Mn Atoms Research Articles

Application of transition metal doped in boron carbide/graphene heterostructures as an electrode for supercapacitors

The density functional theory (DFT) is applied within the current piece of research for exploring the charge storage capacity, quantum or chemical capacitance (QC), electronic structures and the geometry of modified boron carbide (BC3)/graphene (Gr) heterostructure. Also, the impact of doping the Mn atom upon the capacitance behavior of BC3/Gr is explored. Based on the results, doping the Mn atom improved the QC of BC3/Gr. Moreover, doping the Mn atom was more effective than vacancy defect in enhancing the QC of BC3/Gr. The QC of the Mn-doped BC3/Gr was the highest (280.41 F/cm2), which demonstrates its potential application as an encouraging electrode material in supercapacitors (SCs). Based upon the DOS around the Fermi level, doping the Mn atom could be the reason for the increase in the QC. Finally, the results can provide useful insights into designing high-capacitance SCs.

Boosting the Electrocatalytic Oxygen Reduction Activity of MnN4-Doped Graphene by Axial Halogen Ligand Modification.

Exploring highly active electrocatalysts as platinum (Pt) substitutes for the oxygen reduction reaction (ORR) remains a significant challenge. In this work, single Mn embedded nitrogen-doped graphene (MnN4) with and without halogen ligands (F, Cl, Br, and I) modifying were systematically investigated by density functional theory (DFT) calculations. The calculated results indicated that these ligands can transform the dyz and dxz orbitals of Mn atom in MnN4 near the Fermi-level into dz2 orbital, and shift the d-band center away from the Fermi-level to reduce the adsorption capacity for reaction intermediates, thus enhancing the ORR catalytic activity of MnN4. Notably, Br and I modified MnN4 respectively with the lowest overpotentials of 0.41 and 0.39 V, possess superior ORR catalytic activity. This work is helpful for comprehensively understanding the ligand modification mechanism of single-atom catalysts and develops highly active ORR electrocatalysts.

Zr‐doped β‐MnO2 for Low‐temperature Selective Catalytic Reduction of NO by NH3: Preparation, Characterization and Performance

Nanowire‐MnO2 and a series of Zr‐doped MnO2 catalysts with different Zr/Mn molar ratios were successively prepared by hydrothermal and impregnation methods. The Zr‐doped MnO2 catalyst with Zr/Mn molar ratio of 0.04 and calcination temperature of 400°C, proved to be the optimal that possessed the highest low‐temperature denitration efficiency. It showed the NO conversion of ~92% and N2 selectivity of ~80% at 150°C. Characterization results demonstrated that the main active phase of the catalyst was β‐MnO2, Zr atoms interacted with Mn atoms, and Zr doping increased the structural defects, oxygen vacancies and weak acid sites, which effectively enhanced the low‐temperature denitration activity and N2 selectivity of β‐MnO2, also improved the water and sulphur resistance to some extent.

Performance and Mechanism of Co and Mn Loaded on Fe-Metal-Organic Framework Catalysts with Different Morphologies for Simultaneous Degradation of Acetone and NO by Photothermal Coupling.

VOCs can be used instead of ammonia as a reducing agent to remove NO, achieving the effect of removing VOCs and NO simultaneously. Due to the high energy consumption and low photocatalytic efficiency required for conventional thermocatalytic purification, photothermal coupled catalytic purification can integrate the advantages of photocatalysis and thermocatalysis in order to achieve the effect of pollutants being treated efficiently with a low energy consumption. In this study, samples loaded with Co and Mn catalysts were prepared using the hydrothermal method on Fe-MOF with various morphologies. The catalytic performance of each catalyst was analyzed by studying the effects of their physicochemical properties through various characterizations, including XRD, SEM, BET, XPS, H2-TPR, TEM and O2-TPD. The characterization results demonstrated that the specific surface area, pore volume, high valence Co and Mn atoms, surface adsorbed oxygen and the abundance of oxygen lattice defects in the catalysts were the most critical factors affecting the performance of the catalysts. Based on the results of the performance tests, the catalysts prepared with an octahedral-shaped Fe-MOF loaded with Co and Mn showed a better performance than those loaded with Co and Mn on a rod-shaped Fe-MOF. The conversions of acetone and NO reached 50% and 64%, respectively, at 240 °C. The results showed that the catalysts were capable of removing acetone and NO at the same time. Compared with the pure Fe-MOF without Co and Mn, the loaded catalysts showed a significantly higher ability to remove acetone and NO simultaneously under the combination of various factors. The key reaction steps for the catalytic conversion of acetone and NO on the catalyst surface were investigated according to the Mars-van Krevelen (MvK) mechanism, and a possible mechanism was proposed. This study presents a new idea for the simultaneous removal of acetone and NOx by photothermal coupling.

Metallocorroles as bifunctional electrocatalysts for water-splitting: A theoretical investigation

Designing efficient electrocatalysts for the oxygen evolution reaction (OER) and hydrogen evolution reaction (HER) is an important step of the water-splitting procedure, due to the expensive electrocatalysts and the energy loss because of overpotentials. Accordingly, in the present study and based on the newly synthesized copper-corrole complexes, several metallocorroles that can be used as electrocatalysts in water-splitting reaction were theoretically designed. The main objective of the present study is to investigate the electrocatalytic behavior of various metallocorroles toward OER at the anode as well as HER at the cathode. So, our focus will be on the corrole substrates incorporating Cr, Mn, Fe, Co, Ni, and Cu single atoms, nitrogen removal defective complexes, and Cl-functionalized corroles to explore the effect of structural modifications on the catalytic activity of metallocorroles. We found that the Ni- and Cr-corrole are encouraging catalysts for the OER and HER, respectively, outperforming the synthesized copper-based substrate and other designed metallocorroles with low overpotentials (ƞOER=0.68 V and ƞHER=0.10 V). The obtained Gibbs free energies confirm the feasibility of OER on a Ni single atom and HER on a Cr single atom of metallocorroles. The Volcano diagrams also reveal that the metallocorroles with better oxygen and hydrogen desorption correspond to the Ni- and Cr-corrole substrates, respectively. Generally, results show that our designed metallocorroles can be considered competent catalysts for water-splitting reactions.

Cadmium Isotope Fractionation during Adsorption onto Edge Sites and Vacancies in Phyllomanganate.

Cadmium (Cd) geochemical behavior is strongly influenced by its adsorption onto natural phyllomanganates, which contain both layer edge sites and vacancies; however, Cd isotope fractionation mechanisms at these sites have not yet been addressed. In the present work, Cd isotope fractionation during adsorption onto hexagonal (containing both types of sites) and triclinic birnessite (almost only edge sites) was investigated using a combination of batch adsorption experiments, extended X-ray absorption fine structure (EXAFS) spectroscopy, surface complexation modeling, and density functional theory (DFT) calculations. Light Cd isotopes are preferentially enriched on solid surfaces, and the isotope fractionation induced by Cd2+ adsorption on edge sites (Δ114/110Cdedge-solution = -1.54 ± 0.11‰) is smaller than that on vacancies (Δ114/110Cdvacancy-solution = -0.71 ± 0.21‰), independent of surface coverage or pH. Both Cd K-edge EXAFS and DFT results indicate the formation of double corner-sharing complexes on layer edge sites and mainly triple cornering-sharing complexes on vacancies. The distortion of both complexes results in the negative isotope fractionation onto the solids, and the slightly longer first Cd-O distances and a smaller number of nearest Mn atoms around Cd at edge sites probably account for the larger fractionation magnitude compared to that of vacancies. These results provide deep insights into Cd isotope fractionation mechanisms during interactions with phyllomanganates.

Low-coordinated Mn–N2 sites in graphene oxide induce peroxydisulfate activation for tetracycline degradation: Process optimization and theoretical calculation

Atom-dispersed low-coordinated transition metal-Nx catalysts exhibit excellent efficiency in activating peroxydisulfate (PDS) for environmental remediation. However, their catalytic performance is limited due to metal-N coordination number and single-atom loading amount. In this study, low-coordinated nitrogen-doped graphene oxide (GO) confined single-atom Mn catalyst (Mn-SA/NGO) was synthesized by molten salt-assisted pyrolysis and coupled to PDS for degradation of tetracycline (TC) in water. Aberration-corrected high-angle annular dark-field scanning transmission electron microscopy (AC-HAADF-STEM) and X-ray absorption fine structure spectroscopy (XAFS) analysis showed the successful doping of single-atom Mn (weight percentage 1.6%) onto GO and the formation of low-coordinated Mn–N2 sites. The optimized parameters obtained by Box-Behnken Design achieved 100% TC removal in both prediction and experimental results. The Mn-SA/NGO + PDS system had strong anti-interference ability for TC removal in the presence of anions. Besides, Mn-SA/NGO possessed good reusability and stability. O2•−, •OH, and 1O2 were the main active species for TC degradation, and the TC mineralization reached 85.1%. Density functional theory (DFT) calculations confirmed that the introduction of single atoms Mn could effectively enhance adsorption and activation of PDS. The findings provide a reference for the synthesis of high-performance single-atom catalysts for effective removal of antibiotics.

Regulation of d‐Band Center of Ruthenium Sites via Electronic Complementary Effect of C60 Fullerene Molecules and Manganese Atoms for Efficient Alkaline Hydrogen Evolution

AbstractDeveloping advanced electrocatalysts is crucial for alkaline hydrogen evolution reaction (HER). A balance in adsorption energy for each reaction intermediate on the catalyst determines the overall catalytic rate. This balance is closely linked to the d‐band center, which is, in turn, controlled by the electronic structure of the active sites. Herein, C60 molecules with electron‐withdrawing properties and manganese (Mn) atoms with electron‐donating properties to drive charge redistribution on Ru active sites are strategically utilized. The synergistic and complementary effects of C60 and Mn regulate the d‐band centers of Ru sites to an optimal position, optimizing both the water adsorption and hydrogen desorption of the synthesized Ru catalysts. The constructed MnRu/C60‐3 catalyst exhibits a low overpotential of 8 mV at 10 mA cm−2, a large TOF value of 15.5 s−1, and a high mass activity of 2.39 A mg−1Ru at an overpotential of 100 mV in 1.0 m KOH. The anion exchange membrane water electrolyzer, assembled with MnRu/C60‐3 as the cathode, demonstrates excellent water electrolysis performance and high stability under industrial operational conditions. This work offers a fresh perspective on catalyst design principles by manipulating the d‐band centers of active sites using two complementary components.

Revealing the role of electrode potential micro-environments in single Mn atoms for carbon dioxide and oxygen electrolysis

Revealing the role of electrode potential micro-environments in single Mn atoms for carbon dioxide and oxygen electrolysis

A first-principles study of the lithium storage properties of transition metal doped TM-Ti2CO2 (TM=Sc, V, Cr, Mn, Fe, Co, Ni and Cu)

Two-dimensional transition metal carbides, known as MXenes, have garnered significant interest for their potential applications in lithium-ion batteries anode materials, owing to their distinctive properties. Doping, a prevalent method for material modification, involves the substitution of metal atoms within MXenes with other elements to modulate material properties. Given that MXenes inherently contain transition metals, doping with additional transition metals presents an optimal approach for enhancing their performance. In this study, we investigated the effect of doping eight transition metals (Sc, V, Cr, Mn, Fe, Co, Ni, Cu) onto Ti2CO2, aiming to elucidate their impact on the lithium storage properties of the material. Our findings reveal that the introduction of different dopant atoms induces changes in the d-band center of the material, consequently influencing the adsorption energy of lithium ions on the MXene surface in a nearly linear fashion. What’s more, doping with Sc, Cr, and Mn atoms results in an elevation of the migration energy, while doping with Fe, Co, Ni, and Cu atoms leads to a notable increase in the open circuit voltage (OCV). Remarkably, only V atom doping demonstrates an optimal combination of suitable adsorption energy, OCV (0.66 V), and minimal diffusion energy (0.11 eV). These results underscore the significance of transition metal doping in tailoring the lithium storage properties of MXene-based anode materials, offering insights for the design and optimization of next-generation lithium-ion batteries.

Tailoring structural and optical properties of ZnO system through elemental Mn Doping through First-principles calculations

In this study, band structure and optical properties of Manganese (Mn) doped ZnO are investigated adopting first-principles study calculations. It is observed that, by addition of Mn in ZnO crystal, the electrical properties like conductivity and dielectric function of material have been improved. The elastic constants for the elements are also calculated which shows that the element is stable after addition of dopant. The computational study is done on CASTEP and Material Studio. The ZnO system is simulated and atoms of Mn has been added replacing Zn atoms. The properties that studied are band structure and optics including conductivity, reflectivity, dielectric function, absorption and refractive index. Furthermore, this study also includes calculation of Elastic constants, XRD Spectra, Phonon dispersion and Temperature profile of doped ZnO systems. The computational study produced promising results and experimental approach can be adopted to reinforce the outcomes of this study.

Microsolvation of cobalt, nickel, and copper atoms with ammonia: a theoretical study of the solvated electron precursors.

The s-block metals dissolved in ammonia form metal-ammonia complexes with diffuse electrons which could be used for redox catalysis. In this theoretical paper, we investigated the possibility of the d-bloc transition metals (Mn, Fe, Co, Ni, and Cu) solvated by ammonia. It has been demonstrated that both Mn and Fe atoms undergo into an oxidative reaction with NH3 forming an inserted species, HMNH2. On the contrary, the Co, Ni, and Cu atoms can accommodate four NH3, via the coordination bond, to form the first solvation sphere within C2v, D2d, and Td point groups, respectively. Addition of a fifth NH3 constitute the second solvation shell by forming hydrogen bond with the other NH3s. Interestingly, M(NH3)4 (M = Co, Ni, and Cu) is a so-called solvated electron precursor and should be considered as a monocation M(NH3)4+ kernel in tight contact with one electron distributed over its periphery. This nearly free electron could be used to capture a CO2 molecule and engages in a reduction reaction. Geometry optimization of the stationary points on the potential energy surface was performed using density functional theory - CAM-B3LYP functional including the GD3BJ dispersion contribution - in combination with the 6-311 + + G(2d, 2p) basis set for all the atoms. All first-principles calculations were performed using the Gaussian 09 quantum chemical packages. The natural electron configuration of transition atom engaged in the compounds has been found using the natural bond orbital (NBO) method. We used the EDR (electron delocalization range) approach to analyze the structure of solvated electrons in real space. We also used the electron localization function (ELF) to measure the degree of electronic localization within a chemical compound. The EDR and ELF analyses are done using the TopMod and Multiwfn packages, respectively.

Doping engineering in MoS2 as the cathode-host in lithium‑sulfur batteries: A first principles investigation

The practical application of lithium‑sulfur batteries is hindered by the dissolution of lithium polysulfides, causing a reduction in coulombic efficiency and cyclic performance, known as the shuttle effect. Addressing this requires identifying suitable anchoring materials. Metal sulfides, particularly two-dimensional structures like MoS2, emerge as promising candidates for anchoring cathode hosts in lithium‑sulfur batteries. Their attributes include sufficient adsorption energy toward polysulfides and commendable catalytic activity compared to carbon electrodes. However, their limited electrical conductivity poses a significant obstacle to efficient electron flow. In this study, employing density functional theory (DFT), we elucidate strategies for enhancing the electrical conductivity and anchoring capabilities of the basal plane of MoS2 by introducing impurities at S and Mo sites. Our investigation encompasses a range of metal dopants, including V, Ni, Co, Mn, and Fe, and non-metal atoms such as Se and P in combination with vacancies. Through meticulous examination of formation energies and induced electrical conductivity, certain dopants, both in isolation and co-doping configurations, have been identified for further scrutiny. Our findings reveal that P and V dopants exhibit low formation energies within the MoS2 structure while they improve the electrical conductivity compared to other dopants. Additionally, they demonstrate superior adsorption energies required to immobilize lithium polysulfide species effectively. Notably, the synergistic effects observed in co-doped PV-MoS2 samples markedly enhance the binding energy of Li2Sn species on the MoS2 monolayer which is supported by the ICHOP values. This dual-doping approach also facilitates the conversion of polysulfides to final products and has the low energy barrier of Li2S decomposition that accelerates the kinetics of lithium‑sulfur batteries during the charge and discharge process. Overall, our research provides valuable insights into optimizing the electrical and anchoring properties of MoS2 for enhanced performance in lithium‑sulfur batteries.

Mn single atoms coordinated with N and O and embedded in activated carbon for supercapacitor and oxygen evolution reaction applications

With the aim of increasing the potential applications of activated carbon (AC) in supercapacitors and zinc-air batteries, the present work prepared AC composites doped with Mn, N and O using various methods. These materials exhibited superior capacitive and oxygen evolution reaction (OER) electrocatalytic activity. Analytical characterizations and density functional theory calculations demonstrated that the specimen subjected to calcination and heating under N2 and NH3 (AC-Mn-3) had a higher specific surface area, an optimized distribution of pyridinic and pyrrolic N and single Mn atom active sites. These factors improved the supercapacitor performance and OER catalytic activity of this material. The hierarchical pore structure of the AC matrix also facilitated electrolyte transport while simultaneously reducing internal resistance and protecting the electrode structure during cycling. An AC-Mn-3 electrode provided a high specific capacitance of 516.20 F/g at 1 A/g while a symmetric supercapacitor based on this electrode delivered an exceptional energy density of 71.69 Wh/kg at a power density of 500 W/kg. When applied to the OER, the AC-Mn-3 achieved a low overpotential of 270.21 mV at 10 mA/cm2 in 1 M KOH. Theoretical calculations suggested that single Mn atoms coordinated with N and O effectively bound oxygenated intermediates to lower the adsorption energy barrier associated with the OER rate-determining step going from OH* to O*. These results provide new insights concerning the mechanism by which improved supercapacitor performance and OER catalytic activity can be realized and demonstrate an effective strategy for AC modification.

Magnetic properties of CrMnGen (n = 3-20) clusters.

Due to the potential applications in next-generation micro/nano electronic devices and functional materials, magnetic germanium (Ge)-based clusters are receiving increasing attention. In this work, we reported the structures, electronic and magnetic properties of CrMnGen with sizes n = 3-20. Transition metals (TMs) of Cr and Mn tend to stay together and be surrounded by Ge atoms. Small sized clusters with n ≤ 8 prefer to adopt bipyramid-based structures as the motifs with the excess Ge atoms absorbed on the surface. Starting from n = 9, the structure with one TM atom interior appears and persists until n = 16, and for larger sizes n = 17-20, the two TM atoms are full-encapsulated by Ge atoms to form endohedral structures. The Hirshfeld population analyses show that Cr atom always acts as the electron donor, while Mn atom is always the acceptor except for sizes 3 and 6. The average binding energies of these clusters increase with cluster size n, sharing a very similar trend as that of CrMnSin (n = 4-20) clusters, which indicates that it is favorable to form large-sized clusters. CrMnGen (n = 6, 13, 16, 19, and 20) clusters prefer to exhibit ferromagnetic Cr-Mn coupling, while the remaining clusters are ferrimagnetic.

Effect of Ni content on 475°C embrittlement of directed energy deposited duplex stainless steel using a laser beam and wire feedstock

Duplex stainless steel (DSS), specifically the 2209 grade, is increasingly employed in additive manufacturing, particularly in processes like directed energy deposition using a laser beam with wire (DED-LB/w). However, a significant challenge arises when DSS faces brittleness within the temperature range of 250–500 °C. This study employs advanced characterization techniques, including atom probe tomography (APT) and transmission electron microscopy (TEM), to investigate DSS embrittlement after aging at 400 °C for up to 1000 h. The hardness analysis revealed that the higher Ni content in DED-LB/w-fabricated DSS cylinder promotes the age hardening compared to 2205 wrought DSS plate. Furthermore, APT and TEM demonstrated that, alongside the decomposition of ferrite into Fe-rich (α) and Cr-rich (αʹ) phases, clustering of Ni, Mn, and Si atoms contributes to the embrittlement. Although the Ni-Mn-Si-rich clusters could suggest nucleation of G-phase, the G-phase crystal structure was not observed by TEM. This might be attributed to the short aging time or limitations in the characterization technique. This work underscores the impact of characterization techniques on the measurement of spinodal decomposition, with APT providing capability of detecting nanometer sized clusters. By elucidating the complexities of 475 °C-embrittlement in DED-LB/w DSS, this study offers valuable insights for industrial applications and a deeper understanding of age hardening in duplex DSSs under specific manufacturing conditions.

Heterostructure mediated high strength and large ductility in novel medium-Mn steels with low Mn content

Medium-Mn steels (MMnS) exhibit superior strength and ductility via the transformation-induced plasticity (TRIP) of retained austenite. However, to realize the partitioning of Mn atoms into retained austenite for thermal stability optimization, long-term intercritical annealing is required. In addition, the high Mn content of MMnS also causes other issues, e.g., high cost, welding, etc. In this work, instead of utilizing the TRIP effect of retained austenite, heterostructure consisting of alternatively distributed lamellar martensite zones and lamellar ultrafine dual-phase (martensite + ferrite) zones was engineered in a MMnS with low Mn content by a conventional rolling and short-term intercritical annealing process. The formation of the heterostructure was attributed to the heterogeneous distribution of Mn, the formation of highly dispersed martensite-austenite (MA) islands in Mn-poor zones and the low diffusion rate of Mn atoms at the intercritical annealing temperature. Tensile test results show that the steel exhibits superb synergy of a high ultimate tensile strength of 1452 MPa, a large ductility of 17 % and a high work hardening capability. The high work hardening capability and large ductility were mainly attributed to the apparent microhardness difference between the lamellar martensite zones and the ultrafine dual-phase zones that caused a strong hetero-deformation induced (HDI) strengthening effect. This study proposes a novel approach to developing high-performance steels, which provides an effective paradigm for addressing the long-established conflicts between mechanical performance, high Mn content and long intercritical annealing period of MMnS.

Understanding the magnetism-ductility trade-off in FeCoMn alloys: The role of the BCC-B2 transition and Mn occupancies

The magnetism-ductility contradictory relationship presents a significant challenge in the development of magnetic alloys. The impact of the BCC-B2 transition, along with Mn site occupancy, on magnetism and ductility have been investigated by using first-principles calculations. The calculations involved the evaluation of magnetic moments, density of states (DOS), phase stability and ductility of FeCoMn alloys. The results of binary alloys confirm the enhancement of magnetism due to the BCC-B2 transition. Furthermore, the ordering phase transition can strengthen the magnetic interaction between Fe and Mn atoms, which is associated with minimal variations in the density of states of Fe and Mn in the B2 structure. Regarding the ductility of FeCoMn alloys, two factors contribute to increased brittleness. Firstly, the increased covalent component in bonding, as a result of the strong hybridization between different elements, leads to an increased brittleness. Secondly, the increased Peierls stress provides a larger resistance to dislocation motion, which also contributes to the increased brittleness. Finally, the Pearson correlation coefficients and data analysis indicate that VEC, spin polarizations and Mn content provide major contributions to the contradictory relationship between magnetism and ductility.

(2,5-Di-methyl-imidazole){N,N',N'',N'''-[porphyrin-5,10,15,20-tetra-yltetra-(2,1-phenyl-ene)]tetra-kis(pyridine-3-carboxamide)}manganese(II) chloro-benzene disolvate.

In the title compound, [Mn(C68H44N12O4)(C5H8N2)]·2C6H5Cl, the central MnII ion is coordinated by four pyrrole N atoms of the porphyrin core in the basal sites and one N atom of the 2,5-di-methyl-imidazole ligand in the apical site. Two chloro-benzene solvent mol-ecules are also present in the asymmetric unit. Due to the apical imidazole ligand, the Mn atom is displaced out of the 24-atom porphyrin mean plane by 0.66 Å. The average Mn-Np (p = porphyrin) bond length is 2.143 (8) Å, and the axial Mn-NIm (Im = 2,5-di-methyl-imidazole) bond length is 2.171 (8) Å. The structure displays inter-molecular and intra-molecular N-H⋯O, N-H⋯N, C-H⋯O and C-H⋯N hydrogen bonding. The crystal studied was refined as a two-component inversion twin.

Half-Metallic Ferromagnetism in TM-Doped GaN Nanosheet — A Potential Candidate for Spintronics Device Application

Density functional theory (DFT) analyses were carried out to study electronic structures and magnetic properties of Mn- and Cu-doped GaNNS. To investigate the influence of transition metal atoms (TM) on magnetic properties, we substituted Ga atoms with Mn and Cu atoms in different concentrations. Investigation shows that TM leads to electronic structural reconstruction which changes their properties in this way, and plays a significant role in spin polarization. Although the pure nanosheet is a nonmagnetic semiconductor, the doped atoms induce magnetism in the structure. The band gap changes monotonically depending on the concentration of TM atoms. The observed good half-metal ferromagnetism GaNNS:Mn, allows them to be a potential candidate for use in spintronics. The local magnetic moment calculated from Mulliken analyses for the Mn atom is approximately 4.05[Formula: see text][Formula: see text]B.