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DOE OSTI2026

In Situ High-Temperature Ultrafast Electron Diffraction through Integrated Furnace and MEMS Platforms

Temperature fundamentally governs phase stability, defect evolution, and transport behavior in materials. Despite its central role, direct measurements of structural evolution at elevated temperatures on ultrafast timescales have remained limited. Here, we report the design, integration, and validation of 2 complementary in situ heating platforms that substantially extend the thermal operating range of ultrafast electron diffraction (UED). A compact furnace-type heating stage enables stable diffraction measurements from room temperature to 800 K with ±0.1 K stability under ultrahigh vacuum, achieved through multi-sensor feedback control, dual air-cooling channels, and a thermally isolated motion stage. In parallel, a microelectromechanical system (MEMS)-based heating platform provides rapid thermal response and access to extreme temperatures ≥1,373 K with ±0.1 K stability over hundreds-micrometer regions while supporting simultaneous electrical biasing for electrothermal coupling studies. Absolute temperature calibration is established using diffraction-based thermometry via aluminum lattice expansion and independently validated through in situ melting of bismuth thin films. UED measurements further reveal pronounced temperature-dependent nonequilibrium lattice dynamics in bismuth, including modifications to electron–phonon coupling and Debye–Waller behavior, as well as enhanced ultrafast diffuse scattering in aluminum at elevated temperatures. Together, these developments establish a practical framework for quantitative, time-resolved studies of temperature-driven kinetics and nonequilibrium structural dynamics under extreme thermal environments.

Bai, Qianqian [Chinese Academy of Sciences (CAS), ↗

DOE OSTI2019

Quantitative Uncertainty Analysis for Diffraction

Current software uses a least squares statistical method. For each model parameter, current software yields a point estimate and estimated standard error for each point estimate. In contrast, we have employed a Bayesian approach with sampling algorithm to provide a full posterior probability density function on each model parameter. This yields a different type of solution (probabilistic) with better fidelity. The Quantitative Uncertainty Analysis for Diffraction (QUAD) package returns a matrix of affect model parameters as a function of iteration through the MCMC analysis. QUAD is a Python code that allows for analysis of X-ray and neutron diffraction data to infer the structure of materials with quantifiable certainty. The code uses Bayesian statistics and Markov chain sampling algorithms to create posterior probability distributions on all material structure parameters that are modeled by a researcher. The statistical packages use the open source GSASII project as a library to calculate model diffraction patterns.

Fancher, ChristopherM↗

NASA NTRS1974

Electromagnetic and scalar diffraction by a right-angled wedge with a uniform surface impedance

The diffraction of an electromagnetic wave by a perfectly-conducting right-angled wedge with one surface covered by a dielectric slab or absorber is considered. The effect of the coated surface is approximated by a uniform surface impedance. The solution of the normally incident electromagnetic problem is facilitated by introducing two scalar fields which satisfy a mixed boundary condition on one surface of the wedge and a Neumann of Dirichlet boundary condition on the other. A functional transformation is employed to simplify the boundary conditions so that eigenfunction expansions can be obtained for the resulting Green's functions. The eigenfunction expansions are transformed into the integral representations which then are evaluated asymptotically by the modified Pauli-Clemmow method of steepest descent. A far zone approximation is made to obtain the scattered field from which the diffraction coefficient is found for scalar plane, cylindrical or sperical wave incident on the edge. With the introduction of a ray-fixed coordinate system, the dyadic diffraction coefficient for plane or cylindrical EM waves normally indicent on the edge is reduced to the sum of two dyads which can be written alternatively as a 2 X 2 diagonal matrix.

Hwang, Y. M.↗

NASA NTRS1975

Calculation of arbitrary-order diffraction efficiencies of thick gratings with arbitrary grating shape

A method for calculating arbitrary-order diffraction efficiencies of thick, lossless transmission gratings with arbitrary periodic grating shapes has been developed. A Fourier-series representation of the grating is employed, along with a coupled-mode theory of diffraction. For illustration, numerical values of the diffraction efficiencies at the first three Bragg angles are calculated for sinusoidal, square-wave, triangular, and saw-tooth gratings. Numerical results for the same grating shapes with the same parameters are also calculated for comparison, by extending Burckhardt's numerical method for analyzing thick sinusoidal gratings. The comparison shows that the coupled-mode theory provides results with relative computational ease and results that are in agreement with calculations obtained by extending the more-rigorous Burckhardt theory to nonsinusoidal grating shapes and to higher-order Bragg angles.

Su, S. F.↗

NASA NTRS1976

Computer modeling of electromagnetic problems using the geometrical theory of diffraction

Some applications of the geometrical theory of diffraction (GTD), a high frequency ray optical solution to electromagnetic problems, are presented. GTD extends geometric optics, which does not take into account the diffractions occurring at edges, vertices, and various other discontinuities. Diffraction solutions, analysis of basic structures, construction of more complex structures, and coupling using GTD are discussed.

Burnside, W. D.↗

NASA NTRS1970

The far field diffraction pattern for corner reflectors with complex reflection coefficients

The far field diffraction pattern of a geometrically perfect corner reflector is examined analytically for normally incident monochromatic light. The states of polarization and the complex amplitudes of the emerging light are expressed through transformation matrices in terms of those of the original incident light for each sextant of the face in a single coordinate system. The analytic expression of the total diffraction pattern is obtained for a circular face. This expression consists of three component functions in addition to the basic Airy function. The coefficient of each function is expressed in terms of complex coefficients of reflectance of the reflecting surface. Some numerical results for different reflecting surfaces, including total internal reflection, are presented. The iso-intensity contours of the diffraction pattern evaluated from the analytical expressions for an uncoated solid corner reflector are also presented along with the photographs of the pattern.

Chang, R. F.↗

NASA NTRS1978

Effects of diffraction in multiple-grid telescopes for X-ray astronomy

Diffraction effects in modern designs for grid collimator telescopes (assumed to have roughly a 100-micron grid period) are apparent at wavelengths longer than 1 A and are dominant at wavelengths longer than 10 A. In collimators with many grids spaced far apart the effects of diffracation are to reduce strongly the peak transmission of the collimator at longer wavelengths and to broaden it by about the amount expected from Fraunhofer diffraction through a slit the size of the grid openings. Comparisons between two-collimator measurements and the present calculations show reasonable agreement; it is therefore concluded that the present single-collimator calculation gives a good representation of their diffraction-limited angular response.

Lindsey, C. A.↗

NASA NTRS1979

Diffraction by an arbitrary subreflector - GTD solution

The high-frequency asymptotic solution of diffraction by a conducting subreflector is investigated. The scattered field is determined up to and including terms of order k to the -1/2 relative to the incident field by using Keller's geometrical theory of diffraction and the newly developed uniform asymptotic theory of diffraction. The key feature of this approach is that the surface of the subreflector is completely arbitrary; in fact, it is only necessary to specify the surface at a set of discrete points over a random net.

Lee, S.-W.↗

NASA NTRS1980

Comparison of two leading uniform theories of edge diffraction with the exact uniform asymptotic solution

The diffraction of an arbitrary cylindrical wave by a half-plane has been treated by Rahmat-Samii and Mittra who used a spectral domain approach. In this paper, their exact solution for the total field is expressed in terms of a new integral representation. For large wave number k, two rigorous procedures are described for the exact uniform asymptotic expansion of the total field solution. The uniform expansions obtained are valid in the entire space, including transition regions around the shadow boundaries. The final results are compared with the formulations of two leading uniform theories of edge diffraction, namely, the uniform asymptotic theory and the uniform theory of diffraction. Some unique observations and conclusions are made in relating the two theories.

Boersma, J.↗

NASA NTRS1951

X-Ray Diffraction Study of the Internal Structure of Supercooled Water

A Bragg X-ray spectrometer equipped with a volume-sensitive Geiger counter and Soller slits and employing filtered molybdenum Ka radiation was used to obtain a set of diffracted intensity curves as a Punction of angle for supercooled water. Diffracted intensity curves in the temperature region of 21 to -16 C were obtained. The minimum between the two main diffraction peaks deepened continuously with lowering temperature, indicating a gradual change in the internal structure of the water. No discontinuity in this trend was noted at the melting point. The internal structure of supercooled water was concluded to become progressively more ice-like as the temperature is lowered.

Dorsch, Robert G.↗

NASA NTRS1985

Hadron cross sections at ultra high energies and unitarity bounds on diffraction dissociation

It was shown that if unitarity bounds on diffractive cross sections are valid at ultra high energies then diffractive dominance models which ascribe the increase in total hadron-hadron cross sections to diffractive processes only are ruled out. Calculations also show that cosmic ray cross sections derived from air shower experiments at ultra high energies clearly rule out models for hadron-hadron cross sections with nat.log ns energy dependence and favor those with nat.log n(2)s variation.

Yodh, G. B.↗

NASA NTRS1985

A method of rapidly obtaining concentration-depth profiles from X-ray diffraction

A broadened diffraction peak, or intensity band, is observed in the case diffraction from a nonhomogeneous phase in which the variations in compositions result in a range of lattice spacings. An intriguing aspect regarding the relationship between the X-ray diffraction band and the composition-depth profile is the hypersensitivity of the intensity band to the shape of the profile. A number of investigators have sought to use this sensitivity to construct high-precision profiles. Difficulties encountered are related to complications due to intensity broadening, and prohibitive computational requirements. Simulation techniques have provided the most accurate interpretation of the intensity band. However, the involved calculations have been prohibitively long. The present study discusses a technique which has simple computational requirements and is as accurate and flexible as the simulation techniques.

Wiedemann, K. E.↗

NASA NTRS1984

An E-plane analysis of aperture-matched horn antennas using the moment method and the uniform geometrical theory of diffraction

The moment method and the uniform geometrical theory of diffraction are utilized to obtain two separate solutions for the E-plane field pattern of an aperture-matched horn antenna. This particular horn antenna consists of a standard pyramidal horn with the following modifications: a rolled edge section attached to the aperture edges and a curved throat section. The resulting geometry provides significantly better performance in terms of the pattern, impedance, and frequency characteristics than normally obtainable. The moment method is used to calculate the E-plane pattern and BSWR of the antenna. However, at higher frequencies, large amounts of computation time are required. The uniform geometrical theory of diffraction provides a quick and efficient high frequency solution for the E-plane field pattern. In fact, the uniform geometrical theory of diffraction may be used to initially design the antenna; then, the moment method may be applied to fine tune the design. This procedure has been successfully applied to a compact range feed design.

Heedy, D. J.↗

NASA NTRS1984

Neutron and X-ray diffraction of plasma-sprayed zirconia-yttria thermal barrier coatings

ZrO2-7.8mol. pct. YO1.5, a fused powder, and ZrO2-8.7mol. pct. YO1.5, a prereacted powder, were plasma-sprayed onto steel substrates. Neutron diffraction and X-ray diffraction of the as-received powder, the powder plasma sprayed into water, as-sprayed coatings, and coatings heat-treated for 10 and 100 h were carried out to study phase transformations and ordering of the oxygen ions on the oxygen sublattice. The as-received fused powder has a much lower monoclinic percentage than does the pre-reacted powder, this resulting in a much lower monoclinic percentage in the coating. Heat treatment increases the percentages of the cubic and monoclinic phases, while decreasing the tetragonal content. An ordered tetragonal phase is detected by the presence of extra neutron diffraction peaks. These phase transformations and ordering will result in volume changes. The implications of these transformations on the performance of partially stabilized zirconia thermal barrier coatings is discussed.

Shankar, N. R.↗

NASA NTRS1985

A uniform GTD analysis of the EM diffraction by a thin dielectric/ferrite half-plane and related configurations

A uniform geometrical theory of diffraction (UTD) solution is developed for the problem of the diffraction by a thin dielectric/ferrite half plane when it is excited by a plane, cylindrical, or surface wave field. Both transverse electric and transverse magnetic cases are considered. The solution of this problem is synthesized from the solutions to the related problems of EM diffraction by configurations involving perfectly conducting electric and magnetic walls covered by a dielectric/ferrite half-plane of one half the thickness of the original half-plane.

Rojas, Roberto G.↗

NASA NTRS1988

Interior impedance wedge diffraction with surface waves

The exact impedance wedge solution is evaluated asymptotically using the method of steepest descents for plane wave illumination at normal incidence. Uniform but different impedances on each face are considered for both soft and hard polarizations. The asymptotic solution isolates the incident, singly reflected, multiply reflected, diffracted, and surface wave fields. Multiply reflected fields of any order are permitted. The multiply reflected fields from the exact solution are written as ratios of auxiliary Maliuzhinets functions, whereas a geometrical analysis gives the reflected fields as products of reflection coefficients. These two representations are shown to be identical in magnitude, phase and the angular range over which they exist. The diffracted field includes four Fresnel transition functions as in the perfect conductor case, and the expressions for the appropriate discontinuities at the shadow boundaries are presented. The surface wave exists over a finite angular range and only for certain surface impedances. A surface wave transition field is included to retain continuity. Computations are presented for interior wedge diffractions although the formulation is valid for both exterior and interior wedges.

Balanis, Constantine A.↗

NASA NTRS1987

Complex space monofilar approximation of diffraction currents on a conducting half plane

Simple approximation of diffraction surface currents on a conducting half plane, due to an incoming plane wave, is obtained with a line current (monofile) in complex space. When compared to an approximating current at the edge, the diffraction pattern is seen to improve by an order of magnitude for a minimal increase of computation effort. Thus, the inconvient Fresnel integral functions can be avoided for quick calculations of diffracted fields and the accuracy is good in other directions than along the half plane. The method can be applied to general problems involving planar metal edges.

Lindell, I. V.↗

NASA NTRS1987

Higher order diffractions from a circular disk

The backscattering from a circular disk is analyzed using the geometrical theory of diffraction. First-, second-, and third-order diffractions are included in the hard polarization analysis, while first-, second-, and third-order slope diffractions are included for soft polarization. Improvements in the prediction of the monostatic radar cross section over previous works are noted. For hard polarization, an excellent agreement is exhibited between experimental and theoretical results, while a very good agreement is noted for soft polarization. To further improve the soft polarization results for wide angles, a model for the creeping wave or circulating current on the edge of the disk is obtained and used to find an additional component of the backscattered field. The addition of this component significantly improves the results for wide angles, leading to excellent agreement for soft polarization also. An axial-caustic correction method using equivalent currents is also included in the analysis.

Marsland, Diane P.↗