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Theoretical Problems in Materials Science

Interactions between theoretical physics and material sciences to identify problems of common interest in which some of the powerful theoretical approaches developed for other branches of physics may be applied to problems in materials science are presented. A unique structure was identified in rapidly quenched Al-14% Mn. The material has long-range directed bonds with icosahedral symmetry which does not form a regular structure but instead forms an amorphous-like quasiperiodic structure. Finite volume fractions of second phase material is advanced and is coupled with nucleation theory to describe the formation and structure of precipitating phases in alloys. Application of the theory of pattern formation to the problem of dendrite formation is studied.

Langer, J. S.↗

Of mice and genes: evolution of vertebrate brain development

In this review the current understanding of genetic and molecular evolution of development, in particular the formation of the major axis of bilateral animals, is critically evaluated, and the early pattern formation in the hindbrain is related as much as possible to these processes. On the genetic level it is proposed that the exuberant multiplication of regulatory genes compared to that of structural genes relates to the increased flexibility of early vertebrate development. In comparisons to fruit flies, many conserved genes are found to be expressed very differently, while many others seem to reflect a comparable pattern and thus suggest a conservation of function. Even genes with a largely conserved pattern of expression may change the level at which they are expressed and the mechanisms by which they are regulated in their expression. Evolution and development of hindbrain motoneurons is reviewed, and it is concluded that both comparative data as well as more recent experimental data suggest a limited importance for the rhombomeres. Clearly, many cell fate-specifying processes work below the level of rhombomeres or in the absence of rhombomeres. It is suggested that more comparative developmental data are needed to establish firmly the relationship between homeobox genes and rhombomere specification in vertebrates other than a few model species.

NASA Discipline Developmental Biology↗

Unusual Microtopography on an Apollo 12 Soil Grain

We have observed the presence of a previously undescribed microtopography in several regions on the surface of a lunar grain from Apollo regolith sample 12070,29. This microtopography consists of flattened triangular prisms, henceforth referred to as denticles, set in an orderly arrangement. We propose three possible processes to describe the presence of these structures: (1) radiation; (2) aqueous activity; or (3) impact. Radiation—the surface of the Earth’s moon is subject to energetic ion and photon irradiation which can produce a multitude of morphological effects on grain surfaces including erosion/sputtering, vesicle formation, and amorphization of crystalline phases. Under certain conditions surface erosion can result in the formation of well-ordered nanostructures including mounds, dots, wave-shaped, rippled or corrugated features typically <10s nm in size and organized into pattered arrays. However larger pyramid-shaped features up to approx. 300 nm at the base, similar in shape to lunar denticles, were produced on Cu substrates ex-posed to ion beam sputtering.. Aqueous alteration—recent reports of purported water on the Moon imply the possibility of brief, limited exposure of surface materials to aqueous fluids. Aqueous corrosion of silicates can result in the formation of crystallographically controlled denticulated features, up to 10s of micron at the base, arranged in a patterned formation. Impact—the surface of the moon is impacted by meteorites, particularly by micron-size particles, resulting in the formation of a variety of crater types. While it is difficult to envision a scenario in which a patterned array could be formed by impact, fracturing along planes of crystallographic structural weakness due to external stress could explain these features.

Thomas-Keprta, K. L.↗

Revisiting the equatorial Pacific sea surface temperature response to global warming

The relative roles of the oceanic and atmospheric processes in the pattern formation of the equatorial Pacific sea surface temperature (SST) response to global warming is investigated using a set of climate model experiments embedded with a novel partial coupling technique. Here, the modeling results show that the SST response experiences a transition from a La Niña-like warming pattern at the initial stage to an El Niño-like warming pattern at the quasi-equilibrium stage. By decomposing anomalous equatorial Pacific SST into atmosphere-forced passive component and ocean dynamics-induced active component, it is found that the SST warming pattern at both stages is entirely induced by its active component. Specifically, the meridional and vertical ocean circulation changes play a dominant role in forming the La Niña-like SST warming pattern at the initial stage, and the zonal and meridional ocean circulation changes are responsible for the formation of the El Niño-like SST warming pattern at the quasi-equilibrium stage. In contrast, the passive SST at both stages is characterized by a zonally uniform warming along the equator, which can be explained by a balance between the cooling effect associated with mean upwelling and the warming effect due to surface passive heat flux change. In addition, this study finds that it is the slowdown of the Pacific subtropical cells during the transition period that controls the evolution of the equatorial SST warming pattern by changing the meridional and vertical ocean heat transports.

54 ENVIRONMENTAL SCIENCES↗

Structure and Dynamics of Domains in Ferroelectric Nanostructures – Phase-Field Modeling (Final Technical Report)

Domain pattern formation is one of the most common phenomena in nature and is a topic of immense interest in many fields ranging from materials science and physics to chemistry and biology. This DOE sponsored research project explored the basic science concerning the thermodynamic stability of mesoscale polarization domain patterns and their temporal evolution mechanisms during formation and subsequent switching in ferroelectric nanostructures and heterostructures. The project employed the computational phase-field method in combination of microelasticity and electrostatic theories. The research was carried out in close collaboration with a number of experimental groups who used High Resolution Transmission Electron Microscopy (HRTEM), in situ TEM with Scanning Probe Microscopy (SPM), or Piezoresponse Force Microscopy (PFM) to characterize the domain structures and dynamics of ferroelectric thin films and heterostructures and who grow high-quality ferroelectric and multiferroic thin films using advanced growth techniques such as Molecular Beam Epitaxy (MBE), Pulsed Laser Deposition (PLLD), and sputtering. The research efforts of the project help establish the phase-field method as the most powerful method for understanding and predicting domain structures in ferroelectric thin films and nanostructures. The findings of the project led to the basic understanding of stability and switching mechanisms of ferroelectric domains under different mechanical boundary conditions and under either homogeneous capacitor configurations or local fields using metallic probes as electrodes and the emergence of charged domain walls during domain switching. The project predicted the spatial length scales, temperature ranges, and electromechanical conditions for different polar states in heterostructures and guided the discovery of both transient and stable novel polarization states containing vortex lattices in oxide superlattices. The project resulted in 134 journal publications and 6 PhD theses with all the PhD graduates currently working in either academia or industry within the United States. The basic understanding on the stability of mesoscale polar states and pattern evolution achieved by the project improved our ability to control and engineer properties of ferroelectric thin films and heterostructures for potential applications in nanoscale electronic devices.

36 MATERIALS SCIENCE↗

Evaporation of a Reactive Nanofluid Sessile Drop: Capturing Rapid Emergence of Surface Crystals with In Situ Synchrotron X-ray Diffraction

Mechanisms for surface pattern formation from evaporation of a reactive nanofluid sessile drop are not well understood. In contrast to the coffee-ring effect from inert particles, rapid chemical and morphological transformation of reactive nanoparticles upon rapid evaporative drying are challenging to probe experimentally. Here, using grazing-incidence X-ray surface scattering, the nanostructure of nascent surface patterns has been probed as a ZnO nanofluid sessile drop rapidly dries. The high temporal resolution enabled by the high flux of synchrotron X-rays allows the observation of the emergence of Zn(OH) 2 surface crystals from the onset of evaporation and their rapid evolution into the final residual surface pattern, via transient layered complexes evident from the temporary appearance of X-ray diffraction peaks preceding Zn(OH) 2 formation. The results offer mechanistic insights of morphogenesis of surface patterns from evaporation-induced self-assembly and self-organization of reactive nanofluids, previously untenable using other experimental methods.

36 MATERIALS SCIENCE↗

Microstructure Formations in the Two-Phase Region of the Binary Peritectic Organic System TRIS-NPG

In order to prepare for an onboard experiment on the International Space Station (ISS), systematic directional solidification experiments with transparent hypoperitectic alloys were carried out at different solidification rates around the critical velocity for morphological stability of both solid phases. The investigations were done in the peritectic region of the binary transparent organic TRIS-NPG system where the formation of layered structures is expected to occur. The transparent appearance of the liquid and solid phase enables real time observations of the dynamic of pattern formation during solidification. The investigations show that frequently occurring nucleation events govern the peritectic solidification morphology which occurs at the limit of morphological stability. As a consequence, banded structures lead to coupled growth even if the lateral growth is much faster compared to the growth in pulling direction.

Mogeritsch, Johann↗

Cognitive signal processing

Unsupervised signal pattern recognition - computer simulation of noisy signal pattern format, and construction of asymptotic Bayes decision boundary form

BAYESIAN STATISTICS↗

Navigation strategies for multiple autonomous mobile robots moving in formation

The problem of deriving navigation strategies for a fleet of autonomous mobile robots moving in formation is considered. Here, each robot is represented by a particle with a spherical effective spatial domain and a specified cone of visibility. The global motion of each robot in the world space is described by the equations of motion of the robot's center of mass. First, methods for formation generation are discussed. Then, simple navigation strategies for robots moving in formation are derived. A sufficient condition for the stability of a desired formation pattern for a fleet of robots each equipped with the navigation strategy based on nearest neighbor tracking is developed. The dynamic behavior of robot fleets consisting of three or more robots moving in formation in a plane is studied by means of computer simulation.

Wang, P. K. C.↗

Evolution of the vestibulo-ocular system

The evolutionary and developmental changes in the eye muscle innervation, the inner ear, and the vestibulo-ocular reflex are examined. Three eye muscle patterns, based on the innervation by distinct ocular motoneurons populations, can be identified: a lamprey, an elasmobranch, and a bony fish/tetrapod pattern. Four distinct patterns of variation in the vestibular system are described: a hagfish pattern, a lamprey pattern, an elasmobranch pattern, and a bony fish/tetrapod pattern. Developmental data suggest an influence of the hindbrain on ear pattern formation, thus potentially allowing a concomitant change of eye muscle innervation and ear variation. The connections between the ear and the vestibular nuclei and between the vestibular nuclei and ocular motoneurons are reviewed, and the role of neurotrophins for pattern specification is discussed. Three patterns are recognized in central projections: a hagfish pattern, a lamprey pattern, and a pattern for jawed vertebrates. Second-order connections show both similarities and differences between distantly related species such as lampreys and mammals. For example, elasmobranchs lack an internuclear system, which is at best poorly developed in lampreys. It is suggested that the vestibulo-ocular system shows only a limited degree of variation because of the pronounced functional constraints imposed on it.

Non-NASA Center↗

Dynamic evolution of ultracold electron beams from nanostructured cathodes

Dynamic Coulomb expansion of dense, nonuniform particle beamlets can lead to causticlike formations in the charge density profile of the resultant beam. Such features only occur for cold beams where thermal diffusion of the particles is minimized. These phenomena have been observed experimentally for select cases with ion beams but not yet for electron beams as the electron dynamics occur over far faster timescales. We simulate the interaction of electron bunches while varying the initial transverse temperature and density profiles to determine the thresholds that characterize this pattern formation. Furthermore, we extend the simulations to geometric arrangements that are more pertinent to the nanotip cathode application and consider the effects of asymmetries and the impact of a low-density halo on the overall process. The simulations are conducted using a previously documented high-fidelity algorithm for collisional particle dynamics. These studies identify the temperature and density thresholds required for caustic formation and provide guidance for optimizing the design of nanoscale structured cathodes. We also demonstrate that the correlation between the final density patterns and the underlying beam parameters enables a virtual diagnostic tool for measuring ultralow emittance beams solely based on a transverse charge density profile.

43 PARTICLE ACCELERATORS↗

The Toll pathway is required in the epidermis for muscle development in the Drosophila embryo

The Toll signaling pathway functions in several Drosophila processes, including dorsal-ventral pattern formation and the immune response. Here, we demonstrate that this pathway is required in the epidermis for proper muscle development. Previously, we showed that the zygotic Toll protein is necessary for normal muscle development; in the absence of zygotic Toll, close to 50% of hemisegments have muscle patterning defects consisting of missing, duplicated and misinserted muscle fibers (Halfon, M.S., Hashimoto, C., and Keshishian, H., Dev. Biol. 169, 151-167, 1995). We have now also analyzed the requirements for easter, spatzle, tube, and pelle, all of which function in the Toll-mediated dorsal-ventral patterning pathway. We find that spatzle, tube, and pelle, but not easter, are necessary for muscle development. Mutations in these genes give a phenotype identical to that seen in Toll mutants, suggesting that elements of the same pathway used for Toll signaling in dorsal-ventral development are used during muscle development. By expressing the Toll cDNA under the control of distinct Toll enhancer elements in Toll mutant flies, we have examined the spatial requirements for Toll expression during muscle development. Expression of Toll in a subset of epidermal cells that includes the epidermal muscle attachment cells, but not Toll expression in the musculature, is necessary for proper muscle development. Our results suggest that signals received by the epidermis early during muscle development are an important part of the muscle patterning process.

Non-NASA Center↗

Atomistic Mechanism Underlying the Si ( 111 ) - ( 7 × 7 ) Surface Reconstruction Revealed by Artificial Neural-Network Potential

The 7×7 reconstruction of the Si(111) surface represents arguably the most fascinating surface reconstruction so far observed in nature. Yet, the atomistic mechanism underpinning its formation remains unclear after it was discovered sixty years ago. Experimentally, it is observed post priori so that analysis of its formation mechanism can only be carried out in analogy with archaeology. Theoretically, density-functional theory (DFT) correctly predicts the Si(111)-(7×7) ground state but is impractical to simulate its formation process; while empirical potentials failed to produce it as the ground state. Developing an artificial neural-network potential of DFT quality, we carried out accurate large-scale simulations to unravel the formation of the Si(111)-(7×7) surface. We reveal a possible step-mediated atom-pop rate-limiting process that triggers massive nonconserved atomic rearrangements, most remarkably, a critical process of collective vacancy diffusion that mediates a sequence of selective dimer, corner-hole, stacking-fault, and dimer-line pattern formation, to fulfill the 7×7 reconstruction. Our findings may not only solve the long-standing mystery of this famous surface reconstruction but they also illustrate the power of machine learning in studying complex structures.

36 MATERIALS SCIENCE↗

Emergence of complex-regular eutectic patterns in Al–Ge: Observations from correlative nano-imaging

Eutectic solidification exemplifies nonequilibrium pattern formation, making it a well-studied moving boundary problem. Yet the mechanisms behind the formation of complex-regular microstructures – particularly in highly anisotropic systems with a significant volume fraction of a faceted phase – remain poorly understood. Our understanding of such systems is made complicated by the nonlinear interface kinetics and unique growth dynamics characteristic of faceted phases. To address these challenges, we investigate a model Al–Ge eutectic system, where the faceted Ge phase constitutes a substantial volume fraction (~0.35) and where the two solid phases arrange into so-called “fishbone” or “feather” complex-regular patterns. Using synchrotron-based x-ray nano-imaging and nanotomography with high spatial resolution (22 nm per pixel), we capture in real-time the evolution of the solid–liquid interfaces and the resulting three-dimensional microstructures in this faceted/non-faceted eutectic system. By integrating these observations with electron backscattered diffraction, we elucidate the crystallographic biases on the solidification process and the mechanisms driving the formation of such complex-regular microstructures. These findings inform a new growth model for irregular eutectics in (near-)symmetrical phase diagrams, offering insight on advanced microstructural design and processing strategies. More broadly, we demonstrate how interfacial curvature is generated in irregular eutectic alloys and how it depends on the volume fraction of the faceted phase.

36 MATERIALS SCIENCE↗

Beyond the eutectic paradigm: nanolamellar patterns in a rapidly solidified peritectic alloy

Peritectic transformations are central to many structural alloys, yet pattern formation remains poorly understood due to complex growth dynamics and limited three-dimensional data. Here, we report an unusual two-phase microstructure in a Zn–Ag peritectic alloy subjected to rapid solidification by laser surface remelting. Synchrotron X-ray nanotomography reveals a lamellar structure of primary 𝜀-AgZn 3 and peritectic Zn with ∼700 nm spacing. Although resembling a eutectic morphology, this pattern forms without a eutectic reaction through non-steady coupled growth from the liquid. SEM and TEM-EDS confirm interface shapes and phase compositions. These findings expand the design space of peritectics for refined microstructural control.

36 MATERIALS SCIENCE↗

The physics of desiccation cracks 2: Modeling and prediction of the crack patterns

Here, this paper extends the experimental results of our companion paper by modeling and predicting the onset and pattern formation of desiccation cracks in geomaterials (Ruoyu et al., 2023). Thin-layer silt samples in controlled atmospheric conditions were tested to obtain the surface strain maps with the digital image correlation (DIC) method during dehydration. Support experiments, including consolidation and displacement-controlled triaxial tests, were conducted for the properties of geomaterials. These experimental results were used to validate a viscoplastic theoretical model by comparing cracks and singularities locations that distribute following the Cnoidal wave pattern. A critical value exists in the viscoplastic model that determines the number of singularities, which accurately predicts the number of cracks in the experiment. The critical values contain two crucial parameters: rate sensitivity and λ. Rate sensitivity describes the rate-dependent stress–strain relation, while λ shows the ability of pore pressure redistribution under the external mechanical loading rate. These results provide a new view to analyze the desiccation cracks considering the rate-dependent viscoplasticity.

42 ENGINEERING↗

The evolution of embryonic patterning mechanisms in animals

Animals exhibit an enormous diversity of life cycles and larval morphologies. The developmental basis for this diversity is not well understood. It is clear, however, that mechanisms of pattern formation in early embryos differ significantly among and within groups of animals. These differences show surprisingly little correlation with phylogenetic relationships; instead, many are correlated with ecological factors, such as changes in life histories. Copyright 2000 Academic Press.

Review, Tutorial↗