arXiv subjects

Saswata Bhattacharya

Publications and source records attributed to Saswata Bhattacharya.

At least 55 records · Page 3Linked to original sources

arXiv2021

Rashba dominated spin-splitting in the bulk ferroelectric oxide perovskite KIO3

The momentum-dependent Rashba and Dresselhaus spin-splitting has gained much attention for its highly promising applications in spintronics. In the present work, ab initio density functional theory calculations are performed to study the spin-splitting effect in ferroelectric oxide perovskite KIO3. Our calculations are additionally supported by symmetry adapted two-band k.p Hamiltonian. Non-negligible spin-splitting effect is observed at conduction band minimum (CBm) and valence band maximum (VBM) for rhombohedral R3m and R3c phases. Linear Rashba terms successfully explain the splitting at VBM. However, cubic terms become important in realizing spin-orientation near CBm. Our results show the enhancement in Rashba parameters on tuning the ferroelectric order parameter. Further, we have observed reversal of spin-orientation on switching the direction of polarization.

cond-mat.mtrl-sci↗

arXiv2021

MoS$_2$ and Janus (MoSSe) Based 2D van der Waals heterostructures: Emerging Direct Z-scheme Photocatalysts

Two-dimensional (2D) materials viz. transition metal dichalcogenides (TMD) and transition metal oxides (TMO) offer a platform that allows creation of heterostructures with a variety of properties. The optoelectronic industry has observed an upheaval in the research arena of MoS$_2$ based van der Waals (vdW) heterostructures (HTSs) and Janus structures. Therefore, interest towards these structures are backed by the selectivity in terms of electronic and optical properties. The present study investigates the photocatalytic ability of bilayer, MoS$_2$ and Janus (MoSSe) based vdW HTSs viz. MoS$_2$/TMO, MoS$_2$/TMD, MoSSe/TMO and MoSSe/TMD, by first-principles based approach under the framework of (hybrid) density functional theory (DFT) and manybody perturbation theory (GW approximation). We have considered HfS$_2$, ZrS$_2$, TiS$_2$, WS$_2$ and HfO$_2$, T-SnO$_2$, T-PtO$_2$ from the family of TMD and TMO, respectively. The photocatalytic properties of these vdW HTSs are thoroughly investigated and compared with the respective individual monolayers by visualizing their band edge alignment, electron-hole recombination rate and optical properties. Strikingly we observe that, despite most of the individual monolayers do not perform optimally as a photocatalyst, type II band edge alignment is noticed to vdW HTSs and they appear to be efficient for photocatalysis via Z-scheme. Moreover, these HTSs have also shown promising optical response in the visible region. Finally on computing electron-hole recombination rate we find MoSSe/HfS$_2$, MoSSe/TiS$_2$, MoS$_2$/T-SnO$_2$, MoS$_2$/ZrS$_2$ and MoSSe/ZrS$_2$ are probable, most efficient Z-scheme photocatalysts.

cond-mat.mtrl-sci↗

arXiv2021

Exploring Exciton and Polaron Dominated Photo-physical Phenomena in Ruddlesden-Popper Phases of Ban+1ZrnS3n+1 (n=[1-3]) from Many Body Perturbation Theory

Ruddlesden-Popper (RP) phases of Ba$_{\textrm{n+1}}$Zr$_{\textrm{n}}$S$_{\textrm{3n+1}}$ (n=[1-3]) are evolved as new promising class of chalcogenide perovskites in the field of optoelectronics, especially in solar cells. However, detailed studies regarding its optical, excitonic, polaronic and transport properties are hitherto unknown. Here, we have explored the excitonic and polaronic effect in RP phases of Ba$_{\textrm{n+1}}$Zr$_{\textrm{n}}$S$_{\textrm{3n+1}}$ (n=[1-3]) using several first-principles based state-of-the-art methodologies under the framework of Many Body Perturbation Theory. Unlike it's bulk counterpart, the optical and excitonic anisotropy are observed in Ba$_{\textrm{n+1}}$Zr$_{\textrm{n}}$S$_{\textrm{3n+1}}$ (n=[1-3]) RP phases. From Wannier-Mott approach, we show that in the RP phases of this class of chalcogenide perovskites, capturing the ionic contribution to the dielectric constant is important. We report significant ionic contribution and relatively smaller electron-phonon coupling constant for Ba$_{\textrm{n+1}}$Zr$_\textrm{n}$S$_{\textrm{3n+1}}$ in comparison to the bulk BaZrS$_3$. The exciton binding energy is found to be dependent on the presence of large electron-phonon coupling. The charge carrier mobility is maximum in Ba$_2$ZrS$_4$, computed employing deformation potential of the same. As per our analysis, the optical phonon modes are observed to dominate the acoustic phonon modes, leading to decrease in polaron mobility on increasing n in Ba$_{\textrm{n+1}}$Zr$_{\textrm{n}}$S$_{\textrm{3n+1}}$ (n=[1-3]).

cond-mat.mtrl-sci↗

arXiv2021

Optoelectronic Properties of Chalcogenide Perovskites by Many-Body Perturbation Theory

Chalcogenide perovskites have emerged as non-toxic and stable photovoltaic materials, acting as an alternative to lead halide hybrid perovskites having similar optoelectronic properties. In the present work, we report the electronic and optical properties of chalcogenide perovskites AZrS$_3$ (A=Ca, Sr, Ba) by using the density functional theory (DFT) and many-body perturbation theory (MBPT viz. G$_0$W$_0$ and BSE). This study includes excitonic analysis for the aforementioned systems. The exciton binding energy (E$_\textrm{B}$) is found to be larger than that of the halide perovskites, as the ionic contribution to dielectric screening is negligible in the former. We also observe a more stable charge-separated polaronic state as compared to that of the bound exciton. Finally, on the basis of direct gap and absorption coefficient, the estimated spectroscopic limited maximum efficiency (SLME) of the solar cells is large and suggests the applicability of these perovskites in photovoltaics.

cond-mat.mtrl-sci↗

arXiv2021

Formation of solid-state dendrites under the influence of coherency stresses: A diffuse interface approach

In this paper, we have formulated a phase-field model based on the grand-potential functional for the simulation of precipitate growth in the presence of coherency stresses. In particular, we study the development of dendrite-like patterns arising out of diffusive instabilities during the growth of a precipitate in a supersaturated matrix. Here, we characterize the role of elastic energy anisotropy and its strength on the selection of a dendrite tip radius and velocity. We find that there is no selection of a unique tip shape as observed in the case of solidification, and the selection constant $σ^{*}=2d_0D/R_{tip}^{2}V_{tip}$ increases linearly with simulation time for all the simulation conditions (where $R_{tip}$ and $V_{tip}$ are the tip radius and velocity). Therefore, structures derived in solid-state in the presence of elastic anisotropy may only be referred to as dendrite-like.

cond-mat.mtrl-sci↗

arXiv2021

Stability, Evolution and Switching of Ferroelectric Domain Structures in Lead-free BaZr$_{0.2}$Ti$_{0.8}$O$_3$-Ba$_{0.7}$Ca$_{0.3}$TiO$_3$ System: Thermodynamic Analysis and Phase-field Simulations

Enhanced room-temperature electromechanical coupling in the lead-free ferroelectric system $(1-x)$BaZr$_{0.2}$Ti$_{0.8}$O$_{3}$ - $x$Ba$_{0.7}$Ca$_{0.3}$TiO$_{3}$ (abbreviated as BZCT) at $x=0.5$ is attributed to the existence of a morphotropic phase region (MPR) containing an intermediate orthorhombic ($O$) phase between terminal rhombohedral ($R$) BZT and tetragonal ($T$) BCT phases. However, there is ambiguity regarding the morphotropic phase transition in BZCT at room temperature - while some experiments suggest a single $O$ phase within the MPR, others indicate coexistence of three polar phases ($T+R+O$). Therefore, to understand the thermodynamic stability of polar phases and its relation to electromechanical switching during morphotropic phase transition in BZCT, we develop a Landau potential based on the theory of polar anisotropy. Since intrinsic electrostrictive anisotropy changes as a function of electromechanical processing, we establish a correlation between the parameters of our potential and the coefficients of electrostriction. We also conducted phase-field simulations based on this potential to demonstrate changes in domain configuration from single-phase $O$ to three-phase $T+R+O$ at the equimolar composition with the increase in electrostrictive anisotropy. Diffusionless phase diagrams and the corresponding piezoelectric coefficients obtained from our model compare well with the experimental findings. Increase in electrostrictive anisotropy increases the degeneracy of the free energy at ambient temperature and pressure leading to decreasing polar anisotropy, although there is an accompanying increase in the electromechanical anisotropy manifested by an increase in the difference between effective longitudinal and transverse piezo-coefficients, $d_{33}$ and $d_{31}$.

cond-mat.mtrl-sci↗

arXiv2021

Sublattice mixing in Cs$_2$AgInCl$_6$ for enhanced optical properties from first-principles

Lead-free double perovskite materials (viz. Cs$_2$AgInCl$_6$) are being explored as stable and non-toxic alternatives of lead halide perovskites. In order to expand the optical response of Cs$_2$AgInCl$_6$ in visible region, we report here the stability, electronic structure and optical properties of Cs$_2$AgInCl$_6$ by sublattice mixing of various elements. Here, we have employed %high-throughput screening using a hierarchical first-principles based approach starting from density functional theory (DFT) with appropriate exchange-correlation functionals to beyond DFT methods under the framework of many body perturbation theory (viz. G$_0$W$_0$@HSE06). We have started with 32 primary set of combinations of metals M(I), M(II), M(III) and halogen X at Ag/In and Cl site, respectively, where concentration of each set is varied to build a database of nearly 140 combinations. The most suitable mixed sublattices are identified to engineer the band gap of Cs$_2$AgInCl$_6$ to have its application in optoelectronic devices under visible light.

cond-mat.mtrl-sci↗

arXiv2020

Capturing Excitonic Effects in Lead Iodide Perovskites from Many-Body Perturbation Theory

Lead iodide perovskites have attracted considerable interest in the upcoming photovoltaic technologies and optoelectronic devices. Therefore, an accurate theoretical description of the electronic and optical properties especially to understand the excitonic effects in this class of materials is of scientific and practical interest. However, despite several theoretical research endeavours in past, the most accurate analysis of the key electronic parameters for solar cell performance, such as optical properties, effective mass, exciton binding energy (E$_B$) and the radiative exciton lifetime are still largely unknown. Here, we employ state-of-the-art first-principles based methodologies viz. hybrid functional(HSE06) combined with spin-orbit coupling (SOC), many-body perturbation theory (GW, BSE), model-BSE (mBSE), Wannier-Mott (WM) and Density Functional Perturbation Theory (DFPT). By taking a prototypical model system viz. APbI$_3$ (A = Formamidinium (FA), methylammonium (MA), and Cs), an exhaustive analysis is presented on the theoretical understanding of the optical, electronic and excitonic properties. We show that tuning of exact exchange parameter ($α$) in HSE06 calculations incorporating SOC, followed by single shot GW, and BSE play a pivotal role in obtaining a reliable predictions for the experimental bandgap. We demonstrate that mBSE approach improves the feature of optical spectra w.r.t experiments. Furthermore, WM approach and ionic contribution to dielectric screening (below 16 meV) ameliorate the E$_B$. Our results reveal that the direct-indirect band gap transition (Rashba splitting) may be a factor responsible for the reduced charge carrier recombination rate in MAPbI$_3$ and FAPbI$_3$. The role of cation ''A'' for procuring the long-lived exciton lifetime is well understood. This proposed methodology allows to design new materials with tailored excitonic properties.

cond-mat.mtrl-sci↗

arXiv2020

Metastability Triggered Reactivity in Clusters at Realistic Conditions: A Case Study of N-doped (TiO$_2$)$_n$ for Photocatalysis

Here we report a strategy, by taking a prototypical model system for photocatalysis (viz. N-doped (TiO$_2$)$_n$ clusters), to accurately determine low energy metastable structures that can play a major role with enhanced catalytic reactivity. Computational design of specific metastable photocatalyst with enhanced activity is never been easy due to plenty of isomers on potential energy surface. This requires fixing various parameters viz. (i) favorable formation energy, (ii) low fundamental gap, (iii) low excitation energy and (iv) high vertical electron affinity (VEA) and low vertical ionization potential (VIP). We validate here by integrating several first principles based methodologies that consideration of the global minimum structure alone can severely underestimate the activity. As a first step, we have used a suite of genetic algorithms [viz. searching clusters with conventional minimum total energy ((GA)$_\textrm{E}$); searching clusters with specific property i.e. high VEA ((GA)$_\textrm{P}^{\textrm{EA}}$), and low VIP ((GA)$_\textrm{P}^{\textrm{IP}}$)] to model the N-doped (TiO$_2$)$_n$ clusters. Following this, we have identified its free energy using ab initio thermodynamics to confirm that the metastable structures are not too far from the global minima. By analyzing a large dataset, we find that N-substitution ((N)$_\textrm{O}$) prefers to reside at highly coordinated oxygen site to maximize its coordination, whereas N-interstitial ((NO)$_\textrm{O}$) and split-interstitial ((N$_2)_\textrm{O}$) favor the dangling oxygen site. Interestingly, we notice that each types of defect (viz. substitution, interstitials) reduce the fundamental gap and excitation energy substantially. However, (NO)$_\textrm{O}$ and (N$_2)_\textrm{O}$ doped clusters are the potential candidates for overall water splitting, whereas N$_\textrm{O}$ is congenial only for oxygen evolution reaction.

cond-mat.mtrl-sci↗

arXiv2020

High-Throughput Screening for Band gap Engineering by Sublattice Mixing of Cs$_2$AgBiCl$_6$ from First-Principles

The lead-free double perovskite material (viz. Cs$_2$AgBiCl$_6$) has emerged as an efficient and environmentally friendly alternative to lead halide perovskites. To make Cs$_2$AgBiCl$_6$ optically active in the visible region of solar spectrum, band gap engineering approach has been undertaken. Using Cs$_2$AgBiCl$_6$ as a host, band gap and optical properties of Cs$_2$AgBiCl$_6$ have been modulated by alloying with M(I), M(II), and M(III) cations at Ag-/Bi-sites. Here, we have employed density functional theory (DFT) with suitable exchange-correlation functionals in light of spin-orbit coupling (SOC) to determine the stability, band gap and optical properties of different compositions, that are obtained on Ag-Cl and Bi-Cl sublattices mixing. On analyzing the 64 combinations within Cs$_2$AgBiCl$_6$, we have identified 19 promising configurations having band gap sensitive to solar cell applications. The most suitable configurations with Ge(II) and Sn(II) substitutions have spectroscopic limited maximum efficiency (SLME) of 32.08% and 30.91%, respectively, which are apt for solar cell absorber.

cond-mat.mtrl-sci↗

arXiv2020

Theoretical insights of codoping to modulate electronic structure of TiO$_2$ and SrTiO$_3$ for enhanced photocatalytic efficiency

TiO$_2$ and SrTiO$_3$ are well known materials in the field of photocatalysis due to their exceptional electronic structure, high chemical stability, non-toxicity and low cost. However, owing to the wide band gap, these can be utilized only in the UV region. Thus, it's necessary to expand their optical response in visible region by reducing their band gap through doping with metals, nonmetals or the combination of different elements, while retaining intact the photocatalytic efficiency. We report here, the codoping of a metal and a nonmetal in anatase TiO$_2$ and SrTiO$_3$ for efficient photocatalytic water splitting using hybrid density functional theory and \textit{ab initio} atomistic thermodynamics. The latter ensures to capture the environmental effect to understand thermodynamic stability of the charged defects at a realistic condition. We have observed that the charged defects are stable in addition to neutral defects in anatase TiO$_2$ and the codopants act as donor as well as acceptor depending on the nature of doping (p-type or n-type). However, the most stable codopants in SrTiO$_3$ mostly act as donor. Our results reveal that despite the response in visible light region, the codoping in TiO$_2$ and SrTiO$_3$ cannot always enhance the photocatalytic activity due to either the formation of recombination centers or the large shift in the conduction band minimum or valence band maximum. Amongst various metal-nonmetal combinations, Mn$_\textrm{Ti}$S$_\textrm{O}$ (i.e. Mn is substituted at Ti site and S is substituted at O site), S$_\textrm{O}$ in anatase TiO$_2$ and Mn$_\textrm{Ti}$S$_\textrm{O}$, Mn$_\textrm{Sr}$N$_\textrm{O}$ in SrTiO$_3$ are the most potent candidates to enhance the photocatalytic efficiency of anatase TiO$_2$ and SrTiO$_3$ under visible light irradiation.

cond-mat.mtrl-sci↗

arXiv2020

Theoretical Insights into C$-$H Bond Activation of Methane by Transition Metal Clusters: The Role of Anharmonic Effects

Aiming towards materials design for methane activation, we study temperature ($T$), pressure ($p$) dependence of the composition, structure, and stability of metal oxide clusters in a reactive atmosphere using a prototypical model catalyst having wide applications: free transition metal (Ni) clusters in a combined oxygen and methane atmosphere. A robust methodological approach is employed, to show that the conventional harmonic approximation miserably fails for this class of materials and capturing anharmonic effects to the vibration free energy contribution is indispensable. To incorporate the anharmonicity in the vibrational free energy, we evaluate the excess free energy of the clusters numerically by thermodynamic integration method with hybrid density functional theory and {\em ab initio} molecular dynamics simulation inputs. We find that the anharmonic effect has a significant impact in detecting the activation of C$-$H bond, whereas the harmonic infrared spectrum completely fails due to the wrong prediction of the vibrational modes.

cond-mat.mtrl-sci↗

arXiv2020

Role of Defects in Photocatalytic Water Splitting: Monodoped vs Codoped SrTiO$_3$

Using the hybrid density functional theory and \textit{ab initio} atomistic thermodynamics, we report monodoping of non-metal (N) or metal (Mn) in SrTiO$_3$ can induce visible light absorption, but none of them are suitable to ameliorate the photocatalytic activity. Therefore, in order to achieve enhanced photocatalytic activity of SrTiO$_3$, we have employed codoped Mn and N simultaneously in SrTiO$_3$ to modulate its electronic properties effectively. In the codoped SrTiO$_3$, the recombination of photogenerated charge carriers is suppressed, and the diffusion and mobility are increased owing to the passivation of discrete localized states. Our results reveal that Mn$_{\textrm{Sr}}\textrm{N}_\textrm{O}$ (codoping of Mn at Sr site and N at O site) is the most promising candidate for enhancing the photocatalytic activity of SrTiO$_3$ under visible light.

cond-mat.mtrl-sci↗

arXiv2019

Self energy and excitonic effect in (un)doped TiO$_2$ anatase : A comparative study of hybrid DFT, GW and BSE to explore optical properties

TiO$_2$ anatase has its significant importance in energy and environmental research. However, the major drawback of this immensely popular semi-conductor is its large bandgap of 3.2 eV. Several non-metals have been doped experimentally for extending the TiO$_2$ photo-absorption to the visible region. Providing in-depth theoretical guidance to the experimentalists to understand the optical properties of the doped system is therefore extremely important. We report here using state-of-the-art hybrid density functional approach and many body perturbation theory (within the frame work of GW and BSE) the optical properties of p-type (S and Se doped) and n-type (N and C doped) TiO$_2$ anatase. The anisotropy present in non-metal doped TiO$_2$ plays a significant role in the optical spectra. The p-type dopants are optically active only for light polarized along xy direction, whereas the n-type dopants are optically active when light is polarized along xy and z direction in low energy region. We have found that, in all the doped systems optically allowed transitions are introduced well below 3 eV (i.e. visible spectra region). This helps to improve its opto-electronic and solar absorption properties. All the calculations are well validated with respect to the available experimental observation on pristine TiO$_2$ anatase.

cond-mat.mtrl-sci↗

arXiv2019

Effect of elastic anisotropy on phase separation in ternary alloys: A phase-field study

The precipitate shape, size and distribution are crucial factors which determine the properties of several technologically important alloys. Elastic interactions between the inclusions modify their morphology and align them along elastically favourable crystallographic directions. Among the several factors contributing to the elastic interaction energy between precipitating phases, anisotropy in elastic moduli is decisive in the emergence of modulated structures during phase separation in elastically coherent alloy systems. We employ a phase-field model incorporating elastic interaction energy between the misfitting phases to study microstructural evolution in ternary three-phase alloy systems when the elastic moduli are anisotropic. The spatiotemporal evolution of the composition field variables is governed by solving a set of coupled Cahn-Hilliard equations numerically using a semi-implicit Fourier spectral technique. We methodically vary the misfit strains, alloy chemistry and elastic anisotropy to investigate their influence on domain morphology during phase separation. The coherency strains between the phases and alloy composition alter the coherent phase equilibria and decomposition pathways. The degree of anisotropy in elastic moduli modifies the elastic interaction energy between the precipitates depending on the sign and magnitude of relative misfits, and thus determines the shape and alignment of the inclusions in the microstructure.

cond-mat.mtrl-sci↗

arXiv2019

A phase-field study of elastic stress effects on phase separation in ternary alloys

Most of the commercially important alloys are multicomponent, producing multiphase microstructures as a result of processing. When the coexisting phases are elastically coherent, the elastic interactions between these phases play a major role in the development of microstructures. To elucidate the key effects of elastic stress on microstructural evolution when more than two misfitting phases are present in the microstructure, we have developed a microelastic phase-field model in two dimensions to study phase separation in ternary alloy system. Numerical solutions of a set of coupled Cahn-Hilliard equations for the composition fields govern the spatiotemporal evolution of the three-phase microstructure. The model incorporates coherency strain interactions between the phases using Khachaturyan's microelasticity theory. We systematically vary the misfit strains (magnitude and sign) between the phases along with the bulk alloy composition to study their effects on the morphological development of the phases and the resulting phase separation kinetics. We also vary the ratio of interfacial energies between the phases to understand the interplay between elastic and interfacial energies on morphological evolution. The sign and degree of misfit affect strain partitioning between the phases during spinodal decomposition, thereby affecting their compositional history and morphology. Moreover, strain partitioning affects solute partitioning and alters the kinetics of coarsening of the phases. The phases associated with higher misfit strain appear coarser and exhibit wider size distribution compared to those having lower misfit. When the interfacial energies satisfy complete wetting condition, phase separation leads to development of stable core-shell morphology depending on the misfit between the core (wetted) and the shell (wetting) phases.

cond-mat.mtrl-sci↗

arXiv2019

Evolution of interfacial dislocation network during low-stress high temperature creep of particle strengthened alloy system using discrete dislocation dynamics simulations

We use three-dimensional discrete dislocation dynamics simulations (DDD) to study the evolution of interfacial dislocation network (IDN) in particle-strengthened alloy systems subjected to constant stress at high temperatures. We have modified the dislocation mobility laws to incorporate the recovery of the dislocation network by the climb. The microstructure consists of uniformly distributed cuboidal inclusions embedded in the simulation box. Based on the systematic simulations of IDN formation as a function of applied stress for prescribed inter-particle spacing and glide-to-climb mobility ratio, we derive a relation between effective stress and normalized dislocation density. We use link-length analysis to show self-similarity of immobile dislocation links irrespective of the level of applied stress. Moreover, we derive the dependence of effective stress on the ratio between mobile to immobile dislocation density based on the Taylor relation for strain hardening materials. We justify the relation with the help of a theoretical model which takes into account the balance of multiplication and annihilation rates of dislocation density.

cond-mat.mtrl-sci↗

arXiv2019

Oxygen vacancy mediated cubic phase stabilization at room temperature in pure nano-crystalline Zirconia films: A combined experimental and first-principles based investigation

We report the formation of cubic phase, under ambient conditions, in thin films of Zirconia synthesized by electron beam evaporation technique. The stabilization of the cubic phase was achieved without the use of chemical stabilizers and/or concurrent ion beam bombardment. Films of two different thickness (660 nm, 140 nm) were deposited. The 660 nm and 140 nm films were found to be stoichiometric (ZrO2) and off-stoichiometric (ZrO1.7) respectively by Resonant Rutherford back-scattering spectroscopy. While the 660 nm as-deposited films were in the cubic phase, as indicated by X-ray diffraction and Raman spectroscopy measurements, the 140 nm as-deposited films were amorphous and the transformation to cubic phase was obtained after thermal annealing. Extended X-ray absorption fine structure measurements revealed the existence of Oxygen vacancies in the local structure surrounding Zirconium for all films. However, the amount of these Oxygen vacancies was found to be significantly higher for the amorphous films as compared to the films in the cubic phase (both 660 nm as-deposited and 140 nm annealed films). The cubic phase stabilization is explained on the basis of suppression of the soft X2- mode of vibration of the Oxygen sub-lattice due to the presence of the Oxygen vacancies. Our first-principles modeling under the framework of density functional theory shows that the cubic structure with Oxygen vacancies is indeed more stable at ambient conditions than its pristine (without vacancies) counterpart. The requirement of a critical amount of these vacancies for the stabilization of the cubic phase is also discussed.

cond-mat.mtrl-sci↗