computationally intensive to be feasible. Therefore, to determine the thermodynamically stable structure, we use a recently introduced on-the-fly Machine-Learning Force Field method, which reduces the computation time from …
Lead-halide perovskites are promising materials for opto-electronic applications. Recent reports indicated that their mechanical and electronic properties are strongly affected by the lattice vibrations. Herein we report far-infrared spectroscopy measurements of CH$_{3}$NH$_{3}$Pb(I/Br/Cl)$_{3}$ thin films and single crystals at room temperature and a detailed quantitative analysis of the spectra. We find strong broadening and anharmonicity of the lattice vibrations for all three halide perovskites, which indicates dynamic disorder of the lead-halide cage at room temperature. We determine the …
The phonon dispersion relations of crystal lattices can often be well-described with the harmonic approximation. However, when the potential energy landscape exhibits more anharmonicity, for instance, in case of a weakly bonded crystal or when the temperature is raised, the approximation fails to capture all crystal lattice dynamics properly. Phonon-phonon scattering mechanisms become important and limit the phonon lifetimes. We take a novel approach and simulate the phonon dispersion of a complex dynamic solid at elevated temperatures with Machine-Learning Force Fields of near-first-principle…
CsSnI3 is a promising eco-friendly solution for energy harvesting technologies. It exists at room temperature in either a black perovskite polymorph or a yellow 1D double-chain, which irreversibly deteriorates in the air. In this work, we unveil the relative thermodynamic stability between the two structures with a first-principles sampling of the CsSnI3 finite-temperature phase diagram, discovering how it is driven by anomalously large quantum and anharmonic ionic fluctuations. Thanks to a comprehensive treatment of anharmonicity, the simulations deliver a remarkable agreement with known expe…
Strong deviations in the finite temperature atomic structure of halide perovskites from their average geometry can have profound impacts on optoelectronic and other device-relevant properties. Detailed mechanistic understandings of these structural fluctuations and their consequences remain, however, limited by the experimental and theoretical challenges involved in characterizing strongly anharmonic vibrational characteristics and their impact on other properties. We overcome some of these challenges by a theoretical characterization of the vibrational interactions that occur among the atoms …
Inhomogeneous strain may develop in hybrid organic metal-halide perovskite thin films due to thermal expansion mismatch with a fabrication substrate, polycrystallinity or even light soaking. Measuring these spatially varying strains is difficult but of prime importance for understanding the effects on carrier mobility, non-radiative recombination, degradation and other optoelectronic properties. Local strain can be mapped using the shifts in vibrational frequencies using Raman or infrared microscopy. We use density functional theory to investigate the effect of uniaxial strain on the vibration…
Using finite-temperature phonon calculations and the Lyddane-Sachs-Teller relations, we calculate ab initio the static dielectric constants of 78 semiconducting oxides and fluorides with cubic perovskite structures at 1000 K. We first compare our method with experimental measurements, and we find that it succeeds in describing the temperature dependence and the relative ordering of the static dielectric constant $ε_{DC}$ in the series of oxides BaTiO$_{3}$, SrTiO$_{3}$, KTaO$_{3}$. We show that the effects of anharmonicity on the ion-clamped dielectric constant, on Born charges, and on phonon …
The low frequency lattice vibrations and relaxations are investigated in single crystals of the four 3D hybrid organolead perovskites, MAPbBr$_3$, FAPbBr$_3$, MAPbI$_3$, and $α$-FAPbI$_3$, at the Brillouin zone center using Raman and Brillouin scattering and at the zone boundary using inelastic neutron scattering. The temperature dependence of the PbX$_6$ lattice modes in the four compounds can be renormalized into universal curves, highlighting a common vibrational dynamics at the cubic to tetragonal transition. In particular, no soft vibration is observed excluding a displacive-like transiti…
