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At least 163 records · Page 9

Grain refinement of cast zinc through magnesium inoculation: Characterisation and mechanism

It was previously found that peritectic-forming solutes are more favourable for the grain refinement of cast Al alloys than eutectic-forming solutes. In this work, we report that the eutectic-forming solute, Mg, can also significantly grain refine cast Zn. Differential thermal analysis (DTA) of a Zn–Mg alloy, in which efficient grain refinement occurred, evidenced an unexpected peak that appeared before the nucleation of η-Zn grains on the DTA spectrum. Based on extensive examination using X-ray diffraction, high resolution SEM and EDS, it was found that: (a) some faceted Zn–Mg intermetallic particles were reproducibly observed; (b) the particles were located at or near grain centres; (c) the atomic ratio of Mg to Zn in the intermetallic compound was determined to be around 1/2. Using tilting selected area diffraction (SAD) and convergent beam Kikuchi line diffraction pattern (CBKLDP) techniques, these faceted particles were identified as MgZn{sub 2} and an orientation relationship between such grain-centred MgZn{sub 2} particles and the η-Zn matrix was determined. Hence, the unexpected peak on the DTA spectrum is believed to correspond to the formation of MgZn{sub 2} particles, which act as effective heterogeneous nucleation sites in the alloy. Together with the effect of Mg solute on restricting grain growth, such heterogeneous nucleation is cooperatively responsible for the grain size reduction in Zn–Mg alloys. - Highlights: • A new eutectic-based grain refiner for the cast Zn was found. • The formation process of an intermetallic compound (MgZn{sub 2}) was characterised. • MgZn{sub 2} can act as potent heterogeneous nucleation sites above the liquidus. • A new OR between MgZn{sub 2} and η-Zn was determined using the CBKLDP technique.

36 MATERIALS SCIENCE↗

Ferrite grain refinement in low carbon Cu–P–Cr–Ni–Mo weathering steel at various temperatures in the (α + γ) region

Self-designed Cu–P–Cr–Ni–Mo weathering steel was subjected to compression test to determine the mechanism of ferrite grain refinement from 750 °C to 925 °C. Optical microscopic images showed that ferrite grain size declined, whereas the ferrite volume fraction increased with increasing compression temperature. Electron backscatter diffraction patterns revealed that several low-angle boundaries shifted to high-angle boundaries, thereby generating fine ferrite grains surrounded by high-angle boundaries. Numerous low-angle boundaries were observed within ferrite grains at 750 °C, which indicated the existence of pre-eutectoid ferrite. Results showed that ferrite grain refinement could be due to continuous dynamic recrystallization at 750 °C and 775 °C, and deformation-induced ferrite transformation could be the main mechanism at 800 °C and 850 °C. Fine equiaxed ferrite grains with size ranging from 1.77 μm to 2.69 μm were produced in the (α + γ) dual-phase region. - Graphical abstract: There is a close relationship between the microstructure evolution and flow curves during deformation. Fine equiaxed ferrite grains with size ranging from 1.77 μm to 2.69 μm were achieved in the (α + γ) dual-phase region. Ferrite grain refinement could be due to continuous dynamic recrystallization at 750 °C and 775 °C, and deformation-induced ferrite transformation at 800 °C and 850 °C. The occurrence of deformation-induced ferrite transformation and continuous dynamic recrystallization can be monitored by analysis of flow curves and microstructures. Deformation-induced ferrite transformation leads to the dynamic softening in flow curve when temperature just below A{sub r3}, while the dynamic softening in flow curve is ferrite continuous dynamic recrystallization (Special Fig. 5b). - Highlights: • Compression deformation was operated at temperatures from 750 °C to 925 °C at a strain rate of 0.1 s–1, and a strain of 1.2. • Fine equiaxed ferrite grains of ~1.77–2.19 μm were obtained at 750 °C and 775 °C via continuous dynamic recrystallization. • Ferrite grain size of ~2.31–2.69 μm at 800 °C and 850 °C can be obtained by deformation-induced ferrite transformation. • With decreasing deformation temperature the average grain size of ferrite decreased while volume fraction increased. • Ferrite refinement was from deformation-induced ferrite to continuous dynamic recrystallization as temperature reduced.

36 MATERIALS SCIENCE↗

Development in corrosion resistance by microstructural refinement in Zr-16 SS 304 alloy using suction casting technique

Highlights: • Grain refinement was made in Zr–16 wt.% SS alloy while prepared by suction casting process. • Distribution of Laves phase, e.g., Zr{sub 2}(Fe, Cr) was raised in suction cast (SC) Zr–16 wt.% SS. • Corrosion resistance was improved in SC alloy compared to that of arc-melt-cast alloy. • Grain refinement in SC alloy assisted for an increase in its corrosion resistance. - Abstract: Zirconium (Zr)-stainless steel (SS) hybrid alloys are being considered as baseline alloys for developing metallic-waste-form (MWF) with the motivation of disposing of Zr and SS base nuclear metallic wastes. Zr–16 wt.% SS, a MWF alloy optimized from previous studies, exhibit significant grain refinement and changes in phase assemblages (soft phase: Zr{sub 2}(Fe, Cr)/α-Zr vs. hard phase: Zr{sub 3}(Fe, Ni)) when prepared by suction casting (SC) technique in comparison to arc-cast-melt (AMC) route. Variation in Cr-distribution among different phases are found to be low in suction cast alloy, which along with grain refinement restricted Cr-depletion at the Zr{sub 2}(Fe, Cr)/Zr interfaces, prone to localized attack. Hence, SC alloy, compared to AMC alloy, showed lower current density, higher potential at the breakdown of passivity and higher corrosion potential during polarization experiments (carried out under possible geological repository environments, viz., pH 8, 5 and 1) indicating its superior corrosion resistance.

36 MATERIALS SCIENCE↗

Application of mesh refinement to relativistic magnetic reconnection

During relativistic magnetic reconnection, antiparallel magnetic fields undergo a rapid change in topology, releasing a large amount of energy in the form of non-thermal particle acceleration. This work explores the application of mesh refinement to 2D reconnection simulations to efficiently model the inherent disparity in length-scales. We have systematically investigated the effects of mesh refinement and determined necessary modifications to the algorithm required to mitigate non-physical artifacts at the coarse–fine interface. We have used the ultrahigh-order pseudo-spectral analytical time-domain Maxwell solver to analyze how its use can mitigate the numerical dispersion that occurs with the finite-difference time-domain (or “Yee”) method. Absorbing layers are introduced at the coarse–fine interface to eliminate spurious effects that occur with mesh refinement. We also study how damping the electromagnetic fields and current density in the absorbing layer can help prevent the non-physical accumulation of charge and current density at the coarse–fine interface. Using a mesh refinement ratio of 8 for two-dimensional magnetic reconnection simulations, we obtained good agreement with the high-resolution baseline simulation, using only 36% of the macroparticles and 71% of the node-hours needed for the baseline. The methods presented here are especially applicable to 3D systems where higher memory savings are expected than in 2D, enabling comprehensive, computationally efficient 3D reconnection studies in the future.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Data-informed grid refinement to improve traveltime accuracy in the regional seismic traveltime (RSTT) model

The regional seismic traveltime (RSTT) model predicts traveltimes of regional seismic phases accounting for 3-D structure of the crust and the upper mantle on a global scale. Previous versions of the RSTT model have been implemented using nodes separated by ∼1° spacing across the globe. A regional-scale study using regional Pn and Pg traveltimes across Israel and the Middle East demonstrated that data driven, systematic grid refinement reduces traveltime residuals and enhances resolution of smaller tectonic features in regions having dense ray coverage. High density Pn ray coverage in the western US, Europe, Middle East and East Asia can likewise provide the resolution that allows systematic global grid refinement of the RSTT model. In this study, we use a large number of Pn ray paths originating from events located with an epicentral location uncertainty of 25 km (GT25) or better. We conduct targeted grid refinements at 1.0°, 0.5°, 0.25° and 0.125° on a global scale, producing a refined RSTT model that yields a 21.6 per cent reduction in median event location error in Europe and the Middle East, when compared with the original global RSTT model presented in Begnaud et al. The new model also resolves finer tectonic structures in regions with high Pn ray density.

58 GEOSCIENCES↗

Refinement of macromolecular structures against neutron data with SHELXL2013

Some of the improvements in SHELX2013 make SHELXL convenient to use for refinement of macromolecular structures against neutron data without the support of X-ray data. The new NEUT instruction adjusts the behaviour of the SFAC instruction as well as the default bond lengths of the AFIX instructions. This work presents a protocol on how to use SHELXL for refinement of protein structures against neutron data. It includes restraints extending the Engh & Huber [Acta Cryst. (1991), A47, 392-400] restraints to H atoms and discusses several of the features of SHELXL that make the program particularly useful for the investigation of H atoms with neutron diffraction. SHELXL2013 is already adequate for the refinement of small molecules against neutron data, but there is still room for improvement, like the introduction of chain IDs for the refinement of macromolecular structures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Towards solution and refinement of organic crystal structures by fitting to the atomic pair distribution function

In this study, a method towards the solution and refinement of organic crystal structures by fitting to the atomic pair distribution function (PDF) is developed. Approximate lattice parameters and molecular geometry must be given as input. The molecule is generally treated as a rigid body. The positions and orientations of the molecules inside the unit cell are optimized starting from random values. The PDF is obtained from carefully measured X-ray powder diffraction data. The method resembles `real-space' methods for structure solution from powder data, but works with PDF data instead of the diffraction pattern itself. As such it may be used in situations where the organic compounds are not long-range-ordered, are poorly crystalline, or nanocrystalline. The procedure was applied to solve and refine the crystal structures of quinacridone (β phase), naphthalene and allopurinol. In the case of allopurinol it was even possible to successfully solve and refine the structure in P1 with four independent molecules. As an example of a flexible molecule, the crystal structure of paracetamol was refined using restraints for bond lengths, bond angles and selected torsion angles. In all cases, the resulting structures are in excellent agreement with structures from single-crystal data.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Nonconforming Mesh Refinement for High-Order Finite Elements

In this study, we propose a general algorithm for nonconforming adaptive mesh refinement (AMR) of unstructured meshes in high-order finite element codes. Our focus is on $h$-refinement with a fixed polynomial order. The algorithm handles triangular, quadrilateral, hexahedral, and prismatic meshes of arbitrarily high-order curvature, for any order finite element space in the de Rham sequence. We present a flexible data structure for meshes with hanging nodes and a general procedure to construct the conforming interpolation operator, both in serial and in parallel. The algorithm and data structure allow anisotropic refinement of tensor product elements in two and three dimensions and support unlimited refinement ratios of adjacent elements. We report numerical experiments verifying the correctness of the algorithms and perform a parallel scaling study to show that we can adapt meshes containing billions of elements and run efficiently on 393,000 parallel tasks. Finally, we illustrate the integration of dynamic AMR into a high-order Lagrangian hydrodynamics solver.

97 MATHEMATICS AND COMPUTING↗

Preserving Superconvergence of Spectral Elements for Curved Domains via $h$ and $p$-Geometric Refinement

Spectral element methods (SEM), extensions of finite element methods (FEM), have emerged as significant techniques for solving partial differential equations in physics and engineering. SEM can potentially deliver superior accuracy due to the potential superconvergence in nodal solutions for well-shaped tensor-product elements. However, the accuracy of SEM often degrades in complex geometries due to geometric inaccuracies near curved boundaries and the loss of superconvergence with simplicial or non-tensor-product elements. To overcome the first issue, we propose using h- and p-geometric refinement, which refines the mesh near high-curvature regions and increases the degree of geometric basis functions, respectively. We show that when using mixed-element meshes with tensor-product elements in the interior of the domain, curvature-based geometric refinement near boundaries can improve the accuracy of the interior elements by reducing pollution errors and preserving the superconvergence in nodal solutions. To address the second issue, we introduce a post-processing technique using the adaptive extended stencil finite element method (AES-FEM) to recover the accuracy near the curved boundaries. The combination of curvature-based geometric refinement and accurate post-processing offers an effective and easier-to-implement alternative to methods reliant on exact geometries. We demonstrate our techniques by solving the convection-diffusion equation in 2D and show up to two orders of magnitude of improvement in the solution accuracy, even when the elements are poorly shaped near boundaries.

97 MATHEMATICS AND COMPUTING↗

Interaction of Strain Refined Precipitates and Recrystallized Grains in Nb-Ti Microalloyed Steel during Continuous Casting, Hot-Core Heavy Reduction Rolling, and Reheating Process

Hot-core heavy reduction rolling (HHR{sup 2}) is an energy-saving process that directly rolls continuously cast slabs at the end of solidification that have a large temperature gradient. Here, we elucidated the interaction of strain refined precipitates and recrystallized grains in Nb-Ti microalloyed steel during continuous casting, hot-core heavy reduction rolling, and reheating process. Furthermore, theoretical models were established to calculate recrystallization driving force and pinning force at temperatures in the range of 850-1300 °C by a two-stage interrupted compression test using a Gleeble-3800 thermomechanical simulator. The study indicated that a random dispersion of strain refined precipitates with a size range of ~ 6-10 nm was obtained in the hot-core heavy reduction rolled slab, which was different from the coarse and uneven distribution of precipitates in a conventional slab. Upon reheating, the austenite grains in the hot-core heavy reduction rolled slab were significantly refined and evenly distributed along the thickness direction. This is attributed to the random dispersion of strain refined precipitates formed in the HHR{sup 2} process.

36 MATERIALS SCIENCE↗

Deacetylation and Mechanical Refining Pathway for the Bioconversion of Sugarcane Bagasse

Advancing lignocellulose biorefining is imperative for the deployment of cellulosic (2G) biofuels. This work investigates the tailoring of the alkaline deacetylation and mechanical refining (DMR) pathway for the bioconversion of sugarcane bagasse. Experiments are conducted at laboratory and pilot scales, varying the pretreatment conditions (70–92 °C; 48–100 g NaOH /kg) and the mechanical refining technologies (PFI and disk refining). The pretreatments selectively solubilize acetyl groups (> 86%) and lignin (10–63%) while mostly preserving structural carbohydrates in the solid phase. Enzymatic hydrolysis generates hydrolysates of clean sugars (glucose and xylose), with sugar yields increasing up to 81% for glucose and 89% for xylose in response to delignification and mechanical refining. Biochemical methane potential assays reveal specific methane productions of up to 568 NmL CH₄ gVS⁻¹ for alkaline liquor monodigestion and 344 NmL CH₄ gVS⁻¹ for co-digestion with sugarcane vinasse from the conventional (1G) sugarcane ethanol, indicating a strong potential for bioenergy recovery from this process stream. Synergies are identified in integrating 1G ethanol, 2G DMR processing of bagasse, and anaerobic co-digestion of 1G vinasse and 2G DMR alkaline liquor. This technology enables sugarcane biorefineries to enhance the co-production of ethanol, methane, and concentrated streams of CO 2 .

09 BIOMASS FUELS↗

Dependence of Achievable Plan Quality on Treatment Technique and Planning Goal Refinement: A Head-and-Neck Intensity Modulated Radiation Therapy Application

Purpose: To develop a practical workflow for retrospectively analyzing target and normal tissue dose–volume endpoints for various intensity modulated radiation therapy (IMRT) delivery techniques; to develop technique-specific planning goals to improve plan consistency and quality when feasible. Methods and Materials: A total of 165 consecutive head-and-neck patients from our patient registry were selected and retrospectively analyzed. All IMRT plans were generated using the same dose–volume guidelines for TomoTherapy (Tomo, Accuray), TrueBeam (TB, Varian) using fixed-field IMRT (TB-IMRT) or RAPIDARC (TB-RAPIDARC), or Siemens Oncor (Siemens-IMRT, Siemens). A MATLAB-based dose–volume extraction and analysis tool was developed to export dosimetric endpoints for each patient. With a fair stratification of patient cohort, the variation of achieved dosimetric endpoints was analyzed among different treatment techniques. Upon identification of statistically significant variations, technique-specific planning goals were derived from dynamically accumulated institutional data. Results: Retrospective analysis showed that although all techniques yielded comparable target coverage, the doses to the critical structures differed. The maximum cord doses were 34.1 ± 2.6, 42.7 ± 2.1, 43.3 ± 2.0, and 45.1 ± 1.6 Gy for Tomo, TB-IMRT, TB-RAPIDARC, and Siemens-IMRT plans, respectively. Analyses of variance showed significant differences for the maximum cord doses but no significant differences for other selected structures among the investigated IMRT delivery techniques. Subsequently, a refined technique-specific dose–volume guideline for maximum cord dose was derived at a confidence level of 95%. The dosimetric plans that failed the refined technique-specific planning goals were reoptimized according to the refined constraints. We observed better cord sparing with minimal variations for the target coverage and other organ at risk sparing for the Tomo cases, and higher parotid doses for C-arm linear accelerator–based IMRT and RAPIDARC plans. Conclusion: Patient registry–based processes allowed easy and systematic dosimetric assessment of treatment plan quality and consistency. Our analysis revealed the dependence of certain dosimetric endpoints on the treatment techniques. Technique-specific refinement of planning goals may lead to improvement in plan consistency and plan quality.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Local time–space mesh refinement for simulation of elastic wave propagation in multi-scale media

This paper presents an original approach to local time–space grid refinement for the numerical simulation of wave propagation in models with localized clusters of micro-heterogeneities. The main features of the algorithm are –the application of temporal and spatial refinement on two different surfaces; –the use of the embedded-stencil technique for the refinement of grid step with respect to time; –the use of the Fast Fourier Transform (FFT)-based interpolation to couple variables for spatial mesh refinement. The latter makes it possible to perform filtration of high spatial frequencies, which provides stability in the proposed finite-difference schemes. In the present work, the technique is implemented for the finite-difference simulation of seismic wave propagation and the interaction of such waves with fluid-filled fractures and cavities of carbonate reservoirs. However, this approach is easy to adapt and/or combine with other numerical techniques, such as finite elements, discontinuous Galerkin method, or finite volumes used for approximation of various types of linear and nonlinear hyperbolic equations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A space–angle DGFEM approach for the Boltzmann radiation transport equation with local angular refinement

In this paper a new method for the discretization of the radiation transport equation is presented, based on a discontinuous Galerkin method in space and angle that allows for local refinement in angle where any spatial element can support its own angular discretization. To cope with the discontinuous spatial nature of the solution, a generalized Riemann procedure is required to distinguish between incoming and outgoing contributions of the numerical fluxes. A new consistent framework is introduced that is based on the solution of a generalized eigenvalue problem. The resulting numerical fluxes for the various possible cases where neighboring elements have an equal, higher or lower level of refinement in angle are derived based on tensor algebra and the resulting expressions have a very clear physical interpretation. The choice of discontinuous trial functions not only has the advantage of easing local refinement, it also facilitates the use of efficient sweep-based solvers due to decoupling of unknowns on a large scale thereby approaching the efficiency of discrete ordinates methods with local angular resolution. The approach is illustrated by a series of numerical experiments. Results show high orders of convergence for the scalar flux on angular refinement. The generalized Riemann upwinding procedure leads to stable and consistent solutions. Further the sweep-based solver performs well when used as a preconditioner for a Krylov method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Microstructure-refinement–driven enhanced tensile properties of high-pressure die-cast A380 alloy through friction stir processing

This work employs friction stir processing (FSP), a well-known severe plastic deformation technique, to selectively modify the microstructure of thin-walled, high-pressure die-cast (HPDC) aluminum alloy A380, a major HPDC alloy fabricated in the die casting sector. FSP effectively breaks down Al dendrites and acicular Si particles, creating a homogenized distribution of equiaxed Si particles in the aluminum matrix. After FSP, the refined Si particles (~1.5 µm) are smaller than the eutectic Si particles (3–8 µm) in HPDC condition. In addition, interparticle distance has decreased almost 50% compared to dendritic arm spacing, and FSP has reduced the aspect ratio of Si particles to ~2. Furthermore, FSP eliminates porosity, and breaks down needle-like second-phase Fe-Mn and Cu-rich particles, yielding a refined, homogeneous distribution. The FSP-induced microstructural refinement and porosity reduction improve bulk yield strength and ductility by 23% and 66%. Tensile properties are enhanced beyond those of the die skin of the HPDC plate, and the alloy possesses lower defect density and a highly refined microstructure. This study establishes the viability of FSP as a tool for microstructure modification and mechanical property improvement for HPDC Al alloys for the light-weighting goal of the automotive industries.

36 MATERIALS SCIENCE↗

Refinement of Mg{sub 2}Si reinforcement in a commercial Al–20%Mg{sub 2}Si in-situ composite with bismuth, antimony and strontium

Refinement by addition elements of Al–Mg{sub 2}Si alloys is known to result in a change of primary Mg{sub 2}Si morphology. In this paper, the effects of Bi, Sb and Sr on the characteristic parameters of Al–20%Mg{sub 2}Si in-situ composite have been investigated by computer aided cooling curve thermal analysis and microstructural inspection. Size, density and aspect ratio measurements showed that additions of 0.4 wt.% Bi, 0.8 wt.% Sb and 0.01 wt.% Sr refined the Mg{sub 2}Si reinforcement. Exceeding these concentrations, however, resulted in coarsening of Mg{sub 2}Si particles with no change in the morphology. The results also showed that addition elements caused a decrease in the nucleation and growth temperatures of Mg{sub 2}Si particles. The refining effect of Bi, Sb and Sr is likely to be related to the effect of oxide bifilms suspended in the composite melt as favored nucleation substrates for Mg{sub 2}Si particles. - Highlight: • 0.4 wt.%, 0.8 wt.% and 0.01 wt.% is the optimum content for Bi, Sb and Sr addition. • Exceeding optimum concentration resulted in the coarsening of reinforcements. • Nucleation and growth temperatures decrease with addition of Bi, Sb and Sr. • The refining effect of Bi, Sb and Sr is likely to be related to the oxide bifilms.

36 MATERIALS SCIENCE↗

Improving the QBO Forcing by Resolved Waves With Vertical Grid Refinement in E3SMv2

Abstract The quasi‐biennial oscillation (QBO) is the dominate mode of variability in the tropical stratosphere and plays an important role in stratospheric dynamics and chemistry. The QBO is notably deficient in many climate models, including the Energy Exascale Earth System Model (E3SM) developed by the US Department of Energy. In this work, we refine the lower stratospheric vertical grid spacing from roughly 1 km to 500 m to facilitate more realistic equatorial wave activity in the lower stratosphere in E3SM version 2. The refinement results in a simulated QBO with a reasonable amplitude and easterly‐westerly transition in both directions, but still has a longer period than observed, slower easterly downward propagation speed, and shallower vertical depth. Similar refinement in the multi‐scale modeling framework configuration of E3SM yields similar improvements. By analyzing the forcing contributions from different wave types, we find that most of the QBO forcing still comes from parameterized gravity wave drag from convection. The improved QBO forcing contributions from resolved waves, especially equatorial Kelvin waves and resolved small scale waves, can be attributed to the grid refinement.

E3SM↗

Structural refinement of Pbnm-type perovskite films from analysis of half-order diffraction peaks

Engineering structural modifications of epitaxial perovskite thin films is an effective route to induce new functionalities or enhance existing properties due to the close relation of the electronic ground state to the local bonding environment. As such, there is a necessity to systematically refine and precisely quantify these structural displacements, particularly those of the oxygen octahedra, which is a challenge due to the weak scattering factor of oxygen and the small diffraction volume of thin films. In this paper, we present an optimized algorithm to refine the octahedral rotation angles using specific unit-cell-doubling half-order diffraction peaks for the a - a - c + Pbnm structure. The oxygen and A-site positions can be obtained by minimizing the squared-error between calculated and experimentally determined peak intensities using the (1/2 1/2 3/2) and (1/2 1/2 5/2) reflections to determine the rotation angle α about in-plane axes and the (1/2 5/2 1), (1/2 3/2 1), and (1/2 3/2 2) reflections to determine the rotation angle γ about the out-of-plane axis, whereas the convoluting A-site displacements associated with the octahedral rotation pattern can be determined using (1 1 1/2) and (1/2 1/2 1/2) reflections to independently determine A-site positions. The validity of the approach is confirmed by applying the refinement procedure to determine the A-site and oxygen displacements in a NdGaO 3 single crystal. Finally, the ability to refine both the oxygen and A-site displacements relative to the undistorted perovskite structure enables a deeper understanding of how structural modifications alter functionality properties in epitaxial films exhibiting this commonly occurring crystal structure.

74 ATOMIC AND MOLECULAR PHYSICS↗