Search NASA⌕ Search

SEARCH · Search NASA

Results for “Dynamic Timing Analysis”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 289 records · Page 16

Metatranscriptomic reconstruction reveals RNA viruses with the potential to shape carbon cycling in soil

Viruses impact nearly all organisms on Earth, with ripples of influence in agriculture, health, and biogeochemical processes. However, very little is known about RNA viruses in an environmental context, and even less is known about their diversity and ecology in soil, 1 of the most complex microbial systems. Here, we assembled 48 individual metatranscriptomes from 4 habitats within a planted soil sampled over a 22-d time series: Rhizosphere alone, detritosphere alone, rhizosphere with added root detritus, and unamended soil (4 time points and 3 biological replicates). We resolved the RNA viral community, uncovering a high diversity of viral sequences. We also investigated possible host organisms by analyzing metatranscriptome marker genes. Based on viral phylogeny, much of the diversity was Narnaviridae that may parasitize fungi or Leviviridae , which may infect Proteobacteria. Both host and viral communities appear to be highly dynamic, and rapidly diverged depending on experimental conditions. The viral and host communities were structured based on the presence of root litter. Clear temporal dynamics by Leviviridae and their hosts indicated that viruses were replicating. With this time-resolved analysis, we show that RNA viruses are diverse, abundant, and active in soil. When viral infection causes host cell death, it may mobilize cell carbon in a process that may represent an overlooked component of soil carbon cycling.

54 ENVIRONMENTAL SCIENCES↗

DeepGrid: Robust Deep Reinforcement Learning-based Contingency Management

Increasing uncertainty raised by the integration of renewable energy resources requires an enormous number of simulations to be carried out for the security assessment of the power grid. However, it is challenging to assess the steady-state and dynamic security indices for different system contingency events by doing an exhaustive analysis in real-time due to the computational and communication constraints. One promising solution is using data-driven techniques along with the system models to train an intelligent contingency management framework to better handle the contingencies in real-time. Nevertheless, implementing a data-driven technique to obtain the best remedial actions necessitates to account for the effect of the measurement noise on the performance of the contingency management. To tackle these challenges, we leverage a robust deep reinforcement learning (DRL) algorithm called Double Deep Q-Network (DDQN) to design a recommender system capable of prescribing optimal control actions with the help of the real-time digital simulator (RTDS). The use of RTDS system in combination with the advanced DRL algorithm allows to explore a wide variety of system contingencies in order to derive better remedial actions. The performance of the proposed algorithm is evaluated in IEEE 9-bus system under different loading conditions, and different network configurations in presence of noisy measurements.

Ghasemkhani, Amir↗

304L Can Crush Validation Studies

Accurate prediction of ductile behavior of structural alloys up to and including failure is essential in component or system failure assessment, which is necessary for nuclear weapons alteration and life extensions programs of Sandia National Laboratories. Modeling such behavior requires computational capabilities to robustly capture strong nonlinearities (geometric and material), rate- dependent and temperature-dependent properties, and ductile failure mechanisms. This study's objective is to validate numerical simulations of a high-deformation crush of a stainless steel can. The process consists of identifying a suitable can geometry and loading conditions, conducting the laboratory testing, developing a high-quality Sierra/SM simulation, and then drawing comparisons between model and measurement to assess the fitness of the simulation in regards to material model (plasticity), finite element model construction, and failure model. Following previous material model calibration, a J 2 plasticity model with a microstructural BCJ failure model is employed to model the test specimen made of 304L stainless steel. Simulated results are verified and validated through mesh and mass-scaling convergence studies, parameter sensitivity studies, and a comparison to experimental data. The converged mesh and degree of mass-scaling are the mesh discretization with 140,372 elements, and a mass scaling with a target time increment of 1.0e-6 seconds and time step scale factor of 0.5, respectively. Results from the coupled thermal-mechanical explicit dynamic analysis are comparable to the experimental data. Simulated global force vs displacement (F/D) response predicts key points such as yield, ultimate, and kinks of the experimental F/D response. Furthermore, the final deformed shape of the can and field data predicted from the analysis are similar to that of the deformed can, as measured by 3D optical CMM scans and DIC data from the experiment.

36 MATERIALS SCIENCE↗

Arboreal Epiphytes in the Soil-Atmosphere Interface: How Often Are the Biggest “Buckets” in the Canopy Empty?

Arboreal epiphytes (plants residing in forest canopies) are present across all major climate zones and play important roles in forest biogeochemistry. The substantial water storage capacity per unit area of the epiphyte “bucket” is a key attribute underlying their capability to influence forest hydrological processes and their related mass and energy flows. It is commonly assumed that the epiphyte bucket remains saturated, or near-saturated, most of the time; thus, epiphytes (particularly vascular epiphytes) can store little precipitation, limiting their impact on the forest canopy water budget. We present evidence that contradicts this common assumption from (i) an examination of past research; (ii) new datasets on vascular epiphyte and epi-soil water relations at a tropical montane cloud forest (Monteverde, Costa Rica); and (iii) a global evaluation of non-vascular epiphyte saturation state using a process-based vegetation model, LiBry. All analyses found that the external and internal water storage capacity of epiphyte communities is highly dynamic and frequently available to intercept precipitation. Globally, non-vascular epiphytes spend <20% of their time near saturation and regionally, including the humid tropics, model results found that non-vascular epiphytes spend ~1/3 of their time in the dry state (0–10% of water storage capacity). Even data from Costa Rican cloud forest sites found the epiphyte community was saturated only 1/3 of the time and that internal leaf water storage was temporally dynamic enough to aid in precipitation interception. Analysis of the epi-soils associated with epiphytes further revealed the extent to which the epiphyte bucket emptied—as even the canopy soils were often <50% saturated (29–53% of all days observed). Results clearly show that the epiphyte bucket is more dynamic than currently assumed, meriting further research on epiphyte roles in precipitation interception, redistribution to the surface and chemical composition of “net” precipitation waters reaching the surface.

Hargis, Hailey↗

Predicting Initial Trans-Membrane Pressure for Optimized Operations in UF Unit Using Random Forest

With the growing scarcity of freshwater, innovative process design mechanisms like Reverse Osmosis (RO) are increasingly gaining attention among water treatment utilities to address the rising demand. Ensuring reliable water production necessitates efficient resource utilization, minimizing downtime in (ultra-filtration) UF systems. Recent advancements in machine learning (ML) have enabled the development of accurate data-driven models for Model Predictive Control (MPC), often requiring minimal prior knowledge of underlying physical processes. In this study, we present predictive regression models based on Random Forest (RF) and Auto-Regressive (AR) approaches to forecast the initial Trans-Membrane Pressure (TMP) for each filtration cycle in data generated by Direct Potable Reuse (DPR) systems. The proposed RF-based model demonstrates superior performance compared to baseline methods, including historical mean, Last Observation Carried Forward (LOCF), and naïve AR models, across various forecasting horizons in terms of root mean square error (RMSE) metric. To evaluate how different classes of process variables contribute to TMP dynamics over time, we examine the feature importance of independent covariates across multiple forecast horizons. This analysis provides insight into the temporal relevance of operational and sensor-derived features, guiding control and monitoring strategies. Additionally, the impact of hyperparameter tuning on TMP prediction performance is studied for both direct and recursive RF modelling approaches across increasing forecast horizons. Accurate prediction of initial TMP is critical for optimizing RO operations, as it enables the development of robust modelling frameworks by accurately estimating membrane fouling trends, thereby enhancing process efficiency and long-term reliability. The demonstrated efficacy of the RF-based approach highlights its potential as a tool for real-time decision-making in water treatment systems, paving the way for advanced process optimization and sustainable water resource management.

Mukherjee, Subrata [ORNL] (ORCID:0000000309930338)↗

Dispatchable Virtual Oscillator Control for Decentralized Inverter-Dominated Power Systems: Analysis and Experiments: Preprint

This paper presents an analysis and experimental validation of dispatchable virtual oscillator control (dVOC) for inverter-dominated power systems. dVOC is a promising decentralized control strategy that requires only local measurements to induce grid-forming behavior with programmable droop characteristics. It is dispatchable -- i.e., the inverters can vary their power generation via user-defined power set-points and guarantees strong stability. To verify its feasibility, a testbed comprising multiple dVOC-programmed inverters with transmission line impedances is designed. With an embedded synchronization strategy, the dVOC inverters are capable of dynamic synchronization, black start operation, and transient grid voltage regulation with dynamic load sharing, and real-time-programmable droop characteristics for backward compatibility. All these features are experimentally verified.

14 SOLAR ENERGY↗

Modal dynamics of wind turbine wake meandering from lidar observations

Horizontal scans from nacelle-mounted lidars provide time series measurements of wind turbine wakes across diverse atmospheric conditions, enabling analysis of coherent turbulent structures that influence wake meandering through proper orthogonal decomposition (POD). While low-order modes capture the most energetic turbulent structures, our analysis reveals that they do not necessarily dominate wake meandering dynamics. We evaluate more than 16,000 combinatorial reconstructions of the flow field for each inflow case, demonstrating that mode relevance depends on mode symmetry, turbulent kinetic energy content, and inflow characteristics. Cases with low turbulence intensity and large integral timescales show stronger correlations between POD modes and wake meandering, whereas higher turbulence conditions (turbulence intensity > 7%) are less effectively described by reduced-order models. However, the qualitative similarity of POD modes across varied atmospheric conditions suggests the potential existence of a semi-universal basis for representing wind turbine wakes, with implications for improving engineering wake models.

17 WIND ENERGY↗

A hierarchical gray-box dynamic modeling methodology for direct-expansion cooling systems to support control stability analysis; Méthodologie de modélisation dynamique hiérarchique de type boîte grise pour les systèmes de refroidissement à détente directe afin de soutenir l'analyse de stabilité de la commande

In this paper, a gray-box dynamic modeling approach for direct-expansion cooling systems is presented. The overall approach incorporates a multi-stage training procedure that consists of 1) identification of component sub-models from quasi-steady-state performance data, 2) system model integration with estimation of refrigerant charge and 3) fine tuning of thermal capacitances of the evaporator and condenser to capture the system dynamic responses. Compared to traditional physics-based models, the proposed modeling approach has advantages including reduced engineering efforts in the model development phase, improved computational efficiency and enhanced prediction accuracy. The modeling method was validated using a 3-ton variable-speed heat pump and proved to be capable of accurately predicting the system transient behaviors over a wide range of operating conditions. The established dynamic model was then applied for control stability analysis, with a specific goal of determining a proper control execution time step. The case study results showed that the stable control execution time step could change significantly, from 3 sec to 19 sec, as the operating conditions and control settings vary, and a proper selection of the execution time step is critical to ensure stable and reliable operations.

42 ENGINEERING↗

Systematic characterization of unknown compounds via dimensionality reduction of time series

Analysis of ambient aerosols provides valuable insight into particle sources and formation chemistry. However, due to the complexity of atmospheric data and the dynamic nature of aerosol composition, a substantial fraction of data often become discarded by conventional analysis methods. Furthermore, a large fraction of chemical species within those data are unidentifiable due to a lack of matching spectral information, resulting in suboptimal characterization of chemical composition. Previous work has demonstrated techniques for cataloging analytes in a chromatographic dataset by deconvolution of mass spectra, but integration of these analytes throughout a large dataset remains time consuming. Here, we present a method to automatically identify an ion for quantitation for single-ion chromatogram based peak fitting and integration, enabling comprehensive integration of analytes with minimal user interaction. The resulting time series are clustered with a machine-learning based dimensionality reduction technique to systematically investigate the underlying characteristics of the categorized analytes and gain new insights into the chemical composition and physicochemical properties of the unidentifiable analytes. We apply these methods to existing atmospheric datasets collected in Manacapuru, Brazil during the GoAmazon2014/5 campaign to identify new analytes and interpret their variability and transformations in the atmosphere. The analysis results generate 408 time series from cataloged analytes of interest, and the clustering of those time series with spherical k-means results in 8 distinct clusters. We find the analytes form clusters based on their distinct physicochemical properties, demonstrating the method’s ability to systematically identify and selectively filter contaminants and instrumental analytes and characterize the unidentifiable analytes.

54 ENVIRONMENTAL SCIENCES↗

Enhancing Electrophoretic Display Lifetime: Thiol-Polybutadiene Evaporation Barrier Property Response to Network Microstructure

An evaporation barrier is required to enhance the lifetime of electrophoretic deposition (EPD) displays. As EPD functions on the basis of reversible deposition and resuspension of colloids suspended in a solvent, evaporation of the solvent ultimately leads to device failure. Incorporation of a thiol-polybutadiene elastomer into EPD displays enabled display lifetime surpassing six months in counting and catalyzed rigid display transition into a flexible package. Final flexible display transition to mass production compels an electronic-ink approach to encapsulate display suspension within an elastomer shell. Final thiol-polybutadiene photosensitive resin network microstructure was idealized to be dense, homogeneous, and expose an elastic response to deformation. Research at hand details an approach to understanding microstructural change within display elastomers. Polybutadiene-based resin properties are modified via polymer chain structure, with and without added aromatic urethane methacrylate difunctionality, and in measuring network response to variation in thiol and initiator concentration. Dynamic mechanical analysis results signify that cross-linked segments within a difunctionalized polybutadiene network were on average eight times more elastically active than that of linked segments within a non-functionalized polybutadiene network. Difunctionalized polybutadiene samples also showed a 2.5 times greater maximum elastic modulus than non-functionalized samples. Hybrid polymer composed of both polybutadiene chains encompassed TE-2000 stiffness and B-1000 elasticity for use in encapsulating display suspension. Later experiments measured kinetic and rheological response due to alteration in dithiol cross-linker chain length via real time Fourier transform infrared spectroscopy and real-time dynamic rheology. Distinct differences were discovered between dithiol resin systems, as maximum thiol conversion achieved in short and long chain length dithiols was 86% and 11%, respectively. Oscillatory real-time rheological experiments confirmed a more uniform network to better dissipate applied shear in short chain length dithiol systems, as long chain length dithiols relayed a steep internal stress build-up due to less cross-links and chain entanglements. Thorough understanding of network formation aids the production of a stronger and impermeable elastomeric barrier for preservation of EPD displays.

36 MATERIALS SCIENCE↗

Analysis and Strategies of a Successful LDRD Collaboration

This report analyzes the workings of the “Real - time Adaptive Acceleration of Dynamic Experimental Science” LDRD team, led by James Ahrens, Cindy Bolme and Richard Sandberg, using it to outline practices of successful and innovative LDRD collaborations.

99 GENERAL AND MISCELLANEOUS↗

Frequency spectrum analysis code for nuclear noise based on improved wavelet algorithm - 337

The core of the narrow flow channel generally faced the problem of local bubble boiling with the temperature rise of the nuclear fuel element, it is necessary and meaningful to answer and deal with the problem on the technical level. Reactor noise analysis begins with the study of the physical characteristics of the core, after nearly 30 years of research and development it has become a powerful tool in the auxiliary monitoring of the power reactor operating. By using this noise frequency spectrum analysis technology, the reactor dynamic parameter such as prompt neutron decay constant can be measured. Also, through such system, the frequency characteristics of reactor can be real-time monitored, which is helpful for safety operation and fault diagnosis. Spectrum analysis technology in the Fourier analysis era is now barely available, the reason is that the local spectral characteristics of this technology are not obvious, but this defect can be greatly improved by wavelet analysis technique, however, the traditional wavelet analysis will introduce the problem of spectral confusion. To solve the problem, based on the improved wavelet algorithm, frequency spectrum analysis code for nuclear noise is developed,from the perspective of fine spectral analysis, the local boiling accident of the coolant can be prejudged and avoid. Based on the analysis and test of experimental data,The results show that the calculation ability of the code is in accordance with the expected, it can be applied in the operation of research reactor. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Dynamical properties of a room temperature ionic liquid: Using molecular dynamics simulations to implement a dynamic ion cage model [plus supplemental information]

The transport behavior of ionic liquids (ILs) is pivotal for a variety of applications, especially when ILs are used as electrolytes. Many aspects of the transport dynamics of ILs remain to be understood. Here, a common ionic liquid, 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide (BmimNTf 2 ), was studied with molecular dynamics simulations. The results show that BmimNTf 2 displays typical structural relaxation, subdiffusive behavior, and a breakdown of the Stokes-Einstein diffusion relation as in glass-forming liquids. In addition, the simulations show that the translational dynamics, reorientation dynamics, and structural relaxation dynamics are well described by the Vogel-Fulcher-Tammann equation like fragile glass forming liquids. Building on previous work that employed ion cage models, it was found that the diffusion dynamics of the cations and anions were well described by a hopping process random walk where the step time is the ion cage lifetime obtained from the cage correlation function. Detailed analysis of the ion cage structures indicated that the electrostatic potential energy of the ion cage dominates the diffusion dynamics of the caged ion. The ion orientational relaxation dynamics showed that ion reorientation is a necessary step for ion cage restructuring. The dynamic ion cage model description of ion diffusion presented here may have implications for designing ILs to control their transport behavior.

36 MATERIALS SCIENCE↗

Analysis of an all-solid state nanobattery using molecular dynamics simulations under an external electric field

Present Li-ion battery (LIB) technology requires strong improvements in performance, energy capacity, charging-time, and cost to expand their application to e-mobility and grid storage. Li-metal is one of the most promising materials to replace commercial anodes such as graphite because of its 10 times higher specific capacity. However, Li-metal has high reactivity with commercial liquid electrolytes; thus, new solid materials are proposed to replace liquid electrolytes when Li-metal anodes are used. We present a theoretical analysis of the charging process in a full nanobattery, containing a LiCoO 2 cathode, a Li 7 P2S 8 I solid-state electrolyte (SSE), a Li-metal anode as well as Al and Cu collectors for the cathode and anode, respectively. In addition, we added a Li 3 P/Li 2 S film as a solid electrolyte interphase (SEI) layer between the Li-anode and SSE. Thus, we focus this study on the SEI and SSE. We simulated the charging of the nanobattery with an external voltage by applying an electric field. We estimated temperature profiles within the nanobattery and analyzed Li-ion transport through the SSE and SEI. Here, we observed a slight temperature rise at the SEI due to reactions forming $PS_{3}^{–}$ and $P_{2}S_{7}^{4}$$^{–}$ fragments at the interfaces; however, this temperature profile changes due to the charging current under the presence of the external electric field ε = 0.75 V Å –1 . Without the external field, the calculated open-circuit voltage (OCV) was 3.86 V for the battery, which is within the range of values of commercial cobalt-based LIBs. This voltage implies a spontaneous fall of available Li-ions from the anode to the cathode (during discharge). The charge of this nanobattery requires overcoming the OCV plus an additional voltage that determines the charging current. Thus, we applied an external potential able to neutralize the OCV, plus an additional 1.6 V to induce the transport of Li + from the cathode up to the anode. Several interesting details about Li + transport paths through the SSE and SEI are discussed.

25 ENERGY STORAGE↗

Nanoscale chromatin imaging and analysis platform bridges 4D chromatin organization with molecular function

Extending across multiple length scales, dynamic chromatin structure is linked to transcription through the regulation of genome organization. However, no individual technique can fully elucidate this structure and its relation to molecular function at all length and time scales at both a single-cell level and a population level. Here, we present a multitechnique nanoscale chromatin imaging and analysis (nano-ChIA) platform that consolidates electron tomography of the primary chromatin fiber, optical super-resolution imaging of transcription processes, and label-free nano-sensing of chromatin packing and its dynamics in live cells. Using nano-ChIA, we observed that chromatin is localized into spatially separable packing domains, with an average diameter of around 200 nanometers, sub-megabase genomic size, and an internal fractal structure. The chromatin packing behavior of these domains exhibits a complex bidirectional relationship with active gene transcription. Furthermore, we found that properties of PDs are correlated among progenitor and progeny cells across cell division.

59 BASIC BIOLOGICAL SCIENCES↗

Comparison of sparse domain approaches for 4D SPECT dynamic image reconstruction

Purpose: Dynamic imaging (DI) provides additional diagnostic information in emission tomography in comparison to conventional static imaging at the cost of being computationally more challenging. Dynamic single photon emission computed tomography (SPECT) reconstruction is particularly difficult because of the limitations in the sampling geometry present in most existing scanners. We have developed an algorithm Spline Initialized Factor Analysis of Dynamic Structures (SIFADS) that is a matrix factorization method for reconstructing the dynamics of tracers in tissues and blood directly from the projections in dynamic cardiac SPECT, without first resorting to any 3D reconstruction. Methods: SIFADS is different from "pure" factor analysis in dynamic structures (FADS) in that it employs a dedicated spline-based pre-initialization. In this paper, we analyze the convergence properties of SIFADS and FADS using multiple metrics. The performances of the two approaches are evaluated for numerically simulated data and for real dynamic SPECT data from canine and human subjects. Results: For SIFADS, metrics analyzed for reconstruction algorithm convergence show better features of the metric curves vs iterations. In addition, SIAFDS provides better tissue segmentations than that from pure FADS. Measured computational times are also typically better for SIFADS implementations than those with pure FADS. Conclusion: The analysis supports the utility of the pre-initialization of a factorization algorithm for better dynamic SPECT image reconstruction.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Thermally Stable Co@C3N4 Single-Atom Catalysts for CO Oxidation: Atomic-Level Insights into Structure and Activity

Single Co atoms supported on C3N4 (Co@C3N4) have demonstrated high activity and selectivity in photocatalysis. However, the investigation of structure–function relationships and reaction mechanisms under photocatalytic conditions is very challenging due to the complex conditions of light absorption, charge transfer, and catalysis. In this study, we employed thermal CO oxidation as a prototypical probe reaction to benchmark the intrinsic catalytic performance and track the active-site evolution of Co@C3N4. Single Co atoms were identified and shown to be the catalytically active sites for CO oxidation based on control experiments and isotope-labeling experiments. The Co sites remained atomically dispersed before, during, and after the reaction with temperatures up to 400 °C, as established by in situ X-ray absorption fine structure (XAFS) combined with density functional theory (DFT), FDMNES simulations, and dynamic-time-warping (DTW)-assisted X-ray absorption near edge structure (XANES) matching. Together with theoretical calculations, the integrated analysis reveals a stable coordination environment under reaction conditions, which correlates with sustained activity, establishing Co@C3N4 single-atom catalysts as thermally stable CO oxidation catalysts. Beyond these findings, the current study provides a workflow for unambiguously assigning active sites in Co@C3N4 for thermal CO oxidation. This workflow will aid the understanding of their behavior in photocatalysis in the future, where light-driven dynamics obscure direct structure–function links. Notably, this study provides fundamental insights for the rational design of robust single-atom catalysts and a foundation for the broader application of Co@C3N4 catalysts in oxidation reactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Topology driven and soft phonon mode enabled Na-ion diffusion in quaternary chalcogenides, Na 3 ZnGaX 4 (X = S, and Se)

The compounds Na 3 ZnGaX 4 (X = S, Se) are potential solid electrolyte materials in sodium-based batteries, which have certain advantages over oxide materials and have shown significant ionic conductivity at ambient temperature. In this paper, we bring out atomic-level features of the diffusion process in these new materials using the microscopic techniques of inelastic neutron scattering (INS), quasielastic neutron scattering (QENS), and ab initio molecular dynamics (AIMD) simulations. The insights obtained from these techniques are unique and not available from other macroscopic experiments. Neutron scattering experiments have been performed at temperatures from 100 to 700 K. The simulations have been carried out up to 900 K. We have calculated the phonon spectra and the space–time correlation functions and found good agreement with the results of the neutron scattering experiments. The simulations enable detailed analysis of the atomic-site dependent dynamical information. We observe low-energy phonon modes of ~6 meV involving the vibrations of certain Na atoms in the lattice. This reveals that the Na at 32g Wyckoff sites (Na2) has sufficiently shallow potential among the two available crystallographic sites. This shallow potential facilitates diffusion. Furthermore, the specific structural topology of the network of interconnected zig-zag chains of the Na2 atomic sites provides the low-barrier energy pathways for diffusion. A small fraction of vacancy defects appears essential for diffusion. We further observe that the Na2 atoms undergo jump-like diffusion to the vacant next or the 2nd next neighbour sites at ~4 Å. While the QENS experiments reveal the jump-like diffusion and its time scale, detailed analysis of the AIMD simulations shows that the jumps appear mostly along zig-zag chains of the Na2 sites in the tetragonal ab-plane, as well as between the chains along the c-axis. In conclusion, the net diffusion is essentially 3-dimensional, with little anisotropy despite the anisotropy of the tetragonal crystal structure.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗