Low-energy Polymorphs Research Articles

Theoretical approach to ferroelectricity in hafnia and related materials

Hafnia ferroelectrics combine technological promise and remarkable behaviors. Their peculiarity stems from the many active extrinsic mechanisms that contribute to their properties and from a continuously growing number of novel intrinsic features. Partly because of their unconventional nature, basic questions about these materials remain open and one may wonder about the pertinence of some frequent theoretical assumptions. Here, aided by first-principles simulations, we show that, by adopting an original high-symmetry reference phase as the starting point of the analysis, we can develop a mathematically simple and physically transparent treatment of the ferroelectric state of hafnia. The proposed approach describes hafnia as a uniaxial ferroic, as suggested by recent studies of (woken-up) samples with well-developed polarization. Also, it is compatible with the occurrence of polar soft modes and proper ferroelectric order. Further, our theory provides a straightforward and unified description of all low-energy polymorphs, shedding light on old questions such as the prevalence of the monoclinic ground state, pointing at exciting possibilities like an antiferroelastic behavior, and facilitating the future development of perturbative theories, from Landau to second-principles potentials. Our work thus yields a deeper understanding of hafnia ferroelectrics, improving our ability to optimize their properties and induce new ones.

Physics-Guided Descriptors for Prediction of Structural Polymorphs.

We develop a method combining machine learning (ML) and density functional theory (DFT) to predict low-energy polymorphs by introducing physics-guided descriptors based on structural distortion modes. We systematically generate crystal structures utilizing the distortion modes and compute their energies with single-point DFT calculations. We then train a ML model to identify low-energy configurations on the material’s high-dimensional potential energy surface. Here, we use BiFeO3 as a case study and explore its phase space by tuning the amplitudes of linear combinations of a finite set of distinct distortion modes. Our procedure is validated by rediscovering several known metastable phases of BiFeO3 with complex crystal structures, and its efficiency is proved by identifying 21 new low-energy polymorphs. This approach proposes a new avenue toward accelerating the prediction of low-energy polymorphs in solid-state materials.

How many more polymorphs of ROY remain undiscovered.

With 12 crystal forms, 5-methyl-2-[(2-nitrophenyl)amino]-3-thiophenecabonitrile (a.k.a. ROY) holds the current record for the largest number of fully characterized organic crystal polymorphs. Four of these polymorph structures have been reported since 2019, raising the question of how many more ROY polymorphs await future discovery. Employing crystal structure prediction and accurate energy rankings derived from conformational energy-corrected density functional theory, this study presents the first crystal energy landscape for ROY that agrees well with experiment. The lattice energies suggest that the seven most stable ROY polymorphs (and nine of the twelve lowest-energy forms) on the Z′ = 1 landscape have already been discovered experimentally. Discovering any new polymorphs at ambient pressure will likely require specialized crystallization techniques capable of trapping metastable forms. At pressures above 10 GPa, however, a new crystal form is predicted to become enthalpically more stable than all known polymorphs, suggesting that further high-pressure experiments on ROY may be warranted. This work highlights the value of high-accuracy crystal structure prediction for solid-form screening and demonstrates how pragmatic conformational energy corrections can overcome the limitations of conventional density functionals for conformational polymorphs.

Accelerating cathode material discovery through ab initio random structure searching

The choice of cathode material in Li-ion batteries underpins their overall performance. Discovering new cathode materials is a slow process, and all major commercial cathode materials are still based on those identified in the 1990s. Discovery of materials using high-throughput calculations has attracted great research interest; however, reliance on databases of existing materials begs the question of whether these approaches are applicable for finding truly novel materials. In this work, we demonstrate that ab initio random structure searching (AIRSS), a first-principles structure prediction method that does not rely on any pre-existing data, can locate low energy structures of complex cathode materials efficiently based only on chemical composition. We use AIRSS to explore three Fe-containing polyanion compounds as low-cost cathodes. Using known quaternary LiFePO4 and quinary LiFeSO4F cathodes as examples, we easily reproduce the known polymorphs, in addition to predicting other, hitherto unknown, low energy polymorphs and even finding a new polymorph of LiFeSO4F that is more stable than the known ones. We then explore the phase space for Fe-containing fluoroxalates, predicting a range of redox-active phases that are yet to be experimentally synthesized, demonstrating the suitability of AIRSS as a tool for accelerating the discovery of novel cathode materials.

Crystal structure prediction of magnetic materials

We present a methodology to predict magnetic systems using ab initio methods. By employing crystal structure method and spin-polarized calculations, we explore the relation between crystalline structures and their magnetic properties. In this work, testbed cases of transition metal alloys (FeCr, FeMn, FeCo and FeNi) are study in the ferromagnetic case. We find soft-magnetic properties for FeCr, FeMn while for FeCo and FeNi hard-magnetic are predicted. In particular, for the family of FeNi, a candidate structure with energy lower than the tetrataenite was found. The structure has a saturation magnetization (Ms) of 1.2 MA m−1, magnetic anisotropy energy (MAE) above 1200 kJ m−3 and hardness value close to 1. Theoretically, this system made of abundant elements could be the right candidate for permanent magnet applications. Comparing with the state-of-the-art (Nd2Fe14B) hard-magnet, (Ms of 1.28 MA m−1 and MAE of 4900 kJ m−3) is appealing to explore this low energy polymorph of FeNi further. Considering the relatively limited number of magnets, predicting a new system may open routes for free rare-earth magnets. Furthermore, the use of the computational algorithm as the one presented in this work, hold promises in this field for which in near future improvements will allow to study numerous complex systems, larger simulations cells and tackled long-range antiferromagnetic cases.

Lowest-Energy Crystalline Polymorphs of P3HT

We systematically study low-energy crystalline polymorphs of the archetypal conjugated polymer, regioregular poly-3-hexylthiophene (rr-P3HT) using the best available density functional theory methods benchmarked against the ab initio coupled cluster method. A comprehensive conformational search is performed for two-dimensional π-stacks being the most rigid structural unit of bulk P3HT. We have identified a number of nearly isoenergetic polymorphs below the energy level of room-temperature amorphous structures and well below the energy of optimized best-fit experimental models. Classical molecular dynamics simulations show that these crystals retain their structure at least at 200 K. At room temperature, although the conjugated backbone of the π-stack remains ordered, aliphatic side chains are melted, transforming from low-energy folded conformations to high-entropy fully unfolded structures. Our study shows that P3HT is a statistically frustrated system with multiple competing interactions, which complica...

Polymorphism in elemental silicon: Probabilistic interpretation of the realizability of metastable structures

With few systems of technological interest having been studied as extensively as elemental silicon, there currently exists a wide disparity between the number of predicted low-energy silicon polymorphs and those, which have been experimentally realized as metastable at ambient conditions. We put forward an explanation for this disparity wherein the likelihood of formation of a given polymorph under near-equilibrium conditions can be estimated on the basis of mean field isothermal-isobaric (N, p, T) ensemble statistics. The probability that a polymorph will be experimentally realized is shown to depend upon both the hypervolume of that structure's potential energy basin of attraction and a Boltzmann factor weight containing the polymorph's potential enthalpy per particle. Both attributes are calculated using density functional theory relaxations of randomly generated initial structures. We find that the metastable polymorphism displayed by silicon can be accounted for using this framework to the exclusion of a very large number of other low-energy structures.

Cp-Graphyne: A Low-Energy Graphyne Polymorph with Double Distorted Dirac Points.

In the present investigation, we have proposed a novel form of two-dimensional (2D) carbon allotropes with the aid of first-principle density functional theory-based calculations. The carbon polymorph is mainly composed of carbon pentagons (cp) and acetylenic linkers and hence named cp-graphyne. This 2D material is energetically more preferable than the rest of the semimetals of graphyne family, including graphdiyne monolayer. Close inspection of lattice dynamics and thermal and mechanical properties demonstrates the excellent dynamic, thermal, and mechanical stabilities of cp-graphyne. Interestingly, cp-graphyne exhibits a semimetallic nature and possesses double distorted Dirac points in the electronic band spectrum. The Fermi velocities (vf) of cp-graphyne are highly anisotropic and are predicted to be in the range of 1.50–8.20 × 105 m/s. Furthermore, the analysis of structural and electronic properties of the cp-graphyne bilayer discloses the presence of self-doped Dirac-like points nearer to the Fermi level in the electronic spectrum.

Bond-order reactive force fields for molecular dynamics simulations of crystalline silica

This paper investigates the applicability of the bond-order, variable-charge (BOVC) force fields of the Charge-Optimized Many-Body (COMB10), ReaxFFSiOH2O, and ReaxFFSiOGSI, for molecular dynamics (MD) simulations of crystalline SiO2. The calculated lattice constants and densities of the four SiO2 polymorphs, quartz, cristobalite, coesite, and stishovite, are compared to experimental values. Additionally, the calculated pair distribution and bond-angle distribution functions and the α–β transition for quartz, the most stable low-energy polymorph, are compared to experimental results. The simulations with the COMB10 force field accurately predict the properties of the SiO2 polymorphs, except the α-cristobalite, and the quartz α–β transition. The results with ReaxFFSiOH2O and ReaxFFSiOGSI accurately predict the properties of the SiO2 polymorphs, except the stishovite, but those with ReaxFFSiOH2O inaccurately predict the quartz α–β transition.

Low-energy tetrahedral polymorphs of carbon, silicon, and germanium

Searches for low-energy tetrahedral polymorphs of carbon and silicon have been performed using density functional theory computations and the ab initio random structure searching approach. Several of the hypothetical phases obtained in our searches have enthalpies that are lower or comparable to those of other polymorphs of group 14 elements that have either been experimentally synthesized or recently proposed as the structure of unknown phases obtained in experiments, and should thus be considered as particularly interesting candidates. A structure of $Pbam$ symmetry with 24 atoms in the unit cell was found to be a low-energy, low-density metastable polymorph in carbon, silicon, and germanium. In silicon, $Pbam$ is found to have a direct band gap at the zone center with an estimated value of 1.4 eV, which suggests applications as a photovoltaic material. We have also found a low-energy chiral framework structure of $P{4}_{1}{2}_{1}2$ symmetry with 20 atoms per cell containing fivefold spirals of atoms, whose projected topology is that of the so-called Cairo-type two-dimensional pentagonal tiling. We suggest that $P{4}_{1}{2}_{1}2$ is a likely candidate for the structure of the unknown phase XIII of silicon. We discuss $Pbam$ and $P{4}_{1}{2}_{1}2$ in detail, contrasting their energetics and structures with those of other group 14 elements, particularly the recently proposed $P{4}_{2}/ncm$ structure, for which we also provide a detailed interpretation as a network of tilted diamondlike tetrahedra.

Insights into the phase diagram of bismuth ferrite from quasiharmonic free-energy calculations

We have used first-principles methods to investigate the phase diagram of multiferroic bismuth ferrite (BiFeO${}_{3}$ or BFO), revealing the energetic and vibrational features that control the occurrence of various relevant structures. More precisely, we have studied the relative stability of four low-energy BFO polymorphs by computing their free energies within the quasiharmonic approximation, introducing a practical scheme that allows us to account for the main effects of spin disorder. As expected, we find that the ferroelectric ground state of the material (with $R3c$ space group) transforms into an orthorhombic paraelectric phase ($Pnma$) upon heating. We show that this transition is not significantly affected by magnetic disorder, and that the occurrence of the $Pnma$ structure relies on its being vibrationally (although not elastically) softer than the $R3c$ phase. We also investigate a representative member of the family of nanotwinned polymorphs recently predicted for BFO [S. Prosandeev et al., Adv. Funct. Mater. 23, 234 (2013)] and discuss their possible stabilization at the boundaries separating the $R3c$ and $Pnma$ regions in the corresponding pressure-temperature phase diagram. Finally, we elucidate the intriguing case of the so-called supertetragonal phases of BFO: Our results explain why such structures have never been observed in the bulk material, despite their being stable polymorphs of very low energy. Quantitative comparison with experiment is provided whenever possible, and the relative importance of various physical effects (zero-point motion, spin fluctuations, thermal expansion) and technical features (employed exchange-correlation energy density functional) is discussed. Our work attests the validity and usefulness of the quasiharmonic scheme to investigate the phase diagram of this complex oxide, and prospective applications are discussed.

Structural richness of ionic binary materials: An exploration of the energy landscape of magnesium oxide

We search for polymorphs of magnesium oxide (MgO) close in energy to the rocksalt global minimum by using variants of the basin hopping approach. Our exploration clearly demonstrates that the energy landscape of this nominally octahedrally coordinated, densely packed solid is much more complicated than suggested by previous work. Specifically, we find that MgO has a dense spectrum of as yet undiscovered low-energy polymorphs, many of which have a much lower density than the rocksalt structure (as also recently shown for tetrahedrally coordinated binary solids (e.g., ZnO) [Phys. Rev. Lett. 104, 175503 (2010)]). Unlike in the case of tetrahedrally coordinated materials, we further find low-energy crystal structures with four-, five-, or six-coordinated atoms. Strikingly, some of these structures also have pores that are arguably large enough for small molecular species to enter, while others are found to be quasi-amorphous. We also discuss the problem of searching for systems that are currently too large to study by basin hopping (or similar approaches) in a tractable fashion, and the implications of our findings for other solids.

Apparent Scarcity of Low-Density Polymorphs of Inorganic Solids

For most inorganic solids, very few dense polymorphs and no low-density polymorphs are observed. Taking a wide range of tetrahedrally-coordinated binary solids (e.g., ZnO, GaN) as a prototypical system, we show that the apparent scarcity of low- density polymorphs is not due to significant structural or energetic limitations. Using databases of periodic networks as sources of novel crystal structures, followed by ab initio energy minimization, we predict a dense spectrum of low-density low-energy polymorphs. The diverse range of materials considered indicates that this is likely to be a general phenomenon.

The Challenges of Developing an API Crystallization Process for a Complex Polymorphic and Highly Solvating System. Part I

Developing a robust crystallization process for an active pharmaceutical ingredient (API) molecule with a complex polymorphic profile can present a significant challenge. The presented case illustrates an unusual crystallization development problem where a polymorphically complex API has the additional obstacles of poor solubility in standard crystallization solvents as well as a propensity for forming solvates. After early polymorph screening of this candidate highlighted the potential for a complex solid form profile, a variety of experimental approaches was utilized to determine the low-energy polymorph and characterize the various solvates formed. Characterization of the API crystallization process identified a critical solvent composition range for the transformation from a metastable solvate form to the desired polymorph. During subsequent crystallization process development studies, a new lower-energy polymorph was discovered. Examination of the crystal structures led to a rationale for the formati...

Isomorphism of Anhydrous Tetrahedral Halides and Silicon Chalcogenides: Energy Landscape of Crystalline BeF2, BeCl2, SiO2, and SiS2

We employ periodic density functional theory calculations to compare the structural chemistry of silicon chalcogenides (silica, silicon sulfide) and anhydrous tetrahedral halides (beryllium fluoride, beryllium chloride). Despite the different formal oxidation states of the elements involved, the divalent halides are known experimentally to form crystal structures similar to known SiX2 frameworks; the rich polymorphic chemistry of SiO2 is however not matched by divalent halides, for which a very limited number of polymorphs are currently known. The calculated energy landscapes yield a quantitative match between the relative polymorphic stability in the SiO2/BeF2 pair, and a semiquantitative match for the SiS2/BeCl2 pair. The experimentally observed polymorphs are found to lie lowest in energy for each composition studied. For the two BeX2 compounds studied, polymorphs not yet synthesized are predicted to lie very low in energy, either slightly above or even in between the energy of the experimentally observed polymorphs. The experimental lack of polymorphism for tetrahedral halide materials thus does not appear to stem from a lack of low-energy polymorphs but more likely is the result of a lack of experimental exploration. Our calculations further indicate that the rich polymorphic chemistry of SiO2 can be potentially matched, if not extended, by BeF2, provided that milder synthetic conditions similar to those employed in zeolite synthesis are developed for BeF2. Finally, our work demonstrates that both classes of materials show the same behavior upon replacement of the 2p anion with the heavier 3p anion from the same group; the thermodynamic preference shifts from structures with large rings to structures with larger fractions of small two and three membered rings.

A potentiometric titration method for the crystallization of drug-like organic molecules

It is generally accepted, that crystalline solids representing a low energy polymorph should be selected for development of oral dosage forms. As a consequence, efficient and robust procedures are needed at an early stage during drug discovery to prepare crystals from drug-like organic molecules. In contrast to the use of supersaturated solutions, we present a potentiometric crystallization procedure where saturated solutions are prepared in a controlled manner by pH-titration. Crystallization is carried out under defined conditions using the sample concentration and experimental p K a values as input parameters. Crystals of high quality were obtained for 11 drugs selected to demonstrate the efficiency and applicability of the new method. Technical improvements are suggested to overcome practical limitations and to enhance the possibility of obtaining crystals from molecules in their uncharged form.

Molecular Pair Analysis: CH⋅⋅⋅F Interactions in the Crystal Structure of Fluorobenzene? And Related Matters

The crystal structure of fluorobenzene is compared with isomorphous crystal structures of molecules of roughly similar shape. The lowest-energy fluorobenzene dimers are identified by theoretical calculations. Molecular pair analysis of the crystal structure of fluorobenzene and of an isomorphous virtual low-energy polymorph of benzene suggests that the important intermolecular interactions in the two structures are closely similar. In particular, the intermolecular C-H...F interactions in the fluorobenzene crystal have approximately the same structure-directing ability and influence on the intermolecular energy as the corresponding C-H...H interactions in benzene. Molecular pair analysis of the isomorphous crystal structures of benzonitrile, alloxan, and cyclopentene-1,2,3-trione indicates that essentially the same crystal structure can be adopted with quite different patterns of pair energies and atom-atom interactions. The question as to whether the packing radius of organic fluorine is larger or smaller than that of hydrogen, is addressed, but not answered.

Polymorph Generation in Capillary Spaces: The Preparation and Structural Analysis of a Metastable Polymorph of Nabumetone

Crystallization studies of nabumetone (4-(6-methoxy-2-naphthalenyl)-2-butanone) performed in capillary tubes yielded a metastable polymorph. The single-crystal X-ray structure of this high-energy form is presented and compared to the structure of the known low-energy form. The metastable form of nabumetone readily converts to the low-energy form in the solid state upon grinding or seeding with the low-energy polymorph. The instability of the metastable form is believed to be due to the presence of weaker C−H···O interactions when compared to the thermodynamically more stable form.

A Drastic Influence of Point Defects on Phase Stability in MnO2

ABSTRACTDespite its importance as a cathode material in primary alkaline batteries, the structure of γ-MnO2 is still not well determined. Different authors have suggested that a number of different polymorphs, as well as highly disordered phases, may be present in γ-MnO2. The origin of this structural complexity remains largely unexplained. In this paper we use first principles methods to explore the energetics of the MnO2 system. We find a number of low-energy polymorphs with similar energies, suggesting that relatively small changes in the energetics might influence the stable phases. Using nonzero-temperature models we demonstrate that thermal disorder is not the cause of structural disorder in these materials. However, we then show that point (Ruetschi) defects, even in surprisingly low concentrations, have a dramatic effect on the phase stability. We propose that Ruetschi defects may be the key to some of the structural complexity in γ-MnO2, and that any realistic structural study must take them into account.