Low-energy Phase Research Articles

Structure prediction of stable sodium germanides at 0 and 10 GPa

In this paper we used random structure searching (AIRSS) to carry out a systematic search for crystalline Na-Ge materials at both 0 and 10 GPa. The high-throughput structural relaxations were accelerated using a machine-learned interatomic potential (MLIP) fit to density-functional theory (DFT) reference data, allowing ∼1.5 million structures to be relaxed. At ambient conditions we predict three new Zintl phases, Na3Ge2,Na2Ge, and Na9Ge4, to be stable and a number of Ge-rich layered structures to lie in close proximity to the convex hull. The known NaδGe34 clathrate and Na4Ge13 host-guest structures are found to be relatively stabilized at higher temperature by vibrational contributions to the free energy. Overall, the low-energy phases exhibit exceptional structural diversity, with the expected mixture of covalent and ionic bonding confirmed using the electron-localization function (ELF). The local Ge structural motifs present at each composition were determined using smooth overlap of atomic positions (SOAP) descriptors and the Ge-K edge was simulated for representatives of each motif, providing a direct link to experimental x-ray absorption spectroscopy (XAS). Two Ge-rich phases are predicted to be stable at 10 GPa; NaGe3 and NaGe2 have simple kagome and simple hexagonal Ge lattices respectively with Na contained in the pores. NaGe3 is isostructural with the MgB3 and MgSi3 family of kagome superconductors and remains dynamically stable at 0 GPa. Removing the Na from NaGe2 results in the hexagonal lonsdalite Ge allotrope, which has a direct band gap. Published by the American Physical Society 2024

Chemical profile and biotechnological potential larvicidal of a nanoemulsion (o/w) of the essential oil of Salvia officinalis L

This study aims to evaluate the chemical profile and biotechnological larvicidal potential of the nanoemulsion of the essential oil of Salvia officinalis L. The leaves of the plant were collected in São Luís, MA, from January to May 2021. The essential oil was extracted by hydrodistillation at 100°C for 3h. Chemical characterization was obtained by GC-MS. The oil-in-water nanoemulsion was formulated by the low-energy phase inversion method and subjected to thermodynamic stability tests. Antioxidant activity is performed by the spectrophotometric method of scavenging hydroxyl radicals from salicylic acid. For larvicidal activity, Aedes aegypti larvae were subjected to EO solutions and nanoemulsions in concentrations (10-100 mg L-1), larval mortality was evaluated, and the LC50 was determined by the Probit method. The majority compounds of the EO were: eucalyptol with 65.14%, camphor (30.63%), and α-Terpineol (1.53%). The formulations were characterized as nanoemulsions with a droplet size <200 nm. The PDI was <0.200, indicating a narrow size distribution. The antioxidant activity exhibited EC50 of 136.29 mg L-1 and 51.59 mg L-1. The nanoemulsion with larvicidal potential showed an LC50 of 71.17 mg L-1. The nanoemulsion showed bioactive potential for larvicidal action, which may be related to the presence of its chemical compounds, and its use is encouraged in the fight against Aedes aegypti.

Research on Phase Change Cold Storage Materials and Innovative Applications in Air Conditioning Systems

Phase change cold storage materials are functional materials that rely on the latent heat of phase change to absorb and store cold energy. They have significant advantages in slight temperature differences, cold storage, and heat exchange. Based on the research status of phase change cold storage materials and their application in air conditioning systems in recent years, this paper provides an overview of the materials and their enhanced research progress. It summarizes the types of phase change cold storage air conditioning systems, optimization schemes, and system applications. This paper also identifies the current issues in phase change cold storage air conditioning and discusses the development trends in cold storage materials and air conditioning systems. It anticipates that future advancements will focus on composite phase change cold storage materials and low-energy consumption intelligent phase change cold storage air conditioning systems in steam compression using spherical capsules and concave–convex plate PCM.

Facile Coordination Transitions in AgCrX2 (X = S, Se): Unprecedented Electrostrain, Negative Piezoelectricity and Thermal Expansion.

The coefficients of piezoelectricity and thermal expansion are generally positive due to the bond anharmonicity. For converse piezoelectricity, the electrostrain obtained in prevalent ceramics is only around 1%. Here we propose that the coordination transition of metal cations may make a paradigm shift. Through first-principles calculations, we predict a series of low-energy phases with distinct coordinations for Ag ions in superionic conductor AgCrX2 (X = S, Se), including ferroelectric and nonpolar phases with distinct interlayer distances. The mobile feature of Ag ions, which can be attributed to its complex coordination chemistry, can facilitate transformation between various coordination phases. Such facile transitions with ultralow barriers can be driven by applying either pressure, an electric field, or a change in temperature, giving rise to various exotic effects, including electrostrain, negative piezoelectricity, and negative thermal expansion. All with unprecedented giant constants, those mechanisms stem from the coordination transitions, distinct from the weak linear effects in previous reports.

Scale transformations in model exchange potentials in low energy electron-atom scattering

Model exchange potentials are particularly interesting to account for the indistinguishability between the projectile and target electrons in electron-atom scattering in vacuo and plasma environments. It is well known that their performance is pretty satisfactory in the high energies but also that discrepancies from the results obtained with exact exchange are found toward the zero energy limit. In this article, we examine how well established model exchange potentials based on the free electron gas approach compare to phase shifts calculated considering exchange in exact form. In particular, we show that the Hara and the semiclassical exchange potentials are able to reproduce reference low energy phase shifts through a simple scale transformation, in opposition to the previous approaches where energy dependent corrections to the local momentum were adopted. We provide the scale factors and phase shifts for electron scattering by He, Ne and Ar atoms for k< 1,0 a0−1. Such scaling factors can be determined reproducing the scattering length and the number of s-wave bound states from exact exchange calculations. We also show that the scaling procedure works for electronic densities that present the physically correct asymptotic behavior. The present results are important to the research field, since they form the basis to construction of scattering models based on optical potential approaches.

Cooperative dislocations for pressure-dependent sequential deformation of multi-principal element alloys under shock loading

Multi-principal element alloys (MPEAs) are promising materials for structural applications under extreme conditions. Their outstanding mechanical properties are closely related to the activation of multiple deformation modes of dislocation gliding, twinning, and phase transformation that appear in sequence during deformation at low temperatures, high pressures, or high strain rates. However, the inherent correlations among these deformation modes and, thus, underlying deformation mechanisms of MPEAs remain largely unknown. We report soft-recovery plate impact experiments of face-centered-cubic (FCC) CrCoNi MPEAs, demonstrating pressure-dependent deformation modes from low-pressure stacking faults to medium-pressure twinning and high-pressure FCC to hexagonal-close-packed (HCP) phase transformation. Atomic-scale characterizations unveil that the sequential deformation is manipulated by the cooperation of 90° and 30° Shockley partial dislocations at deformation fronts, which is facilitated by low stacking fault energy and pressure-dependent phase stability of the MPEAs. Moreover, the cooperative dislocation behavior can also be observed at twin fronts of shock-loaded CrMnFeCoNi MPEA, validating the universality of the cooperative deformation mode in FCC alloys with a low stacking fault energy. Theoretical analyses suggest that the distinctive cooperative dislocation behavior results in the self-compensation of dislocation strain fields and the minimization of interfacial elastic energy at incoherent twin and FCC/HCP interfaces.

Strain-Phonon Cooperation as a Necessary Ingredient to Understand the Jahn-Teller Effect in Solids.

Spatial degeneracy is the cause of the complex electronic, geometrical, and magnetic structures found in a number of materials whose more representative example is KCuF3. In the literature the properties of this lattice are usually explained through the Kugel--Khomskii model, based on superexchange interactions. Here we provide rigorous theoretical and computational arguments against this view proving that structural and magnetic properties essentially arise from electron-vibration (vibronic) interactions. Moreover, based on the work of Öpik and Pryce, we show that the coupling between lattice (homogeneous strain) and motif (phonons) distortions is essential to understand the main stable configurations of the lattice. Using this information, we predict a new low-energy phase in KCuF3 that could strongly alter its properties and provide guidance on how to stabilize it through strain engineering.

Enhancing strength-ductility properties of immiscible W–Cu composite by creating low-energy phase interfaces

The immiscible bimetallic composites play an important role in civilian industries and aerospace fields owing to their integrated mechanical and physical properties. However, metallic composites of immiscible constituents suffer from one critical drawback of weak interface bonding, which makes the composites particularly vulnerable at elevated service temperatures. Here we proposed a novel strategy to resolve the challenge by creating low-energy phase interfaces in a typical immiscible bimetallic W–Cu composite. This was achieved by in-situ reactions of WO3 and CuO with WC, which acts in a dual function as the reducing agent for the reactions and an interface forming agent. The sintered W-WC-Cu composite possessed a significant number of low-energy WC/W and WC/Cu interfaces and exhibited a compressive strength of 609 MPa and a compressive ductility of 22.6 % at 600 °C, which ranks among the highest in similar composites. The characteristics of WC/W and WC/Cu interfaces and their effects on the mechanical behavior of the composite were demonstrated by the timely and atomic-resolved high-temperature mechanical investigations. The introduced stable interfaces were also found to induce [1‾ 11]BCC→ [011]FCC phase transformation of W as another mechanism of plastic deformation in addition to dislocation activities in W and Cu. This study provides a new approach to greatly enhance the mechanical properties of the immiscible metallic composites.

SPIRAL2 commissioning and operations

The SPIRAL2 linac is now successfully commissioned; H+, 4He2+, D+ and 18O6+ have been accelerated up to nominal parameters and 18O7+ and 40Ar14+ beams have been also accelerated up to 7 MeV/A. The main steps with 5 mA H+, D+ beams and with 0.6 mA 18O6+ are described. The general results of the commissioning of the RF, cryogenic and diagnostics systems, as well as the preliminary results of the first experiments on NFS are presented. In addition of an improvement of the matching to the linac, the tuning procedures of the 3 Medium Energy Beam Transport (MEBT) rebunchers and 26 linac SC cavities were progressively improved to reach the nominal parameters in operation, starting from the classical “signature matching method”. The different cavity tuning methods developed to take into account our particular situation (very low energy and large phase extension) are described. The tools developed for an efficient linac tuning in operation, e.g. beam energy and intensity changes are also discussed.

Application Prospect of Carbon Dioxide Hydrogenation to Methanol Technology in the New Electric Power Systems

The new electric power systems based on new energy is a power system that is supported by source-grid-load-storage interaction and multi-energy complementarity, in order to reduce the carbon emission level of the new electric power systems, it is necessary to change the existing energy structure of the system through different energy carriers. Through technology comparison and analysis, seawater in-situ electrolysis hydrogen production technology can make full use of offshore renewable energy, which can effectively reduce the production cost of hydrogen production by electrolysis. With the development and industrial application of the third-generation low-energy phase change absorber, the technology of carbon dioxide capture by phase change solvent has great application prospects. The industrial application of carbon dioxide hydrogenation to methanol can rely on the existing mature C1 chemical system, and the new carbon dioxide hydrogenation to methanol device can improve the effective utilization rate of carbon dioxide and reduce the emission of tail gas. On this basis, the application scheme of carbon dioxide hydrogenation to methanol technology in the new power system is proposed: centered on the power grid, renewable energy is used to generate electricity, and part of the electricity is sent to the grid; part of the electricity is sent to the seawater in-situ electrolysis hydrogen production unit to produce hydrogen; the main product hydrogen is stored in the hydrogen storage equipment, and the by-product oxygen is used comprehensively; the carbon dioxide generated in the process of fossil fuel power generation is captured by phase change solvent, and then the new carbon dioxide hydrogenation to methanol device is used to synthesize carbon dioxide and hydrogen into methanol under the action of catalyst, part of the methanol is converted into hydrogen by cracking and stored, and the other part of methanol is directly used as the fuel of internal combustion power locomotives, when the power output of the grid is insufficient, methanol can be used as fuel for internal combustion generators, which are used to generate electricity and sent to the grid, and the stored hydrogen can also be used as fuel for hydrogen fuel cells, which are used to generate electricity and sent to the grid.

Structural mode coupling in perovskite oxides using hypothesis-driven active learning

Finding the ground-state structure with minimum energy is paramount to designing any material. In ABO3-type perovskite oxides with Pnma symmetry, the lowest energy phase is driven by an inherent trilinear coupling between the two primary order parameters such as rotation and tilt with antiferroelectric displacement of the A-site cations as established via hybrid improper ferroelectric mechanism. Conventionally, finding the relevant mode coupling driving phase transition requires performing first-principles calculations which is computationally time-consuming as well as expensive. It involves following an intuitive iterative hit and trial method of (a) adding two or multiple mode vectors, followed by (b) evaluating which combination would lead to the ground-state energy. In this study, we show how a hypothesis-driven active learning framework can identify suitable mode couplings within the Landau free energy expansion with minimal information on amplitudes of modes for a series of double perovskite oxides with A-site layered, columnar and rocksalt ordering. This scheme is expected to be applicable universally for understanding atomistic mechanisms derived from various structural mode couplings behind functionalities, for e.g. polarization, magnetization and metal–insulator transitions.

Melting-free integrated photonic memory with layered polymorphs

Abstract Chalcogenide-based nonvolatile phase change materials (PCMs) have a long history of usage, from bulk disk memory to all-optic neuromorphic computing circuits. Being able to perform uniform phase transitions over a subwavelength scale makes PCMs particularly suitable for photonic applications. For switching between nonvolatile states, the conventional chalcogenide phase change materials are brought to a melting temperature to break the covalent bonds. The cooling rate determines the final state. Reversible polymorphic layered materials provide an alternative atomic transition mechanism for low-energy electronic (small domain size) and photonic nonvolatile memories (which require a large effective tuning area). The small energy barrier of breaking van der Waals force facilitates low energy, fast-reset, and melting-free phase transitions, which reduces the chance of element segregation-associated device failure. The search for such material families starts with polymorphic In2Se3, which has two layered structures that are topologically similar and stable at room temperature. In this perspective, we first review the history of different memory schemes, compare the thermal dynamics of phase transitions in amorphous-crystalline and In2Se3, detail the device implementations for all-optical memory, and discuss the challenges and opportunities associated with polymorphic memory.

Quartz Grain Microtextures in the Paleogene Sosnov Formation: Implications for Sediment Provenance in the Eastern Russian Platform

The purpose of the research. The chief task of the research is to examine the microtextures of quartz grains in the Paleogene Sosnov Formation, which is a sedimentary unit located in the Ulyanovsk-Syzran Volga Region of the Russian Platform. By examining the microtextures, which include mechanical, chemical and mechanical/chemical features, it becomes possible to find out the mechanisms by which grains were transported and subsequently modified. The relevance of the research. The relevance of this research lies in the fact that the analysis of quartz grain microtextures provides valuable insights into sediment provenance of sedimentary deposits is crucial for reconstructing past geological environments and unraveling depositional histories. Research methodology. Twenty quartz grains were collected from sands of the Paleogene Sosnovka Formation, exposed by the Eastern-Tashlinsky and the Kuchurovsky quarries to a depth of 5 and 7.5 m, respectively. The research methodology involved scanning electron microscopy (SEM) to investigate the microtextures of quartz grains. Results and conclusions. The study reveals 19 microtextures types, which were categorized into mechanical, chemical, and combined mechanical/chemical microtextures. An analysis of SEM indicated that chemical microtextures are present in the Paleogene Sosnov Formation, which made it possible to suggest that the sands passed through a low-energy phase during their transition. The data obtained enables us to reconstruct the diverse depositional paleoenvironments, including eolian, subaqueous, mixed subaqueous-eolian, and pedological settings.

Strain-Induced Structural Phase Transitions in Epitaxial (001) BiCoO3 Films: A First-Principles Study.

We have simulated BiCoO3 films epitaxially grown along (001) direction with density functional theory computations. Leading candidates for the lowest-energy phases have been identified. The tensile strains induce magnetic phase transition in the ground state (P4mm symmetry) from a C-type antiferromagnetic order to a G-type order for the in-plane lattice parameter above 3.922 Å. The G-type antiferromagnetic order will be maintained with larger tensile strains; however, a continuous structural phase transition will occur, combining the ferroelectric and antiferrodistortive modes. In particular, the larger tensile strain allows an isostructural transition, the so-called Cowley's ''Type Zero'' phase transitions, from Cc-(I) to Cc-(II), with a slight volume collapse. The orientation of ferroelectric polarization changes from the out-of-plane direction in the P4mm to the in-plane direction in the Pmc21 state under epitaxial tensile strain; meanwhile, the magnetic ordering temperature TN can be strikingly affected by the variation of misfit strain.

Understanding the mechanism of performance difference when substituting Al for different transition metal ions in Li-rich Mn-based cathode materials

The Al-doped modification strategy by substituting Al for different transition metal ions (TMs, TM = Mn, Ni, Co) has achieved excellent results in improving the cyclic performance of Li-rich Mn-based cathode materials (LRMs). However, the traditional explanation known as “pegging effect” is hard to distinguish how Al works in different TM substitutions. Herein, the electrochemical performances of Li1.2Mn0.52Ni0.13Co0.13Al0.02O2 (LRM-Mn), Li1.2Mn0.54Ni0.11Co0.13Al0.02O2 (LRM-Ni) and Li1.2Mn0.54Ni0.13Co0.11Al0.02O2 (LRM-Co) are studied, and LRM-Mn shows the superior long-term cycling stability, especially at the high temperature of 55 °C. Density functional theory (DFT) reveals that LRM-Mn crystal structure has higher thermodynamic stability than any other sample, which is advantageous for inhibiting the transition of LRMs to low-energy stable phases during cycling (e.g., spinel phase and rock salt phase). Combined with density of states and Bader charge analyses, we think that the increased thermodynamic stability of LRM-Mn results from the reduction of the charge transfer of Mn and Co ions in a single delithiation process, which lowers the reactivity of TMs, alleviates the Li/TM mixing and inhibits the irreversible oxygen release. In addition, the biggest volume change during the delithiation process was observed when Al was substituted for Co, which results in the materials’ premature production of fatigue stresses and intergranular cracking. This work comprehensively explains the modification mechanism of Al-doped in LRMs. It demonstrates practical significance for both the rational design of materials and the electrode electrochemical performance prediction.

Associations of obesity phenotypes with weight change, cardiometabolic benefits, and type 2 diabetes incidence during a lifestyle intervention: results from the PREVIEW study.

Some individuals with overweight/obesity may be relatively metabolically healthy (MHO) and have a lower risk of cardiovascular disease than those with metabolically unhealthy overweight/obesity (MUO). We aimed to compare changes in body weight and cardiometabolic risk factors and type 2 diabetes incidence during a lifestyle intervention between individuals with MHO vs MUO. This post-hoc analysis included 1012 participants with MHO and 1153 participants with MUO at baseline in the randomized trial PREVIEW. Participants underwent an eight-week low-energy diet phase followed by a 148-week lifestyle-based weight-maintenance intervention. Adjusted linear mixed models and Cox proportional hazards regression models were used. There were no statistically significant differences in weight loss (%) between participants with MHO vs MUO over 156 weeks. At the end of the study, weight loss was 2.7% (95% CI, 1.7%-3.6%) in participants with MHO and 3.0% (2.1%-4.0%) in those with MUO. After the low-energy diet phase, participants with MHO had smaller decreases in triglyceride (mean difference between MHO vs MUO 0.08 mmol·L-1 [95% CI, 0.04-0.12]; P < 0.001) but similar reductions in fasting glucose and HOMA-IR than those with MUO. However, at the end of weight maintenance, those with MHO had greater reductions in triglyceride (mean difference -0.08 mmol·L-1 [-0.12--0.04]; P < 0.001), fasting glucose, 2-hour glucose (difference -0.28 mmol·L-1 [-0.41--0.16]; P < 0.001), and HOMA-IR than those with MUO. Participants with MHO had smaller decreases in diastolic blood pressure and HbA1c and greater decreases in HDL cholesterol after weight loss than those with MUO, whereas the statistically significant differences disappeared at the end of weight maintenance. Participants with MHO had lower 3-year type 2 diabetes incidence than those with MUO (adjusted hazard ratio 0.37 [0.20-0.66]; P < 0.001). Individuals with MUO had greater improvements in some cardiometabolic risk factors during the low-energy diet phase, but had smaller improvements during long-term lifestyle intervention than those with MHO.

Innovative Aqueous Nanoemulsion Prepared by Phase Inversion Emulsification with Exceptional Homogeneity.

Formulating low-solubility or low-permeability drugs is a challenge, particularly with the low administration volumes required in intranasal drug delivery. Nanoemulsions (NE) can solve both issues, but their production and physical stability can be challenging, particularly when a high proportion of lipids is necessary. Hence, the aim of the present work was to develop a NE with good solubilization capacity for lipophilic drugs like simvastatin and able to promote the absorption of drugs with low permeability like fosphenytoin. Compositions with high proportion of two lipids were screened and characterized. Surprisingly, one of the compositions did not require high energy methods for high droplet size homogeneity. To better understand formulation factors important for this feature, several related compositions were evaluated, and their relative cytotoxicity was screened. Optimized compositions contained a high proportion of propylene glycol monocaprylate NF, formed very homogenous NE using a low-energy phase inversion method, solubilized simvastatin at high drug strength, and promoted a faster intranasal absorption of the hydrophilic prodrug fosphenytoin. Hence, a new highly homogeneous NE obtained by a simple low-energy method was successfully developed, which is a potential alternative for industrial application for the solubilization and protection of lipophilic actives, as well as (co-)administration of hydrophilic molecules.

Study of nanoemulsions using carvacrol/MCT-(Oleic acid-potassium oleate)/ Tween 80 ®- water system by low energy method

Carvacrol is studied in different fields due to its microbial and antioxidant properties. Its use is limited because of the water insolubility and its strong taste. To overcome these problems, carvacrol has been successfully loaded into nanoemulsions. The low-energy emulsification method Phase Inversion Composition (PIC) is used to prepare oil-in-water nanoemulsions in the carvacrol/medium chain triglycerides (MCT)-(oleic acid-potassium oleate/Tween 80 ®)-water system. Oleic acid acts as a co-surfactant when it is neutralized with KOH along the emulsification path changing the spontaneous curvature of the interface when increasing the HLB number from 1 for the oleic acid to 20 for the potassium oleate and, therefore, changing the HLB number of the surfactant mixture. The phases diagrams are studied in order to understand the behaviour of the system and to establish the composition range where nanoemulsions can be obtained. Nanoemulsions are formed when the emulsification path crosses a region of direct or planar structure without excess of oil. Experimental design is performed in order to study the influence of composition variables as carvacrol/MCT ratio and (oleic-oleate)/Tween 80 ® ratio (OL-OT/T80 ratio) on the diameter of the nanoemulsions and their stability. It has been observed the importance of the HLB number of the surfactants mixture in order to obtain small-sized stable nanoemulsions. Surface response graphic shows that (OL-OT)/T80 ratio is a significant parameter in the mean diameter of the nanoemulsions. A minimum diameter is obtained for a (OL-OT)/T80 ratio 45/55 due to the fact that ratio is near the preferred HLB of the oil mixture and the emulsification path contains a wide liquid crystal monophasic region with all the oil incorporated in the structure.Diameters of 19 nm for carvacrol/MCT ratio of 30/70 or diameters of 30 nm for ratios of 45/55 with high stability values presented a good potential to be incorporated into edible films in the future.Regarding nanoemulsions stability an optimum value is also observed for a carvacrol/MCT ratio.The addition of another carrier oil as olive oil instead of MCT showed an improvement of the nanoemulsions stability against Ostwald ripening, probably due to the smaller solubility of olive oil. The use of olive oil does not significantly change the diameter of the nanoemulsion.

Statistical aspects of a quantum Hopfield model

In this paper, we study the eigenstate properties of a quantum Hopfield model by the exact diagonalization method. The local permutational symmetry in this model organizes the spins into clusters, which can each be considered a large quantum spin interacting with others. It is shown that such a quantum Hopfield model, even though without dissipation, is interesting in its own right as an example of quantum frustrated magnetism and quantum spin glass. It exhibits three distinct phases: a low-energy spin-glass phase at a low transverse field, a thermal paramagnetic phase at a high transverse field, and a nonthermal high-energy paramagnetic phase. The dynamics of the revival probability starting from a memory pattern in such a closed quantum many-body model has also been studied.

Structural and dynamical phase transitions of NaNbO3 from first-principles calculations

The crystal structures and phase transitions of ${\mathrm{NaNbO}}_{3}$ are analyzed with density fonctional theory through generalized gradient approximation-PBEsol (GGA-PBEsol) and local density approximations (LDA). The phonon dispersion curves from the high-symmetry cubic perovskite phase are reported to have many unstable branches, predisposing to several combinations of phase transitions to various distorted structures. The coupling between the modes and the strain relaxation play a key role in the condensation of the ground state of sodium niobate. The instabilities at $R$ and $M$ points of the first Brillouin zone and along the line $T$ (connecting the $M$ and $R$ points) are very important for stabilizing the low-energy phases. Within the GGA-PBEsol approximation, the ground state is rhombohedral ferroelectric/antiferrodistortive (FE/AFD) $R3c$, while in LDA it is rather the orthorhombic FE/AFD $Pmc{2}_{1}$ structure that stabilizes the lowest energy in this compound. In both calculations, there is only a small energy difference between the three lowest-energy phases $Pmc{2}_{1}$ (FE/AFD[110]), $\mathit{Pbcm}$ (antiferroelectric/AFD), and $R3c$ (FE/AFD[111]), which is a key characteristic of antiferroelectricity. The GGA-PBEsol approach provides more sensible results than the LDA approximation.