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At least 253 records · Page 14

Parameter Sensitivity Analysis of the SparTen High Performance Sparse Tensor Decomposition Software (Extended Analysis)

Tensor decomposition models play an increasingly important role in modern data science applications. One problem of particular interest is fitting a low-rank Canonical Polyadic (CP) tensor decomposition model when the tensor has sparse structure and the tensor elements are nonnegative count data. SparTen is a high-performance C++ library which computes a low-rank decomposition using different solvers: a first-order quasi-Newton or a second-order damped Newton method, along with the appropriate choice of runtime parameters. Since default parameters in SparTen are tuned to experimental results in prior published work on a single real-world dataset conducted using MATLAB implementations of these methods, it remains unclear if the parameter defaults in SparTen are appropriate for general tensor data. Furthermore, it is unknown how sensitive algorithm convergence is to changes in the input parameter values. This report addresses these unresolved issues with large-scale experimentation on three benchmark tensor data sets. Experiments were conducted on several different CPU architectures and replicated with many initial states to establish generalized profiles of algorithm convergence behavior.

97 MATHEMATICS AND COMPUTING↗

Insight of Synthesis of Single Crystal Ni-Rich LiNi 1-x-y Co x Mn y O 2 Cathodes

Single-crystal Ni-rich LiNi 1-x-y Co x Mn y O 2 (NCM) cathodes have garnered widespread attention in the lithium-ion battery community due to their unique advantages in mechanical performance and their ability to minimize interfacial electrochemical side reactions. The synthesis of single-crystal materials with monodisperse and appropriate size, minimal lattice defects, and highly ordered structures is the key for high-performance batteries. However, achieving this goal poses challenges due to the lack of in-depth understanding regarding specific experimental parameters and the solid reaction mechanism during the synthesis process. Further, in this review, the aim is to provide an in-depth analysis of the critical process parameters involved in the synthesis and their impact on crystal morphology, structure, and electrochemical performance. Consequently, the first section focuses on the effect of the precursor morphology, lithium salt, atmosphere, and sintering procedure. In the second section, the study delves into an in-depth discussion of the solid reaction and crystal growth mechanism. Lastly, it is concluded by highlighting the prospects and challenges associated with the synthesis and application of single-crystal Ni-rich NCM cathodes.

25 ENERGY STORAGE↗

Two Spacers, One Perovskite: Integrating Ruddlesden–Popper and Dion–Jacobson Halide Perovskites

Hybrid organic–inorganic perovskites are a rapidly developing class of materials due to their desirable properties for optoelectronic applications such as their ease of synthesis, solution-processable film formation, tunable band gap, strong photoluminescence, good charge carrier mobilities, and high defect tolerance. Here, we present a novel 2D perovskite motif that seamlessly integrates the structural elements from both Ruddlesden–Popper and Dion–Jacobson halide perovskites. We demonstrate the incorporation of two different organic spacer cations in an ordered manner in 5 novel 2D perovskite iodide materials. Both a cyclic diammonium cation 3-(aminomethyl)piperidinium (3AMP) and a linear alkyl monoammonium cation (Cn = C n H 2n+4 N, n = 4–8) are present in distinct alternating layers, making the new series (Cn) 2 (3AMP)[PbI 4 ] 2 . The crystallization of these materials was optimized through careful temperature control to obtain precise crystal structures via single-crystal X-ray diffraction (XRD) which confirmed the presence of the two cations in distinct layers. The influence of the two spacers on optical properties including the band gaps and photoluminescence spectra are found to more closely resemble (3AMP)PbI 4 than (Cn) 2 PbI 4 , which can be attributed to the amount of distortion imposed by the 3AMP spacer on the lead iodide layers. The findings are supported by density functional theory calculations. The strong photoelectric response of solution-processed thin films shows the potential of these materials in photodetectors or photovoltaics. This unprecedented amalgamation of RP–DJ in (Cn) 2 (3AMP)[PbI 4 ] 2 in a structurally ordered fashion suggests a potential vastly underexplored phase space of 2D perovskites in which there are chemically different spacers in distinct layers of the structure, providing an additional parameter to tune perovskite properties.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Using the Carbon Capture Simulation Initiative (CCSI) Tool to Design the Experiments in the Parametric Campaign of a Novel Compact Absorber for Carbon Capture

Gas absorption towers with structured packing and solvent have been used for Carbon Dioxide (CO 2 ) Capture for about many decades. To overcome process limitations and practical disadvantages for CO 2 capture from the stationary emitter (e.g. NG and coal power plant), many new designs have been proposed and explored at the various scales in the last decade with aim of either low energy penalty or low capital cost. To reduce the size of the absorption tower and hence the total cost of CO 2 capture, the University of Kentucky Center for Applied Energy Research Center (UK CAER) has designed and built a novel CO 2 capture absorption tower or Compact Absorber, integrated into an existing large-bench scale CO 2 capture unit. The Compact Absorber has three sections. The top of the column is a fogging section where the solvent is sprayed through a nozzle producing droplets flowing downward in a co-current fashion with the flue gas. The center of the column is a frothing section where the solvent and flue gas flow through regenerative frothing screens designed by Industrial Climate Solutions, Inc. The bottom of the column is a typical structured packing section were the flue gas and solvent flow in a counter-current fashion. The parametric campaign will be conducted in order to optimize the operating parameters for CO 2 capture including liquid/gas ratio, lean loading, and temperature, liquid residence time. A simulated flue gas with 14% CO 2 will be used along with a UK CAER developed proprietary solvent. The 100-hour parametric campaign is designed using a statistical approach of the Sequential Design of Experiments (sDOE). sDOE is one of the CCSI tools that provides an adaptive statistical approach for designing future experiments based on the results of previous experiments. Application of a typical DOE provides the user with the minimum number of experiments required to get the same data, but sDOE allows the user to make an informed choice of experiments based on the results of previous experiments. The complete absorption column has been constructed and has been partially commissioned. Initial data has been collected by operating using the fogging section and the frothing section. The fogging section produces solvent droplets of about 100 μm sauter mean diameter and as small as 25 μm using a hydraulic nozzle by BETE. The frothing section produces bubbles of about 5mm with high mixing of solvent promoting the higher mass transfer from gas to liquid. The absorber reaches the capture efficiency of about 50% with only two sections in operation. Based on the current results, it can be deduced that increasing the solvent feed temperature and including the packed section for absorption the capture efficiency will increase further. Initial data will be collected using all three sections of the absorber and will be used for sDOE. Non-Uniform Space Filling model of sDOE will be used to prioritize the input conditions resulting into maximum capture efficiency. sDOE is performed using the platform called Framework Optimization, Quantification of Uncertainty, and Surrogates (FOQUS). The method and results demonstrating the progress of the parametric campaign from the initial set of experiments to the final stage of obtaining optimized parameters using sDOE tool will be presented in detail.

20 FOSSIL-FUELED POWER PLANTS↗

A mutagenic analysis of NahE, a hydratase-aldolase in the naphthalene degradative pathway

NahE is a hydratase-aldolase that converts o-substituted trans-benzylidenepyruvates (H, OH, or CO 2 - ) to benzaldehyde, salicylaldehyde, or 2-carboxybenzaldehyde, respectively, and pyruvate. The enzyme is in a bacterial degradative pathway for naphthalene, which is a toxic and persistent environmental contaminant. Sequence, crystallographic, and mutagenic analysis identified the enzyme as a member of the N-acetylneuraminate lyase (NAL) subgroup in the aldolase superfamily. As such, it has a conserved lysine (Lys183) and tyrosine (Tyr155), for Schiff base formation, as well as a GXXGE motif for binding of the pyruvoyl carboxylate group. A crystal structure of the selenomethionine derivative of NahE shows these active site elements along with nearby residues that might be involved in the mechanism and/or specificity. Mutations of five active site amino acids (Thr65, Trp128, Tyr155, Asn157, and Asn281) were constructed and kinetic parameters measured in order to assess the effect(s) on catalysis. Here, the results show that the two Trp128 mutants (Phe and Tyr) have the least effect on catalysis, whereas amino acids with bulky side chains at Thr65 (Val) and Asn281 (Leu) have the greatest effect. Changing Tyr155 to Phe and Asn157 to Ala also hinders catalysis, and the effects fall in between these extremes. These observations are put into a structural context using a crystal structure of the Schiff base of the reaction intermediate. Trapping experiments with substrate, Na(CN)BH 3 , and wild type enzyme and selected mutants mostly paralleled the kinetic analysis, and identified two salicylaldehyde-modified lysines: the active site lysine (Lys183) and one outside the active site (Lys279). The latter could be responsible for the observed inhibition of NahE by salicylaldehyde. Together, the results provide new insights into the NahE-catalyzed reaction.

59 BASIC BIOLOGICAL SCIENCES↗

First-principles calculation of lattice distortions in four single phase high entropy alloys with experimental validation

Exceptional properties of high entropy alloys (HEAs) are attributed to the disordered random solid solution of multiple alloying elements. Despite numerous studies, the fundamental understanding at the electronic and atomic levels is still missing. We report a comparative study of four fcc HEAs of NiFeCoCr and NiFeCoCrX (X = Mn, Cu, or Pd) based on ab initio calculations using large supercells with 500 atoms in equal composition. After fully optimizing their structures using the VASP package, their electronic structure, interatomic bonding, partial charge distribution, and mechanical properties are calculated and compared, revealing the intricate interdependence among them. A novel parameter based on the quantum mechanical metric for internal cohesion, the total bond order density (TBOD), is used to interpret the calculated properties. The highest TBOD is found in Cantor alloy NiFeCoCrMn but lower in NiFeCoCrPd. The atomic radii vary depending on their local chemical environment. The resulting lattice distortions is validated experimentally in NiFeCoCrMn and NiFeCoCrPd. Moreover, modeling of Cu and Pd clustering in the supercell shows they have lower total energy in agreement with the observation of Cu-enhanced nano-participates in NiFeCoCrCu and Pd-induced concentration wave in NiFeCoCrPd HEAs.

36 MATERIALS SCIENCE↗

Review: knots and other new topological effects in liquid crystals and colloids

Abstract Humankind has been obsessed with knots in religion, culture and daily life for millennia, while physicists like Gauss, Kelvin and Maxwell already involved them in models centuries ago. Nowadays, colloidal particles can be fabricated to have shapes of knots and links with arbitrary complexity. In liquid crystals, closed loops of singular vortex lines can be knotted by using colloidal particles and laser tweezers, as well as by confining nematic fluids into micrometer-sized droplets with complex topology. Knotted and linked colloidal particles induce knots and links of singular defects, which can be interlinked (or not) with colloidal particle knots, revealing the diversity of interactions between topologies of knotted fields and topologically nontrivial surfaces of colloidal objects. Even more diverse knotted structures emerge in nonsingular molecular alignment and magnetization fields in liquid crystals and colloidal ferromagnets. The topological solitons include hopfions, skyrmions, heliknotons, torons and other spatially localized continuous structures, which are classified based on homotopy theory, characterized by integer-valued topological invariants and often contain knotted or linked preimages, nonsingular regions of space corresponding to single points of the order parameter space. A zoo of topological solitons in liquid crystals, colloids and ferromagnets promises new breeds of information displays and a plethora of data storage, electro-optic and photonic applications. Their particle-like collective dynamics echoes coherent motions in active matter, ranging from crowds of people to schools of fish. This review discusses the state of the art in the field, as well as highlights recent developments and open questions in physics of knotted soft matter. We systematically overview knotted field configurations, the allowed transformations between them, their physical stability and how one can use one form of knotted fields to model, create and imprint other forms. The large variety of symmetries accessible to liquid crystals and colloids offer insights into stability, transformation and emergent dynamics of fully nonsingular and singular knotted fields of fundamental and applied importance. The common thread of this review is the ability to experimentally visualize these knots in real space. The review concludes with a discussion of how the studies of knots in liquid crystals and colloids can offer insights into topologically related structures in other branches of physics, with answers to many open questions, as well as how these experimentally observable knots hold a strong potential for providing new inspirations to the mathematical knot theory.

Physics↗

Structural mode coupling in perovskite oxides using hypothesis-driven active learning

Abstract Finding the ground-state structure with minimum energy is paramount to designing any material. In ABO 3 -type perovskite oxides with Pnma symmetry, the lowest energy phase is driven by an inherent trilinear coupling between the two primary order parameters such as rotation and tilt with antiferroelectric displacement of the A-site cations as established via hybrid improper ferroelectric mechanism. Conventionally, finding the relevant mode coupling driving phase transition requires performing first-principles calculations which is computationally time-consuming as well as expensive. It involves following an intuitive iterative hit and trial method of (a) adding two or multiple mode vectors, followed by (b) evaluating which combination would lead to the ground-state energy. In this study, we show how a hypothesis-driven active learning framework can identify suitable mode couplings within the Landau free energy expansion with minimal information on amplitudes of modes for a series of double perovskite oxides with A-site layered, columnar and rocksalt ordering. This scheme is expected to be applicable universally for understanding atomistic mechanisms derived from various structural mode couplings behind functionalities, for e.g. polarization, magnetization and metal–insulator transitions.

36 MATERIALS SCIENCE↗

Limits on assigning a shape to a nucleus

The interpretation of nuclear observables in the laboratory frame in terms of the intrinsic deformation parameters β and γ is a classical theme in nuclear structure. Here we use the quadrupole invariants, calculated within the framework of the configuration-interaction shell model, to clarify the meaning and limitations of nuclear shapes. In this work we introduce a novel method that enables us to calculate accurately higher-order invariants and, therefore, the fluctuations in both β and γ. We find that the shape parameter β often has a non-negligible degree of softness and that the angle γ is usually characterized by large fluctuations, rendering its effective value not meaningful. Contrary to common belief, we conclude that doubly magic nuclei are not spherical, because the notion of a well-defined shape does not apply to them.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Rational surfaces, flows and radial structure in the TJ-II stellarator

Abstract In this work, we report on the results obtained by measuring several turbulent quantities well inside the plasma edge by means of a Langmuir probe during dynamical rotational transform scans in the TJ-II stellarator, while applying a radial electric field to the edge plasma using a biasing probe. By calculating the intermittence parameter from floating potential measurements, we are able to identify a major low order rational surface and hence relate the probe measurements to the local value of the rotational transform. Based on the former, we are able to show that the poloidal plasma velocity (and hence radial electric field) has a significant radial structure that is clearly related to the rotational transform profile and in particular the lowest order rational surfaces in the range studied. The poloidal velocity is also affected by the edge biasing. The particle flux Γ was also found to exhibit a radial pattern, as did the flow shear suppression term ω E × B , but the relation of the former to the low-order rational surfaces was less clear. We surmise that this lack of direct correspondence is due to an unknown term in the turbulence evolution equation: the instability growth rate, γ . We make use of a reduced Magnetohydrodynamic turbulence model to interpret the results. Overall, a picture is obtained in which the plasma self-organizes towards a state with a clear radial pattern of the radial electric field, in line with expectations from some numerical studies describing the spontaneous formation of an ‘ E × B staircase’, consisting of alternating layers with fast and slow radial transport. In this state, the radial profiles of various quantities (density, temperature, pressure) will not be smooth.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Temperature-induced hexagonal–orthorhombic phase transition in lutetium ferrite nanoparticles

The x-ray diffraction, Raman, and infrared spectroscopies and magnetic measurements were used to explore the correlated changes of the structure, lattice dynamics, and magnetic properties of the LuFeO3 nanoparticles, which appear in dependence on their sintering temperature. We revealed a gradual substitution of the hexagonal phase by the orthorhombic phase in the nanoparticles, with sintering temperature increasing from 700 to 1100 °C. The origin and stability of the hexagonal phase in the LuFeO3 nanoparticles are of the special interest, because the nanoparticles in the phase can be a room-temperature multiferroic with a weak ferromagnetic and pronounced structural and ferroelectric long-range ordering. The antiferromagnetic and nonpolar orthorhombic phase is more stable in the bulk LuFeO3. To define the ranges of the hexagonal phase stability, we determine the bulk and interface energy densities of different phases from the comparison of the Gibbs model with experimental results. Using effective parameters of the Gibbs model, we predict the influence of size effects and temperature on the structural and polar properties of the LuFeO3 nanoparticles. Analysis of the obtained results shows that the combination of the x-ray diffraction, Raman and infrared spectroscopies, magnetic measurements, and theoretical modeling of structural and polar properties allows us to establish the interplay between the phase composition, lattice dynamics, and multiferroic properties of the LuFeO3 nanoparticles prepared under different conditions.

Materials Science↗

OFraMP: a fragment-based tool to facilitate the parametrization of large molecules

Abstract An Online tool for Fragment-based Molecule Parametrization (OFraMP) is described. OFraMP is a web application for assigning atomic interaction parameters to large molecules by matching sub-fragments within the target molecule to equivalent sub-fragments within the Automated Topology Builder (ATB, atb.uq.edu.au) database. OFraMP identifies and compares alternative molecular fragments from the ATB database, which contains over 890,000 pre-parameterized molecules, using a novel hierarchical matching procedure. Atoms are considered within the context of an extended local environment (buffer region) with the degree of similarity between an atom in the target molecule and that in the proposed match controlled by varying the size of the buffer region. Adjacent matching atoms are combined into progressively larger matched sub-structures. The user then selects the most appropriate match. OFraMP also allows users to manually alter interaction parameters and automates the submission of missing substructures to the ATB in order to generate parameters for atoms in environments not represented in the existing database. The utility of OFraMP is illustrated using the anti-cancer agent paclitaxel and a dendrimer used in organic semiconductor devices. Graphical abstract OFraMP applied to paclitaxel (ATB ID 35922).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Novel strategies for modal-based structural material identification

Here, we present modal-based methods for model calibration in structural dynamics, and address several key challenges in the solution of gradient-based optimization problems with eigenvalues and eigenvectors, including the solution of singular Helmholtz problems encountered in sensitivity calculations, non-differentiable objective functions caused by mode swapping during optimization, and cases with repeated eigenvalues. Unlike previous literature that relied on direct solution of the eigenvector adjoint equations, we present a parallel iterative domain decomposition strategy (Adjoint Computation via Modal Superposition with Truncation Augmentation) for the solution of the singular Helmholtz problems. For problems with repeated eigenvalues we present a novel Mode Separation via Projection algorithm, and in order to address mode swapping between inverse iterations we present a novel Injective mode ordering metric. We present the implementation of these methods in a massively parallel finite element framework with the ability to use measured modal data to extract unknown structural model parameters from large complex problems. A series of increasingly complex numerical examples are presented that demonstrate the implementation and performance of the methods in a massively parallel finite element framework [7], [5], using gradient-based optimization techniques in the Rapid Optimization Library (ROL) [21].

36 MATERIALS SCIENCE↗

A coarse-grain force field based on quantum mechanics (CGq FF) for molecular dynamics simulation of poly(ethylene glycol)- block -poly(ε-caprolactone) (PEG- b -PCL) micelles

In order to provide the means to predict from molecular dynamics (MD) simulations the structures of copolymer-based micelles in solution, we developed coarse grain force field (CGq FF) parameters for poly(ethylene glycol) (PEG) and for poly(ε-caprolactone) (PCL). A key advance here is the use of quantum mechanics to train the parameters describing the non-bonded (NB) interactions between the CG beads. The functional forms are the same as the MARTINI CG FF so standard MD codes can be used. Our CGq FF describes well the experimentally observed properties for the polymer–air and polymer–water interfaces, indicating the accuracy of the NB interactions. Additionally, the structural properties (density, radius of gyration ( R g ), and end-to-end distance ( h )) match both experiment and all atom (AA) simulations. We illustrate the application of this CGq FF by following the formation of a spherical micelle from 250 chains of PEG 23 - b -PCL 9 diblock copolymer, each block with molecular weight of 1000 Daltons (10 500 beads, corresponding to 123 250 atoms), in a water box with 119 139 water beads (426 553 water molecules).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

High-throughput determination of Hubbard $U$ and Hund $J$ values for transition metal oxides via the linear response formalism

DFT+U provides a convenient, cost-effective correction for the self-interaction error (SIE) that arises when describing correlated electronic states using conventional approximate density functional theory (DFT). The success of a DFT+U(+J) calculation hinges on the accurate determination of its Hubbard U and Hund J parameters, and the linear response (LR) methodology has proven to be computationally effective and accurate for calculating these parameters. This study provides a high-throughput computational analysis of the U and J values for transition metal d-electron states in a representative set of over 1000 magnetic transition metal oxides (TMOs), providing a frame of reference for researchers who use DFT+U to study transition metal oxides. In order to perform this high-throughput study, an ATOMATE workflow is developed for calculating U and J values automatically on massively parallel supercomputing architectures. Here, to demonstrate an application of this workflow, the spin-canting magnetic structure and unit cell parameters of the multiferroic olivine LiNiPO4 are calculated using the computed Hubbard U and Hund J values for Ni-d and O-p states, and are compared with experiment. Both the Ni-d U and J corrections have a strong effect on the Ni-moment canting angle. Additionally, including a O-pU value results in a significantly improved agreement between the computed lattice parameters and experiment

36 MATERIALS SCIENCE↗

Evidence of Long-Range and Short-Range Magnetic Ordering in the Honeycomb Na 3 Mn 2 SbO 6 Oxide

We present a comprehensive study of the synthesis, structure, and magnetic properties of the honeycomb oxide Na 3 Mn 2 SbO 6 supported by neutron diffraction, heat capacity, and magnetization measurements. The refinements of the neutron diffraction patterns (150, 50, and 45 K) using the Rietveld method confirm the monoclinic (S. G. C2/m) structure. Temperature-dependent magnetic susceptibilities measured at varying fields along with the heat capacity measurements demonstrate the coexistence of long-range ordering (∼42 K) and short-range ordering (∼65 K). The field-dependent isothermal magnetization measurements at 5 K indicate a spin-flop transition around 5 T. Rietveld refinements of the low-temperature (below 45 K) neutron diffraction data further confirm the long-range magnetic ordering. In addition, the temperature variation of the lattice parameters obtained from the neutron powder diffraction analysis exhibited a distinct anomaly near the antiferromagnetic transition temperature. The appearance of the concomitant broadened backgrounds in the neutron powder diffraction data collected at 80, 50, and 45 K supports the short-range ordering. The resultant magnetic structure consists of spins that are aligned antiparallel with the nearest neighbors and also with the spins of the adjacent honeycomb layers. The occurrence of a fully ordered magnetic ground state (Neel antiferromagnetic (AFM)) in Na3Mn 2 SbO 6 consolidates the significance of fabricating new honeycomb oxides.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Majorana modes with side features in magnet-superconductor hybrid systems

Magnet-superconductor hybrid (MSH) systems represent promising platforms to host Majorana zero modes (MZMs), the elemental building blocks for fault-tolerant quantum computers. Theoretical description of such MSH structures is mostly based on simplified models, not accounting for the complexity of real materials. Here, based on density functional theory, we derive a superconducting 80-band model to study an MSH system consisting of a magnetic manganese chain on the s wave superconductor niobium. For a wide range of values of the superconducting order parameter, the system is a topological superconductor, with MZMs exhibiting non-universal spatial patterns and a drastic accumulation of spectral weight on both sides along the magnetic chain. These side feature states can be explained by an effective model which is guided by the ab initio results. Performing scanning tunneling spectroscopy experiments on the same system, we observe a spatial structure in the low-energy local density of states that is consistent with the theoretical findings. Our results open a first-principle approach to the discovery of topological superconductors.

36 MATERIALS SCIENCE↗

Electrochemical Study on the Kinetic Properties of Fe 2+ /Fe, Ni 2+ /Ni, Cr 2+ /Cr and Cr 3+ /Cr 2+ in Molten MgCl 2 -KCl-NaCl Salts

Here, the fundamental kinetic parameters of corrosion product ions (Fe, Ni and Cr ions) are of significant importance to understand the corrosion mechanisms of the structural materials in the molten salts. In the present study, the fundamental data of Fe 2+ , Ni 2+ , Cr 2+ and Cr 3+ (diffusion coefficient D, exchange current density i 0 , charge transfer coefficient α, limiting current density i L and standard rate constant k0) were measured at different concentrations (1.53 × 10 –6 –7.48 × 10 –4 mol cm –3 ) and temperatures (600 °C–800 °C). The values of D are independent of concentrations and follow Arrhenius law with temperature, which descend in the order of D Cr 2+ > D Fe 2+ > D Cr 3+ > D Ni 2+ with values ranging from 0.94 × 10 –5 to 3.31 × 10 –5 cm 2 s –1 . Both i 0 and k 0 depend on the temperatures, which also follow Arrhenius law.

14 SOLAR ENERGY↗