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At least 1,063 records · Page 59

Cation-Driven Assembly of Bilayered Vanadium Oxide and Graphene Oxide Nanoflakes to Form Two-Dimensional Heterostructure Electrodes for Li-Ion Batteries

Lithium preintercalated bilayered vanadium oxide (LVO or δ-Li x V 2 O 5 ·nH 2 O) and graphene oxide (GO) nanoflakes were assembled using a concentrated lithium chloride solution and annealed under vacuum at 200 °C to form two-dimensional (2D) δ-Li x V 2 O 5 ·nH 2 O and reduced GO (rGO) heterostructures. Here we found that the Li + ions from LiCl enhanced the oxide/carbon heterointerface formation and served as stabilizing ions to improve structural and electrochemical stability. The graphitic content of the heterostructure could be easily controlled by changing the initial GO concentration prior to assembly. We found that increasing the GO content in our heterostructure composition helped inhibit the electrochemical degradation of LVO during cycling and improved the rate capability of the heterostructure. A combination of scanning electron microscopy and X-ray diffraction was used to help confirm that a 2D heterointerface formed between LVO and GO, and the final phase composition was determined using energy-dispersive X-ray spectroscopy and thermogravimetric analysis. Scanning transmission electron microscopy and electron energy-loss spectroscopy were additionally used to examine the heterostructures at high resolution, mapping the orientations of rGO and LVO layers and locally imaging their interlayer spacings. Further, electrochemical cycling of the cation-assembled LVO/rGO heterostructures in Li-ion cells with a non-aqueous electrolyte revealed that increasing the rGO content led to improved cycling stability and rate performance, despite slightly decreased charge storage capacity. The heterostructures with 0, 10, 20, and 35 wt % rGO exhibited capacities of 237, 216, 174, and 150 mAh g –1 , respectively. Moreover, the LVO/rGO-35 wt % and LVO/rGO-20 wt % heterostructures retained 75% (110 mAh g–1) and 67% (120 mAh g –1 ) of their initial capacities after increasing the specific current from 20 to 200 mA g –1 , while the LVO/rGO-10 wt % sample retained only 48% (107 mAh g –1 ) of its initial capacity under the same cycling conditions. In addition, the cation-assembled LVO/rGO electrodes exhibited enhanced electrochemical stability compared to electrodes prepared through physical mixing of LVO and GO nanoflakes in the same ratios as the heterostructure electrodes, further revealing the stabilizing effect of a 2D heterointerface. The cation-driven assembly approach, explored in this work using Li + cations, was found to induce and stabilize the formation of stacked 2D layers of rGO and exfoliated LVO. The reported assembly methodology can be applied for a variety of systems utilizing 2D materials with complementary properties for applications as electrodes in energy storage devices.

25 ENERGY STORAGE↗

Eutectic Processing of Semiconductor Colloidal Nanocrystals for Energy Applications

Colloidal semiconductor nanocrystals (NCs) offer a costeffective platform for light-energy conversion in X-ray scintillators, photovoltaics, lasers, and display technologies. Yet, device-relevant NCs often require complex heterostructured compositions, where lattice imperfections compromise the efficiency and stability of photoconversion processes. Here, we show that a simple synthetic detour through a eutectic state of II−VI semiconductor NCs (e.g., CdSe, ZnSe) with halide salts (e.g., CdCl 2 , ZnCl 2 ) overcomes this limitation by melting and reconstructing NC lattices into defect-free alloyed and core/shell architectures. Applied to ternary CdSeTe NCs, this process produces downconverters with record brightness and minimal line widths, delivering a 3-fold increase in film-side external quantum efficiency of commercial CdTe photovoltaic modules (First Solar Inc.). Meanwhile, eutectic processing of CdSe-based core/shell emitters yields an 8-fold enhancement in their photoluminescence stability under backlight operation, addressing the reliability bottleneck for display technologies. Together, these findings establish eutectic NC processing as a scalable route to efficient, durable photoconversion materials for energy applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Inverter Intensive Hybrid Power Plant Modeling with Small-Signal Stability Augmentation through Flexible Operation Mode Transition

Hybrid power plants (HPPs) prompt the penetration of inverter-based renewable energy sources (RES) in transmission systems; however, given their low-inertia nature, HPPs are dominated by power electronic inverters, so there are inevitable challenges in system stability when increasing numbers of HPPs are integrated into the modern power grids. To boost the penetration level of HPPs without jeopardizing system stability, it is desirable to equip them with operational characteristics (i.e., grid-forming capabilities) that are comparable to those of conventional power plants dominated by synchronous generators (SGs). In this paper, a holistic model of inverter intensive HPP is derived and a bi-level hierarchical control is developed to allow HPPs to flexibly switch among the designed operation modes (i.e., P-Q, P-V, and isochronous modes). Compared to SGs, which have limited controllability, the operation mode of each HPP could vary as requested. Such flexible mode transitions could be integrated into the secondary plant-level control and be leveraged as an additional control degree to further augment system stability. Further, the system small-signal stability margin is quantified with varying HPP operation modes. More importantly, modal analysis is thereby conducted to quantify the impacts of mode transition on the system oscillatory modes. The effectiveness of the proposed HPP bi-level hierarchical control is verified using extensive case studies based on the simplified real-world island power grid, and the results validate that the system small-signal stability margin can be enhanced with the additional degree of control flexibility enabled by HPP operation mode transition. The real-time hardware-in-the-loop (HIL) results are also provided to verify the proposed method.

grid-forming control↗

Designing lithium halide solid electrolytes

All-solid-state lithium batteries have attracted widespread attention for next-generation energy storage, potentially providing enhanced safety and cycling stability. The performance of such batteries relies on solid electrolyte materials; hence many structures/phases are being investigated with increasing compositional complexity. Among the various solid electrolytes, lithium halides show promising ionic conductivity and cathode compatibility, however, there are no effective guidelines when moving toward complex compositions that go beyond ab -initio modeling. Here, we show that ionic potential, the ratio of charge number and ion radius, can effectively capture the key interactions within halide materials, making it possible to guide the design of the representative crystal structures. This is demonstrated by the preparation of a family of complex layered halides that combine an enhanced conductivity with a favorable isometric morphology, induced by the high configurational entropy. This work provides insights into the characteristics of complex halide phases and presents a methodology for designing solid materials.

25 ENERGY STORAGE↗

Achieving uniaxial magnetic anisotropy in Ce2⁢Fe17⁢N3 through Co- and Sm-substitution

Th2⁢Zn17−type structure-based permanent magnets, such as Sm2⁢Fe17⁢N3, offer strong potential as alternatives to neodymium magnets (NdFeB), but their practical use is limited by phase stability and the scarcity of Sm. Ce-based counterparts, particularly Ce2⁢Fe17⁢N3, are attractive low-cost candidates, yet their intrinsic planar magnetic anisotropy restricts permanent-magnet performance. Here, we induce uniaxial magnetic anisotropy in Ce2⁢Fe17⁢N3 through two approaches: (i) Co substitution on the Fe sublattice and (ii) partial substitution of Ce with Sm. Combined density functional theory and experimental results show that both strategies modify the 3⁢𝑑–4⁢𝑓 interactions and band filling, yielding magnetization values up to ∼1.2T and magnetocrystalline anisotropy energies exceeding 1MJ/m3 for Co-alloyed compositions, with significantly larger anisotropy achieved upon Sm substitution. In addition, the Sm-substituted Ce2⁢Fe17⁢N3 samples exhibit enhanced high-temperature stability compared to Sm2⁢Fe17⁢N3. These findings demonstrate that Ce2⁢Fe17⁢N3-based alloys can deliver magnetic performance suitable for permanent-magnet applications while reducing cost and reliance on critical rare-earth elements, and they provide practical design guidelines for rare-earth-lean magnets for energy and industrial applications.

Pokhrel, Nabaraj [ORNL] (ORCID:0000000328283076)↗

Microwave resonance enhanced CO 2 reduction using biochar

The conventional process for CO 2 conversion requires high energy and expensive catalysts, and shows poor product selectivity. Here, in this study, we address these challenges by investigating an environmentally friendly method for CO production through the variable frequency microwave-driven CO 2 Boudouard reaction over biochar. We hypothesized that tuning the microwave frequency to align with the dielectric properties of biochar, and thereby induce a resonance effect, could significantly enhance reaction efficiency. Experiments were conducted to explore the effect of microwave frequency on CO 2 conversion efficiency in the variable frequency microwave reactor operating within a frequency range of 2430–6000 MHz. Results reveal a significant resonance effect at 4225 MHz resulting in an outstanding CO 2 conversion of 96.3%, in sharp contrast to the complete absence of conversion observed at the conventional 2450 MHz. The resonance frequency not only facilitated exceptional conversion but also remarkably improved energy efficiency, yielding a productivity of 1427.5 µmol/kJ of CO. This represents a remarkable 474-fold increase compared to electrical heating. Furthermore, continuous microwave irradiation at this optimized frequency demonstrated remarkable stability and induced substantial enhancements in the pore structure and surface area of biochar. This innovative approach provides promising insights into sustainable and efficient CO production processes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Low-dimensional carbon materials decorated FAPbI 3 for carbon-based perovskite solar cells

Carbon nanomaterials are at the forefront of research in perovskite solar cells (PSCs) due to their exceptional electrical, optical, and stability properties. Their diverse applications include serving as interfacial layers, additives, hole and electron transport materials, and back electrodes. While the influence of various low-dimensional carbon nanomaterial structures on crystallinity, optical and electrical performance, and overall device efficiency has been a topic of interest, it has not been thoroughly explored until now. In this study, we effectively integrated carbon quantum dots (CQDs), multi-walled carbon nanotubes (MWCNTs), and graphene into the FAPbI 3 photoactive layer using a two-step sequential deposition method. Our experiments revealed marked improvements in the photovoltaic performance of PSCs that incorporated all three types of carbon nanomaterials. In particular, the data shows significant enhancements in power conversion efficiency, demonstrating the effectiveness of these materials in optimizing device functionality. Notably, MWCNTs distinguished themselves by exhibiting a remarkable potential for enhancing long-term stability. This finding underscores the importance of selecting the right carbon nanomaterials for future PSC developments, paving the way for more reliable and efficient solar energy solutions. As a result, our research highlights the critical role of carbon nanomaterials in advancing perovskite solar technology.

14 SOLAR ENERGY↗

On the Origin of Sinter‐Resistance and Catalyst Accessibility in Raspberry‐Colloid‐Templated Catalyst Design

Abstract Nanoparticle (NP) sintering is a major cause of the deactivation of supported catalysts. Raspberry‐colloid‐templated (RCT) catalysts are an emerging class of materials that show an unprecedented level of sinter‐resistance and exhibit high catalytic activity. Here a comprehensive study of the origin of NP stability and accessibility in RCT catalysts using theoretical modeling, 3D electron microscopy, and epitaxial overgrowth is reported. The approach is showcased for silica‐based RCT catalysts containing dilute Pd‐in‐Au NPs previously used in hydrogenation and oxidation catalysis. Modeling of the contact line of the silica precursor infiltrating into the assembled raspberry colloids suggests that a large part of the particles must be embedded into silica, which is confirmed by quantitative visualization of >200 individual NPs by dual‐axis electron tomography. The RCT catalysts have a unique structure in which all NPs reside at the pore wall but have >50% of their surface embedded in the matrix, giving rise to the strongly enhanced thermal and mechanical stability. Importantly, epitaxial overgrowth of Ag on the supported NPs reveals that not only the NP surface exposed to the pore but the embedded interface as well remained chemically accessible. This mechanistic understanding provides valuable guidance in the design of stable catalytic materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

How do super concentrated electrolytes push the Li-ion batteries and supercapacitors beyond their thermodynamic and electrochemical limits?

Increasing the energy density of energy storage devices is currently the key target of many battery and supercapacitor research activities. For both types of devices, the electrochemical stability window (ESW) determines the effective energy density of the device. ESWs are defined by the effective oxidation and reduction potentials of the electrolyte, which are controlled by many various factors, including the HOMO/LUMO (highest/lowest unoccupied molecular orbital) energies of the electrolyte molecules, the nature of the electrode/electrolyte interphases, and other physicochemical properties. The concentration of the electrolyte would affect the HOMO/ LUMO levels thus also change the ESW. A higher concentration of salt induces specific arrangements among the anion, cation, and solvent molecules of an electrolyte, altering the bulk behavior of the electrolyte, resulting in drastic change in the electrode interfaces. These uniquely modified physicochemical properties extend the ESW in several different ways, including the enhancement in the kinetic stability of the electrodes, as well as the thermodynamic and Nernst shifts of the oxidation/reduction potentials of the electrolyte. For organic electrolytes, it is the reduced amount of free solvent molecules that plays the key role in such changes; whereas for aqueous electrolytes, it is the scarcity of free water molecules and the reduced water activity that control the key properties of the electrolyte. Here, we focus on elucidating the fundamental structural changes occurring within an electrolyte system with increasing salt concentrations. The underlying mechanisms which not only facilitates the extension of the ESW, but also enables higher rate capabilities and mitigates aluminum dissolution for batteries with organic electrolytes, are meticulously explained. Further, we thoroughly discuss the importance of high-voltage stability in aqueous battery systems by exploiting the changed properties observed with higher concentrations of salts. To finish, high-voltage supercapacitors enabled by superconcentrated electrolytes are also explored.

25 ENERGY STORAGE↗

Effective Corrosion-Resistant Single-Atom Alloy Catalyst on HfO 2 -Passivated BiVO 4 Photoanode for Durable (≈800 h) Solar Water Oxidation

Green hydrogen (H 2 ) production from solar water splitting necessitates photoelectrodes with superior photoelectrochemical (PEC) activity and durability. However, surface defects and photocorrosion instability—especially at high potentials—limit PEC performance and stability. Herein, the prototypical bismuth vanadate (BiVO 4 ) photoanode is used to demonstrate a holistic approach to improve photocurrent density and long-term stability. In this approach, high surface-area nanostructuring of BiVO 4 is combined with barium (Ba) doping with semi-crystalline hafnium oxide (HfO 2 ) surface passivation and single-atom nickel platinum (NiPt) catalysts. The introduction of Ba 2+ ions into BiVO 4 increases the concentration of conductive V 4+ ions or the ratio of V 4+ ions to oxygen vacancies, avoiding V 5+ dissolution during water oxidation. The semi-crystalline HfO 2 , which serves as a passivation layer, prevents BiVO 4 photocorrosion by suppressing harmful chemical reactions when holes are transferred to the electrolyte. The synergistic use of isolated single-atom and Ni-Pt coordination improves charge transfer at the photoanode/electrolyte interface, leading to enhanced PEC kinetics and stability. As a result, a photoelectrode is demonstrated with ≈6.5 mA cm -2 at 1.23 V versus a reversible hydrogen electrode (RHE) and continuous operation for 800 h with a negligible degradation rate. This work provides a promising approach to improve photoanodes for PEC H 2 production.

08 HYDROGEN↗

Flexible Launch Vehicle Stability Analysis Using Steady and Unsteady Computational Fluid Dynamics

Launch vehicles frequently experience a reduced stability margin through the transonic Mach number range. This reduced stability margin can be caused by the aerodynamic undamping one of the lower-frequency flexible or rigid body modes. Analysis of the behavior of a flexible vehicle is routinely performed with quasi-steady aerodynamic line loads derived from steady rigid aerodynamics. However, a quasi-steady aeroelastic stability analysis can be unconservative at the critical Mach numbers, where experiment or unsteady computational aeroelastic analysis show a reduced or even negative aerodynamic damping.Amethod of enhancing the quasi-steady aeroelastic stability analysis of a launch vehicle with unsteady aerodynamics is developed that uses unsteady computational fluid dynamics to compute the response of selected lower-frequency modes. The response is contained in a time history of the vehicle line loads. A proper orthogonal decomposition of the unsteady aerodynamic line-load response is used to reduce the scale of data volume and system identification is used to derive the aerodynamic stiffness, damping, and mass matrices. The results are compared with the damping and frequency computed from unsteady computational aeroelasticity and from a quasi-steady analysis. The results show that incorporating unsteady aerodynamics in this way brings the enhanced quasi-steady aeroelastic stability analysis into close agreement with the unsteady computational aeroelastic results.

Bartels, Robert E.↗

DEVELOPMENT OF STABLE ANODE AND CATHODE MATERIALS FOR RECHARGEABLE BATTERIES

Batteries have been employed in a variety of applications, such as portable electronics, electric vehicles (EVs), and stationary energy storage to preserve energy from other renewable sources (like wind or solar energy). The ultimate goal is to develop high energy density, long life span, better safety, and low cost of the batteries. However, current commercialized batteries (like lead-acid, zinc-alkaline, lithium-ion batteries (LIBs)) could not fulfill all the demands of diversified applications. LIBs predominate the market because of their high energy density. To achieve a higher capacity of the cell, high-nickel layered (Ni > 90%) cathode materials are promising candidates since they compose high specific capacity and discharge voltage. In chapter 1, an introduction to cell energy density and the development of high-nickel layered cathode materials along with associated obstacles of poor cycling stability and thermal stability have been discussed. Associated works like doping or surface coating have also been mentioned in this section. In chapter 2, Al doping in high-nickel layered cathode materials to enhance the structural and thermal stability was introduced. Uniform incorporation of Al doping is achieved by mechanical fusion and calcination processes. The Al doping not only decreased the Li/Ni mixing ratio but also enhance the thermal resistance to oxygen evolution because of strong Al-O bonding, which leads to elevated electrochemical and thermal stability. In chapter 3, TiN is implemented as a Ti dopant for high-nickel layered cathode materials to improve the electrochemical performance in the LIBs. The Ti not only diffused within the bulk structure but also formed segregation on the surface, which improved the structural stability and led to better cycling performance. Although LIBs deliver high energy density, safety concerns of flammable organic electrolytes have not been resolved yet. Therefore, the aqueous rechargeable zinc-ion batteries (ZIB) have been praised for their safe, low-cost, eco-friendly stationary energy storage, which is considered as a complementary system to LIBs. In chapter 4, the mechanism, advantages, and challenges of ZIBs would be given and the strategies for solving the zinc metal anode issues have been discussed in this section. In chapter 5, a polymer coating method was reported to facilitate Zn deposition/ stripping by coordination with Zn2+ and prevented direct contact with aqueous electrolyte to block corrosion side-reactions. With this coating, a boost in a lifetime (up to 400 hours) and lower polarization under extremely high current conditions (10 mA cm-2) have been achieved in repeated Zn deposition/ stripping cycling.

25 ENERGY STORAGE↗

Impact of Linker Engineering in Core‐Linked Dimeric Acceptors for High‐Performance Organic Solar Cells

Abstract The dimerization of small molecule acceptors (SMAs) is a promising strategy for enhancing the long‐term stability and power conversion efficiency (PCE) of organic solar cells (OSCs). However, the reported DSMAs are primarily limited to end‐linked molecular configurations, highlighting the need for further exploration of various dimer architectures. Herein, the development of two distinct core‐linked dimerized SMAs (DYF‐V and DYF‐E) are reported with tailored linker structures (vinylene and ethynyl, respectively), achieving high‐performance OSCs (PCE = 18.53%). Interestingly, a subtle change in the linker structures results in markedly different molecular properties and photovoltaic performances of the dimer acceptors. DYF‐E with an ethynyl linker exhibits more twisted backbone conformation and mitigated aggregation property compared to DYF‐V, inducing desirable blend morphologies with a polymer donor including high crystallinity, face‐on oriented packing structures, and well‐intermixed domains. Thus, the DYF‐E‐based OSCs exhibit a high PCE (17.02%), which significantly outperforms the DYF‐V‐based OSCs (PCE = 9.98%). Furthermore, the ternary OSCs based on DYF‐E achieve a higher PCE of 18.53%. Thus, this study highlights the significance of selecting an appropriate linker in core‐linked dimerized SMAs for producing high‐performance OSCs.

Oh, Shinbee↗

Ligand-Exchange-Induced Amorphization of Pd Nanomaterials for Highly Efficient Electrocatalytic Hydrogen Evolution Reaction

Various kinds of amorphous materials, such as transition metal dichalcogenides, metal oxides, and metal phosphates, have demonstrated superior electrocatalytic performance compared with their crystalline counterparts. Compared to other materials for electrocatalysis, noble metals exhibit intrinsically high activity and excellent durability. However, it is still very challenging to prepare amorphous noble-metal nanomaterials due to the strong interatomic metallic bonding. Herein, the discovery of a unique thiol molecule is reported, namely bismuthiol I, which can induce the transformation of Pd nanomaterials from face-centered-cubic (fcc) phase into amorphous phase without destroying their integrity. This ligand-induced amorphization is realized by post-synthetic ligand exchange under ambient conditions, and is applicable to fcc Pd nanomaterials with different capping ligands. Importantly, the obtained amorphous Pd nanoparticles exhibit remarkably enhanced activity and excellent stability toward electrocatalytic hydrogen evolution in acidic solution. This work provides a facile and effective method for preparing amorphous Pd nanomaterials, and demonstrates their promising electrocatalytic application.

36 MATERIALS SCIENCE↗

A Flexible, Redox-Active, Aqueous Electrolyte-Based Asymmetric Supercapacitor with High Energy Density Based on Keratin-Derived Renewable Carbon

This work exploits the advantage of asymmetric configuration over symmetric supercapacitor in designing high energy density flexible devices from two active electrode materials–keratin-based renewable-resource hierarchically porous carbon and hydrous ruthenium oxide (RuO 2 ). Here, the asymmetric device exhibits significantly high capacitance. Conventional estimation of energy storage parameters, however, cannot be applied for devices with a Faradaic energy storage contribution via redox charge transfer mechanism. Therefore, this work applies a precise measurement of pseudocapacitance contribution at various scan rates to correct the device data that reveals effective capacitance of 120 F g –1 with the energy density of 37 W h kg –1 at 776 W kg –1 . It also retains excellent rate capability, >74% at high current density 25 A g –1 . The charge storage activity and device stability can be further enhanced by introducing redox-active electrolytes that improve specific capacitance, but the rate capabilities deteriorate at high current densities. Further, the principle of asymmetric electrode design is applied to fabricate a bending-tolerant, flexible device by depositing active electrode material on wire-shaped current collector followed by coupling those separated with polyvinyl alcohol gel containing redox electrolyte; it yields 36.8 mF cm –1 specific capacitance at a 0.2 mA cm –1 current density.

36 MATERIALS SCIENCE↗

Designing Electrolytes With Controlled Solvation Structure for Fast‐Charging Lithium‐Ion Batteries

Recharging battery-powered electric vehicles (EVs) in a similar timeframe as those used for refueling gas-powered internal combustion vehicles is highly desirable for rapid penetration of the EV market. It is well known that the electrolyte in a battery plays a critical role in fast-charging capability of the battery because it determines the rate of ion transport together with its derived electrode/electrolyte interphases on both cathode and anode of the battery. In this study, the effects of contents of salt, coordinating solvent, and noncoordinating diluent on salt dissociation degree and electrolyte ionic conductivity are investigated, and a controlled solvation structure electrolyte is developed to improve the lithium ion mobility and conductivity in the electrolyte and to enhance the kinetics and stability of the electrode/electrolyte interphases in the battery. This electrolyte enables fast-charging capability of high energy density lithium-ion batteries (LIBs) at up to 5 C rate (12-min charging), which significantly outperforms the state-of-the-art electrolyte. The controlled solvation structure sheds light on the future electrolyte design for fast-charging LIBs.

25 ENERGY STORAGE↗

Why Perovskite Thermal Stress is Unaffected by Thin Contact Layers

Metal halide perovskite photovoltaics have emerged as a high efficiency, low-cost alternative that can potentially rival or enhance conventional silicon technology. Despite exceptional initial power conversion efficiencies, achieving compliance with international standards and widespread adoption requires further enhancements to their operational stability. Notably, addressing mechanical strain and stress in brittle perovskites has emerged as a pivotal approach to mitigate chemical degradation and improve reliability during thermal cycling. Here, in this study, a popularized strain engineering strategy is investigated in which a high coefficient of thermal expansion (CTE) hole transport layer (i.e., PDCBT) is cast onto inorganic perovskite (CsPbI 2 Br) at 100 °C. Contrary to previously published results, the X-ray diffraction (XRD):Sin 2 ψ and substrate curvature measurement techniques show that the hole transport layer has no discernible impact on perovskite strain. The accuracy of the XRD:Sin 2 ψ method for measuring strain is highlighted in contrast to an analysis based on shifts of single XRD peaks which can be influenced by multiple artifacts. The findings in this study are in accordance with mechanics theory: thin layers are unable to induce significant strain changes in perovskite thin films as the force they apply is negligible compared to that applied by a thick and stiff substrate.

14 SOLAR ENERGY↗