Low energy paths for octahedral tilting in inorganic halide perovskites

Instabilities relating to cooperative octahedral tilting is common in materials with perovskite structures, and in particular in the sub class of halide perovskites. In this work, the energetics of octahedral tilting in the inorganic metal halide perovskites CsPbI$_3$ and CsSnI$_3$ are investigated using first-principles density functional theory calculations. Several low energy paths between symmetry equivalent variants of the stable orthorhombic (\textit{Pnma}) perovskite variant are identified and investigated. The results are in favor of the presence of dynamic disorder in the octahedral tilting phase transitions of inorganic halide perovskites. In particular, one specific type of path, corresponding to an out-of-phase "tilt switch", is found to have significantly lower energy barrier than the others, which indicates the existence of a temperature range where the dynamic fluctuations of the octahedra follow only this type of path. This could produce a time averaged structure corresponding to the intermediate tetragonal (\textit{P4/mbm}) structure observed in experiments. Deficiencies of the commonly employed simple one-dimensional "double well" potentials in describing the dynamics of the octahedra are pointed out and discussed.Comment: Revised versio

Existence results for a contact problem with varying friction coefficient and nonlinear forces

We consider the rate-independent problem of a particle moving in a three - dimensional half space subject to a time-dependent nonlinear restoring force having a convex potential and to Coulomb friction along the flat boundary of the half space, where the friction coefficient may vary along the boundary. Our existence result allows for solutions that may switch arbitrarily often between unconstrained motion in the interior and contact where the solutions may switch between sticking and frictional sliding. However, our existence result is local and guarantees continuous solutions only as long as the convexity of the potential is strong enough to compensate the variation of the friction coefficient times the contact pressure. By simple examples we show that our sufficient conditions are also necessary. Our method is based on the energetic formulation of rate-independent systems as developed by Mielke and co-workers. We generalize the time-incremental minimization procedure of Mielke and Rossi for the present situation of a non-associative flow rule

Shakedown in elastic contact problems with Coulomb friction

AbstractElastic systems with frictional interfaces subjected to periodic loading are sometimes predicted to ‘shake down’ in the sense that frictional slip ceases after the first few loading cycles. The similarities in behaviour between such systems and monolithic bodies with elastic–plastic constitutive behaviour have prompted various authors to speculate that Melan’s theorem might apply to them – i.e., that the existence of a state of residual stress sufficient to prevent further slip is a sufficient condition for the system to shake down.In this paper, we prove this result for ‘complete’ contact problems in the discrete formulation (i) for systems with no coupling between relative tangential displacements at the interface and the corresponding normal contact tractions and (ii) for certain two-dimensional problems in which the friction coefficient at each node is less than a certain critical value. We also present counter-examples for all systems that do not fall into these categories, thus giving a definitive statement of the conditions under which Melan’s theorem can be used to predict whether such a system will shake down

Phase stability of Fe from first-principles: atomistic spin dynamics coupled with ab initio molecular dynamics simulations and thermodynamic integration

The calculation of free energies from first principles in materials is a formidable task which enables the prediction of phase stability with high accuracy; these calculations are complicated in magnetic materials by the interplay of electronic, magnetic, and vibrational degrees of freedom. In this work, we show the feasibility and accuracy of the calculation of phase stability in magnetic systems with ab initio methods and thermodynamic integration by sampling the magnetic and vibrational phase space with coupled atomistic spin dynamics-ab initio molecular dynamics (ASD-AIMD) simulations [Stockem et al., PRL 121, 125902 (2018)], where energies and interatomic forces are calculated with density functional theory (DFT). We employ the method to calculate the phase stability of Fe at ambient pressure from 800 K up to 1800 K. The Gibbs free energy difference between fcc and bcc Fe at zero pressure as a function of temperature is calculated carrying out thermodynamic integration over temperature on the energies at the DFT level from ASD-AIMD, using a reference free energy difference calculated in the paramagnetic state at temperatures much higher than the magnetic transition temperatures with thermodynamic integration over stress-strain variables with disordered local moment (DLM)-AIMD simulations. We show the importance of the magnetic ordering temperature of bcc Fe on the $\alpha$ to $\gamma$ structural transition temperature, whereas the $\gamma$ to $\delta$ transition is well reproduced independently of the exchange interactions. The Gibbs free energy difference between the two structures is within 5 meV/atom from the CALPHAD estimate, and both transition temperatures are reproduced within 150 K. The present work paves the way to free energy calculations in magnetic materials from first principles with accuracy in the order of 1 meV/atom

Ab initio Determination of Phase Stabilities of Dynamically Disordered Solids: rotational C2 disorder in Li2C2

The temperature-induced orthorhombic to cubic phase transition in Li2C2is a prototypical ex-ample of a solid to solid phase transformation between an ordered phase, which is well describedwithin the phonon theory, and a dynamically disordered phase with rotating molecules, for which the standard phonon theory is not applicable. The transformation in Li2C2 happens from a phase with directionally ordered C2 dimers to a structure, where they are dynamically disordered. We provide a description of this transition within the recently developed method (Klarbring et al.,Phys.Rev. Lett. 121, 225702 (2018)) employing ab initio molecular dynamics (AIMD) based stress-strain thermodynamic integration on a deformation path that connects the ordered and dynamically disordered phases. The free energy difference between the two phases is obtained. The entropy that stabilizes the dynamically disordered cubic phase is captured by the behavior of the stress on the deformation path

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 modelling 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 (CH$_3$NH$_3$PbBr$_3$) 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 CsPbI$_3$ 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.Comment: 10 figure

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

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-H-2 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 similar to 5 GPa, face-centered cubic (fcc) Na3NiH5 forms above 430 degrees C. Upon cooling, it undergoes a rapid and reversible phase transition at 330 degrees 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 NiH53-. 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 NiH53- 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](-).Funding Agencies|Swedish Research Council (VR)Swedish Research Council [2019-05551]; Swedish Government Strategic Research Area in Materials Science on Advanced Functional Materials at at Linkoping University (Faculty Grant SFO-Mat-LiU) [200900971]; Carl Tryggers Stiftelse (CTS) [16:198, 17:206]</p

Global and clustered approaches for stress constrained topology optimization and deactivation of design variables

Abstract We present a global (one constraint) version of the clustered approach previously developed for stress constraints, and also applied to fatigue constraints, in topology optimization. The global approach gives designs without large stress concentrations or geometric shapes that would cause stress singularities. For example, we solve the well known L-beam problem and obtain a radius at the internal corner. The main reason for using a global stress constraint in topology optimization is to reduce the computational cost that a high number of constraints impose. In this paper we compare the computational cost and the results obtained using a global stress constraint versus using a number of clustered stress constraints. We also present a method for deactivating those design variables that are not expected to change in the current iteration. The deactivation of design variables provides a considerable decrease of the computational cost and it is made in such a way that approximately the same final design is obtained as if all design variables are active. 2. Keywords: Topology optimization, Stress constraints, Global, Clustered, Deactivated variables Introduction In many industrial applications, the aim of structural optimization is to find the lightest design that meets the structural requirements. However, most commercial optimization software in industrial use are based on the traditional formulation of finding the stiffest structure for a prescribed amount of material: a formulation which does not necessarily yield a design that is feasible with respect to actual structural requirements, such as stress and fatigue. Furthermore, in many industrial applications, the stiffness does not necessarily have to be maximized and by allowing a slightly lower stiffness we might find a lighter and more mature design. The reason for using this stiffness based formulation is mostly computational efficiency: the optimization is driven by a global measure (compliance) and no extra (adjoint) system of equations needs to be solved in the sensitivity analysis. Stress constraints on the other hand give a much more expensive problem as stress is a local measure; i.e., a local (every stress evaluation point) quantity has to be constrained rather than a global, which increases the computational cost. However, minimizing the mass subjected to stress constraints has the potential of yielding a more mature and useful final design. Stress constraints have been discussed since the very first papers on topology optimization: Bendsøe and Kikuchi The clustered approach developed by Holmberg et al