Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “energy density functional”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 667 records · Page 37

Covalent Functionalization of Nickel Phosphide Nanocrystals with Aryl-Diazonium Salts

Covalent functionalization of Ni 2 P nanocrystals was demonstrated using aryl-diazonium salts. Spontaneous adsorption of aryl functional groups was observed, with surface coverages ranging from 20 to 96% depending on the native reactivity of the salt as determined by the aryl substitution pattern. Increased coverage was possible for low reactivity species using a sacrificial reductant. Functionalization was confirmed using thermogravimetric analysis, Fourier transform infrared spectroscopy, and X-ray photoelectron spectroscopy. The structure and energetics of this nanocrystal electrocatalyst system, as a function of ligand coverage, were explored with density functional theory calculations. The Hammett parameter of the surface functional group was found to linearly correlate with the change in Ni and P core-electron binding energies and the nanocrystal's experimentally and computationally determined work function. The electrocatalytic activity and stability of the functionalized nanocrystals for hydrogen evolution were also improved when compared to the unfunctionalized material, but a simple trend based on electrostatics was not evident. Density functional theory was used to understand this discrepancy, revealing that H adsorption energies on the covalently functionalized Ni 2 P also do not follow the electrostatic trend and are predictive descriptors of the experimental results.

14 SOLAR ENERGY↗

First Principles Nonadiabatic Excited-State Molecular Dynamics in NWChem

Computational simulation of non-adiabatic molecular dynamics is an indispensable tool for understanding complex photoinduced processes such as internal conversion, energy transfer, charge separation, and spatial localization of excitons, to name a few. Here, we report an implementation of the fewest-switches surface hopping algorithm in the NWChem computational chemistry program. Here the surface hopping method is combined with linear-response time-dependent density functional theory calculations of adiabatic excited state potential energy surfaces. To treat quantum transitions between arbitrary electronic Born{Oppenheimer states, we have implemented both numerical and analytical differentiation schemes for derivative non-adiabatic couplings. A numerical approach for the time-derivative non-adiabatic couplings together with an analytical method for calculating non-adiabatic coupling vectors is an efficient combination for surface hopping approaches. Additionally, electronic decoherence schemes and a state reassigned unavoided crossings algorithm are also implemented to improve the accuracy of the simulated dynamics and to handle trivial unavoided crossings. We apply our code to study the ultrafast decay of photoexcited benzene, including a detailed analysis of the potential energy surface, population decay time scales, and vibrational coordinates coupled to the excitation dynamics. The development presented in this work is a baseline for future implementations of more sophisticated frameworks for simulating of non-adiabatic molecular dynamics in NWChem.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Leptodermic corrections to the TOV equations and nuclear astrophysics within the effective surface approximation

The macroscopic model for a neutron star (NS) as a liquid drop at the equilibrium is used to extend the Tolman-Oppenheimer-Volkoff (TOV) equations taking into account the gradient terms responsible for the system surface. The parameters of the Schwarzschild metric in the spherical case are found with these surface corrections to the known leading (zero) order of the leptodermic approximation a/R << 1, where a is the NS effective-surface (ES) thickness, and R is the effective NS radius. The energy density $\mathscr{E}$ is considered in a general form including the functions of the particle number density and of its gradient terms. The macroscopic gravitational component $Φ$(ρ) of the energy density is taken into account in the simplest form as expansion in powers of $ρ$ – $\overline{ρ}$, where $\overline{ρ}$ is the saturation density, up to second order, in terms of its contributions to the separation particle energy and incompressibility. Density distributions ρ across the NS ES in the normal direction to the ES, which are derived in the simple analytical form at the same leading approximation, was used for the derivation of the modified TOV (MTOV) equations by accounting for their NS surface corrections. As a result, the MTOV equations are analytically solved at first order and the results are compared with the standard TOV approach of the zero order.

Magner, A. G. [Institute for Nuclear Research, Kyi↗

Hybrid interatomic potential for Sn

To design materials for extreme applications, it is important to understand and predict phase transitions and their influence on material properties under high pressures and temperatures. Atomistic modeling can be a useful tool to assess these behaviors. However, this can be difficult due to the lack of fidelity of the interatomic potentials in reproducing this high pressure and temperature extreme behavior. Here, in this work, a hybrid EAM-R—which is the combination of embedded atom method (EAM) and rapid artificial neural network potential—for Tin (Sn) is described which is capable of accurately modeling the complex sequence of phase transitions between different metallic polymorphs as a function of pressure. This hybrid approach ensures that a basic empirical potential like EAM is used as a lower energy bound. By using the final activation function, the neural network contribution to energy must be positive, assuring stability over the whole configuration space. This implementation has the capacity to reproduce density functional theory results at 6 orders of magnitude slower than a pair potential for molecular dynamics simulation, including elastic and plastic characteristics and relative energies of each phase. Using calculations of the Gibbs free energy, it is demonstrated that the potential precisely predicts the experimentally observed phase changes at temperatures and pressures across the whole phase diagram. At 10.2 GPa, the present potential predicts a first-order phase transition between body-centered tetragonal (BCT) β-Sn and another polymorph of BCT-Sn. This structure transforms into body-centered cubic near the experimentally reported value at 33 GPa. Thus, the Sn potential developed in this paper can be used to study complex deformation mechanisms under extreme conditions of high pressure and strain rates unlike existing potentials. Moreover, the framework developed in this paper can be extended for different material systems with complex phase diagrams.

36 MATERIALS SCIENCE↗

Why Conventional Design Rules for C–H Activation Fail for Open-Shell Transition-Metal Catalysts

The design of selective and active C–H activation catalysts for direct methane-to-methanol conversion is challenging. Bioinspired complexes that form high-valent metal–oxo intermediates capable of hydrogen abstraction and rebound hydroxylation are promising candidates. This promise has made them a target for computational high-throughput screening, typically simplified through the use of linear free energy relationships (LFERs). However, their mid-row transition-metal centers have numerous accessible spin and oxidation states that increase the combinatorial scale of design efforts. Here, we carry out a computational design screen of over 2500 mid-row 3d transition-metal complexes with four metals in numerous spin and oxidation states. We demonstrate the importance of spin/oxidation state in dictating design principles, limiting the generalization of strategies derived for widely studied high-spin Fe(II) catalysts to other metals or spin/oxidation states. Combined assessment of the effect of ligand-field tuning on reaction step energetics and on the identity of the ground state allows us to propose refined design strategies for spin-allowed methane-to-methanol catalysis. We observe weak coupling of energetics and design principles between reaction steps (e.g., oxo formation vs methanol release), meaning that LFERs do not generalize across our larger catalyst set. To rationalize relative reactivity in known catalysts, we instead compute independent reaction energies and propose strategies for further improvements in catalyst design.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Structure and Synthesizability of Iron–Sulfur Metal–Organic Frameworks

Sulfur-based metal–organic frameworks (MOFs) and coordination polymers (CPs) are an emerging class of hybrid materials that have received growing attention due to their magnetic, conductive, and catalytic properties with potential applications in electrocatalysis and energy storage. In this work, we report a high-throughput virtual screening protocol to predict the synthesizability of candidate metal–sulfur MOFs/CPs by computing the thermodynamically stable structures resulting from a particular combination of metal cluster, linker, cation, and synthetic conditions. Free energies are computed by using all-atom classical mechanical thermodynamic integration. Low-free-energy structures are refined using ab initio density functional theory, and pair distribution functions and powder X-ray diffraction patterns are calculated to complement and guide experimental structure determination. We validate the computational approach by retrospective predictions of the stable structure produced by experimental syntheses, and a subsequent screen predicts Fe 4 S 4 -BDT–TPP as a new thermodynamically stable one-dimensional (1D) CP comprising a redox-active Fe 4 S 4 cluster, a 1,4-benzenedithiolate (BDT) linker, and a tetraphenylphosphonium (TPP) countercation. Furthermore, this material is experimentally synthesized, and the 1D chain structure of the crystal is confirmed using microcrystal electron diffraction. The computational screening pipeline is generically transferable to neutral and ionic MOFs/CPs comprising arbitrary metal clusters, linkers, cations, and synthetic conditions, and we make it freely available as an open source tool to guide and accelerate the discovery and engineering of novel porous materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Analytic Nuclear Gradients for Complete Active Space Linearized Pair-Density Functional Theory

Accurately modeling photochemical reactions is difficult due to the presence of conical intersections and locally avoided crossings, as well as the inherently multiconfigurational character of excited states. As such, one needs a multistate method that incorporates state interaction in order to accurately model the potential energy surface at all nuclear coordinates. The recently developed linearized pair-density functional theory (L-PDFT) is a multistate extension of multiconfiguration PDFT, and it has been shown to be a cost-effective post-MCSCF method (as compared to more traditional and expensive multireference many-body perturbation methods or multireference configuration interaction methods) that can accurately model potential energy surfaces in regions of strong nuclear–electronic coupling in addition to accurately predicting Franck–Condon vertical excitations. Here, in this paper, we report the derivation of analytic gradients for L-PDFT and their implementation in the PySCF-forge software, and we illustrate the utility of these gradients for predicting ground- and excited-state equilibrium geometries and adiabatic excitation energies for formaldehyde, s-trans-butadiene, phenol, and cytosine.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Surface Charge and Electrostatic Spin Crossover Effects in CoN 4 Electrocatalysts

Carbon materials doped with nitrogen and 3d transition metals have attracted a great deal of interest for catalyzing electrochemical reactions such as water splitting, oxygen reduction, and carbon dioxide reduction. Here, we employed density functional theory to study Co–N-doped carbon as electrocatalysts for the oxygen reduction and oxygen evolution reactions. Specifically, we investigated the interplay among adsorption energies, the spin state of the CoN 4 active center, and the applied potential. We found that adsorption energies strongly depend on both the applied potential and the spin state of the Co center. Furthermore, spin state transitions induced by the applied potential also play an important role in determining the adsorption energies. Here, this effect originates from a different potential of zero charge and capacitance of each spin state.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Computational Approaches for Clean Energy Materials

Currently, 80% of the global final energy consumption occurs in form of fuels and only 20% as electricity. On the other hand, renewable energy additions come almost exclusively in the form of electricity (dominantly photovoltaics and wind). Thus, a successful energy transition will require enormous growth in renewables, sufficient to convert excess electricity into fuels, as well as the development of non-electricity based solar fuel technologies. As much as photovoltaic capacities have grown over the past 20 years, it is far from clear that current technologies and materials are up to the task to grow from here by yet another factor 100 until 2050. Therefore, sustained research efforts on emerging inorganic semiconductors for solar electricity and fuels are essential for facing the double challenge of climate change and energy security. Computational materials science can make important contributions, guiding and supporting research activities through both materials search and discovery and through detailed studies that help to develop a mechanistic understanding of materials performance and bottlenecks. This presentation will highlight three recent computational projects with relevance for photovoltaics and solar fuels (1) Defect graph neural networks (dGNN) for materials discovery in solar thermochemical hydrogen (STCH) [1]. The dGNN approach facilitates broad and fast materials screening for defect properties. (2) Modeling highly off-stoichiometric systems by evaluating the free energy of defect interaction [2]. This approach allows quantitative prediction of H2 production in complex STCH oxides. (3) First-principles atomic structure prediction for interfaces [3]. This work showed how an atomically thin CdCl2 interlayer phase enables in principle ideal electron transport across the incommensurate SnO2/CdTe interface. [1] M.D. Witman, A. Goyal, T. Ogitsu, A.H. McDaniel, S. Lany, Nat. Comput. Sci. (2023). https://doi.org/10.1038/s43588-023-00495-2. [2] A. Goyal, M.D. Sanders, R.P. O'Hayre, S. Lany, PRX Energy 3, 013008 (2024). https://doi.org/10.1103/PRXEnergy.3.013008. [3] A. Sharan, M. Nardone, D. Krasikov, N. Singh, S. Lany, Appl. Phys. Rev. 9, 041411 (2022). https://doi.org/10.1063/5.0104008.

density functional theory↗

Using distributions to understand neutron and x-ray production in ICF ignition capsules and other high energy density plasmas

Here this paper describes how x-ray and neutron distribution functions can be useful tools to visualize the conditions measured in many types of plasma physics experiments. In particular, we model a standard inertial confinement fusion ignition capsule that consists of a Si doped plastic ablator surrounding a layer of deuterium–tritium (DT) ice as the yield varies from 18 kJ to 16.7 MJ and use the distribution functions to show that neutrons and high energy x rays (15 keV) are produced under similar conditions when the yield is low. However, as the capsule starts to support a propagating burn due to alpha heating, the x rays and neutrons are produced under somewhat different conditions in different parts of the plasma. In particular, the x-ray production takes place mainly in the hot plastic ablator for the full yield ignition capsule under quite different plasma conditions from the DT region producing the 14 MeV neutrons, which results in x-ray images with larger radii than the corresponding neutron images. These same distribution functions can be applied to many other plasma physics experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Using data-science approaches to unravel insights for enhanced transport of lithium ions in single-ion conducting polymer electrolyte

Solid polymer electrolytes have yet to achieve the an ionic conductivity > 1 mS/cm at room temperature for realistic applications. This target implies the need to reduce the effective energy barriers of ion transport in polymer electrolytes to around 20 kJ/mol. In this work, we combine information extracted from existing experimental results with theoretical calculations to provide insights into ion transport in single-ion conductors (SICs) with a focus on lithium ion SICs. Through the analysis of temperature-dependent ionic conductivity data obtained from the literature, we evaluate different methods of extracting energy barriers for lithium transport. The traditional Arrhenius fit to the temperature-dependent ionic conductivity data indicates that the Meyer-Neldel rule holds for SICs. However, the values of the fitting parameters remain unphysical. Our modified approach based on recent work (Macromolecules, 56, 15, 6051(2023)), which incorporates a fixed pre-exponential factor, reveals that the energy barriers exhibit temperature dependence over a wide range of temperatures. Using this approach, we identify a series of anions leading to the energy barriers less than 30 kJ/mol, which include trifluoromethane sulfonimide (TFSI), fluoromethane sulfonimide (FSI), and boron-based organic anions. In our efforts to design the next generation of anions, which can exhibit the energy barriers less than 20 kJ/mol, we focused on boron-containing SICs, and performed density functional theory (DFT) based calculations to connect the chemical structures via the binding energy of cation (lithium)-anion pairs with the experimentally derived effective energy barriers for ion transport. Not only have we identified a correlation between the binding energy and the energy barriers, but we also propose a strategy to design new boron-based anions by using the correlation. This combined approach involving experiments and theoretical calculations is capable of facilitating the identification of promising new anions, which can exhibit ionic conductivity $> 1$ mS/cm near room temperature, thereby expediting the development of novel superionic single-ion conducting polymer electrolytes. The published datasets include all the temperature-dependent ionic conductivity collected from the literature with literature DOIs, DFT calculated binding energies, and python scripts to analyze data, construct statistical models, and generate plots.

36 MATERIALS SCIENCE↗

Design Strategies of Spinel Oxide Frameworks Enabling Reversible Mg-Ion Intercalation

In this study, reversible Mg 2+ intercalation in metal oxides frameworks is a key enabler for an operational Mg ion battery with high energy density needed for the next generation of energy storage technologies. While functional Mg-ion batteries have been achieved in structures with soft anions (e.g., S 2- and Se 2- ), they do not meet energy density requirements to compete with the current rechargeable lithium-ion batteries due to their low insertion potentials, emphasizing the necessity of finding an oxide-based cathode that operates at high potentials. A leading hypothesis to explain the limited availability of oxide Mg-ion cathodes is the belief that Mg 2+ has sluggish diffusion kinetics in oxides due to strong electrostatic interactions between the Mg 2+ ions and oxide anions in the lattice. From this assessment, it can be hypothesized that such rate limiting kinetic shortcomings can be mitigated by tailoring an oxide framework through creating less stable Mg 2+ - O 2- coordination.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Assessment of exchange-correlation functionals on oxygen vacancy formation energies of metal oxides

Oxygen vacancies are a common defect in oxides and play vital roles in many technological applications such as oxygen separation, catalytic reactors, solid oxide fuel cells, and solar thermochemical water splitting. The oxygen vacancy formation energy is directly related to the oxide reduction enthalpy and the vacancy concentration and, therefore, is a key quantity underlying these applications. The complexity of measuring oxygen vacancy formation energies experimentally suggests the utility of calculations based on density functional theory (DFT). However, the calculated results are strongly dependent on the exchange-correlation functionals and other parameters such as the Hubbard U . In this work, we compare the performance of the meta-GGA strongly constrained and appropriately normed (SCAN) functional and the commonly used semilocal generalized gradient approximation (GGA) functionals with experimental values of structural parameters, band gaps, magnetic structures, and oxygen vacancy formation energies for six representative oxides, i.e., CaMnO 3 , SrMnO 3 , LaMnO 3 , YMnO 3 , LaFeO 3 , and CeO 2 . Further, our results show that SCAN usually has better agreement with the experimental lattice constants and band gaps and larger magnetic moments than the commonly used GGA functionals. Although SCAN overestimates the oxygen vacancy formation energies of transition metal oxides and therefore requires unusually large Hubbard U values to reproduce the experimental reduction enthalpies, it does predict the correct oxygen vacancy formation energy of CeO 2 , which challenges the commonly used GGA and hybrid functionals. Our results underscore the challenges that exist in describing these complex oxides by DFT and may shed light on developing more accurate exchange-correlation functionals for oxygen vacancy formation energy calculations.

36 MATERIALS SCIENCE↗

Asymmetric equilibrium core structures of pyramidal-II < c + a > dislocations in ten hexagonal-close-packed metals

The structures of pyramidal-II < c + a > dislocations, one of the most important defects in structural hexagonal-close-packed (HCP) metals, have not been fully characterized for many of the HCP metals in use today. Here, we employ ab initio informed phase-field dislocation dynamics to determine the minimum energy structure of pyramidal {1¯1¯22} < 11¯23 > dislocations in ten HCP metals, including Be, Co, Mg, Re, Ti, Zn, Cd, Hf, Y, and Zr. As input for the simulations, we calculate, using first-principles density functional theory, the {1¯1¯22} generalized stacking fault energy (GSFE) curves for all ten metals. From these calculations, it is found that magnetism in Co is necessary for achieving a local minimum in the GSFE curve. We observe in simulations that edge and screw character dislocations split into two partials separated by a low-energy intrinsic stacking fault. The splitting distance is shown to scale inversely with the local minimum energy normalized by the product of its shear modulus and Burgers vector. Interestingly, some HCP metals exhibit an asymmetric structure, with either unequal partial Burgers vectors or widths, in contrast to the symmetric configuration expected from linear elastic dislocation theory. We explain these structures by properties of the local maxima in their GSFE curves. Metals with larger degrees of elastic anisotropy result in dislocations with larger splitting distances than would be expected under the commonly used assumption of elastic isotropy. Furthermore, these findings on the sizes and asymmetry in the structures of pyramidal-II < c + a > dislocations are fundamental to understanding how these dislocations glide and interact or react with other defects when these metals are mechanically strained.

36 MATERIALS SCIENCE↗

Cosmological decoherence from thermal gravitons

A bstract We study the effects of gravitationally-driven decoherence on tunneling processes associated with false vacuum decays, such as the Coleman-De Luccia instanton. We compute the thermal graviton-induced decoherence rate for a wave function describing a perfect fluid of nonzero energy density in a finite region. When the effective cosmological constant is positive, the thermal graviton background sourced by a de Sitter horizon provides an unavoidable decoherence effect, which may have important consequences for tunneling processes in cosmological history. We discuss generalizations and consequences of this effect and comment on its observability and applications to black hole physics.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Application of machine learning interatomic potentials in heterogeneous catalysis

Heterogeneous catalysts are crucial in modern societies as they promote sustainability by enabling lower-energy pathways for various chemical reactions. While Density Functional Theory (DFT) computations can provide critical insights into how heterogeneous catalysts operate at the atomic level, they are limited by computational costs and unfavorable scaling with system size. Recently, machine learning interatomic potentials (MLIPs) have emerged as a promising alternative to DFT, offering near-DFT accuracy at significantly reduced cost. Here, in this perspective, we discuss the application of MLIPs in heterogeneous catalyst modeling as a surrogate for DFT. We detail how MLIPs have been applied in thermal catalysis to probe active sites, enable studying complex metallic and nanoporous catalysts, and investigate the reconstruction of catalytic surfaces. We review the use of MLIPs in electrocatalysis and photocatalysis, emphasizing their capabilities in studying transition metal oxide surfaces and solid–liquid interfaces. We also discuss the current limitations of MLIPs, particularly their challenges with transferability and description of non-local interactions. Finally, we conclude by identifying promising and underexplored domains in which MLIPs can further advance our understanding of heterogeneous catalysts.

Catalytic surfaces↗

Effect of static local distortions vs. dynamic motions on the stability and band gaps of cubic oxide and halide perovskites

Ternary ABX 3 perovskites made of corner-sharing BX 6 octahedra have long featured prominently in solid-state chemistry and condensed matter physics. Still, the joint understanding of their two main subgroups—halides and oxides—has not been fully developed. Indeed, unlike the case in simpler compounds having a single, robust repeated motif (“monomorphous”), certain cubic perovskites can manifest a non-thermal (= intrinsic) distribution of local motifs (“polymorphous networks”). Such static deformations can include positional degrees of freedom (e.g., atomic displacements and octahedral tilting) or magnetic moment degrees of freedom in paramagnets. Unlike thermal motion, such static distortions do not time-average to zero, being an expression of the intrinsic symmetry breaking preference of the chemical bonding. Here, the present study compares electronic structure features of oxide and halide perovskites starting from the static polymorphous distribution of motifs described by Density Functional Theory (DFT) minimization of the internal energy, continuing to finite temperature thermal disorder modeled via finite temperature DFT molecular dynamics. We find that (i) different oxide vs. halide ABX 3 compounds adopt different energy-lowering symmetry-breaking modes. The calculated pair distribution function (PDF) of SrTiO 3 from the first-principles agrees with recently measured PDF. (ii) In both oxides and halides, such static distortions lead to band gap blueshifts with respect to undistorted cubic Pm-3m structure. (iii) For oxide perovskites, high-temperature molecular dynamics simulations initiated from the statically distorted polymorphous structures reveal that the thermally-induced distortions can lead to a band gap redshift. (iv) In contrast, for cubic halide perovskite CsPbI 3 , both the intrinsic distortions and the thermal distortions contribute in tandem to band gap blueshift, the former, intrinsic effect being dominant. (v) In the oxide SrTiO 3 and CaTiO 3 (but not in halide) perovskites, octahedral tilting leads to the emergence of a distinct Γ–Γ direct band gap component as a secondary valley minimum to the well-known indirect R–Γ gap. Understanding such intrinsic vs. thermal effects on oxide vs. halide perovskites holds the potential for designing target electronic properties.

36 MATERIALS SCIENCE↗

MnRhBi 3 : A Cleavable Antiferromagnetic Metal

Cleavable metallic antiferromagnets may be of use for low-dissipation spintronic devices; however, few are currently known. Here, in this study, we present orthorhombic MnRhBi 3 as one such compound and present a thorough study of its physical properties. Exfoliation is demonstrated experimentally, and the cleavage energy and electronic structure are examined by density functional theory calculations. It is concluded that MnRhBi 3 is a van der Waals-layered material that cleaves easily between neighboring Bi layers and that the Bi atoms have lone pairs extending into the van der Waals gaps. A series of four phase transitions are observed below room temperature, and neutron diffraction shows that at least two of the transitions involve the formation of antiferromagnetic order. Anomalous thermal expansion points to a crystallographic phase transition and/or strong magnetoelastic coupling. This work reveals a complex phase evolution in MnRhBi 3 and establishes this cleavable antiferromagnetic metal as an interesting material for studying the interplay of structure, magnetism, and transport in the bulk and ultrathin limits, as well as the role of lone pair electrons in interface chemistry and proximity effects in van der Waals heterostructures.

36 MATERIALS SCIENCE↗