Thermodynamic Phase Stability Research Articles

A machine learning model for screening thermodynamic stable lead-free halide double perovskites

Halide double perovskites have garnered significant interest due to their outstanding photovoltaic properties. The thermodynamic stability of compounds is one of the most significant properties for materials screening, which can be well indicated by the energy above the convex hull (Ehull). The Ehull of compounds can be calculated from Density Functional Theory (DFT) requiring significant computational time and cost, making it almost impossible to be utilized for screening large numbers of possible compounds. To address this challenge, a data-driven approach implemented by machine learning (ML) algorithms has been employed to obtain the optimal model for predicting the thermodynamic phase stability of Lead-free halide double perovskite through a dataset containing 469 A2B′ BX6 double perovskites with DFT-calculated Ehull values and 24 primary features from periodic table. The results indicate that XGBoost algorithm provides more excellent predictions in both classification and regression by comparing performances of various ML algorithms under 5-folds cross validation. Furthermore, the optimal model was utilized to predict the stability of 22 completely new A2B′ BX6 compounds with known experimental results, and the experiment results demonstrated that our proposed model can be effective method for screening halide double perovskite with thermodynamic stability. Finally, we employ SHapley Additive exPlanations (SHAP) for feature analysis for ML models to reveal the relationships between the feature values and target properties, which provides important guidance for material design and screening with thermodynamic stability in the future.

Effect of alloying on the phase stability and elastic properties of L12 Cu3Pt crystal structure

The alloying effect of three elements, namely Al, Cr and Zn, on the Pt site of L12 Cu3Pt phase was investigated using DFT (density functional theory) based first-principle calculations in attempt to stabilize it in the form of L12 Cu3Pt1-xYx ternary alloy. On the basis of phase stability and elastic properties, the substitution behaviour of all three alloying elements were compared with properties of thermodynamically sluggish Cu3Pt phase. The calculated heats of formation reveal that the thermodynamic phase stability is gradually enhanced with increasing content of aluminium alloying and diminished with increasing content of zinc and chromium. In this current work, the stress-strain approach was used according to Hooke’s law to calculate elastic properties such as elastic constants, Young’s modulus E, shear modulus G, bulk modulus B and Poisson’s ratio v, as they play an important role to investigate the resulting mechanical properties. The calculated results show that alloying with all three elements maintains the mechanical stability criteria of cubic crystals. Considered L12 Cu3Pt1-xYx ternary alloys exhibit the most ductile character with Al addition, followed by Cr, whereas introduction of Zn yielded lowest ductility at higher compositions.

First-principles study of phase transition of BaF <sub>2</sub> under high pressue

There have been some theoretical studies of high pressure phase transition behavior of BaF <sub>2</sub>, while in most cases the attention is paid mainly to the optical and electrical properties of BaF <sub>2</sub> under increasing pressure. To date, there has been still a lack of theoretical explanation for the hysteresis phenomenon of high-pressure phase of BaF <sub>2</sub> when the pressure is released. In addition, the pressure-dependent behavior of the BaF <sub>2</sub> band gap is still under controversy, and there are few studies of its high-pressure Raman spectra. Therefore, first principle is used to make a supplementary calculation of the high pressure behavior of BaF <sub>2</sub>. For a given pressure <i>P</i> and temperature <i>T</i>, the thermodynamic stable phase has the lowest Gibbs free energy. The calculations are performed at zero temperature and hence, the Gibbs free energy becomes equal to the enthalpy. Thus, the variation of enthalpy is calculated as a function of pressure to study the high-pressure phase stability of BaF <sub>2</sub> based on density functional theory as implemented in the Vienna ab initio simulation package (VASP). The results show that the BaF <sub>2</sub> undergoes two structural phase transitions from <i>Fm</i>3 <i>m</i>(cubic) to <i>Pnma</i> (orthorhombic) and then to <i>P</i>6 <sub>3</sub>/ <i>mmc</i>(hexagonal) with increasing pressure, and their corresponding transition pressures are 3.5 and 18.3 GPa, respectively. By calculating the evolution of lattice constant with pressure, it is found that at about 15 GPa (near the second phase transition pressure), the lattice constants of the <i>Pnma</i> structure show abnormal behavior (a slight increase in <i>b</i> <sub>o</sub> and a slight decrease in <i>a</i> <sub>o</sub>). We suggest that this behavior leads the band gap to decrease, indicated by analyzing the calculated results of <i>Pnma</i> structure of other materials. The <i>Pnma</i> structure completely transforms into <i>P</i>6 <sub>3</sub>/ <i>mmc</i> structure at about 20 GPa. By analyzing the phonon dispersion curves of BaF <sub>2</sub> as a function of pressure, the structural stability information of the material can also be obtained. Then the density functional perturbation theory (DFPT) is used to calculate the phonon dispersion curves of BaF <sub>2</sub> by VASP code and Phonopy code. The hysteresis phenomenon of the <i>P</i>6 <sub>3</sub>/ <i>mmc</i> structure, when the pressure is released, is explained by the kinetic stability. The results predict that the <i>P</i>6 <sub>3</sub>/ <i>mmc</i> structure can be stabilized at least to 80 GPa.

Temperature and pressure induced electronic topological transitions in titanium

The electronic topological transitions (ETT) in d-transition metals are considered using titanium as an example. It is shown that, upon a temperature- or pressure-induced transition from the ω-phase to the α-phase, the chemical potential shifts to the region of topological features of the electronic energy spectrum, characterized by a negative curvature of the density of states of d-electrons (DOS). As a result, the sign of the mode-mode interaction parameter changes. The ETT leads to an increase in paramagnon Bose excitations and to the appearance of spatial fluctuations of electron density waves. It is shown that a sharp decrease in volume during the transition from the hp ω-to hcp α-phase is the result of the ETT. In this case, the obtained numerical values are in agreement with the experimental data at normal pressure. Entropy calculations show that paramagnons and spatial fluctuations of the electron density are of the most important reasons for the thermodynamic stability of the titanium structural phases.

Structure and stability of δ-UZr2 phase in U-50 wt% Zr alloy

ABSTRACT Thermodynamic stability of the hexagonal delta phase has been discussed for the U-50 wt% Zr alloy composition based on the XRD, FESEM, and EDS results, further corroborated by the ab-initio calculations. It has been shown that U-50 wt% Zr composition falls into a two-phase region in the U–Zr phase diagram at about 573 K, in contradiction to the published phase diagram. Crystallographic structure of the delta phase in terms of the atomic occupation has been elucidated using the near-neighbour analysis obtained from the EXAFS results. It is shown here that the (111) plane collapse mechanism of the parent bcc phase is not complete in the delta phase even after the sample was aged for 864 ks (240 h) at 573 K.

Layered Transition Metal Oxides as Ca Intercalation Cathodes: A Systematic First‐Principles Evaluation

AbstractFinding high‐voltage Ca cathode materials is a critical step to unleashing the full potential of high‐energy‐density Ca‐ion batteries. First‐principles calculations are used to demonstrate that P‐type layered calcium transition metal (TM) oxide materials (CaTM2O4) with a range of TM substitutions (TM = Ti, V, Cr, Mn, Fe, Co, and Ni) have excellent battery‐related properties including thermodynamic stability, average voltage, energy density, synthesizability, ionic mobility, and electronic structure. However, the thermodynamic stability of the charged phase and TM redox activity are shown to be sensitive to TM selection, with CaCo2O4 having the best balance of all considered properties. The utility of combining multiple TMs to expand the chemical search space for TM substitutions is demonstrated by mixing Co and Ni in layered CaTM2O4.

Study on the Strengthening Mechanism of Rare Earth Ce in Magnesium Alloys, Based on First-Principle Calculations and Electronegativity Theory.

Since the commercial applications of rare earth magnesium alloys are increasing gradually, there are considerable advantages to developing lower cost and higher performance magnesium alloys with high abundance rare earth (RE) elements. However, the alloying order of a matrix magnesium alloy is completely changed with the addition of RE elements. Therefore, further study of the strengthening mechanism of Ce element in magnesium alloys is required. In this work, the thermodynamic stability of the possible second phases in a Mg-Al-Mn-Ce multicomponent magnesium alloy were analyzed, based on first-principle calculations, and the precipitation sequence of the key RE phases was deduced as a consequence. Combined with Scanning Electron Microscope (SEM), X-ray Diffractometer (XRD), Energy Dispersive Spectrometer (EDS), and other experimental methods, it was investigated whether the preferentially precipitated second phases were the nucleation core of primary α-Mg. The complex alloying problem and strengthening mechanism in a multi-elemental magnesium alloy system were simplified with the aid of electronegativity theory. The results showed that the preferentially precipitated Al11Ce3 and Al10Ce2Mn7 phases could not be the nucleation core of primary α-Mg, and the grain refinement mechanism was such that the second phases at the grain boundary prevented the growth of magnesium grains. Moreover, the tensile test results showed that the reinforced structure, in which the Al-Ce phase was mixed with Mg-Al phase, was beneficial for improving the mechanical properties of magnesium alloys, at both ambient temperature and high temperature.

Predicting the thermodynamic stability of perovskite oxides using multiple machine learning techniques

The ultimate objective of material science and engineering is to design a material which gives good property. As part of reaching that aim, the material science community has been working hard to build massive data sets of material characteristics so that researchers can quickly get the properties of identified materials. The development of systems that utilize machine learning techniques to derive prediction models from current materials data is a current active field of research in material science. In this work, we used a dataset which has DFT-calculated perovskite oxide energies to create machine learning models to predict the thermodynamic phase stability of perovskite oxides. Convex hull analysis was used to determine phase stability, with Ehull (energy above the convex hull) providing a direct measure of the stability. Machine learning techniques like K-nearest Neighbor (K-NN), Decision Tree, Support Vector Machine (SVM), Random Forest, Neural Network (NN) and AdaBoost classifiers are used. Found that Out of all these classifiers AdaBoost works better.

Compositional heterogeneity in multiphase steels: Characterization and influence on local properties

Local variations in chemical composition, i.e., compositional heterogeneities, play an important role in the thermodynamic stability and spatial distribution of phases in multiphase steels. The influence of heterogeneous elemental distribution on the resulting local microstructure and mechanical properties has been investigated in the present work. Two steels, one with dual-phase (DP) and one with complex-phase (CP) microstructure, were fabricated from the same cast but differently heat treated in the intercritical annealing regime to yield variations in local microstructure formation. The heterogenous distribution of C and Mn that exists on different length scales are quantified by a characterization approach correlating local chemistry, microstructure, and hardness by using electron probe microanalysis (EPMA), electron backscattered diffraction (EBSD), and nanoindentation. Mn was alternately enriched and depleted in bands parallel to the rolling direction caused by segregation during continuous casting. The local C content was closely associated with the spatial phase distribution resulting from intercritical annealing. In the DP steel, the heterogeneity of C distribution was more pronounced and martensite inherited from the Mn banding due to the lower intercritical annealing temperature. On the other hand, the CP steel, heat treated at higher intercritical annealing temperature, exhibited a more homogenous C distribution resulting in a homogeneous distribution of martensite. In addition to their varying partitioning into the present phases, C and Mn in large martensite islands tended to concentrate in the vicinity of phase interfaces and deplete in the center. Furthermore, chemical boundaries with the smooth transition in local properties were observed in the CP steel. The Mn segregation bands and their impact on martensite morphology and location is reflected by the local hardness distribution. The correlation between compositional heterogeneity, microstructure formation, and microscopic as well as macroscopic mechanical properties is discussed in detail.

Methane hydrate thermodynamic phase stability predictions in the presence of salt inhibitors and their mixture for offshore operations

A thermodynamic model is developed and used in this study to predict the phase equilibrium conditions of a methane -aqueous salt inhibitor -water hydrate system. The modified van der Waals-Platteeuw (vdWP) model is used to calculate the equilibrium condition of the hydrate phase. To compute the fugacities of gas and liquid phases, the Peng-Robinson equation of state (PR-EoS) and a previously developed Pitzer-Mayorga-Zavitsas-hydration model are used. The model predictions are compared to experimental results on methane hydrate phase equilibrium in the presence of an aqueous salt inhibitor. The absolute average relative deviation in predicted methane -aqueous salt inhibitor -water hydrate equilibrium pressure (AARD-P%) with the developed Pitzer-Mayorga-Zavitsas-Hydration model is 3.59% for CH4+NaCl, 1.52% for CH4+KCl, and 2.70% for CH4+ CaCl2. Finally, the hydrate suppression temperature caused by aqueous salt inhibitors and their mixtures on methane hydrate phase stability is calculated, and it is CaCl2>KCl>NaCl in that order. This work's phase equilibrium model demonstrates the potential application of determining methane hydrate equilibrium conditions in the presence of aqueous salt inhibitors and their mixtures used in offshore oil field applications.

Sputtering and Characterization of MAX‐Phase Forming Cr–Al–C and Ti–Al–C Coatings and Their Application on γ‐Based Titanium Aluminides

MAX‐phases are of increasing interest as coating material for high temperature applications due to their unique metallic as well as ceramic properties. Herein, the deposition of Cr2AlC and Ti3AlC2 or Ti2AlC MAX‐phase forming coatings by magnetron sputtering is demonstrated. Using pure elemental targets, the manufacturing with a coating thickness of above 7 μm is established. The MAX‐phase forming coatings are characterized by high‐temperature X‐ray diffraction (HT‐XRD) measurements and provide a good oxidation behavior due to the development of protective thermally grown oxide layers. The performance of the MAX‐phases is strongly depended on the substrate material and the accompanying interdiffusion processes. Therefore, the Ti–Al–C coating is favored for TiAl alloys due to the thermodynamic stability of the Ti2AlC MAX phase in particular in the presence of the γ‐TiAl phase. An excellent oxidation behavior is confirmed up to 300 h at 850 °C due to the development of an alumina layer above a homogenous Ti2AlC phase coating. The Cr2AlC MAX‐phase coating degrades after 100 h at 800 °C due to interdiffusion processes between coating and substrate and the accompanying development of carbides and nitride phases. Nevertheless, the oxidation resistance of the Cr–Al–C‐coated TiAl alloy is given by the formation of the Ti2AlC MAX‐phase.

First principles study of d0-d half-Heusler alloys containing group-IV, -V, and -VI sp atoms as prospective half-metals for real spintronic applications

Employing the full-potential linearized augmented plane-wave method in framework of the density functional theory, the electronic structure, magnetism, structural stability, and half-metallicity of 420 XYZ d0-d half-Heusler alloys composed of d0 alkali metals X = K, Rb, Cs; 3d transition-metals Y = Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn; and group-IV, -V, and -VI elements Z = C, Si, Ge, Sn, Pb, N, P, As, Sb, Bi, O, S, Se, Te are systematically investigated with a goal of identifying compounds of interest for spintronic devices. The calculations led to the introduction of eighty nine new robust half-metallic ferromagnetic compounds with half-metallic gaps in the range 0.04–1.12 eV (within GGA) at the corresponding optimized lattice constants and atomic arrangements. The robustness of these half-metallic gaps against uniform and uniaxial strains are tested. The calculated total spin magnetic moments of all half-metallic structures were integer quantities in units of Bohr magneton, in agreement with either Slater-Pauling rule Mt = (Zt − 8) or Mt = (Zt − 18). It is estimated using Monte Carlo simulations that the Curie temperatures of the half metals, in most cases, are notably higher than the room-temperature. To study the thermodynamic and mechanical (dynamic) phase stability of these half-metallic structures at ambient conditions, the convex hull construction and elastic constants analysis have been employed, respectively. These considerations reveal that many of the d0-d half-metallic structures introduced here may be grown epitaxially under appropriate conditions for real spintronic applications.

Thermodynamics and Na kinetics in P2-type oxygen redox Mn-Ni binary layered oxides manipulated via Li substitution

Sodium-ion batteries (SIBs) have attracted significant attention as promising replacements for lithium-ion batteries (LIBs) due to the wide availability of sodium. However, compared with LIBs, the relatively low energy density, accompanied by fast cycling and rate-performance degradation of SIBs, impedes their practical use. Exploiting oxygen redox reactions increases energy density but induces severe thermodynamic instability with concomitant irreversible capacity decay and large hysteresis. Herein, a combined experimental and theoretical understanding of the P2-type oxygen redox Na2/3[Li1/8Mn5/8Ni2/8]O2 is elucidated from three perspectives: i) electrochemical and structural characterization coupled with thermodynamic phase stability, ii) Na kinetics in terms of various physicochemical factors, and iii) charge compensation mechanism based on Ni and oxygen redox, which is compared with a binary oxide without Li substitution. The experimental results indicate that a quasi-single-phase reaction of Na2/3[Li1/8Mn5/8Ni2/8]O2 occurs during (de)intercalation. It is supported by the thermodynamic formation energies using first-principles calculations. Experimental and computational results consistently reveal improved phase stability compared with the pristine Mn-Ni binary oxide. The kinetic favorability of Na2/3[Li1/8Mn5/8Ni2/8]O2 is theoretically explained by elastic softness, lowered Na migration barrier, and phase stability. X-ray photoelectron spectroscopy and X-ray absorption spectroscopy identifies oxygen redox (above 4.0 V) occurring after the dominant two-electron Ni2+/Ni4+ redox reactions, which is also confirmed by qualitative and quantitative electronic structure analyses. Based on these concrete considerations, the superior cycle and rate performance features of Na2/3[Li1/8Mn5/8Ni2/8]O2 compared with Na2/3[Mn6/8Ni2/8]O2 are demonstrated. This study can serve as a guide to exploit the full potential of oxygen redox properties enabling further advances in SIBs.

Controlled recrystallization from the melt of the organic n-type small molecule semiconductor 2-decyl-7-phenyl-[1]benzothieno[3,2-b][1]benzothiophene S,S,S′,S′-tetraoxide

Recrystallization from the melt of the n-type BTBT derivative 2-dectyl-7-phenyl-[1]benzothieno[3,2-b][1]benzothiophene S,S,S',S'-tetraoxide (Ph-BTBTOx2-10) reveals a defined crystal structure of the molecule. It leads to the formation of alternating nano-segregated layers consisting of parallelly stacked aromatic units and alkyl units. This polymorph appears to be the thermodynamic stable phase. Charge carrier mobility measurements indicate an electron mobility of 4*10−6 cm2 V−1 s−1 for this phase.

Effects of the Chromium Content in (TiVNb)100−xCrx Body-Centered Cubic High Entropy Alloys Designed for Hydrogen Storage Applications

In this paper, we report an investigation of adding a non-hydride forming element in the multicomponent Ti-V-Nb-M system. By the Calculation of Phase Diagrams approach (CALPHAD), the thermodynamic phase stability of the TiVNbT (T = Cr, Mn, Fe, Co, and Ni) was investigated, and Cr was selected as the fourth alloying element due its high tendency to stabilize body-centered cubic solid solutions (BCC). The (TiVNb)100−xCrx alloys (with x = 15, 25, and 35 at.% Cr) were synthesized by arc-melting. The structural characterization reveals that the three alloys were composed of a major BCC phase, which agrees with the thermodynamic calculations. The three alloys absorb hydrogen at room temperature without any activation treatment, achieving a hydrogen uptake of about H/M = 2. The Pressure-Composition-Isotherms curves (PCI) has shown that increasing the Cr amount increases the equilibrium pressures, indicating that tunable H storage properties can be achieved by controlling the alloys’ Cr content.

The Phase Stability of Al3Er Studied by the First-Principles Calculations and Experimental Analysis

The thermodynamics of five Al3Er compounds were investigated through first-principles density-functional theory (DFT) and experimental analysis. The Al3Er compounds with Al3Ho.hR20 (prototype Al3Ho, Pearson symbol hR20), Cu3Au.cP4, AlNd3.hP8, Ni3Ti.hP16 and Al3Gd.hR12 structures exhibited formation energies of −0.412(−0.417), −0.411(−0.416), −0.400(−0.413), −0.399(−0.345) and −0.342(−0.345) meV/atom when using DFT with “standard” potential (“frozen core” potential) of Er. The results indicated that the Al3Ho.hR20 structure was the thermodynamic stable phase and the other structures were metastable. The formation energy of Cu3Au.cP4 structure was only 1 meV/atom less than that of Al3Ho.hR20. Experimentally, the Al-30 wt.% Er alloys were cooled from 900 °C to 500 °C at the rate of 5 ± 2 °C/h and 60 ± 2 °C/h, respectively. The corresponding XRD analysis showed that the Al3Ho.hR20 was formed at the cooling rate of 5 ± 2 °C/h and the Cu3Au.cP4 was formed at the cooling rate of 60 ± 2 °C/h, which indicated that the Al3Ho.hR20 was in a thermodynamic stable phase and the Cu3Au.cP4 was in a metastable phase with high stability. The structural analysis indicated that the tiny energy difference between Al3Ho.hR20 and Cu3Au.cP4 might be attributed to a similar structure with varied stacking sequences.

Investigation of Grain Boundary Influence on the Thermodynamic Phase Stability of Nanocrystalline Iron by Using the Molecular Dynamics Simulation Method

The thermodynamics of allotropic transformation in nanocrystalline Fe is studied. For this purpose, the grain boundary structure is initially examined using a novel method based on molecular dynamics (MD) simulation, the results of which are exploited to determine grain boundary thickness and excess volume for different grain sizes. The dilated crystal model and the quasi-harmonic Debye approximation method are subsequently employed to calculate the values of Gibbs free energy for grain boundaries of different allotropic phases. Using the quantitative parameters obtained from the simulations, the relevant Gibbs free energy curves are plotted in terms of grain size and analyzed for different temperatures. This is followed by deriving stability curves for the γ-Fe and α-Fe phases in terms of grain size for different temperatures. Ultimately, the parameters obtained from MD simulation studies and the stability diagrams thus obtained are used to explore the changes in the γ→α allotropic transformation temperature of iron nanocrystal for different grain sizes. It will be that allotropic transformation temperature declines from 900 to 300 K with rising grain size from 4 to 33 nm.

Effect of Hot-Dip Galvanizing Process on Selective Oxidation and Galvanizability of Medium Manganese Steel for Automotive Application

A medium manganese steel with 7.5 wt.% Mn for automobile application was galvanized in a continuous Hot Dip Galvanizing (HDG) simulator under different galvanizing conditions. It was shown that the effects of dew point, annealing temperature and annealing atmosphere on the surface oxidation of steel could be comprehensively evaluated by the consideration of oxygen partial pressure P(O2). Although Mn2SiO4 was a thermodynamic stable phase when P(O2) varied from 10−28 to 10−21 atm, it was difficult to form Mn–Si–O composite oxide because there was no enrichment of silicon on the steel surface. So, this oxide was generally formed in the Fe substrate and had little effect on the galvanizability. With the increase in P(O2) above 10−25 atm, MnO particles in the form of the thermodynamic stable phase became coarser and tended to aggregate, which hindered the formation of a continuous inhibition layer, resulting in the defects of bare spots on the galvanized surface of the steel. When the oxygen partial pressure greater than 10−22 atm, film-like MnO layer was formed on the surface of steel sample, which obviously deteriorated the galvanizability. The galvanizability of the steel can be improved by the regulation of oxygen partial pressure; based on this, the reasonable zinc plating process parameters can be developed.

Phase stability condition and liquid–liquid phase separation under mesoscale confinement

Here we establish the thermodynamic phase stability condition under mesoscale confinement, which is essential in elucidating how the confinement of solutions inside a droplet, cell or liposome may influence phase separation. To clarify how phase stability is affected by external conditions, a formal analogy between a partially open ensemble and a mesoscopic system will be exploited, through which the nonnegligible role of the system boundary will be identified as the crucial difference from the macroscopic stability condition. The thermodynamic stability condition extended for mesoscale is shown to involve several different orders of magnitude that are all considered to be O(1) at a macroscopic limit. Phase instability in mesoscale is shown to ensue when the difference between self-association (relative self-fluctuation of particle number) and mutual association (relative number correlation between different species) reaches the mesoscopic order of magnitude, in contrast to the divergence of particle number fluctuation (namely, reaching a macroscopic order of magnitude) required in macroscale. Thus, confinement may enhance phase instability.

Shallow Iodine Defects Accelerate the Degradation of α-Phase Formamidinium Perovskite

Summary Shallow defects are mostly benign in covalent semiconductors, such as silicon, given that they do not constitute non-radiative recombination sites. In contrast, the existence of shallow defects in ionic perovskite crystals might have significant repercussions on the long-term stability of perovskite solar cells (PSCs) because of the metastability of the ubiquitous formamidinium lead triiodide (FAPbI3) perovskite and the migration of charged point defects. Here, we show that shallow iodine interstitial defects ( I i ) can be generated unintentionally during commonly used post-fabrication treatments, which can lower the cubic-to-hexagonal transformation barrier of FAPbI3-based perovskites to accelerate its phase degradation. We demonstrate that concurrently avoiding the generation of I i and the more effective passivation of iodine vacancies ( V I ) can improve the thermodynamic stability of the films and operational stability of the PSCs. Our most stable PSC retained 92.1 % of its initial performance after nearly 1,000 h of continuous illumination operational stability testing.