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At least 181 records · Page 10

Synthesis and Crystal Structure of the Zintl Phases NaSrSb, NaBaSb and NaEuSb

This work details the synthesis and the crystal structures of the ternary compounds NaSrSb, NaBaSb and NaEuSb. They are isostructural and adopt the hexagonal ZrNiAl-type structure (space group P6¯2m; Pearson code hP9). The structure determination in all three cases was performed using single-crystal X-ray diffraction methods. The structure features isolated Sb3– anions arranged in layers stacked along the crystallographic c-axis. In the interstices, alkali and alkaline-earth metal cations are found in tetrahedral and square pyramidal coordination environments, respectively. The formal partitioning of the valence electrons adheres to the valence rules, i.e., Na+Sr2+Sb3–, Na+Ba2+Sb3– and Na+Eu2+Sb3– can be considered as Zintl phases with intrinsic semiconductor behavior. Electronic band structure calculations conducted for NaBaSb are consistent with this notion and show a direct gap of approx. 0.9 eV. Additionally, the calculations hint at possible inverted Dirac cones, a feature that is reminiscent of topological quantum materials.

36 MATERIALS SCIENCE↗

Zentropy Theory for Transformative Functionalities of Magnetic and Superconducting Materials

The proposed research developed the zentropy theory through applications to complex magnetic materials and superconductors under the hypothesis that the emergent properties of complex magnetic materials and superconductors can be predicted by statistical mechanics of ergodic microstates with their partition functions computed from DFT-predicted free energies. The key objective is to develop approaches to systematically determine the types and number of microstates and the supercell size in DFT-based calculations through convergency of macroscopic functionalities, with the incorporation of our mixed-space approach accounting for the interactions between periodic supercells. In addition to use scientific intuitions to guide the design of important microstates, the key innovation of the proposed research is to integrate the domain knowledge and the material-property-descriptor database (MPDD) with 4 million microstates, which is supported by our deep neural network machine learning models (SIPFENN: structure-informed prediction of formation energy using neural networks) and integrated with our high throughput DFT Tool Kit (DFTTK). For complex magnetic materials, one of the objectives is to develop approaches to calculate short-range ordering from the statistical distribution of each microstate. For superconductors, the divergency of quasiparticle effective mass at a quantum critical point will be investigated, and the superconducting and non-superconducting microstates will be delineated through analysis of electronic band structure, density of states, charge density, and Fermi surface.

36 MATERIALS SCIENCE↗

Observation of paramagnetic spin-degeneracy lifting in EuZn 2 Sb 2

Taken together, time-reversal and spatial inversion symmetries impose a twofold spin degeneracy of the electronic states in crystals. In centrosymmetric materials, this degeneracy can be lifted by introducing magnetism, either via an externally applied field or through internal magnetization. However, a correlated alignment of spins, even in the paramagnetic phase, can lift the spin degeneracy of electronic states. Here, we report an in-depth study of the electronic band structure of the Eu-ternary pnictide EuZn 2 Sb 2 through a combination of high-resolution angle-resolved photoemission spectroscopy measurements and first-principles calculations. An analysis of the photoemission line shapes over a range of incident photon energies and sample temperatures is shown to reveal the presence of band spin-degeneracy lifting in the paramagnetic phase. Our angle-resolved photoemission spectroscopy results are in good agreement with theoretical ferromagnetic-phase calculations, which indicates the importance of ferromagnetic fluctuations in the system. Through our calculations, we predict that spin-polarized bands in EuZn 2 Sb 2 generate a single pair of Weyl nodes. Our observation of band splittingin EuZn 2 Sb 2 provides a key step toward realizing time-reversal symmetry breaking physics in the absence of long-range magnetic order.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Observation of Electrically Tunable van Hove Singularities in Twisted Bilayer Graphene from NanoARPES

The possibility of triggering correlated phenomena by placing a singularity of the density of states near the Fermi energy remains an intriguing avenue toward engineering the properties of quantum materials. Twisted bilayer graphene is a key material in this regard because the superlattice produced by the rotated graphene layers introduces a van Hove singularity and flat bands near the Fermi energy that cause the emergence of numerous correlated phases, including superconductivity. Direct demonstration of electrostatic control of the superlattice bands over a wide energy range has, so far, been critically missing. This work examines the effect of electrical doping on the electronic band structure of twisted bilayer graphene using a back-gated device architecture for angle-resolved photoemission measurements with a nano-focused light spot. A twist angle of 12.2° is selected such that the superlattice Brillouin zone is sufficiently large to enable identification of van Hove singularities and flat band segments in momentum space. Finally, the doping dependence of these features is extracted over an energy range of 0.4 eV, expanding the combinations of twist angle and doping where they can be placed at the Fermi energy and thereby induce new correlated electronic phases in twisted bilayer graphene.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

THz Plasmonics and Topological Optics of Weyl Semimetals

THz magneto-optical properties of 3D topological Weyl semimetals were investigated with both THz spectroscopy and THz pump-probe measurements. The unique THz effects predicted in these materials may have important applications in THz technology. The electronic band structure was characterized spectroscopically through THz zero-field reflectance and/or cyclotron resonance measurements. The studies included the dynamic chiral pumping and the study of the predicted novel magneto-electric effects arising from the underlying Berry curvature and magneto plasmonic-like effects in the absence of an applied magnetic field. Chiral pumping in the extreme quantum limit was studied on Weyl semimetals to directly probe the chiral N=0 Landau level. Non-linear pump-probe measurements were used to measure the chiral pumping lifetime. Solids with topologically robust electronic states exhibit unusual electronic and optical transport properties that do not exist in other materials. A particularly interesting example is chiral charge pumping, the so-called chiral anomaly, in recently discovered topological Weyl and Dirac semimetals, where simultaneous application of parallel DC electric and magnetic fields creates an imbalance in the number of carriers of opposite topological charge (chirality). In an earlier study we investigated the Weyl metals Na 3 Bi and Cd 3 As 2 . In this grant we followed up with magneto-optical studies of TaAs, another Weyl semimetal. More recently, we have also characterized other Weyl and Dirac systems that have come on line. The Physics community is still looking for the “hydrogen atom” of the Weyl semimetal. CoSi is one promising new system which features Weyl node spacing comparable to the Brillouin zone size. This system may be suitable for study of the predicted chiral plasmons that arise from the Berry curvature in Weyl materials. In other experiments gates can be applied to the samples in order to study the Fermi arc surface states by modulation reflectance spectroscopy at THz frequencies.

36 MATERIALS SCIENCE↗

IrGe 4 : A Predicted Weyl-Metal with a Chiral Crystal Structure

Polycrystalline IrGe4 was synthesized by annealing elements at 800 °C for 240 h, and the composition was confirmed by energy-dispersive X-ray spectroscopy. IrGe 4 adopts a chiral crystal structure (space group P3 1 21) instead of a polar crystal structure (P3 1 ), which was corroborated by the convergent-beam electron diffraction and Rietveld refinements using synchrotron powder X-ray diffraction data. The crystal structure features layers of IrGe 8 polyhedra along the b axis, and the layers are connected by edge- and corner-sharing. Each layer consists of corner-shared [Ir 3 Ge 20 ] trimers, which are formed by three IrGe 8 polyhedra connected by edge-sharing. Temperature-dependent resistivity indicates metallic behavior. The magnetoresistance increases with increasing applied magnetic field, and the nonsaturating magnetoresistance reaches 11.5% at 9 T and 10 K. The Hall resistivity suggests that holes are the majority carrier type, with a carrier concentration of 4.02 × 10 21 cm –3 at 300 K. In conclusion, electronic band structures calculated by density functional theory reveal a Weyl point with a chiral charge of +3 above the Fermi level.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Crystal growth and magnetic structure of ternary silicide Eu Pd 3 Si 2

The hexagonal CaCu 5 –type structure (P6/mmm) is the prototype for more than 100 ternary borides, gallides, and silicides, with general stoichiometry of RTM 3 X 2 (R=lanthanide/alkaline earth; TM=transition metal; X=B, Ga, Si, Ge). Here we report the synthesis, crystal structure, and bulk magnetic properties of polycrystalline and single crystal samples of EuPd 3 Si 2 and its nonmagnetic analog SrPd 3 Si 2 . Both compounds crystallize in the orthorhombic space group symmetry Imma (no. 74, Z = 2, oI12) displaying pseudohexagonal symmetry. Ferromagnetic (FM) order of Eu 2+ at T C1 =78K and a spin-reorientation transition at T C2 =5K appear as distinctive features in bulk magnetization, specific heat, and resistivity/resistance measurements. Neutron powder diffraction measurements on EuPd 3 Si 2 confirm FM order of the Eu 2+ spins below T C1 , with the spins aligned along the a axis below T C2 . Electronic band structure calculations corroborate the crystal structure and the FM state for EuPd 3 Si 2 , with a Pd d–band polarization in the same direction as the Eu 4f polarization, enhancing the observed spin moment.

36 MATERIALS SCIENCE↗

Reconfiguration of Amorphous Complex Oxides: A Route to a Broad Range of Assembly Phenomena, Hybrid Materials, and Novel Functionalities

This work demonstrate that reconfiguration of amorphous oxide layers drives the assembly of oxide-based and freestanding nanomembranes into 3D structures with a radius of a few hundred nanometers. Reconfiguration-driven assembly is a versatile approach to impart large strains and strain gradients in a broad palette of complex oxides. This capability allows for manipulating and enhancing ferroelectricity, flexoelectricity, piezoelectricity, superconductivity, and ferromagnetism in complex oxides. Moreover, by the approach presented in this work, strain-engineered oxides are obtained in the form of 3D structures that can be fabricated in parallel on any substrate, including large-area and single crystalline semiconductor substrates. This approach will create a vast expanse of possibilities to investigate and leverage strain-tunable effects in amorphous, poly-crystalline, and single-crystalline complex oxides. Reconfiguration-driven assembly of NMs also allows combining different materials in a radial geometry and through scalable processes. For example, radial superlattices of Si (or GaAs) and various complex oxides or alternating layers of different complex oxides (e.g., SrTiO 3 and LaAlO 3 ) could be fabricated by release and heating of bilayer NMs. Here, a broad palette of electronic band structures and spin–orbit interactions could then be obtained by tailoring the curvature of the self-assembled NMs and the materials that the heterostructure comprises.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

A Ba 6 Cu 31 Te 22 ( A = K, Rb, Cs) Featuring Polyanionic Copper–Telluride Frameworks with Ultralow Thermal Conductivity

In this study, hree polyanionic tellurides, ABa 6 Cu 31 Te 22 (A = K, Rb, Cs), were synthesized in salt flux. The isostructural tellurides crystallize in a new structure type, in the cubic Pa$\overline{3}$ space group with a Wyckoff sequence of d 10 c 2 b 1 and large unit cell volumes of over 5500 Å 3 . The structures feature a framework of [CuTe 4 ] tetrahedra and [CuTe 3 ] trigonal pyramids with disorder in the Cu sites. The polyanionic frameworks have large square antiprism and cuboctahedral voids where Ba and alkali metal cations are situated, forming [BaTe 8 ] and [ATe 12 ], respectively. The overall compositions are close to being charge balanced. The large [ATe 12 ] cuboctahedra allowed for significant anisotropic displacement of the A cations, as observed from both single crystal X-ray diffraction and heat capacity studies. Alkali cations rattling together with Cu atom displacement and disorder leads to the dispersion of phonons, thus softening the lattice and subsequently reducing the thermal conductivity. Evaluations of the electronic band structure revealed the occurrence of a narrow bandgap together with the presence of a flat band near the valence band maximum, giving rise to the high thermopower. The Cs and Rb analogues show a slope change in the temperature dependence of electrical resistivity around room temperature, which is typical for semimetals or degenerate semiconductors. For the as-synthesized and unoptimized materials, high values of the thermoelectric figure-of-merit of ~0.2 were observed at 623 K.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Synthesis, Stability, and Magnetic Properties of Antiperovskite Co 3 PdN

Experimental synthesis and characterization of theoretically predicted compounds are important steps in the materials discovery pipeline. Here, we report on the synthesis of Co 3 PdN, which was recently predicted to be a stable magnetic antiperovskite. The Co 3 PdN thin films were grown by reactive sputtering and were confirmed to form in an antiperovskite crystal structure. The thermal stability of the compound is demonstrated up to 600 K by in situ X-ray diffraction, though the phase persists at slightly higher temperatures (700 K) in an air-free magnetometer. Both ab initio calculations and magnetization measurements find Co 3 PdN to be ferromagnetic with an experimentally determined Curie temperature of T C = 560 ± 5 K. The saturation magnetization of 1.2 μ B /Co found in the experiment is slightly lower than the 1.7 μ B /Co value expected by theory. A narrow magnetic hysteresis loop with a coercive field of 100 Oe at low temperature suggests that Co 3 PdN might be useful in electronic applications requiring fast switching of the magnetization vector. While prior prediction of Co 3 PdN showed a gapped electronic band structure for each spin channel, we show that this was due to incomplete sampling of Brillouin zone paths and that band crossings exist along R-X|M and X|M-R paths. The metallic nature of Co 3 PdN is further confirmed by temperature-dependent transport measurements, which also show a considerable anomalous Hall effect. Altogether, this work represents an appreciable step toward understanding the synthesis, structure, stability, and properties of a new magnetic material.

14 SOLAR ENERGY↗

Uncovering the spin ordering in magic-angle graphene via edge state equilibration

Abstract The flat bands in magic-angle twisted bilayer graphene (MATBG) provide an especially rich arena to investigate interaction-driven ground states. While progress has been made in identifying the correlated insulators and their excitations at commensurate moiré filling factors, the spin-valley polarizations of the topological states that emerge at high magnetic field remain unknown. Here we introduce a technique based on twist-decoupled van der Waals layers that enables measurement of their electronic band structure and–by studying the backscattering between counter-propagating edge states–the determination of the relative spin polarization of their edge modes. We find that the symmetry-broken quantum Hall states that extend from the charge neutrality point in MATBG are spin unpolarized at even integer filling factors. The measurements also indicate that the correlated Chern insulator emerging from half filling of the flat valence band is spin unpolarized and suggest that its conduction band counterpart may be spin polarized.

36 MATERIALS SCIENCE↗

When van der Waals Met Kagome: A 2D Antimonide with a Vanadium-Kagome Network

2D materials showcase unconventional properties emerging from quantum confinement effects. In this work, a “soft chemical” route allows for the deintercalation of K + from the layered antimonide KV 6 Sb 6 , resulting in the discovery of a new metastable 2D-Kagome antimonide K 0.1(1) V 6 Sb 6 with a van der Waals gap of 3.2 Å. The structure of K 0.1(1) V 6 Sb 6 was determined via the synergistic techniques, including X-ray pair distribution function analysis, advanced transmission electron microscopy, and density functional theory calculations. The K 0.1(1) V 6 Sb 6 compound crystallizes in the monoclinic space group C2/m (a = 9.57(2) Å, b = 5.502(8) Å, c = 10.23(2) Å, β = 97.6(2)°, Z = 2). The [V 6 Sb 6 ] layers in K 0.1(1) V 6 Sb 6 are retained upon deintercalation and closely resemble the layers in the parent compound, yet deintercalation results in a relative shift of the adjacent [V 6 Sb 6 ] layers. The magnetic properties of the K 0.1(1) V 6 Sb 6 phase in the 2–300 K range are comparable to those of KV 6 Sb 6 and another Kagome antimonide KV 3 Sb 5 , consistent with nearly temperature-independent paramagnetism. Electronic band structure calculation suggests a nontrivial band topology with flat bands and opening of band crossing afforded by deintercalation. Transport property measurements reveal a metallic nature for K 0.1(1) V 6 Sb 6 and a low thermal conductivity of 0.6 W K –1 m –1 at 300 K. Additionally, ion exchange in KV 6 Sb 6 via a solvothermal route leads to a successful partial exchange of K + with A + (A = Na, Rb, and Cs). Here, this study highlights the tunability of the layered structure of the KV 6 Sb 6 compound, providing a rich playground for the realization of new 2D materials.

2D↗

Cubic Crystal Structure Formation and Optical Properties within the Ag–B II –M IV –X (B II = Sr, Pb; M IV = Si, Ge, Sn; X = S, Se) Family of Semiconductors

Quaternary chalcogenide semiconductors are promising materials for energy conversion and nonlinear optical applications, with properties tunable primarily by varying the elemental composition and crystal structure. Here, we first analyze the connections among several cubic crystal structure types, as well as the orthorhombic Ag 2 PbGeS 4 -type structure, reported for select members within the Ag–B II –M IV –X (B II = Sr, Pb; M IV = Si, Ge, Sn; X = S, Se) compositional space. Focusing on the Ag–Pb–Si–S and Ag–Sr–Sn–S systems, we show that one structure type, with the formulas Ag 2 Pb 3 Si 2 S 8 and Ag 2 Sr 3 Sn 2 S 8 , is favored. We have prepared powder and single-crystal samples of Ag 2 Pb 3 Si 2 S 8 and Ag 2 Sr 3 Sn 2 S 8 , showing that each takes on the noncentrosymmetric cubic space group I$\bar{43}$d and is isostructural to the previously reported compound Ag 2 Sr 3 Ge 2 Se 8 . Through hybrid density functional theory calculations, these cubic compounds are demonstrated to be (quasi-)direct band gap semiconductors with high densities of states at the band maxima. Furthermore, the band-gap energies are measured by reflectance spectroscopy as 1.95(3) and 2.66(4) eV for Ag 2 Pb 3 Si 2 S 8 and Ag 2 Sr 3 Sn 2 S 8 , respectively. We further measure the optical properties and show the electronic band structures of three other isostructural A I –B II –M IV –X-type materials, i.e., Ag 2 Sr 3 Si 2 S 8 , Ag 2 Sr 3 Ge 2 S 8 , and Ag 2 Sr 3 Ge 2 Se 8 , showing that the band gaps can be predictably tuned by element substitution. Detailed visual analyses of the different structures and of their relationships with other members of the Ag–B II –M IV –X compositional family provide a basis for a broader understanding of the structure formation and optoelectronic properties within the quaternary chalcogenide semiconductor family.

14 SOLAR ENERGY↗

High-temperature ferromagnetism in Cr 1+x Pt 5-x P

In this work, we present the growth and basic magnetic and transport properties of Cr 1+x Pt 5-x P. We show that single crystals can readily be grown from a high-temperature solution created by adding dilute quantities of Cr to Pt-P based melts. Like other 1-5-1 compounds, Cr 1+x Pt 5-x P adopts a tetragonal P4/mmm, structure composed facesharing CrPts like slabs that are broken up along the c-axis by sheets of P atoms. EDS and X-ray diffraction measurements both suggest Cr 1+x Pt 5-x P has mixed occupancy between Cr and Pt atoms, similar to what is found in the closely related compound CrPtg, giving real compositions of Cr 1.5 Pt 4.5 P (x = 0.5). We report that Cr 1.5 Pt 4.5 P orders ferromagnetically at T c = 464.5 K with a saturated moment of ≈ 2.1 μs/Cr at 1.8 K. Likely owing to the strong spin-orbit coupling associated with the large quantity of high Z, Pt atoms, Cr 1.5 Pt 4.5 P has exceptionally strong planar anisotropy with estimated anisotropy fields of 345 kOe and 220 kOe at 1.8 K and 300 K respectively. The resistance of Cr 1.5 Pt 4.5 P has a metallic temperature dependence with relatively weak magnetoresistance. Electronic band structure calculations show that CrPt 5 P has a large peak in the density of states near the Fermi level which is split into spin majority and minority bands in the ferromagnetic state. Furthermore, the calculations suggest substantial hybridization between Cr-3d and Pt-5d states near the Fermi level, in agreement with the experimentally measured anisotropy.

36 MATERIALS SCIENCE↗

The superatomic state beyond conventional magic numbers: Ligated metal chalcogenide superatoms

The field of cluster science is drawing increasing attention due to the strong size and composition-dependent properties of clusters and the exciting prospect of clusters serving as the building blocks for materials with tailored properties. However, identifying a unifying central paradigm that provides a framework for classifying and understanding the diverse behaviors is an outstanding challenge. One such central paradigm is the superatom concept that was developed for metallic and ligand-protected metallic clusters. The periodic electronic and geometric closed shells in clusters result in their properties being based on the stability they gain when they achieve closed shells. This stabilization results in the clusters having a well-defined valence allowing them to be classified as superatoms – thus, extending the periodic table to a third dimension. This perspective focuses on extending the superatomic concept to ligated metal-chalcogen clusters that have recently been synthesized in solutions and form assemblies with counterions that have wide-ranging applications. Here we illustrate that the periodic patterns emerge in the electronic structure of ligated metal-chalcogenide clusters. The stabilization gained by the closing of their electronic shells allows for the prediction of their redox properties. Further investigations reveal how the selection of ligands may control the redox properties of the superatoms. These ligated clusters may serve as chemical dopants for two-dimensional semiconductors to control their transport characteristics. Superatomic molecules of multiple metal-chalcogen superatoms allow for the formation of nano pn junctions ideal for directed transport and photon harvesting. As a result, the perspective outlines future developments, including the synthesis of magnetic superatoms.

36 MATERIALS SCIENCE↗

Alkaline Earth-Based Ternary Chalcogenide Nanocrystals: Cadmium- and Lead-Free Optical Materials

As some of the most abundant elements on the Earth’s crust, alkaline earths bear great potential in Cd- and Pb-free catalytic, energy conversion, and light-emitting devices. Further, because large electropositive alkaline earths (Ae) can adopt high coordination numbers, they offer structural complexity beyond the tetrahedral (c-Si, II–VI, III–V) or octahedral (IV–VI) atomic sites that─with the notable exception of halide perovskites─are ubiquitous among nanocrystalline semiconductors. Here, in this work, we present a general route to photoluminescent 6–125 nm nanocrystals of ternary AeIn 2 Ch 4 semiconductors (Ae = Sr, Ba; Ch = S, Se) featuring eight- (Ae) as well as four-coordinate (In and Ch) atomic sites. Powder X-ray diffraction, electron microscopy, optical absorption, photoluminescence, and solid-state (ss)NMR spectroscopies attest to the ternary composition and phase purity of the nanocrystals. Continuous shape measures pinpoint the degree of distortion of individual crystallographic sites from ideal coordination polyhedra, allowing us to identify two very distinct types of Se coordination environments. Based on their higher order, pseudo-3-fold rotational symmetry, we assign 77 Se ssNMR peaks with negligible chemical shift anisotropy (CSA) to pyramidalized Se sites with vacant-trigonal bipyramid-like geometries and those with larger CSA to lower symmetry Se sites with seesaw-distorted geometries. Calculations help to better understand the electronic band structure of these materials. The nanocrystals are stable at room temperature in open air for several weeks, and some compositions up to 1000 °C under Ar, making them strong candidates for practical applications.

alkaline earth↗

Ultrafast valley polarization in bilayer graphene

We study theoretically the interaction of a bilayer graphene with a circularly polarized ultrafast optical pulse of a single oscillation at an oblique incidence. The normal component of the pulse breaks the inversion symmetry of the system and opens up a dynamical bandgap due to which a valley-selective population of the conduction band becomes sensitive to the angle of incident of the pulse. We show that the magnitude of the valley polarization can be controlled by the angle of incidence, the amplitude, and the angle of in-plane polarization of the chiral optical pulse. Subsequently, a sequence of a circularly polarized pulse followed by a linearly polarized femtosecond-long pulse can be used to control and probe the valley polarization created by the preceding pulse. Our protocol provides a favorable platform to design ultrafast all-optical valleytronic information processing.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Tuning time and energy resolution in time-resolved photoemission spectroscopy with nonlinear crystals

Time- and angle-resolved photoemission spectroscopy is a powerful probe of electronic band structures out of equilibrium. Tuning time and energy resolution to suit a particular scientific question has become an increasingly important experimental consideration. Many instruments use cascaded frequency doubling in nonlinear crystals to generate the required ultraviolet probe pulses. In this work, we demonstrate how calculations clarify the relationship between laser bandwidth and nonlinear crystal thickness contributing to experimental resolutions and place intrinsic limits on the achievable time-bandwidth product. Experimentally, we tune time and energy resolution by varying the thickness of nonlinear β-BaB 2 O 4 crystals for frequency upconversion, providing a flexible experiment design. We achieve time resolutions of 58–103 fs and corresponding energy resolutions of 55–27 meV. We propose a method to select crystal thickness based on desired experimental resolutions.

36 MATERIALS SCIENCE↗