Electrodeposition Of Pb Research Articles

New perspective on the electrodeposition of Pb, Cd and Zn in electrode modified with bismuth film: A theoretical–experimental approach

Understanding electrode-analyte interactions at the atomic level is vital for improving analytical techniques, yet the complexity of these interactions poses a significant challenge for refinement.In this study, we investigate the detection of transition metals using Bi film electrodes, combining Density Functional Theory (DFT) simulations with experimental Anodic Stripping Voltammetry (ASV). Our experiments focus on the electrodeposition and detection of Zn2+, Cd2+, and Pb2+using Bi-modified carbon electrodes. The ASV experiments reveal a notably higher sensitivity for Pb2+detection compared to Zn2+and Cd2+, whether evaluated individually or simultaneously. DFT calculations demonstrate that the higher adsorption energy of Pb on the Bi surface promotes a uniform distribution of Pb atoms, resulting in a homogeneous phase. Conversely, Cd and Zn tend to present lower adsorption energies and form metallic clusters, leading to phase segregation. The correlation between theoretical and experimental data suggests that a more uniform deposition of Pb on the electrode surface facilitates a regular sweep in the redissolution step, achieving a detection limit as low as 0.062 nM for Pb. This synergistic approach not only enhances our understanding of electrode-analyte interactions but also provides valuable insights for optimizing electrode materials and detection methodologies in analytical chemistry.

Electrosynthesis of Quasi-Epitaxial Crystals on Liquid Metals.

Electrosynthesis of single-crystalline metallic and intermetallic particles with a preferred orientation onto liquid metal electrodes has been performed. Liquid gallium electrodes immersed in aqueous alkaline electrolytes without any molecular additive or external solid seeding substrates were used to electroreduce separately Pb2+, Bi3+, Pd2+, and Mn2+. The crystallinity, composition, and orientation of the electrodeposition products were characterized by using scanning electron microscopy, transmission electron microscopy, selected area electron diffraction, grazing incidence X-ray diffraction, and energy-dispersive X-ray spectroscopy. Electrodeposition of Pb and Bi results in the incipient formation of two-dimensional (2D) nuclei that subsequently direct the growth of Pb and Bi single crystals along the most close-packed [111] and [0001] directions, respectively. The absence of any intervening surface oxides and a low electroreduction flux are necessary to avoid polycrystalline dendrite formation. Under comparable conditions, the electrodeposition of Pd and Mn results in single-crystalline intermetallic particles at the interface. Each crystal exhibits a preferred orientation consistent with the unique atomic packing of the near-surface region of the liquid Ga. The presented study suggests a new concept in electrodeposition processes where the liquid metal structure imparts quasi-epitaxial growth in a system in which the electrode material specifically has no crystallinity or long-range order. This study is thus the first demonstration of highly oriented electrodeposition at a liquid/liquid interface under ambient conditions, highlighting the unique solvation environment of liquid metal interfaces for forming thin metallic and intermetallic films.

Amino acid based ionic liquids for revitalization of sulfated lead anodes

Lead acid batteries (LABs) are currently recycled using hazardous, polluting, and energy intensive procedures. Here we report a novel LAB recycling strategy with hydrophilic amino acid-based ionic liquids (ILs) to dissolve the water-insoluble PbSO4 crystals formed during deleterious hard sulfation at the anodes and then electrodeposit metallic Pb on a new surface. We identified two ILs, [Ch][Ser] and [Ch][Thr] ILs that show dramatic solubility towards PbSO4 at room temperature. [Ch][Ser] IL was successfully used in refurbishing hard sulfated anodes that had lost 99 % of their original capacity into a fresh Pb surface. More than 75 % of the capacity was renewed after a complete treatment on a half-cell. Electrodeposition of Pb from the Pb-[Ch][Ser] complex produced a uniform Pb microstructure. A remarkable 99 % of the IL-dissolved Pb2+ ions was electrodeposited. Furthermore, we solved the first crystal structure of the compound formed between Pb2+ and the amino acid-based IL. Based on 1H Nuclear Magnetic Resonance (NMR) spectrum of PbSO4 dissolved in the [Ch][Ser] IL and single crystal X-ray diffraction (XRD) studies, we discovered that the Pb2+ was coordinated with two [Ser] molecules and displayed a hemidirected five-coordinate geometry. ILs that can selectively dissolve PbSO4 thus hold promise for an environment-friendly alternative recycling paradigm for the LAB industry.

In Situ Electrodeposition of Pb and Ag Applied on Fluorine Doped Tin Oxide Substrates: Comparative Experimental and Theoretical Study.

A comparison between lead and silver electrodeposition onto fluorine-doped tin oxide (FTO) electrodes from nitrate solution was investigated in this work. Chronoamperometry has been used as an in situ technique to track the dynamics of the electrodeposition during advanced nucleation phases. The experimental results are correlated with a theoretical evaluation. It has shown that they have a strong correlation with each other. After that, the obtained deposits are characterized and compared as well by X-ray diffraction (XRD), energy dispersive X-ray analysis (EDX), scanning electron microscopy (SEM), and impedance spectroscopy. The data reflects the effect of the material under investigation on current density, deposition density, and dielectric properties. Additionally, the electrodeposition approach (a two-in-one technique) can be followed in order to make well-controlled thin films that can be used for various purposes in addition to recovering heavy metals from wastewater.

Weatherability of soluble lead flow batteries using the electrolytes of Pb(CH3SO3)2 and CH3SO3H/HBF4

An electrolyte of Pb(CH3SO3)2 and CH3SO3H/HBF4 mixed acids is utilized to investigate the cycling performance of soluble lead flow batteries over the range −40 °C–50 °C. The solution containing 1.0 M Pb(CH3SO3)2 + 0.4 M CH3SO3H + 1.6 M HBF4 is optimized as the electrolyte based on its freezing point, conductivity and dynamic viscosity. At low temperature, its charge transfer resistance is lower than that in Pb(CH3SO3)2 + CH3SO3H solution. The side reactions of hydrogen and oxygen evolutions are reduced that is beneficial for the electrodeposition of PbO2 and Pb. At high temperature, the hydrolysis of HBF4 could be inhibited by CH3SO3H. The corrosion current density is reduced to effectively avoid the corrosion and failure of graphite electrodes. The coulombic efficiency of cells is maintained at 87.3 %–95.1 % within the range −40 °C–50 °C. The energy efficiency is higher than 74 %. The soluble lead flow battery exhibits an excellent weatherability.

Electrodeposition of Pb and PbO2 on Graphite Felt in Membraneless Flow-Through Reactor: A Method to Prepare Lightweight Electrode Grids for Lead-Acid Batteries.

One of the possible ways of mitigating the primary lead-acid battery downside—mass— is to replace the heavy lead grids that can add up to half of the total electrode’s mass. The grids can be exchanged for a lightweight, chemically inert, and conductive material such as graphite felt. To reduce carbon surface area, Pb/PbO2 can be electrochemically deposited on graphite felt. A flow-through reactor was applied to enhance penetration of adequate coverage of graphite felt fibers. Three types of electrolytes (acetate, nitrate, and methanesulfonate) and two additives (ligninsulfonate and Triton X-100) were tested. The prepared composite electrodes showed greater mechanical strength, up to 5 times lower electrical resistivity, and acted as Pb and PbO2 electrodes in sulfuric acid electrolytes.

Reconstruction of Lead Acid Battery Negative Electrodes after Hard Sulfation Using Controlled Chelation Chemistry

Lead acid batteries (LABs) remain an inexpensive energy storage technology with a wide application base. However, their short cycle lifetimes necessitate improved recycling and maintenance technologies to combat their various failure modes. One major cause of failure is hard sulfation, where the formation of large PbSO4 crystals on the negative active material impedes electron transfer. Here, we introduce a protocol to remove hard sulfate deposits on the negative electrode while maintaining their electrochemical viability for subsequent electrodeposition into active Pb. Soaking the hard sulfate negative electrode in an alkaline EDTA solution reshaped the surface by solubilizing PbSO4 to Pb-EDTA while avoiding underlying Pb phases. Thereafter, we explored electrodeposition of the Pb-EDTA complex as fresh electrode material and found reduction of Pb-EDTA required lower deposition overpotentials with decreasing pH. We used electrodeposited films on gold to demonstrate cycling of the restored active Pb in H2SO4. The film’s capacity gradually faded with cycling and PbSO4 formation, alike to commercial LABs. Lastly, we demonstrated the electrodeposition of Pb directly onto negative electrodes from a commercial LAB. Our unique approach seeds opportunity for recycling the electrode materials inside LABs without disassembly or extensive material processing.

Combined Experimental and Theoretical Study of the Structure of AuPt Nanoparticles Prepared by Galvanic Exchange.

In this article, experiment and theory are combined to analyze Pb and Cu underpotential deposition (UPD) on ∼1.7 nm Au nanoparticles (NPs) and the AuPt structures that result after galvanic exchange (GE) of the UPD layer for Pt. Experimental Pb (0.49 ML) and Pt (0.50 ML) coverages are close to values predicted by density functional theory-molecular dynamics (DFT-MD, 0.59 ML). DFT-MD reveals that the AuNPs spontaneously reconstruct from cuboctahedral to a (111)-like structure prior to UPD. In the case of Pb, this results in the random electrodeposition of Pb onto the Au surface. This mechanism is a consequence of opposing trends in Pb-Pb and Pb-Au coordination numbers as a function of Pb coverage. Cu UPD is more complex, and agreement between theory and experiment takes into account ligand effects (e.g., SO42- present as the electrolyte) and the electric double layer. Importantly, AuPt structures formed upon Pt GE are found to differ markedly depending on the UPD metal. Specifically, cyclic voltammetry indicates that the Pt coverage is ∼0.20 ML greater for Cu UPD/Pt GE (0.70 ML) than for Pb UPD/Pt GE (0.50 ML). This difference is corroborated by DFT-MD theoretical predictions. Finally, DFT-MD calculations predict the formation of surface alloy and core@shell structures for Pb UPD/Pt GE and Cu UPD/Pt GE, respectively.

Surface Investigation on Electrochemically Deposited Lead on Gold

Electrodeposition of Pb on Au has been of interest for the variety of surface phenomena such as the UnderPotential Deposition (UPD) and surface alloying. Here, we examined the interface between the electrodeposited Pb film on Au, using surface sensitive techniques such as X-ray Photoelectron Spectroscopy (XPS), Ultraviolet Photoelectron Spectroscopy (UPS), Energy-Filtered Photoemission Electron Microscopy (EF-PEEM) and Work Function (WF) mapping. The initially electrodeposited Pb overlayer (~4 ML equivalent thickness) was transferred from the electrochemical cell to the UHV system. The deposited Pb layer was subjected to Argon sputtering cycles to remove oxide formed due to air exposure and gradually thinned down to a monolayer level. Surface science acquisitions showed the existence of a mixed oxide/metallic Pb overlayer at the monolayer level that transformed to a metallic Pb upon high temperature annealing (380 °C for 1 h) and measured changes of the electronic interaction that can be explained by Pb/Au surface alloy formation. The results show the electronic interaction between metallic Pb and Au is different from the interaction of Au with the PbO and Pb/PbO mixed layer; the oxide interface is less strained so the surface stress driven mixing between Au is not favored. The work illustrates applications of highly surface sensitive methods in the characterization of the surface alloy systems that can be extended to other complex and ultrathin mixed-metallic systems (designed or spontaneously formed).

Template electrodeposition and characterization of nanostructured Pb as a negative electrode for lead-acid battery

Despite Lead Acid Battery (LAB) is the oldest electrochemical energy storage system, diffusion in the emerging sectors of technological interest is inhibited by its drawbacks. The principal ones are low energy density and negative plate sulphating on high rate discharging. In this work, it is shown the possibility of overcoming such drawbacks by using nanostructured lead as a negative electrode. Lead nanowires (NWs) were fabricated by electrochemical deposition in template, which is an easy, cheap, and easily scalable process. Their morphology and crystal structure have been characterized by electron microscopy and X-ray diffraction, respectively. An electrochemical cell simulating LAB has been assembled with PbO2 as a counter electrode and an AGM separator, both from commercial battery. Cycling tests were conducted at 10C-rate, setting the cut-off voltage on discharging at 1.2 V. For comparison, also cycling tests at 1C-rate have been carried out, in otherwise identical conditions. At both C-rates, performances in terms of cycling efficiency and lifetime were found a lot better than those of current LABs. The high porosity formed under cycling at 10C-rate provides a reliable explanation of the results.

Electrolyte dynamics in reversible metal electrodeposition for dynamic windows

Dynamic windows based on the reversible electrodeposition of metals are the promising alternatives to those based on other technologies such as electrochromic materials. In this article, we use spectroelectrochemistry to study Cu and Pb electrodeposition and dissolution as related to dynamic window electrolytes. The presence of Cl− in the aqueous electrolyte accelerates the deposition and dissolution processes, and leads to the formation of Cu–Cl equilibria that evolve during electrode cycling. The electrolyte only supports reversible metal deposition after cycling, a process known as electrolytic conditioning. We demonstrate that the conditioning process increases the concentration of Cu–Cl complexes in the electrolyte, which facilitates reversible and kinetically facile electrodeposition. The conditioned electrolyte enables the construction of 25 cm2 dynamic windows harnessing reversible metal electrodeposition that exhibit uniform tinting, minute-order switching times, and high optical contrast. Understanding electrolyte dynamics is key to constructing 25 cm2 dynamics windows with electronically controlled transparency based on the reversible metal electrodeposition of Pb and Cu.

Electrodeposition of Pb from PbO in urea and 1-butyl-3-methylimidazolium chloride deep eutectic solutions

In this work, urea and 1-butyl-3-methylimidazolium chloride (urea-BMIC) deep eutectic solutions were used as electrolytes for electrodeposition of lead from lead oxide. The electrochemical behavior of Pb (II) ions was investigated by cyclic voltammetry, chronopotentiometry, and chronoamperometry techniques at 353–373K. Cyclic voltammograms and chronopotentiograms indicate that the reduction of Pb (II) ions to Pb is a diffusion-controlled quasi-reversible process and it proceeds via one step two-electron transfer process at −0.38V (vs. Ag). The diffusion coefficient of Pb (II) ions increases from 3.22×10−8cm2s−1 to 1.49×10−7cm2s−1 as temperature increases from 353K to 373K. The activation energy for diffusion is determined to be 83.93kJmol−1. In addition, results from chronoamperometry show that lead deposition involves in a three-dimensional instantaneous nucleation and diffusion-controlled growth. On the other hand, the electrodeposit on a Cu substrate was pure Pb as confirmed by X-ray diffraction (XRD) and energy dispersive spectroscopy (EDS). Scanning electron microscopy (SEM) image indicated that a uniform, dense, and non-dendritic coating with grain size of 3μm in diameter was prepared by potentiostatic electrolysis at −0.4V (vs. Ag). The optimized current efficiency (96.17%) and energy consumption (0.11kWhkg−1) was obtained by potentiostatic electrolysis at −0.4V (vs. Ag) and 373K from urea-BMIC deep eutectic solutions containing 0.072moldm−3 PbO.

Electrodeposition of Lead–Cobalt Anodes: The Effect of Electrolyte pH on Film Properties

Electrodeposited lead (Pb)–cobalt (Co) coatings are an effective electrocatalyst in the oxygen-evolution reaction. We studied the effect of an electrolytic bath pH on the electrodeposition of Pb–Co coatings, and the coating properties were analyzed. The pH was varied from 1 to 6 for a solution without and with ascorbic acid as complexing agent. Cathodic polarization curves show that the deposition conditions have a greater effect on the reduction potential of Co2+ than the reduction potential of Pb2+. Energy–dispersive X–ray spectrometer analysis shows that a pH higher than 4 promotes Co deposition and yields a [Pb]/[Co] film ratio lower than 1. Scanning electron micrographs showed that samples grown at a pH higher than 2 were covered with Co dendrites, and that the sample grown with ascorbic acid at pH 1 exhibited a compact morphology. Anodic polarization curves showed that Pb–Co-coated anodes grown at pH 1 with a complexing agent evolved oxygen at c.a. 1.6 V vs. normal hydrogen electrode, which lead to a 40% reduction in the required overpotential (η) for the oxygen-evolution reaction compared with conventional Pb–Ca–Sn anodes.

A novel Pb-poly aminophenol glassy carbon electrode for determination of tetracycline by adsorptive differential pulse cathodic stripping voltammetry

A novel type of Pb-polyaminophenol filmed glassy carbon electrode for adsorptive cathodic stripping analysis of trace amounts of tetracycline was developed. The Pb-polymer electrode was fabricated in situ by simultaneous electrodeposition of Pb and cathodic electropolymerization of 4-nitrophenol in a sodium acetate medium at −1.5volt. The prepared Pb-polymeric film was characterized by CV, FT-IR (ATR), H-NMR, SEM, EDS and a suitable mechanism for the electrode-reaction was proposed. The outputs of some experiments showed that tetracycline can be adsorbed on the surface of this Pb-polymer filmed electrode in an open circuit condition. Therefore it was used in adsorptive cathodic stripping analysis of tetracycline. The response of the electrode was enhanced in the presence of cetyltrimethylammonium bromide. Some parameters affecting the performance of the electrode were studied and optimized. The response of the electrode was linear in the range of 5×10−8−1×10−5molL−1 of tetracycline with a correlation coefficient of 0.9981. The relative standard deviation for 5×10−7molL−1 of tetracycline was 1.8% (n=5). The L.O.D and L.O.Q were 4×10−9 and 1.3×10−8molL−1 of tetracycline, respectively. The introduced electrode was used for determination of tetracycline residues in some samples and the obtained results were in good agreement with the results of HPLC.

Effect of different complexing agents on Pb–Co thin-film electrodeposition

Lead (Pb)–cobalt (Co) films have been studied by several researchers regarding their electrocatalytic activity when used as anodes in oxygen evolution reactions. Although several authors have suggested that the electrodeposition technique is the best alternative to Pb–Co film deposition, the process is complex. In many cases, the use of complexing agents facilitates the electrodeposition of multi-element coatings; but this performance has not been reported in the literature for Pb–Co electrodeposition. In this work, the effect of three different complexing agents (tartaric acid, sodium citrate, and ascorbic acid) on Pb–Co electrodeposition was studied. Speciation diagrams and polarization curves have been used to determine the reduction potentials of Pb2+ and Co2+ ions in the different systems studied. Speciation diagram predictions were incapable of revealing all species present in solution and for an accurate prediction of the actual electrochemical functioning of the system; the information given by the speciation diagrams and polarization curves must be considered together. Additionally, electrodeposition of Pb–Co films was achieved without complexing agent and using the three complexing agents. Morphological and chemical properties of these coatings are shown and discussed in terms of the electrochemical functioning of each system. Finally, the electrocatalytic ability of the Pb–Co films was investigated by means of polarization curves.

Electrochemical study and recovery of Pb using 1:2 choline chloride/urea deep eutectic solvent: A variety of Pb species PbSO4, PbO2, and PbO exhibits the analogous thermodynamic behavior

Water-insoluble PbSO4, PbO2, and PbO are fairly soluble in choline chloride/urea deep eutectic solvent (ChCl/urea DES) in 1:2 molar ratio. Very interestingly, solution prepared from PbO2 exhibits the almost identical electrochemical behavior as those from PbSO4 and PbO, indicating that Pb(II) is formed in the DES regardless of what Pb compound is introduced. The electrochemical reduction of the Pb(II) species is determined as an irreversible process, and involves the three-dimensional (3D) instantaneous nucleation with diffusion-controlled growth. From the dependence of the diffusion coefficient on temperature, the activation energy for diffusion of PbSO4 and PbO2 is determined to be 33.7 and 34.1kJmol−1, respectively. Electrodeposition of Pb was achieved potentiostatically and galvanostatically. The surface morphology of Pb deposits significantly depends on the applied potential and current. The coulombic efficiency of Pb electrodeposition is higher than 90%. Electrodeposition of Pb from a wet DES containing a mixture of three different Pb sources is also investigated. The XRD analysis confirmed that the electrodeposits consisted of metallic Pb.

Voltammetric study and electrodeposition of tellurium, lead, and lead telluride in room-temperature ionic liquid 1-ethyl-3-methylimidazolium tetrafluoroborate

Room-temperature ionic liquid 1-ethyl-3-methylimidazolium tetrafluoroborate (RTIL EMI-BF4) was used as the electrolyte to study the voltammetric behavior of Te(IV), Pb(II), and their mixtures. Te(IV) and Pb(II) were introduced into the IL by the addition of TeCl4 and PbCl2, respectively, with sufficient 1-ethyl-3-methylimidazolium chloride (EMIC). The electrodeposition of Te, Pb, and PbTe was achieved under constant applied potential at nickel electrodes. The nucleation mechanisms of Te and Pb were determined to be three-dimensional instantaneous nucleation with diffusion-controlled growth. Crystalline stoichiometric PbTe electrodeposits were obtained via Pb under-potential deposition at the continuously growing surface of Te. They exhibited an energy bandgap of 0.22eV.

Electrodeposition of Lead from 1-butyl-1-methylpyrrolidinium Bis(trifluoromethylsulfonyl)amide Ionic Liquid

The electrochemical behavior of lead (Pb) was investigated in an amide-type ionic liquid, 1-butyl-1-methylpyrrolidinium bis(trifluoromethylsulfonyl)amide (BMPTFSA), containing Pb(TFSA)2. The cathodic and anodic currents corresponding to electrodeposition and stripping of Pb, respectively, were observed by cyclic voltammetry. The formal potential of Pb(II)/Pb couple was found to be −0.68 V vs. Ag/Ag(I), which is more negative by 0.11 V than that of Sn(II)/Sn couple. The diffusion coefficient of Pb(II) at 25°C was 0.8 × 10−7 cm2 s−1, which was close to those of divalent metal species in BMPTFSA. The local change of the viscosity and density of the ionic liquid near the electrode surface during electrodeposition and stripping of Pb was confirmed by electrochemical quartz crystal microbalance. The nucleation process and the morphology of electrodeposited Pb were found to be dependent on the deposition potential, probably due to accumulation of BMP+ at the surface of the negatively polarized electrode.

Taking part of the lab to the sample: On-site electrodeposition of Pb followed by measurement in a lab using electrothermal, near-torch vaporization sample introduction and inductively coupled plasma-atomic emission spectrometry

An electrodeposition method for preconcentration and separation of labile Pb from liquid samples with a complex matrix is described. For the first time, Pb was electrodeposited on-site on Re coiled-filament assemblies that were developed for use with an electrothermal, near-torch vaporization (NTV) sample introduction system and inductively coupled plasma-atomic emission spectrometry (ICP-AES). The coiled-filament assemblies (or simply coils) were purposely designed to be removable and were fabricated to have identical coupling-mechanisms so that they can be used interchangeably. In addition to their small size (2.75cm long and 0.65cm wide), coiled-filament assemblies weighed only 1.4g, which made them portable for on-site use. The detection limit from diluted seawater Certified Reference Material (CRM) and NTV-ICP-AES was 25pg/mL following a 3min electrodeposition. This detection limit represents a 40-fold improvement as compared to the detection limit obtained by pipetting 5μL of dilute Pb standard solution directly on the coil. The detection limit improved by 400-times (to 2pg/mL) when the electrodeposition time was increased to 60min. Lead from very hard tap water was electrodeposited on coiled filaments on-site using a shirt-pocket size, battery-operated potentiostat and portable electrodeposition instrumentation. Concentration was determined in the lab using NTV-ICP-AES. The Pb concentration was used to test for compliance with the Pb–Cu rule set by the United States Environmental Protection Agency (US EPA). Overall, on-site electrodeposition permitted determination of Pb at the environmental conditions (e.g., pH, temperature) recorded at the time of sampling. On-site electrodeposition also opens the possibility for shipping portable coils with Pb electrodeposited on them to the lab rather than shipping large volumes of sample, thus reducing shipping, handling and storage costs.

In-situ EQCM evaluation of the formation of UPD and OPD during electrodeposition of Pb on gold

Underpotential (UPD) and overpotential (OPD) deposition of Pb from a perchlorate solution on gold substrate was studied using in-situ electrochemical quartz crystal microbalance (EQCM) method. Cyclic voltammograms and current-transients recorded during potentiostatic electrochemical deposition were measured simultaneously with EQCM data including frequency and resistance. Results show that underpotential deposition (UPD) of Pb occurs before overpotential deposition (OPD) of Pb starts to grow, based on both massogram and cyclic voltammogram. The OPD of Pb grows at higher overpotentials which significantly influence the mechanism of nucleation and growth. EQCM reveals that the mass to charge ratio of OPD is different at different overpotentials, owing to the mechanism of nucleation and growth and possible roughening of grown Pb or hydrogen evolution. A comparison between our experimental data with the Scharifker-Hills theory based on non-dimensional plots shows an instantaneous mechanism. Scanning electron microscope taken from the electrodeposited lead on gold confirms the behaviour exhibiting almost same size of nuclei.