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At least 667 records · Page 37

HTESP (High-throughput electronic structure package): A package for high-throughput ab initio calculations

High-throughput ab initio calculations are the indispensable parts of data-driven discovery of new materials with desirable properties, as reflected in the establishment of several online material databases. The accumulation of extensive theoretical data through computations enables data-driven discovery by constructing machine learning and artificial intelligence models to predict novel compounds and forecast their properties. Efficient usage and extraction of data from these existing online material databases can accelerate the next stage materials discovery that targets different and more advanced properties, such as electron–phonon coupling for phonon-mediated superconductivity. However, extracting data from these databases, generating tailored input files for different ab initio calculations, performing such calculations, and analyzing new results can be demanding tasks. Here, in this work, we introduce a software package named “HTESP” (High-Throughput Electronic Structure Package) written in Python and Bash languages, which automates the entire workflow including data extraction, input file generation, calculation submission, result collection and plotting. Our HTESP will help speed up future computational materials discovery processes.

36 MATERIALS SCIENCE↗

Speciation and Electronic Structure of La 1-x Sr x CoO 3-δ During Oxygen Electrolysis

Cobalt-containing perovskite oxides are promising electrocatalysts for the oxygen evolution reaction (OER) in alkaline electrolyzers. However, a lack of fundamental understanding of oxide surfaces impedes rational catalyst design for improved activity and stability. We couple electrochemical studies of epitaxial La 1-x Sr x CoO 3-δ films with in situ and operando ambient pressure X-ray photoelectron spectroscopy to investigate the surface stoichiometry, adsorbates, and electronic structure. Additionally, in situ investigations spanning electrode compositions in a humid environment indicate that hydroxyl and carbonate affinity increase with Sr content, leading to an increase in binding energy of metal core levels and the valence band edge from the formation of a surface dipole. The maximum in hydroxylation at 40% Sr is commensurate with the highest OER activity, where activity scales with greater hole carrier concentration and mobility. Furthermore, operando measurements of the 20% Sr-doped oxide in alkaline electrolyte indicate that the surface stoichiometry remains constant during OER, supporting the idea that the oxide electrocatalyst is stable and behaves as a metal, with the voltage drop confined to the electrolyte. Furthermore, hydroxyl and carbonate species are present on the electrode surface even under oxidizing conditions, and may impact the availability of active sites or the binding strength of adsorbed intermediates via adsorbate–adsorbate interactions. For covalent oxides with facile charge transfer kinetics, the accumulation of hydroxyl species with oxidative potentials suggests the rate of reaction could be limited by proton transfer kinetics. This operando insight will help guide modeling of self-consistent oxide electrocatalysts, and highlights the potential importance of carbonates in oxygen electrocatalysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Electronic structure of a nodal line semimetal candidate TbSbTe

The 𝐿⁢𝑛⁢SbTe (𝐿⁢𝑛 = Lanthanides) family, like isostructural ZrSiS-type compounds, has emerged as a fertile playground for exploring the interaction of electronic correlations and magnetic ordering with the nodal line band topology. Here, we report on a detailed electronic band structure investigation of TbSbTe, corroborated by electrical transport, thermodynamic, and magnetic studies. Temperature-dependent magnetic susceptibility and thermodynamic transport studies indicate the onset of antiferromagnetic ordering below 𝑇 𝑁 ∼ 5.8K. The electronic band structure study, carried out with high-resolution angle-resolved photoemission spectroscopy measurements aided with density functional theory–based first-principles calculations reveal presence of a nonsymmorphic symmetry-protected Dirac crossing in the Γ-X high-symmetry (HS) direction, which is part of a nodal line along the X-R HS direction. Another Dirac crossing occurs along the Γ-X direction at a relatively higher binding energy, which occurs from $\tilde{𝒞}$ 2⁢𝜈⁢ 𝒫 symmetry which is gapped in the theoretical calculations with the effect of spin-orbit coupling considered. Parallel to this direction, our theoretical calculations and experimental results exhibit strongly momentum-dependent surface bands. In this study, we open an avenue to further uncover the intricate interplay among symmetry-protected topological band structure, spin-orbit coupling, and magnetism in this material and the 𝐿⁢𝑛⁢SbTe family, in general.

Angle-resolved photoemission spectroscopy↗

Electronic structure of GaP/Si (001) heterojunctions and the role of hydrogen passivation

Abstract Epitaxially grown single crystal GaP on Si is of considerable interest due to being nearly lattice matched to Si, making it attractive for III‐V/Si solar cells. GaP has been used as a buffer layer for III‐V/Si solar cells and also in selective contact Si solar cells. The performance and functionality of such devices are strongly influenced by the presence of localized states at the GaP/Si interface. Here, we examine the electronic structure of GaP/Si(001) heterojunctions and the effect of hydrogen (H) passivation at the interface, in contrast to interface mixing, through density functional theory calculations. Our calculations show that due to the heterovalent mismatch nature of the GaP/Si interface, there is a high density of localized states at the abrupt GaP/Si interface due to the excess charge associated with heterovalent bonding, as reported elsewhere. We find that the addition of H leads to additional bonding at the interface, which mitigates the charge imbalance, and greatly reduces the density of localized states, leading to a nearly ideal heterojunction. A similar result is found with a completely intermixed interface (alternating cation and anion bonding) in terms of low interface state density. However, when the intermixing occurs through single‐layer or double‐layer terraces, the benefits of intermixing are lost and the interface state density reverts more to the abrupt interface case.

Meidanshahi, Reza Vatan↗

Electronic Structure Calculations for improving Catalyst Design for Use in the Hybrid Sulfur Cycle

The hybrid sulfur cycle is a promising means for efficient production of large quantities of hydrogen with a small carbon footprint. Furthermore, there is a demonstrated need to design catalysts that are sulfur tolerant and have stability at high temperatures and reduced activation energies. Theoretical calculations can serve as a blueprint for fulfilling these needs by providing fundamental mechanistic insights to guide future experimental studies. Density functional theory was used to calculate the energetics of Pt-Au systems. Adsorption energetics for the unary and binary structures were investigated to provide mechanistic insights for improved catalyst design. Results conclude that adsorption of the SO 2 molecule is further stabilized on the Pt surface with a Pt-0 dative bond compared to Au. Energetics suggest that the adsorbates are more stabilized in the Pt surface due to a stabilization of the S p bands in the electronic structure. Examination of the density of states support the postulation that SO 2 is more weakly bound to Au, thereby leading to better catalytic performance compared to Pt. These results are encouraging and we expect there to be a weakening effect of ligand adsorption on the Pt/Au surfaces when an electric field is applied.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Electronic structure with direct diagonalization on a D-wave quantum annealer

Quantum chemistry is regarded to be one of the first disciplines that will be revolutionized by quantum computing. Although universal quantum computers of practical scale may be years away, various approaches are currently being pursued to solve quantum chemistry problems on near-term gate-based quantum computers and quantum annealers by developing the appropriate algorithm and software base. This work implements the general Quantum Annealer Eigensolver (QAE) algorithm to solve the molecular electronic Hamiltonian eigenvalue-eigenvector problem on a D-Wave 2000Q quantum annealer. The approach is based on the matrix formulation, efficiently uses qubit resources based on a power-of-two encoding scheme and is hardware-dominant relying on only one classically optimized parameter. We demonstrate the use of D-Wave hardware for obtaining ground and excited electronic states across a variety of small molecular systems. The approach can be adapted for use by a vast majority of electronic structure methods currently implemented in conventional quantum-chemical packages. The results of this work will encourage further development of software such as qbsolv which has promising applications in emerging quantum information processing hardware and has expectation to address large and complex optimization problems intractable for classical computers.

97 MATHEMATICS AND COMPUTING↗

Electronic Structures of an [Fe(NNR 2 )] +/0/– Redox Series: Ligand Noninnocence and Implications for Catalytic Nitrogen Fixation

The intermediacy of metal–NNH 2 complexes has been implicated in the catalytic cycles of several examples of transition-metal-mediated nitrogen (N 2 ) fixation. In this context, we have shown that triphosphine-supported Fe(N 2 ) complexes can be reduced and protonated at the distal N atom to yield Fe(NNH2) complexes over an array of charge and oxidation states. Upon exposure to further H + /e – equivalents, these species either continue down a distal-type Chatt pathway to yield a terminal iron(IV) nitride or instead follow a distal-to-alternating pathway resulting in N–H bond formation at the proximal N atom. To understand the origin of this divergent selectivity, herein we synthesize and elucidate the electronic structures of a redox series of Fe(NNMe 2 ) complexes, which serve as spectroscopic models for their reactive protonated congeners.Using a combination of spectroscopies, in concert with density functional theory and correlated ab initio calculations, we evidence one-electron redox noninnocence of the "NNMe 2 / moiety. Specifically, although two closed-shell configurations of the "NNR/ ligand have been commonly considered in the literature-isodiazene and hydrazido(2-)-we provide evidence suggesting that, in their reduced forms, the present iron complexes are best viewed in terms of an open-shell [NNR 2i ] •- ligand coupled antiferromagnetically to the Fe center. Lastly. this one-electron redox noninnocence resembles that of the classically noninnocent ligand NO and may have mechanistic implications for selectivity in N 2 fixation activity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Bulk electronic structure of non-centrosymmetric EuTGe 3 (T=Co, Ni, Rh, Ir) studied by hard x-ray photoelectron spectroscopy

Non-centrosymmetric EuTGe 3 ( T = Co, Ni, Rh, and Ir) possesses magnetic Eu 2+ ions, and antiferromagnetic ordering appears at low temperatures. Transition-metal substitution leads to changes in the unit-cell volume and in the magnetic ordering. However, the magnetic ordering temperature does not scale with the volume change, and the Eu valence is expected to remain divalent. Here we study the bulk electronic structure of non-centrosymmetric Eu T Ge 3 ( T = Co, Ni, Rh, and Ir) by hard x-ray photoelectron spectroscopy. The Eu 3d core-level spectrum confirms the robust Eu 2+ valence state against the transition-metal substitution with a small contribution from Eu 3+ . The estimated Eu mean valence is around 2.1 in these compounds, as confirmed by multiplet calculations. In contrast, the Ge 2p spectrum shifts to higher binding energy upon cha nging the transition metal from 3d to 4d to 5d elements, hinting at a change in the Ge- T bonding strength. The valence bands of the different compounds are found to be well reproduced by ab initio band structure calculations.

36 MATERIALS SCIENCE↗

Synthesis, Crystal and Electronic Structure of the New Ternary Compound Ca3InAs3

Crystals of a new ternary compound in the Ca-In-As family, Ca3InAs3, have been successfully synthesized via flux growth techniques. This is only the third known compound between the respective elements. As elucidated by single-crystal X-ray diffraction measurements, Ca3InAs3 crystallizes in the orthorhombic space group Pnma (No. 62, Pearson symbol oP28) with unit cell parameters a = 12.296(2) Å, b = 4.2553(7) Å, and c = 13.735(2) Å. The smallest building motifs of the structure are InAs4 tetrahedra, which are connected to one another by shared As corners, forming infinite [InAs2As2/2] chains. The latter propagate along the crystallographic b-axis. The As-In-As bond angles within the InAs4 tetrahedra deviate from the ideal 109.5° value and range from 98.12(2)° to 116.53(2)°, attesting to a small distortion from the regular tetrahedral geometry. Electronic structure calculations indicate the opening of a bandgap, consistent with the expected (Ca2+)3(In3+)(As3–)3 formula breakdown based on conventional oxidation numbers. The calculations also show that the Ca–As interactions are an intermediate between covalent and ionic, while providing evidence of strong covalent features of the In–As interactions. Weak s-p hybridization of In states was observed, supporting the experimentally found deviation of the InAs4 moiety from the ideal tetrahedral symmetry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Towards exact finite temperature electronic structure in solids and molecules (Final Technical Report)

This report describes the University of Iowa portion of a project that is now continuing at Michigan State University. We are developing novel methods, algorithms, and software to enable simulations of molecules and materials at high temperature. This is a key challenge in chemistry and materials science. By refining an approach called Density Matrix Quantum Monte Carlo (DMQMC), we developed faster and more accurate ways to conduct these simulations. These advances will help us understand how temperature affects the behavior of electrons, chemical bonds, and phase transitions in solids and molecules. These breakthroughs are especially important for applications where light and heat drive chemical reactions, superconductivity, and materials used in energy and sensing. In addition, this project involved the development of the open-source HANDE-QMC software package, supporting the broader community in benchmarking and developing finite-temperature electronic structure methods.

36 MATERIALS SCIENCE↗

Electronic structure theory on modeling short-range noncovalent interactions between amino acids

While short-range noncovalent interactions (NCIs) are proving to be of importance in many chemical and biological systems, these atypical bindings happen within the so-called van der Waals envelope and pose an enormous challenge for current computational methods. We introduce SNCIAA, a database of 723 benchmark interaction energies of short-range noncovalent interactions between neutral/charged amino acids originated from protein x-ray crystal structures at the “gold standard” coupled-cluster with singles, doubles, and perturbative triples/complete basis set [CCSD(T)/CBS] level of theory with a mean absolute binding uncertainty less than 0.1 kcal/mol. Subsequently, a systematic assessment of commonly used computational methods, such as the second-order Møller−Plesset theory (MP2), density functional theory (DFT), symmetry-adapted perturbation theory (SAPT), composite electronic-structure methods, semiempirical approaches, and the physical-based potentials with machine learning (IPML) on SNCIAA is carried out. It is shown that the inclusion of dispersion corrections is essential even though these dimers are dominated by electrostatics, such as hydrogen bondings and salt bridges. Overall, MP2, ωB97M-V, and B3LYP+D4 turned out to be the most reliable methods for the description of short-range NCIs even in strongly attractive/repulsive complexes. SAPT is also recommended in describing short-range NCIs only if the δMP2 correction has been included. The good performance of IPML for dimers at close-equilibrium and long-range conditions is not transferable to the short-range. We expect that SNCIAA will assist the development/improvement/validation of computational methods, such as DFT, force-fields, and ML models, in describing NCIs across entire potential energy surfaces (short-, intermediate-, and long-range NCIs) on the same footing.

Chemistry↗

Electronic structure and spatial inhomogeneity of iron-based superconductor FeS

Iron-based superconductor family FeX (X = S, Se, Te) has been one of the research foci in physics and material science due to their record-breaking superconducting temperature (FeSe film) and rich physical phenomena. Recently, FeS, the least studied FeX compound (due to the difficulty in synthesizing high quality macroscopic crystals) attracted much attention because of its puzzling superconducting pairing symmetry. In this work, combining scanning tunneling microscopy and angle resolved photoemission spectroscopy (ARPES) with sub-micron spatial resolution, we investigate the intrinsic electronic structures of superconducting FeS from individual single crystalline domains. Unlike FeTe or FeSe, FeS remains identical tetragonal structure from room temperature down to 5 K, and the band structures observed can be well reproduced by our ab-initio calculations. Remarkably, mixed with the 1 × 1 tetragonal metallic phase, we also observe the coexistence of √5 x √5 reconstructed insulating phase in the crystal, which not only helps explain the unusual properties of FeS, but also demonstrates the importance of using spatially resolved experimental tools in the study of this compound.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Satellites, core hole excitations, and spin-resolved electronic structure in the spectroscopy of half-metallic CrO 2

Photoelectron satellites—the structures appearing on the low kinetic or high binding-energy side of the “main” or “elastic” photopeak—betray the complex many-body interactions set in motion by the sudden creation of the core hole. In this work, we demonstrate, using the technologically important ferromagnetic half-metal CrO 2 , how such satellites can manifest themselves in other core-level spectroscopies of the material and how they can reveal important details pertinent to its electronic structure. Specifically, we identify a fluorescence satellite in the Cr 𝐿 3 resonant x-ray-emission spectra that radiates at a constant emission energy across the Cr 𝐿 3 x-ray edge with energy ≈1.3 eV above the ordinary valence fluorescence. Here, we provide evidence that this feature arises from the valence recombination of the Cr 2⁢𝑝 core hole “dressed” by the same shakeup charge-transfer process present in both the Cr x-ray photoelectron and the Cr x-ray absorption spectra with its energy uniquely measuring the exchange splitting of the Cr 3⁢𝑑 level. Further analysis of the x-ray emission data reveals three additional features that radiate at constant loss energy that are attributed to combinations of Cr 3⁢𝑑⁢(𝑡 2⁢𝑔 ) → Cr 3⁢𝑑⁢(𝑡 2⁢𝑔 ), charge-transfer O 2⁢𝑝→Cr 3⁢𝑑, and crystal-field Cr⁢ 3⁢𝑑⁡(𝑡 2⁢𝑔 )→Cr⁢ 3⁢𝑑⁡(𝑒 𝑔 ) excitations. These assignments and their energies are supported by density-functional theory calculations, the accuracy of which we demonstrate by hard x-ray valence-photoemission measurements. Atomic multiplet calculations, which include crystal-field effects, help interpret x-ray photoelectron and x-ray absorption spectra of the covalently mixed Cr ion. Resonant Cr K-𝐿 2,3 ⁢𝐿 2,3 Auger-electron emission spectra support a ligand-to-metal nature of the charge-transfer process while highlighting the charge sensitivity differences between photon-in/electron-out and photon-in/photon-out spectroscopies.

36 MATERIALS SCIENCE↗

Electronic structure of the frustrated diamond lattice magnet NiRh 2 O 4

We report the A -site spinel NiRh 2 O 4 is the only known realization of a spin-1 diamond lattice magnet and is predicted to host unconventional magnetic phenomena driven by frustrated nearest and next-nearest neighbor exchange as well as orbital degeneracy. Previous works found no sign of magnetic order but found a gapped dispersive magnetic excitation indicating a possible valence bond magnetic ground state. However, the presence of many competing low energy degrees of freedom and limited empirical microscopic constraints complicates further analysis. Here we carry out resonant inelastic x-ray scattering (RIXS), x-ray absorption spectroscopy (XAS), and inelastic neutron scattering (INS) to characterize the local electronic structure and lattice dynamics of NiRh 2 O 4 . The RIXS data can be partly described by a single-ion model for tetrahedrally coordinated Ni 2+ and indicates a tetragonal distortion Δt 2 = 70 meV that splits the t 2 orbitals into a high energy orbital singlet and lower energy orbital doublet. We identify features of the RIXS spectra that are consistent with a Rh-Ni two-site excitation indicating strong metal-metal hybridization mediated by oxygen in NiRh 2 O 4 . We also identify signatures of electron-phonon coupling through the appearance of phonon sidebands that dress crystal field excitations. These results establish the key energy scales relevant to the magnetism in NiRh 2 O 4 and further demonstrate that covalency and lattice dynamics play essential roles in controlling the magnetic ground states of A -site spinels.

36 MATERIALS SCIENCE↗

Projected Commutator DIIS Method for Accelerating Hybrid Functional Electronic Structure Calculations

The commutator direct inversion of the iterative subspace (commutator DIIS or C-DIIS) method developed by Pulay is an efficient and the most widely used scheme in quantum chemistry to accelerate the convergence of self-consistent field (SCF) iterations in Hartree–Fock theory and Kohn–Sham density functional theory. The C-DIIS method requires the explicit storage of the density matrix, the Fock matrix, and the commutator matrix. Hence, the method can only be used for systems with a relatively small basis set, such as the Gaussian basis set. We develop a new method that enables the C-DIIS method to be efficiently employed in electronic structure calculations with a large basis set such as planewaves for the first time. The key ingredient is the projection of both the density matrix and the commutator matrix to an auxiliary matrix called the gauge-fixing matrix. The resulting projected commutator-DIIS method (PC-DIIS) only operates on matrices of the same dimension as that consists of Kohn–Sham orbitals. The cost of the method is comparable to that of standard charge mixing schemes used in large basis set calculations. The PC-DIIS method is gauge-invariant, which guarantees that its performance is invariant with respect to any unitary transformation of the Kohn–Sham orbitals. We demonstrate that the PC-DIIS method can be viewed as an extension of an iterative eigensolver for nonlinear problems. We use the PC-DIIS method for accelerating Kohn–Sham density functional theory calculations with hybrid exchange–correlation functionals, and demonstrate its superior performance compared to the commonly used nested two-level SCF iteration procedure. Furthermore, we demonstrate that in the context of ab initio molecular dynamics (MD) simulation with hybrid functionals one can extrapolate the gauge-fixing matrix to achieve the goal of extrapolating the entire density matrix implicitly along the MD trajectory. Here, numerical results indicate that the new method significantly reduces the number of SCF iterations per MD step, compared to the commonly used strategy of extrapolating the electron density.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Temperature-dependent electronic structure in a higher-order topological insulator candidate EuIn 2 As 2

Higher-order topological insulators (HOTIs) have enticed enormous research interests owing to their novelty in supporting gapless states along the hinges of a crystal. Despite several theoretical predictions, enough experimental confirmation of the HOTI state in crystalline solids is still lacking. Here, it is shown that interplay between topology and magnetism can give rise to various magnetic topological states, including HOTI and axion insulator states. Here, using high-resolution angle-resolved photoemission spectroscopy combined with the first-principles calculations, we report a systematic study of the electronic structure and its evolution across the magnetic phase transition in EuIn 2 As 2 which possesses an antiferromagnetic ground state below 16 K. Antiferromagnetic EuIn 2 As 2 has been predicted to host both the axion insulator and the HOTI states.We directly observe the linearly dispersing holelike bands crossing the Fermi level and the change in their dispersion across the magnetic phase transition. Our paper points to EuIn 2 As 2 as being a promising material for the exploration of interplay between topology and magnetism.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Effect of 3d/4p Mixing on 1s2p Resonant Inelastic X-ray Scattering: Electronic Structure of Oxo-Bridged Iron Dimers

1s2p resonant inelastic X-ray scattering (1s2p RIXS) has proven successful in the determination of the differential orbital covalency (DOC, the amount of metal vs ligand character in each d molecular orbital) of highly covalent centrosymmetric iron environments including heme models and enzymes. However, many reactive intermediates have noncentrosymmetric environments, e.g., the presence of strong metal-oxo bonds, which results in the mixing of metal 4p character into the 3d orbitals. This leads to significant intensity enhancement in the metal K-pre-edge and as shown here, the associated 1s2p RIXS features, which impact their insight into electronic structure. Binuclear oxo bridged high spin Fe(III) complexes are used to determine the effects of 4p mixing on 1s2p RIXS spectra. In addition to developing the analysis of 4p mixing on K-edge XAS and 1s2p RIXS data, this study explains the selective nature of the 4p mixing that also enhances the analysis of L-edge XAS intensity in terms of DOC. These 1s2p RIXS biferric model studies enable new structural insight from related data on peroxo bridged biferric enzyme intermediates. The dimeric nature of the oxo bridged Fe(III) complexes further results in ligand-to-ligand interactions between the Fe(III) sites and angle dependent features just above the pre-edge that reflect the superexchange pathway of the oxo bridge. Lastly, we present a methodology that enables DOC to be obtained when L-edge XAS is inaccessible and only 1s2p RIXS experiments can be performed as in many metalloenzyme intermediates in solution.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Electronic structure of epitaxial half-Heusler Co 1-x Ni x TiSb across the semiconductor to metal transition

In this paper, we report on the growth, electronic, and surface properties of the electron-doped half-Heusler series Co 1-x Ni x TiSb (001) grown by molecular beam epitaxy. High-quality epitaxial growth of thin films is achieved on InP (001) substrates using an InAlAs buffer layer for all nickel concentrations. The semiconductor to metal transition as a function of substitutional alloying was examined using electrical transport, Seebeck measurements, and angle-resolved photoemission spectroscopy (ARPES). Temperature-dependent electrical transport measurements of films with composition x ≤ 0.1 exhibit thermally activated behavior while x > 0.1 exhibit metallic behavior. Smooth, highly ordered film surfaces can be achieved following ex-situ transfer of the films and subsequent desorption of a sacrificial, protective antimony capping layer. Using this transfer technique, ARPES experiments were performed to investigate the effects of nickel alloying on the electronic band structure. Finally, an electron pocket is observed below the Fermi level at the bulk X point for compositions x > 0.1, in accordance with the crossover from semiconducting to metallic behavior observed in the transport measurements.

36 MATERIALS SCIENCE↗